Merge pull request #44 from Lerentis/dependabot/go_modules/github.com/hashicorp/terraform-plugin-sdk/v2-2.27.0
Bump github.com/hashicorp/terraform-plugin-sdk/v2 from 2.26.1 to 2.27.0
This commit is contained in:
Tobias Trabelsi
GitHub
commit
e8584b0270
48
go.mod
48
go.mod
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@ -5,39 +5,41 @@ go 1.18
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require (
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code.gitea.io/sdk/gitea v0.15.1
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github.com/hashicorp/terraform-plugin-docs v0.14.1
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github.com/hashicorp/terraform-plugin-log v0.8.0
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github.com/hashicorp/terraform-plugin-sdk/v2 v2.26.1
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github.com/hashicorp/terraform-plugin-log v0.9.0
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github.com/hashicorp/terraform-plugin-sdk/v2 v2.27.0
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)
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require (
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github.com/Masterminds/goutils v1.1.1 // indirect
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github.com/Masterminds/semver/v3 v3.1.1 // indirect
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github.com/Masterminds/sprig/v3 v3.2.2 // indirect
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github.com/ProtonMail/go-crypto v0.0.0-20230217124315-7d5c6f04bbb8 // indirect
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github.com/agext/levenshtein v1.2.2 // indirect
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github.com/apparentlymart/go-textseg/v13 v13.0.0 // indirect
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github.com/armon/go-radix v1.0.0 // indirect
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github.com/bgentry/speakeasy v0.1.0 // indirect
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github.com/cloudflare/circl v1.3.3 // indirect
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github.com/fatih/color v1.13.0 // indirect
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github.com/golang/protobuf v1.5.2 // indirect
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github.com/golang/protobuf v1.5.3 // indirect
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github.com/google/go-cmp v0.5.9 // indirect
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github.com/google/uuid v1.3.0 // indirect
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github.com/hashicorp/errwrap v1.1.0 // indirect
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github.com/hashicorp/go-checkpoint v0.5.0 // indirect
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github.com/hashicorp/go-cleanhttp v0.5.2 // indirect
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github.com/hashicorp/go-cty v1.4.1-0.20200414143053-d3edf31b6320 // indirect
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github.com/hashicorp/go-hclog v1.4.0 // indirect
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github.com/hashicorp/go-hclog v1.5.0 // indirect
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github.com/hashicorp/go-multierror v1.1.1 // indirect
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github.com/hashicorp/go-plugin v1.4.8 // indirect
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github.com/hashicorp/go-plugin v1.4.10 // indirect
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github.com/hashicorp/go-uuid v1.0.3 // indirect
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github.com/hashicorp/go-version v1.6.0 // indirect
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github.com/hashicorp/hc-install v0.5.0 // indirect
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github.com/hashicorp/hcl/v2 v2.16.2 // indirect
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github.com/hashicorp/hc-install v0.5.2 // indirect
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github.com/hashicorp/hcl/v2 v2.17.0 // indirect
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github.com/hashicorp/logutils v1.0.0 // indirect
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github.com/hashicorp/terraform-exec v0.18.1 // indirect
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github.com/hashicorp/terraform-json v0.16.0 // indirect
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github.com/hashicorp/terraform-plugin-go v0.14.3 // indirect
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github.com/hashicorp/terraform-registry-address v0.1.0 // indirect
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github.com/hashicorp/terraform-svchost v0.0.0-20200729002733-f050f53b9734 // indirect
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github.com/hashicorp/terraform-json v0.17.0 // indirect
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github.com/hashicorp/terraform-plugin-go v0.16.0 // indirect
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github.com/hashicorp/terraform-registry-address v0.2.1 // indirect
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github.com/hashicorp/terraform-svchost v0.1.1 // indirect
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github.com/hashicorp/yamux v0.0.0-20181012175058-2f1d1f20f75d // indirect
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github.com/huandu/xstrings v1.3.2 // indirect
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github.com/imdario/mergo v0.3.13 // indirect
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@ -55,16 +57,16 @@ require (
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github.com/shopspring/decimal v1.3.1 // indirect
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github.com/spf13/cast v1.5.0 // indirect
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github.com/vmihailenco/msgpack v4.0.4+incompatible // indirect
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github.com/vmihailenco/msgpack/v4 v4.3.12 // indirect
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github.com/vmihailenco/tagparser v0.1.1 // indirect
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github.com/zclconf/go-cty v1.13.1 // indirect
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golang.org/x/crypto v0.7.0 // indirect
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golang.org/x/mod v0.8.0 // indirect
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golang.org/x/net v0.8.0 // indirect
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golang.org/x/sys v0.6.0 // indirect
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golang.org/x/text v0.8.0 // indirect
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google.golang.org/appengine v1.6.6 // indirect
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google.golang.org/genproto v0.0.0-20200711021454-869866162049 // indirect
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google.golang.org/grpc v1.51.0 // indirect
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google.golang.org/protobuf v1.28.1 // indirect
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github.com/vmihailenco/msgpack/v5 v5.3.5 // indirect
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github.com/vmihailenco/tagparser/v2 v2.0.0 // indirect
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github.com/zclconf/go-cty v1.13.2 // indirect
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golang.org/x/crypto v0.10.0 // indirect
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golang.org/x/mod v0.10.0 // indirect
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golang.org/x/net v0.11.0 // indirect
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golang.org/x/sys v0.9.0 // indirect
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golang.org/x/text v0.10.0 // indirect
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google.golang.org/appengine v1.6.7 // indirect
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google.golang.org/genproto v0.0.0-20230410155749-daa745c078e1 // indirect
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google.golang.org/grpc v1.56.0 // indirect
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google.golang.org/protobuf v1.30.0 // indirect
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)
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250
go.sum
250
go.sum
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@ -1,9 +1,6 @@
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cloud.google.com/go v0.26.0/go.mod h1:aQUYkXzVsufM+DwF1aE+0xfcU+56JwCaLick0ClmMTw=
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cloud.google.com/go v0.34.0/go.mod h1:aQUYkXzVsufM+DwF1aE+0xfcU+56JwCaLick0ClmMTw=
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code.gitea.io/gitea-vet v0.2.1/go.mod h1:zcNbT/aJEmivCAhfmkHOlT645KNOf9W2KnkLgFjGGfE=
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code.gitea.io/sdk/gitea v0.15.1 h1:WJreC7YYuxbn0UDaPuWIe/mtiNKTvLN8MLkaw71yx/M=
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code.gitea.io/sdk/gitea v0.15.1/go.mod h1:klY2LVI3s3NChzIk/MzMn7G1FHrfU7qd63iSMVoHRBA=
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github.com/BurntSushi/toml v0.3.1/go.mod h1:xHWCNGjB5oqiDr8zfno3MHue2Ht5sIBksp03qcyfWMU=
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github.com/Masterminds/goutils v1.1.1 h1:5nUrii3FMTL5diU80unEVvNevw1nH4+ZV4DSLVJLSYI=
|
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github.com/Masterminds/goutils v1.1.1/go.mod h1:8cTjp+g8YejhMuvIA5y2vz3BpJxksy863GQaJW2MFNU=
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github.com/Masterminds/semver/v3 v3.1.1 h1:hLg3sBzpNErnxhQtUy/mmLR2I9foDujNK030IGemrRc=
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|
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@ -11,71 +8,42 @@ github.com/Masterminds/semver/v3 v3.1.1/go.mod h1:VPu/7SZ7ePZ3QOrcuXROw5FAcLl4a0
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github.com/Masterminds/sprig/v3 v3.2.1/go.mod h1:UoaO7Yp8KlPnJIYWTFkMaqPUYKTfGFPhxNuwnnxkKlk=
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github.com/Masterminds/sprig/v3 v3.2.2 h1:17jRggJu518dr3QaafizSXOjKYp94wKfABxUmyxvxX8=
|
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github.com/Masterminds/sprig/v3 v3.2.2/go.mod h1:UoaO7Yp8KlPnJIYWTFkMaqPUYKTfGFPhxNuwnnxkKlk=
|
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github.com/Microsoft/go-winio v0.4.14/go.mod h1:qXqCSQ3Xa7+6tgxaGTIe4Kpcdsi+P8jBhyzoq1bpyYA=
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github.com/Microsoft/go-winio v0.4.16 h1:FtSW/jqD+l4ba5iPBj9CODVtgfYAD8w2wS923g/cFDk=
|
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github.com/Microsoft/go-winio v0.4.16/go.mod h1:XB6nPKklQyQ7GC9LdcBEcBl8PF76WugXOPRXwdLnMv0=
|
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github.com/ProtonMail/go-crypto v0.0.0-20210428141323-04723f9f07d7 h1:YoJbenK9C67SkzkDfmQuVln04ygHj3vjZfd9FL+GmQQ=
|
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github.com/ProtonMail/go-crypto v0.0.0-20210428141323-04723f9f07d7/go.mod h1:z4/9nQmJSSwwds7ejkxaJwO37dru3geImFUdJlaLzQo=
|
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github.com/acomagu/bufpipe v1.0.3 h1:fxAGrHZTgQ9w5QqVItgzwj235/uYZYgbXitB+dLupOk=
|
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github.com/acomagu/bufpipe v1.0.3/go.mod h1:mxdxdup/WdsKVreO5GpW4+M/1CE2sMG4jeGJ2sYmHc4=
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github.com/Microsoft/go-winio v0.5.2 h1:a9IhgEQBCUEk6QCdml9CiJGhAws+YwffDHEMp1VMrpA=
|
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github.com/ProtonMail/go-crypto v0.0.0-20230217124315-7d5c6f04bbb8 h1:wPbRQzjjwFc0ih8puEVAOFGELsn1zoIIYdxvML7mDxA=
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github.com/ProtonMail/go-crypto v0.0.0-20230217124315-7d5c6f04bbb8/go.mod h1:I0gYDMZ6Z5GRU7l58bNFSkPTFN6Yl12dsUlAZ8xy98g=
|
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github.com/acomagu/bufpipe v1.0.4 h1:e3H4WUzM3npvo5uv95QuJM3cQspFNtFBzvJ2oNjKIDQ=
|
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github.com/agext/levenshtein v1.2.2 h1:0S/Yg6LYmFJ5stwQeRp6EeOcCbj7xiqQSdNelsXvaqE=
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github.com/agext/levenshtein v1.2.2/go.mod h1:JEDfjyjHDjOF/1e4FlBE/PkbqA9OfWu2ki2W0IB5558=
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github.com/anmitsu/go-shlex v0.0.0-20161002113705-648efa622239/go.mod h1:2FmKhYUyUczH0OGQWaF5ceTx0UBShxjsH6f8oGKYe2c=
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github.com/apparentlymart/go-textseg v1.0.0/go.mod h1:z96Txxhf3xSFMPmb5X/1W05FF/Nj9VFpLOpjS5yuumk=
|
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github.com/apparentlymart/go-textseg/v12 v12.0.0/go.mod h1:S/4uRK2UtaQttw1GenVJEynmyUenKwP++x/+DdGV/Ec=
|
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github.com/apparentlymart/go-textseg/v13 v13.0.0 h1:Y+KvPE1NYz0xl601PVImeQfFyEy6iT90AvPUL1NNfNw=
|
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github.com/apparentlymart/go-textseg/v13 v13.0.0/go.mod h1:ZK2fH7c4NqDTLtiYLvIkEghdlcqw7yxLeM89kiTRPUo=
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github.com/armon/go-radix v0.0.0-20180808171621-7fddfc383310/go.mod h1:ufUuZ+zHj4x4TnLV4JWEpy2hxWSpsRywHrMgIH9cCH8=
|
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github.com/armon/go-radix v1.0.0 h1:F4z6KzEeeQIMeLFa97iZU6vupzoecKdU5TX24SNppXI=
|
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github.com/armon/go-radix v1.0.0/go.mod h1:ufUuZ+zHj4x4TnLV4JWEpy2hxWSpsRywHrMgIH9cCH8=
|
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github.com/armon/go-socks5 v0.0.0-20160902184237-e75332964ef5/go.mod h1:wHh0iHkYZB8zMSxRWpUBQtwG5a7fFgvEO+odwuTv2gs=
|
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github.com/bgentry/speakeasy v0.1.0 h1:ByYyxL9InA1OWqxJqqp2A5pYHUrCiAL6K3J+LKSsQkY=
|
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github.com/bgentry/speakeasy v0.1.0/go.mod h1:+zsyZBPWlz7T6j88CTgSN5bM796AkVf0kBD4zp0CCIs=
|
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github.com/census-instrumentation/opencensus-proto v0.2.1/go.mod h1:f6KPmirojxKA12rnyqOA5BBL4O983OfeGPqjHWSTneU=
|
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github.com/client9/misspell v0.3.4/go.mod h1:qj6jICC3Q7zFZvVWo7KLAzC3yx5G7kyvSDkc90ppPyw=
|
||||
github.com/creack/pty v1.1.9/go.mod h1:oKZEueFk5CKHvIhNR5MUki03XCEU+Q6VDXinZuGJ33E=
|
||||
github.com/bwesterb/go-ristretto v1.2.0/go.mod h1:fUIoIZaG73pV5biE2Blr2xEzDoMj7NFEuV9ekS419A0=
|
||||
github.com/cloudflare/circl v1.1.0/go.mod h1:prBCrKB9DV4poKZY1l9zBXg2QJY7mvgRvtMxxK7fi4I=
|
||||
github.com/cloudflare/circl v1.3.3 h1:fE/Qz0QdIGqeWfnwq0RE0R7MI51s0M2E4Ga9kq5AEMs=
|
||||
github.com/cloudflare/circl v1.3.3/go.mod h1:5XYMA4rFBvNIrhs50XuiBJ15vF2pZn4nnUKZrLbUZFA=
|
||||
github.com/davecgh/go-spew v1.1.0/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
|
||||
github.com/davecgh/go-spew v1.1.1 h1:vj9j/u1bqnvCEfJOwUhtlOARqs3+rkHYY13jYWTU97c=
|
||||
github.com/davecgh/go-spew v1.1.1/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
|
||||
github.com/emirpasic/gods v1.12.0 h1:QAUIPSaCu4G+POclxeqb3F+WPpdKqFGlw36+yOzGlrg=
|
||||
github.com/emirpasic/gods v1.12.0/go.mod h1:YfzfFFoVP/catgzJb4IKIqXjX78Ha8FMSDh3ymbK86o=
|
||||
github.com/envoyproxy/go-control-plane v0.9.1-0.20191026205805-5f8ba28d4473/go.mod h1:YTl/9mNaCwkRvm6d1a2C3ymFceY/DCBVvsKhRF0iEA4=
|
||||
github.com/envoyproxy/protoc-gen-validate v0.1.0/go.mod h1:iSmxcyjqTsJpI2R4NaDN7+kN2VEUnK/pcBlmesArF7c=
|
||||
github.com/emirpasic/gods v1.18.1 h1:FXtiHYKDGKCW2KzwZKx0iC0PQmdlorYgdFG9jPXJ1Bc=
|
||||
github.com/fatih/color v1.7.0/go.mod h1:Zm6kSWBoL9eyXnKyktHP6abPY2pDugNf5KwzbycvMj4=
|
||||
github.com/fatih/color v1.13.0 h1:8LOYc1KYPPmyKMuN8QV2DNRWNbLo6LZ0iLs8+mlH53w=
|
||||
github.com/fatih/color v1.13.0/go.mod h1:kLAiJbzzSOZDVNGyDpeOxJ47H46qBXwg5ILebYFFOfk=
|
||||
github.com/flynn/go-shlex v0.0.0-20150515145356-3f9db97f8568/go.mod h1:xEzjJPgXI435gkrCt3MPfRiAkVrwSbHsst4LCFVfpJc=
|
||||
github.com/frankban/quicktest v1.14.3 h1:FJKSZTDHjyhriyC81FLQ0LY93eSai0ZyR/ZIkd3ZUKE=
|
||||
github.com/gliderlabs/ssh v0.2.2/go.mod h1:U7qILu1NlMHj9FlMhZLlkCdDnU1DBEAqr0aevW3Awn0=
|
||||
github.com/go-git/gcfg v1.5.0 h1:Q5ViNfGF8zFgyJWPqYwA7qGFoMTEiBmdlkcfRmpIMa4=
|
||||
github.com/go-git/gcfg v1.5.0/go.mod h1:5m20vg6GwYabIxaOonVkTdrILxQMpEShl1xiMF4ua+E=
|
||||
github.com/go-git/go-billy/v5 v5.2.0/go.mod h1:pmpqyWchKfYfrkb/UVH4otLvyi/5gJlGI4Hb3ZqZ3W0=
|
||||
github.com/go-git/go-billy/v5 v5.3.1 h1:CPiOUAzKtMRvolEKw+bG1PLRpT7D3LIs3/3ey4Aiu34=
|
||||
github.com/go-git/go-billy/v5 v5.3.1/go.mod h1:pmpqyWchKfYfrkb/UVH4otLvyi/5gJlGI4Hb3ZqZ3W0=
|
||||
github.com/go-git/go-git-fixtures/v4 v4.2.1/go.mod h1:K8zd3kDUAykwTdDCr+I0per6Y6vMiRR/nnVTBtavnB0=
|
||||
github.com/go-git/go-git/v5 v5.4.2 h1:BXyZu9t0VkbiHtqrsvdq39UDhGJTl1h55VW6CSC4aY4=
|
||||
github.com/go-git/go-git/v5 v5.4.2/go.mod h1:gQ1kArt6d+n+BGd+/B/I74HwRTLhth2+zti4ihgckDc=
|
||||
github.com/go-git/go-billy/v5 v5.4.1 h1:Uwp5tDRkPr+l/TnbHOQzp+tmJfLceOlbVucgpTz8ix4=
|
||||
github.com/go-git/go-git/v5 v5.6.1 h1:q4ZRqQl4pR/ZJHc1L5CFjGA1a10u76aV1iC+nh+bHsk=
|
||||
github.com/go-test/deep v1.0.3 h1:ZrJSEWsXzPOxaZnFteGEfooLba+ju3FYIbOrS+rQd68=
|
||||
github.com/golang/glog v0.0.0-20160126235308-23def4e6c14b/go.mod h1:SBH7ygxi8pfUlaOkMMuAQtPIUF8ecWP5IEl/CR7VP2Q=
|
||||
github.com/golang/mock v1.1.1/go.mod h1:oTYuIxOrZwtPieC+H1uAHpcLFnEyAGVDL/k47Jfbm0A=
|
||||
github.com/golang/protobuf v1.1.0/go.mod h1:6lQm79b+lXiMfvg/cZm0SGofjICqVBUtrP5yJMmIC1U=
|
||||
github.com/golang/protobuf v1.2.0/go.mod h1:6lQm79b+lXiMfvg/cZm0SGofjICqVBUtrP5yJMmIC1U=
|
||||
github.com/golang/protobuf v1.3.1/go.mod h1:6lQm79b+lXiMfvg/cZm0SGofjICqVBUtrP5yJMmIC1U=
|
||||
github.com/golang/protobuf v1.3.2/go.mod h1:6lQm79b+lXiMfvg/cZm0SGofjICqVBUtrP5yJMmIC1U=
|
||||
github.com/golang/protobuf v1.3.4/go.mod h1:vzj43D7+SQXF/4pzW/hwtAqwc6iTitCiVSaWz5lYuqw=
|
||||
github.com/golang/protobuf v1.4.0-rc.1/go.mod h1:ceaxUfeHdC40wWswd/P6IGgMaK3YpKi5j83Wpe3EHw8=
|
||||
github.com/golang/protobuf v1.4.0-rc.1.0.20200221234624-67d41d38c208/go.mod h1:xKAWHe0F5eneWXFV3EuXVDTCmh+JuBKY0li0aMyXATA=
|
||||
github.com/golang/protobuf v1.4.0-rc.2/go.mod h1:LlEzMj4AhA7rCAGe4KMBDvJI+AwstrUpVNzEA03Pprs=
|
||||
github.com/golang/protobuf v1.4.0-rc.4.0.20200313231945-b860323f09d0/go.mod h1:WU3c8KckQ9AFe+yFwt9sWVRKCVIyN9cPHBJSNnbL67w=
|
||||
github.com/golang/protobuf v1.4.0/go.mod h1:jodUvKwWbYaEsadDk5Fwe5c77LiNKVO9IDvqG2KuDX0=
|
||||
github.com/golang/protobuf v1.4.1/go.mod h1:U8fpvMrcmy5pZrNK1lt4xCsGvpyWQ/VVv6QDs8UjoX8=
|
||||
github.com/golang/protobuf v1.5.0/go.mod h1:FsONVRAS9T7sI+LIUmWTfcYkHO4aIWwzhcaSAoJOfIk=
|
||||
github.com/golang/protobuf v1.5.2 h1:ROPKBNFfQgOUMifHyP+KYbvpjbdoFNs+aK7DXlji0Tw=
|
||||
github.com/golang/protobuf v1.5.2/go.mod h1:XVQd3VNwM+JqD3oG2Ue2ip4fOMUkwXdXDdiuN0vRsmY=
|
||||
github.com/google/go-cmp v0.2.0/go.mod h1:oXzfMopK8JAjlY9xF4vHSVASa0yLyX7SntLO5aqRK0M=
|
||||
github.com/google/go-cmp v0.3.0/go.mod h1:8QqcDgzrUqlUb/G2PQTWiueGozuR1884gddMywk6iLU=
|
||||
github.com/golang/protobuf v1.5.3 h1:KhyjKVUg7Usr/dYsdSqoFveMYd5ko72D+zANwlG1mmg=
|
||||
github.com/golang/protobuf v1.5.3/go.mod h1:XVQd3VNwM+JqD3oG2Ue2ip4fOMUkwXdXDdiuN0vRsmY=
|
||||
github.com/google/go-cmp v0.3.1/go.mod h1:8QqcDgzrUqlUb/G2PQTWiueGozuR1884gddMywk6iLU=
|
||||
github.com/google/go-cmp v0.4.0/go.mod h1:v8dTdLbMG2kIc/vJvl+f65V22dbkXbowE6jgT/gNBxE=
|
||||
github.com/google/go-cmp v0.5.5/go.mod h1:v8dTdLbMG2kIc/vJvl+f65V22dbkXbowE6jgT/gNBxE=
|
||||
github.com/google/go-cmp v0.5.9 h1:O2Tfq5qg4qc4AmwVlvv0oLiVAGB7enBSJ2x2DqQFi38=
|
||||
github.com/google/go-cmp v0.5.9/go.mod h1:17dUlkBOakJ0+DkrSSNjCkIjxS6bF9zb3elmeNGIjoY=
|
||||
|
|
@ -89,73 +57,62 @@ github.com/hashicorp/errwrap v1.1.0/go.mod h1:YH+1FKiLXxHSkmPseP+kNlulaMuP3n2brv
|
|||
github.com/hashicorp/go-checkpoint v0.5.0 h1:MFYpPZCnQqQTE18jFwSII6eUQrD/oxMFp3mlgcqk5mU=
|
||||
github.com/hashicorp/go-checkpoint v0.5.0/go.mod h1:7nfLNL10NsxqO4iWuW6tWW0HjZuDrwkBuEQsVcpCOgg=
|
||||
github.com/hashicorp/go-cleanhttp v0.5.0/go.mod h1:JpRdi6/HCYpAwUzNwuwqhbovhLtngrth3wmdIIUrZ80=
|
||||
github.com/hashicorp/go-cleanhttp v0.5.1/go.mod h1:JpRdi6/HCYpAwUzNwuwqhbovhLtngrth3wmdIIUrZ80=
|
||||
github.com/hashicorp/go-cleanhttp v0.5.2 h1:035FKYIWjmULyFRBKPs8TBQoi0x6d9G4xc9neXJWAZQ=
|
||||
github.com/hashicorp/go-cleanhttp v0.5.2/go.mod h1:kO/YDlP8L1346E6Sodw+PrpBSV4/SoxCXGY6BqNFT48=
|
||||
github.com/hashicorp/go-cty v1.4.1-0.20200414143053-d3edf31b6320 h1:1/D3zfFHttUKaCaGKZ/dR2roBXv0vKbSCnssIldfQdI=
|
||||
github.com/hashicorp/go-cty v1.4.1-0.20200414143053-d3edf31b6320/go.mod h1:EiZBMaudVLy8fmjf9Npq1dq9RalhveqZG5w/yz3mHWs=
|
||||
github.com/hashicorp/go-hclog v1.4.0 h1:ctuWFGrhFha8BnnzxqeRGidlEcQkDyL5u8J8t5eA11I=
|
||||
github.com/hashicorp/go-hclog v1.4.0/go.mod h1:W4Qnvbt70Wk/zYJryRzDRU/4r0kIg0PVHBcfoyhpF5M=
|
||||
github.com/hashicorp/go-hclog v1.5.0 h1:bI2ocEMgcVlz55Oj1xZNBsVi900c7II+fWDyV9o+13c=
|
||||
github.com/hashicorp/go-hclog v1.5.0/go.mod h1:W4Qnvbt70Wk/zYJryRzDRU/4r0kIg0PVHBcfoyhpF5M=
|
||||
github.com/hashicorp/go-multierror v1.0.0/go.mod h1:dHtQlpGsu+cZNNAkkCN/P3hoUDHhCYQXV3UM06sGGrk=
|
||||
github.com/hashicorp/go-multierror v1.1.1 h1:H5DkEtf6CXdFp0N0Em5UCwQpXMWke8IA0+lD48awMYo=
|
||||
github.com/hashicorp/go-multierror v1.1.1/go.mod h1:iw975J/qwKPdAO1clOe2L8331t/9/fmwbPZ6JB6eMoM=
|
||||
github.com/hashicorp/go-plugin v1.4.8 h1:CHGwpxYDOttQOY7HOWgETU9dyVjOXzniXDqJcYJE1zM=
|
||||
github.com/hashicorp/go-plugin v1.4.8/go.mod h1:viDMjcLJuDui6pXb8U4HVfb8AamCWhHGUjr2IrTF67s=
|
||||
github.com/hashicorp/go-plugin v1.4.10 h1:xUbmA4jC6Dq163/fWcp8P3JuHilrHHMLNRxzGQJ9hNk=
|
||||
github.com/hashicorp/go-plugin v1.4.10/go.mod h1:6/1TEzT0eQznvI/gV2CM29DLSkAK/e58mUWKVsPaph0=
|
||||
github.com/hashicorp/go-uuid v1.0.0/go.mod h1:6SBZvOh/SIDV7/2o3Jml5SYk/TvGqwFJ/bN7x4byOro=
|
||||
github.com/hashicorp/go-uuid v1.0.3 h1:2gKiV6YVmrJ1i2CKKa9obLvRieoRGviZFL26PcT/Co8=
|
||||
github.com/hashicorp/go-uuid v1.0.3/go.mod h1:6SBZvOh/SIDV7/2o3Jml5SYk/TvGqwFJ/bN7x4byOro=
|
||||
github.com/hashicorp/go-version v1.2.0/go.mod h1:fltr4n8CU8Ke44wwGCBoEymUuxUHl09ZGVZPK5anwXA=
|
||||
github.com/hashicorp/go-version v1.2.1/go.mod h1:fltr4n8CU8Ke44wwGCBoEymUuxUHl09ZGVZPK5anwXA=
|
||||
github.com/hashicorp/go-version v1.6.0 h1:feTTfFNnjP967rlCxM/I9g701jU+RN74YKx2mOkIeek=
|
||||
github.com/hashicorp/go-version v1.6.0/go.mod h1:fltr4n8CU8Ke44wwGCBoEymUuxUHl09ZGVZPK5anwXA=
|
||||
github.com/hashicorp/hc-install v0.5.0 h1:D9bl4KayIYKEeJ4vUDe9L5huqxZXczKaykSRcmQ0xY0=
|
||||
github.com/hashicorp/hc-install v0.5.0/go.mod h1:JyzMfbzfSBSjoDCRPna1vi/24BEDxFaCPfdHtM5SCdo=
|
||||
github.com/hashicorp/hcl/v2 v2.16.2 h1:mpkHZh/Tv+xet3sy3F9Ld4FyI2tUpWe9x3XtPx9f1a0=
|
||||
github.com/hashicorp/hcl/v2 v2.16.2/go.mod h1:JRmR89jycNkrrqnMmvPDMd56n1rQJ2Q6KocSLCMCXng=
|
||||
github.com/hashicorp/hc-install v0.5.2 h1:SfwMFnEXVVirpwkDuSF5kymUOhrUxrTq3udEseZdOD0=
|
||||
github.com/hashicorp/hc-install v0.5.2/go.mod h1:9QISwe6newMWIfEiXpzuu1k9HAGtQYgnSH8H9T8wmoI=
|
||||
github.com/hashicorp/hcl/v2 v2.17.0 h1:z1XvSUyXd1HP10U4lrLg5e0JMVz6CPaJvAgxM0KNZVY=
|
||||
github.com/hashicorp/hcl/v2 v2.17.0/go.mod h1:gJyW2PTShkJqQBKpAmPO3yxMxIuoXkOF2TpqXzrQyx4=
|
||||
github.com/hashicorp/logutils v1.0.0 h1:dLEQVugN8vlakKOUE3ihGLTZJRB4j+M2cdTm/ORI65Y=
|
||||
github.com/hashicorp/logutils v1.0.0/go.mod h1:QIAnNjmIWmVIIkWDTG1z5v++HQmx9WQRO+LraFDTW64=
|
||||
github.com/hashicorp/terraform-exec v0.18.1 h1:LAbfDvNQU1l0NOQlTuudjczVhHj061fNX5H8XZxHlH4=
|
||||
github.com/hashicorp/terraform-exec v0.18.1/go.mod h1:58wg4IeuAJ6LVsLUeD2DWZZoc/bYi6dzhLHzxM41980=
|
||||
github.com/hashicorp/terraform-json v0.16.0 h1:UKkeWRWb23do5LNAFlh/K3N0ymn1qTOO8c+85Albo3s=
|
||||
github.com/hashicorp/terraform-json v0.16.0/go.mod h1:v0Ufk9jJnk6tcIZvScHvetlKfiNTC+WS21mnXIlc0B0=
|
||||
github.com/hashicorp/terraform-json v0.17.0 h1:EiA1Wp07nknYQAiv+jIt4dX4Cq5crgP+TsTE45MjMmM=
|
||||
github.com/hashicorp/terraform-json v0.17.0/go.mod h1:Huy6zt6euxaY9knPAFKjUITn8QxUFIe9VuSzb4zn/0o=
|
||||
github.com/hashicorp/terraform-plugin-docs v0.14.1 h1:MikFi59KxrP/ewrZoaowrB9he5Vu4FtvhamZFustiA4=
|
||||
github.com/hashicorp/terraform-plugin-docs v0.14.1/go.mod h1:k2NW8+t113jAus6bb5tQYQgEAX/KueE/u8X2Z45V1GM=
|
||||
github.com/hashicorp/terraform-plugin-go v0.14.3 h1:nlnJ1GXKdMwsC8g1Nh05tK2wsC3+3BL/DBBxFEki+j0=
|
||||
github.com/hashicorp/terraform-plugin-go v0.14.3/go.mod h1:7ees7DMZ263q8wQ6E4RdIdR6nHHJtrdt4ogX5lPkX1A=
|
||||
github.com/hashicorp/terraform-plugin-log v0.8.0 h1:pX2VQ/TGKu+UU1rCay0OlzosNKe4Nz1pepLXj95oyy0=
|
||||
github.com/hashicorp/terraform-plugin-log v0.8.0/go.mod h1:1myFrhVsBLeylQzYYEV17VVjtG8oYPRFdaZs7xdW2xs=
|
||||
github.com/hashicorp/terraform-plugin-sdk/v2 v2.26.1 h1:G9WAfb8LHeCxu7Ae8nc1agZlQOSCUWsb610iAogBhCs=
|
||||
github.com/hashicorp/terraform-plugin-sdk/v2 v2.26.1/go.mod h1:xcOSYlRVdPLmDUoqPhO9fiO/YCN/l6MGYeTzGt5jgkQ=
|
||||
github.com/hashicorp/terraform-registry-address v0.1.0 h1:W6JkV9wbum+m516rCl5/NjKxCyTVaaUBbzYcMzBDO3U=
|
||||
github.com/hashicorp/terraform-registry-address v0.1.0/go.mod h1:EnyO2jYO6j29DTHbJcm00E5nQTFeTtyZH3H5ycydQ5A=
|
||||
github.com/hashicorp/terraform-svchost v0.0.0-20200729002733-f050f53b9734 h1:HKLsbzeOsfXmKNpr3GiT18XAblV0BjCbzL8KQAMZGa0=
|
||||
github.com/hashicorp/terraform-svchost v0.0.0-20200729002733-f050f53b9734/go.mod h1:kNDNcF7sN4DocDLBkQYz73HGKwN1ANB1blq4lIYLYvg=
|
||||
github.com/hashicorp/terraform-plugin-go v0.16.0 h1:DSOQ0rz5FUiVO4NUzMs8ln9gsPgHMTsfns7Nk+6gPuE=
|
||||
github.com/hashicorp/terraform-plugin-go v0.16.0/go.mod h1:4sn8bFuDbt+2+Yztt35IbOrvZc0zyEi87gJzsTgCES8=
|
||||
github.com/hashicorp/terraform-plugin-log v0.9.0 h1:i7hOA+vdAItN1/7UrfBqBwvYPQ9TFvymaRGZED3FCV0=
|
||||
github.com/hashicorp/terraform-plugin-log v0.9.0/go.mod h1:rKL8egZQ/eXSyDqzLUuwUYLVdlYeamldAHSxjUFADow=
|
||||
github.com/hashicorp/terraform-plugin-sdk/v2 v2.27.0 h1:I8efBnjuDrgPjNF1MEypHy48VgcTIUY4X6rOFunrR3Y=
|
||||
github.com/hashicorp/terraform-plugin-sdk/v2 v2.27.0/go.mod h1:cUEP4ly/nxlHy5HzD6YRrHydtlheGvGRJDhiWqqVik4=
|
||||
github.com/hashicorp/terraform-registry-address v0.2.1 h1:QuTf6oJ1+WSflJw6WYOHhLgwUiQ0FrROpHPYFtwTYWM=
|
||||
github.com/hashicorp/terraform-registry-address v0.2.1/go.mod h1:BSE9fIFzp0qWsJUUyGquo4ldV9k2n+psif6NYkBRS3Y=
|
||||
github.com/hashicorp/terraform-svchost v0.1.1 h1:EZZimZ1GxdqFRinZ1tpJwVxxt49xc/S52uzrw4x0jKQ=
|
||||
github.com/hashicorp/terraform-svchost v0.1.1/go.mod h1:mNsjQfZyf/Jhz35v6/0LWcv26+X7JPS+buii2c9/ctc=
|
||||
github.com/hashicorp/yamux v0.0.0-20181012175058-2f1d1f20f75d h1:kJCB4vdITiW1eC1vq2e6IsrXKrZit1bv/TDYFGMp4BQ=
|
||||
github.com/hashicorp/yamux v0.0.0-20181012175058-2f1d1f20f75d/go.mod h1:+NfK9FKeTrX5uv1uIXGdwYDTeHna2qgaIlx54MXqjAM=
|
||||
github.com/huandu/xstrings v1.3.1/go.mod h1:y5/lhBue+AyNmUVz9RLU9xbLR0o4KIIExikq4ovT0aE=
|
||||
github.com/huandu/xstrings v1.3.2 h1:L18LIDzqlW6xN2rEkpdV8+oL/IXWJ1APd+vsdYy4Wdw=
|
||||
github.com/huandu/xstrings v1.3.2/go.mod h1:y5/lhBue+AyNmUVz9RLU9xbLR0o4KIIExikq4ovT0aE=
|
||||
github.com/imdario/mergo v0.3.11/go.mod h1:jmQim1M+e3UYxmgPu/WyfjB3N3VflVyUjjjwH0dnCYA=
|
||||
github.com/imdario/mergo v0.3.12/go.mod h1:jmQim1M+e3UYxmgPu/WyfjB3N3VflVyUjjjwH0dnCYA=
|
||||
github.com/imdario/mergo v0.3.13 h1:lFzP57bqS/wsqKssCGmtLAb8A0wKjLGrve2q3PPVcBk=
|
||||
github.com/imdario/mergo v0.3.13/go.mod h1:4lJ1jqUDcsbIECGy0RUJAXNIhg+6ocWgb1ALK2O4oXg=
|
||||
github.com/jbenet/go-context v0.0.0-20150711004518-d14ea06fba99 h1:BQSFePA1RWJOlocH6Fxy8MmwDt+yVQYULKfN0RoTN8A=
|
||||
github.com/jbenet/go-context v0.0.0-20150711004518-d14ea06fba99/go.mod h1:1lJo3i6rXxKeerYnT8Nvf0QmHCRC1n8sfWVwXF2Frvo=
|
||||
github.com/jessevdk/go-flags v1.5.0/go.mod h1:Fw0T6WPc1dYxT4mKEZRfG5kJhaTDP9pj1c2EWnYs/m4=
|
||||
github.com/jhump/protoreflect v1.6.0 h1:h5jfMVslIg6l29nsMs0D8Wj17RDVdNYti0vDN/PZZoE=
|
||||
github.com/kevinburke/ssh_config v0.0.0-20201106050909-4977a11b4351 h1:DowS9hvgyYSX4TO5NpyC606/Z4SxnNYbT+WX27or6Ck=
|
||||
github.com/kevinburke/ssh_config v0.0.0-20201106050909-4977a11b4351/go.mod h1:CT57kijsi8u/K/BOFA39wgDQJ9CxiF4nAY/ojJ6r6mM=
|
||||
github.com/konsorten/go-windows-terminal-sequences v1.0.1/go.mod h1:T0+1ngSBFLxvqU3pZ+m/2kptfBszLMUkC4ZK/EgS/cQ=
|
||||
github.com/kevinburke/ssh_config v1.2.0 h1:x584FjTGwHzMwvHx18PXxbBVzfnxogHaAReU4gf13a4=
|
||||
github.com/kr/pretty v0.1.0/go.mod h1:dAy3ld7l9f0ibDNOQOHHMYYIIbhfbHSm3C4ZsoJORNo=
|
||||
github.com/kr/pretty v0.2.1/go.mod h1:ipq/a2n7PKx3OHsz4KJII5eveXtPO4qwEXGdVfWzfnI=
|
||||
github.com/kr/pretty v0.3.0 h1:WgNl7dwNpEZ6jJ9k1snq4pZsg7DOEN8hP9Xw0Tsjwk0=
|
||||
github.com/kr/pty v1.1.1/go.mod h1:pFQYn66WHrOpPYNljwOMqo10TkYh1fy3cYio2l3bCsQ=
|
||||
github.com/kr/text v0.1.0/go.mod h1:4Jbv+DJW3UT/LiOwJeYQe1efqtUx/iVham/4vfdArNI=
|
||||
github.com/kr/text v0.2.0 h1:5Nx0Ya0ZqY2ygV366QzturHI13Jq95ApcVaJBhpS+AY=
|
||||
github.com/kr/text v0.2.0/go.mod h1:eLer722TekiGuMkidMxC/pM04lWEeraHUUmBw8l2grE=
|
||||
github.com/kylelemons/godebug v0.0.0-20170820004349-d65d576e9348/go.mod h1:B69LEHPfb2qLo0BaaOLcbitczOKLWTsrBG9LczfCD4k=
|
||||
github.com/kylelemons/godebug v1.1.0 h1:RPNrshWIDI6G2gRW9EHilWtl7Z6Sb1BR0xunSBf0SNc=
|
||||
github.com/matryer/is v1.2.0/go.mod h1:2fLPjFQM9rhQ15aVEtbuwhJinnOqrmgXPNdZsdwlWXA=
|
||||
github.com/mattn/go-colorable v0.0.9/go.mod h1:9vuHe8Xs5qXnSaW/c/ABM9alt+Vo+STaOChaDxuIBZU=
|
||||
github.com/mattn/go-colorable v0.1.9/go.mod h1:u6P/XSegPjTcexA+o6vUJrdnUu04hMope9wVRipJSqc=
|
||||
github.com/mattn/go-colorable v0.1.12/go.mod h1:u5H1YNBxpqRaxsYJYSkiCWKzEfiAb1Gb520KVy5xxl4=
|
||||
|
|
@ -171,8 +128,6 @@ github.com/mitchellh/cli v1.1.5/go.mod h1:v8+iFts2sPIKUV1ltktPXMCC8fumSKFItNcD2c
|
|||
github.com/mitchellh/copystructure v1.0.0/go.mod h1:SNtv71yrdKgLRyLFxmLdkAbkKEFWgYaq1OVrnRcwhnw=
|
||||
github.com/mitchellh/copystructure v1.2.0 h1:vpKXTN4ewci03Vljg/q9QvCGUDttBOGBIa15WveJJGw=
|
||||
github.com/mitchellh/copystructure v1.2.0/go.mod h1:qLl+cE2AmVv+CoeAwDPye/v+N2HKCj9FbZEVFJRxO9s=
|
||||
github.com/mitchellh/go-homedir v1.1.0 h1:lukF9ziXFxDFPkA1vsr5zpc1XuPDn/wFntq5mG+4E0Y=
|
||||
github.com/mitchellh/go-homedir v1.1.0/go.mod h1:SfyaCUpYCn1Vlf4IUYiD9fPX4A5wJrkLzIz1N1q0pr0=
|
||||
github.com/mitchellh/go-testing-interface v1.14.1 h1:jrgshOhYAUVNMAJiKbEu7EqAwgJJ2JqpQmpLJOu07cU=
|
||||
github.com/mitchellh/go-testing-interface v1.14.1/go.mod h1:gfgS7OtZj6MA4U1UrDRp04twqAjfvlZyCfX3sDjEym8=
|
||||
github.com/mitchellh/go-wordwrap v1.0.0 h1:6GlHJ/LTGMrIJbwgdqdl2eEH8o+Exx/0m8ir9Gns0u4=
|
||||
|
|
@ -182,185 +137,106 @@ github.com/mitchellh/mapstructure v1.5.0/go.mod h1:bFUtVrKA4DC2yAKiSyO/QUcy7e+RR
|
|||
github.com/mitchellh/reflectwalk v1.0.0/go.mod h1:mSTlrgnPZtwu0c4WaC2kGObEpuNDbx0jmZXqmk4esnw=
|
||||
github.com/mitchellh/reflectwalk v1.0.2 h1:G2LzWKi524PWgd3mLHV8Y5k7s6XUvT0Gef6zxSIeXaQ=
|
||||
github.com/mitchellh/reflectwalk v1.0.2/go.mod h1:mSTlrgnPZtwu0c4WaC2kGObEpuNDbx0jmZXqmk4esnw=
|
||||
github.com/niemeyer/pretty v0.0.0-20200227124842-a10e7caefd8e/go.mod h1:zD1mROLANZcx1PVRCS0qkT7pwLkGfwJo4zjcN/Tysno=
|
||||
github.com/oklog/run v1.0.0 h1:Ru7dDtJNOyC66gQ5dQmaCa0qIsAUFY3sFpK1Xk8igrw=
|
||||
github.com/oklog/run v1.0.0/go.mod h1:dlhp/R75TPv97u0XWUtDeV/lRKWPKSdTuV0TZvrmrQA=
|
||||
github.com/pkg/errors v0.8.1/go.mod h1:bwawxfHBFNV+L2hUp1rHADufV3IMtnDRdf1r5NINEl0=
|
||||
github.com/pkg/errors v0.9.1/go.mod h1:bwawxfHBFNV+L2hUp1rHADufV3IMtnDRdf1r5NINEl0=
|
||||
github.com/pjbgf/sha1cd v0.3.0 h1:4D5XXmUUBUl/xQ6IjCkEAbqXskkq/4O7LmGn0AqMDs4=
|
||||
github.com/pmezard/go-difflib v1.0.0 h1:4DBwDE0NGyQoBHbLQYPwSUPoCMWR5BEzIk/f1lZbAQM=
|
||||
github.com/pmezard/go-difflib v1.0.0/go.mod h1:iKH77koFhYxTK1pcRnkKkqfTogsbg7gZNVY4sRDYZ/4=
|
||||
github.com/posener/complete v1.1.1/go.mod h1:em0nMJCgc9GFtwrmVmEMR/ZL6WyhyjMBndrE9hABlRI=
|
||||
github.com/posener/complete v1.2.3 h1:NP0eAhjcjImqslEwo/1hq7gpajME0fTLTezBKDqfXqo=
|
||||
github.com/posener/complete v1.2.3/go.mod h1:WZIdtGGp+qx0sLrYKtIRAruyNpv6hFCicSgv7Sy7s/s=
|
||||
github.com/prometheus/client_model v0.0.0-20190812154241-14fe0d1b01d4/go.mod h1:xMI15A0UPsDsEKsMN9yxemIoYk6Tm2C1GtYGdfGttqA=
|
||||
github.com/rogpeppe/go-internal v1.6.1 h1:/FiVV8dS/e+YqF2JvO3yXRFbBLTIuSDkuC7aBOAvL+k=
|
||||
github.com/russross/blackfriday v1.6.0 h1:KqfZb0pUVN2lYqZUYRddxF4OR8ZMURnJIG5Y3VRLtww=
|
||||
github.com/russross/blackfriday v1.6.0/go.mod h1:ti0ldHuxg49ri4ksnFxlkCfN+hvslNlmVHqNRXXJNAY=
|
||||
github.com/sergi/go-diff v1.1.0/go.mod h1:STckp+ISIX8hZLjrqAeVduY0gWCT9IjLuqbuNXdaHfM=
|
||||
github.com/sergi/go-diff v1.2.0 h1:XU+rvMAioB0UC3q1MFrIQy4Vo5/4VsRDQQXHsEya6xQ=
|
||||
github.com/shopspring/decimal v1.2.0/go.mod h1:DKyhrW/HYNuLGql+MJL6WCR6knT2jwCFRcu2hWCYk4o=
|
||||
github.com/shopspring/decimal v1.3.1 h1:2Usl1nmF/WZucqkFZhnfFYxxxu8LG21F6nPQBE5gKV8=
|
||||
github.com/shopspring/decimal v1.3.1/go.mod h1:DKyhrW/HYNuLGql+MJL6WCR6knT2jwCFRcu2hWCYk4o=
|
||||
github.com/sirupsen/logrus v1.4.1/go.mod h1:ni0Sbl8bgC9z8RoU9G6nDWqqs/fq4eDPysMBDgk/93Q=
|
||||
github.com/skeema/knownhosts v1.1.0 h1:Wvr9V0MxhjRbl3f9nMnKnFfiWTJmtECJ9Njkea3ysW0=
|
||||
github.com/spf13/cast v1.3.1/go.mod h1:Qx5cxh0v+4UWYiBimWS+eyWzqEqokIECu5etghLkUJE=
|
||||
github.com/spf13/cast v1.5.0 h1:rj3WzYc11XZaIZMPKmwP96zkFEnnAmV8s6XbB2aY32w=
|
||||
github.com/spf13/cast v1.5.0/go.mod h1:SpXXQ5YoyJw6s3/6cMTQuxvgRl3PCJiyaX9p6b155UU=
|
||||
github.com/stretchr/objx v0.1.0/go.mod h1:HFkY916IF+rwdDfMAkV7OtwuqBVzrE8GR6GFx+wExME=
|
||||
github.com/stretchr/objx v0.1.1/go.mod h1:HFkY916IF+rwdDfMAkV7OtwuqBVzrE8GR6GFx+wExME=
|
||||
github.com/stretchr/testify v1.2.2/go.mod h1:a8OnRcib4nhh0OaRAV+Yts87kKdq0PP7pXfy6kDkUVs=
|
||||
github.com/stretchr/testify v1.4.0/go.mod h1:j7eGeouHqKxXV5pUuKE4zz7dFj8WfuZ+81PSLYec5m4=
|
||||
github.com/stretchr/testify v1.5.1/go.mod h1:5W2xD1RspED5o8YsWQXVCued0rvSQ+mT+I5cxcmMvtA=
|
||||
github.com/stretchr/testify v1.6.1/go.mod h1:6Fq8oRcR53rry900zMqJjRRixrwX3KX962/h/Wwjteg=
|
||||
github.com/stretchr/testify v1.7.0/go.mod h1:6Fq8oRcR53rry900zMqJjRRixrwX3KX962/h/Wwjteg=
|
||||
github.com/stretchr/testify v1.7.2 h1:4jaiDzPyXQvSd7D0EjG45355tLlV3VOECpq10pLC+8s=
|
||||
github.com/stretchr/testify v1.7.2/go.mod h1:R6va5+xMeoiuVRoj+gSkQ7d3FALtqAAGI1FQKckRals=
|
||||
github.com/vmihailenco/msgpack v3.3.3+incompatible/go.mod h1:fy3FlTQTDXWkZ7Bh6AcGMlsjHatGryHQYUTf1ShIgkk=
|
||||
github.com/vmihailenco/msgpack v4.0.4+incompatible h1:dSLoQfGFAo3F6OoNhwUmLwVgaUXK79GlxNBwueZn0xI=
|
||||
github.com/vmihailenco/msgpack v4.0.4+incompatible/go.mod h1:fy3FlTQTDXWkZ7Bh6AcGMlsjHatGryHQYUTf1ShIgkk=
|
||||
github.com/vmihailenco/msgpack/v4 v4.3.12 h1:07s4sz9IReOgdikxLTKNbBdqDMLsjPKXwvCazn8G65U=
|
||||
github.com/vmihailenco/msgpack/v4 v4.3.12/go.mod h1:gborTTJjAo/GWTqqRjrLCn9pgNN+NXzzngzBKDPIqw4=
|
||||
github.com/vmihailenco/tagparser v0.1.1 h1:quXMXlA39OCbd2wAdTsGDlK9RkOk6Wuw+x37wVyIuWY=
|
||||
github.com/vmihailenco/tagparser v0.1.1/go.mod h1:OeAg3pn3UbLjkWt+rN9oFYB6u/cQgqMEUPoW2WPyhdI=
|
||||
github.com/xanzy/ssh-agent v0.3.0 h1:wUMzuKtKilRgBAD1sUb8gOwwRr2FGoBVumcjoOACClI=
|
||||
github.com/xanzy/ssh-agent v0.3.0/go.mod h1:3s9xbODqPuuhK9JV1R321M/FlMZSBvE5aY6eAcqrDh0=
|
||||
github.com/vmihailenco/msgpack/v5 v5.3.5 h1:5gO0H1iULLWGhs2H5tbAHIZTV8/cYafcFOr9znI5mJU=
|
||||
github.com/vmihailenco/msgpack/v5 v5.3.5/go.mod h1:7xyJ9e+0+9SaZT0Wt1RGleJXzli6Q/V5KbhBonMG9jc=
|
||||
github.com/vmihailenco/tagparser/v2 v2.0.0 h1:y09buUbR+b5aycVFQs/g70pqKVZNBmxwAhO7/IwNM9g=
|
||||
github.com/vmihailenco/tagparser/v2 v2.0.0/go.mod h1:Wri+At7QHww0WTrCBeu4J6bNtoV6mEfg5OIWRZA9qds=
|
||||
github.com/xanzy/ssh-agent v0.3.3 h1:+/15pJfg/RsTxqYcX6fHqOXZwwMP+2VyYWJeWM2qQFM=
|
||||
github.com/yuin/goldmark v1.1.25/go.mod h1:3hX8gzYuyVAZsxl0MRgGTJEmQBFcNTphYh9decYSb74=
|
||||
github.com/yuin/goldmark v1.4.13/go.mod h1:6yULJ656Px+3vBD8DxQVa3kxgyrAnzto9xy5taEt/CY=
|
||||
github.com/zclconf/go-cty v1.1.0/go.mod h1:xnAOWiHeOqg2nWS62VtQ7pbOu17FtxJNW8RLEih+O3s=
|
||||
github.com/zclconf/go-cty v1.13.1 h1:0a6bRwuiSHtAmqCqNOE+c2oHgepv0ctoxU4FUe43kwc=
|
||||
github.com/zclconf/go-cty v1.13.1/go.mod h1:YKQzy/7pZ7iq2jNFzy5go57xdxdWoLLpaEp4u238AE0=
|
||||
golang.org/x/crypto v0.0.0-20190219172222-a4c6cb3142f2/go.mod h1:6SG95UA2DQfeDnfUPMdvaQW0Q7yPrPDi9nlGo2tz2b4=
|
||||
github.com/zclconf/go-cty v1.13.2 h1:4GvrUxe/QUDYuJKAav4EYqdM47/kZa672LwmXFmEKT0=
|
||||
github.com/zclconf/go-cty v1.13.2/go.mod h1:YKQzy/7pZ7iq2jNFzy5go57xdxdWoLLpaEp4u238AE0=
|
||||
golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
|
||||
golang.org/x/crypto v0.0.0-20191011191535-87dc89f01550/go.mod h1:yigFU9vqHzYiE8UmvKecakEJjdnWj3jj499lnFckfCI=
|
||||
golang.org/x/crypto v0.0.0-20200414173820-0848c9571904/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto=
|
||||
golang.org/x/crypto v0.0.0-20200820211705-5c72a883971a/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto=
|
||||
golang.org/x/crypto v0.0.0-20210322153248-0c34fe9e7dc2/go.mod h1:T9bdIzuCu7OtxOm1hfPfRQxPLYneinmdGuTeoZ9dtd4=
|
||||
golang.org/x/crypto v0.0.0-20210421170649-83a5a9bb288b/go.mod h1:T9bdIzuCu7OtxOm1hfPfRQxPLYneinmdGuTeoZ9dtd4=
|
||||
golang.org/x/crypto v0.0.0-20210921155107-089bfa567519/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc=
|
||||
golang.org/x/crypto v0.5.0/go.mod h1:NK/OQwhpMQP3MwtdjgLlYHnH9ebylxKWv3e0fK+mkQU=
|
||||
golang.org/x/crypto v0.7.0 h1:AvwMYaRytfdeVt3u6mLaxYtErKYjxA2OXjJ1HHq6t3A=
|
||||
golang.org/x/crypto v0.7.0/go.mod h1:pYwdfH91IfpZVANVyUOhSIPZaFoJGxTFbZhFTx+dXZU=
|
||||
golang.org/x/exp v0.0.0-20190121172915-509febef88a4/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA=
|
||||
golang.org/x/lint v0.0.0-20181026193005-c67002cb31c3/go.mod h1:UVdnD1Gm6xHRNCYTkRU2/jEulfH38KcIWyp/GAMgvoE=
|
||||
golang.org/x/lint v0.0.0-20190227174305-5b3e6a55c961/go.mod h1:wehouNa3lNwaWXcvxsM5YxQ5yQlVC4a0KAMCusXpPoU=
|
||||
golang.org/x/lint v0.0.0-20190313153728-d0100b6bd8b3/go.mod h1:6SW0HCj/g11FgYtHlgUYUwCkIfeOF89ocIRzGO/8vkc=
|
||||
golang.org/x/crypto v0.10.0 h1:LKqV2xt9+kDzSTfOhx4FrkEBcMrAgHSYgzywV9zcGmM=
|
||||
golang.org/x/crypto v0.10.0/go.mod h1:o4eNf7Ede1fv+hwOwZsTHl9EsPFO6q6ZvYR8vYfY45I=
|
||||
golang.org/x/mod v0.2.0/go.mod h1:s0Qsj1ACt9ePp/hMypM3fl4fZqREWJwdYDEqhRiZZUA=
|
||||
golang.org/x/mod v0.6.0-dev.0.20220419223038-86c51ed26bb4/go.mod h1:jJ57K6gSWd91VN4djpZkiMVwK6gcyfeH4XE8wZrZaV4=
|
||||
golang.org/x/mod v0.7.0/go.mod h1:iBbtSCu2XBx23ZKBPSOrRkjjQPZFPuis4dIYUhu/chs=
|
||||
golang.org/x/mod v0.8.0 h1:LUYupSeNrTNCGzR/hVBk2NHZO4hXcVaW1k4Qx7rjPx8=
|
||||
golang.org/x/mod v0.8.0/go.mod h1:iBbtSCu2XBx23ZKBPSOrRkjjQPZFPuis4dIYUhu/chs=
|
||||
golang.org/x/net v0.0.0-20180724234803-3673e40ba225/go.mod h1:mL1N/T3taQHkDXs73rZJwtUhF3w3ftmwwsq0BUmARs4=
|
||||
golang.org/x/net v0.0.0-20180811021610-c39426892332/go.mod h1:mL1N/T3taQHkDXs73rZJwtUhF3w3ftmwwsq0BUmARs4=
|
||||
golang.org/x/net v0.0.0-20180826012351-8a410e7b638d/go.mod h1:mL1N/T3taQHkDXs73rZJwtUhF3w3ftmwwsq0BUmARs4=
|
||||
golang.org/x/net v0.0.0-20190108225652-1e06a53dbb7e/go.mod h1:mL1N/T3taQHkDXs73rZJwtUhF3w3ftmwwsq0BUmARs4=
|
||||
golang.org/x/net v0.0.0-20190213061140-3a22650c66bd/go.mod h1:mL1N/T3taQHkDXs73rZJwtUhF3w3ftmwwsq0BUmARs4=
|
||||
golang.org/x/net v0.0.0-20190311183353-d8887717615a/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
|
||||
golang.org/x/mod v0.10.0 h1:lFO9qtOdlre5W1jxS3r/4szv2/6iXxScdzjoBMXNhYk=
|
||||
golang.org/x/mod v0.10.0/go.mod h1:iBbtSCu2XBx23ZKBPSOrRkjjQPZFPuis4dIYUhu/chs=
|
||||
golang.org/x/net v0.0.0-20190404232315-eb5bcb51f2a3/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
|
||||
golang.org/x/net v0.0.0-20190603091049-60506f45cf65/go.mod h1:HSz+uSET+XFnRR8LxR5pz3Of3rY3CfYBVs4xY44aLks=
|
||||
golang.org/x/net v0.0.0-20190620200207-3b0461eec859/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s=
|
||||
golang.org/x/net v0.0.0-20191009170851-d66e71096ffb/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s=
|
||||
golang.org/x/net v0.0.0-20200226121028-0de0cce0169b/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s=
|
||||
golang.org/x/net v0.0.0-20200301022130-244492dfa37a/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s=
|
||||
golang.org/x/net v0.0.0-20210119194325-5f4716e94777/go.mod h1:m0MpNAwzfU5UDzcl9v0D8zg8gWTRqZa9RBIspLL5mdg=
|
||||
golang.org/x/net v0.0.0-20210226172049-e18ecbb05110/go.mod h1:m0MpNAwzfU5UDzcl9v0D8zg8gWTRqZa9RBIspLL5mdg=
|
||||
golang.org/x/net v0.0.0-20210326060303-6b1517762897/go.mod h1:uSPa2vr4CLtc/ILN5odXGNXS6mhrKVzTaCXzk9m6W3k=
|
||||
golang.org/x/net v0.0.0-20220722155237-a158d28d115b/go.mod h1:XRhObCWvk6IyKnWLug+ECip1KBveYUHfp+8e9klMJ9c=
|
||||
golang.org/x/net v0.5.0/go.mod h1:DivGGAXEgPSlEBzxGzZI+ZLohi+xUj054jfeKui00ws=
|
||||
golang.org/x/net v0.8.0 h1:Zrh2ngAOFYneWTAIAPethzeaQLuHwhuBkuV6ZiRnUaQ=
|
||||
golang.org/x/net v0.8.0/go.mod h1:QVkue5JL9kW//ek3r6jTKnTFis1tRmNAW2P1shuFdJc=
|
||||
golang.org/x/oauth2 v0.0.0-20180821212333-d2e6202438be/go.mod h1:N/0e6XlmueqKjAGxoOufVs8QHGRruUQn6yWY3a++T0U=
|
||||
golang.org/x/oauth2 v0.0.0-20190604053449-0f29369cfe45/go.mod h1:gOpvHmFTYa4IltrdGE7lF6nIHvwfUNPOp7c8zoXwtLw=
|
||||
golang.org/x/net v0.11.0 h1:Gi2tvZIJyBtO9SDr1q9h5hEQCp/4L2RQ+ar0qjx2oNU=
|
||||
golang.org/x/net v0.11.0/go.mod h1:2L/ixqYpgIVXmeoSA/4Lu7BzTG4KIyPIryS4IsOd1oQ=
|
||||
golang.org/x/sync v0.0.0-20180314180146-1d60e4601c6f/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
|
||||
golang.org/x/sync v0.0.0-20181108010431-42b317875d0f/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
|
||||
golang.org/x/sync v0.0.0-20181221193216-37e7f081c4d4/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
|
||||
golang.org/x/sync v0.0.0-20190423024810-112230192c58/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
|
||||
golang.org/x/sync v0.0.0-20190911185100-cd5d95a43a6e/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
|
||||
golang.org/x/sync v0.0.0-20220722155255-886fb9371eb4/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
|
||||
golang.org/x/sys v0.0.0-20180830151530-49385e6e1522/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
|
||||
golang.org/x/sys v0.0.0-20180905080454-ebe1bf3edb33/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
|
||||
golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
|
||||
golang.org/x/sys v0.0.0-20190412213103-97732733099d/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
|
||||
golang.org/x/sys v0.0.0-20190507160741-ecd444e8653b/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
|
||||
golang.org/x/sys v0.0.0-20190916202348-b4ddaad3f8a3/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
|
||||
golang.org/x/sys v0.0.0-20200116001909-b77594299b42/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
|
||||
golang.org/x/sys v0.0.0-20200223170610-d5e6a3e2c0ae/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
|
||||
golang.org/x/sys v0.0.0-20200302150141-5c8b2ff67527/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
|
||||
golang.org/x/sys v0.0.0-20201119102817-f84b799fce68/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
|
||||
golang.org/x/sys v0.0.0-20210320140829-1e4c9ba3b0c4/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
|
||||
golang.org/x/sys v0.0.0-20210324051608-47abb6519492/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
|
||||
golang.org/x/sys v0.0.0-20210502180810-71e4cd670f79/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
|
||||
golang.org/x/sys v0.0.0-20210615035016-665e8c7367d1/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
|
||||
golang.org/x/sys v0.0.0-20210630005230-0f9fa26af87c/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
|
||||
golang.org/x/sys v0.0.0-20210927094055-39ccf1dd6fa6/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
|
||||
golang.org/x/sys v0.0.0-20211007075335-d3039528d8ac/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
|
||||
golang.org/x/sys v0.0.0-20220503163025-988cb79eb6c6/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
|
||||
golang.org/x/sys v0.0.0-20220520151302-bc2c85ada10a/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
|
||||
golang.org/x/sys v0.0.0-20220722155257-8c9f86f7a55f/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
|
||||
golang.org/x/sys v0.0.0-20220811171246-fbc7d0a398ab/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
|
||||
golang.org/x/sys v0.4.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
|
||||
golang.org/x/sys v0.6.0 h1:MVltZSvRTcU2ljQOhs94SXPftV6DCNnZViHeQps87pQ=
|
||||
golang.org/x/sys v0.6.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
|
||||
golang.org/x/sys v0.9.0 h1:KS/R3tvhPqvJvwcKfnBHJwwthS11LRhmM5D59eEXa0s=
|
||||
golang.org/x/sys v0.9.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
|
||||
golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo=
|
||||
golang.org/x/term v0.0.0-20210927222741-03fcf44c2211/go.mod h1:jbD1KX2456YbFQfuXm/mYQcufACuNUgVhRMnK/tPxf8=
|
||||
golang.org/x/term v0.4.0/go.mod h1:9P2UbLfCdcvo3p/nzKvsmas4TnlujnuoV9hGgYzW1lQ=
|
||||
golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
|
||||
golang.org/x/text v0.3.2/go.mod h1:bEr9sfX3Q8Zfm5fL9x+3itogRgK3+ptLWKqgva+5dAk=
|
||||
golang.org/x/text v0.3.3/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
|
||||
golang.org/x/text v0.3.7/go.mod h1:u+2+/6zg+i71rQMx5EYifcz6MCKuco9NR6JIITiCfzQ=
|
||||
golang.org/x/text v0.6.0/go.mod h1:mrYo+phRRbMaCq/xk9113O4dZlRixOauAjOtrjsXDZ8=
|
||||
golang.org/x/text v0.8.0 h1:57P1ETyNKtuIjB4SRd15iJxuhj8Gc416Y78H3qgMh68=
|
||||
golang.org/x/text v0.8.0/go.mod h1:e1OnstbJyHTd6l/uOt8jFFHp6TRDWZR/bV3emEE/zU8=
|
||||
golang.org/x/text v0.10.0 h1:UpjohKhiEgNc0CSauXmwYftY1+LlaC75SJwh0SgCX58=
|
||||
golang.org/x/text v0.10.0/go.mod h1:TvPlkZtksWOMsz7fbANvkp4WM8x/WCo/om8BMLbz+aE=
|
||||
golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
|
||||
golang.org/x/tools v0.0.0-20190114222345-bf090417da8b/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
|
||||
golang.org/x/tools v0.0.0-20190226205152-f727befe758c/go.mod h1:9Yl7xja0Znq3iFh3HoIrodX9oNMXvdceNzlUR8zjMvY=
|
||||
golang.org/x/tools v0.0.0-20190311212946-11955173bddd/go.mod h1:LCzVGOaR6xXOjkQ3onu1FJEFr0SW1gC7cKk1uF8kGRs=
|
||||
golang.org/x/tools v0.0.0-20190524140312-2c0ae7006135/go.mod h1:RgjU9mgBXZiqYHBnxXauZ1Gv1EHHAz9KjViQ78xBX0Q=
|
||||
golang.org/x/tools v0.0.0-20191119224855-298f0cb1881e/go.mod h1:b+2E5dAYhXwXZwtnZ6UAqBI28+e2cm9otk0dWdXHAEo=
|
||||
golang.org/x/tools v0.0.0-20200325010219-a49f79bcc224/go.mod h1:Sl4aGygMT6LrqrWclx+PTx3U+LnKx/seiNR+3G19Ar8=
|
||||
golang.org/x/tools v0.1.12/go.mod h1:hNGJHUnrk76NpqgfD5Aqm5Crs+Hm0VOH/i9J2+nxYbc=
|
||||
golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
|
||||
golang.org/x/xerrors v0.0.0-20191011141410-1b5146add898/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
|
||||
golang.org/x/xerrors v0.0.0-20191204190536-9bdfabe68543/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
|
||||
google.golang.org/appengine v1.1.0/go.mod h1:EbEs0AVv82hx2wNQdGPgUI5lhzA/G0D9YwlJXL52JkM=
|
||||
google.golang.org/appengine v1.4.0/go.mod h1:xpcJRLb0r/rnEns0DIKYYv+WjYCduHsrkT7/EB5XEv4=
|
||||
google.golang.org/appengine v1.6.5/go.mod h1:8WjMMxjGQR8xUklV/ARdw2HLXBOI7O7uCIDZVag1xfc=
|
||||
google.golang.org/appengine v1.6.6 h1:lMO5rYAqUxkmaj76jAkRUvt5JZgFymx/+Q5Mzfivuhc=
|
||||
google.golang.org/appengine v1.6.6/go.mod h1:8WjMMxjGQR8xUklV/ARdw2HLXBOI7O7uCIDZVag1xfc=
|
||||
google.golang.org/genproto v0.0.0-20180817151627-c66870c02cf8/go.mod h1:JiN7NxoALGmiZfu7CAH4rXhgtRTLTxftemlI0sWmxmc=
|
||||
google.golang.org/genproto v0.0.0-20190819201941-24fa4b261c55/go.mod h1:DMBHOl98Agz4BDEuKkezgsaosCRResVns1a3J2ZsMNc=
|
||||
google.golang.org/genproto v0.0.0-20200526211855-cb27e3aa2013/go.mod h1:NbSheEEYHJ7i3ixzK3sjbqSGDJWnxyFXZblF3eUsNvo=
|
||||
google.golang.org/genproto v0.0.0-20200711021454-869866162049 h1:YFTFpQhgvrLrmxtiIncJxFXeCyq84ixuKWVCaCAi9Oc=
|
||||
google.golang.org/genproto v0.0.0-20200711021454-869866162049/go.mod h1:FWY/as6DDZQgahTzZj3fqbO1CbirC29ZNUFHwi0/+no=
|
||||
google.golang.org/grpc v1.19.0/go.mod h1:mqu4LbDTu4XGKhr4mRzUsmM4RtVoemTSY81AxZiDr8c=
|
||||
google.golang.org/grpc v1.23.0/go.mod h1:Y5yQAOtifL1yxbo5wqy6BxZv8vAUGQwXBOALyacEbxg=
|
||||
google.golang.org/grpc v1.27.0/go.mod h1:qbnxyOmOxrQa7FizSgH+ReBfzJrCY1pSN7KXBS8abTk=
|
||||
google.golang.org/grpc v1.51.0 h1:E1eGv1FTqoLIdnBCZufiSHgKjlqG6fKFf6pPWtMTh8U=
|
||||
google.golang.org/grpc v1.51.0/go.mod h1:wgNDFcnuBGmxLKI/qn4T+m5BtEBYXJPvibbUPsAIPww=
|
||||
google.golang.org/protobuf v0.0.0-20200109180630-ec00e32a8dfd/go.mod h1:DFci5gLYBciE7Vtevhsrf46CRTquxDuWsQurQQe4oz8=
|
||||
google.golang.org/protobuf v0.0.0-20200221191635-4d8936d0db64/go.mod h1:kwYJMbMJ01Woi6D6+Kah6886xMZcty6N08ah7+eCXa0=
|
||||
google.golang.org/protobuf v0.0.0-20200228230310-ab0ca4ff8a60/go.mod h1:cfTl7dwQJ+fmap5saPgwCLgHXTUD7jkjRqWcaiX5VyM=
|
||||
google.golang.org/protobuf v1.20.1-0.20200309200217-e05f789c0967/go.mod h1:A+miEFZTKqfCUM6K7xSMQL9OKL/b6hQv+e19PK+JZNE=
|
||||
google.golang.org/protobuf v1.21.0/go.mod h1:47Nbq4nVaFHyn7ilMalzfO3qCViNmqZ2kzikPIcrTAo=
|
||||
google.golang.org/protobuf v1.22.0/go.mod h1:EGpADcykh3NcUnDUJcl1+ZksZNG86OlYog2l/sGQquU=
|
||||
google.golang.org/protobuf v1.23.1-0.20200526195155-81db48ad09cc/go.mod h1:EGpADcykh3NcUnDUJcl1+ZksZNG86OlYog2l/sGQquU=
|
||||
google.golang.org/protobuf v1.24.0/go.mod h1:r/3tXBNzIEhYS9I1OUVjXDlt8tc493IdKGjtUeSXeh4=
|
||||
google.golang.org/appengine v1.6.7 h1:FZR1q0exgwxzPzp/aF+VccGrSfxfPpkBqjIIEq3ru6c=
|
||||
google.golang.org/appengine v1.6.7/go.mod h1:8WjMMxjGQR8xUklV/ARdw2HLXBOI7O7uCIDZVag1xfc=
|
||||
google.golang.org/genproto v0.0.0-20230410155749-daa745c078e1 h1:KpwkzHKEF7B9Zxg18WzOa7djJ+Ha5DzthMyZYQfEn2A=
|
||||
google.golang.org/genproto v0.0.0-20230410155749-daa745c078e1/go.mod h1:nKE/iIaLqn2bQwXBg8f1g2Ylh6r5MN5CmZvuzZCgsCU=
|
||||
google.golang.org/grpc v1.56.0 h1:+y7Bs8rtMd07LeXmL3NxcTLn7mUkbKZqEpPhMNkwJEE=
|
||||
google.golang.org/grpc v1.56.0/go.mod h1:I9bI3vqKfayGqPUAwGdOSu7kt6oIJLixfffKrpXqQ9s=
|
||||
google.golang.org/protobuf v1.26.0-rc.1/go.mod h1:jlhhOSvTdKEhbULTjvd4ARK9grFBp09yW+WbY/TyQbw=
|
||||
google.golang.org/protobuf v1.26.0/go.mod h1:9q0QmTI4eRPtz6boOQmLYwt+qCgq0jsYwAQnmE0givc=
|
||||
google.golang.org/protobuf v1.28.1 h1:d0NfwRgPtno5B1Wa6L2DAG+KivqkdutMf1UhdNx175w=
|
||||
google.golang.org/protobuf v1.28.1/go.mod h1:HV8QOd/L58Z+nl8r43ehVNZIU/HEI6OcFqwMG9pJV4I=
|
||||
google.golang.org/protobuf v1.30.0 h1:kPPoIgf3TsEvrm0PFe15JQ+570QVxYzEvvHqChK+cng=
|
||||
google.golang.org/protobuf v1.30.0/go.mod h1:HV8QOd/L58Z+nl8r43ehVNZIU/HEI6OcFqwMG9pJV4I=
|
||||
gopkg.in/check.v1 v0.0.0-20161208181325-20d25e280405/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
|
||||
gopkg.in/check.v1 v1.0.0-20180628173108-788fd7840127 h1:qIbj1fsPNlZgppZ+VLlY7N33q108Sa+fhmuc+sWQYwY=
|
||||
gopkg.in/check.v1 v1.0.0-20180628173108-788fd7840127/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
|
||||
gopkg.in/check.v1 v1.0.0-20190902080502-41f04d3bba15/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
|
||||
gopkg.in/check.v1 v1.0.0-20200227125254-8fa46927fb4f/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
|
||||
gopkg.in/check.v1 v1.0.0-20201130134442-10cb98267c6c h1:Hei/4ADfdWqJk1ZMxUNpqntNwaWcugrBjAiHlqqRiVk=
|
||||
gopkg.in/check.v1 v1.0.0-20201130134442-10cb98267c6c/go.mod h1:JHkPIbrfpd72SG/EVd6muEfDQjcINNoR0C8j2r3qZ4Q=
|
||||
gopkg.in/warnings.v0 v0.1.2 h1:wFXVbFY8DY5/xOe1ECiWdKCzZlxgshcYVNkBHstARME=
|
||||
gopkg.in/warnings.v0 v0.1.2/go.mod h1:jksf8JmL6Qr/oQM2OXTHunEvvTAsrWBLb6OOjuVWRNI=
|
||||
gopkg.in/yaml.v2 v2.2.2/go.mod h1:hI93XBmqTisBFMUTm0b8Fm+jr3Dg1NNxqwp+5A1VGuI=
|
||||
gopkg.in/yaml.v2 v2.2.4/go.mod h1:hI93XBmqTisBFMUTm0b8Fm+jr3Dg1NNxqwp+5A1VGuI=
|
||||
gopkg.in/yaml.v2 v2.3.0/go.mod h1:hI93XBmqTisBFMUTm0b8Fm+jr3Dg1NNxqwp+5A1VGuI=
|
||||
gopkg.in/yaml.v3 v3.0.0-20200313102051-9f266ea9e77c/go.mod h1:K4uyk7z7BCEPqu6E+C64Yfv1cQ7kz7rIZviUmN+EgEM=
|
||||
gopkg.in/yaml.v3 v3.0.0-20210107192922-496545a6307b/go.mod h1:K4uyk7z7BCEPqu6E+C64Yfv1cQ7kz7rIZviUmN+EgEM=
|
||||
gopkg.in/yaml.v3 v3.0.0/go.mod h1:K4uyk7z7BCEPqu6E+C64Yfv1cQ7kz7rIZviUmN+EgEM=
|
||||
gopkg.in/yaml.v3 v3.0.1 h1:fxVm/GzAzEWqLHuvctI91KS9hhNmmWOoWu0XTYJS7CA=
|
||||
gopkg.in/yaml.v3 v3.0.1/go.mod h1:K4uyk7z7BCEPqu6E+C64Yfv1cQ7kz7rIZviUmN+EgEM=
|
||||
honnef.co/go/tools v0.0.0-20190102054323-c2f93a96b099/go.mod h1:rf3lG4BRIbNafJWhAfAdb/ePZxsR/4RtNHQocxwk9r4=
|
||||
honnef.co/go/tools v0.0.0-20190523083050-ea95bdfd59fc/go.mod h1:rf3lG4BRIbNafJWhAfAdb/ePZxsR/4RtNHQocxwk9r4=
|
||||
|
|
|
|||
|
|
@ -0,0 +1,3 @@
|
|||
# This source code refers to The Go Authors for copyright purposes.
|
||||
# The master list of authors is in the main Go distribution,
|
||||
# visible at https://tip.golang.org/AUTHORS.
|
||||
|
|
@ -0,0 +1,3 @@
|
|||
# This source code was written by the Go contributors.
|
||||
# The master list of contributors is in the main Go distribution,
|
||||
# visible at https://tip.golang.org/CONTRIBUTORS.
|
||||
|
|
@ -0,0 +1,27 @@
|
|||
Copyright (c) 2009 The Go Authors. All rights reserved.
|
||||
|
||||
Redistribution and use in source and binary forms, with or without
|
||||
modification, are permitted provided that the following conditions are
|
||||
met:
|
||||
|
||||
* Redistributions of source code must retain the above copyright
|
||||
notice, this list of conditions and the following disclaimer.
|
||||
* Redistributions in binary form must reproduce the above
|
||||
copyright notice, this list of conditions and the following disclaimer
|
||||
in the documentation and/or other materials provided with the
|
||||
distribution.
|
||||
* Neither the name of Google Inc. nor the names of its
|
||||
contributors may be used to endorse or promote products derived from
|
||||
this software without specific prior written permission.
|
||||
|
||||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||||
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
||||
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
|
||||
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
||||
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
||||
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
||||
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
||||
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||||
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
||||
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
|
|
@ -0,0 +1,22 @@
|
|||
Additional IP Rights Grant (Patents)
|
||||
|
||||
"This implementation" means the copyrightable works distributed by
|
||||
Google as part of the Go project.
|
||||
|
||||
Google hereby grants to You a perpetual, worldwide, non-exclusive,
|
||||
no-charge, royalty-free, irrevocable (except as stated in this section)
|
||||
patent license to make, have made, use, offer to sell, sell, import,
|
||||
transfer and otherwise run, modify and propagate the contents of this
|
||||
implementation of Go, where such license applies only to those patent
|
||||
claims, both currently owned or controlled by Google and acquired in
|
||||
the future, licensable by Google that are necessarily infringed by this
|
||||
implementation of Go. This grant does not include claims that would be
|
||||
infringed only as a consequence of further modification of this
|
||||
implementation. If you or your agent or exclusive licensee institute or
|
||||
order or agree to the institution of patent litigation against any
|
||||
entity (including a cross-claim or counterclaim in a lawsuit) alleging
|
||||
that this implementation of Go or any code incorporated within this
|
||||
implementation of Go constitutes direct or contributory patent
|
||||
infringement, or inducement of patent infringement, then any patent
|
||||
rights granted to you under this License for this implementation of Go
|
||||
shall terminate as of the date such litigation is filed.
|
||||
|
|
@ -0,0 +1,381 @@
|
|||
package bitcurves
|
||||
|
||||
// Copyright 2010 The Go Authors. All rights reserved.
|
||||
// Copyright 2011 ThePiachu. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package bitelliptic implements several Koblitz elliptic curves over prime
|
||||
// fields.
|
||||
|
||||
// This package operates, internally, on Jacobian coordinates. For a given
|
||||
// (x, y) position on the curve, the Jacobian coordinates are (x1, y1, z1)
|
||||
// where x = x1/z1² and y = y1/z1³. The greatest speedups come when the whole
|
||||
// calculation can be performed within the transform (as in ScalarMult and
|
||||
// ScalarBaseMult). But even for Add and Double, it's faster to apply and
|
||||
// reverse the transform than to operate in affine coordinates.
|
||||
|
||||
import (
|
||||
"crypto/elliptic"
|
||||
"io"
|
||||
"math/big"
|
||||
"sync"
|
||||
)
|
||||
|
||||
// A BitCurve represents a Koblitz Curve with a=0.
|
||||
// See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html
|
||||
type BitCurve struct {
|
||||
Name string
|
||||
P *big.Int // the order of the underlying field
|
||||
N *big.Int // the order of the base point
|
||||
B *big.Int // the constant of the BitCurve equation
|
||||
Gx, Gy *big.Int // (x,y) of the base point
|
||||
BitSize int // the size of the underlying field
|
||||
}
|
||||
|
||||
// Params returns the parameters of the given BitCurve (see BitCurve struct)
|
||||
func (bitCurve *BitCurve) Params() (cp *elliptic.CurveParams) {
|
||||
cp = new(elliptic.CurveParams)
|
||||
cp.Name = bitCurve.Name
|
||||
cp.P = bitCurve.P
|
||||
cp.N = bitCurve.N
|
||||
cp.Gx = bitCurve.Gx
|
||||
cp.Gy = bitCurve.Gy
|
||||
cp.BitSize = bitCurve.BitSize
|
||||
return cp
|
||||
}
|
||||
|
||||
// IsOnCurve returns true if the given (x,y) lies on the BitCurve.
|
||||
func (bitCurve *BitCurve) IsOnCurve(x, y *big.Int) bool {
|
||||
// y² = x³ + b
|
||||
y2 := new(big.Int).Mul(y, y) //y²
|
||||
y2.Mod(y2, bitCurve.P) //y²%P
|
||||
|
||||
x3 := new(big.Int).Mul(x, x) //x²
|
||||
x3.Mul(x3, x) //x³
|
||||
|
||||
x3.Add(x3, bitCurve.B) //x³+B
|
||||
x3.Mod(x3, bitCurve.P) //(x³+B)%P
|
||||
|
||||
return x3.Cmp(y2) == 0
|
||||
}
|
||||
|
||||
// affineFromJacobian reverses the Jacobian transform. See the comment at the
|
||||
// top of the file.
|
||||
func (bitCurve *BitCurve) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) {
|
||||
if z.Cmp(big.NewInt(0)) == 0 {
|
||||
panic("bitcurve: Can't convert to affine with Jacobian Z = 0")
|
||||
}
|
||||
// x = YZ^2 mod P
|
||||
zinv := new(big.Int).ModInverse(z, bitCurve.P)
|
||||
zinvsq := new(big.Int).Mul(zinv, zinv)
|
||||
|
||||
xOut = new(big.Int).Mul(x, zinvsq)
|
||||
xOut.Mod(xOut, bitCurve.P)
|
||||
// y = YZ^3 mod P
|
||||
zinvsq.Mul(zinvsq, zinv)
|
||||
yOut = new(big.Int).Mul(y, zinvsq)
|
||||
yOut.Mod(yOut, bitCurve.P)
|
||||
return xOut, yOut
|
||||
}
|
||||
|
||||
// Add returns the sum of (x1,y1) and (x2,y2)
|
||||
func (bitCurve *BitCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
|
||||
z := new(big.Int).SetInt64(1)
|
||||
x, y, z := bitCurve.addJacobian(x1, y1, z, x2, y2, z)
|
||||
return bitCurve.affineFromJacobian(x, y, z)
|
||||
}
|
||||
|
||||
// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and
|
||||
// (x2, y2, z2) and returns their sum, also in Jacobian form.
|
||||
func (bitCurve *BitCurve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) {
|
||||
// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl
|
||||
z1z1 := new(big.Int).Mul(z1, z1)
|
||||
z1z1.Mod(z1z1, bitCurve.P)
|
||||
z2z2 := new(big.Int).Mul(z2, z2)
|
||||
z2z2.Mod(z2z2, bitCurve.P)
|
||||
|
||||
u1 := new(big.Int).Mul(x1, z2z2)
|
||||
u1.Mod(u1, bitCurve.P)
|
||||
u2 := new(big.Int).Mul(x2, z1z1)
|
||||
u2.Mod(u2, bitCurve.P)
|
||||
h := new(big.Int).Sub(u2, u1)
|
||||
if h.Sign() == -1 {
|
||||
h.Add(h, bitCurve.P)
|
||||
}
|
||||
i := new(big.Int).Lsh(h, 1)
|
||||
i.Mul(i, i)
|
||||
j := new(big.Int).Mul(h, i)
|
||||
|
||||
s1 := new(big.Int).Mul(y1, z2)
|
||||
s1.Mul(s1, z2z2)
|
||||
s1.Mod(s1, bitCurve.P)
|
||||
s2 := new(big.Int).Mul(y2, z1)
|
||||
s2.Mul(s2, z1z1)
|
||||
s2.Mod(s2, bitCurve.P)
|
||||
r := new(big.Int).Sub(s2, s1)
|
||||
if r.Sign() == -1 {
|
||||
r.Add(r, bitCurve.P)
|
||||
}
|
||||
r.Lsh(r, 1)
|
||||
v := new(big.Int).Mul(u1, i)
|
||||
|
||||
x3 := new(big.Int).Set(r)
|
||||
x3.Mul(x3, x3)
|
||||
x3.Sub(x3, j)
|
||||
x3.Sub(x3, v)
|
||||
x3.Sub(x3, v)
|
||||
x3.Mod(x3, bitCurve.P)
|
||||
|
||||
y3 := new(big.Int).Set(r)
|
||||
v.Sub(v, x3)
|
||||
y3.Mul(y3, v)
|
||||
s1.Mul(s1, j)
|
||||
s1.Lsh(s1, 1)
|
||||
y3.Sub(y3, s1)
|
||||
y3.Mod(y3, bitCurve.P)
|
||||
|
||||
z3 := new(big.Int).Add(z1, z2)
|
||||
z3.Mul(z3, z3)
|
||||
z3.Sub(z3, z1z1)
|
||||
if z3.Sign() == -1 {
|
||||
z3.Add(z3, bitCurve.P)
|
||||
}
|
||||
z3.Sub(z3, z2z2)
|
||||
if z3.Sign() == -1 {
|
||||
z3.Add(z3, bitCurve.P)
|
||||
}
|
||||
z3.Mul(z3, h)
|
||||
z3.Mod(z3, bitCurve.P)
|
||||
|
||||
return x3, y3, z3
|
||||
}
|
||||
|
||||
// Double returns 2*(x,y)
|
||||
func (bitCurve *BitCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
|
||||
z1 := new(big.Int).SetInt64(1)
|
||||
return bitCurve.affineFromJacobian(bitCurve.doubleJacobian(x1, y1, z1))
|
||||
}
|
||||
|
||||
// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
|
||||
// returns its double, also in Jacobian form.
|
||||
func (bitCurve *BitCurve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
|
||||
// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
|
||||
|
||||
a := new(big.Int).Mul(x, x) //X1²
|
||||
b := new(big.Int).Mul(y, y) //Y1²
|
||||
c := new(big.Int).Mul(b, b) //B²
|
||||
|
||||
d := new(big.Int).Add(x, b) //X1+B
|
||||
d.Mul(d, d) //(X1+B)²
|
||||
d.Sub(d, a) //(X1+B)²-A
|
||||
d.Sub(d, c) //(X1+B)²-A-C
|
||||
d.Mul(d, big.NewInt(2)) //2*((X1+B)²-A-C)
|
||||
|
||||
e := new(big.Int).Mul(big.NewInt(3), a) //3*A
|
||||
f := new(big.Int).Mul(e, e) //E²
|
||||
|
||||
x3 := new(big.Int).Mul(big.NewInt(2), d) //2*D
|
||||
x3.Sub(f, x3) //F-2*D
|
||||
x3.Mod(x3, bitCurve.P)
|
||||
|
||||
y3 := new(big.Int).Sub(d, x3) //D-X3
|
||||
y3.Mul(e, y3) //E*(D-X3)
|
||||
y3.Sub(y3, new(big.Int).Mul(big.NewInt(8), c)) //E*(D-X3)-8*C
|
||||
y3.Mod(y3, bitCurve.P)
|
||||
|
||||
z3 := new(big.Int).Mul(y, z) //Y1*Z1
|
||||
z3.Mul(big.NewInt(2), z3) //3*Y1*Z1
|
||||
z3.Mod(z3, bitCurve.P)
|
||||
|
||||
return x3, y3, z3
|
||||
}
|
||||
|
||||
//TODO: double check if it is okay
|
||||
// ScalarMult returns k*(Bx,By) where k is a number in big-endian form.
|
||||
func (bitCurve *BitCurve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
|
||||
// We have a slight problem in that the identity of the group (the
|
||||
// point at infinity) cannot be represented in (x, y) form on a finite
|
||||
// machine. Thus the standard add/double algorithm has to be tweaked
|
||||
// slightly: our initial state is not the identity, but x, and we
|
||||
// ignore the first true bit in |k|. If we don't find any true bits in
|
||||
// |k|, then we return nil, nil, because we cannot return the identity
|
||||
// element.
|
||||
|
||||
Bz := new(big.Int).SetInt64(1)
|
||||
x := Bx
|
||||
y := By
|
||||
z := Bz
|
||||
|
||||
seenFirstTrue := false
|
||||
for _, byte := range k {
|
||||
for bitNum := 0; bitNum < 8; bitNum++ {
|
||||
if seenFirstTrue {
|
||||
x, y, z = bitCurve.doubleJacobian(x, y, z)
|
||||
}
|
||||
if byte&0x80 == 0x80 {
|
||||
if !seenFirstTrue {
|
||||
seenFirstTrue = true
|
||||
} else {
|
||||
x, y, z = bitCurve.addJacobian(Bx, By, Bz, x, y, z)
|
||||
}
|
||||
}
|
||||
byte <<= 1
|
||||
}
|
||||
}
|
||||
|
||||
if !seenFirstTrue {
|
||||
return nil, nil
|
||||
}
|
||||
|
||||
return bitCurve.affineFromJacobian(x, y, z)
|
||||
}
|
||||
|
||||
// ScalarBaseMult returns k*G, where G is the base point of the group and k is
|
||||
// an integer in big-endian form.
|
||||
func (bitCurve *BitCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
|
||||
return bitCurve.ScalarMult(bitCurve.Gx, bitCurve.Gy, k)
|
||||
}
|
||||
|
||||
var mask = []byte{0xff, 0x1, 0x3, 0x7, 0xf, 0x1f, 0x3f, 0x7f}
|
||||
|
||||
//TODO: double check if it is okay
|
||||
// GenerateKey returns a public/private key pair. The private key is generated
|
||||
// using the given reader, which must return random data.
|
||||
func (bitCurve *BitCurve) GenerateKey(rand io.Reader) (priv []byte, x, y *big.Int, err error) {
|
||||
byteLen := (bitCurve.BitSize + 7) >> 3
|
||||
priv = make([]byte, byteLen)
|
||||
|
||||
for x == nil {
|
||||
_, err = io.ReadFull(rand, priv)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
// We have to mask off any excess bits in the case that the size of the
|
||||
// underlying field is not a whole number of bytes.
|
||||
priv[0] &= mask[bitCurve.BitSize%8]
|
||||
// This is because, in tests, rand will return all zeros and we don't
|
||||
// want to get the point at infinity and loop forever.
|
||||
priv[1] ^= 0x42
|
||||
x, y = bitCurve.ScalarBaseMult(priv)
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Marshal converts a point into the form specified in section 4.3.6 of ANSI
|
||||
// X9.62.
|
||||
func (bitCurve *BitCurve) Marshal(x, y *big.Int) []byte {
|
||||
byteLen := (bitCurve.BitSize + 7) >> 3
|
||||
|
||||
ret := make([]byte, 1+2*byteLen)
|
||||
ret[0] = 4 // uncompressed point
|
||||
|
||||
xBytes := x.Bytes()
|
||||
copy(ret[1+byteLen-len(xBytes):], xBytes)
|
||||
yBytes := y.Bytes()
|
||||
copy(ret[1+2*byteLen-len(yBytes):], yBytes)
|
||||
return ret
|
||||
}
|
||||
|
||||
// Unmarshal converts a point, serialised by Marshal, into an x, y pair. On
|
||||
// error, x = nil.
|
||||
func (bitCurve *BitCurve) Unmarshal(data []byte) (x, y *big.Int) {
|
||||
byteLen := (bitCurve.BitSize + 7) >> 3
|
||||
if len(data) != 1+2*byteLen {
|
||||
return
|
||||
}
|
||||
if data[0] != 4 { // uncompressed form
|
||||
return
|
||||
}
|
||||
x = new(big.Int).SetBytes(data[1 : 1+byteLen])
|
||||
y = new(big.Int).SetBytes(data[1+byteLen:])
|
||||
return
|
||||
}
|
||||
|
||||
//curve parameters taken from:
|
||||
//http://www.secg.org/collateral/sec2_final.pdf
|
||||
|
||||
var initonce sync.Once
|
||||
var secp160k1 *BitCurve
|
||||
var secp192k1 *BitCurve
|
||||
var secp224k1 *BitCurve
|
||||
var secp256k1 *BitCurve
|
||||
|
||||
func initAll() {
|
||||
initS160()
|
||||
initS192()
|
||||
initS224()
|
||||
initS256()
|
||||
}
|
||||
|
||||
func initS160() {
|
||||
// See SEC 2 section 2.4.1
|
||||
secp160k1 = new(BitCurve)
|
||||
secp160k1.Name = "secp160k1"
|
||||
secp160k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73", 16)
|
||||
secp160k1.N, _ = new(big.Int).SetString("0100000000000000000001B8FA16DFAB9ACA16B6B3", 16)
|
||||
secp160k1.B, _ = new(big.Int).SetString("0000000000000000000000000000000000000007", 16)
|
||||
secp160k1.Gx, _ = new(big.Int).SetString("3B4C382CE37AA192A4019E763036F4F5DD4D7EBB", 16)
|
||||
secp160k1.Gy, _ = new(big.Int).SetString("938CF935318FDCED6BC28286531733C3F03C4FEE", 16)
|
||||
secp160k1.BitSize = 160
|
||||
}
|
||||
|
||||
func initS192() {
|
||||
// See SEC 2 section 2.5.1
|
||||
secp192k1 = new(BitCurve)
|
||||
secp192k1.Name = "secp192k1"
|
||||
secp192k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37", 16)
|
||||
secp192k1.N, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D", 16)
|
||||
secp192k1.B, _ = new(big.Int).SetString("000000000000000000000000000000000000000000000003", 16)
|
||||
secp192k1.Gx, _ = new(big.Int).SetString("DB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D", 16)
|
||||
secp192k1.Gy, _ = new(big.Int).SetString("9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D", 16)
|
||||
secp192k1.BitSize = 192
|
||||
}
|
||||
|
||||
func initS224() {
|
||||
// See SEC 2 section 2.6.1
|
||||
secp224k1 = new(BitCurve)
|
||||
secp224k1.Name = "secp224k1"
|
||||
secp224k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D", 16)
|
||||
secp224k1.N, _ = new(big.Int).SetString("010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7", 16)
|
||||
secp224k1.B, _ = new(big.Int).SetString("00000000000000000000000000000000000000000000000000000005", 16)
|
||||
secp224k1.Gx, _ = new(big.Int).SetString("A1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C", 16)
|
||||
secp224k1.Gy, _ = new(big.Int).SetString("7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5", 16)
|
||||
secp224k1.BitSize = 224
|
||||
}
|
||||
|
||||
func initS256() {
|
||||
// See SEC 2 section 2.7.1
|
||||
secp256k1 = new(BitCurve)
|
||||
secp256k1.Name = "secp256k1"
|
||||
secp256k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", 16)
|
||||
secp256k1.N, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 16)
|
||||
secp256k1.B, _ = new(big.Int).SetString("0000000000000000000000000000000000000000000000000000000000000007", 16)
|
||||
secp256k1.Gx, _ = new(big.Int).SetString("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 16)
|
||||
secp256k1.Gy, _ = new(big.Int).SetString("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 16)
|
||||
secp256k1.BitSize = 256
|
||||
}
|
||||
|
||||
// S160 returns a BitCurve which implements secp160k1 (see SEC 2 section 2.4.1)
|
||||
func S160() *BitCurve {
|
||||
initonce.Do(initAll)
|
||||
return secp160k1
|
||||
}
|
||||
|
||||
// S192 returns a BitCurve which implements secp192k1 (see SEC 2 section 2.5.1)
|
||||
func S192() *BitCurve {
|
||||
initonce.Do(initAll)
|
||||
return secp192k1
|
||||
}
|
||||
|
||||
// S224 returns a BitCurve which implements secp224k1 (see SEC 2 section 2.6.1)
|
||||
func S224() *BitCurve {
|
||||
initonce.Do(initAll)
|
||||
return secp224k1
|
||||
}
|
||||
|
||||
// S256 returns a BitCurve which implements bitcurves (see SEC 2 section 2.7.1)
|
||||
func S256() *BitCurve {
|
||||
initonce.Do(initAll)
|
||||
return secp256k1
|
||||
}
|
||||
|
|
@ -0,0 +1,134 @@
|
|||
// Package brainpool implements Brainpool elliptic curves.
|
||||
// Implementation of rcurves is from github.com/ebfe/brainpool
|
||||
// Note that these curves are implemented with naive, non-constant time operations
|
||||
// and are likely not suitable for environments where timing attacks are a concern.
|
||||
package brainpool
|
||||
|
||||
import (
|
||||
"crypto/elliptic"
|
||||
"math/big"
|
||||
"sync"
|
||||
)
|
||||
|
||||
var (
|
||||
once sync.Once
|
||||
p256t1, p384t1, p512t1 *elliptic.CurveParams
|
||||
p256r1, p384r1, p512r1 *rcurve
|
||||
)
|
||||
|
||||
func initAll() {
|
||||
initP256t1()
|
||||
initP384t1()
|
||||
initP512t1()
|
||||
initP256r1()
|
||||
initP384r1()
|
||||
initP512r1()
|
||||
}
|
||||
|
||||
func initP256t1() {
|
||||
p256t1 = &elliptic.CurveParams{Name: "brainpoolP256t1"}
|
||||
p256t1.P, _ = new(big.Int).SetString("A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377", 16)
|
||||
p256t1.N, _ = new(big.Int).SetString("A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7", 16)
|
||||
p256t1.B, _ = new(big.Int).SetString("662C61C430D84EA4FE66A7733D0B76B7BF93EBC4AF2F49256AE58101FEE92B04", 16)
|
||||
p256t1.Gx, _ = new(big.Int).SetString("A3E8EB3CC1CFE7B7732213B23A656149AFA142C47AAFBC2B79A191562E1305F4", 16)
|
||||
p256t1.Gy, _ = new(big.Int).SetString("2D996C823439C56D7F7B22E14644417E69BCB6DE39D027001DABE8F35B25C9BE", 16)
|
||||
p256t1.BitSize = 256
|
||||
}
|
||||
|
||||
func initP256r1() {
|
||||
twisted := p256t1
|
||||
params := &elliptic.CurveParams{
|
||||
Name: "brainpoolP256r1",
|
||||
P: twisted.P,
|
||||
N: twisted.N,
|
||||
BitSize: twisted.BitSize,
|
||||
}
|
||||
params.Gx, _ = new(big.Int).SetString("8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262", 16)
|
||||
params.Gy, _ = new(big.Int).SetString("547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997", 16)
|
||||
z, _ := new(big.Int).SetString("3E2D4BD9597B58639AE7AA669CAB9837CF5CF20A2C852D10F655668DFC150EF0", 16)
|
||||
p256r1 = newrcurve(twisted, params, z)
|
||||
}
|
||||
|
||||
func initP384t1() {
|
||||
p384t1 = &elliptic.CurveParams{Name: "brainpoolP384t1"}
|
||||
p384t1.P, _ = new(big.Int).SetString("8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB71123ACD3A729901D1A71874700133107EC53", 16)
|
||||
p384t1.N, _ = new(big.Int).SetString("8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC3103B883202E9046565", 16)
|
||||
p384t1.B, _ = new(big.Int).SetString("7F519EADA7BDA81BD826DBA647910F8C4B9346ED8CCDC64E4B1ABD11756DCE1D2074AA263B88805CED70355A33B471EE", 16)
|
||||
p384t1.Gx, _ = new(big.Int).SetString("18DE98B02DB9A306F2AFCD7235F72A819B80AB12EBD653172476FECD462AABFFC4FF191B946A5F54D8D0AA2F418808CC", 16)
|
||||
p384t1.Gy, _ = new(big.Int).SetString("25AB056962D30651A114AFD2755AD336747F93475B7A1FCA3B88F2B6A208CCFE469408584DC2B2912675BF5B9E582928", 16)
|
||||
p384t1.BitSize = 384
|
||||
}
|
||||
|
||||
func initP384r1() {
|
||||
twisted := p384t1
|
||||
params := &elliptic.CurveParams{
|
||||
Name: "brainpoolP384r1",
|
||||
P: twisted.P,
|
||||
N: twisted.N,
|
||||
BitSize: twisted.BitSize,
|
||||
}
|
||||
params.Gx, _ = new(big.Int).SetString("1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10E8E826E03436D646AAEF87B2E247D4AF1E", 16)
|
||||
params.Gy, _ = new(big.Int).SetString("8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129280E4646217791811142820341263C5315", 16)
|
||||
z, _ := new(big.Int).SetString("41DFE8DD399331F7166A66076734A89CD0D2BCDB7D068E44E1F378F41ECBAE97D2D63DBC87BCCDDCCC5DA39E8589291C", 16)
|
||||
p384r1 = newrcurve(twisted, params, z)
|
||||
}
|
||||
|
||||
func initP512t1() {
|
||||
p512t1 = &elliptic.CurveParams{Name: "brainpoolP512t1"}
|
||||
p512t1.P, _ = new(big.Int).SetString("AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3", 16)
|
||||
p512t1.N, _ = new(big.Int).SetString("AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA70330870553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069", 16)
|
||||
p512t1.B, _ = new(big.Int).SetString("7CBBBCF9441CFAB76E1890E46884EAE321F70C0BCB4981527897504BEC3E36A62BCDFA2304976540F6450085F2DAE145C22553B465763689180EA2571867423E", 16)
|
||||
p512t1.Gx, _ = new(big.Int).SetString("640ECE5C12788717B9C1BA06CBC2A6FEBA85842458C56DDE9DB1758D39C0313D82BA51735CDB3EA499AA77A7D6943A64F7A3F25FE26F06B51BAA2696FA9035DA", 16)
|
||||
p512t1.Gy, _ = new(big.Int).SetString("5B534BD595F5AF0FA2C892376C84ACE1BB4E3019B71634C01131159CAE03CEE9D9932184BEEF216BD71DF2DADF86A627306ECFF96DBB8BACE198B61E00F8B332", 16)
|
||||
p512t1.BitSize = 512
|
||||
}
|
||||
|
||||
func initP512r1() {
|
||||
twisted := p512t1
|
||||
params := &elliptic.CurveParams{
|
||||
Name: "brainpoolP512r1",
|
||||
P: twisted.P,
|
||||
N: twisted.N,
|
||||
BitSize: twisted.BitSize,
|
||||
}
|
||||
params.Gx, _ = new(big.Int).SetString("81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D0098EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822", 16)
|
||||
params.Gy, _ = new(big.Int).SetString("7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F8111B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892", 16)
|
||||
z, _ := new(big.Int).SetString("12EE58E6764838B69782136F0F2D3BA06E27695716054092E60A80BEDB212B64E585D90BCE13761F85C3F1D2A64E3BE8FEA2220F01EBA5EEB0F35DBD29D922AB", 16)
|
||||
p512r1 = newrcurve(twisted, params, z)
|
||||
}
|
||||
|
||||
// P256t1 returns a Curve which implements Brainpool P256t1 (see RFC 5639, section 3.4)
|
||||
func P256t1() elliptic.Curve {
|
||||
once.Do(initAll)
|
||||
return p256t1
|
||||
}
|
||||
|
||||
// P256r1 returns a Curve which implements Brainpool P256r1 (see RFC 5639, section 3.4)
|
||||
func P256r1() elliptic.Curve {
|
||||
once.Do(initAll)
|
||||
return p256r1
|
||||
}
|
||||
|
||||
// P384t1 returns a Curve which implements Brainpool P384t1 (see RFC 5639, section 3.6)
|
||||
func P384t1() elliptic.Curve {
|
||||
once.Do(initAll)
|
||||
return p384t1
|
||||
}
|
||||
|
||||
// P384r1 returns a Curve which implements Brainpool P384r1 (see RFC 5639, section 3.6)
|
||||
func P384r1() elliptic.Curve {
|
||||
once.Do(initAll)
|
||||
return p384r1
|
||||
}
|
||||
|
||||
// P512t1 returns a Curve which implements Brainpool P512t1 (see RFC 5639, section 3.7)
|
||||
func P512t1() elliptic.Curve {
|
||||
once.Do(initAll)
|
||||
return p512t1
|
||||
}
|
||||
|
||||
// P512r1 returns a Curve which implements Brainpool P512r1 (see RFC 5639, section 3.7)
|
||||
func P512r1() elliptic.Curve {
|
||||
once.Do(initAll)
|
||||
return p512r1
|
||||
}
|
||||
|
|
@ -0,0 +1,83 @@
|
|||
package brainpool
|
||||
|
||||
import (
|
||||
"crypto/elliptic"
|
||||
"math/big"
|
||||
)
|
||||
|
||||
var _ elliptic.Curve = (*rcurve)(nil)
|
||||
|
||||
type rcurve struct {
|
||||
twisted elliptic.Curve
|
||||
params *elliptic.CurveParams
|
||||
z *big.Int
|
||||
zinv *big.Int
|
||||
z2 *big.Int
|
||||
z3 *big.Int
|
||||
zinv2 *big.Int
|
||||
zinv3 *big.Int
|
||||
}
|
||||
|
||||
var (
|
||||
two = big.NewInt(2)
|
||||
three = big.NewInt(3)
|
||||
)
|
||||
|
||||
func newrcurve(twisted elliptic.Curve, params *elliptic.CurveParams, z *big.Int) *rcurve {
|
||||
zinv := new(big.Int).ModInverse(z, params.P)
|
||||
return &rcurve{
|
||||
twisted: twisted,
|
||||
params: params,
|
||||
z: z,
|
||||
zinv: zinv,
|
||||
z2: new(big.Int).Exp(z, two, params.P),
|
||||
z3: new(big.Int).Exp(z, three, params.P),
|
||||
zinv2: new(big.Int).Exp(zinv, two, params.P),
|
||||
zinv3: new(big.Int).Exp(zinv, three, params.P),
|
||||
}
|
||||
}
|
||||
|
||||
func (curve *rcurve) toTwisted(x, y *big.Int) (*big.Int, *big.Int) {
|
||||
var tx, ty big.Int
|
||||
tx.Mul(x, curve.z2)
|
||||
tx.Mod(&tx, curve.params.P)
|
||||
ty.Mul(y, curve.z3)
|
||||
ty.Mod(&ty, curve.params.P)
|
||||
return &tx, &ty
|
||||
}
|
||||
|
||||
func (curve *rcurve) fromTwisted(tx, ty *big.Int) (*big.Int, *big.Int) {
|
||||
var x, y big.Int
|
||||
x.Mul(tx, curve.zinv2)
|
||||
x.Mod(&x, curve.params.P)
|
||||
y.Mul(ty, curve.zinv3)
|
||||
y.Mod(&y, curve.params.P)
|
||||
return &x, &y
|
||||
}
|
||||
|
||||
func (curve *rcurve) Params() *elliptic.CurveParams {
|
||||
return curve.params
|
||||
}
|
||||
|
||||
func (curve *rcurve) IsOnCurve(x, y *big.Int) bool {
|
||||
return curve.twisted.IsOnCurve(curve.toTwisted(x, y))
|
||||
}
|
||||
|
||||
func (curve *rcurve) Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int) {
|
||||
tx1, ty1 := curve.toTwisted(x1, y1)
|
||||
tx2, ty2 := curve.toTwisted(x2, y2)
|
||||
return curve.fromTwisted(curve.twisted.Add(tx1, ty1, tx2, ty2))
|
||||
}
|
||||
|
||||
func (curve *rcurve) Double(x1, y1 *big.Int) (x, y *big.Int) {
|
||||
return curve.fromTwisted(curve.twisted.Double(curve.toTwisted(x1, y1)))
|
||||
}
|
||||
|
||||
func (curve *rcurve) ScalarMult(x1, y1 *big.Int, scalar []byte) (x, y *big.Int) {
|
||||
tx1, ty1 := curve.toTwisted(x1, y1)
|
||||
return curve.fromTwisted(curve.twisted.ScalarMult(tx1, ty1, scalar))
|
||||
}
|
||||
|
||||
func (curve *rcurve) ScalarBaseMult(scalar []byte) (x, y *big.Int) {
|
||||
return curve.fromTwisted(curve.twisted.ScalarBaseMult(scalar))
|
||||
}
|
||||
|
|
@ -0,0 +1,162 @@
|
|||
// Copyright (C) 2019 ProtonTech AG
|
||||
|
||||
// Package eax provides an implementation of the EAX
|
||||
// (encrypt-authenticate-translate) mode of operation, as described in
|
||||
// Bellare, Rogaway, and Wagner "THE EAX MODE OF OPERATION: A TWO-PASS
|
||||
// AUTHENTICATED-ENCRYPTION SCHEME OPTIMIZED FOR SIMPLICITY AND EFFICIENCY."
|
||||
// In FSE'04, volume 3017 of LNCS, 2004
|
||||
package eax
|
||||
|
||||
import (
|
||||
"crypto/cipher"
|
||||
"crypto/subtle"
|
||||
"errors"
|
||||
"github.com/ProtonMail/go-crypto/internal/byteutil"
|
||||
)
|
||||
|
||||
const (
|
||||
defaultTagSize = 16
|
||||
defaultNonceSize = 16
|
||||
)
|
||||
|
||||
type eax struct {
|
||||
block cipher.Block // Only AES-{128, 192, 256} supported
|
||||
tagSize int // At least 12 bytes recommended
|
||||
nonceSize int
|
||||
}
|
||||
|
||||
func (e *eax) NonceSize() int {
|
||||
return e.nonceSize
|
||||
}
|
||||
|
||||
func (e *eax) Overhead() int {
|
||||
return e.tagSize
|
||||
}
|
||||
|
||||
// NewEAX returns an EAX instance with AES-{KEYLENGTH} and default nonce and
|
||||
// tag lengths. Supports {128, 192, 256}- bit key length.
|
||||
func NewEAX(block cipher.Block) (cipher.AEAD, error) {
|
||||
return NewEAXWithNonceAndTagSize(block, defaultNonceSize, defaultTagSize)
|
||||
}
|
||||
|
||||
// NewEAXWithNonceAndTagSize returns an EAX instance with AES-{keyLength} and
|
||||
// given nonce and tag lengths in bytes. Panics on zero nonceSize and
|
||||
// exceedingly long tags.
|
||||
//
|
||||
// It is recommended to use at least 12 bytes as tag length (see, for instance,
|
||||
// NIST SP 800-38D).
|
||||
//
|
||||
// Only to be used for compatibility with existing cryptosystems with
|
||||
// non-standard parameters. For all other cases, prefer NewEAX.
|
||||
func NewEAXWithNonceAndTagSize(
|
||||
block cipher.Block, nonceSize, tagSize int) (cipher.AEAD, error) {
|
||||
if nonceSize < 1 {
|
||||
return nil, eaxError("Cannot initialize EAX with nonceSize = 0")
|
||||
}
|
||||
if tagSize > block.BlockSize() {
|
||||
return nil, eaxError("Custom tag length exceeds blocksize")
|
||||
}
|
||||
return &eax{
|
||||
block: block,
|
||||
tagSize: tagSize,
|
||||
nonceSize: nonceSize,
|
||||
}, nil
|
||||
}
|
||||
|
||||
func (e *eax) Seal(dst, nonce, plaintext, adata []byte) []byte {
|
||||
if len(nonce) > e.nonceSize {
|
||||
panic("crypto/eax: Nonce too long for this instance")
|
||||
}
|
||||
ret, out := byteutil.SliceForAppend(dst, len(plaintext) + e.tagSize)
|
||||
omacNonce := e.omacT(0, nonce)
|
||||
omacAdata := e.omacT(1, adata)
|
||||
|
||||
// Encrypt message using CTR mode and omacNonce as IV
|
||||
ctr := cipher.NewCTR(e.block, omacNonce)
|
||||
ciphertextData := out[:len(plaintext)]
|
||||
ctr.XORKeyStream(ciphertextData, plaintext)
|
||||
|
||||
omacCiphertext := e.omacT(2, ciphertextData)
|
||||
|
||||
tag := out[len(plaintext):]
|
||||
for i := 0; i < e.tagSize; i++ {
|
||||
tag[i] = omacCiphertext[i] ^ omacNonce[i] ^ omacAdata[i]
|
||||
}
|
||||
return ret
|
||||
}
|
||||
|
||||
func (e* eax) Open(dst, nonce, ciphertext, adata []byte) ([]byte, error) {
|
||||
if len(nonce) > e.nonceSize {
|
||||
panic("crypto/eax: Nonce too long for this instance")
|
||||
}
|
||||
if len(ciphertext) < e.tagSize {
|
||||
return nil, eaxError("Ciphertext shorter than tag length")
|
||||
}
|
||||
sep := len(ciphertext) - e.tagSize
|
||||
|
||||
// Compute tag
|
||||
omacNonce := e.omacT(0, nonce)
|
||||
omacAdata := e.omacT(1, adata)
|
||||
omacCiphertext := e.omacT(2, ciphertext[:sep])
|
||||
|
||||
tag := make([]byte, e.tagSize)
|
||||
for i := 0; i < e.tagSize; i++ {
|
||||
tag[i] = omacCiphertext[i] ^ omacNonce[i] ^ omacAdata[i]
|
||||
}
|
||||
|
||||
// Compare tags
|
||||
if subtle.ConstantTimeCompare(ciphertext[sep:], tag) != 1 {
|
||||
return nil, eaxError("Tag authentication failed")
|
||||
}
|
||||
|
||||
// Decrypt ciphertext
|
||||
ret, out := byteutil.SliceForAppend(dst, len(ciphertext))
|
||||
ctr := cipher.NewCTR(e.block, omacNonce)
|
||||
ctr.XORKeyStream(out, ciphertext[:sep])
|
||||
|
||||
return ret[:sep], nil
|
||||
}
|
||||
|
||||
// Tweakable OMAC - Calls OMAC_K([t]_n || plaintext)
|
||||
func (e *eax) omacT(t byte, plaintext []byte) []byte {
|
||||
blockSize := e.block.BlockSize()
|
||||
byteT := make([]byte, blockSize)
|
||||
byteT[blockSize-1] = t
|
||||
concat := append(byteT, plaintext...)
|
||||
return e.omac(concat)
|
||||
}
|
||||
|
||||
func (e *eax) omac(plaintext []byte) []byte {
|
||||
blockSize := e.block.BlockSize()
|
||||
// L ← E_K(0^n); B ← 2L; P ← 4L
|
||||
L := make([]byte, blockSize)
|
||||
e.block.Encrypt(L, L)
|
||||
B := byteutil.GfnDouble(L)
|
||||
P := byteutil.GfnDouble(B)
|
||||
|
||||
// CBC with IV = 0
|
||||
cbc := cipher.NewCBCEncrypter(e.block, make([]byte, blockSize))
|
||||
padded := e.pad(plaintext, B, P)
|
||||
cbcCiphertext := make([]byte, len(padded))
|
||||
cbc.CryptBlocks(cbcCiphertext, padded)
|
||||
|
||||
return cbcCiphertext[len(cbcCiphertext)-blockSize:]
|
||||
}
|
||||
|
||||
func (e *eax) pad(plaintext, B, P []byte) []byte {
|
||||
// if |M| in {n, 2n, 3n, ...}
|
||||
blockSize := e.block.BlockSize()
|
||||
if len(plaintext) != 0 && len(plaintext)%blockSize == 0 {
|
||||
return byteutil.RightXor(plaintext, B)
|
||||
}
|
||||
|
||||
// else return (M || 1 || 0^(n−1−(|M| % n))) xor→ P
|
||||
ending := make([]byte, blockSize-len(plaintext)%blockSize)
|
||||
ending[0] = 0x80
|
||||
padded := append(plaintext, ending...)
|
||||
return byteutil.RightXor(padded, P)
|
||||
}
|
||||
|
||||
func eaxError(err string) error {
|
||||
return errors.New("crypto/eax: " + err)
|
||||
}
|
||||
|
|
@ -0,0 +1,58 @@
|
|||
package eax
|
||||
|
||||
// Test vectors from
|
||||
// https://web.cs.ucdavis.edu/~rogaway/papers/eax.pdf
|
||||
var testVectors = []struct {
|
||||
msg, key, nonce, header, ciphertext string
|
||||
}{
|
||||
{"",
|
||||
"233952DEE4D5ED5F9B9C6D6FF80FF478",
|
||||
"62EC67F9C3A4A407FCB2A8C49031A8B3",
|
||||
"6BFB914FD07EAE6B",
|
||||
"E037830E8389F27B025A2D6527E79D01"},
|
||||
{"F7FB",
|
||||
"91945D3F4DCBEE0BF45EF52255F095A4",
|
||||
"BECAF043B0A23D843194BA972C66DEBD",
|
||||
"FA3BFD4806EB53FA",
|
||||
"19DD5C4C9331049D0BDAB0277408F67967E5"},
|
||||
{"1A47CB4933",
|
||||
"01F74AD64077F2E704C0F60ADA3DD523",
|
||||
"70C3DB4F0D26368400A10ED05D2BFF5E",
|
||||
"234A3463C1264AC6",
|
||||
"D851D5BAE03A59F238A23E39199DC9266626C40F80"},
|
||||
{"481C9E39B1",
|
||||
"D07CF6CBB7F313BDDE66B727AFD3C5E8",
|
||||
"8408DFFF3C1A2B1292DC199E46B7D617",
|
||||
"33CCE2EABFF5A79D",
|
||||
"632A9D131AD4C168A4225D8E1FF755939974A7BEDE"},
|
||||
{"40D0C07DA5E4",
|
||||
"35B6D0580005BBC12B0587124557D2C2",
|
||||
"FDB6B06676EEDC5C61D74276E1F8E816",
|
||||
"AEB96EAEBE2970E9",
|
||||
"071DFE16C675CB0677E536F73AFE6A14B74EE49844DD"},
|
||||
{"4DE3B35C3FC039245BD1FB7D",
|
||||
"BD8E6E11475E60B268784C38C62FEB22",
|
||||
"6EAC5C93072D8E8513F750935E46DA1B",
|
||||
"D4482D1CA78DCE0F",
|
||||
"835BB4F15D743E350E728414ABB8644FD6CCB86947C5E10590210A4F"},
|
||||
{"8B0A79306C9CE7ED99DAE4F87F8DD61636",
|
||||
"7C77D6E813BED5AC98BAA417477A2E7D",
|
||||
"1A8C98DCD73D38393B2BF1569DEEFC19",
|
||||
"65D2017990D62528",
|
||||
"02083E3979DA014812F59F11D52630DA30137327D10649B0AA6E1C181DB617D7F2"},
|
||||
{"1BDA122BCE8A8DBAF1877D962B8592DD2D56",
|
||||
"5FFF20CAFAB119CA2FC73549E20F5B0D",
|
||||
"DDE59B97D722156D4D9AFF2BC7559826",
|
||||
"54B9F04E6A09189A",
|
||||
"2EC47B2C4954A489AFC7BA4897EDCDAE8CC33B60450599BD02C96382902AEF7F832A"},
|
||||
{"6CF36720872B8513F6EAB1A8A44438D5EF11",
|
||||
"A4A4782BCFFD3EC5E7EF6D8C34A56123",
|
||||
"B781FCF2F75FA5A8DE97A9CA48E522EC",
|
||||
"899A175897561D7E",
|
||||
"0DE18FD0FDD91E7AF19F1D8EE8733938B1E8E7F6D2231618102FDB7FE55FF1991700"},
|
||||
{"CA40D7446E545FFAED3BD12A740A659FFBBB3CEAB7",
|
||||
"8395FCF1E95BEBD697BD010BC766AAC3",
|
||||
"22E7ADD93CFC6393C57EC0B3C17D6B44",
|
||||
"126735FCC320D25A",
|
||||
"CB8920F87A6C75CFF39627B56E3ED197C552D295A7CFC46AFC253B4652B1AF3795B124AB6E"},
|
||||
}
|
||||
|
|
@ -0,0 +1,131 @@
|
|||
// These vectors include key length in {128, 192, 256}, tag size 128, and
|
||||
// random nonce, header, and plaintext lengths.
|
||||
|
||||
// This file was automatically generated.
|
||||
|
||||
package eax
|
||||
|
||||
var randomVectors = []struct {
|
||||
key, nonce, header, plaintext, ciphertext string
|
||||
}{
|
||||
{"DFDE093F36B0356E5A81F609786982E3",
|
||||
"1D8AC604419001816905BA72B14CED7E",
|
||||
"152A1517A998D7A24163FCDD146DE81AC347C8B97088F502093C1ABB8F6E33D9A219C34D7603A18B1F5ABE02E56661B7D7F67E81EC08C1302EF38D80A859486D450E94A4F26AD9E68EEBBC0C857A0FC5CF9E641D63D565A7E361BC8908F5A8DC8FD6",
|
||||
"1C8EAAB71077FE18B39730A3156ADE29C5EE824C7EE86ED2A253B775603FB237116E654F6FEC588DD27F523A0E01246FE73FE348491F2A8E9ABC6CA58D663F71CDBCF4AD798BE46C42AE6EE8B599DB44A1A48D7BBBBA0F7D2750181E1C5E66967F7D57CBD30AFBDA5727",
|
||||
"79E7E150934BBEBF7013F61C60462A14D8B15AF7A248AFB8A344EF021C1500E16666891D6E973D8BB56B71A371F12CA34660C4410C016982B20F547E3762A58B7BF4F20236CADCF559E2BE7D783B13723B2741FC7CDC8997D839E39A3DDD2BADB96743DD7049F1BDB0516A262869915B3F70498AFB7B191BF960"},
|
||||
{"F10619EF02E5D94D7550EB84ED364A21",
|
||||
"8DC0D4F2F745BBAE835CC5574B942D20",
|
||||
"FE561358F2E8DF7E1024FF1AE9A8D36EBD01352214505CB99D644777A8A1F6027FA2BDBFC529A9B91136D5F2416CFC5F0F4EC3A1AFD32BDDA23CA504C5A5CB451785FABF4DFE4CD50D817491991A60615B30286361C100A95D1712F2A45F8E374461F4CA2B",
|
||||
"D7B5A971FC219631D30EFC3664AE3127D9CF3097DAD9C24AC7905D15E8D9B25B026B31D68CAE00975CDB81EB1FD96FD5E1A12E2BB83FA25F1B1D91363457657FC03875C27F2946C5",
|
||||
"2F336ED42D3CC38FC61660C4CD60BA4BD438B05F5965D8B7B399D2E7167F5D34F792D318F94DB15D67463AC449E13D568CC09BFCE32A35EE3EE96A041927680AE329811811E27F2D1E8E657707AF99BA96D13A478D695D59"},
|
||||
{"429F514EFC64D98A698A9247274CFF45",
|
||||
"976AA5EB072F912D126ACEBC954FEC38",
|
||||
"A71D89DC5B6CEDBB7451A27C3C2CAE09126DB4C421",
|
||||
"5632FE62AB1DC549D54D3BC3FC868ACCEDEFD9ECF5E9F8",
|
||||
"848AE4306CA8C7F416F8707625B7F55881C0AB430353A5C967CDA2DA787F581A70E34DBEBB2385"},
|
||||
{"398138F309085F47F8457CDF53895A63",
|
||||
"F8A8A7F2D28E5FFF7BBC2F24353F7A36",
|
||||
"5D633C21BA7764B8855CAB586F3746E236AD486039C83C6B56EFA9C651D38A41D6B20DAEE3418BFEA44B8BD6",
|
||||
"A3BBAA91920AF5E10659818B1B3B300AC79BFC129C8329E75251F73A66D3AE0128EB91D5031E0A65C329DB7D1E9C0493E268",
|
||||
"D078097267606E5FB07CFB7E2B4B718172A82C6A4CEE65D549A4DFB9838003BD2FBF64A7A66988AC1A632FD88F9E9FBB57C5A78AD2E086EACBA3DB68511D81C2970A"},
|
||||
{"7A4151EBD3901B42CBA45DAFB2E931BA",
|
||||
"0FC88ACEE74DD538040321C330974EB8",
|
||||
"250464FB04733BAB934C59E6AD2D6AE8D662CBCFEFBE61E5A308D4211E58C4C25935B72C69107722E946BFCBF416796600542D76AEB73F2B25BF53BAF97BDEB36ED3A7A51C31E7F170EB897457E7C17571D1BA0A908954E9",
|
||||
"88C41F3EBEC23FAB8A362D969CAC810FAD4F7CA6A7F7D0D44F060F92E37E1183768DD4A8C733F71C96058D362A39876D183B86C103DE",
|
||||
"74A25B2182C51096D48A870D80F18E1CE15867778E34FCBA6BD7BFB3739FDCD42AD0F2D9F4EBA29085285C6048C15BCE5E5166F1F962D3337AA88E6062F05523029D0A7F0BF9"},
|
||||
{"BFB147E1CD5459424F8C0271FC0E0DC5",
|
||||
"EABCC126442BF373969EA3015988CC45",
|
||||
"4C0880E1D71AA2C7",
|
||||
"BE1B5EC78FBF73E7A6682B21BA7E0E5D2D1C7ABE",
|
||||
"5660D7C1380E2F306895B1402CB2D6C37876504276B414D120F4CF92FDDDBB293A238EA0"},
|
||||
{"595DD6F52D18BC2CA8EB4EDAA18D9FA3",
|
||||
"0F84B5D36CF4BC3B863313AF3B4D2E97",
|
||||
"30AE6CC5F99580F12A779D98BD379A60948020C0B6FBD5746B30BA3A15C6CD33DAF376C70A9F15B6C0EB410A93161F7958AE23",
|
||||
"8EF3687A1642B070970B0B91462229D1D76ABC154D18211F7152AA9FF368",
|
||||
"317C1DDB11417E5A9CC4DDE7FDFF6659A5AC4B31DE025212580A05CDAC6024D3E4AE7C2966E52B9129E9ECDBED86"},
|
||||
{"44E6F2DC8FDC778AD007137D11410F50",
|
||||
"270A237AD977F7187AA6C158A0BAB24F",
|
||||
"509B0F0EB12E2AA5C5BA2DE553C07FAF4CE0C9E926531AA709A3D6224FCB783ACCF1559E10B1123EBB7D52E8AB54E6B5352A9ED0D04124BF0E9D9BACFD7E32B817B2E625F5EE94A64EDE9E470DE7FE6886C19B294F9F828209FE257A78",
|
||||
"8B3D7815DF25618A5D0C55A601711881483878F113A12EC36CF64900549A3199555528559DC118F789788A55FAFD944E6E99A9CA3F72F238CD3F4D88223F7A745992B3FAED1848",
|
||||
"1CC00D79F7AD82FDA71B58D286E5F34D0CC4CEF30704E771CC1E50746BDF83E182B078DB27149A42BAE619DF0F85B0B1090AD55D3B4471B0D6F6ECCD09C8F876B30081F0E7537A9624F8AAF29DA85E324122EFB4D68A56"},
|
||||
{"BB7BC352A03044B4428D8DBB4B0701FDEC4649FD17B81452",
|
||||
"8B4BBE26CCD9859DCD84884159D6B0A4",
|
||||
"2212BEB0E78E0F044A86944CF33C8D5C80D9DBE1034BF3BCF73611835C7D3A52F5BD2D81B68FD681B68540A496EE5DA16FD8AC8824E60E1EC2042BE28FB0BFAD4E4B03596446BDD8C37D936D9B3D5295BE19F19CF5ACE1D33A46C952CE4DE5C12F92C1DD051E04AEED",
|
||||
"9037234CC44FFF828FABED3A7084AF40FA7ABFF8E0C0EFB57A1CC361E18FC4FAC1AB54F3ABFE9FF77263ACE16C3A",
|
||||
"A9391B805CCD956081E0B63D282BEA46E7025126F1C1631239C33E92AA6F92CD56E5A4C56F00FF9658E93D48AF4EF0EF81628E34AD4DB0CDAEDCD2A17EE7"},
|
||||
{"99C0AD703196D2F60A74E6B378B838B31F82EA861F06FC4E",
|
||||
"92745C018AA708ECFEB1667E9F3F1B01",
|
||||
"828C69F376C0C0EC651C67749C69577D589EE39E51404D80EBF70C8660A8F5FD375473F4A7C611D59CB546A605D67446CE2AA844135FCD78BB5FBC90222A00D42920BB1D7EEDFB0C4672554F583EF23184F89063CDECBE482367B5F9AF3ACBC3AF61392BD94CBCD9B64677",
|
||||
"A879214658FD0A5B0E09836639BF82E05EC7A5EF71D4701934BDA228435C68AC3D5CEB54997878B06A655EEACEFB1345C15867E7FE6C6423660C8B88DF128EBD6BCD85118DBAE16E9252FFB204324E5C8F38CA97759BDBF3CB0083",
|
||||
"51FE87996F194A2585E438B023B345439EA60D1AEBED4650CDAF48A4D4EEC4FC77DC71CC4B09D3BEEF8B7B7AF716CE2B4EFFB3AC9E6323C18AC35E0AA6E2BBBC8889490EB6226C896B0D105EAB42BFE7053CCF00ED66BA94C1BA09A792AA873F0C3B26C5C5F9A936E57B25"},
|
||||
{"7086816D00D648FB8304AA8C9E552E1B69A9955FB59B25D1",
|
||||
"0F45CF7F0BF31CCEB85D9DA10F4D749F",
|
||||
"93F27C60A417D9F0669E86ACC784FC8917B502DAF30A6338F11B30B94D74FEFE2F8BE1BBE2EAD10FAB7EED3C6F72B7C3ECEE1937C32ED4970A6404E139209C05",
|
||||
"877F046601F3CBE4FB1491943FA29487E738F94B99AF206262A1D6FF856C9AA0B8D4D08A54370C98F8E88FA3DCC2B14C1F76D71B2A4C7963AEE8AF960464C5BEC8357AD00DC8",
|
||||
"FE96906B895CE6A8E72BC72344E2C8BB3C63113D70EAFA26C299BAFE77A8A6568172EB447FB3E86648A0AF3512DEB1AAC0819F3EC553903BF28A9FB0F43411237A774BF9EE03E445D280FBB9CD12B9BAAB6EF5E52691"},
|
||||
{"062F65A896D5BF1401BADFF70E91B458E1F9BD4888CB2E4D",
|
||||
"5B11EA1D6008EBB41CF892FCA5B943D1",
|
||||
"BAF4FF5C8242",
|
||||
"A8870E091238355984EB2F7D61A865B9170F440BFF999A5993DD41A10F4440D21FF948DDA2BF663B2E03AC3324492DC5E40262ECC6A65C07672353BE23E7FB3A9D79FF6AA38D97960905A38DECC312CB6A59E5467ECF06C311CD43ADC0B543EDF34FE8BE611F176460D5627CA51F8F8D9FED71F55C",
|
||||
"B10E127A632172CF8AA7539B140D2C9C2590E6F28C3CB892FC498FCE56A34F732FBFF32E79C7B9747D9094E8635A0C084D6F0247F9768FB5FF83493799A9BEC6C39572120C40E9292C8C947AE8573462A9108C36D9D7112E6995AE5867E6C8BB387D1C5D4BEF524F391B9FD9F0A3B4BFA079E915BCD920185CFD38D114C558928BD7D47877"},
|
||||
{"38A8E45D6D705A11AF58AED5A1344896998EACF359F2E26A",
|
||||
"FD82B5B31804FF47D44199B533D0CF84",
|
||||
"DE454D4E62FE879F2050EE3E25853623D3E9AC52EEC1A1779A48CFAF5ECA0BFDE44749391866D1",
|
||||
"B804",
|
||||
"164BB965C05EBE0931A1A63293EDF9C38C27"},
|
||||
{"34C33C97C6D7A0850DA94D78A58DC61EC717CD7574833068",
|
||||
"343BE00DA9483F05C14F2E9EB8EA6AE8",
|
||||
"78312A43EFDE3CAE34A65796FF059A3FE15304EEA5CF1D9306949FE5BF3349D4977D4EBE76C040FE894C5949E4E4D6681153DA87FB9AC5062063CA2EA183566343362370944CE0362D25FC195E124FD60E8682E665D13F2229DDA3E4B2CB1DCA",
|
||||
"CC11BB284B1153578E4A5ED9D937B869DAF00F5B1960C23455CA9CC43F486A3BE0B66254F1041F04FDF459C8640465B6E1D2CF899A381451E8E7FCB50CF87823BE77E24B132BBEEDC72E53369B275E1D8F49ECE59F4F215230AC4FE133FC80E4F634EE80BA4682B62C86",
|
||||
"E7F703DC31A95E3A4919FF957836CB76C063D81702AEA4703E1C2BF30831E58C4609D626EC6810E12EAA5B930F049FF9EFC22C3E3F1EBD4A1FB285CB02A1AC5AD46B425199FC0A85670A5C4E3DAA9636C8F64C199F42F18AAC8EA7457FD377F322DD7752D7D01B946C8F0A97E6113F0D50106F319AFD291AAACE"},
|
||||
{"C6ECF7F053573E403E61B83052A343D93CBCC179D1E835BE",
|
||||
"E280E13D7367042E3AA09A80111B6184",
|
||||
"21486C9D7A9647",
|
||||
"5F2639AFA6F17931853791CD8C92382BBB677FD72D0AB1A080D0E49BFAA21810E963E4FACD422E92F65CBFAD5884A60CD94740DF31AF02F95AA57DA0C4401B0ED906",
|
||||
"5C51DB20755302070C45F52E50128A67C8B2E4ED0EACB7E29998CCE2E8C289DD5655913EC1A51CC3AABE5CDC2402B2BE7D6D4BF6945F266FBD70BA9F37109067157AE7530678B45F64475D4EBFCB5FFF46A5"},
|
||||
{"5EC6CF7401BC57B18EF154E8C38ACCA8959E57D2F3975FF5",
|
||||
"656B41CB3F9CF8C08BAD7EBFC80BD225",
|
||||
"6B817C2906E2AF425861A7EF59BA5801F143EE2A139EE72697CDE168B4",
|
||||
"2C0E1DDC9B1E5389BA63845B18B1F8A1DB062037151BCC56EF7C21C0BB4DAE366636BBA975685D7CC5A94AFBE89C769016388C56FB7B57CE750A12B718A8BDCF70E80E8659A8330EFC8F86640F21735E8C80E23FE43ABF23507CE3F964AE4EC99D",
|
||||
"ED780CF911E6D1AA8C979B889B0B9DC1ABE261832980BDBFB576901D9EF5AB8048998E31A15BE54B3E5845A4D136AD24D0BDA1C3006168DF2F8AC06729CB0818867398150020131D8F04EDF1923758C9EABB5F735DE5EA1758D4BC0ACFCA98AFD202E9839B8720253693B874C65586C6F0"},
|
||||
{"C92F678EB2208662F5BCF3403EC05F5961E957908A3E79421E1D25FC19054153",
|
||||
"DA0F3A40983D92F2D4C01FED33C7A192",
|
||||
"2B6E9D26DB406A0FAB47608657AA10EFC2B4AA5F459B29FF85AC9A40BFFE7AEB04F77E9A11FAAA116D7F6D4DA417671A9AB02C588E0EF59CB1BFB4B1CC931B63A3B3A159FCEC97A04D1E6F0C7E6A9CEF6B0ABB04758A69F1FE754DF4C2610E8C46B6CF413BDB31351D55BEDCB7B4A13A1C98E10984475E0F2F957853",
|
||||
"F37326A80E08",
|
||||
"83519E53E321D334F7C10B568183775C0E9AAE55F806"},
|
||||
{"6847E0491BE57E72995D186D50094B0B3593957A5146798FCE68B287B2FB37B5",
|
||||
"3EE1182AEBB19A02B128F28E1D5F7F99",
|
||||
"D9F35ABB16D776CE",
|
||||
"DB7566ED8EA95BDF837F23DB277BAFBC5E70D1105ADFD0D9EF15475051B1EF94709C67DCA9F8D5",
|
||||
"2CDCED0C9EBD6E2A508822A685F7DCD1CDD99E7A5FCA786C234E7F7F1D27EC49751AD5DCFA30C5EDA87C43CAE3B919B6BBCFE34C8EDA59"},
|
||||
{"82B019673642C08388D3E42075A4D5D587558C229E4AB8F660E37650C4C41A0A",
|
||||
"336F5D681E0410FAE7B607246092C6DC",
|
||||
"D430CBD8FE435B64214E9E9CDC5DE99D31CFCFB8C10AA0587A49DF276611",
|
||||
"998404153AD77003E1737EDE93ED79859EE6DCCA93CB40C4363AA817ABF2DBBD46E42A14A7183B6CC01E12A577888141363D0AE011EB6E8D28C0B235",
|
||||
"9BEF69EEB60BD3D6065707B7557F25292A8872857CFBD24F2F3C088E4450995333088DA50FD9121221C504DF1D0CD5EFE6A12666C5D5BB12282CF4C19906E9CFAB97E9BDF7F49DC17CFC384B"},
|
||||
{"747B2E269B1859F0622C15C8BAD6A725028B1F94B8DB7326948D1E6ED663A8BC",
|
||||
"AB91F7245DDCE3F1C747872D47BE0A8A",
|
||||
"3B03F786EF1DDD76E1D42646DA4CD2A5165DC5383CE86D1A0B5F13F910DC278A4E451EE0192CBA178E13B3BA27FDC7840DF73D2E104B",
|
||||
"6B803F4701114F3E5FE21718845F8416F70F626303F545BE197189E0A2BA396F37CE06D389EB2658BC7D56D67868708F6D0D32",
|
||||
"1570DDB0BCE75AA25D1957A287A2C36B1A5F2270186DA81BA6112B7F43B0F3D1D0ED072591DCF1F1C99BBB25621FC39B896FF9BD9413A2845363A9DCD310C32CF98E57"},
|
||||
{"02E59853FB29AEDA0FE1C5F19180AD99A12FF2F144670BB2B8BADF09AD812E0A",
|
||||
"C691294EF67CD04D1B9242AF83DD1421",
|
||||
"879334DAE3",
|
||||
"1E17F46A98FEF5CBB40759D95354",
|
||||
"FED8C3FF27DDF6313AED444A2985B36CBA268AAD6AAC563C0BA28F6DB5DB"},
|
||||
{"F6C1FB9B4188F2288FF03BD716023198C3582CF2A037FC2F29760916C2B7FCDB",
|
||||
"4228DA0678CA3534588859E77DFF014C",
|
||||
"D8153CAF35539A61DD8D05B3C9B44F01E564FB9348BCD09A1C23B84195171308861058F0A3CD2A55B912A3AAEE06FF4D356C77275828F2157C2FC7C115DA39E443210CCC56BEDB0CC99BBFB227ABD5CC454F4E7F547C7378A659EEB6A7E809101A84F866503CB18D4484E1FA09B3EC7FC75EB2E35270800AA7",
|
||||
"23B660A779AD285704B12EC1C580387A47BEC7B00D452C6570",
|
||||
"5AA642BBABA8E49849002A2FAF31DB8FC7773EFDD656E469CEC19B3206D4174C9A263D0A05484261F6"},
|
||||
{"8FF6086F1FADB9A3FBE245EAC52640C43B39D43F89526BB5A6EBA47710931446",
|
||||
"943188480C99437495958B0AE4831AA9",
|
||||
"AD5CD0BDA426F6EBA23C8EB23DC73FF9FEC173355EDBD6C9344C4C4383F211888F7CE6B29899A6801DF6B38651A7C77150941A",
|
||||
"80CD5EA8D7F81DDF5070B934937912E8F541A5301877528EB41AB60C020968D459960ED8FB73083329841A",
|
||||
"ABAE8EB7F36FCA2362551E72DAC890BA1BB6794797E0FC3B67426EC9372726ED4725D379EA0AC9147E48DCD0005C502863C2C5358A38817C8264B5"},
|
||||
{"A083B54E6B1FE01B65D42FCD248F97BB477A41462BBFE6FD591006C022C8FD84",
|
||||
"B0490F5BD68A52459556B3749ACDF40E",
|
||||
"8892E047DA5CFBBDF7F3CFCBD1BD21C6D4C80774B1826999234394BD3E513CC7C222BB40E1E3140A152F19B3802F0D036C24A590512AD0E8",
|
||||
"D7B15752789DC94ED0F36778A5C7BBB207BEC32BAC66E702B39966F06E381E090C6757653C3D26A81EC6AD6C364D66867A334C91BB0B8A8A4B6EACDF0783D09010AEBA2DD2062308FE99CC1F",
|
||||
"C071280A732ADC93DF272BF1E613B2BB7D46FC6665EF2DC1671F3E211D6BDE1D6ADDD28DF3AA2E47053FC8BB8AE9271EC8BC8B2CFFA320D225B451685B6D23ACEFDD241FE284F8ADC8DB07F456985B14330BBB66E0FB212213E05B3E"},
|
||||
}
|
||||
92
vendor/github.com/ProtonMail/go-crypto/internal/byteutil/byteutil.go
generated
vendored
Normal file
92
vendor/github.com/ProtonMail/go-crypto/internal/byteutil/byteutil.go
generated
vendored
Normal file
|
|
@ -0,0 +1,92 @@
|
|||
// Copyright (C) 2019 ProtonTech AG
|
||||
// This file contains necessary tools for the aex and ocb packages.
|
||||
//
|
||||
// These functions SHOULD NOT be used elsewhere, since they are optimized for
|
||||
// specific input nature in the EAX and OCB modes of operation.
|
||||
|
||||
package byteutil
|
||||
|
||||
// GfnDouble computes 2 * input in the field of 2^n elements.
|
||||
// The irreducible polynomial in the finite field for n=128 is
|
||||
// x^128 + x^7 + x^2 + x + 1 (equals 0x87)
|
||||
// Constant-time execution in order to avoid side-channel attacks
|
||||
func GfnDouble(input []byte) []byte {
|
||||
if len(input) != 16 {
|
||||
panic("Doubling in GFn only implemented for n = 128")
|
||||
}
|
||||
// If the first bit is zero, return 2L = L << 1
|
||||
// Else return (L << 1) xor 0^120 10000111
|
||||
shifted := ShiftBytesLeft(input)
|
||||
shifted[15] ^= ((input[0] >> 7) * 0x87)
|
||||
return shifted
|
||||
}
|
||||
|
||||
// ShiftBytesLeft outputs the byte array corresponding to x << 1 in binary.
|
||||
func ShiftBytesLeft(x []byte) []byte {
|
||||
l := len(x)
|
||||
dst := make([]byte, l)
|
||||
for i := 0; i < l-1; i++ {
|
||||
dst[i] = (x[i] << 1) | (x[i+1] >> 7)
|
||||
}
|
||||
dst[l-1] = x[l-1] << 1
|
||||
return dst
|
||||
}
|
||||
|
||||
// ShiftNBytesLeft puts in dst the byte array corresponding to x << n in binary.
|
||||
func ShiftNBytesLeft(dst, x []byte, n int) {
|
||||
// Erase first n / 8 bytes
|
||||
copy(dst, x[n/8:])
|
||||
|
||||
// Shift the remaining n % 8 bits
|
||||
bits := uint(n % 8)
|
||||
l := len(dst)
|
||||
for i := 0; i < l-1; i++ {
|
||||
dst[i] = (dst[i] << bits) | (dst[i+1] >> uint(8 - bits))
|
||||
}
|
||||
dst[l-1] = dst[l-1] << bits
|
||||
|
||||
// Append trailing zeroes
|
||||
dst = append(dst, make([]byte, n/8)...)
|
||||
}
|
||||
|
||||
// XorBytesMut assumes equal input length, replaces X with X XOR Y
|
||||
func XorBytesMut(X, Y []byte) {
|
||||
for i := 0; i < len(X); i++ {
|
||||
X[i] ^= Y[i]
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// XorBytes assumes equal input length, puts X XOR Y into Z
|
||||
func XorBytes(Z, X, Y []byte) {
|
||||
for i := 0; i < len(X); i++ {
|
||||
Z[i] = X[i] ^ Y[i]
|
||||
}
|
||||
}
|
||||
|
||||
// RightXor XORs smaller input (assumed Y) at the right of the larger input (assumed X)
|
||||
func RightXor(X, Y []byte) []byte {
|
||||
offset := len(X) - len(Y)
|
||||
xored := make([]byte, len(X));
|
||||
copy(xored, X)
|
||||
for i := 0; i < len(Y); i++ {
|
||||
xored[offset + i] ^= Y[i]
|
||||
}
|
||||
return xored
|
||||
}
|
||||
|
||||
// SliceForAppend takes a slice and a requested number of bytes. It returns a
|
||||
// slice with the contents of the given slice followed by that many bytes and a
|
||||
// second slice that aliases into it and contains only the extra bytes. If the
|
||||
// original slice has sufficient capacity then no allocation is performed.
|
||||
func SliceForAppend(in []byte, n int) (head, tail []byte) {
|
||||
if total := len(in) + n; cap(in) >= total {
|
||||
head = in[:total]
|
||||
} else {
|
||||
head = make([]byte, total)
|
||||
copy(head, in)
|
||||
}
|
||||
tail = head[len(in):]
|
||||
return
|
||||
}
|
||||
|
||||
|
|
@ -0,0 +1,317 @@
|
|||
// Copyright (C) 2019 ProtonTech AG
|
||||
|
||||
// Package ocb provides an implementation of the OCB (offset codebook) mode of
|
||||
// operation, as described in RFC-7253 of the IRTF and in Rogaway, Bellare,
|
||||
// Black and Krovetz - OCB: A BLOCK-CIPHER MODE OF OPERATION FOR EFFICIENT
|
||||
// AUTHENTICATED ENCRYPTION (2003).
|
||||
// Security considerations (from RFC-7253): A private key MUST NOT be used to
|
||||
// encrypt more than 2^48 blocks. Tag length should be at least 12 bytes (a
|
||||
// brute-force forging adversary succeeds after 2^{tag length} attempts). A
|
||||
// single key SHOULD NOT be used to decrypt ciphertext with different tag
|
||||
// lengths. Nonces need not be secret, but MUST NOT be reused.
|
||||
// This package only supports underlying block ciphers with 128-bit blocks,
|
||||
// such as AES-{128, 192, 256}, but may be extended to other sizes.
|
||||
package ocb
|
||||
|
||||
import (
|
||||
"bytes"
|
||||
"crypto/cipher"
|
||||
"crypto/subtle"
|
||||
"errors"
|
||||
"github.com/ProtonMail/go-crypto/internal/byteutil"
|
||||
"math/bits"
|
||||
)
|
||||
|
||||
type ocb struct {
|
||||
block cipher.Block
|
||||
tagSize int
|
||||
nonceSize int
|
||||
mask mask
|
||||
// Optimized en/decrypt: For each nonce N used to en/decrypt, the 'Ktop'
|
||||
// internal variable can be reused for en/decrypting with nonces sharing
|
||||
// all but the last 6 bits with N. The prefix of the first nonce used to
|
||||
// compute the new Ktop, and the Ktop value itself, are stored in
|
||||
// reusableKtop. If using incremental nonces, this saves one block cipher
|
||||
// call every 63 out of 64 OCB encryptions, and stores one nonce and one
|
||||
// output of the block cipher in memory only.
|
||||
reusableKtop reusableKtop
|
||||
}
|
||||
|
||||
type mask struct {
|
||||
// L_*, L_$, (L_i)_{i ∈ N}
|
||||
lAst []byte
|
||||
lDol []byte
|
||||
L [][]byte
|
||||
}
|
||||
|
||||
type reusableKtop struct {
|
||||
noncePrefix []byte
|
||||
Ktop []byte
|
||||
}
|
||||
|
||||
const (
|
||||
defaultTagSize = 16
|
||||
defaultNonceSize = 15
|
||||
)
|
||||
|
||||
const (
|
||||
enc = iota
|
||||
dec
|
||||
)
|
||||
|
||||
func (o *ocb) NonceSize() int {
|
||||
return o.nonceSize
|
||||
}
|
||||
|
||||
func (o *ocb) Overhead() int {
|
||||
return o.tagSize
|
||||
}
|
||||
|
||||
// NewOCB returns an OCB instance with the given block cipher and default
|
||||
// tag and nonce sizes.
|
||||
func NewOCB(block cipher.Block) (cipher.AEAD, error) {
|
||||
return NewOCBWithNonceAndTagSize(block, defaultNonceSize, defaultTagSize)
|
||||
}
|
||||
|
||||
// NewOCBWithNonceAndTagSize returns an OCB instance with the given block
|
||||
// cipher, nonce length, and tag length. Panics on zero nonceSize and
|
||||
// exceedingly long tag size.
|
||||
//
|
||||
// It is recommended to use at least 12 bytes as tag length.
|
||||
func NewOCBWithNonceAndTagSize(
|
||||
block cipher.Block, nonceSize, tagSize int) (cipher.AEAD, error) {
|
||||
if block.BlockSize() != 16 {
|
||||
return nil, ocbError("Block cipher must have 128-bit blocks")
|
||||
}
|
||||
if nonceSize < 1 {
|
||||
return nil, ocbError("Incorrect nonce length")
|
||||
}
|
||||
if nonceSize >= block.BlockSize() {
|
||||
return nil, ocbError("Nonce length exceeds blocksize - 1")
|
||||
}
|
||||
if tagSize > block.BlockSize() {
|
||||
return nil, ocbError("Custom tag length exceeds blocksize")
|
||||
}
|
||||
return &ocb{
|
||||
block: block,
|
||||
tagSize: tagSize,
|
||||
nonceSize: nonceSize,
|
||||
mask: initializeMaskTable(block),
|
||||
reusableKtop: reusableKtop{
|
||||
noncePrefix: nil,
|
||||
Ktop: nil,
|
||||
},
|
||||
}, nil
|
||||
}
|
||||
|
||||
func (o *ocb) Seal(dst, nonce, plaintext, adata []byte) []byte {
|
||||
if len(nonce) > o.nonceSize {
|
||||
panic("crypto/ocb: Incorrect nonce length given to OCB")
|
||||
}
|
||||
ret, out := byteutil.SliceForAppend(dst, len(plaintext)+o.tagSize)
|
||||
o.crypt(enc, out, nonce, adata, plaintext)
|
||||
return ret
|
||||
}
|
||||
|
||||
func (o *ocb) Open(dst, nonce, ciphertext, adata []byte) ([]byte, error) {
|
||||
if len(nonce) > o.nonceSize {
|
||||
panic("Nonce too long for this instance")
|
||||
}
|
||||
if len(ciphertext) < o.tagSize {
|
||||
return nil, ocbError("Ciphertext shorter than tag length")
|
||||
}
|
||||
sep := len(ciphertext) - o.tagSize
|
||||
ret, out := byteutil.SliceForAppend(dst, len(ciphertext))
|
||||
ciphertextData := ciphertext[:sep]
|
||||
tag := ciphertext[sep:]
|
||||
o.crypt(dec, out, nonce, adata, ciphertextData)
|
||||
if subtle.ConstantTimeCompare(ret[sep:], tag) == 1 {
|
||||
ret = ret[:sep]
|
||||
return ret, nil
|
||||
}
|
||||
for i := range out {
|
||||
out[i] = 0
|
||||
}
|
||||
return nil, ocbError("Tag authentication failed")
|
||||
}
|
||||
|
||||
// On instruction enc (resp. dec), crypt is the encrypt (resp. decrypt)
|
||||
// function. It returns the resulting plain/ciphertext with the tag appended.
|
||||
func (o *ocb) crypt(instruction int, Y, nonce, adata, X []byte) []byte {
|
||||
//
|
||||
// Consider X as a sequence of 128-bit blocks
|
||||
//
|
||||
// Note: For encryption (resp. decryption), X is the plaintext (resp., the
|
||||
// ciphertext without the tag).
|
||||
blockSize := o.block.BlockSize()
|
||||
|
||||
//
|
||||
// Nonce-dependent and per-encryption variables
|
||||
//
|
||||
// Zero out the last 6 bits of the nonce into truncatedNonce to see if Ktop
|
||||
// is already computed.
|
||||
truncatedNonce := make([]byte, len(nonce))
|
||||
copy(truncatedNonce, nonce)
|
||||
truncatedNonce[len(truncatedNonce)-1] &= 192
|
||||
Ktop := make([]byte, blockSize)
|
||||
if bytes.Equal(truncatedNonce, o.reusableKtop.noncePrefix) {
|
||||
Ktop = o.reusableKtop.Ktop
|
||||
} else {
|
||||
// Nonce = num2str(TAGLEN mod 128, 7) || zeros(120 - bitlen(N)) || 1 || N
|
||||
paddedNonce := append(make([]byte, blockSize-1-len(nonce)), 1)
|
||||
paddedNonce = append(paddedNonce, truncatedNonce...)
|
||||
paddedNonce[0] |= byte(((8 * o.tagSize) % (8 * blockSize)) << 1)
|
||||
// Last 6 bits of paddedNonce are already zero. Encrypt into Ktop
|
||||
paddedNonce[blockSize-1] &= 192
|
||||
Ktop = paddedNonce
|
||||
o.block.Encrypt(Ktop, Ktop)
|
||||
o.reusableKtop.noncePrefix = truncatedNonce
|
||||
o.reusableKtop.Ktop = Ktop
|
||||
}
|
||||
|
||||
// Stretch = Ktop || ((lower half of Ktop) XOR (lower half of Ktop << 8))
|
||||
xorHalves := make([]byte, blockSize/2)
|
||||
byteutil.XorBytes(xorHalves, Ktop[:blockSize/2], Ktop[1:1+blockSize/2])
|
||||
stretch := append(Ktop, xorHalves...)
|
||||
bottom := int(nonce[len(nonce)-1] & 63)
|
||||
offset := make([]byte, len(stretch))
|
||||
byteutil.ShiftNBytesLeft(offset, stretch, bottom)
|
||||
offset = offset[:blockSize]
|
||||
|
||||
//
|
||||
// Process any whole blocks
|
||||
//
|
||||
// Note: For encryption Y is ciphertext || tag, for decryption Y is
|
||||
// plaintext || tag.
|
||||
checksum := make([]byte, blockSize)
|
||||
m := len(X) / blockSize
|
||||
for i := 0; i < m; i++ {
|
||||
index := bits.TrailingZeros(uint(i + 1))
|
||||
if len(o.mask.L)-1 < index {
|
||||
o.mask.extendTable(index)
|
||||
}
|
||||
byteutil.XorBytesMut(offset, o.mask.L[bits.TrailingZeros(uint(i+1))])
|
||||
blockX := X[i*blockSize : (i+1)*blockSize]
|
||||
blockY := Y[i*blockSize : (i+1)*blockSize]
|
||||
byteutil.XorBytes(blockY, blockX, offset)
|
||||
switch instruction {
|
||||
case enc:
|
||||
o.block.Encrypt(blockY, blockY)
|
||||
byteutil.XorBytesMut(blockY, offset)
|
||||
byteutil.XorBytesMut(checksum, blockX)
|
||||
case dec:
|
||||
o.block.Decrypt(blockY, blockY)
|
||||
byteutil.XorBytesMut(blockY, offset)
|
||||
byteutil.XorBytesMut(checksum, blockY)
|
||||
}
|
||||
}
|
||||
//
|
||||
// Process any final partial block and compute raw tag
|
||||
//
|
||||
tag := make([]byte, blockSize)
|
||||
if len(X)%blockSize != 0 {
|
||||
byteutil.XorBytesMut(offset, o.mask.lAst)
|
||||
pad := make([]byte, blockSize)
|
||||
o.block.Encrypt(pad, offset)
|
||||
chunkX := X[blockSize*m:]
|
||||
chunkY := Y[blockSize*m : len(X)]
|
||||
byteutil.XorBytes(chunkY, chunkX, pad[:len(chunkX)])
|
||||
// P_* || bit(1) || zeroes(127) - len(P_*)
|
||||
switch instruction {
|
||||
case enc:
|
||||
paddedY := append(chunkX, byte(128))
|
||||
paddedY = append(paddedY, make([]byte, blockSize-len(chunkX)-1)...)
|
||||
byteutil.XorBytesMut(checksum, paddedY)
|
||||
case dec:
|
||||
paddedX := append(chunkY, byte(128))
|
||||
paddedX = append(paddedX, make([]byte, blockSize-len(chunkY)-1)...)
|
||||
byteutil.XorBytesMut(checksum, paddedX)
|
||||
}
|
||||
byteutil.XorBytes(tag, checksum, offset)
|
||||
byteutil.XorBytesMut(tag, o.mask.lDol)
|
||||
o.block.Encrypt(tag, tag)
|
||||
byteutil.XorBytesMut(tag, o.hash(adata))
|
||||
copy(Y[blockSize*m+len(chunkY):], tag[:o.tagSize])
|
||||
} else {
|
||||
byteutil.XorBytes(tag, checksum, offset)
|
||||
byteutil.XorBytesMut(tag, o.mask.lDol)
|
||||
o.block.Encrypt(tag, tag)
|
||||
byteutil.XorBytesMut(tag, o.hash(adata))
|
||||
copy(Y[blockSize*m:], tag[:o.tagSize])
|
||||
}
|
||||
return Y
|
||||
}
|
||||
|
||||
// This hash function is used to compute the tag. Per design, on empty input it
|
||||
// returns a slice of zeros, of the same length as the underlying block cipher
|
||||
// block size.
|
||||
func (o *ocb) hash(adata []byte) []byte {
|
||||
//
|
||||
// Consider A as a sequence of 128-bit blocks
|
||||
//
|
||||
A := make([]byte, len(adata))
|
||||
copy(A, adata)
|
||||
blockSize := o.block.BlockSize()
|
||||
|
||||
//
|
||||
// Process any whole blocks
|
||||
//
|
||||
sum := make([]byte, blockSize)
|
||||
offset := make([]byte, blockSize)
|
||||
m := len(A) / blockSize
|
||||
for i := 0; i < m; i++ {
|
||||
chunk := A[blockSize*i : blockSize*(i+1)]
|
||||
index := bits.TrailingZeros(uint(i + 1))
|
||||
// If the mask table is too short
|
||||
if len(o.mask.L)-1 < index {
|
||||
o.mask.extendTable(index)
|
||||
}
|
||||
byteutil.XorBytesMut(offset, o.mask.L[index])
|
||||
byteutil.XorBytesMut(chunk, offset)
|
||||
o.block.Encrypt(chunk, chunk)
|
||||
byteutil.XorBytesMut(sum, chunk)
|
||||
}
|
||||
|
||||
//
|
||||
// Process any final partial block; compute final hash value
|
||||
//
|
||||
if len(A)%blockSize != 0 {
|
||||
byteutil.XorBytesMut(offset, o.mask.lAst)
|
||||
// Pad block with 1 || 0 ^ 127 - bitlength(a)
|
||||
ending := make([]byte, blockSize-len(A)%blockSize)
|
||||
ending[0] = 0x80
|
||||
encrypted := append(A[blockSize*m:], ending...)
|
||||
byteutil.XorBytesMut(encrypted, offset)
|
||||
o.block.Encrypt(encrypted, encrypted)
|
||||
byteutil.XorBytesMut(sum, encrypted)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
func initializeMaskTable(block cipher.Block) mask {
|
||||
//
|
||||
// Key-dependent variables
|
||||
//
|
||||
lAst := make([]byte, block.BlockSize())
|
||||
block.Encrypt(lAst, lAst)
|
||||
lDol := byteutil.GfnDouble(lAst)
|
||||
L := make([][]byte, 1)
|
||||
L[0] = byteutil.GfnDouble(lDol)
|
||||
|
||||
return mask{
|
||||
lAst: lAst,
|
||||
lDol: lDol,
|
||||
L: L,
|
||||
}
|
||||
}
|
||||
|
||||
// Extends the L array of mask m up to L[limit], with L[i] = GfnDouble(L[i-1])
|
||||
func (m *mask) extendTable(limit int) {
|
||||
for i := len(m.L); i <= limit; i++ {
|
||||
m.L = append(m.L, byteutil.GfnDouble(m.L[i-1]))
|
||||
}
|
||||
}
|
||||
|
||||
func ocbError(err string) error {
|
||||
return errors.New("crypto/ocb: " + err)
|
||||
}
|
||||
|
|
@ -0,0 +1,136 @@
|
|||
// In the test vectors provided by RFC 7253, the "bottom"
|
||||
// internal variable, which defines "offset" for the first time, does not
|
||||
// exceed 15. However, it can attain values up to 63.
|
||||
|
||||
// These vectors include key length in {128, 192, 256}, tag size 128, and
|
||||
// random nonce, header, and plaintext lengths.
|
||||
|
||||
// This file was automatically generated.
|
||||
|
||||
package ocb
|
||||
|
||||
var randomVectors = []struct {
|
||||
key, nonce, header, plaintext, ciphertext string
|
||||
}{
|
||||
|
||||
{"9438C5D599308EAF13F800D2D31EA7F0",
|
||||
"C38EE4801BEBFFA1CD8635BE",
|
||||
"0E507B7DADD8A98CDFE272D3CB6B3E8332B56AE583FB049C0874D4200BED16BD1A044182434E9DA0E841F182DFD5B3016B34641CED0784F1745F63AB3D0DA22D3351C9EF9A658B8081E24498EBF61FCE40DA6D8E184536",
|
||||
"962D227786FB8913A8BAD5DC3250",
|
||||
"EEDEF5FFA5986D1E3BF86DDD33EF9ADC79DCA06E215FA772CCBA814F63AD"},
|
||||
{"BA7DE631C7D6712167C6724F5B9A2B1D",
|
||||
"35263EBDA05765DC0E71F1F5",
|
||||
"0103257B4224507C0242FEFE821EA7FA42E0A82863E5F8B68F7D881B4B44FA428A2B6B21D2F591260802D8AB6D83",
|
||||
"9D6D1FC93AE8A64E7889B7B2E3521EFA9B920A8DDB692E6F833DDC4A38AFA535E5E2A3ED82CB7E26404AB86C54D01C4668F28398C2DF33D5D561CBA1C8DCFA7A912F5048E545B59483C0E3221F54B14DAA2E4EB657B3BEF9554F34CAD69B2724AE962D3D8A",
|
||||
"E93852D1985C5E775655E937FA79CE5BF28A585F2AF53A5018853B9634BE3C84499AC0081918FDCE0624494D60E25F76ACD6853AC7576E3C350F332249BFCABD4E73CEABC36BE4EDDA40914E598AE74174A0D7442149B26990899491BDDFE8FC54D6C18E83AE9E9A6FFBF5D376565633862EEAD88D"},
|
||||
{"2E74B25289F6FD3E578C24866E9C72A5",
|
||||
"FD912F15025AF8414642BA1D1D",
|
||||
"FB5FB8C26F365EEDAB5FE260C6E3CCD27806729C8335F146063A7F9EA93290E56CF84576EB446350D22AD730547C267B1F0BBB97EB34E1E2C41A",
|
||||
"6C092EBF78F76EE8C1C6E592277D9545BA16EDB67BC7D8480B9827702DC2F8A129E2B08A2CE710CA7E1DA45CE162BB6CD4B512E632116E2211D3C90871EFB06B8D4B902681C7FB",
|
||||
"6AC0A77F26531BF4F354A1737F99E49BE32ECD909A7A71AD69352906F54B08A9CE9B8CA5D724CBFFC5673437F23F630697F3B84117A1431D6FA8CC13A974FB4AD360300522E09511B99E71065D5AC4BBCB1D791E864EF4"},
|
||||
{"E7EC507C802528F790AFF5303A017B17",
|
||||
"4B97A7A568940A9E3CE7A99E93031E",
|
||||
"28349BDC5A09390C480F9B8AA3EDEA3DDB8B9D64BCA322C570B8225DF0E31190DAB25A4014BA39519E02ABFB12B89AA28BBFD29E486E7FB28734258C817B63CED9912DBAFEBB93E2798AB2890DE3B0ACFCFF906AB15563EF7823CE83D27CDB251195E22BD1337BCBDE65E7C2C427321C463C2777BFE5AEAA",
|
||||
"9455B3EA706B74",
|
||||
"7F33BA3EA848D48A96B9530E26888F43EBD4463C9399B6"},
|
||||
{"6C928AA3224736F28EE7378DE0090191",
|
||||
"8936138E2E4C6A13280017A1622D",
|
||||
"6202717F2631565BDCDC57C6584543E72A7C8BD444D0D108ED35069819633C",
|
||||
"DA0691439E5F035F3E455269D14FE5C201C8C9B0A3FE2D3F86BCC59387C868FE65733D388360B31E3CE28B4BF6A8BE636706B536D5720DB66B47CF1C7A5AFD6F61E0EF90F1726D6B0E169F9A768B2B7AE4EE00A17F630AC905FCAAA1B707FFF25B3A1AAE83B504837C64A5639B2A34002B300EC035C9B43654DA55",
|
||||
"B8804D182AB0F0EEB464FA7BD1329AD6154F982013F3765FEDFE09E26DAC078C9C1439BFC1159D6C02A25E3FF83EF852570117B315852AD5EE20E0FA3AA0A626B0E43BC0CEA38B44579DD36803455FB46989B90E6D229F513FD727AF8372517E9488384C515D6067704119C931299A0982EDDFB9C2E86A90C450C077EB222511EC9CCABC9FCFDB19F70088"},
|
||||
{"ECEA315CA4B3F425B0C9957A17805EA4",
|
||||
"664CDAE18403F4F9BA13015A44FC",
|
||||
"642AFB090D6C6DB46783F08B01A3EF2A8FEB5736B531EAC226E7888FCC8505F396818F83105065FACB3267485B9E5E4A0261F621041C08FCCB2A809A49AB5252A91D0971BCC620B9D614BD77E57A0EED2FA5",
|
||||
"6852C31F8083E20E364CEA21BB7854D67CEE812FE1C9ED2425C0932A90D3780728D1BB",
|
||||
"2ECEF962A9695A463ADABB275BDA9FF8B2BA57AEC2F52EFFB700CD9271A74D2A011C24AEA946051BD6291776429B7E681BA33E"},
|
||||
{"4EE616C4A58AAA380878F71A373461F6",
|
||||
"91B8C9C176D9C385E9C47E52",
|
||||
"CDA440B7F9762C572A718AC754EDEECC119E5EE0CCB9FEA4FFB22EEE75087C032EBF3DA9CDD8A28CC010B99ED45143B41A4BA50EA2A005473F89639237838867A57F23B0F0ED3BF22490E4501DAC9C658A9B9F",
|
||||
"D6E645FA9AE410D15B8123FD757FA356A8DBE9258DDB5BE88832E615910993F497EC",
|
||||
"B70ED7BF959FB2AAED4F36174A2A99BFB16992C8CDF369C782C4DB9C73DE78C5DB8E0615F647243B97ACDB24503BC9CADC48"},
|
||||
{"DCD475773136C830D5E3D0C5FE05B7FF",
|
||||
"BB8E1FBB483BE7616A922C4A",
|
||||
"36FEF2E1CB29E76A6EA663FC3AF66ECD7404F466382F7B040AABED62293302B56E8783EF7EBC21B4A16C3E78A7483A0A403F253A2CDC5BBF79DC3DAE6C73F39A961D8FBBE8D41B",
|
||||
"441E886EA38322B2437ECA7DEB5282518865A66780A454E510878E61BFEC3106A3CD93D2A02052E6F9E1832F9791053E3B76BF4C07EFDD6D4106E3027FABB752E60C1AA425416A87D53938163817A1051EBA1D1DEEB4B9B25C7E97368B52E5911A31810B0EC5AF547559B6142D9F4C4A6EF24A4CF75271BF9D48F62B",
|
||||
"1BE4DD2F4E25A6512C2CC71D24BBB07368589A94C2714962CD0ACE5605688F06342587521E75F0ACAFFD86212FB5C34327D238DB36CF2B787794B9A4412E7CD1410EA5DDD2450C265F29CF96013CD213FD2880657694D718558964BC189B4A84AFCF47EB012935483052399DBA5B088B0A0477F20DFE0E85DCB735E21F22A439FB837DD365A93116D063E607"},
|
||||
{"3FBA2B3D30177FFE15C1C59ED2148BB2C091F5615FBA7C07",
|
||||
"FACF804A4BEBF998505FF9DE",
|
||||
"8213B9263B2971A5BDA18DBD02208EE1",
|
||||
"15B323926993B326EA19F892D704439FC478828322AF72118748284A1FD8A6D814E641F70512FD706980337379F31DC63355974738D7FEA87AD2858C0C2EBBFBE74371C21450072373C7B651B334D7C4D43260B9D7CCD3AF9EDB",
|
||||
"6D35DC1469B26E6AAB26272A41B46916397C24C485B61162E640A062D9275BC33DDCFD3D9E1A53B6C8F51AC89B66A41D59B3574197A40D9B6DCF8A4E2A001409C8112F16B9C389E0096179DB914E05D6D11ED0005AD17E1CE105A2F0BAB8F6B1540DEB968B7A5428FF44"},
|
||||
{"53B52B8D4D748BCDF1DDE68857832FA46227FA6E2F32EFA1",
|
||||
"0B0EF53D4606B28D1398355F",
|
||||
"F23882436349094AF98BCACA8218E81581A043B19009E28EFBF2DE37883E04864148CC01D240552CA8844EC1456F42034653067DA67E80F87105FD06E14FF771246C9612867BE4D215F6D761",
|
||||
"F15030679BD4088D42CAC9BF2E9606EAD4798782FA3ED8C57EBE7F84A53236F51B25967C6489D0CD20C9EEA752F9BC",
|
||||
"67B96E2D67C3729C96DAEAEDF821D61C17E648643A2134C5621FEC621186915AD80864BFD1EB5B238BF526A679385E012A457F583AFA78134242E9D9C1B4E4"},
|
||||
{"0272DD80F23399F49BFC320381A5CD8225867245A49A7D41",
|
||||
"5C83F4896D0738E1366B1836",
|
||||
"69B0337289B19F73A12BAEEA857CCAF396C11113715D9500CCCF48BA08CFF12BC8B4BADB3084E63B85719DB5058FA7C2C11DEB096D7943CFA7CAF5",
|
||||
"C01AD10FC8B562CD17C7BC2FAB3E26CBDFF8D7F4DEA816794BBCC12336991712972F52816AABAB244EB43B0137E2BAC1DD413CE79531E78BEF782E6B439612BB3AEF154DE3502784F287958EBC159419F9EBA27916A28D6307324129F506B1DE80C1755A929F87",
|
||||
"FEFE52DD7159C8DD6E8EC2D3D3C0F37AB6CB471A75A071D17EC4ACDD8F3AA4D7D4F7BB559F3C09099E3D9003E5E8AA1F556B79CECDE66F85B08FA5955E6976BF2695EA076388A62D2AD5BAB7CBF1A7F3F4C8D5CDF37CDE99BD3E30B685D9E5EEE48C7C89118EF4878EB89747F28271FA2CC45F8E9E7601"},
|
||||
{"3EEAED04A455D6E5E5AB53CFD5AFD2F2BC625C7BF4BE49A5",
|
||||
"36B88F63ADBB5668588181D774",
|
||||
"D367E3CB3703E762D23C6533188EF7028EFF9D935A3977150361997EC9DEAF1E4794BDE26AA8B53C124980B1362EC86FCDDFC7A90073171C1BAEE351A53234B86C66E8AB92FAE99EC6967A6D3428892D80",
|
||||
"573454C719A9A55E04437BF7CBAAF27563CCCD92ADD5E515CD63305DFF0687E5EEF790C5DCA5C0033E9AB129505E2775438D92B38F08F3B0356BA142C6F694",
|
||||
"E9F79A5B432D9E682C9AAA5661CFC2E49A0FCB81A431E54B42EB73DD3BED3F377FEC556ABA81624BA64A5D739AD41467460088F8D4F442180A9382CA635745473794C382FCDDC49BA4EB6D8A44AE3C"},
|
||||
{"B695C691538F8CBD60F039D0E28894E3693CC7C36D92D79D",
|
||||
"BC099AEB637361BAC536B57618",
|
||||
"BFFF1A65AE38D1DC142C71637319F5F6508E2CB33C9DCB94202B359ED5A5ED8042E7F4F09231D32A7242976677E6F4C549BF65FADC99E5AF43F7A46FD95E16C2",
|
||||
"081DF3FD85B415D803F0BE5AC58CFF0023FDDED99788296C3731D8",
|
||||
"E50C64E3614D94FE69C47092E46ACC9957C6FEA2CCBF96BC62FBABE7424753C75F9C147C42AE26FE171531"},
|
||||
{"C9ACBD2718F0689A1BE9802A551B6B8D9CF5614DAF5E65ED",
|
||||
"B1B0AAF373B8B026EB80422051D8",
|
||||
"6648C0E61AC733C76119D23FB24548D637751387AA2EAE9D80E912B7BD486CAAD9EAF4D7A5FE2B54AAD481E8EC94BB4D558000896E2010462B70C9FED1E7273080D1",
|
||||
"189F591F6CB6D59AFEDD14C341741A8F1037DC0DF00FC57CE65C30F49E860255CEA5DC6019380CC0FE8880BC1A9E685F41C239C38F36E3F2A1388865C5C311059C0A",
|
||||
"922A5E949B61D03BE34AB5F4E58607D4504EA14017BB363DAE3C873059EA7A1C77A746FB78981671D26C2CF6D9F24952D510044CE02A10177E9DB42D0145211DFE6E84369C5E3BC2669EAB4147B2822895F9"},
|
||||
{"7A832BD2CF5BF4919F353CE2A8C86A5E406DA2D52BE16A72",
|
||||
"2F2F17CECF7E5A756D10785A3CB9DB",
|
||||
"61DA05E3788CC2D8405DBA70C7A28E5AF699863C9F72E6C6770126929F5D6FA267F005EBCF49495CB46400958A3AE80D1289D1C671",
|
||||
"44E91121195A41AF14E8CFDBD39A4B517BE0DF1A72977ED8A3EEF8EEDA1166B2EB6DB2C4AE2E74FA0F0C74537F659BFBD141E5DDEC67E64EDA85AABD3F52C85A785B9FB3CECD70E7DF",
|
||||
"BEDF596EA21288D2B84901E188F6EE1468B14D5161D3802DBFE00D60203A24E2AB62714BF272A45551489838C3A7FEAADC177B591836E73684867CCF4E12901DCF2064058726BBA554E84ADC5136F507E961188D4AF06943D3"},
|
||||
{"1508E8AE9079AA15F1CEC4F776B4D11BCCB061B58AA56C18",
|
||||
"BCA625674F41D1E3AB47672DC0C3",
|
||||
"8B12CF84F16360F0EAD2A41BC021530FFCEC7F3579CAE658E10E2D3D81870F65AFCED0C77C6C4C6E6BA424FF23088C796BA6195ABA35094BF1829E089662E7A95FC90750AE16D0C8AFA55DAC789D7735B970B58D4BE7CEC7341DA82A0179A01929C27A59C5063215B859EA43",
|
||||
"E525422519ECE070E82C",
|
||||
"B47BC07C3ED1C0A43BA52C43CBACBCDBB29CAF1001E09FDF7107"},
|
||||
{"7550C2761644E911FE9ADD119BAC07376BEA442845FEAD876D7E7AC1B713E464",
|
||||
"36D2EC25ADD33CDEDF495205BBC923",
|
||||
"7FCFE81A3790DE97FFC3DE160C470847EA7E841177C2F759571CBD837EA004A6CA8C6F4AEBFF2E9FD552D73EB8A30705D58D70C0B67AEEA280CBBF0A477358ACEF1E7508F2735CD9A0E4F9AC92B8C008F575D3B6278F1C18BD01227E3502E5255F3AB1893632AD00C717C588EF652A51A43209E7EE90",
|
||||
"2B1A62F8FDFAA3C16470A21AD307C9A7D03ADE8EF72C69B06F8D738CDE578D7AEFD0D40BD9C022FB9F580DF5394C998ACCCEFC5471A3996FB8F1045A81FDC6F32D13502EA65A211390C8D882B8E0BEFD8DD8CBEF51D1597B124E9F7F",
|
||||
"C873E02A22DB89EB0787DB6A60B99F7E4A0A085D5C4232A81ADCE2D60AA36F92DDC33F93DD8640AC0E08416B187FB382B3EC3EE85A64B0E6EE41C1366A5AD2A282F66605E87031CCBA2FA7B2DA201D975994AADE3DD1EE122AE09604AD489B84BF0C1AB7129EE16C6934850E"},
|
||||
{"A51300285E554FDBDE7F771A9A9A80955639DD87129FAEF74987C91FB9687C71",
|
||||
"81691D5D20EC818FCFF24B33DECC",
|
||||
"C948093218AA9EB2A8E44A87EEA73FC8B6B75A196819A14BD83709EA323E8DF8B491045220E1D88729A38DBCFFB60D3056DAD4564498FD6574F74512945DEB34B69329ACED9FFC05D5D59DFCD5B973E2ACAFE6AD1EF8BBBC49351A2DD12508ED89ED",
|
||||
"EB861165DAF7625F827C6B574ED703F03215",
|
||||
"C6CD1CE76D2B3679C1B5AA1CFD67CCB55444B6BFD3E22C81CBC9BB738796B83E54E3"},
|
||||
{"8CE0156D26FAEB7E0B9B800BBB2E9D4075B5EAC5C62358B0E7F6FCE610223282",
|
||||
"D2A7B94DD12CDACA909D3AD7",
|
||||
"E021A78F374FC271389AB9A3E97077D755",
|
||||
"7C26000B58929F5095E1CEE154F76C2A299248E299F9B5ADE6C403AA1FD4A67FD4E0232F214CE7B919EE7A1027D2B76C57475715CD078461",
|
||||
"C556FB38DF069B56F337B5FF5775CE6EAA16824DFA754F20B78819028EA635C3BB7AA731DE8776B2DCB67DCA2D33EEDF3C7E52EA450013722A41755A0752433ED17BDD5991AAE77A"},
|
||||
{"1E8000A2CE00A561C9920A30BF0D7B983FEF8A1014C8F04C35CA6970E6BA02BD",
|
||||
"65ED3D63F79F90BBFD19775E",
|
||||
"336A8C0B7243582A46B221AA677647FCAE91",
|
||||
"134A8B34824A290E7B",
|
||||
"914FBEF80D0E6E17F8BDBB6097EBF5FBB0554952DC2B9E5151"},
|
||||
{"53D5607BBE690B6E8D8F6D97F3DF2BA853B682597A214B8AA0EA6E598650AF15",
|
||||
"C391A856B9FE234E14BA1AC7BB40FF",
|
||||
"479682BC21349C4BE1641D5E78FE2C79EC1B9CF5470936DCAD9967A4DCD7C4EFADA593BC9EDE71E6A08829B8580901B61E274227E9D918502DE3",
|
||||
"EAD154DC09C5E26C5D26FF33ED148B27120C7F2C23225CC0D0631B03E1F6C6D96FEB88C1A4052ACB4CE746B884B6502931F407021126C6AAB8C514C077A5A38438AE88EE",
|
||||
"938821286EBB671D999B87C032E1D6055392EB564E57970D55E545FC5E8BAB90E6E3E3C0913F6320995FC636D72CD9919657CC38BD51552F4A502D8D1FE56DB33EBAC5092630E69EBB986F0E15CEE9FC8C052501"},
|
||||
{"294362FCC984F440CEA3E9F7D2C06AF20C53AAC1B3738CA2186C914A6E193ABB",
|
||||
"B15B61C8BB39261A8F55AB178EC3",
|
||||
"D0729B6B75BB",
|
||||
"2BD089ADCE9F334BAE3B065996C7D616DD0C27DF4218DCEEA0FBCA0F968837CE26B0876083327E25681FDDD620A32EC0DA12F73FAE826CC94BFF2B90A54D2651",
|
||||
"AC94B25E4E21DE2437B806966CCD5D9385EF0CD4A51AB9FA6DE675C7B8952D67802E9FEC1FDE9F5D1EAB06057498BC0EEA454804FC9D2068982A3E24182D9AC2E7AB9994DDC899A604264583F63D066B"},
|
||||
{"959DBFEB039B1A5B8CE6A44649B602AAA5F98A906DB96143D202CD2024F749D9",
|
||||
"01D7BDB1133E9C347486C1EFA6",
|
||||
"F3843955BD741F379DD750585EDC55E2CDA05CCBA8C1F4622AC2FE35214BC3A019B8BD12C4CC42D9213D1E1556941E8D8450830287FFB3B763A13722DD4140ED9846FB5FFF745D7B0B967D810A068222E10B259AF1D392035B0D83DC1498A6830B11B2418A840212599171E0258A1C203B05362978",
|
||||
"A21811232C950FA8B12237C2EBD6A7CD2C3A155905E9E0C7C120",
|
||||
"63C1CE397B22F1A03F1FA549B43178BC405B152D3C95E977426D519B3DFCA28498823240592B6EEE7A14"},
|
||||
{"096AE499F5294173F34FF2B375F0E5D5AB79D0D03B33B1A74D7D576826345DF4",
|
||||
"0C52B3D11D636E5910A4DD76D32C",
|
||||
"229E9ECA3053789E937447BC719467075B6138A142DA528DA8F0CF8DDF022FD9AF8E74779BA3AC306609",
|
||||
"8B7A00038783E8BAF6EDEAE0C4EAB48FC8FD501A588C7E4A4DB71E3604F2155A97687D3D2FFF8569261375A513CF4398CE0F87CA1658A1050F6EF6C4EA3E25",
|
||||
"C20B6CF8D3C8241825FD90B2EDAC7593600646E579A8D8DAAE9E2E40C3835FE801B2BE4379131452BC5182C90307B176DFBE2049544222FE7783147B690774F6D9D7CEF52A91E61E298E9AA15464AC"},
|
||||
}
|
||||
78
vendor/github.com/ProtonMail/go-crypto/ocb/rfc7253_test_vectors_suite_a.go
generated
vendored
Normal file
78
vendor/github.com/ProtonMail/go-crypto/ocb/rfc7253_test_vectors_suite_a.go
generated
vendored
Normal file
|
|
@ -0,0 +1,78 @@
|
|||
package ocb
|
||||
|
||||
import (
|
||||
"encoding/hex"
|
||||
)
|
||||
|
||||
// Test vectors from https://tools.ietf.org/html/rfc7253. Note that key is
|
||||
// shared across tests.
|
||||
var testKey, _ = hex.DecodeString("000102030405060708090A0B0C0D0E0F")
|
||||
|
||||
var rfc7253testVectors = []struct {
|
||||
nonce, header, plaintext, ciphertext string
|
||||
}{
|
||||
{"BBAA99887766554433221100",
|
||||
"",
|
||||
"",
|
||||
"785407BFFFC8AD9EDCC5520AC9111EE6"},
|
||||
{"BBAA99887766554433221101",
|
||||
"0001020304050607",
|
||||
"0001020304050607",
|
||||
"6820B3657B6F615A5725BDA0D3B4EB3A257C9AF1F8F03009"},
|
||||
{"BBAA99887766554433221102",
|
||||
"0001020304050607",
|
||||
"",
|
||||
"81017F8203F081277152FADE694A0A00"},
|
||||
{"BBAA99887766554433221103",
|
||||
"",
|
||||
"0001020304050607",
|
||||
"45DD69F8F5AAE72414054CD1F35D82760B2CD00D2F99BFA9"},
|
||||
{"BBAA99887766554433221104",
|
||||
"000102030405060708090A0B0C0D0E0F",
|
||||
"000102030405060708090A0B0C0D0E0F",
|
||||
"571D535B60B277188BE5147170A9A22C3AD7A4FF3835B8C5701C1CCEC8FC3358"},
|
||||
{"BBAA99887766554433221105",
|
||||
"000102030405060708090A0B0C0D0E0F",
|
||||
"",
|
||||
"8CF761B6902EF764462AD86498CA6B97"},
|
||||
{"BBAA99887766554433221106",
|
||||
"",
|
||||
"000102030405060708090A0B0C0D0E0F",
|
||||
"5CE88EC2E0692706A915C00AEB8B2396F40E1C743F52436BDF06D8FA1ECA343D"},
|
||||
{"BBAA99887766554433221107",
|
||||
"000102030405060708090A0B0C0D0E0F1011121314151617",
|
||||
"000102030405060708090A0B0C0D0E0F1011121314151617",
|
||||
"1CA2207308C87C010756104D8840CE1952F09673A448A122C92C62241051F57356D7F3C90BB0E07F"},
|
||||
{"BBAA99887766554433221108",
|
||||
"000102030405060708090A0B0C0D0E0F1011121314151617",
|
||||
"",
|
||||
"6DC225A071FC1B9F7C69F93B0F1E10DE"},
|
||||
{"BBAA99887766554433221109",
|
||||
"",
|
||||
"000102030405060708090A0B0C0D0E0F1011121314151617",
|
||||
"221BD0DE7FA6FE993ECCD769460A0AF2D6CDED0C395B1C3CE725F32494B9F914D85C0B1EB38357FF"},
|
||||
{"BBAA9988776655443322110A",
|
||||
"000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F",
|
||||
"000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F",
|
||||
"BD6F6C496201C69296C11EFD138A467ABD3C707924B964DEAFFC40319AF5A48540FBBA186C5553C68AD9F592A79A4240"},
|
||||
{"BBAA9988776655443322110B",
|
||||
"000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F",
|
||||
"",
|
||||
"FE80690BEE8A485D11F32965BC9D2A32"},
|
||||
{"BBAA9988776655443322110C",
|
||||
"",
|
||||
"000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F",
|
||||
"2942BFC773BDA23CABC6ACFD9BFD5835BD300F0973792EF46040C53F1432BCDFB5E1DDE3BC18A5F840B52E653444D5DF"},
|
||||
{"BBAA9988776655443322110D",
|
||||
"000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021222324252627",
|
||||
"000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021222324252627",
|
||||
"D5CA91748410C1751FF8A2F618255B68A0A12E093FF454606E59F9C1D0DDC54B65E8628E568BAD7AED07BA06A4A69483A7035490C5769E60"},
|
||||
{"BBAA9988776655443322110E",
|
||||
"000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021222324252627",
|
||||
"",
|
||||
"C5CD9D1850C141E358649994EE701B68"},
|
||||
{"BBAA9988776655443322110F",
|
||||
"",
|
||||
"000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021222324252627",
|
||||
"4412923493C57D5DE0D700F753CCE0D1D2D95060122E9F15A5DDBFC5787E50B5CC55EE507BCB084E479AD363AC366B95A98CA5F3000B1479"},
|
||||
}
|
||||
24
vendor/github.com/ProtonMail/go-crypto/ocb/rfc7253_test_vectors_suite_b.go
generated
vendored
Normal file
24
vendor/github.com/ProtonMail/go-crypto/ocb/rfc7253_test_vectors_suite_b.go
generated
vendored
Normal file
|
|
@ -0,0 +1,24 @@
|
|||
package ocb
|
||||
|
||||
// Second set of test vectors from https://tools.ietf.org/html/rfc7253
|
||||
var rfc7253TestVectorTaglen96 = struct {
|
||||
key, nonce, header, plaintext, ciphertext string
|
||||
}{"0F0E0D0C0B0A09080706050403020100",
|
||||
"BBAA9988776655443322110D",
|
||||
"000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021222324252627",
|
||||
"000102030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021222324252627",
|
||||
"1792A4E31E0755FB03E31B22116E6C2DDF9EFD6E33D536F1A0124B0A55BAE884ED93481529C76B6AD0C515F4D1CDD4FDAC4F02AA"}
|
||||
|
||||
var rfc7253AlgorithmTest = []struct {
|
||||
KEYLEN, TAGLEN int
|
||||
OUTPUT string }{
|
||||
{128, 128, "67E944D23256C5E0B6C61FA22FDF1EA2"},
|
||||
{192, 128, "F673F2C3E7174AAE7BAE986CA9F29E17"},
|
||||
{256, 128, "D90EB8E9C977C88B79DD793D7FFA161C"},
|
||||
{128, 96, "77A3D8E73589158D25D01209"},
|
||||
{192, 96, "05D56EAD2752C86BE6932C5E"},
|
||||
{256, 96, "5458359AC23B0CBA9E6330DD"},
|
||||
{128, 64, "192C9B7BD90BA06A"},
|
||||
{192, 64, "0066BC6E0EF34E24"},
|
||||
{256, 64, "7D4EA5D445501CBE"},
|
||||
}
|
||||
153
vendor/github.com/ProtonMail/go-crypto/openpgp/aes/keywrap/keywrap.go
generated
vendored
Normal file
153
vendor/github.com/ProtonMail/go-crypto/openpgp/aes/keywrap/keywrap.go
generated
vendored
Normal file
|
|
@ -0,0 +1,153 @@
|
|||
// Copyright 2014 Matthew Endsley
|
||||
// All rights reserved
|
||||
//
|
||||
// Redistribution and use in source and binary forms, with or without
|
||||
// modification, are permitted providing that the following conditions
|
||||
// are met:
|
||||
// 1. Redistributions of source code must retain the above copyright
|
||||
// notice, this list of conditions and the following disclaimer.
|
||||
// 2. Redistributions in binary form must reproduce the above copyright
|
||||
// notice, this list of conditions and the following disclaimer in the
|
||||
// documentation and/or other materials provided with the distribution.
|
||||
//
|
||||
// THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
|
||||
// IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
||||
// WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
// ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
|
||||
// DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
// OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
|
||||
// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING
|
||||
// IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
// POSSIBILITY OF SUCH DAMAGE.
|
||||
|
||||
// Package keywrap is an implementation of the RFC 3394 AES key wrapping
|
||||
// algorithm. This is used in OpenPGP with elliptic curve keys.
|
||||
package keywrap
|
||||
|
||||
import (
|
||||
"crypto/aes"
|
||||
"encoding/binary"
|
||||
"errors"
|
||||
)
|
||||
|
||||
var (
|
||||
// ErrWrapPlaintext is returned if the plaintext is not a multiple
|
||||
// of 64 bits.
|
||||
ErrWrapPlaintext = errors.New("keywrap: plainText must be a multiple of 64 bits")
|
||||
|
||||
// ErrUnwrapCiphertext is returned if the ciphertext is not a
|
||||
// multiple of 64 bits.
|
||||
ErrUnwrapCiphertext = errors.New("keywrap: cipherText must by a multiple of 64 bits")
|
||||
|
||||
// ErrUnwrapFailed is returned if unwrapping a key fails.
|
||||
ErrUnwrapFailed = errors.New("keywrap: failed to unwrap key")
|
||||
|
||||
// NB: the AES NewCipher call only fails if the key is an invalid length.
|
||||
|
||||
// ErrInvalidKey is returned when the AES key is invalid.
|
||||
ErrInvalidKey = errors.New("keywrap: invalid AES key")
|
||||
)
|
||||
|
||||
// Wrap a key using the RFC 3394 AES Key Wrap Algorithm.
|
||||
func Wrap(key, plainText []byte) ([]byte, error) {
|
||||
if len(plainText)%8 != 0 {
|
||||
return nil, ErrWrapPlaintext
|
||||
}
|
||||
|
||||
c, err := aes.NewCipher(key)
|
||||
if err != nil {
|
||||
return nil, ErrInvalidKey
|
||||
}
|
||||
|
||||
nblocks := len(plainText) / 8
|
||||
|
||||
// 1) Initialize variables.
|
||||
var block [aes.BlockSize]byte
|
||||
// - Set A = IV, an initial value (see 2.2.3)
|
||||
for ii := 0; ii < 8; ii++ {
|
||||
block[ii] = 0xA6
|
||||
}
|
||||
|
||||
// - For i = 1 to n
|
||||
// - Set R[i] = P[i]
|
||||
intermediate := make([]byte, len(plainText))
|
||||
copy(intermediate, plainText)
|
||||
|
||||
// 2) Calculate intermediate values.
|
||||
for ii := 0; ii < 6; ii++ {
|
||||
for jj := 0; jj < nblocks; jj++ {
|
||||
// - B = AES(K, A | R[i])
|
||||
copy(block[8:], intermediate[jj*8:jj*8+8])
|
||||
c.Encrypt(block[:], block[:])
|
||||
|
||||
// - A = MSB(64, B) ^ t where t = (n*j)+1
|
||||
t := uint64(ii*nblocks + jj + 1)
|
||||
val := binary.BigEndian.Uint64(block[:8]) ^ t
|
||||
binary.BigEndian.PutUint64(block[:8], val)
|
||||
|
||||
// - R[i] = LSB(64, B)
|
||||
copy(intermediate[jj*8:jj*8+8], block[8:])
|
||||
}
|
||||
}
|
||||
|
||||
// 3) Output results.
|
||||
// - Set C[0] = A
|
||||
// - For i = 1 to n
|
||||
// - C[i] = R[i]
|
||||
return append(block[:8], intermediate...), nil
|
||||
}
|
||||
|
||||
// Unwrap a key using the RFC 3394 AES Key Wrap Algorithm.
|
||||
func Unwrap(key, cipherText []byte) ([]byte, error) {
|
||||
if len(cipherText)%8 != 0 {
|
||||
return nil, ErrUnwrapCiphertext
|
||||
}
|
||||
|
||||
c, err := aes.NewCipher(key)
|
||||
if err != nil {
|
||||
return nil, ErrInvalidKey
|
||||
}
|
||||
|
||||
nblocks := len(cipherText)/8 - 1
|
||||
|
||||
// 1) Initialize variables.
|
||||
var block [aes.BlockSize]byte
|
||||
// - Set A = C[0]
|
||||
copy(block[:8], cipherText[:8])
|
||||
|
||||
// - For i = 1 to n
|
||||
// - Set R[i] = C[i]
|
||||
intermediate := make([]byte, len(cipherText)-8)
|
||||
copy(intermediate, cipherText[8:])
|
||||
|
||||
// 2) Compute intermediate values.
|
||||
for jj := 5; jj >= 0; jj-- {
|
||||
for ii := nblocks - 1; ii >= 0; ii-- {
|
||||
// - B = AES-1(K, (A ^ t) | R[i]) where t = n*j+1
|
||||
// - A = MSB(64, B)
|
||||
t := uint64(jj*nblocks + ii + 1)
|
||||
val := binary.BigEndian.Uint64(block[:8]) ^ t
|
||||
binary.BigEndian.PutUint64(block[:8], val)
|
||||
|
||||
copy(block[8:], intermediate[ii*8:ii*8+8])
|
||||
c.Decrypt(block[:], block[:])
|
||||
|
||||
// - R[i] = LSB(B, 64)
|
||||
copy(intermediate[ii*8:ii*8+8], block[8:])
|
||||
}
|
||||
}
|
||||
|
||||
// 3) Output results.
|
||||
// - If A is an appropriate initial value (see 2.2.3),
|
||||
for ii := 0; ii < 8; ii++ {
|
||||
if block[ii] != 0xA6 {
|
||||
return nil, ErrUnwrapFailed
|
||||
}
|
||||
}
|
||||
|
||||
// - For i = 1 to n
|
||||
// - P[i] = R[i]
|
||||
return intermediate, nil
|
||||
}
|
||||
|
|
@ -4,33 +4,25 @@
|
|||
|
||||
// Package armor implements OpenPGP ASCII Armor, see RFC 4880. OpenPGP Armor is
|
||||
// very similar to PEM except that it has an additional CRC checksum.
|
||||
//
|
||||
// Deprecated: this package is unmaintained except for security fixes. New
|
||||
// applications should consider a more focused, modern alternative to OpenPGP
|
||||
// for their specific task. If you are required to interoperate with OpenPGP
|
||||
// systems and need a maintained package, consider a community fork.
|
||||
// See https://golang.org/issue/44226.
|
||||
package armor // import "golang.org/x/crypto/openpgp/armor"
|
||||
package armor // import "github.com/ProtonMail/go-crypto/openpgp/armor"
|
||||
|
||||
import (
|
||||
"bufio"
|
||||
"bytes"
|
||||
"encoding/base64"
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"io"
|
||||
)
|
||||
|
||||
// A Block represents an OpenPGP armored structure.
|
||||
//
|
||||
// The encoded form is:
|
||||
// -----BEGIN Type-----
|
||||
// Headers
|
||||
//
|
||||
// -----BEGIN Type-----
|
||||
// Headers
|
||||
//
|
||||
// base64-encoded Bytes
|
||||
// '=' base64 encoded checksum
|
||||
// -----END Type-----
|
||||
//
|
||||
// base64-encoded Bytes
|
||||
// '=' base64 encoded checksum
|
||||
// -----END Type-----
|
||||
// where Headers is a possibly empty sequence of Key: Value lines.
|
||||
//
|
||||
// Since the armored data can be very large, this package presents a streaming
|
||||
|
|
@ -156,7 +148,7 @@ func (r *openpgpReader) Read(p []byte) (n int, err error) {
|
|||
n, err = r.b64Reader.Read(p)
|
||||
r.currentCRC = crc24(r.currentCRC, p[:n])
|
||||
|
||||
if err == io.EOF && r.lReader.crcSet && r.lReader.crc != r.currentCRC&crc24Mask {
|
||||
if err == io.EOF && r.lReader.crcSet && r.lReader.crc != uint32(r.currentCRC&crc24Mask) {
|
||||
return 0, ArmorCorrupt
|
||||
}
|
||||
|
||||
|
|
@ -96,8 +96,7 @@ func (l *lineBreaker) Close() (err error) {
|
|||
// trailer.
|
||||
//
|
||||
// It's built into a stack of io.Writers:
|
||||
//
|
||||
// encoding -> base64 encoder -> lineBreaker -> out
|
||||
// encoding -> base64 encoder -> lineBreaker -> out
|
||||
type encoding struct {
|
||||
out io.Writer
|
||||
breaker *lineBreaker
|
||||
|
|
@ -4,7 +4,10 @@
|
|||
|
||||
package openpgp
|
||||
|
||||
import "hash"
|
||||
import (
|
||||
"hash"
|
||||
"io"
|
||||
)
|
||||
|
||||
// NewCanonicalTextHash reformats text written to it into the canonical
|
||||
// form and then applies the hash h. See RFC 4880, section 5.2.1.
|
||||
|
|
@ -19,28 +22,31 @@ type canonicalTextHash struct {
|
|||
|
||||
var newline = []byte{'\r', '\n'}
|
||||
|
||||
func (cth *canonicalTextHash) Write(buf []byte) (int, error) {
|
||||
func writeCanonical(cw io.Writer, buf []byte, s *int) (int, error) {
|
||||
start := 0
|
||||
|
||||
for i, c := range buf {
|
||||
switch cth.s {
|
||||
switch *s {
|
||||
case 0:
|
||||
if c == '\r' {
|
||||
cth.s = 1
|
||||
*s = 1
|
||||
} else if c == '\n' {
|
||||
cth.h.Write(buf[start:i])
|
||||
cth.h.Write(newline)
|
||||
cw.Write(buf[start:i])
|
||||
cw.Write(newline)
|
||||
start = i + 1
|
||||
}
|
||||
case 1:
|
||||
cth.s = 0
|
||||
*s = 0
|
||||
}
|
||||
}
|
||||
|
||||
cth.h.Write(buf[start:])
|
||||
cw.Write(buf[start:])
|
||||
return len(buf), nil
|
||||
}
|
||||
|
||||
func (cth *canonicalTextHash) Write(buf []byte) (int, error) {
|
||||
return writeCanonical(cth.h, buf, &cth.s)
|
||||
}
|
||||
|
||||
func (cth *canonicalTextHash) Sum(in []byte) []byte {
|
||||
return cth.h.Sum(in)
|
||||
}
|
||||
|
|
@ -0,0 +1,206 @@
|
|||
// Copyright 2017 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package ecdh implements ECDH encryption, suitable for OpenPGP,
|
||||
// as specified in RFC 6637, section 8.
|
||||
package ecdh
|
||||
|
||||
import (
|
||||
"bytes"
|
||||
"errors"
|
||||
"io"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/aes/keywrap"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/algorithm"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/ecc"
|
||||
)
|
||||
|
||||
type KDF struct {
|
||||
Hash algorithm.Hash
|
||||
Cipher algorithm.Cipher
|
||||
}
|
||||
|
||||
type PublicKey struct {
|
||||
curve ecc.ECDHCurve
|
||||
Point []byte
|
||||
KDF
|
||||
}
|
||||
|
||||
type PrivateKey struct {
|
||||
PublicKey
|
||||
D []byte
|
||||
}
|
||||
|
||||
func NewPublicKey(curve ecc.ECDHCurve, kdfHash algorithm.Hash, kdfCipher algorithm.Cipher) *PublicKey {
|
||||
return &PublicKey{
|
||||
curve: curve,
|
||||
KDF: KDF{
|
||||
Hash: kdfHash,
|
||||
Cipher: kdfCipher,
|
||||
},
|
||||
}
|
||||
}
|
||||
|
||||
func NewPrivateKey(key PublicKey) *PrivateKey {
|
||||
return &PrivateKey{
|
||||
PublicKey: key,
|
||||
}
|
||||
}
|
||||
|
||||
func (pk *PublicKey) GetCurve() ecc.ECDHCurve {
|
||||
return pk.curve
|
||||
}
|
||||
|
||||
func (pk *PublicKey) MarshalPoint() []byte {
|
||||
return pk.curve.MarshalBytePoint(pk.Point)
|
||||
}
|
||||
|
||||
func (pk *PublicKey) UnmarshalPoint(p []byte) error {
|
||||
pk.Point = pk.curve.UnmarshalBytePoint(p)
|
||||
if pk.Point == nil {
|
||||
return errors.New("ecdh: failed to parse EC point")
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
func (sk *PrivateKey) MarshalByteSecret() []byte {
|
||||
return sk.curve.MarshalByteSecret(sk.D)
|
||||
}
|
||||
|
||||
func (sk *PrivateKey) UnmarshalByteSecret(d []byte) error {
|
||||
sk.D = sk.curve.UnmarshalByteSecret(d)
|
||||
|
||||
if sk.D == nil {
|
||||
return errors.New("ecdh: failed to parse scalar")
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
func GenerateKey(rand io.Reader, c ecc.ECDHCurve, kdf KDF) (priv *PrivateKey, err error) {
|
||||
priv = new(PrivateKey)
|
||||
priv.PublicKey.curve = c
|
||||
priv.PublicKey.KDF = kdf
|
||||
priv.PublicKey.Point, priv.D, err = c.GenerateECDH(rand)
|
||||
return
|
||||
}
|
||||
|
||||
func Encrypt(random io.Reader, pub *PublicKey, msg, curveOID, fingerprint []byte) (vsG, c []byte, err error) {
|
||||
if len(msg) > 40 {
|
||||
return nil, nil, errors.New("ecdh: message too long")
|
||||
}
|
||||
// the sender MAY use 21, 13, and 5 bytes of padding for AES-128,
|
||||
// AES-192, and AES-256, respectively, to provide the same number of
|
||||
// octets, 40 total, as an input to the key wrapping method.
|
||||
padding := make([]byte, 40-len(msg))
|
||||
for i := range padding {
|
||||
padding[i] = byte(40 - len(msg))
|
||||
}
|
||||
m := append(msg, padding...)
|
||||
|
||||
ephemeral, zb, err := pub.curve.Encaps(random, pub.Point)
|
||||
if err != nil {
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
vsG = pub.curve.MarshalBytePoint(ephemeral)
|
||||
|
||||
z, err := buildKey(pub, zb, curveOID, fingerprint, false, false)
|
||||
if err != nil {
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
if c, err = keywrap.Wrap(z, m); err != nil {
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
return vsG, c, nil
|
||||
|
||||
}
|
||||
|
||||
func Decrypt(priv *PrivateKey, vsG, c, curveOID, fingerprint []byte) (msg []byte, err error) {
|
||||
var m []byte
|
||||
zb, err := priv.PublicKey.curve.Decaps(priv.curve.UnmarshalBytePoint(vsG), priv.D)
|
||||
|
||||
// Try buildKey three times to workaround an old bug, see comments in buildKey.
|
||||
for i := 0; i < 3; i++ {
|
||||
var z []byte
|
||||
// RFC6637 §8: "Compute Z = KDF( S, Z_len, Param );"
|
||||
z, err = buildKey(&priv.PublicKey, zb, curveOID, fingerprint, i == 1, i == 2)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
// RFC6637 §8: "Compute C = AESKeyWrap( Z, c ) as per [RFC3394]"
|
||||
m, err = keywrap.Unwrap(z, c)
|
||||
if err == nil {
|
||||
break
|
||||
}
|
||||
}
|
||||
|
||||
// Only return an error after we've tried all (required) variants of buildKey.
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
// RFC6637 §8: "m = symm_alg_ID || session key || checksum || pkcs5_padding"
|
||||
// The last byte should be the length of the padding, as per PKCS5; strip it off.
|
||||
return m[:len(m)-int(m[len(m)-1])], nil
|
||||
}
|
||||
|
||||
func buildKey(pub *PublicKey, zb []byte, curveOID, fingerprint []byte, stripLeading, stripTrailing bool) ([]byte, error) {
|
||||
// Param = curve_OID_len || curve_OID || public_key_alg_ID || 03
|
||||
// || 01 || KDF_hash_ID || KEK_alg_ID for AESKeyWrap
|
||||
// || "Anonymous Sender " || recipient_fingerprint;
|
||||
param := new(bytes.Buffer)
|
||||
if _, err := param.Write(curveOID); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
algKDF := []byte{18, 3, 1, pub.KDF.Hash.Id(), pub.KDF.Cipher.Id()}
|
||||
if _, err := param.Write(algKDF); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
if _, err := param.Write([]byte("Anonymous Sender ")); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
// For v5 keys, the 20 leftmost octets of the fingerprint are used.
|
||||
if _, err := param.Write(fingerprint[:20]); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
if param.Len() - len(curveOID) != 45 {
|
||||
return nil, errors.New("ecdh: malformed KDF Param")
|
||||
}
|
||||
|
||||
// MB = Hash ( 00 || 00 || 00 || 01 || ZB || Param );
|
||||
h := pub.KDF.Hash.New()
|
||||
if _, err := h.Write([]byte{0x0, 0x0, 0x0, 0x1}); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
zbLen := len(zb)
|
||||
i := 0
|
||||
j := zbLen - 1
|
||||
if stripLeading {
|
||||
// Work around old go crypto bug where the leading zeros are missing.
|
||||
for ; i < zbLen && zb[i] == 0; i++ {}
|
||||
}
|
||||
if stripTrailing {
|
||||
// Work around old OpenPGP.js bug where insignificant trailing zeros in
|
||||
// this little-endian number are missing.
|
||||
// (See https://github.com/openpgpjs/openpgpjs/pull/853.)
|
||||
for ; j >= 0 && zb[j] == 0; j-- {}
|
||||
}
|
||||
if _, err := h.Write(zb[i:j+1]); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
if _, err := h.Write(param.Bytes()); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
mb := h.Sum(nil)
|
||||
|
||||
return mb[:pub.KDF.Cipher.KeySize()], nil // return oBits leftmost bits of MB.
|
||||
|
||||
}
|
||||
|
||||
func Validate(priv *PrivateKey) error {
|
||||
return priv.curve.ValidateECDH(priv.Point, priv.D)
|
||||
}
|
||||
|
|
@ -0,0 +1,80 @@
|
|||
// Package ecdsa implements ECDSA signature, suitable for OpenPGP,
|
||||
// as specified in RFC 6637, section 5.
|
||||
package ecdsa
|
||||
|
||||
import (
|
||||
"errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/ecc"
|
||||
"io"
|
||||
"math/big"
|
||||
)
|
||||
|
||||
type PublicKey struct {
|
||||
X, Y *big.Int
|
||||
curve ecc.ECDSACurve
|
||||
}
|
||||
|
||||
type PrivateKey struct {
|
||||
PublicKey
|
||||
D *big.Int
|
||||
}
|
||||
|
||||
func NewPublicKey(curve ecc.ECDSACurve) *PublicKey {
|
||||
return &PublicKey{
|
||||
curve: curve,
|
||||
}
|
||||
}
|
||||
|
||||
func NewPrivateKey(key PublicKey) *PrivateKey {
|
||||
return &PrivateKey{
|
||||
PublicKey: key,
|
||||
}
|
||||
}
|
||||
|
||||
func (pk *PublicKey) GetCurve() ecc.ECDSACurve {
|
||||
return pk.curve
|
||||
}
|
||||
|
||||
func (pk *PublicKey) MarshalPoint() []byte {
|
||||
return pk.curve.MarshalIntegerPoint(pk.X, pk.Y)
|
||||
}
|
||||
|
||||
func (pk *PublicKey) UnmarshalPoint(p []byte) error {
|
||||
pk.X, pk.Y = pk.curve.UnmarshalIntegerPoint(p)
|
||||
if pk.X == nil {
|
||||
return errors.New("ecdsa: failed to parse EC point")
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
func (sk *PrivateKey) MarshalIntegerSecret() []byte {
|
||||
return sk.curve.MarshalIntegerSecret(sk.D)
|
||||
}
|
||||
|
||||
func (sk *PrivateKey) UnmarshalIntegerSecret(d []byte) error {
|
||||
sk.D = sk.curve.UnmarshalIntegerSecret(d)
|
||||
|
||||
if sk.D == nil {
|
||||
return errors.New("ecdsa: failed to parse scalar")
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
func GenerateKey(rand io.Reader, c ecc.ECDSACurve) (priv *PrivateKey, err error) {
|
||||
priv = new(PrivateKey)
|
||||
priv.PublicKey.curve = c
|
||||
priv.PublicKey.X, priv.PublicKey.Y, priv.D, err = c.GenerateECDSA(rand)
|
||||
return
|
||||
}
|
||||
|
||||
func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err error) {
|
||||
return priv.PublicKey.curve.Sign(rand, priv.X, priv.Y, priv.D, hash)
|
||||
}
|
||||
|
||||
func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool {
|
||||
return pub.curve.Verify(pub.X, pub.Y, hash, r, s)
|
||||
}
|
||||
|
||||
func Validate(priv *PrivateKey) error {
|
||||
return priv.curve.ValidateECDSA(priv.X, priv.Y, priv.D.Bytes())
|
||||
}
|
||||
|
|
@ -0,0 +1,91 @@
|
|||
// Package eddsa implements EdDSA signature, suitable for OpenPGP, as specified in
|
||||
// https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-13.7
|
||||
package eddsa
|
||||
|
||||
import (
|
||||
"errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/ecc"
|
||||
"io"
|
||||
)
|
||||
|
||||
type PublicKey struct {
|
||||
X []byte
|
||||
curve ecc.EdDSACurve
|
||||
}
|
||||
|
||||
type PrivateKey struct {
|
||||
PublicKey
|
||||
D []byte
|
||||
}
|
||||
|
||||
func NewPublicKey(curve ecc.EdDSACurve) *PublicKey {
|
||||
return &PublicKey{
|
||||
curve: curve,
|
||||
}
|
||||
}
|
||||
|
||||
func NewPrivateKey(key PublicKey) *PrivateKey {
|
||||
return &PrivateKey{
|
||||
PublicKey: key,
|
||||
}
|
||||
}
|
||||
|
||||
func (pk *PublicKey) GetCurve() ecc.EdDSACurve {
|
||||
return pk.curve
|
||||
}
|
||||
|
||||
func (pk *PublicKey) MarshalPoint() []byte {
|
||||
return pk.curve.MarshalBytePoint(pk.X)
|
||||
}
|
||||
|
||||
func (pk *PublicKey) UnmarshalPoint(x []byte) error {
|
||||
pk.X = pk.curve.UnmarshalBytePoint(x)
|
||||
|
||||
if pk.X == nil {
|
||||
return errors.New("eddsa: failed to parse EC point")
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
func (sk *PrivateKey) MarshalByteSecret() []byte {
|
||||
return sk.curve.MarshalByteSecret(sk.D)
|
||||
}
|
||||
|
||||
func (sk *PrivateKey) UnmarshalByteSecret(d []byte) error {
|
||||
sk.D = sk.curve.UnmarshalByteSecret(d)
|
||||
|
||||
if sk.D == nil {
|
||||
return errors.New("eddsa: failed to parse scalar")
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
func GenerateKey(rand io.Reader, c ecc.EdDSACurve) (priv *PrivateKey, err error) {
|
||||
priv = new(PrivateKey)
|
||||
priv.PublicKey.curve = c
|
||||
priv.PublicKey.X, priv.D, err = c.GenerateEdDSA(rand)
|
||||
return
|
||||
}
|
||||
|
||||
func Sign(priv *PrivateKey, message []byte) (r, s []byte, err error) {
|
||||
sig, err := priv.PublicKey.curve.Sign(priv.PublicKey.X, priv.D, message)
|
||||
if err != nil {
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
r, s = priv.PublicKey.curve.MarshalSignature(sig)
|
||||
return
|
||||
}
|
||||
|
||||
func Verify(pub *PublicKey, message, r, s []byte) bool {
|
||||
sig := pub.curve.UnmarshalSignature(r, s)
|
||||
if sig == nil {
|
||||
return false
|
||||
}
|
||||
|
||||
return pub.curve.Verify(pub.X, message, sig)
|
||||
}
|
||||
|
||||
func Validate(priv *PrivateKey) error {
|
||||
return priv.curve.ValidateEdDSA(priv.PublicKey.X, priv.D)
|
||||
}
|
||||
|
|
@ -10,13 +10,7 @@
|
|||
// This form of ElGamal embeds PKCS#1 v1.5 padding, which may make it
|
||||
// unsuitable for other protocols. RSA should be used in preference in any
|
||||
// case.
|
||||
//
|
||||
// Deprecated: this package was only provided to support ElGamal encryption in
|
||||
// OpenPGP. The golang.org/x/crypto/openpgp package is now deprecated (see
|
||||
// https://golang.org/issue/44226), and ElGamal in the OpenPGP ecosystem has
|
||||
// compatibility and security issues (see https://eprint.iacr.org/2021/923).
|
||||
// Moreover, this package doesn't protect against side-channel attacks.
|
||||
package elgamal // import "golang.org/x/crypto/openpgp/elgamal"
|
||||
package elgamal // import "github.com/ProtonMail/go-crypto/openpgp/elgamal"
|
||||
|
||||
import (
|
||||
"crypto/rand"
|
||||
|
|
@ -77,8 +71,8 @@ func Encrypt(random io.Reader, pub *PublicKey, msg []byte) (c1, c2 *big.Int, err
|
|||
// returns the plaintext of the message. An error can result only if the
|
||||
// ciphertext is invalid. Users should keep in mind that this is a padding
|
||||
// oracle and thus, if exposed to an adaptive chosen ciphertext attack, can
|
||||
// be used to break the cryptosystem. See “Chosen Ciphertext Attacks
|
||||
// Against Protocols Based on the RSA Encryption Standard PKCS #1”, Daniel
|
||||
// be used to break the cryptosystem. See ``Chosen Ciphertext Attacks
|
||||
// Against Protocols Based on the RSA Encryption Standard PKCS #1'', Daniel
|
||||
// Bleichenbacher, Advances in Cryptology (Crypto '98),
|
||||
func Decrypt(priv *PrivateKey, c1, c2 *big.Int) (msg []byte, err error) {
|
||||
s := new(big.Int).Exp(c1, priv.X, priv.P)
|
||||
|
|
@ -3,13 +3,7 @@
|
|||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package errors contains common error types for the OpenPGP packages.
|
||||
//
|
||||
// Deprecated: this package is unmaintained except for security fixes. New
|
||||
// applications should consider a more focused, modern alternative to OpenPGP
|
||||
// for their specific task. If you are required to interoperate with OpenPGP
|
||||
// systems and need a maintained package, consider a community fork.
|
||||
// See https://golang.org/issue/44226.
|
||||
package errors // import "golang.org/x/crypto/openpgp/errors"
|
||||
package errors // import "github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
|
||||
import (
|
||||
"strconv"
|
||||
|
|
@ -47,6 +41,25 @@ func (b SignatureError) Error() string {
|
|||
return "openpgp: invalid signature: " + string(b)
|
||||
}
|
||||
|
||||
var ErrMDCHashMismatch error = SignatureError("MDC hash mismatch")
|
||||
var ErrMDCMissing error = SignatureError("MDC packet not found")
|
||||
|
||||
type signatureExpiredError int
|
||||
|
||||
func (se signatureExpiredError) Error() string {
|
||||
return "openpgp: signature expired"
|
||||
}
|
||||
|
||||
var ErrSignatureExpired error = signatureExpiredError(0)
|
||||
|
||||
type keyExpiredError int
|
||||
|
||||
func (ke keyExpiredError) Error() string {
|
||||
return "openpgp: key expired"
|
||||
}
|
||||
|
||||
var ErrKeyExpired error = keyExpiredError(0)
|
||||
|
||||
type keyIncorrectError int
|
||||
|
||||
func (ki keyIncorrectError) Error() string {
|
||||
|
|
@ -55,6 +68,14 @@ func (ki keyIncorrectError) Error() string {
|
|||
|
||||
var ErrKeyIncorrect error = keyIncorrectError(0)
|
||||
|
||||
// KeyInvalidError indicates that the public key parameters are invalid
|
||||
// as they do not match the private ones
|
||||
type KeyInvalidError string
|
||||
|
||||
func (e KeyInvalidError) Error() string {
|
||||
return "openpgp: invalid key: " + string(e)
|
||||
}
|
||||
|
||||
type unknownIssuerError int
|
||||
|
||||
func (unknownIssuerError) Error() string {
|
||||
|
|
@ -76,3 +97,20 @@ type UnknownPacketTypeError uint8
|
|||
func (upte UnknownPacketTypeError) Error() string {
|
||||
return "openpgp: unknown packet type: " + strconv.Itoa(int(upte))
|
||||
}
|
||||
|
||||
// AEADError indicates that there is a problem when initializing or using a
|
||||
// AEAD instance, configuration struct, nonces or index values.
|
||||
type AEADError string
|
||||
|
||||
func (ae AEADError) Error() string {
|
||||
return "openpgp: aead error: " + string(ae)
|
||||
}
|
||||
|
||||
// ErrDummyPrivateKey results when operations are attempted on a private key
|
||||
// that is just a dummy key. See
|
||||
// https://git.gnupg.org/cgi-bin/gitweb.cgi?p=gnupg.git;a=blob;f=doc/DETAILS;h=fe55ae16ab4e26d8356dc574c9e8bc935e71aef1;hb=23191d7851eae2217ecdac6484349849a24fd94a#l1109
|
||||
type ErrDummyPrivateKey string
|
||||
|
||||
func (dke ErrDummyPrivateKey) Error() string {
|
||||
return "openpgp: s2k GNU dummy key: " + string(dke)
|
||||
}
|
||||
65
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/aead.go
generated
vendored
Normal file
65
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/aead.go
generated
vendored
Normal file
|
|
@ -0,0 +1,65 @@
|
|||
// Copyright (C) 2019 ProtonTech AG
|
||||
|
||||
package algorithm
|
||||
|
||||
import (
|
||||
"crypto/cipher"
|
||||
"github.com/ProtonMail/go-crypto/eax"
|
||||
"github.com/ProtonMail/go-crypto/ocb"
|
||||
)
|
||||
|
||||
// AEADMode defines the Authenticated Encryption with Associated Data mode of
|
||||
// operation.
|
||||
type AEADMode uint8
|
||||
|
||||
// Supported modes of operation (see RFC4880bis [EAX] and RFC7253)
|
||||
const (
|
||||
AEADModeEAX = AEADMode(1)
|
||||
AEADModeOCB = AEADMode(2)
|
||||
AEADModeGCM = AEADMode(3)
|
||||
)
|
||||
|
||||
// TagLength returns the length in bytes of authentication tags.
|
||||
func (mode AEADMode) TagLength() int {
|
||||
switch mode {
|
||||
case AEADModeEAX:
|
||||
return 16
|
||||
case AEADModeOCB:
|
||||
return 16
|
||||
case AEADModeGCM:
|
||||
return 16
|
||||
default:
|
||||
return 0
|
||||
}
|
||||
}
|
||||
|
||||
// NonceLength returns the length in bytes of nonces.
|
||||
func (mode AEADMode) NonceLength() int {
|
||||
switch mode {
|
||||
case AEADModeEAX:
|
||||
return 16
|
||||
case AEADModeOCB:
|
||||
return 15
|
||||
case AEADModeGCM:
|
||||
return 12
|
||||
default:
|
||||
return 0
|
||||
}
|
||||
}
|
||||
|
||||
// New returns a fresh instance of the given mode
|
||||
func (mode AEADMode) New(block cipher.Block) (alg cipher.AEAD) {
|
||||
var err error
|
||||
switch mode {
|
||||
case AEADModeEAX:
|
||||
alg, err = eax.NewEAX(block)
|
||||
case AEADModeOCB:
|
||||
alg, err = ocb.NewOCB(block)
|
||||
case AEADModeGCM:
|
||||
alg, err = cipher.NewGCM(block)
|
||||
}
|
||||
if err != nil {
|
||||
panic(err.Error())
|
||||
}
|
||||
return alg
|
||||
}
|
||||
107
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/cipher.go
generated
vendored
Normal file
107
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/cipher.go
generated
vendored
Normal file
|
|
@ -0,0 +1,107 @@
|
|||
// Copyright 2017 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package algorithm
|
||||
|
||||
import (
|
||||
"crypto/aes"
|
||||
"crypto/cipher"
|
||||
"crypto/des"
|
||||
|
||||
"golang.org/x/crypto/cast5"
|
||||
)
|
||||
|
||||
// Cipher is an official symmetric key cipher algorithm. See RFC 4880,
|
||||
// section 9.2.
|
||||
type Cipher interface {
|
||||
// Id returns the algorithm ID, as a byte, of the cipher.
|
||||
Id() uint8
|
||||
// KeySize returns the key size, in bytes, of the cipher.
|
||||
KeySize() int
|
||||
// BlockSize returns the block size, in bytes, of the cipher.
|
||||
BlockSize() int
|
||||
// New returns a fresh instance of the given cipher.
|
||||
New(key []byte) cipher.Block
|
||||
}
|
||||
|
||||
// The following constants mirror the OpenPGP standard (RFC 4880).
|
||||
const (
|
||||
TripleDES = CipherFunction(2)
|
||||
CAST5 = CipherFunction(3)
|
||||
AES128 = CipherFunction(7)
|
||||
AES192 = CipherFunction(8)
|
||||
AES256 = CipherFunction(9)
|
||||
)
|
||||
|
||||
// CipherById represents the different block ciphers specified for OpenPGP. See
|
||||
// http://www.iana.org/assignments/pgp-parameters/pgp-parameters.xhtml#pgp-parameters-13
|
||||
var CipherById = map[uint8]Cipher{
|
||||
TripleDES.Id(): TripleDES,
|
||||
CAST5.Id(): CAST5,
|
||||
AES128.Id(): AES128,
|
||||
AES192.Id(): AES192,
|
||||
AES256.Id(): AES256,
|
||||
}
|
||||
|
||||
type CipherFunction uint8
|
||||
|
||||
// ID returns the algorithm Id, as a byte, of cipher.
|
||||
func (sk CipherFunction) Id() uint8 {
|
||||
return uint8(sk)
|
||||
}
|
||||
|
||||
var keySizeByID = map[uint8]int{
|
||||
TripleDES.Id(): 24,
|
||||
CAST5.Id(): cast5.KeySize,
|
||||
AES128.Id(): 16,
|
||||
AES192.Id(): 24,
|
||||
AES256.Id(): 32,
|
||||
}
|
||||
|
||||
// KeySize returns the key size, in bytes, of cipher.
|
||||
func (cipher CipherFunction) KeySize() int {
|
||||
switch cipher {
|
||||
case TripleDES:
|
||||
return 24
|
||||
case CAST5:
|
||||
return cast5.KeySize
|
||||
case AES128:
|
||||
return 16
|
||||
case AES192:
|
||||
return 24
|
||||
case AES256:
|
||||
return 32
|
||||
}
|
||||
return 0
|
||||
}
|
||||
|
||||
// BlockSize returns the block size, in bytes, of cipher.
|
||||
func (cipher CipherFunction) BlockSize() int {
|
||||
switch cipher {
|
||||
case TripleDES:
|
||||
return des.BlockSize
|
||||
case CAST5:
|
||||
return 8
|
||||
case AES128, AES192, AES256:
|
||||
return 16
|
||||
}
|
||||
return 0
|
||||
}
|
||||
|
||||
// New returns a fresh instance of the given cipher.
|
||||
func (cipher CipherFunction) New(key []byte) (block cipher.Block) {
|
||||
var err error
|
||||
switch cipher {
|
||||
case TripleDES:
|
||||
block, err = des.NewTripleDESCipher(key)
|
||||
case CAST5:
|
||||
block, err = cast5.NewCipher(key)
|
||||
case AES128, AES192, AES256:
|
||||
block, err = aes.NewCipher(key)
|
||||
}
|
||||
if err != nil {
|
||||
panic(err.Error())
|
||||
}
|
||||
return
|
||||
}
|
||||
143
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/hash.go
generated
vendored
Normal file
143
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/hash.go
generated
vendored
Normal file
|
|
@ -0,0 +1,143 @@
|
|||
// Copyright 2017 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package algorithm
|
||||
|
||||
import (
|
||||
"crypto"
|
||||
"fmt"
|
||||
"hash"
|
||||
)
|
||||
|
||||
// Hash is an official hash function algorithm. See RFC 4880, section 9.4.
|
||||
type Hash interface {
|
||||
// Id returns the algorithm ID, as a byte, of Hash.
|
||||
Id() uint8
|
||||
// Available reports whether the given hash function is linked into the binary.
|
||||
Available() bool
|
||||
// HashFunc simply returns the value of h so that Hash implements SignerOpts.
|
||||
HashFunc() crypto.Hash
|
||||
// New returns a new hash.Hash calculating the given hash function. New
|
||||
// panics if the hash function is not linked into the binary.
|
||||
New() hash.Hash
|
||||
// Size returns the length, in bytes, of a digest resulting from the given
|
||||
// hash function. It doesn't require that the hash function in question be
|
||||
// linked into the program.
|
||||
Size() int
|
||||
// String is the name of the hash function corresponding to the given
|
||||
// OpenPGP hash id.
|
||||
String() string
|
||||
}
|
||||
|
||||
// The following vars mirror the crypto/Hash supported hash functions.
|
||||
var (
|
||||
SHA1 Hash = cryptoHash{2, crypto.SHA1}
|
||||
SHA256 Hash = cryptoHash{8, crypto.SHA256}
|
||||
SHA384 Hash = cryptoHash{9, crypto.SHA384}
|
||||
SHA512 Hash = cryptoHash{10, crypto.SHA512}
|
||||
SHA224 Hash = cryptoHash{11, crypto.SHA224}
|
||||
SHA3_256 Hash = cryptoHash{12, crypto.SHA3_256}
|
||||
SHA3_512 Hash = cryptoHash{14, crypto.SHA3_512}
|
||||
)
|
||||
|
||||
// HashById represents the different hash functions specified for OpenPGP. See
|
||||
// http://www.iana.org/assignments/pgp-parameters/pgp-parameters.xhtml#pgp-parameters-14
|
||||
var (
|
||||
HashById = map[uint8]Hash{
|
||||
SHA256.Id(): SHA256,
|
||||
SHA384.Id(): SHA384,
|
||||
SHA512.Id(): SHA512,
|
||||
SHA224.Id(): SHA224,
|
||||
SHA3_256.Id(): SHA3_256,
|
||||
SHA3_512.Id(): SHA3_512,
|
||||
}
|
||||
)
|
||||
|
||||
// cryptoHash contains pairs relating OpenPGP's hash identifier with
|
||||
// Go's crypto.Hash type. See RFC 4880, section 9.4.
|
||||
type cryptoHash struct {
|
||||
id uint8
|
||||
crypto.Hash
|
||||
}
|
||||
|
||||
// Id returns the algorithm ID, as a byte, of cryptoHash.
|
||||
func (h cryptoHash) Id() uint8 {
|
||||
return h.id
|
||||
}
|
||||
|
||||
var hashNames = map[uint8]string{
|
||||
SHA256.Id(): "SHA256",
|
||||
SHA384.Id(): "SHA384",
|
||||
SHA512.Id(): "SHA512",
|
||||
SHA224.Id(): "SHA224",
|
||||
SHA3_256.Id(): "SHA3-256",
|
||||
SHA3_512.Id(): "SHA3-512",
|
||||
}
|
||||
|
||||
func (h cryptoHash) String() string {
|
||||
s, ok := hashNames[h.id]
|
||||
if !ok {
|
||||
panic(fmt.Sprintf("Unsupported hash function %d", h.id))
|
||||
}
|
||||
return s
|
||||
}
|
||||
|
||||
// HashIdToHash returns a crypto.Hash which corresponds to the given OpenPGP
|
||||
// hash id.
|
||||
func HashIdToHash(id byte) (h crypto.Hash, ok bool) {
|
||||
if hash, ok := HashById[id]; ok {
|
||||
return hash.HashFunc(), true
|
||||
}
|
||||
return 0, false
|
||||
}
|
||||
|
||||
// HashIdToHashWithSha1 returns a crypto.Hash which corresponds to the given OpenPGP
|
||||
// hash id, allowing sha1.
|
||||
func HashIdToHashWithSha1(id byte) (h crypto.Hash, ok bool) {
|
||||
if hash, ok := HashById[id]; ok {
|
||||
return hash.HashFunc(), true
|
||||
}
|
||||
|
||||
if id == SHA1.Id() {
|
||||
return SHA1.HashFunc(), true
|
||||
}
|
||||
|
||||
return 0, false
|
||||
}
|
||||
|
||||
// HashIdToString returns the name of the hash function corresponding to the
|
||||
// given OpenPGP hash id.
|
||||
func HashIdToString(id byte) (name string, ok bool) {
|
||||
if hash, ok := HashById[id]; ok {
|
||||
return hash.String(), true
|
||||
}
|
||||
return "", false
|
||||
}
|
||||
|
||||
// HashToHashId returns an OpenPGP hash id which corresponds the given Hash.
|
||||
func HashToHashId(h crypto.Hash) (id byte, ok bool) {
|
||||
for id, hash := range HashById {
|
||||
if hash.HashFunc() == h {
|
||||
return id, true
|
||||
}
|
||||
}
|
||||
|
||||
return 0, false
|
||||
}
|
||||
|
||||
// HashToHashIdWithSha1 returns an OpenPGP hash id which corresponds the given Hash,
|
||||
// allowing instances of SHA1
|
||||
func HashToHashIdWithSha1(h crypto.Hash) (id byte, ok bool) {
|
||||
for id, hash := range HashById {
|
||||
if hash.HashFunc() == h {
|
||||
return id, true
|
||||
}
|
||||
}
|
||||
|
||||
if h == SHA1.HashFunc() {
|
||||
return SHA1.Id(), true
|
||||
}
|
||||
|
||||
return 0, false
|
||||
}
|
||||
171
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curve25519.go
generated
vendored
Normal file
171
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curve25519.go
generated
vendored
Normal file
|
|
@ -0,0 +1,171 @@
|
|||
// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
|
||||
package ecc
|
||||
|
||||
import (
|
||||
"crypto/subtle"
|
||||
"io"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
x25519lib "github.com/cloudflare/circl/dh/x25519"
|
||||
)
|
||||
|
||||
type curve25519 struct {}
|
||||
|
||||
func NewCurve25519() *curve25519 {
|
||||
return &curve25519{}
|
||||
}
|
||||
|
||||
func (c *curve25519) GetCurveName() string {
|
||||
return "curve25519"
|
||||
}
|
||||
|
||||
// MarshalBytePoint encodes the public point from native format, adding the prefix.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6
|
||||
func (c *curve25519) MarshalBytePoint(point [] byte) []byte {
|
||||
return append([]byte{0x40}, point...)
|
||||
}
|
||||
|
||||
// UnmarshalBytePoint decodes the public point to native format, removing the prefix.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6
|
||||
func (c *curve25519) UnmarshalBytePoint(point []byte) []byte {
|
||||
if len(point) != x25519lib.Size + 1 {
|
||||
return nil
|
||||
}
|
||||
|
||||
// Remove prefix
|
||||
return point[1:]
|
||||
}
|
||||
|
||||
// MarshalByteSecret encodes the secret scalar from native format.
|
||||
// Note that the EC secret scalar differs from the definition of public keys in
|
||||
// [Curve25519] in two ways: (1) the byte-ordering is big-endian, which is
|
||||
// more uniform with how big integers are represented in OpenPGP, and (2) the
|
||||
// leading zeros are truncated.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6.1.1
|
||||
// Note that leading zero bytes are stripped later when encoding as an MPI.
|
||||
func (c *curve25519) MarshalByteSecret(secret []byte) []byte {
|
||||
d := make([]byte, x25519lib.Size)
|
||||
copyReversed(d, secret)
|
||||
|
||||
// The following ensures that the private key is a number of the form
|
||||
// 2^{254} + 8 * [0, 2^{251}), in order to avoid the small subgroup of
|
||||
// the curve.
|
||||
//
|
||||
// This masking is done internally in the underlying lib and so is unnecessary
|
||||
// for security, but OpenPGP implementations require that private keys be
|
||||
// pre-masked.
|
||||
d[0] &= 127
|
||||
d[0] |= 64
|
||||
d[31] &= 248
|
||||
|
||||
return d
|
||||
}
|
||||
|
||||
// UnmarshalByteSecret decodes the secret scalar from native format.
|
||||
// Note that the EC secret scalar differs from the definition of public keys in
|
||||
// [Curve25519] in two ways: (1) the byte-ordering is big-endian, which is
|
||||
// more uniform with how big integers are represented in OpenPGP, and (2) the
|
||||
// leading zeros are truncated.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6.1.1
|
||||
func (c *curve25519) UnmarshalByteSecret(d []byte) []byte {
|
||||
if len(d) > x25519lib.Size {
|
||||
return nil
|
||||
}
|
||||
|
||||
// Ensure truncated leading bytes are re-added
|
||||
secret := make([]byte, x25519lib.Size)
|
||||
copyReversed(secret, d)
|
||||
|
||||
return secret
|
||||
}
|
||||
|
||||
// generateKeyPairBytes Generates a private-public key-pair.
|
||||
// 'priv' is a private key; a little-endian scalar belonging to the set
|
||||
// 2^{254} + 8 * [0, 2^{251}), in order to avoid the small subgroup of the
|
||||
// curve. 'pub' is simply 'priv' * G where G is the base point.
|
||||
// See https://cr.yp.to/ecdh.html and RFC7748, sec 5.
|
||||
func (c *curve25519) generateKeyPairBytes(rand io.Reader) (priv, pub x25519lib.Key, err error) {
|
||||
_, err = io.ReadFull(rand, priv[:])
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
x25519lib.KeyGen(&pub, &priv)
|
||||
return
|
||||
}
|
||||
|
||||
func (c *curve25519) GenerateECDH(rand io.Reader) (point []byte, secret []byte, err error) {
|
||||
priv, pub, err := c.generateKeyPairBytes(rand)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
return pub[:], priv[:], nil
|
||||
}
|
||||
|
||||
func (c *genericCurve) MaskSecret(secret []byte) []byte {
|
||||
return secret
|
||||
}
|
||||
|
||||
func (c *curve25519) Encaps(rand io.Reader, point []byte) (ephemeral, sharedSecret []byte, err error) {
|
||||
// RFC6637 §8: "Generate an ephemeral key pair {v, V=vG}"
|
||||
// ephemeralPrivate corresponds to `v`.
|
||||
// ephemeralPublic corresponds to `V`.
|
||||
ephemeralPrivate, ephemeralPublic, err := c.generateKeyPairBytes(rand)
|
||||
if err != nil {
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
// RFC6637 §8: "Obtain the authenticated recipient public key R"
|
||||
// pubKey corresponds to `R`.
|
||||
var pubKey x25519lib.Key
|
||||
copy(pubKey[:], point)
|
||||
|
||||
// RFC6637 §8: "Compute the shared point S = vR"
|
||||
// "VB = convert point V to the octet string"
|
||||
// sharedPoint corresponds to `VB`.
|
||||
var sharedPoint x25519lib.Key
|
||||
x25519lib.Shared(&sharedPoint, &ephemeralPrivate, &pubKey)
|
||||
|
||||
return ephemeralPublic[:], sharedPoint[:], nil
|
||||
}
|
||||
|
||||
func (c *curve25519) Decaps(vsG, secret []byte) (sharedSecret []byte, err error) {
|
||||
var ephemeralPublic, decodedPrivate, sharedPoint x25519lib.Key
|
||||
// RFC6637 §8: "The decryption is the inverse of the method given."
|
||||
// All quoted descriptions in comments below describe encryption, and
|
||||
// the reverse is performed.
|
||||
// vsG corresponds to `VB` in RFC6637 §8 .
|
||||
|
||||
// RFC6637 §8: "VB = convert point V to the octet string"
|
||||
copy(ephemeralPublic[:], vsG)
|
||||
|
||||
// decodedPrivate corresponds to `r` in RFC6637 §8 .
|
||||
copy(decodedPrivate[:], secret)
|
||||
|
||||
// RFC6637 §8: "Note that the recipient obtains the shared secret by calculating
|
||||
// S = rV = rvG, where (r,R) is the recipient's key pair."
|
||||
// sharedPoint corresponds to `S`.
|
||||
x25519lib.Shared(&sharedPoint, &decodedPrivate, &ephemeralPublic)
|
||||
|
||||
return sharedPoint[:], nil
|
||||
}
|
||||
|
||||
func (c *curve25519) ValidateECDH(point []byte, secret []byte) (err error) {
|
||||
var pk, sk x25519lib.Key
|
||||
copy(sk[:], secret)
|
||||
x25519lib.KeyGen(&pk, &sk)
|
||||
|
||||
if subtle.ConstantTimeCompare(point, pk[:]) == 0 {
|
||||
return errors.KeyInvalidError("ecc: invalid curve25519 public point")
|
||||
}
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
func copyReversed(out []byte, in []byte) {
|
||||
l := len(in)
|
||||
for i := 0; i < l; i++ {
|
||||
out[i] = in[l-i-1]
|
||||
}
|
||||
}
|
||||
140
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curve_info.go
generated
vendored
Normal file
140
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curve_info.go
generated
vendored
Normal file
|
|
@ -0,0 +1,140 @@
|
|||
// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
|
||||
package ecc
|
||||
|
||||
import (
|
||||
"bytes"
|
||||
"crypto/elliptic"
|
||||
"github.com/ProtonMail/go-crypto/bitcurves"
|
||||
"github.com/ProtonMail/go-crypto/brainpool"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/encoding"
|
||||
)
|
||||
|
||||
type CurveInfo struct {
|
||||
GenName string
|
||||
Oid *encoding.OID
|
||||
Curve Curve
|
||||
}
|
||||
|
||||
var Curves = []CurveInfo{
|
||||
{
|
||||
// NIST P-256
|
||||
GenName: "P256",
|
||||
Oid: encoding.NewOID([]byte{0x2A, 0x86, 0x48, 0xCE, 0x3D, 0x03, 0x01, 0x07}),
|
||||
Curve: NewGenericCurve(elliptic.P256()),
|
||||
},
|
||||
{
|
||||
// NIST P-384
|
||||
GenName: "P384",
|
||||
Oid: encoding.NewOID([]byte{0x2B, 0x81, 0x04, 0x00, 0x22}),
|
||||
Curve: NewGenericCurve(elliptic.P384()),
|
||||
},
|
||||
{
|
||||
// NIST P-521
|
||||
GenName: "P521",
|
||||
Oid: encoding.NewOID([]byte{0x2B, 0x81, 0x04, 0x00, 0x23}),
|
||||
Curve: NewGenericCurve(elliptic.P521()),
|
||||
},
|
||||
{
|
||||
// SecP256k1
|
||||
GenName: "SecP256k1",
|
||||
Oid: encoding.NewOID([]byte{0x2B, 0x81, 0x04, 0x00, 0x0A}),
|
||||
Curve: NewGenericCurve(bitcurves.S256()),
|
||||
},
|
||||
{
|
||||
// Curve25519
|
||||
GenName: "Curve25519",
|
||||
Oid: encoding.NewOID([]byte{0x2B, 0x06, 0x01, 0x04, 0x01, 0x97, 0x55, 0x01, 0x05, 0x01}),
|
||||
Curve: NewCurve25519(),
|
||||
},
|
||||
{
|
||||
// X448
|
||||
GenName: "Curve448",
|
||||
Oid: encoding.NewOID([]byte{0x2B, 0x65, 0x6F}),
|
||||
Curve: NewX448(),
|
||||
},
|
||||
{
|
||||
// Ed25519
|
||||
GenName: "Curve25519",
|
||||
Oid: encoding.NewOID([]byte{0x2B, 0x06, 0x01, 0x04, 0x01, 0xDA, 0x47, 0x0F, 0x01}),
|
||||
Curve: NewEd25519(),
|
||||
},
|
||||
{
|
||||
// Ed448
|
||||
GenName: "Curve448",
|
||||
Oid: encoding.NewOID([]byte{0x2B, 0x65, 0x71}),
|
||||
Curve: NewEd448(),
|
||||
},
|
||||
{
|
||||
// BrainpoolP256r1
|
||||
GenName: "BrainpoolP256",
|
||||
Oid: encoding.NewOID([]byte{0x2B, 0x24, 0x03, 0x03, 0x02, 0x08, 0x01, 0x01, 0x07}),
|
||||
Curve: NewGenericCurve(brainpool.P256r1()),
|
||||
},
|
||||
{
|
||||
// BrainpoolP384r1
|
||||
GenName: "BrainpoolP384",
|
||||
Oid: encoding.NewOID([]byte{0x2B, 0x24, 0x03, 0x03, 0x02, 0x08, 0x01, 0x01, 0x0B}),
|
||||
Curve: NewGenericCurve(brainpool.P384r1()),
|
||||
},
|
||||
{
|
||||
// BrainpoolP512r1
|
||||
GenName: "BrainpoolP512",
|
||||
Oid: encoding.NewOID([]byte{0x2B, 0x24, 0x03, 0x03, 0x02, 0x08, 0x01, 0x01, 0x0D}),
|
||||
Curve: NewGenericCurve(brainpool.P512r1()),
|
||||
},
|
||||
}
|
||||
|
||||
func FindByCurve(curve Curve) *CurveInfo {
|
||||
for _, curveInfo := range Curves {
|
||||
if curveInfo.Curve.GetCurveName() == curve.GetCurveName() {
|
||||
return &curveInfo
|
||||
}
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
func FindByOid(oid encoding.Field) *CurveInfo {
|
||||
var rawBytes = oid.Bytes()
|
||||
for _, curveInfo := range Curves {
|
||||
if bytes.Equal(curveInfo.Oid.Bytes(), rawBytes) {
|
||||
return &curveInfo
|
||||
}
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
func FindEdDSAByGenName(curveGenName string) EdDSACurve {
|
||||
for _, curveInfo := range Curves {
|
||||
if curveInfo.GenName == curveGenName {
|
||||
curve, ok := curveInfo.Curve.(EdDSACurve)
|
||||
if ok {
|
||||
return curve
|
||||
}
|
||||
}
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
func FindECDSAByGenName(curveGenName string) ECDSACurve {
|
||||
for _, curveInfo := range Curves {
|
||||
if curveInfo.GenName == curveGenName {
|
||||
curve, ok := curveInfo.Curve.(ECDSACurve)
|
||||
if ok {
|
||||
return curve
|
||||
}
|
||||
}
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
func FindECDHByGenName(curveGenName string) ECDHCurve {
|
||||
for _, curveInfo := range Curves {
|
||||
if curveInfo.GenName == curveGenName {
|
||||
curve, ok := curveInfo.Curve.(ECDHCurve)
|
||||
if ok {
|
||||
return curve
|
||||
}
|
||||
}
|
||||
}
|
||||
return nil
|
||||
}
|
||||
48
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curves.go
generated
vendored
Normal file
48
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curves.go
generated
vendored
Normal file
|
|
@ -0,0 +1,48 @@
|
|||
// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
|
||||
package ecc
|
||||
|
||||
import (
|
||||
"io"
|
||||
"math/big"
|
||||
)
|
||||
|
||||
type Curve interface {
|
||||
GetCurveName() string
|
||||
}
|
||||
|
||||
type ECDSACurve interface {
|
||||
Curve
|
||||
MarshalIntegerPoint(x, y *big.Int) []byte
|
||||
UnmarshalIntegerPoint([]byte) (x, y *big.Int)
|
||||
MarshalIntegerSecret(d *big.Int) []byte
|
||||
UnmarshalIntegerSecret(d []byte) *big.Int
|
||||
GenerateECDSA(rand io.Reader) (x, y, secret *big.Int, err error)
|
||||
Sign(rand io.Reader, x, y, d *big.Int, hash []byte) (r, s *big.Int, err error)
|
||||
Verify(x, y *big.Int, hash []byte, r, s *big.Int) bool
|
||||
ValidateECDSA(x, y *big.Int, secret []byte) error
|
||||
}
|
||||
|
||||
type EdDSACurve interface {
|
||||
Curve
|
||||
MarshalBytePoint(x []byte) []byte
|
||||
UnmarshalBytePoint([]byte) (x []byte)
|
||||
MarshalByteSecret(d []byte) []byte
|
||||
UnmarshalByteSecret(d []byte) []byte
|
||||
MarshalSignature(sig []byte) (r, s []byte)
|
||||
UnmarshalSignature(r, s []byte) (sig []byte)
|
||||
GenerateEdDSA(rand io.Reader) (pub, priv []byte, err error)
|
||||
Sign(publicKey, privateKey, message []byte) (sig []byte, err error)
|
||||
Verify(publicKey, message, sig []byte) bool
|
||||
ValidateEdDSA(publicKey, privateKey []byte) (err error)
|
||||
}
|
||||
type ECDHCurve interface {
|
||||
Curve
|
||||
MarshalBytePoint([]byte) (encoded []byte)
|
||||
UnmarshalBytePoint(encoded []byte) ([]byte)
|
||||
MarshalByteSecret(d []byte) []byte
|
||||
UnmarshalByteSecret(d []byte) []byte
|
||||
GenerateECDH(rand io.Reader) (point []byte, secret []byte, err error)
|
||||
Encaps(rand io.Reader, point []byte) (ephemeral, sharedSecret []byte, err error)
|
||||
Decaps(ephemeral, secret []byte) (sharedSecret []byte, err error)
|
||||
ValidateECDH(public []byte, secret []byte) error
|
||||
}
|
||||
111
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/ed25519.go
generated
vendored
Normal file
111
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/ed25519.go
generated
vendored
Normal file
|
|
@ -0,0 +1,111 @@
|
|||
// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
|
||||
package ecc
|
||||
|
||||
import (
|
||||
"crypto/subtle"
|
||||
"io"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
ed25519lib "github.com/cloudflare/circl/sign/ed25519"
|
||||
)
|
||||
|
||||
const ed25519Size = 32
|
||||
type ed25519 struct {}
|
||||
|
||||
func NewEd25519() *ed25519 {
|
||||
return &ed25519{}
|
||||
}
|
||||
|
||||
func (c *ed25519) GetCurveName() string {
|
||||
return "ed25519"
|
||||
}
|
||||
|
||||
// MarshalBytePoint encodes the public point from native format, adding the prefix.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
|
||||
func (c *ed25519) MarshalBytePoint(x []byte) []byte {
|
||||
return append([]byte{0x40}, x...)
|
||||
}
|
||||
|
||||
// UnmarshalBytePoint decodes a point from prefixed format to native.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
|
||||
func (c *ed25519) UnmarshalBytePoint(point []byte) (x []byte) {
|
||||
if len(point) != ed25519lib.PublicKeySize + 1 {
|
||||
return nil
|
||||
}
|
||||
|
||||
// Return unprefixed
|
||||
return point[1:]
|
||||
}
|
||||
|
||||
// MarshalByteSecret encodes a scalar in native format.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
|
||||
func (c *ed25519) MarshalByteSecret(d []byte) []byte {
|
||||
return d
|
||||
}
|
||||
|
||||
// UnmarshalByteSecret decodes a scalar in native format and re-adds the stripped leading zeroes
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
|
||||
func (c *ed25519) UnmarshalByteSecret(s []byte) (d []byte) {
|
||||
if len(s) > ed25519lib.SeedSize {
|
||||
return nil
|
||||
}
|
||||
|
||||
// Handle stripped leading zeroes
|
||||
d = make([]byte, ed25519lib.SeedSize)
|
||||
copy(d[ed25519lib.SeedSize - len(s):], s)
|
||||
return
|
||||
}
|
||||
|
||||
// MarshalSignature splits a signature in R and S.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.2.3.3.1
|
||||
func (c *ed25519) MarshalSignature(sig []byte) (r, s []byte) {
|
||||
return sig[:ed25519Size], sig[ed25519Size:]
|
||||
}
|
||||
|
||||
// UnmarshalSignature decodes R and S in the native format, re-adding the stripped leading zeroes
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.2.3.3.1
|
||||
func (c *ed25519) UnmarshalSignature(r, s []byte) (sig []byte) {
|
||||
// Check size
|
||||
if len(r) > 32 || len(s) > 32 {
|
||||
return nil
|
||||
}
|
||||
|
||||
sig = make([]byte, ed25519lib.SignatureSize)
|
||||
|
||||
// Handle stripped leading zeroes
|
||||
copy(sig[ed25519Size-len(r):ed25519Size], r)
|
||||
copy(sig[ed25519lib.SignatureSize-len(s):], s)
|
||||
return sig
|
||||
}
|
||||
|
||||
func (c *ed25519) GenerateEdDSA(rand io.Reader) (pub, priv []byte, err error) {
|
||||
pk, sk, err := ed25519lib.GenerateKey(rand)
|
||||
|
||||
if err != nil {
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
return pk, sk[:ed25519lib.SeedSize], nil
|
||||
}
|
||||
|
||||
func getEd25519Sk(publicKey, privateKey []byte) ed25519lib.PrivateKey {
|
||||
return append(privateKey, publicKey...)
|
||||
}
|
||||
|
||||
func (c *ed25519) Sign(publicKey, privateKey, message []byte) (sig []byte, err error) {
|
||||
sig = ed25519lib.Sign(getEd25519Sk(publicKey, privateKey), message)
|
||||
return sig, nil
|
||||
}
|
||||
|
||||
func (c *ed25519) Verify(publicKey, message, sig []byte) bool {
|
||||
return ed25519lib.Verify(publicKey, message, sig)
|
||||
}
|
||||
|
||||
func (c *ed25519) ValidateEdDSA(publicKey, privateKey []byte) (err error) {
|
||||
priv := getEd25519Sk(publicKey, privateKey)
|
||||
expectedPriv := ed25519lib.NewKeyFromSeed(priv.Seed())
|
||||
if subtle.ConstantTimeCompare(priv, expectedPriv) == 0 {
|
||||
return errors.KeyInvalidError("ecc: invalid ed25519 secret")
|
||||
}
|
||||
return nil
|
||||
}
|
||||
111
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/ed448.go
generated
vendored
Normal file
111
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/ed448.go
generated
vendored
Normal file
|
|
@ -0,0 +1,111 @@
|
|||
// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
|
||||
package ecc
|
||||
|
||||
import (
|
||||
"crypto/subtle"
|
||||
"io"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
ed448lib "github.com/cloudflare/circl/sign/ed448"
|
||||
)
|
||||
|
||||
type ed448 struct {}
|
||||
|
||||
func NewEd448() *ed448 {
|
||||
return &ed448{}
|
||||
}
|
||||
|
||||
func (c *ed448) GetCurveName() string {
|
||||
return "ed448"
|
||||
}
|
||||
|
||||
// MarshalBytePoint encodes the public point from native format, adding the prefix.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
|
||||
func (c *ed448) MarshalBytePoint(x []byte) []byte {
|
||||
// Return prefixed
|
||||
return append([]byte{0x40}, x...)
|
||||
}
|
||||
|
||||
// UnmarshalBytePoint decodes a point from prefixed format to native.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
|
||||
func (c *ed448) UnmarshalBytePoint(point []byte) (x []byte) {
|
||||
if len(point) != ed448lib.PublicKeySize + 1 {
|
||||
return nil
|
||||
}
|
||||
|
||||
// Strip prefix
|
||||
return point[1:]
|
||||
}
|
||||
|
||||
// MarshalByteSecret encoded a scalar from native format to prefixed.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
|
||||
func (c *ed448) MarshalByteSecret(d []byte) []byte {
|
||||
// Return prefixed
|
||||
return append([]byte{0x40}, d...)
|
||||
}
|
||||
|
||||
// UnmarshalByteSecret decodes a scalar from prefixed format to native.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
|
||||
func (c *ed448) UnmarshalByteSecret(s []byte) (d []byte) {
|
||||
// Check prefixed size
|
||||
if len(s) != ed448lib.SeedSize + 1 {
|
||||
return nil
|
||||
}
|
||||
|
||||
// Strip prefix
|
||||
return s[1:]
|
||||
}
|
||||
|
||||
// MarshalSignature splits a signature in R and S, where R is in prefixed native format and
|
||||
// S is an MPI with value zero.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.2.3.3.2
|
||||
func (c *ed448) MarshalSignature(sig []byte) (r, s []byte) {
|
||||
return append([]byte{0x40}, sig...), []byte{}
|
||||
}
|
||||
|
||||
// UnmarshalSignature decodes R and S in the native format. Only R is used, in prefixed native format.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.2.3.3.2
|
||||
func (c *ed448) UnmarshalSignature(r, s []byte) (sig []byte) {
|
||||
if len(r) != ed448lib.SignatureSize + 1 {
|
||||
return nil
|
||||
}
|
||||
|
||||
return r[1:]
|
||||
}
|
||||
|
||||
func (c *ed448) GenerateEdDSA(rand io.Reader) (pub, priv []byte, err error) {
|
||||
pk, sk, err := ed448lib.GenerateKey(rand)
|
||||
|
||||
if err != nil {
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
return pk, sk[:ed448lib.SeedSize], nil
|
||||
}
|
||||
|
||||
func getEd448Sk(publicKey, privateKey []byte) ed448lib.PrivateKey {
|
||||
return append(privateKey, publicKey...)
|
||||
}
|
||||
|
||||
func (c *ed448) Sign(publicKey, privateKey, message []byte) (sig []byte, err error) {
|
||||
// Ed448 is used with the empty string as a context string.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-13.7
|
||||
sig = ed448lib.Sign(getEd448Sk(publicKey, privateKey), message, "")
|
||||
|
||||
return sig, nil
|
||||
}
|
||||
|
||||
func (c *ed448) Verify(publicKey, message, sig []byte) bool {
|
||||
// Ed448 is used with the empty string as a context string.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-13.7
|
||||
return ed448lib.Verify(publicKey, message, sig, "")
|
||||
}
|
||||
|
||||
func (c *ed448) ValidateEdDSA(publicKey, privateKey []byte) (err error) {
|
||||
priv := getEd448Sk(publicKey, privateKey)
|
||||
expectedPriv := ed448lib.NewKeyFromSeed(priv.Seed())
|
||||
if subtle.ConstantTimeCompare(priv, expectedPriv) == 0 {
|
||||
return errors.KeyInvalidError("ecc: invalid ed448 secret")
|
||||
}
|
||||
return nil
|
||||
}
|
||||
149
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/generic.go
generated
vendored
Normal file
149
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/generic.go
generated
vendored
Normal file
|
|
@ -0,0 +1,149 @@
|
|||
// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
|
||||
package ecc
|
||||
|
||||
import (
|
||||
"crypto/ecdsa"
|
||||
"crypto/elliptic"
|
||||
"fmt"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"io"
|
||||
"math/big"
|
||||
)
|
||||
|
||||
type genericCurve struct {
|
||||
Curve elliptic.Curve
|
||||
}
|
||||
|
||||
func NewGenericCurve(c elliptic.Curve) *genericCurve {
|
||||
return &genericCurve{
|
||||
Curve: c,
|
||||
}
|
||||
}
|
||||
|
||||
func (c *genericCurve) GetCurveName() string {
|
||||
return c.Curve.Params().Name
|
||||
}
|
||||
|
||||
func (c *genericCurve) MarshalBytePoint(point []byte) []byte {
|
||||
return point
|
||||
}
|
||||
|
||||
func (c *genericCurve) UnmarshalBytePoint(point []byte) []byte {
|
||||
return point
|
||||
}
|
||||
|
||||
func (c *genericCurve) MarshalIntegerPoint(x, y *big.Int) []byte {
|
||||
return elliptic.Marshal(c.Curve, x, y)
|
||||
}
|
||||
|
||||
func (c *genericCurve) UnmarshalIntegerPoint(point []byte) (x, y *big.Int) {
|
||||
return elliptic.Unmarshal(c.Curve, point)
|
||||
}
|
||||
|
||||
func (c *genericCurve) MarshalByteSecret(d []byte) []byte {
|
||||
return d
|
||||
}
|
||||
|
||||
func (c *genericCurve) UnmarshalByteSecret(d []byte) []byte {
|
||||
return d
|
||||
}
|
||||
|
||||
func (c *genericCurve) MarshalIntegerSecret(d *big.Int) []byte {
|
||||
return d.Bytes()
|
||||
}
|
||||
|
||||
func (c *genericCurve) UnmarshalIntegerSecret(d []byte) *big.Int {
|
||||
return new(big.Int).SetBytes(d)
|
||||
}
|
||||
|
||||
func (c *genericCurve) GenerateECDH(rand io.Reader) (point, secret []byte, err error) {
|
||||
secret, x, y, err := elliptic.GenerateKey(c.Curve, rand)
|
||||
if err != nil {
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
point = elliptic.Marshal(c.Curve, x, y)
|
||||
return point, secret, nil
|
||||
}
|
||||
|
||||
func (c *genericCurve) GenerateECDSA(rand io.Reader) (x, y, secret *big.Int, err error) {
|
||||
priv, err := ecdsa.GenerateKey(c.Curve, rand)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
return priv.X, priv.Y, priv.D, nil
|
||||
}
|
||||
|
||||
func (c *genericCurve) Encaps(rand io.Reader, point []byte) (ephemeral, sharedSecret []byte, err error) {
|
||||
xP, yP := elliptic.Unmarshal(c.Curve, point)
|
||||
if xP == nil {
|
||||
panic("invalid point")
|
||||
}
|
||||
|
||||
d, x, y, err := elliptic.GenerateKey(c.Curve, rand)
|
||||
if err != nil {
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
vsG := elliptic.Marshal(c.Curve, x, y)
|
||||
zbBig, _ := c.Curve.ScalarMult(xP, yP, d)
|
||||
|
||||
byteLen := (c.Curve.Params().BitSize + 7) >> 3
|
||||
zb := make([]byte, byteLen)
|
||||
zbBytes := zbBig.Bytes()
|
||||
copy(zb[byteLen-len(zbBytes):], zbBytes)
|
||||
|
||||
return vsG, zb, nil
|
||||
}
|
||||
|
||||
func (c *genericCurve) Decaps(ephemeral, secret []byte) (sharedSecret []byte, err error) {
|
||||
x, y := elliptic.Unmarshal(c.Curve, ephemeral)
|
||||
zbBig, _ := c.Curve.ScalarMult(x, y, secret)
|
||||
byteLen := (c.Curve.Params().BitSize + 7) >> 3
|
||||
zb := make([]byte, byteLen)
|
||||
zbBytes := zbBig.Bytes()
|
||||
copy(zb[byteLen-len(zbBytes):], zbBytes)
|
||||
|
||||
return zb, nil
|
||||
}
|
||||
|
||||
func (c *genericCurve) Sign(rand io.Reader, x, y, d *big.Int, hash []byte) (r, s *big.Int, err error) {
|
||||
priv := &ecdsa.PrivateKey{D: d, PublicKey: ecdsa.PublicKey{X: x, Y: y, Curve: c.Curve}}
|
||||
return ecdsa.Sign(rand, priv, hash)
|
||||
}
|
||||
|
||||
func (c *genericCurve) Verify(x, y *big.Int, hash []byte, r, s *big.Int) bool {
|
||||
pub := &ecdsa.PublicKey{X: x, Y: y, Curve: c.Curve}
|
||||
return ecdsa.Verify(pub, hash, r, s)
|
||||
}
|
||||
|
||||
func (c *genericCurve) validate(xP, yP *big.Int, secret []byte) error {
|
||||
// the public point should not be at infinity (0,0)
|
||||
zero := new(big.Int)
|
||||
if xP.Cmp(zero) == 0 && yP.Cmp(zero) == 0 {
|
||||
return errors.KeyInvalidError(fmt.Sprintf("ecc (%s): infinity point", c.Curve.Params().Name))
|
||||
}
|
||||
|
||||
// re-derive the public point Q' = (X,Y) = dG
|
||||
// to compare to declared Q in public key
|
||||
expectedX, expectedY := c.Curve.ScalarBaseMult(secret)
|
||||
if xP.Cmp(expectedX) != 0 || yP.Cmp(expectedY) != 0 {
|
||||
return errors.KeyInvalidError(fmt.Sprintf("ecc (%s): invalid point", c.Curve.Params().Name))
|
||||
}
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
func (c *genericCurve) ValidateECDSA(xP, yP *big.Int, secret []byte) error {
|
||||
return c.validate(xP, yP, secret)
|
||||
}
|
||||
|
||||
func (c *genericCurve) ValidateECDH(point []byte, secret []byte) error {
|
||||
xP, yP := elliptic.Unmarshal(c.Curve, point)
|
||||
if xP == nil {
|
||||
return errors.KeyInvalidError(fmt.Sprintf("ecc (%s): invalid point", c.Curve.Params().Name))
|
||||
}
|
||||
|
||||
return c.validate(xP, yP, secret)
|
||||
}
|
||||
105
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/x448.go
generated
vendored
Normal file
105
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/x448.go
generated
vendored
Normal file
|
|
@ -0,0 +1,105 @@
|
|||
// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
|
||||
package ecc
|
||||
|
||||
import (
|
||||
"crypto/subtle"
|
||||
"io"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
x448lib "github.com/cloudflare/circl/dh/x448"
|
||||
)
|
||||
|
||||
type x448 struct {}
|
||||
|
||||
func NewX448() *x448 {
|
||||
return &x448{}
|
||||
}
|
||||
|
||||
func (c *x448) GetCurveName() string {
|
||||
return "x448"
|
||||
}
|
||||
|
||||
// MarshalBytePoint encodes the public point from native format, adding the prefix.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6
|
||||
func (c *x448) MarshalBytePoint(point []byte) []byte {
|
||||
return append([]byte{0x40}, point...)
|
||||
}
|
||||
|
||||
// UnmarshalBytePoint decodes a point from prefixed format to native.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6
|
||||
func (c *x448) UnmarshalBytePoint(point []byte) []byte {
|
||||
if len(point) != x448lib.Size + 1 {
|
||||
return nil
|
||||
}
|
||||
|
||||
return point[1:]
|
||||
}
|
||||
|
||||
// MarshalByteSecret encoded a scalar from native format to prefixed.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6.1.2
|
||||
func (c *x448) MarshalByteSecret(d []byte) []byte {
|
||||
return append([]byte{0x40}, d...)
|
||||
}
|
||||
|
||||
// UnmarshalByteSecret decodes a scalar from prefixed format to native.
|
||||
// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6.1.2
|
||||
func (c *x448) UnmarshalByteSecret(d []byte) []byte {
|
||||
if len(d) != x448lib.Size + 1 {
|
||||
return nil
|
||||
}
|
||||
|
||||
// Store without prefix
|
||||
return d[1:]
|
||||
}
|
||||
|
||||
func (c *x448) generateKeyPairBytes(rand io.Reader) (sk, pk x448lib.Key, err error) {
|
||||
if _, err = rand.Read(sk[:]); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
x448lib.KeyGen(&pk, &sk)
|
||||
return
|
||||
}
|
||||
|
||||
func (c *x448) GenerateECDH(rand io.Reader) (point []byte, secret []byte, err error) {
|
||||
priv, pub, err := c.generateKeyPairBytes(rand)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
return pub[:], priv[:], nil
|
||||
}
|
||||
|
||||
func (c *x448) Encaps(rand io.Reader, point []byte) (ephemeral, sharedSecret []byte, err error) {
|
||||
var pk, ss x448lib.Key
|
||||
seed, e, err := c.generateKeyPairBytes(rand)
|
||||
|
||||
copy(pk[:], point)
|
||||
x448lib.Shared(&ss, &seed, &pk)
|
||||
|
||||
return e[:], ss[:], nil
|
||||
}
|
||||
|
||||
func (c *x448) Decaps(ephemeral, secret []byte) (sharedSecret []byte, err error) {
|
||||
var ss, sk, e x448lib.Key
|
||||
|
||||
copy(sk[:], secret)
|
||||
copy(e[:], ephemeral)
|
||||
x448lib.Shared(&ss, &sk, &e)
|
||||
|
||||
return ss[:], nil
|
||||
}
|
||||
|
||||
func (c *x448) ValidateECDH(point []byte, secret []byte) error {
|
||||
var sk, pk, expectedPk x448lib.Key
|
||||
|
||||
copy(pk[:], point)
|
||||
copy(sk[:], secret)
|
||||
x448lib.KeyGen(&expectedPk, &sk)
|
||||
|
||||
if subtle.ConstantTimeCompare(expectedPk[:], pk[:]) == 0 {
|
||||
return errors.KeyInvalidError("ecc: invalid curve25519 public point")
|
||||
}
|
||||
|
||||
return nil
|
||||
}
|
||||
27
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/encoding.go
generated
vendored
Normal file
27
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/encoding.go
generated
vendored
Normal file
|
|
@ -0,0 +1,27 @@
|
|||
// Copyright 2017 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package encoding implements openpgp packet field encodings as specified in
|
||||
// RFC 4880 and 6637.
|
||||
package encoding
|
||||
|
||||
import "io"
|
||||
|
||||
// Field is an encoded field of an openpgp packet.
|
||||
type Field interface {
|
||||
// Bytes returns the decoded data.
|
||||
Bytes() []byte
|
||||
|
||||
// BitLength is the size in bits of the decoded data.
|
||||
BitLength() uint16
|
||||
|
||||
// EncodedBytes returns the encoded data.
|
||||
EncodedBytes() []byte
|
||||
|
||||
// EncodedLength is the size in bytes of the encoded data.
|
||||
EncodedLength() uint16
|
||||
|
||||
// ReadFrom reads the next Field from r.
|
||||
ReadFrom(r io.Reader) (int64, error)
|
||||
}
|
||||
91
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/mpi.go
generated
vendored
Normal file
91
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/mpi.go
generated
vendored
Normal file
|
|
@ -0,0 +1,91 @@
|
|||
// Copyright 2017 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package encoding
|
||||
|
||||
import (
|
||||
"io"
|
||||
"math/big"
|
||||
"math/bits"
|
||||
)
|
||||
|
||||
// An MPI is used to store the contents of a big integer, along with the bit
|
||||
// length that was specified in the original input. This allows the MPI to be
|
||||
// reserialized exactly.
|
||||
type MPI struct {
|
||||
bytes []byte
|
||||
bitLength uint16
|
||||
}
|
||||
|
||||
// NewMPI returns a MPI initialized with bytes.
|
||||
func NewMPI(bytes []byte) *MPI {
|
||||
for len(bytes) != 0 && bytes[0] == 0 {
|
||||
bytes = bytes[1:]
|
||||
}
|
||||
if len(bytes) == 0 {
|
||||
bitLength := uint16(0)
|
||||
return &MPI{bytes, bitLength}
|
||||
}
|
||||
bitLength := 8*uint16(len(bytes)-1) + uint16(bits.Len8(bytes[0]))
|
||||
return &MPI{bytes, bitLength}
|
||||
}
|
||||
|
||||
// Bytes returns the decoded data.
|
||||
func (m *MPI) Bytes() []byte {
|
||||
return m.bytes
|
||||
}
|
||||
|
||||
// BitLength is the size in bits of the decoded data.
|
||||
func (m *MPI) BitLength() uint16 {
|
||||
return m.bitLength
|
||||
}
|
||||
|
||||
// EncodedBytes returns the encoded data.
|
||||
func (m *MPI) EncodedBytes() []byte {
|
||||
return append([]byte{byte(m.bitLength >> 8), byte(m.bitLength)}, m.bytes...)
|
||||
}
|
||||
|
||||
// EncodedLength is the size in bytes of the encoded data.
|
||||
func (m *MPI) EncodedLength() uint16 {
|
||||
return uint16(2 + len(m.bytes))
|
||||
}
|
||||
|
||||
// ReadFrom reads into m the next MPI from r.
|
||||
func (m *MPI) ReadFrom(r io.Reader) (int64, error) {
|
||||
var buf [2]byte
|
||||
n, err := io.ReadFull(r, buf[0:])
|
||||
if err != nil {
|
||||
if err == io.EOF {
|
||||
err = io.ErrUnexpectedEOF
|
||||
}
|
||||
return int64(n), err
|
||||
}
|
||||
|
||||
m.bitLength = uint16(buf[0])<<8 | uint16(buf[1])
|
||||
m.bytes = make([]byte, (int(m.bitLength)+7)/8)
|
||||
|
||||
nn, err := io.ReadFull(r, m.bytes)
|
||||
if err == io.EOF {
|
||||
err = io.ErrUnexpectedEOF
|
||||
}
|
||||
|
||||
// remove leading zero bytes from malformed GnuPG encoded MPIs:
|
||||
// https://bugs.gnupg.org/gnupg/issue1853
|
||||
// for _, b := range m.bytes {
|
||||
// if b != 0 {
|
||||
// break
|
||||
// }
|
||||
// m.bytes = m.bytes[1:]
|
||||
// m.bitLength -= 8
|
||||
// }
|
||||
|
||||
return int64(n) + int64(nn), err
|
||||
}
|
||||
|
||||
// SetBig initializes m with the bits from n.
|
||||
func (m *MPI) SetBig(n *big.Int) *MPI {
|
||||
m.bytes = n.Bytes()
|
||||
m.bitLength = uint16(n.BitLen())
|
||||
return m
|
||||
}
|
||||
88
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/oid.go
generated
vendored
Normal file
88
vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/oid.go
generated
vendored
Normal file
|
|
@ -0,0 +1,88 @@
|
|||
// Copyright 2017 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package encoding
|
||||
|
||||
import (
|
||||
"io"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
)
|
||||
|
||||
// OID is used to store a variable-length field with a one-octet size
|
||||
// prefix. See https://tools.ietf.org/html/rfc6637#section-9.
|
||||
type OID struct {
|
||||
bytes []byte
|
||||
}
|
||||
|
||||
const (
|
||||
// maxOID is the maximum number of bytes in a OID.
|
||||
maxOID = 254
|
||||
// reservedOIDLength1 and reservedOIDLength2 are OID lengths that the RFC
|
||||
// specifies are reserved.
|
||||
reservedOIDLength1 = 0
|
||||
reservedOIDLength2 = 0xff
|
||||
)
|
||||
|
||||
// NewOID returns a OID initialized with bytes.
|
||||
func NewOID(bytes []byte) *OID {
|
||||
switch len(bytes) {
|
||||
case reservedOIDLength1, reservedOIDLength2:
|
||||
panic("encoding: NewOID argument length is reserved")
|
||||
default:
|
||||
if len(bytes) > maxOID {
|
||||
panic("encoding: NewOID argument too large")
|
||||
}
|
||||
}
|
||||
|
||||
return &OID{
|
||||
bytes: bytes,
|
||||
}
|
||||
}
|
||||
|
||||
// Bytes returns the decoded data.
|
||||
func (o *OID) Bytes() []byte {
|
||||
return o.bytes
|
||||
}
|
||||
|
||||
// BitLength is the size in bits of the decoded data.
|
||||
func (o *OID) BitLength() uint16 {
|
||||
return uint16(len(o.bytes) * 8)
|
||||
}
|
||||
|
||||
// EncodedBytes returns the encoded data.
|
||||
func (o *OID) EncodedBytes() []byte {
|
||||
return append([]byte{byte(len(o.bytes))}, o.bytes...)
|
||||
}
|
||||
|
||||
// EncodedLength is the size in bytes of the encoded data.
|
||||
func (o *OID) EncodedLength() uint16 {
|
||||
return uint16(1 + len(o.bytes))
|
||||
}
|
||||
|
||||
// ReadFrom reads into b the next OID from r.
|
||||
func (o *OID) ReadFrom(r io.Reader) (int64, error) {
|
||||
var buf [1]byte
|
||||
n, err := io.ReadFull(r, buf[:])
|
||||
if err != nil {
|
||||
if err == io.EOF {
|
||||
err = io.ErrUnexpectedEOF
|
||||
}
|
||||
return int64(n), err
|
||||
}
|
||||
|
||||
switch buf[0] {
|
||||
case reservedOIDLength1, reservedOIDLength2:
|
||||
return int64(n), errors.UnsupportedError("reserved for future extensions")
|
||||
}
|
||||
|
||||
o.bytes = make([]byte, buf[0])
|
||||
|
||||
nn, err := io.ReadFull(r, o.bytes)
|
||||
if err == io.EOF {
|
||||
err = io.ErrUnexpectedEOF
|
||||
}
|
||||
|
||||
return int64(n) + int64(nn), err
|
||||
}
|
||||
|
|
@ -0,0 +1,389 @@
|
|||
// Copyright 2011 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package openpgp
|
||||
|
||||
import (
|
||||
"crypto"
|
||||
"crypto/rand"
|
||||
"crypto/rsa"
|
||||
goerrors "errors"
|
||||
"io"
|
||||
"math/big"
|
||||
"time"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/ecdh"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/ecdsa"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/eddsa"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/algorithm"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/ecc"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/packet"
|
||||
)
|
||||
|
||||
// NewEntity returns an Entity that contains a fresh RSA/RSA keypair with a
|
||||
// single identity composed of the given full name, comment and email, any of
|
||||
// which may be empty but must not contain any of "()<>\x00".
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func NewEntity(name, comment, email string, config *packet.Config) (*Entity, error) {
|
||||
creationTime := config.Now()
|
||||
keyLifetimeSecs := config.KeyLifetime()
|
||||
|
||||
// Generate a primary signing key
|
||||
primaryPrivRaw, err := newSigner(config)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
primary := packet.NewSignerPrivateKey(creationTime, primaryPrivRaw)
|
||||
if config != nil && config.V5Keys {
|
||||
primary.UpgradeToV5()
|
||||
}
|
||||
|
||||
e := &Entity{
|
||||
PrimaryKey: &primary.PublicKey,
|
||||
PrivateKey: primary,
|
||||
Identities: make(map[string]*Identity),
|
||||
Subkeys: []Subkey{},
|
||||
}
|
||||
|
||||
err = e.addUserId(name, comment, email, config, creationTime, keyLifetimeSecs)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
// NOTE: No key expiry here, but we will not return this subkey in EncryptionKey()
|
||||
// if the primary/master key has expired.
|
||||
err = e.addEncryptionSubkey(config, creationTime, 0)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
return e, nil
|
||||
}
|
||||
|
||||
func (t *Entity) AddUserId(name, comment, email string, config *packet.Config) error {
|
||||
creationTime := config.Now()
|
||||
keyLifetimeSecs := config.KeyLifetime()
|
||||
return t.addUserId(name, comment, email, config, creationTime, keyLifetimeSecs)
|
||||
}
|
||||
|
||||
func (t *Entity) addUserId(name, comment, email string, config *packet.Config, creationTime time.Time, keyLifetimeSecs uint32) error {
|
||||
uid := packet.NewUserId(name, comment, email)
|
||||
if uid == nil {
|
||||
return errors.InvalidArgumentError("user id field contained invalid characters")
|
||||
}
|
||||
|
||||
if _, ok := t.Identities[uid.Id]; ok {
|
||||
return errors.InvalidArgumentError("user id exist")
|
||||
}
|
||||
|
||||
primary := t.PrivateKey
|
||||
|
||||
isPrimaryId := len(t.Identities) == 0
|
||||
|
||||
selfSignature := createSignaturePacket(&primary.PublicKey, packet.SigTypePositiveCert, config)
|
||||
selfSignature.CreationTime = creationTime
|
||||
selfSignature.KeyLifetimeSecs = &keyLifetimeSecs
|
||||
selfSignature.IsPrimaryId = &isPrimaryId
|
||||
selfSignature.FlagsValid = true
|
||||
selfSignature.FlagSign = true
|
||||
selfSignature.FlagCertify = true
|
||||
selfSignature.SEIPDv1 = true // true by default, see 5.8 vs. 5.14
|
||||
selfSignature.SEIPDv2 = config.AEAD() != nil
|
||||
|
||||
// Set the PreferredHash for the SelfSignature from the packet.Config.
|
||||
// If it is not the must-implement algorithm from rfc4880bis, append that.
|
||||
hash, ok := algorithm.HashToHashId(config.Hash())
|
||||
if !ok {
|
||||
return errors.UnsupportedError("unsupported preferred hash function")
|
||||
}
|
||||
|
||||
selfSignature.PreferredHash = []uint8{hash}
|
||||
if config.Hash() != crypto.SHA256 {
|
||||
selfSignature.PreferredHash = append(selfSignature.PreferredHash, hashToHashId(crypto.SHA256))
|
||||
}
|
||||
|
||||
// Likewise for DefaultCipher.
|
||||
selfSignature.PreferredSymmetric = []uint8{uint8(config.Cipher())}
|
||||
if config.Cipher() != packet.CipherAES128 {
|
||||
selfSignature.PreferredSymmetric = append(selfSignature.PreferredSymmetric, uint8(packet.CipherAES128))
|
||||
}
|
||||
|
||||
// We set CompressionNone as the preferred compression algorithm because
|
||||
// of compression side channel attacks, then append the configured
|
||||
// DefaultCompressionAlgo if any is set (to signal support for cases
|
||||
// where the application knows that using compression is safe).
|
||||
selfSignature.PreferredCompression = []uint8{uint8(packet.CompressionNone)}
|
||||
if config.Compression() != packet.CompressionNone {
|
||||
selfSignature.PreferredCompression = append(selfSignature.PreferredCompression, uint8(config.Compression()))
|
||||
}
|
||||
|
||||
// And for DefaultMode.
|
||||
modes := []uint8{uint8(config.AEAD().Mode())}
|
||||
if config.AEAD().Mode() != packet.AEADModeOCB {
|
||||
modes = append(modes, uint8(packet.AEADModeOCB))
|
||||
}
|
||||
|
||||
// For preferred (AES256, GCM), we'll generate (AES256, GCM), (AES256, OCB), (AES128, GCM), (AES128, OCB)
|
||||
for _, cipher := range selfSignature.PreferredSymmetric {
|
||||
for _, mode := range modes {
|
||||
selfSignature.PreferredCipherSuites = append(selfSignature.PreferredCipherSuites, [2]uint8{cipher, mode})
|
||||
}
|
||||
}
|
||||
|
||||
// User ID binding signature
|
||||
err := selfSignature.SignUserId(uid.Id, &primary.PublicKey, primary, config)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
t.Identities[uid.Id] = &Identity{
|
||||
Name: uid.Id,
|
||||
UserId: uid,
|
||||
SelfSignature: selfSignature,
|
||||
Signatures: []*packet.Signature{selfSignature},
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
// AddSigningSubkey adds a signing keypair as a subkey to the Entity.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (e *Entity) AddSigningSubkey(config *packet.Config) error {
|
||||
creationTime := config.Now()
|
||||
keyLifetimeSecs := config.KeyLifetime()
|
||||
|
||||
subPrivRaw, err := newSigner(config)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
sub := packet.NewSignerPrivateKey(creationTime, subPrivRaw)
|
||||
sub.IsSubkey = true
|
||||
if config != nil && config.V5Keys {
|
||||
sub.UpgradeToV5()
|
||||
}
|
||||
|
||||
subkey := Subkey{
|
||||
PublicKey: &sub.PublicKey,
|
||||
PrivateKey: sub,
|
||||
}
|
||||
subkey.Sig = createSignaturePacket(e.PrimaryKey, packet.SigTypeSubkeyBinding, config)
|
||||
subkey.Sig.CreationTime = creationTime
|
||||
subkey.Sig.KeyLifetimeSecs = &keyLifetimeSecs
|
||||
subkey.Sig.FlagsValid = true
|
||||
subkey.Sig.FlagSign = true
|
||||
subkey.Sig.EmbeddedSignature = createSignaturePacket(subkey.PublicKey, packet.SigTypePrimaryKeyBinding, config)
|
||||
subkey.Sig.EmbeddedSignature.CreationTime = creationTime
|
||||
|
||||
err = subkey.Sig.EmbeddedSignature.CrossSignKey(subkey.PublicKey, e.PrimaryKey, subkey.PrivateKey, config)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
err = subkey.Sig.SignKey(subkey.PublicKey, e.PrivateKey, config)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
e.Subkeys = append(e.Subkeys, subkey)
|
||||
return nil
|
||||
}
|
||||
|
||||
// AddEncryptionSubkey adds an encryption keypair as a subkey to the Entity.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (e *Entity) AddEncryptionSubkey(config *packet.Config) error {
|
||||
creationTime := config.Now()
|
||||
keyLifetimeSecs := config.KeyLifetime()
|
||||
return e.addEncryptionSubkey(config, creationTime, keyLifetimeSecs)
|
||||
}
|
||||
|
||||
func (e *Entity) addEncryptionSubkey(config *packet.Config, creationTime time.Time, keyLifetimeSecs uint32) error {
|
||||
subPrivRaw, err := newDecrypter(config)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
sub := packet.NewDecrypterPrivateKey(creationTime, subPrivRaw)
|
||||
sub.IsSubkey = true
|
||||
if config != nil && config.V5Keys {
|
||||
sub.UpgradeToV5()
|
||||
}
|
||||
|
||||
subkey := Subkey{
|
||||
PublicKey: &sub.PublicKey,
|
||||
PrivateKey: sub,
|
||||
}
|
||||
subkey.Sig = createSignaturePacket(e.PrimaryKey, packet.SigTypeSubkeyBinding, config)
|
||||
subkey.Sig.CreationTime = creationTime
|
||||
subkey.Sig.KeyLifetimeSecs = &keyLifetimeSecs
|
||||
subkey.Sig.FlagsValid = true
|
||||
subkey.Sig.FlagEncryptStorage = true
|
||||
subkey.Sig.FlagEncryptCommunications = true
|
||||
|
||||
err = subkey.Sig.SignKey(subkey.PublicKey, e.PrivateKey, config)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
e.Subkeys = append(e.Subkeys, subkey)
|
||||
return nil
|
||||
}
|
||||
|
||||
// Generates a signing key
|
||||
func newSigner(config *packet.Config) (signer interface{}, err error) {
|
||||
switch config.PublicKeyAlgorithm() {
|
||||
case packet.PubKeyAlgoRSA:
|
||||
bits := config.RSAModulusBits()
|
||||
if bits < 1024 {
|
||||
return nil, errors.InvalidArgumentError("bits must be >= 1024")
|
||||
}
|
||||
if config != nil && len(config.RSAPrimes) >= 2 {
|
||||
primes := config.RSAPrimes[0:2]
|
||||
config.RSAPrimes = config.RSAPrimes[2:]
|
||||
return generateRSAKeyWithPrimes(config.Random(), 2, bits, primes)
|
||||
}
|
||||
return rsa.GenerateKey(config.Random(), bits)
|
||||
case packet.PubKeyAlgoEdDSA:
|
||||
curve := ecc.FindEdDSAByGenName(string(config.CurveName()))
|
||||
if curve == nil {
|
||||
return nil, errors.InvalidArgumentError("unsupported curve")
|
||||
}
|
||||
|
||||
priv, err := eddsa.GenerateKey(config.Random(), curve)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
return priv, nil
|
||||
case packet.PubKeyAlgoECDSA:
|
||||
curve := ecc.FindECDSAByGenName(string(config.CurveName()))
|
||||
if curve == nil {
|
||||
return nil, errors.InvalidArgumentError("unsupported curve")
|
||||
}
|
||||
|
||||
priv, err := ecdsa.GenerateKey(config.Random(), curve)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
return priv, nil
|
||||
default:
|
||||
return nil, errors.InvalidArgumentError("unsupported public key algorithm")
|
||||
}
|
||||
}
|
||||
|
||||
// Generates an encryption/decryption key
|
||||
func newDecrypter(config *packet.Config) (decrypter interface{}, err error) {
|
||||
switch config.PublicKeyAlgorithm() {
|
||||
case packet.PubKeyAlgoRSA:
|
||||
bits := config.RSAModulusBits()
|
||||
if bits < 1024 {
|
||||
return nil, errors.InvalidArgumentError("bits must be >= 1024")
|
||||
}
|
||||
if config != nil && len(config.RSAPrimes) >= 2 {
|
||||
primes := config.RSAPrimes[0:2]
|
||||
config.RSAPrimes = config.RSAPrimes[2:]
|
||||
return generateRSAKeyWithPrimes(config.Random(), 2, bits, primes)
|
||||
}
|
||||
return rsa.GenerateKey(config.Random(), bits)
|
||||
case packet.PubKeyAlgoEdDSA, packet.PubKeyAlgoECDSA:
|
||||
fallthrough // When passing EdDSA or ECDSA, we generate an ECDH subkey
|
||||
case packet.PubKeyAlgoECDH:
|
||||
var kdf = ecdh.KDF{
|
||||
Hash: algorithm.SHA512,
|
||||
Cipher: algorithm.AES256,
|
||||
}
|
||||
curve := ecc.FindECDHByGenName(string(config.CurveName()))
|
||||
if curve == nil {
|
||||
return nil, errors.InvalidArgumentError("unsupported curve")
|
||||
}
|
||||
return ecdh.GenerateKey(config.Random(), curve, kdf)
|
||||
default:
|
||||
return nil, errors.InvalidArgumentError("unsupported public key algorithm")
|
||||
}
|
||||
}
|
||||
|
||||
var bigOne = big.NewInt(1)
|
||||
|
||||
// generateRSAKeyWithPrimes generates a multi-prime RSA keypair of the
|
||||
// given bit size, using the given random source and prepopulated primes.
|
||||
func generateRSAKeyWithPrimes(random io.Reader, nprimes int, bits int, prepopulatedPrimes []*big.Int) (*rsa.PrivateKey, error) {
|
||||
priv := new(rsa.PrivateKey)
|
||||
priv.E = 65537
|
||||
|
||||
if nprimes < 2 {
|
||||
return nil, goerrors.New("generateRSAKeyWithPrimes: nprimes must be >= 2")
|
||||
}
|
||||
|
||||
if bits < 1024 {
|
||||
return nil, goerrors.New("generateRSAKeyWithPrimes: bits must be >= 1024")
|
||||
}
|
||||
|
||||
primes := make([]*big.Int, nprimes)
|
||||
|
||||
NextSetOfPrimes:
|
||||
for {
|
||||
todo := bits
|
||||
// crypto/rand should set the top two bits in each prime.
|
||||
// Thus each prime has the form
|
||||
// p_i = 2^bitlen(p_i) × 0.11... (in base 2).
|
||||
// And the product is:
|
||||
// P = 2^todo × α
|
||||
// where α is the product of nprimes numbers of the form 0.11...
|
||||
//
|
||||
// If α < 1/2 (which can happen for nprimes > 2), we need to
|
||||
// shift todo to compensate for lost bits: the mean value of 0.11...
|
||||
// is 7/8, so todo + shift - nprimes * log2(7/8) ~= bits - 1/2
|
||||
// will give good results.
|
||||
if nprimes >= 7 {
|
||||
todo += (nprimes - 2) / 5
|
||||
}
|
||||
for i := 0; i < nprimes; i++ {
|
||||
var err error
|
||||
if len(prepopulatedPrimes) == 0 {
|
||||
primes[i], err = rand.Prime(random, todo/(nprimes-i))
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
} else {
|
||||
primes[i] = prepopulatedPrimes[0]
|
||||
prepopulatedPrimes = prepopulatedPrimes[1:]
|
||||
}
|
||||
|
||||
todo -= primes[i].BitLen()
|
||||
}
|
||||
|
||||
// Make sure that primes is pairwise unequal.
|
||||
for i, prime := range primes {
|
||||
for j := 0; j < i; j++ {
|
||||
if prime.Cmp(primes[j]) == 0 {
|
||||
continue NextSetOfPrimes
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
n := new(big.Int).Set(bigOne)
|
||||
totient := new(big.Int).Set(bigOne)
|
||||
pminus1 := new(big.Int)
|
||||
for _, prime := range primes {
|
||||
n.Mul(n, prime)
|
||||
pminus1.Sub(prime, bigOne)
|
||||
totient.Mul(totient, pminus1)
|
||||
}
|
||||
if n.BitLen() != bits {
|
||||
// This should never happen for nprimes == 2 because
|
||||
// crypto/rand should set the top two bits in each prime.
|
||||
// For nprimes > 2 we hope it does not happen often.
|
||||
continue NextSetOfPrimes
|
||||
}
|
||||
|
||||
priv.D = new(big.Int)
|
||||
e := big.NewInt(int64(priv.E))
|
||||
ok := priv.D.ModInverse(e, totient)
|
||||
|
||||
if ok != nil {
|
||||
priv.Primes = primes
|
||||
priv.N = n
|
||||
break
|
||||
}
|
||||
}
|
||||
|
||||
priv.Precompute()
|
||||
return priv, nil
|
||||
}
|
||||
|
|
@ -5,13 +5,13 @@
|
|||
package openpgp
|
||||
|
||||
import (
|
||||
"crypto/rsa"
|
||||
goerrors "errors"
|
||||
"io"
|
||||
"time"
|
||||
|
||||
"golang.org/x/crypto/openpgp/armor"
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"golang.org/x/crypto/openpgp/packet"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/armor"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/packet"
|
||||
)
|
||||
|
||||
// PublicKeyType is the armor type for a PGP public key.
|
||||
|
|
@ -37,15 +37,17 @@ type Identity struct {
|
|||
Name string // by convention, has the form "Full Name (comment) <email@example.com>"
|
||||
UserId *packet.UserId
|
||||
SelfSignature *packet.Signature
|
||||
Signatures []*packet.Signature
|
||||
Revocations []*packet.Signature
|
||||
Signatures []*packet.Signature // all (potentially unverified) self-signatures, revocations, and third-party signatures
|
||||
}
|
||||
|
||||
// A Subkey is an additional public key in an Entity. Subkeys can be used for
|
||||
// encryption.
|
||||
type Subkey struct {
|
||||
PublicKey *packet.PublicKey
|
||||
PrivateKey *packet.PrivateKey
|
||||
Sig *packet.Signature
|
||||
PublicKey *packet.PublicKey
|
||||
PrivateKey *packet.PrivateKey
|
||||
Sig *packet.Signature
|
||||
Revocations []*packet.Signature
|
||||
}
|
||||
|
||||
// A Key identifies a specific public key in an Entity. This is either the
|
||||
|
|
@ -55,13 +57,14 @@ type Key struct {
|
|||
PublicKey *packet.PublicKey
|
||||
PrivateKey *packet.PrivateKey
|
||||
SelfSignature *packet.Signature
|
||||
Revocations []*packet.Signature
|
||||
}
|
||||
|
||||
// A KeyRing provides access to public and private keys.
|
||||
type KeyRing interface {
|
||||
// KeysById returns the set of keys that have the given key id.
|
||||
KeysById(id uint64) []Key
|
||||
// KeysByIdUsage returns the set of keys with the given id
|
||||
// KeysByIdAndUsage returns the set of keys with the given id
|
||||
// that also meet the key usage given by requiredUsage.
|
||||
// The requiredUsage is expressed as the bitwise-OR of
|
||||
// packet.KeyFlag* values.
|
||||
|
|
@ -71,33 +74,71 @@ type KeyRing interface {
|
|||
DecryptionKeys() []Key
|
||||
}
|
||||
|
||||
// primaryIdentity returns the Identity marked as primary or the first identity
|
||||
// if none are so marked.
|
||||
func (e *Entity) primaryIdentity() *Identity {
|
||||
var firstIdentity *Identity
|
||||
// PrimaryIdentity returns an Identity, preferring non-revoked identities,
|
||||
// identities marked as primary, or the latest-created identity, in that order.
|
||||
func (e *Entity) PrimaryIdentity() *Identity {
|
||||
var primaryIdentity *Identity
|
||||
for _, ident := range e.Identities {
|
||||
if firstIdentity == nil {
|
||||
firstIdentity = ident
|
||||
}
|
||||
if ident.SelfSignature.IsPrimaryId != nil && *ident.SelfSignature.IsPrimaryId {
|
||||
return ident
|
||||
if shouldPreferIdentity(primaryIdentity, ident) {
|
||||
primaryIdentity = ident
|
||||
}
|
||||
}
|
||||
return firstIdentity
|
||||
return primaryIdentity
|
||||
}
|
||||
|
||||
// encryptionKey returns the best candidate Key for encrypting a message to the
|
||||
// given Entity.
|
||||
func (e *Entity) encryptionKey(now time.Time) (Key, bool) {
|
||||
candidateSubkey := -1
|
||||
func shouldPreferIdentity(existingId, potentialNewId *Identity) bool {
|
||||
if existingId == nil {
|
||||
return true
|
||||
}
|
||||
|
||||
// Iterate the keys to find the newest key
|
||||
if len(existingId.Revocations) > len(potentialNewId.Revocations) {
|
||||
return true
|
||||
}
|
||||
|
||||
if len(existingId.Revocations) < len(potentialNewId.Revocations) {
|
||||
return false
|
||||
}
|
||||
|
||||
if existingId.SelfSignature == nil {
|
||||
return true
|
||||
}
|
||||
|
||||
if existingId.SelfSignature.IsPrimaryId != nil && *existingId.SelfSignature.IsPrimaryId &&
|
||||
!(potentialNewId.SelfSignature.IsPrimaryId != nil && *potentialNewId.SelfSignature.IsPrimaryId) {
|
||||
return false
|
||||
}
|
||||
|
||||
if !(existingId.SelfSignature.IsPrimaryId != nil && *existingId.SelfSignature.IsPrimaryId) &&
|
||||
potentialNewId.SelfSignature.IsPrimaryId != nil && *potentialNewId.SelfSignature.IsPrimaryId {
|
||||
return true
|
||||
}
|
||||
|
||||
return potentialNewId.SelfSignature.CreationTime.After(existingId.SelfSignature.CreationTime)
|
||||
}
|
||||
|
||||
// EncryptionKey returns the best candidate Key for encrypting a message to the
|
||||
// given Entity.
|
||||
func (e *Entity) EncryptionKey(now time.Time) (Key, bool) {
|
||||
// Fail to find any encryption key if the...
|
||||
i := e.PrimaryIdentity()
|
||||
if e.PrimaryKey.KeyExpired(i.SelfSignature, now) || // primary key has expired
|
||||
i.SelfSignature == nil || // user ID has no self-signature
|
||||
i.SelfSignature.SigExpired(now) || // user ID self-signature has expired
|
||||
e.Revoked(now) || // primary key has been revoked
|
||||
i.Revoked(now) { // user ID has been revoked
|
||||
return Key{}, false
|
||||
}
|
||||
|
||||
// Iterate the keys to find the newest, unexpired one
|
||||
candidateSubkey := -1
|
||||
var maxTime time.Time
|
||||
for i, subkey := range e.Subkeys {
|
||||
if subkey.Sig.FlagsValid &&
|
||||
subkey.Sig.FlagEncryptCommunications &&
|
||||
subkey.PublicKey.PubKeyAlgo.CanEncrypt() &&
|
||||
!subkey.Sig.KeyExpired(now) &&
|
||||
!subkey.PublicKey.KeyExpired(subkey.Sig, now) &&
|
||||
!subkey.Sig.SigExpired(now) &&
|
||||
!subkey.Revoked(now) &&
|
||||
(maxTime.IsZero() || subkey.Sig.CreationTime.After(maxTime)) {
|
||||
candidateSubkey = i
|
||||
maxTime = subkey.Sig.CreationTime
|
||||
|
|
@ -106,55 +147,136 @@ func (e *Entity) encryptionKey(now time.Time) (Key, bool) {
|
|||
|
||||
if candidateSubkey != -1 {
|
||||
subkey := e.Subkeys[candidateSubkey]
|
||||
return Key{e, subkey.PublicKey, subkey.PrivateKey, subkey.Sig}, true
|
||||
return Key{e, subkey.PublicKey, subkey.PrivateKey, subkey.Sig, subkey.Revocations}, true
|
||||
}
|
||||
|
||||
// If we don't have any candidate subkeys for encryption and
|
||||
// the primary key doesn't have any usage metadata then we
|
||||
// assume that the primary key is ok. Or, if the primary key is
|
||||
// marked as ok to encrypt to, then we can obviously use it.
|
||||
i := e.primaryIdentity()
|
||||
// marked as ok to encrypt with, then we can obviously use it.
|
||||
if !i.SelfSignature.FlagsValid || i.SelfSignature.FlagEncryptCommunications &&
|
||||
e.PrimaryKey.PubKeyAlgo.CanEncrypt() &&
|
||||
!i.SelfSignature.KeyExpired(now) {
|
||||
return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature}, true
|
||||
e.PrimaryKey.PubKeyAlgo.CanEncrypt() {
|
||||
return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature, e.Revocations}, true
|
||||
}
|
||||
|
||||
// This Entity appears to be signing only.
|
||||
return Key{}, false
|
||||
}
|
||||
|
||||
// signingKey return the best candidate Key for signing a message with this
|
||||
// Entity.
|
||||
func (e *Entity) signingKey(now time.Time) (Key, bool) {
|
||||
candidateSubkey := -1
|
||||
|
||||
for i, subkey := range e.Subkeys {
|
||||
// CertificationKey return the best candidate Key for certifying a key with this
|
||||
// Entity.
|
||||
func (e *Entity) CertificationKey(now time.Time) (Key, bool) {
|
||||
return e.CertificationKeyById(now, 0)
|
||||
}
|
||||
|
||||
// CertificationKeyById return the Key for key certification with this
|
||||
// Entity and keyID.
|
||||
func (e *Entity) CertificationKeyById(now time.Time, id uint64) (Key, bool) {
|
||||
return e.signingKeyByIdUsage(now, id, packet.KeyFlagCertify)
|
||||
}
|
||||
|
||||
// SigningKey return the best candidate Key for signing a message with this
|
||||
// Entity.
|
||||
func (e *Entity) SigningKey(now time.Time) (Key, bool) {
|
||||
return e.SigningKeyById(now, 0)
|
||||
}
|
||||
|
||||
// SigningKeyById return the Key for signing a message with this
|
||||
// Entity and keyID.
|
||||
func (e *Entity) SigningKeyById(now time.Time, id uint64) (Key, bool) {
|
||||
return e.signingKeyByIdUsage(now, id, packet.KeyFlagSign)
|
||||
}
|
||||
|
||||
func (e *Entity) signingKeyByIdUsage(now time.Time, id uint64, flags int) (Key, bool) {
|
||||
// Fail to find any signing key if the...
|
||||
i := e.PrimaryIdentity()
|
||||
if e.PrimaryKey.KeyExpired(i.SelfSignature, now) || // primary key has expired
|
||||
i.SelfSignature == nil || // user ID has no self-signature
|
||||
i.SelfSignature.SigExpired(now) || // user ID self-signature has expired
|
||||
e.Revoked(now) || // primary key has been revoked
|
||||
i.Revoked(now) { // user ID has been revoked
|
||||
return Key{}, false
|
||||
}
|
||||
|
||||
// Iterate the keys to find the newest, unexpired one
|
||||
candidateSubkey := -1
|
||||
var maxTime time.Time
|
||||
for idx, subkey := range e.Subkeys {
|
||||
if subkey.Sig.FlagsValid &&
|
||||
subkey.Sig.FlagSign &&
|
||||
(flags & packet.KeyFlagCertify == 0 || subkey.Sig.FlagCertify) &&
|
||||
(flags & packet.KeyFlagSign == 0 || subkey.Sig.FlagSign) &&
|
||||
subkey.PublicKey.PubKeyAlgo.CanSign() &&
|
||||
!subkey.Sig.KeyExpired(now) {
|
||||
candidateSubkey = i
|
||||
break
|
||||
!subkey.PublicKey.KeyExpired(subkey.Sig, now) &&
|
||||
!subkey.Sig.SigExpired(now) &&
|
||||
!subkey.Revoked(now) &&
|
||||
(maxTime.IsZero() || subkey.Sig.CreationTime.After(maxTime)) &&
|
||||
(id == 0 || subkey.PublicKey.KeyId == id) {
|
||||
candidateSubkey = idx
|
||||
maxTime = subkey.Sig.CreationTime
|
||||
}
|
||||
}
|
||||
|
||||
if candidateSubkey != -1 {
|
||||
subkey := e.Subkeys[candidateSubkey]
|
||||
return Key{e, subkey.PublicKey, subkey.PrivateKey, subkey.Sig}, true
|
||||
return Key{e, subkey.PublicKey, subkey.PrivateKey, subkey.Sig, subkey.Revocations}, true
|
||||
}
|
||||
|
||||
// If we have no candidate subkey then we assume that it's ok to sign
|
||||
// with the primary key.
|
||||
i := e.primaryIdentity()
|
||||
if !i.SelfSignature.FlagsValid || i.SelfSignature.FlagSign &&
|
||||
!i.SelfSignature.KeyExpired(now) {
|
||||
return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature}, true
|
||||
// with the primary key. Or, if the primary key is marked as ok to
|
||||
// sign with, then we can use it.
|
||||
if !i.SelfSignature.FlagsValid || (
|
||||
(flags & packet.KeyFlagCertify == 0 || i.SelfSignature.FlagCertify) &&
|
||||
(flags & packet.KeyFlagSign == 0 || i.SelfSignature.FlagSign)) &&
|
||||
e.PrimaryKey.PubKeyAlgo.CanSign() &&
|
||||
(id == 0 || e.PrimaryKey.KeyId == id) {
|
||||
return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature, e.Revocations}, true
|
||||
}
|
||||
|
||||
// No keys with a valid Signing Flag or no keys matched the id passed in
|
||||
return Key{}, false
|
||||
}
|
||||
|
||||
func revoked(revocations []*packet.Signature, now time.Time) bool {
|
||||
for _, revocation := range revocations {
|
||||
if revocation.RevocationReason != nil && *revocation.RevocationReason == packet.KeyCompromised {
|
||||
// If the key is compromised, the key is considered revoked even before the revocation date.
|
||||
return true
|
||||
}
|
||||
if !revocation.SigExpired(now) {
|
||||
return true
|
||||
}
|
||||
}
|
||||
return false
|
||||
}
|
||||
|
||||
// Revoked returns whether the entity has any direct key revocation signatures.
|
||||
// Note that third-party revocation signatures are not supported.
|
||||
// Note also that Identity and Subkey revocation should be checked separately.
|
||||
func (e *Entity) Revoked(now time.Time) bool {
|
||||
return revoked(e.Revocations, now)
|
||||
}
|
||||
|
||||
// Revoked returns whether the identity has been revoked by a self-signature.
|
||||
// Note that third-party revocation signatures are not supported.
|
||||
func (i *Identity) Revoked(now time.Time) bool {
|
||||
return revoked(i.Revocations, now)
|
||||
}
|
||||
|
||||
// Revoked returns whether the subkey has been revoked by a self-signature.
|
||||
// Note that third-party revocation signatures are not supported.
|
||||
func (s *Subkey) Revoked(now time.Time) bool {
|
||||
return revoked(s.Revocations, now)
|
||||
}
|
||||
|
||||
// Revoked returns whether the key or subkey has been revoked by a self-signature.
|
||||
// Note that third-party revocation signatures are not supported.
|
||||
// Note also that Identity revocation should be checked separately.
|
||||
// Normally, it's not necessary to call this function, except on keys returned by
|
||||
// KeysById or KeysByIdUsage.
|
||||
func (key *Key) Revoked(now time.Time) bool {
|
||||
return revoked(key.Revocations, now)
|
||||
}
|
||||
|
||||
// An EntityList contains one or more Entities.
|
||||
type EntityList []*Entity
|
||||
|
||||
|
|
@ -162,41 +284,26 @@ type EntityList []*Entity
|
|||
func (el EntityList) KeysById(id uint64) (keys []Key) {
|
||||
for _, e := range el {
|
||||
if e.PrimaryKey.KeyId == id {
|
||||
var selfSig *packet.Signature
|
||||
for _, ident := range e.Identities {
|
||||
if selfSig == nil {
|
||||
selfSig = ident.SelfSignature
|
||||
} else if ident.SelfSignature.IsPrimaryId != nil && *ident.SelfSignature.IsPrimaryId {
|
||||
selfSig = ident.SelfSignature
|
||||
break
|
||||
}
|
||||
}
|
||||
keys = append(keys, Key{e, e.PrimaryKey, e.PrivateKey, selfSig})
|
||||
ident := e.PrimaryIdentity()
|
||||
selfSig := ident.SelfSignature
|
||||
keys = append(keys, Key{e, e.PrimaryKey, e.PrivateKey, selfSig, e.Revocations})
|
||||
}
|
||||
|
||||
for _, subKey := range e.Subkeys {
|
||||
if subKey.PublicKey.KeyId == id {
|
||||
keys = append(keys, Key{e, subKey.PublicKey, subKey.PrivateKey, subKey.Sig})
|
||||
keys = append(keys, Key{e, subKey.PublicKey, subKey.PrivateKey, subKey.Sig, subKey.Revocations})
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// KeysByIdUsage returns the set of keys with the given id that also meet
|
||||
// KeysByIdAndUsage returns the set of keys with the given id that also meet
|
||||
// the key usage given by requiredUsage. The requiredUsage is expressed as
|
||||
// the bitwise-OR of packet.KeyFlag* values.
|
||||
func (el EntityList) KeysByIdUsage(id uint64, requiredUsage byte) (keys []Key) {
|
||||
for _, key := range el.KeysById(id) {
|
||||
if len(key.Entity.Revocations) > 0 {
|
||||
continue
|
||||
}
|
||||
|
||||
if key.SelfSignature.RevocationReason != nil {
|
||||
continue
|
||||
}
|
||||
|
||||
if key.SelfSignature.FlagsValid && requiredUsage != 0 {
|
||||
if key.SelfSignature != nil && key.SelfSignature.FlagsValid && requiredUsage != 0 {
|
||||
var usage byte
|
||||
if key.SelfSignature.FlagCertify {
|
||||
usage |= packet.KeyFlagCertify
|
||||
|
|
@ -225,7 +332,7 @@ func (el EntityList) DecryptionKeys() (keys []Key) {
|
|||
for _, e := range el {
|
||||
for _, subKey := range e.Subkeys {
|
||||
if subKey.PrivateKey != nil && (!subKey.Sig.FlagsValid || subKey.Sig.FlagEncryptStorage || subKey.Sig.FlagEncryptCommunications) {
|
||||
keys = append(keys, Key{e, subKey.PublicKey, subKey.PrivateKey, subKey.Sig})
|
||||
keys = append(keys, Key{e, subKey.PublicKey, subKey.PrivateKey, subKey.Sig, subKey.Revocations})
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
@ -420,11 +527,24 @@ func addUserID(e *Entity, packets *packet.Reader, pkt *packet.UserId) error {
|
|||
break
|
||||
}
|
||||
|
||||
if (sig.SigType == packet.SigTypePositiveCert || sig.SigType == packet.SigTypeGenericCert) && sig.IssuerKeyId != nil && *sig.IssuerKeyId == e.PrimaryKey.KeyId {
|
||||
if sig.SigType != packet.SigTypeGenericCert &&
|
||||
sig.SigType != packet.SigTypePersonaCert &&
|
||||
sig.SigType != packet.SigTypeCasualCert &&
|
||||
sig.SigType != packet.SigTypePositiveCert &&
|
||||
sig.SigType != packet.SigTypeCertificationRevocation {
|
||||
return errors.StructuralError("user ID signature with wrong type")
|
||||
}
|
||||
|
||||
if sig.CheckKeyIdOrFingerprint(e.PrimaryKey) {
|
||||
if err = e.PrimaryKey.VerifyUserIdSignature(pkt.Id, e.PrimaryKey, sig); err != nil {
|
||||
return errors.StructuralError("user ID self-signature invalid: " + err.Error())
|
||||
}
|
||||
identity.SelfSignature = sig
|
||||
if sig.SigType == packet.SigTypeCertificationRevocation {
|
||||
identity.Revocations = append(identity.Revocations, sig)
|
||||
} else if identity.SelfSignature == nil || sig.CreationTime.After(identity.SelfSignature.CreationTime) {
|
||||
identity.SelfSignature = sig
|
||||
}
|
||||
identity.Signatures = append(identity.Signatures, sig)
|
||||
e.Identities[pkt.Id] = identity
|
||||
} else {
|
||||
identity.Signatures = append(identity.Signatures, sig)
|
||||
|
|
@ -463,10 +583,9 @@ func addSubkey(e *Entity, packets *packet.Reader, pub *packet.PublicKey, priv *p
|
|||
|
||||
switch sig.SigType {
|
||||
case packet.SigTypeSubkeyRevocation:
|
||||
subKey.Sig = sig
|
||||
subKey.Revocations = append(subKey.Revocations, sig)
|
||||
case packet.SigTypeSubkeyBinding:
|
||||
|
||||
if shouldReplaceSubkeySig(subKey.Sig, sig) {
|
||||
if subKey.Sig == nil || sig.CreationTime.After(subKey.Sig.CreationTime) {
|
||||
subKey.Sig = sig
|
||||
}
|
||||
}
|
||||
|
|
@ -481,131 +600,59 @@ func addSubkey(e *Entity, packets *packet.Reader, pub *packet.PublicKey, priv *p
|
|||
return nil
|
||||
}
|
||||
|
||||
func shouldReplaceSubkeySig(existingSig, potentialNewSig *packet.Signature) bool {
|
||||
if potentialNewSig == nil {
|
||||
return false
|
||||
}
|
||||
|
||||
if existingSig == nil {
|
||||
return true
|
||||
}
|
||||
|
||||
if existingSig.SigType == packet.SigTypeSubkeyRevocation {
|
||||
return false // never override a revocation signature
|
||||
}
|
||||
|
||||
return potentialNewSig.CreationTime.After(existingSig.CreationTime)
|
||||
}
|
||||
|
||||
const defaultRSAKeyBits = 2048
|
||||
|
||||
// NewEntity returns an Entity that contains a fresh RSA/RSA keypair with a
|
||||
// single identity composed of the given full name, comment and email, any of
|
||||
// which may be empty but must not contain any of "()<>\x00".
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func NewEntity(name, comment, email string, config *packet.Config) (*Entity, error) {
|
||||
creationTime := config.Now()
|
||||
|
||||
bits := defaultRSAKeyBits
|
||||
if config != nil && config.RSABits != 0 {
|
||||
bits = config.RSABits
|
||||
}
|
||||
|
||||
uid := packet.NewUserId(name, comment, email)
|
||||
if uid == nil {
|
||||
return nil, errors.InvalidArgumentError("user id field contained invalid characters")
|
||||
}
|
||||
signingPriv, err := rsa.GenerateKey(config.Random(), bits)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
encryptingPriv, err := rsa.GenerateKey(config.Random(), bits)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
e := &Entity{
|
||||
PrimaryKey: packet.NewRSAPublicKey(creationTime, &signingPriv.PublicKey),
|
||||
PrivateKey: packet.NewRSAPrivateKey(creationTime, signingPriv),
|
||||
Identities: make(map[string]*Identity),
|
||||
}
|
||||
isPrimaryId := true
|
||||
e.Identities[uid.Id] = &Identity{
|
||||
Name: uid.Id,
|
||||
UserId: uid,
|
||||
SelfSignature: &packet.Signature{
|
||||
CreationTime: creationTime,
|
||||
SigType: packet.SigTypePositiveCert,
|
||||
PubKeyAlgo: packet.PubKeyAlgoRSA,
|
||||
Hash: config.Hash(),
|
||||
IsPrimaryId: &isPrimaryId,
|
||||
FlagsValid: true,
|
||||
FlagSign: true,
|
||||
FlagCertify: true,
|
||||
IssuerKeyId: &e.PrimaryKey.KeyId,
|
||||
},
|
||||
}
|
||||
err = e.Identities[uid.Id].SelfSignature.SignUserId(uid.Id, e.PrimaryKey, e.PrivateKey, config)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
// If the user passes in a DefaultHash via packet.Config,
|
||||
// set the PreferredHash for the SelfSignature.
|
||||
if config != nil && config.DefaultHash != 0 {
|
||||
e.Identities[uid.Id].SelfSignature.PreferredHash = []uint8{hashToHashId(config.DefaultHash)}
|
||||
}
|
||||
|
||||
// Likewise for DefaultCipher.
|
||||
if config != nil && config.DefaultCipher != 0 {
|
||||
e.Identities[uid.Id].SelfSignature.PreferredSymmetric = []uint8{uint8(config.DefaultCipher)}
|
||||
}
|
||||
|
||||
e.Subkeys = make([]Subkey, 1)
|
||||
e.Subkeys[0] = Subkey{
|
||||
PublicKey: packet.NewRSAPublicKey(creationTime, &encryptingPriv.PublicKey),
|
||||
PrivateKey: packet.NewRSAPrivateKey(creationTime, encryptingPriv),
|
||||
Sig: &packet.Signature{
|
||||
CreationTime: creationTime,
|
||||
SigType: packet.SigTypeSubkeyBinding,
|
||||
PubKeyAlgo: packet.PubKeyAlgoRSA,
|
||||
Hash: config.Hash(),
|
||||
FlagsValid: true,
|
||||
FlagEncryptStorage: true,
|
||||
FlagEncryptCommunications: true,
|
||||
IssuerKeyId: &e.PrimaryKey.KeyId,
|
||||
},
|
||||
}
|
||||
e.Subkeys[0].PublicKey.IsSubkey = true
|
||||
e.Subkeys[0].PrivateKey.IsSubkey = true
|
||||
err = e.Subkeys[0].Sig.SignKey(e.Subkeys[0].PublicKey, e.PrivateKey, config)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
return e, nil
|
||||
}
|
||||
|
||||
// SerializePrivate serializes an Entity, including private key material, but
|
||||
// excluding signatures from other entities, to the given Writer.
|
||||
// Identities and subkeys are re-signed in case they changed since NewEntry.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (e *Entity) SerializePrivate(w io.Writer, config *packet.Config) (err error) {
|
||||
if e.PrivateKey.Dummy() {
|
||||
return errors.ErrDummyPrivateKey("dummy private key cannot re-sign identities")
|
||||
}
|
||||
return e.serializePrivate(w, config, true)
|
||||
}
|
||||
|
||||
// SerializePrivateWithoutSigning serializes an Entity, including private key
|
||||
// material, but excluding signatures from other entities, to the given Writer.
|
||||
// Self-signatures of identities and subkeys are not re-signed. This is useful
|
||||
// when serializing GNU dummy keys, among other things.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (e *Entity) SerializePrivateWithoutSigning(w io.Writer, config *packet.Config) (err error) {
|
||||
return e.serializePrivate(w, config, false)
|
||||
}
|
||||
|
||||
func (e *Entity) serializePrivate(w io.Writer, config *packet.Config, reSign bool) (err error) {
|
||||
if e.PrivateKey == nil {
|
||||
return goerrors.New("openpgp: private key is missing")
|
||||
}
|
||||
err = e.PrivateKey.Serialize(w)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
for _, revocation := range e.Revocations {
|
||||
err := revocation.Serialize(w)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
}
|
||||
for _, ident := range e.Identities {
|
||||
err = ident.UserId.Serialize(w)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
err = ident.SelfSignature.SignUserId(ident.UserId.Id, e.PrimaryKey, e.PrivateKey, config)
|
||||
if err != nil {
|
||||
return
|
||||
if reSign {
|
||||
if ident.SelfSignature == nil {
|
||||
return goerrors.New("openpgp: can't re-sign identity without valid self-signature")
|
||||
}
|
||||
err = ident.SelfSignature.SignUserId(ident.UserId.Id, e.PrimaryKey, e.PrivateKey, config)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
}
|
||||
err = ident.SelfSignature.Serialize(w)
|
||||
if err != nil {
|
||||
return
|
||||
for _, sig := range ident.Signatures {
|
||||
err = sig.Serialize(w)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
}
|
||||
}
|
||||
for _, subkey := range e.Subkeys {
|
||||
|
|
@ -613,9 +660,24 @@ func (e *Entity) SerializePrivate(w io.Writer, config *packet.Config) (err error
|
|||
if err != nil {
|
||||
return
|
||||
}
|
||||
err = subkey.Sig.SignKey(subkey.PublicKey, e.PrivateKey, config)
|
||||
if err != nil {
|
||||
return
|
||||
if reSign {
|
||||
err = subkey.Sig.SignKey(subkey.PublicKey, e.PrivateKey, config)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
if subkey.Sig.EmbeddedSignature != nil {
|
||||
err = subkey.Sig.EmbeddedSignature.CrossSignKey(subkey.PublicKey, e.PrimaryKey,
|
||||
subkey.PrivateKey, config)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
}
|
||||
}
|
||||
for _, revocation := range subkey.Revocations {
|
||||
err := revocation.Serialize(w)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
}
|
||||
err = subkey.Sig.Serialize(w)
|
||||
if err != nil {
|
||||
|
|
@ -632,12 +694,14 @@ func (e *Entity) Serialize(w io.Writer) error {
|
|||
if err != nil {
|
||||
return err
|
||||
}
|
||||
for _, ident := range e.Identities {
|
||||
err = ident.UserId.Serialize(w)
|
||||
for _, revocation := range e.Revocations {
|
||||
err := revocation.Serialize(w)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
err = ident.SelfSignature.Serialize(w)
|
||||
}
|
||||
for _, ident := range e.Identities {
|
||||
err = ident.UserId.Serialize(w)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
|
|
@ -653,6 +717,12 @@ func (e *Entity) Serialize(w io.Writer) error {
|
|||
if err != nil {
|
||||
return err
|
||||
}
|
||||
for _, revocation := range subkey.Revocations {
|
||||
err := revocation.Serialize(w)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
}
|
||||
err = subkey.Sig.Serialize(w)
|
||||
if err != nil {
|
||||
return err
|
||||
|
|
@ -667,27 +737,68 @@ func (e *Entity) Serialize(w io.Writer) error {
|
|||
// necessary.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (e *Entity) SignIdentity(identity string, signer *Entity, config *packet.Config) error {
|
||||
if signer.PrivateKey == nil {
|
||||
return errors.InvalidArgumentError("signing Entity must have a private key")
|
||||
certificationKey, ok := signer.CertificationKey(config.Now())
|
||||
if !ok {
|
||||
return errors.InvalidArgumentError("no valid certification key found")
|
||||
}
|
||||
if signer.PrivateKey.Encrypted {
|
||||
|
||||
if certificationKey.PrivateKey.Encrypted {
|
||||
return errors.InvalidArgumentError("signing Entity's private key must be decrypted")
|
||||
}
|
||||
|
||||
ident, ok := e.Identities[identity]
|
||||
if !ok {
|
||||
return errors.InvalidArgumentError("given identity string not found in Entity")
|
||||
}
|
||||
|
||||
sig := &packet.Signature{
|
||||
SigType: packet.SigTypeGenericCert,
|
||||
PubKeyAlgo: signer.PrivateKey.PubKeyAlgo,
|
||||
Hash: config.Hash(),
|
||||
CreationTime: config.Now(),
|
||||
IssuerKeyId: &signer.PrivateKey.KeyId,
|
||||
sig := createSignaturePacket(certificationKey.PublicKey, packet.SigTypeGenericCert, config)
|
||||
|
||||
signingUserID := config.SigningUserId()
|
||||
if signingUserID != "" {
|
||||
if _, ok := signer.Identities[signingUserID]; !ok {
|
||||
return errors.InvalidArgumentError("signer identity string not found in signer Entity")
|
||||
}
|
||||
sig.SignerUserId = &signingUserID
|
||||
}
|
||||
if err := sig.SignUserId(identity, e.PrimaryKey, signer.PrivateKey, config); err != nil {
|
||||
|
||||
if err := sig.SignUserId(identity, e.PrimaryKey, certificationKey.PrivateKey, config); err != nil {
|
||||
return err
|
||||
}
|
||||
ident.Signatures = append(ident.Signatures, sig)
|
||||
return nil
|
||||
}
|
||||
|
||||
// RevokeKey generates a key revocation signature (packet.SigTypeKeyRevocation) with the
|
||||
// specified reason code and text (RFC4880 section-5.2.3.23).
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (e *Entity) RevokeKey(reason packet.ReasonForRevocation, reasonText string, config *packet.Config) error {
|
||||
revSig := createSignaturePacket(e.PrimaryKey, packet.SigTypeKeyRevocation, config)
|
||||
revSig.RevocationReason = &reason
|
||||
revSig.RevocationReasonText = reasonText
|
||||
|
||||
if err := revSig.RevokeKey(e.PrimaryKey, e.PrivateKey, config); err != nil {
|
||||
return err
|
||||
}
|
||||
e.Revocations = append(e.Revocations, revSig)
|
||||
return nil
|
||||
}
|
||||
|
||||
// RevokeSubkey generates a subkey revocation signature (packet.SigTypeSubkeyRevocation) for
|
||||
// a subkey with the specified reason code and text (RFC4880 section-5.2.3.23).
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (e *Entity) RevokeSubkey(sk *Subkey, reason packet.ReasonForRevocation, reasonText string, config *packet.Config) error {
|
||||
if err := e.PrimaryKey.VerifyKeySignature(sk.PublicKey, sk.Sig); err != nil {
|
||||
return errors.InvalidArgumentError("given subkey is not associated with this key")
|
||||
}
|
||||
|
||||
revSig := createSignaturePacket(e.PrimaryKey, packet.SigTypeSubkeyRevocation, config)
|
||||
revSig.RevocationReason = &reason
|
||||
revSig.RevocationReasonText = reasonText
|
||||
|
||||
if err := revSig.RevokeSubkey(sk.PublicKey, e.PrivateKey, config); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
sk.Revocations = append(sk.Revocations, revSig)
|
||||
return nil
|
||||
}
|
||||
File diff suppressed because one or more lines are too long
67
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_config.go
generated
vendored
Normal file
67
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_config.go
generated
vendored
Normal file
|
|
@ -0,0 +1,67 @@
|
|||
// Copyright (C) 2019 ProtonTech AG
|
||||
|
||||
package packet
|
||||
|
||||
import "math/bits"
|
||||
|
||||
// CipherSuite contains a combination of Cipher and Mode
|
||||
type CipherSuite struct {
|
||||
// The cipher function
|
||||
Cipher CipherFunction
|
||||
// The AEAD mode of operation.
|
||||
Mode AEADMode
|
||||
}
|
||||
|
||||
// AEADConfig collects a number of AEAD parameters along with sensible defaults.
|
||||
// A nil AEADConfig is valid and results in all default values.
|
||||
type AEADConfig struct {
|
||||
// The AEAD mode of operation.
|
||||
DefaultMode AEADMode
|
||||
// Amount of octets in each chunk of data
|
||||
ChunkSize uint64
|
||||
}
|
||||
|
||||
// Mode returns the AEAD mode of operation.
|
||||
func (conf *AEADConfig) Mode() AEADMode {
|
||||
// If no preference is specified, OCB is used (which is mandatory to implement).
|
||||
if conf == nil || conf.DefaultMode == 0 {
|
||||
return AEADModeOCB
|
||||
}
|
||||
|
||||
mode := conf.DefaultMode
|
||||
if mode != AEADModeEAX && mode != AEADModeOCB && mode != AEADModeGCM {
|
||||
panic("AEAD mode unsupported")
|
||||
}
|
||||
return mode
|
||||
}
|
||||
|
||||
// ChunkSizeByte returns the byte indicating the chunk size. The effective
|
||||
// chunk size is computed with the formula uint64(1) << (chunkSizeByte + 6)
|
||||
// limit to 16 = 4 MiB
|
||||
// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-5.13.2
|
||||
func (conf *AEADConfig) ChunkSizeByte() byte {
|
||||
if conf == nil || conf.ChunkSize == 0 {
|
||||
return 12 // 1 << (12 + 6) == 262144 bytes
|
||||
}
|
||||
|
||||
chunkSize := conf.ChunkSize
|
||||
exponent := bits.Len64(chunkSize) - 1
|
||||
switch {
|
||||
case exponent < 6:
|
||||
exponent = 6
|
||||
case exponent > 16:
|
||||
exponent = 16
|
||||
}
|
||||
|
||||
return byte(exponent - 6)
|
||||
}
|
||||
|
||||
// decodeAEADChunkSize returns the effective chunk size. In 32-bit systems, the
|
||||
// maximum returned value is 1 << 30.
|
||||
func decodeAEADChunkSize(c byte) int {
|
||||
size := uint64(1 << (c + 6))
|
||||
if size != uint64(int(size)) {
|
||||
return 1 << 30
|
||||
}
|
||||
return int(size)
|
||||
}
|
||||
265
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_crypter.go
generated
vendored
Normal file
265
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_crypter.go
generated
vendored
Normal file
|
|
@ -0,0 +1,265 @@
|
|||
// Copyright (C) 2019 ProtonTech AG
|
||||
|
||||
package packet
|
||||
|
||||
import (
|
||||
"bytes"
|
||||
"crypto/cipher"
|
||||
"encoding/binary"
|
||||
"io"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
)
|
||||
|
||||
// aeadCrypter is an AEAD opener/sealer, its configuration, and data for en/decryption.
|
||||
type aeadCrypter struct {
|
||||
aead cipher.AEAD
|
||||
chunkSize int
|
||||
initialNonce []byte
|
||||
associatedData []byte // Chunk-independent associated data
|
||||
chunkIndex []byte // Chunk counter
|
||||
packetTag packetType
|
||||
bytesProcessed int // Amount of plaintext bytes encrypted/decrypted
|
||||
buffer bytes.Buffer // Buffered bytes across chunks
|
||||
}
|
||||
|
||||
// computeNonce takes the incremental index and computes an eXclusive OR with
|
||||
// the least significant 8 bytes of the receivers' initial nonce (see sec.
|
||||
// 5.16.1 and 5.16.2). It returns the resulting nonce.
|
||||
func (wo *aeadCrypter) computeNextNonce() (nonce []byte) {
|
||||
if wo.packetTag == packetTypeSymmetricallyEncryptedIntegrityProtected {
|
||||
return append(wo.initialNonce, wo.chunkIndex...)
|
||||
}
|
||||
|
||||
nonce = make([]byte, len(wo.initialNonce))
|
||||
copy(nonce, wo.initialNonce)
|
||||
offset := len(wo.initialNonce) - 8
|
||||
for i := 0; i < 8; i++ {
|
||||
nonce[i+offset] ^= wo.chunkIndex[i]
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// incrementIndex performs an integer increment by 1 of the integer represented by the
|
||||
// slice, modifying it accordingly.
|
||||
func (wo *aeadCrypter) incrementIndex() error {
|
||||
index := wo.chunkIndex
|
||||
if len(index) == 0 {
|
||||
return errors.AEADError("Index has length 0")
|
||||
}
|
||||
for i := len(index) - 1; i >= 0; i-- {
|
||||
if index[i] < 255 {
|
||||
index[i]++
|
||||
return nil
|
||||
}
|
||||
index[i] = 0
|
||||
}
|
||||
return errors.AEADError("cannot further increment index")
|
||||
}
|
||||
|
||||
// aeadDecrypter reads and decrypts bytes. It buffers extra decrypted bytes when
|
||||
// necessary, similar to aeadEncrypter.
|
||||
type aeadDecrypter struct {
|
||||
aeadCrypter // Embedded ciphertext opener
|
||||
reader io.Reader // 'reader' is a partialLengthReader
|
||||
peekedBytes []byte // Used to detect last chunk
|
||||
eof bool
|
||||
}
|
||||
|
||||
// Read decrypts bytes and reads them into dst. It decrypts when necessary and
|
||||
// buffers extra decrypted bytes. It returns the number of bytes copied into dst
|
||||
// and an error.
|
||||
func (ar *aeadDecrypter) Read(dst []byte) (n int, err error) {
|
||||
// Return buffered plaintext bytes from previous calls
|
||||
if ar.buffer.Len() > 0 {
|
||||
return ar.buffer.Read(dst)
|
||||
}
|
||||
|
||||
// Return EOF if we've previously validated the final tag
|
||||
if ar.eof {
|
||||
return 0, io.EOF
|
||||
}
|
||||
|
||||
// Read a chunk
|
||||
tagLen := ar.aead.Overhead()
|
||||
cipherChunkBuf := new(bytes.Buffer)
|
||||
_, errRead := io.CopyN(cipherChunkBuf, ar.reader, int64(ar.chunkSize + tagLen))
|
||||
cipherChunk := cipherChunkBuf.Bytes()
|
||||
if errRead != nil && errRead != io.EOF {
|
||||
return 0, errRead
|
||||
}
|
||||
decrypted, errChunk := ar.openChunk(cipherChunk)
|
||||
if errChunk != nil {
|
||||
return 0, errChunk
|
||||
}
|
||||
|
||||
// Return decrypted bytes, buffering if necessary
|
||||
if len(dst) < len(decrypted) {
|
||||
n = copy(dst, decrypted[:len(dst)])
|
||||
ar.buffer.Write(decrypted[len(dst):])
|
||||
} else {
|
||||
n = copy(dst, decrypted)
|
||||
}
|
||||
|
||||
// Check final authentication tag
|
||||
if errRead == io.EOF {
|
||||
errChunk := ar.validateFinalTag(ar.peekedBytes)
|
||||
if errChunk != nil {
|
||||
return n, errChunk
|
||||
}
|
||||
ar.eof = true // Mark EOF for when we've returned all buffered data
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Close is noOp. The final authentication tag of the stream was already
|
||||
// checked in the last Read call. In the future, this function could be used to
|
||||
// wipe the reader and peeked, decrypted bytes, if necessary.
|
||||
func (ar *aeadDecrypter) Close() (err error) {
|
||||
return nil
|
||||
}
|
||||
|
||||
// openChunk decrypts and checks integrity of an encrypted chunk, returning
|
||||
// the underlying plaintext and an error. It accesses peeked bytes from next
|
||||
// chunk, to identify the last chunk and decrypt/validate accordingly.
|
||||
func (ar *aeadDecrypter) openChunk(data []byte) ([]byte, error) {
|
||||
tagLen := ar.aead.Overhead()
|
||||
// Restore carried bytes from last call
|
||||
chunkExtra := append(ar.peekedBytes, data...)
|
||||
// 'chunk' contains encrypted bytes, followed by an authentication tag.
|
||||
chunk := chunkExtra[:len(chunkExtra)-tagLen]
|
||||
ar.peekedBytes = chunkExtra[len(chunkExtra)-tagLen:]
|
||||
|
||||
adata := ar.associatedData
|
||||
if ar.aeadCrypter.packetTag == packetTypeAEADEncrypted {
|
||||
adata = append(ar.associatedData, ar.chunkIndex...)
|
||||
}
|
||||
|
||||
nonce := ar.computeNextNonce()
|
||||
plainChunk, err := ar.aead.Open(nil, nonce, chunk, adata)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
ar.bytesProcessed += len(plainChunk)
|
||||
if err = ar.aeadCrypter.incrementIndex(); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
return plainChunk, nil
|
||||
}
|
||||
|
||||
// Checks the summary tag. It takes into account the total decrypted bytes into
|
||||
// the associated data. It returns an error, or nil if the tag is valid.
|
||||
func (ar *aeadDecrypter) validateFinalTag(tag []byte) error {
|
||||
// Associated: tag, version, cipher, aead, chunk size, ...
|
||||
amountBytes := make([]byte, 8)
|
||||
binary.BigEndian.PutUint64(amountBytes, uint64(ar.bytesProcessed))
|
||||
|
||||
adata := ar.associatedData
|
||||
if ar.aeadCrypter.packetTag == packetTypeAEADEncrypted {
|
||||
// ... index ...
|
||||
adata = append(ar.associatedData, ar.chunkIndex...)
|
||||
}
|
||||
|
||||
// ... and total number of encrypted octets
|
||||
adata = append(adata, amountBytes...)
|
||||
nonce := ar.computeNextNonce()
|
||||
_, err := ar.aead.Open(nil, nonce, tag, adata)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
// aeadEncrypter encrypts and writes bytes. It encrypts when necessary according
|
||||
// to the AEAD block size, and buffers the extra encrypted bytes for next write.
|
||||
type aeadEncrypter struct {
|
||||
aeadCrypter // Embedded plaintext sealer
|
||||
writer io.WriteCloser // 'writer' is a partialLengthWriter
|
||||
}
|
||||
|
||||
|
||||
// Write encrypts and writes bytes. It encrypts when necessary and buffers extra
|
||||
// plaintext bytes for next call. When the stream is finished, Close() MUST be
|
||||
// called to append the final tag.
|
||||
func (aw *aeadEncrypter) Write(plaintextBytes []byte) (n int, err error) {
|
||||
// Append plaintextBytes to existing buffered bytes
|
||||
n, err = aw.buffer.Write(plaintextBytes)
|
||||
if err != nil {
|
||||
return n, err
|
||||
}
|
||||
// Encrypt and write chunks
|
||||
for aw.buffer.Len() >= aw.chunkSize {
|
||||
plainChunk := aw.buffer.Next(aw.chunkSize)
|
||||
encryptedChunk, err := aw.sealChunk(plainChunk)
|
||||
if err != nil {
|
||||
return n, err
|
||||
}
|
||||
_, err = aw.writer.Write(encryptedChunk)
|
||||
if err != nil {
|
||||
return n, err
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Close encrypts and writes the remaining buffered plaintext if any, appends
|
||||
// the final authentication tag, and closes the embedded writer. This function
|
||||
// MUST be called at the end of a stream.
|
||||
func (aw *aeadEncrypter) Close() (err error) {
|
||||
// Encrypt and write a chunk if there's buffered data left, or if we haven't
|
||||
// written any chunks yet.
|
||||
if aw.buffer.Len() > 0 || aw.bytesProcessed == 0 {
|
||||
plainChunk := aw.buffer.Bytes()
|
||||
lastEncryptedChunk, err := aw.sealChunk(plainChunk)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
_, err = aw.writer.Write(lastEncryptedChunk)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
}
|
||||
// Compute final tag (associated data: packet tag, version, cipher, aead,
|
||||
// chunk size...
|
||||
adata := aw.associatedData
|
||||
|
||||
if aw.aeadCrypter.packetTag == packetTypeAEADEncrypted {
|
||||
// ... index ...
|
||||
adata = append(aw.associatedData, aw.chunkIndex...)
|
||||
}
|
||||
|
||||
// ... and total number of encrypted octets
|
||||
amountBytes := make([]byte, 8)
|
||||
binary.BigEndian.PutUint64(amountBytes, uint64(aw.bytesProcessed))
|
||||
adata = append(adata, amountBytes...)
|
||||
|
||||
nonce := aw.computeNextNonce()
|
||||
finalTag := aw.aead.Seal(nil, nonce, nil, adata)
|
||||
_, err = aw.writer.Write(finalTag)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
return aw.writer.Close()
|
||||
}
|
||||
|
||||
// sealChunk Encrypts and authenticates the given chunk.
|
||||
func (aw *aeadEncrypter) sealChunk(data []byte) ([]byte, error) {
|
||||
if len(data) > aw.chunkSize {
|
||||
return nil, errors.AEADError("chunk exceeds maximum length")
|
||||
}
|
||||
if aw.associatedData == nil {
|
||||
return nil, errors.AEADError("can't seal without headers")
|
||||
}
|
||||
adata := aw.associatedData
|
||||
if aw.aeadCrypter.packetTag == packetTypeAEADEncrypted {
|
||||
adata = append(aw.associatedData, aw.chunkIndex...)
|
||||
}
|
||||
|
||||
nonce := aw.computeNextNonce()
|
||||
encrypted := aw.aead.Seal(nil, nonce, data, adata)
|
||||
aw.bytesProcessed += len(data)
|
||||
if err := aw.aeadCrypter.incrementIndex(); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
return encrypted, nil
|
||||
}
|
||||
96
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_encrypted.go
generated
vendored
Normal file
96
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_encrypted.go
generated
vendored
Normal file
|
|
@ -0,0 +1,96 @@
|
|||
// Copyright (C) 2019 ProtonTech AG
|
||||
|
||||
package packet
|
||||
|
||||
import (
|
||||
"io"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/algorithm"
|
||||
)
|
||||
|
||||
// AEADEncrypted represents an AEAD Encrypted Packet.
|
||||
// See https://www.ietf.org/archive/id/draft-koch-openpgp-2015-rfc4880bis-00.html#name-aead-encrypted-data-packet-t
|
||||
type AEADEncrypted struct {
|
||||
cipher CipherFunction
|
||||
mode AEADMode
|
||||
chunkSizeByte byte
|
||||
Contents io.Reader // Encrypted chunks and tags
|
||||
initialNonce []byte // Referred to as IV in RFC4880-bis
|
||||
}
|
||||
|
||||
// Only currently defined version
|
||||
const aeadEncryptedVersion = 1
|
||||
|
||||
func (ae *AEADEncrypted) parse(buf io.Reader) error {
|
||||
headerData := make([]byte, 4)
|
||||
if n, err := io.ReadFull(buf, headerData); n < 4 {
|
||||
return errors.AEADError("could not read aead header:" + err.Error())
|
||||
}
|
||||
// Read initial nonce
|
||||
mode := AEADMode(headerData[2])
|
||||
nonceLen := mode.IvLength()
|
||||
|
||||
// This packet supports only EAX and OCB
|
||||
// https://www.ietf.org/archive/id/draft-koch-openpgp-2015-rfc4880bis-00.html#name-aead-encrypted-data-packet-t
|
||||
if nonceLen == 0 || mode > AEADModeOCB {
|
||||
return errors.AEADError("unknown mode")
|
||||
}
|
||||
|
||||
initialNonce := make([]byte, nonceLen)
|
||||
if n, err := io.ReadFull(buf, initialNonce); n < nonceLen {
|
||||
return errors.AEADError("could not read aead nonce:" + err.Error())
|
||||
}
|
||||
ae.Contents = buf
|
||||
ae.initialNonce = initialNonce
|
||||
c := headerData[1]
|
||||
if _, ok := algorithm.CipherById[c]; !ok {
|
||||
return errors.UnsupportedError("unknown cipher: " + string(c))
|
||||
}
|
||||
ae.cipher = CipherFunction(c)
|
||||
ae.mode = mode
|
||||
ae.chunkSizeByte = headerData[3]
|
||||
return nil
|
||||
}
|
||||
|
||||
// Decrypt returns a io.ReadCloser from which decrypted bytes can be read, or
|
||||
// an error.
|
||||
func (ae *AEADEncrypted) Decrypt(ciph CipherFunction, key []byte) (io.ReadCloser, error) {
|
||||
return ae.decrypt(key)
|
||||
}
|
||||
|
||||
// decrypt prepares an aeadCrypter and returns a ReadCloser from which
|
||||
// decrypted bytes can be read (see aeadDecrypter.Read()).
|
||||
func (ae *AEADEncrypted) decrypt(key []byte) (io.ReadCloser, error) {
|
||||
blockCipher := ae.cipher.new(key)
|
||||
aead := ae.mode.new(blockCipher)
|
||||
// Carry the first tagLen bytes
|
||||
tagLen := ae.mode.TagLength()
|
||||
peekedBytes := make([]byte, tagLen)
|
||||
n, err := io.ReadFull(ae.Contents, peekedBytes)
|
||||
if n < tagLen || (err != nil && err != io.EOF) {
|
||||
return nil, errors.AEADError("Not enough data to decrypt:" + err.Error())
|
||||
}
|
||||
chunkSize := decodeAEADChunkSize(ae.chunkSizeByte)
|
||||
return &aeadDecrypter{
|
||||
aeadCrypter: aeadCrypter{
|
||||
aead: aead,
|
||||
chunkSize: chunkSize,
|
||||
initialNonce: ae.initialNonce,
|
||||
associatedData: ae.associatedData(),
|
||||
chunkIndex: make([]byte, 8),
|
||||
packetTag: packetTypeAEADEncrypted,
|
||||
},
|
||||
reader: ae.Contents,
|
||||
peekedBytes: peekedBytes}, nil
|
||||
}
|
||||
|
||||
// associatedData for chunks: tag, version, cipher, mode, chunk size byte
|
||||
func (ae *AEADEncrypted) associatedData() []byte {
|
||||
return []byte{
|
||||
0xD4,
|
||||
aeadEncryptedVersion,
|
||||
byte(ae.cipher),
|
||||
byte(ae.mode),
|
||||
ae.chunkSizeByte}
|
||||
}
|
||||
|
|
@ -8,7 +8,7 @@ import (
|
|||
"compress/bzip2"
|
||||
"compress/flate"
|
||||
"compress/zlib"
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"io"
|
||||
"strconv"
|
||||
)
|
||||
|
|
@ -47,6 +47,8 @@ func (c *Compressed) parse(r io.Reader) error {
|
|||
}
|
||||
|
||||
switch buf[0] {
|
||||
case 0:
|
||||
c.Body = r
|
||||
case 1:
|
||||
c.Body = flate.NewReader(r)
|
||||
case 2:
|
||||
|
|
@ -0,0 +1,224 @@
|
|||
// Copyright 2012 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package packet
|
||||
|
||||
import (
|
||||
"crypto"
|
||||
"crypto/rand"
|
||||
"io"
|
||||
"math/big"
|
||||
"time"
|
||||
)
|
||||
|
||||
// Config collects a number of parameters along with sensible defaults.
|
||||
// A nil *Config is valid and results in all default values.
|
||||
type Config struct {
|
||||
// Rand provides the source of entropy.
|
||||
// If nil, the crypto/rand Reader is used.
|
||||
Rand io.Reader
|
||||
// DefaultHash is the default hash function to be used.
|
||||
// If zero, SHA-256 is used.
|
||||
DefaultHash crypto.Hash
|
||||
// DefaultCipher is the cipher to be used.
|
||||
// If zero, AES-128 is used.
|
||||
DefaultCipher CipherFunction
|
||||
// Time returns the current time as the number of seconds since the
|
||||
// epoch. If Time is nil, time.Now is used.
|
||||
Time func() time.Time
|
||||
// DefaultCompressionAlgo is the compression algorithm to be
|
||||
// applied to the plaintext before encryption. If zero, no
|
||||
// compression is done.
|
||||
DefaultCompressionAlgo CompressionAlgo
|
||||
// CompressionConfig configures the compression settings.
|
||||
CompressionConfig *CompressionConfig
|
||||
// S2KCount is only used for symmetric encryption. It
|
||||
// determines the strength of the passphrase stretching when
|
||||
// the said passphrase is hashed to produce a key. S2KCount
|
||||
// should be between 1024 and 65011712, inclusive. If Config
|
||||
// is nil or S2KCount is 0, the value 65536 used. Not all
|
||||
// values in the above range can be represented. S2KCount will
|
||||
// be rounded up to the next representable value if it cannot
|
||||
// be encoded exactly. When set, it is strongly encrouraged to
|
||||
// use a value that is at least 65536. See RFC 4880 Section
|
||||
// 3.7.1.3.
|
||||
S2KCount int
|
||||
// RSABits is the number of bits in new RSA keys made with NewEntity.
|
||||
// If zero, then 2048 bit keys are created.
|
||||
RSABits int
|
||||
// The public key algorithm to use - will always create a signing primary
|
||||
// key and encryption subkey.
|
||||
Algorithm PublicKeyAlgorithm
|
||||
// Some known primes that are optionally prepopulated by the caller
|
||||
RSAPrimes []*big.Int
|
||||
// Curve configures the desired packet.Curve if the Algorithm is PubKeyAlgoECDSA,
|
||||
// PubKeyAlgoEdDSA, or PubKeyAlgoECDH. If empty Curve25519 is used.
|
||||
Curve Curve
|
||||
// AEADConfig configures the use of the new AEAD Encrypted Data Packet,
|
||||
// defined in the draft of the next version of the OpenPGP specification.
|
||||
// If a non-nil AEADConfig is passed, usage of this packet is enabled. By
|
||||
// default, it is disabled. See the documentation of AEADConfig for more
|
||||
// configuration options related to AEAD.
|
||||
// **Note: using this option may break compatibility with other OpenPGP
|
||||
// implementations, as well as future versions of this library.**
|
||||
AEADConfig *AEADConfig
|
||||
// V5Keys configures version 5 key generation. If false, this package still
|
||||
// supports version 5 keys, but produces version 4 keys.
|
||||
V5Keys bool
|
||||
// "The validity period of the key. This is the number of seconds after
|
||||
// the key creation time that the key expires. If this is not present
|
||||
// or has a value of zero, the key never expires. This is found only on
|
||||
// a self-signature.""
|
||||
// https://tools.ietf.org/html/rfc4880#section-5.2.3.6
|
||||
KeyLifetimeSecs uint32
|
||||
// "The validity period of the signature. This is the number of seconds
|
||||
// after the signature creation time that the signature expires. If
|
||||
// this is not present or has a value of zero, it never expires."
|
||||
// https://tools.ietf.org/html/rfc4880#section-5.2.3.10
|
||||
SigLifetimeSecs uint32
|
||||
// SigningKeyId is used to specify the signing key to use (by Key ID).
|
||||
// By default, the signing key is selected automatically, preferring
|
||||
// signing subkeys if available.
|
||||
SigningKeyId uint64
|
||||
// SigningIdentity is used to specify a user ID (packet Signer's User ID, type 28)
|
||||
// when producing a generic certification signature onto an existing user ID.
|
||||
// The identity must be present in the signer Entity.
|
||||
SigningIdentity string
|
||||
// InsecureAllowUnauthenticatedMessages controls, whether it is tolerated to read
|
||||
// encrypted messages without Modification Detection Code (MDC).
|
||||
// MDC is mandated by the IETF OpenPGP Crypto Refresh draft and has long been implemented
|
||||
// in most OpenPGP implementations. Messages without MDC are considered unnecessarily
|
||||
// insecure and should be prevented whenever possible.
|
||||
// In case one needs to deal with messages from very old OpenPGP implementations, there
|
||||
// might be no other way than to tolerate the missing MDC. Setting this flag, allows this
|
||||
// mode of operation. It should be considered a measure of last resort.
|
||||
InsecureAllowUnauthenticatedMessages bool
|
||||
// KnownNotations is a map of Notation Data names to bools, which controls
|
||||
// the notation names that are allowed to be present in critical Notation Data
|
||||
// signature subpackets.
|
||||
KnownNotations map[string]bool
|
||||
// SignatureNotations is a list of Notations to be added to any signatures.
|
||||
SignatureNotations []*Notation
|
||||
}
|
||||
|
||||
func (c *Config) Random() io.Reader {
|
||||
if c == nil || c.Rand == nil {
|
||||
return rand.Reader
|
||||
}
|
||||
return c.Rand
|
||||
}
|
||||
|
||||
func (c *Config) Hash() crypto.Hash {
|
||||
if c == nil || uint(c.DefaultHash) == 0 {
|
||||
return crypto.SHA256
|
||||
}
|
||||
return c.DefaultHash
|
||||
}
|
||||
|
||||
func (c *Config) Cipher() CipherFunction {
|
||||
if c == nil || uint8(c.DefaultCipher) == 0 {
|
||||
return CipherAES128
|
||||
}
|
||||
return c.DefaultCipher
|
||||
}
|
||||
|
||||
func (c *Config) Now() time.Time {
|
||||
if c == nil || c.Time == nil {
|
||||
return time.Now()
|
||||
}
|
||||
return c.Time()
|
||||
}
|
||||
|
||||
// KeyLifetime returns the validity period of the key.
|
||||
func (c *Config) KeyLifetime() uint32 {
|
||||
if c == nil {
|
||||
return 0
|
||||
}
|
||||
return c.KeyLifetimeSecs
|
||||
}
|
||||
|
||||
// SigLifetime returns the validity period of the signature.
|
||||
func (c *Config) SigLifetime() uint32 {
|
||||
if c == nil {
|
||||
return 0
|
||||
}
|
||||
return c.SigLifetimeSecs
|
||||
}
|
||||
|
||||
func (c *Config) Compression() CompressionAlgo {
|
||||
if c == nil {
|
||||
return CompressionNone
|
||||
}
|
||||
return c.DefaultCompressionAlgo
|
||||
}
|
||||
|
||||
func (c *Config) PasswordHashIterations() int {
|
||||
if c == nil || c.S2KCount == 0 {
|
||||
return 0
|
||||
}
|
||||
return c.S2KCount
|
||||
}
|
||||
|
||||
func (c *Config) RSAModulusBits() int {
|
||||
if c == nil || c.RSABits == 0 {
|
||||
return 2048
|
||||
}
|
||||
return c.RSABits
|
||||
}
|
||||
|
||||
func (c *Config) PublicKeyAlgorithm() PublicKeyAlgorithm {
|
||||
if c == nil || c.Algorithm == 0 {
|
||||
return PubKeyAlgoRSA
|
||||
}
|
||||
return c.Algorithm
|
||||
}
|
||||
|
||||
func (c *Config) CurveName() Curve {
|
||||
if c == nil || c.Curve == "" {
|
||||
return Curve25519
|
||||
}
|
||||
return c.Curve
|
||||
}
|
||||
|
||||
func (c *Config) AEAD() *AEADConfig {
|
||||
if c == nil {
|
||||
return nil
|
||||
}
|
||||
return c.AEADConfig
|
||||
}
|
||||
|
||||
func (c *Config) SigningKey() uint64 {
|
||||
if c == nil {
|
||||
return 0
|
||||
}
|
||||
return c.SigningKeyId
|
||||
}
|
||||
|
||||
func (c *Config) SigningUserId() string {
|
||||
if c == nil {
|
||||
return ""
|
||||
}
|
||||
return c.SigningIdentity
|
||||
}
|
||||
|
||||
func (c *Config) AllowUnauthenticatedMessages() bool {
|
||||
if c == nil {
|
||||
return false
|
||||
}
|
||||
return c.InsecureAllowUnauthenticatedMessages
|
||||
}
|
||||
|
||||
func (c *Config) KnownNotation(notationName string) bool {
|
||||
if c == nil {
|
||||
return false
|
||||
}
|
||||
return c.KnownNotations[notationName]
|
||||
}
|
||||
|
||||
func (c *Config) Notations() []*Notation {
|
||||
if c == nil {
|
||||
return nil
|
||||
}
|
||||
return c.SignatureNotations
|
||||
}
|
||||
|
|
@ -12,8 +12,10 @@ import (
|
|||
"math/big"
|
||||
"strconv"
|
||||
|
||||
"golang.org/x/crypto/openpgp/elgamal"
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/ecdh"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/elgamal"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/encoding"
|
||||
)
|
||||
|
||||
const encryptedKeyVersion = 3
|
||||
|
|
@ -23,10 +25,10 @@ const encryptedKeyVersion = 3
|
|||
type EncryptedKey struct {
|
||||
KeyId uint64
|
||||
Algo PublicKeyAlgorithm
|
||||
CipherFunc CipherFunction // only valid after a successful Decrypt
|
||||
CipherFunc CipherFunction // only valid after a successful Decrypt for a v3 packet
|
||||
Key []byte // only valid after a successful Decrypt
|
||||
|
||||
encryptedMPI1, encryptedMPI2 parsedMPI
|
||||
encryptedMPI1, encryptedMPI2 encoding.Field
|
||||
}
|
||||
|
||||
func (e *EncryptedKey) parse(r io.Reader) (err error) {
|
||||
|
|
@ -42,17 +44,28 @@ func (e *EncryptedKey) parse(r io.Reader) (err error) {
|
|||
e.Algo = PublicKeyAlgorithm(buf[9])
|
||||
switch e.Algo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly:
|
||||
e.encryptedMPI1.bytes, e.encryptedMPI1.bitLength, err = readMPI(r)
|
||||
if err != nil {
|
||||
e.encryptedMPI1 = new(encoding.MPI)
|
||||
if _, err = e.encryptedMPI1.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
case PubKeyAlgoElGamal:
|
||||
e.encryptedMPI1.bytes, e.encryptedMPI1.bitLength, err = readMPI(r)
|
||||
if err != nil {
|
||||
e.encryptedMPI1 = new(encoding.MPI)
|
||||
if _, err = e.encryptedMPI1.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
e.encryptedMPI2.bytes, e.encryptedMPI2.bitLength, err = readMPI(r)
|
||||
if err != nil {
|
||||
|
||||
e.encryptedMPI2 = new(encoding.MPI)
|
||||
if _, err = e.encryptedMPI2.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
case PubKeyAlgoECDH:
|
||||
e.encryptedMPI1 = new(encoding.MPI)
|
||||
if _, err = e.encryptedMPI1.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
e.encryptedMPI2 = new(encoding.OID)
|
||||
if _, err = e.encryptedMPI2.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
}
|
||||
|
|
@ -72,6 +85,16 @@ func checksumKeyMaterial(key []byte) uint16 {
|
|||
// private key must have been decrypted first.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (e *EncryptedKey) Decrypt(priv *PrivateKey, config *Config) error {
|
||||
if e.KeyId != 0 && e.KeyId != priv.KeyId {
|
||||
return errors.InvalidArgumentError("cannot decrypt encrypted session key for key id " + strconv.FormatUint(e.KeyId, 16) + " with private key id " + strconv.FormatUint(priv.KeyId, 16))
|
||||
}
|
||||
if e.Algo != priv.PubKeyAlgo {
|
||||
return errors.InvalidArgumentError("cannot decrypt encrypted session key of type " + strconv.Itoa(int(e.Algo)) + " with private key of type " + strconv.Itoa(int(priv.PubKeyAlgo)))
|
||||
}
|
||||
if priv.Dummy() {
|
||||
return errors.ErrDummyPrivateKey("dummy key found")
|
||||
}
|
||||
|
||||
var err error
|
||||
var b []byte
|
||||
|
||||
|
|
@ -81,13 +104,18 @@ func (e *EncryptedKey) Decrypt(priv *PrivateKey, config *Config) error {
|
|||
case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly:
|
||||
// Supports both *rsa.PrivateKey and crypto.Decrypter
|
||||
k := priv.PrivateKey.(crypto.Decrypter)
|
||||
b, err = k.Decrypt(config.Random(), padToKeySize(k.Public().(*rsa.PublicKey), e.encryptedMPI1.bytes), nil)
|
||||
b, err = k.Decrypt(config.Random(), padToKeySize(k.Public().(*rsa.PublicKey), e.encryptedMPI1.Bytes()), nil)
|
||||
case PubKeyAlgoElGamal:
|
||||
c1 := new(big.Int).SetBytes(e.encryptedMPI1.bytes)
|
||||
c2 := new(big.Int).SetBytes(e.encryptedMPI2.bytes)
|
||||
c1 := new(big.Int).SetBytes(e.encryptedMPI1.Bytes())
|
||||
c2 := new(big.Int).SetBytes(e.encryptedMPI2.Bytes())
|
||||
b, err = elgamal.Decrypt(priv.PrivateKey.(*elgamal.PrivateKey), c1, c2)
|
||||
case PubKeyAlgoECDH:
|
||||
vsG := e.encryptedMPI1.Bytes()
|
||||
m := e.encryptedMPI2.Bytes()
|
||||
oid := priv.PublicKey.oid.EncodedBytes()
|
||||
b, err = ecdh.Decrypt(priv.PrivateKey.(*ecdh.PrivateKey), vsG, m, oid, priv.PublicKey.Fingerprint[:])
|
||||
default:
|
||||
err = errors.InvalidArgumentError("cannot decrypted encrypted session key with private key of type " + strconv.Itoa(int(priv.PubKeyAlgo)))
|
||||
err = errors.InvalidArgumentError("cannot decrypt encrypted session key with private key of type " + strconv.Itoa(int(priv.PubKeyAlgo)))
|
||||
}
|
||||
|
||||
if err != nil {
|
||||
|
|
@ -95,6 +123,10 @@ func (e *EncryptedKey) Decrypt(priv *PrivateKey, config *Config) error {
|
|||
}
|
||||
|
||||
e.CipherFunc = CipherFunction(b[0])
|
||||
if !e.CipherFunc.IsSupported() {
|
||||
return errors.UnsupportedError("unsupported encryption function")
|
||||
}
|
||||
|
||||
e.Key = b[1 : len(b)-2]
|
||||
expectedChecksum := uint16(b[len(b)-2])<<8 | uint16(b[len(b)-1])
|
||||
checksum := checksumKeyMaterial(e.Key)
|
||||
|
|
@ -110,14 +142,19 @@ func (e *EncryptedKey) Serialize(w io.Writer) error {
|
|||
var mpiLen int
|
||||
switch e.Algo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly:
|
||||
mpiLen = 2 + len(e.encryptedMPI1.bytes)
|
||||
mpiLen = int(e.encryptedMPI1.EncodedLength())
|
||||
case PubKeyAlgoElGamal:
|
||||
mpiLen = 2 + len(e.encryptedMPI1.bytes) + 2 + len(e.encryptedMPI2.bytes)
|
||||
mpiLen = int(e.encryptedMPI1.EncodedLength()) + int(e.encryptedMPI2.EncodedLength())
|
||||
case PubKeyAlgoECDH:
|
||||
mpiLen = int(e.encryptedMPI1.EncodedLength()) + int(e.encryptedMPI2.EncodedLength())
|
||||
default:
|
||||
return errors.InvalidArgumentError("don't know how to serialize encrypted key type " + strconv.Itoa(int(e.Algo)))
|
||||
}
|
||||
|
||||
serializeHeader(w, packetTypeEncryptedKey, 1 /* version */ +8 /* key id */ +1 /* algo */ +mpiLen)
|
||||
err := serializeHeader(w, packetTypeEncryptedKey, 1 /* version */ +8 /* key id */ +1 /* algo */ +mpiLen)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
w.Write([]byte{encryptedKeyVersion})
|
||||
binary.Write(w, binary.BigEndian, e.KeyId)
|
||||
|
|
@ -125,14 +162,23 @@ func (e *EncryptedKey) Serialize(w io.Writer) error {
|
|||
|
||||
switch e.Algo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly:
|
||||
writeMPIs(w, e.encryptedMPI1)
|
||||
_, err := w.Write(e.encryptedMPI1.EncodedBytes())
|
||||
return err
|
||||
case PubKeyAlgoElGamal:
|
||||
writeMPIs(w, e.encryptedMPI1, e.encryptedMPI2)
|
||||
if _, err := w.Write(e.encryptedMPI1.EncodedBytes()); err != nil {
|
||||
return err
|
||||
}
|
||||
_, err := w.Write(e.encryptedMPI2.EncodedBytes())
|
||||
return err
|
||||
case PubKeyAlgoECDH:
|
||||
if _, err := w.Write(e.encryptedMPI1.EncodedBytes()); err != nil {
|
||||
return err
|
||||
}
|
||||
_, err := w.Write(e.encryptedMPI2.EncodedBytes())
|
||||
return err
|
||||
default:
|
||||
panic("internal error")
|
||||
}
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
// SerializeEncryptedKey serializes an encrypted key packet to w that contains
|
||||
|
|
@ -156,6 +202,8 @@ func SerializeEncryptedKey(w io.Writer, pub *PublicKey, cipherFunc CipherFunctio
|
|||
return serializeEncryptedKeyRSA(w, config.Random(), buf, pub.PublicKey.(*rsa.PublicKey), keyBlock)
|
||||
case PubKeyAlgoElGamal:
|
||||
return serializeEncryptedKeyElGamal(w, config.Random(), buf, pub.PublicKey.(*elgamal.PublicKey), keyBlock)
|
||||
case PubKeyAlgoECDH:
|
||||
return serializeEncryptedKeyECDH(w, config.Random(), buf, pub.PublicKey.(*ecdh.PublicKey), keyBlock, pub.oid, pub.Fingerprint)
|
||||
case PubKeyAlgoDSA, PubKeyAlgoRSASignOnly:
|
||||
return errors.InvalidArgumentError("cannot encrypt to public key of type " + strconv.Itoa(int(pub.PubKeyAlgo)))
|
||||
}
|
||||
|
|
@ -169,7 +217,8 @@ func serializeEncryptedKeyRSA(w io.Writer, rand io.Reader, header [10]byte, pub
|
|||
return errors.InvalidArgumentError("RSA encryption failed: " + err.Error())
|
||||
}
|
||||
|
||||
packetLen := 10 /* header length */ + 2 /* mpi size */ + len(cipherText)
|
||||
cipherMPI := encoding.NewMPI(cipherText)
|
||||
packetLen := 10 /* header length */ + int(cipherMPI.EncodedLength())
|
||||
|
||||
err = serializeHeader(w, packetTypeEncryptedKey, packetLen)
|
||||
if err != nil {
|
||||
|
|
@ -179,7 +228,8 @@ func serializeEncryptedKeyRSA(w io.Writer, rand io.Reader, header [10]byte, pub
|
|||
if err != nil {
|
||||
return err
|
||||
}
|
||||
return writeMPI(w, 8*uint16(len(cipherText)), cipherText)
|
||||
_, err = w.Write(cipherMPI.EncodedBytes())
|
||||
return err
|
||||
}
|
||||
|
||||
func serializeEncryptedKeyElGamal(w io.Writer, rand io.Reader, header [10]byte, pub *elgamal.PublicKey, keyBlock []byte) error {
|
||||
|
|
@ -200,9 +250,37 @@ func serializeEncryptedKeyElGamal(w io.Writer, rand io.Reader, header [10]byte,
|
|||
if err != nil {
|
||||
return err
|
||||
}
|
||||
err = writeBig(w, c1)
|
||||
if _, err = w.Write(new(encoding.MPI).SetBig(c1).EncodedBytes()); err != nil {
|
||||
return err
|
||||
}
|
||||
_, err = w.Write(new(encoding.MPI).SetBig(c2).EncodedBytes())
|
||||
return err
|
||||
}
|
||||
|
||||
func serializeEncryptedKeyECDH(w io.Writer, rand io.Reader, header [10]byte, pub *ecdh.PublicKey, keyBlock []byte, oid encoding.Field, fingerprint []byte) error {
|
||||
vsG, c, err := ecdh.Encrypt(rand, pub, keyBlock, oid.EncodedBytes(), fingerprint)
|
||||
if err != nil {
|
||||
return errors.InvalidArgumentError("ECDH encryption failed: " + err.Error())
|
||||
}
|
||||
|
||||
g := encoding.NewMPI(vsG)
|
||||
m := encoding.NewOID(c)
|
||||
|
||||
packetLen := 10 /* header length */
|
||||
packetLen += int(g.EncodedLength()) + int(m.EncodedLength())
|
||||
|
||||
err = serializeHeader(w, packetTypeEncryptedKey, packetLen)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
return writeBig(w, c2)
|
||||
|
||||
_, err = w.Write(header[:])
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
if _, err = w.Write(g.EncodedBytes()); err != nil {
|
||||
return err
|
||||
}
|
||||
_, err = w.Write(m.EncodedBytes())
|
||||
return err
|
||||
}
|
||||
|
|
@ -11,6 +11,7 @@ import (
|
|||
|
||||
// LiteralData represents an encrypted file. See RFC 4880, section 5.9.
|
||||
type LiteralData struct {
|
||||
Format uint8
|
||||
IsBinary bool
|
||||
FileName string
|
||||
Time uint32 // Unix epoch time. Either creation time or modification time. 0 means undefined.
|
||||
|
|
@ -31,7 +32,8 @@ func (l *LiteralData) parse(r io.Reader) (err error) {
|
|||
return
|
||||
}
|
||||
|
||||
l.IsBinary = buf[0] == 'b'
|
||||
l.Format = buf[0]
|
||||
l.IsBinary = l.Format == 'b'
|
||||
fileNameLen := int(buf[1])
|
||||
|
||||
_, err = readFull(r, buf[:fileNameLen])
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
package packet
|
||||
|
||||
// Notation type represents a Notation Data subpacket
|
||||
// see https://tools.ietf.org/html/rfc4880#section-5.2.3.16
|
||||
type Notation struct {
|
||||
Name string
|
||||
Value []byte
|
||||
IsCritical bool
|
||||
IsHumanReadable bool
|
||||
}
|
||||
|
||||
func (notation *Notation) getData() []byte {
|
||||
nameData := []byte(notation.Name)
|
||||
nameLen := len(nameData)
|
||||
valueLen := len(notation.Value)
|
||||
|
||||
data := make([]byte, 8+nameLen+valueLen)
|
||||
if notation.IsHumanReadable {
|
||||
data[0] = 0x80
|
||||
}
|
||||
|
||||
data[4] = byte(nameLen >> 8)
|
||||
data[5] = byte(nameLen)
|
||||
data[6] = byte(valueLen >> 8)
|
||||
data[7] = byte(valueLen)
|
||||
copy(data[8:8+nameLen], nameData)
|
||||
copy(data[8+nameLen:], notation.Value)
|
||||
return data
|
||||
}
|
||||
|
|
@ -85,8 +85,7 @@ type ocfbDecrypter struct {
|
|||
// NewOCFBDecrypter returns a cipher.Stream which decrypts data with OpenPGP's
|
||||
// cipher feedback mode using the given cipher.Block. Prefix must be the first
|
||||
// blockSize + 2 bytes of the ciphertext, where blockSize is the cipher.Block's
|
||||
// block size. If an incorrect key is detected then nil is returned. On
|
||||
// successful exit, blockSize+2 bytes of decrypted data are written into
|
||||
// block size. On successful exit, blockSize+2 bytes of decrypted data are written into
|
||||
// prefix. Resync determines if the "resynchronization step" from RFC 4880,
|
||||
// 13.9 step 7 is performed. Different parts of OpenPGP vary on this point.
|
||||
func NewOCFBDecrypter(block cipher.Block, prefix []byte, resync OCFBResyncOption) cipher.Stream {
|
||||
|
|
@ -112,11 +111,6 @@ func NewOCFBDecrypter(block cipher.Block, prefix []byte, resync OCFBResyncOption
|
|||
prefixCopy[blockSize] ^= x.fre[0]
|
||||
prefixCopy[blockSize+1] ^= x.fre[1]
|
||||
|
||||
if prefixCopy[blockSize-2] != prefixCopy[blockSize] ||
|
||||
prefixCopy[blockSize-1] != prefixCopy[blockSize+1] {
|
||||
return nil
|
||||
}
|
||||
|
||||
if resync {
|
||||
block.Encrypt(x.fre, prefix[2:])
|
||||
} else {
|
||||
|
|
@ -7,8 +7,8 @@ package packet
|
|||
import (
|
||||
"crypto"
|
||||
"encoding/binary"
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"golang.org/x/crypto/openpgp/s2k"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/algorithm"
|
||||
"io"
|
||||
"strconv"
|
||||
)
|
||||
|
|
@ -37,7 +37,7 @@ func (ops *OnePassSignature) parse(r io.Reader) (err error) {
|
|||
}
|
||||
|
||||
var ok bool
|
||||
ops.Hash, ok = s2k.HashIdToHash(buf[2])
|
||||
ops.Hash, ok = algorithm.HashIdToHashWithSha1(buf[2])
|
||||
if !ok {
|
||||
return errors.UnsupportedError("hash function: " + strconv.Itoa(int(buf[2])))
|
||||
}
|
||||
|
|
@ -55,7 +55,7 @@ func (ops *OnePassSignature) Serialize(w io.Writer) error {
|
|||
buf[0] = onePassSignatureVersion
|
||||
buf[1] = uint8(ops.SigType)
|
||||
var ok bool
|
||||
buf[2], ok = s2k.HashToHashId(ops.Hash)
|
||||
buf[2], ok = algorithm.HashToHashId(ops.Hash)
|
||||
if !ok {
|
||||
return errors.UnsupportedError("hash type: " + strconv.Itoa(int(ops.Hash)))
|
||||
}
|
||||
|
|
@ -7,8 +7,9 @@ package packet
|
|||
import (
|
||||
"bytes"
|
||||
"io"
|
||||
"io/ioutil"
|
||||
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
)
|
||||
|
||||
// OpaquePacket represents an OpenPGP packet as raw, unparsed data. This is
|
||||
|
|
@ -25,7 +26,7 @@ type OpaquePacket struct {
|
|||
}
|
||||
|
||||
func (op *OpaquePacket) parse(r io.Reader) (err error) {
|
||||
op.Contents, err = io.ReadAll(r)
|
||||
op.Contents, err = ioutil.ReadAll(r)
|
||||
return
|
||||
}
|
||||
|
||||
|
|
@ -83,8 +84,9 @@ func (or *OpaqueReader) Next() (op *OpaquePacket, err error) {
|
|||
// OpaqueSubpacket represents an unparsed OpenPGP subpacket,
|
||||
// as found in signature and user attribute packets.
|
||||
type OpaqueSubpacket struct {
|
||||
SubType uint8
|
||||
Contents []byte
|
||||
SubType uint8
|
||||
EncodedLength []byte // Store the original encoded length for signature verifications.
|
||||
Contents []byte
|
||||
}
|
||||
|
||||
// OpaqueSubpackets extracts opaque, unparsed OpenPGP subpackets from
|
||||
|
|
@ -108,6 +110,7 @@ func OpaqueSubpackets(contents []byte) (result []*OpaqueSubpacket, err error) {
|
|||
func nextSubpacket(contents []byte) (subHeaderLen int, subPacket *OpaqueSubpacket, err error) {
|
||||
// RFC 4880, section 5.2.3.1
|
||||
var subLen uint32
|
||||
var encodedLength []byte
|
||||
if len(contents) < 1 {
|
||||
goto Truncated
|
||||
}
|
||||
|
|
@ -118,6 +121,7 @@ func nextSubpacket(contents []byte) (subHeaderLen int, subPacket *OpaqueSubpacke
|
|||
if len(contents) < subHeaderLen {
|
||||
goto Truncated
|
||||
}
|
||||
encodedLength = contents[0:1]
|
||||
subLen = uint32(contents[0])
|
||||
contents = contents[1:]
|
||||
case contents[0] < 255:
|
||||
|
|
@ -125,6 +129,7 @@ func nextSubpacket(contents []byte) (subHeaderLen int, subPacket *OpaqueSubpacke
|
|||
if len(contents) < subHeaderLen {
|
||||
goto Truncated
|
||||
}
|
||||
encodedLength = contents[0:2]
|
||||
subLen = uint32(contents[0]-192)<<8 + uint32(contents[1]) + 192
|
||||
contents = contents[2:]
|
||||
default:
|
||||
|
|
@ -132,16 +137,19 @@ func nextSubpacket(contents []byte) (subHeaderLen int, subPacket *OpaqueSubpacke
|
|||
if len(contents) < subHeaderLen {
|
||||
goto Truncated
|
||||
}
|
||||
encodedLength = contents[0:5]
|
||||
subLen = uint32(contents[1])<<24 |
|
||||
uint32(contents[2])<<16 |
|
||||
uint32(contents[3])<<8 |
|
||||
uint32(contents[4])
|
||||
contents = contents[5:]
|
||||
|
||||
}
|
||||
if subLen > uint32(len(contents)) || subLen == 0 {
|
||||
goto Truncated
|
||||
}
|
||||
subPacket.SubType = contents[0]
|
||||
subPacket.EncodedLength = encodedLength
|
||||
subPacket.Contents = contents[1:subLen]
|
||||
return
|
||||
Truncated:
|
||||
|
|
@ -151,7 +159,9 @@ Truncated:
|
|||
|
||||
func (osp *OpaqueSubpacket) Serialize(w io.Writer) (err error) {
|
||||
buf := make([]byte, 6)
|
||||
n := serializeSubpacketLength(buf, len(osp.Contents)+1)
|
||||
copy(buf, osp.EncodedLength)
|
||||
n := len(osp.EncodedLength)
|
||||
|
||||
buf[n] = osp.SubType
|
||||
if _, err = w.Write(buf[:n+1]); err != nil {
|
||||
return
|
||||
|
|
@ -4,26 +4,16 @@
|
|||
|
||||
// Package packet implements parsing and serialization of OpenPGP packets, as
|
||||
// specified in RFC 4880.
|
||||
//
|
||||
// Deprecated: this package is unmaintained except for security fixes. New
|
||||
// applications should consider a more focused, modern alternative to OpenPGP
|
||||
// for their specific task. If you are required to interoperate with OpenPGP
|
||||
// systems and need a maintained package, consider a community fork.
|
||||
// See https://golang.org/issue/44226.
|
||||
package packet // import "golang.org/x/crypto/openpgp/packet"
|
||||
package packet // import "github.com/ProtonMail/go-crypto/openpgp/packet"
|
||||
|
||||
import (
|
||||
"bufio"
|
||||
"crypto/aes"
|
||||
"bytes"
|
||||
"crypto/cipher"
|
||||
"crypto/des"
|
||||
"crypto/rsa"
|
||||
"io"
|
||||
"math/big"
|
||||
"math/bits"
|
||||
|
||||
"golang.org/x/crypto/cast5"
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/algorithm"
|
||||
)
|
||||
|
||||
// readFull is the same as io.ReadFull except that reading zero bytes returns
|
||||
|
|
@ -106,68 +96,43 @@ func (r *partialLengthReader) Read(p []byte) (n int, err error) {
|
|||
// See RFC 4880, section 4.2.2.4.
|
||||
type partialLengthWriter struct {
|
||||
w io.WriteCloser
|
||||
buf bytes.Buffer
|
||||
lengthByte [1]byte
|
||||
sentFirst bool
|
||||
buf []byte
|
||||
}
|
||||
|
||||
// RFC 4880 4.2.2.4: the first partial length MUST be at least 512 octets long.
|
||||
const minFirstPartialWrite = 512
|
||||
|
||||
func (w *partialLengthWriter) Write(p []byte) (n int, err error) {
|
||||
off := 0
|
||||
if !w.sentFirst {
|
||||
if len(w.buf) > 0 || len(p) < minFirstPartialWrite {
|
||||
off = len(w.buf)
|
||||
w.buf = append(w.buf, p...)
|
||||
if len(w.buf) < minFirstPartialWrite {
|
||||
return len(p), nil
|
||||
bufLen := w.buf.Len()
|
||||
if bufLen > 512 {
|
||||
for power := uint(30); ; power-- {
|
||||
l := 1 << power
|
||||
if bufLen >= l {
|
||||
w.lengthByte[0] = 224 + uint8(power)
|
||||
_, err = w.w.Write(w.lengthByte[:])
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
var m int
|
||||
m, err = w.w.Write(w.buf.Next(l))
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
if m != l {
|
||||
return 0, io.ErrShortWrite
|
||||
}
|
||||
break
|
||||
}
|
||||
p = w.buf
|
||||
w.buf = nil
|
||||
}
|
||||
w.sentFirst = true
|
||||
}
|
||||
|
||||
power := uint8(30)
|
||||
for len(p) > 0 {
|
||||
l := 1 << power
|
||||
if len(p) < l {
|
||||
power = uint8(bits.Len32(uint32(len(p)))) - 1
|
||||
l = 1 << power
|
||||
}
|
||||
w.lengthByte[0] = 224 + power
|
||||
_, err = w.w.Write(w.lengthByte[:])
|
||||
if err == nil {
|
||||
var m int
|
||||
m, err = w.w.Write(p[:l])
|
||||
n += m
|
||||
}
|
||||
if err != nil {
|
||||
if n < off {
|
||||
return 0, err
|
||||
}
|
||||
return n - off, err
|
||||
}
|
||||
p = p[l:]
|
||||
}
|
||||
return n - off, nil
|
||||
return w.buf.Write(p)
|
||||
}
|
||||
|
||||
func (w *partialLengthWriter) Close() error {
|
||||
if len(w.buf) > 0 {
|
||||
// In this case we can't send a 512 byte packet.
|
||||
// Just send what we have.
|
||||
p := w.buf
|
||||
w.sentFirst = true
|
||||
w.buf = nil
|
||||
if _, err := w.Write(p); err != nil {
|
||||
return err
|
||||
}
|
||||
func (w *partialLengthWriter) Close() (err error) {
|
||||
len := w.buf.Len()
|
||||
err = serializeLength(w.w, len)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
w.lengthByte[0] = 0
|
||||
_, err := w.w.Write(w.lengthByte[:])
|
||||
_, err = w.buf.WriteTo(w.w)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
|
|
@ -252,25 +217,43 @@ func readHeader(r io.Reader) (tag packetType, length int64, contents io.Reader,
|
|||
// serializeHeader writes an OpenPGP packet header to w. See RFC 4880, section
|
||||
// 4.2.
|
||||
func serializeHeader(w io.Writer, ptype packetType, length int) (err error) {
|
||||
var buf [6]byte
|
||||
err = serializeType(w, ptype)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
return serializeLength(w, length)
|
||||
}
|
||||
|
||||
// serializeType writes an OpenPGP packet type to w. See RFC 4880, section
|
||||
// 4.2.
|
||||
func serializeType(w io.Writer, ptype packetType) (err error) {
|
||||
var buf [1]byte
|
||||
buf[0] = 0x80 | 0x40 | byte(ptype)
|
||||
_, err = w.Write(buf[:])
|
||||
return
|
||||
}
|
||||
|
||||
// serializeLength writes an OpenPGP packet length to w. See RFC 4880, section
|
||||
// 4.2.2.
|
||||
func serializeLength(w io.Writer, length int) (err error) {
|
||||
var buf [5]byte
|
||||
var n int
|
||||
|
||||
buf[0] = 0x80 | 0x40 | byte(ptype)
|
||||
if length < 192 {
|
||||
buf[1] = byte(length)
|
||||
n = 2
|
||||
buf[0] = byte(length)
|
||||
n = 1
|
||||
} else if length < 8384 {
|
||||
length -= 192
|
||||
buf[1] = 192 + byte(length>>8)
|
||||
buf[2] = byte(length)
|
||||
n = 3
|
||||
buf[0] = 192 + byte(length>>8)
|
||||
buf[1] = byte(length)
|
||||
n = 2
|
||||
} else {
|
||||
buf[1] = 255
|
||||
buf[2] = byte(length >> 24)
|
||||
buf[3] = byte(length >> 16)
|
||||
buf[4] = byte(length >> 8)
|
||||
buf[5] = byte(length)
|
||||
n = 6
|
||||
buf[0] = 255
|
||||
buf[1] = byte(length >> 24)
|
||||
buf[2] = byte(length >> 16)
|
||||
buf[3] = byte(length >> 8)
|
||||
buf[4] = byte(length)
|
||||
n = 5
|
||||
}
|
||||
|
||||
_, err = w.Write(buf[:n])
|
||||
|
|
@ -281,9 +264,7 @@ func serializeHeader(w io.Writer, ptype packetType, length int) (err error) {
|
|||
// length of the packet is unknown. It returns a io.WriteCloser which can be
|
||||
// used to write the contents of the packet. See RFC 4880, section 4.2.
|
||||
func serializeStreamHeader(w io.WriteCloser, ptype packetType) (out io.WriteCloser, err error) {
|
||||
var buf [1]byte
|
||||
buf[0] = 0x80 | 0x40 | byte(ptype)
|
||||
_, err = w.Write(buf[:])
|
||||
err = serializeType(w, ptype)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
|
@ -321,33 +302,27 @@ func consumeAll(r io.Reader) (n int64, err error) {
|
|||
type packetType uint8
|
||||
|
||||
const (
|
||||
packetTypeEncryptedKey packetType = 1
|
||||
packetTypeSignature packetType = 2
|
||||
packetTypeSymmetricKeyEncrypted packetType = 3
|
||||
packetTypeOnePassSignature packetType = 4
|
||||
packetTypePrivateKey packetType = 5
|
||||
packetTypePublicKey packetType = 6
|
||||
packetTypePrivateSubkey packetType = 7
|
||||
packetTypeCompressed packetType = 8
|
||||
packetTypeSymmetricallyEncrypted packetType = 9
|
||||
packetTypeLiteralData packetType = 11
|
||||
packetTypeUserId packetType = 13
|
||||
packetTypePublicSubkey packetType = 14
|
||||
packetTypeUserAttribute packetType = 17
|
||||
packetTypeSymmetricallyEncryptedMDC packetType = 18
|
||||
packetTypeEncryptedKey packetType = 1
|
||||
packetTypeSignature packetType = 2
|
||||
packetTypeSymmetricKeyEncrypted packetType = 3
|
||||
packetTypeOnePassSignature packetType = 4
|
||||
packetTypePrivateKey packetType = 5
|
||||
packetTypePublicKey packetType = 6
|
||||
packetTypePrivateSubkey packetType = 7
|
||||
packetTypeCompressed packetType = 8
|
||||
packetTypeSymmetricallyEncrypted packetType = 9
|
||||
packetTypeLiteralData packetType = 11
|
||||
packetTypeUserId packetType = 13
|
||||
packetTypePublicSubkey packetType = 14
|
||||
packetTypeUserAttribute packetType = 17
|
||||
packetTypeSymmetricallyEncryptedIntegrityProtected packetType = 18
|
||||
packetTypeAEADEncrypted packetType = 20
|
||||
)
|
||||
|
||||
// peekVersion detects the version of a public key packet about to
|
||||
// be read. A bufio.Reader at the original position of the io.Reader
|
||||
// is returned.
|
||||
func peekVersion(r io.Reader) (bufr *bufio.Reader, ver byte, err error) {
|
||||
bufr = bufio.NewReader(r)
|
||||
var verBuf []byte
|
||||
if verBuf, err = bufr.Peek(1); err != nil {
|
||||
return
|
||||
}
|
||||
ver = verBuf[0]
|
||||
return
|
||||
// EncryptedDataPacket holds encrypted data. It is currently implemented by
|
||||
// SymmetricallyEncrypted and AEADEncrypted.
|
||||
type EncryptedDataPacket interface {
|
||||
Decrypt(CipherFunction, []byte) (io.ReadCloser, error)
|
||||
}
|
||||
|
||||
// Read reads a single OpenPGP packet from the given io.Reader. If there is an
|
||||
|
|
@ -362,16 +337,7 @@ func Read(r io.Reader) (p Packet, err error) {
|
|||
case packetTypeEncryptedKey:
|
||||
p = new(EncryptedKey)
|
||||
case packetTypeSignature:
|
||||
var version byte
|
||||
// Detect signature version
|
||||
if contents, version, err = peekVersion(contents); err != nil {
|
||||
return
|
||||
}
|
||||
if version < 4 {
|
||||
p = new(SignatureV3)
|
||||
} else {
|
||||
p = new(Signature)
|
||||
}
|
||||
p = new(Signature)
|
||||
case packetTypeSymmetricKeyEncrypted:
|
||||
p = new(SymmetricKeyEncrypted)
|
||||
case packetTypeOnePassSignature:
|
||||
|
|
@ -383,16 +349,8 @@ func Read(r io.Reader) (p Packet, err error) {
|
|||
}
|
||||
p = pk
|
||||
case packetTypePublicKey, packetTypePublicSubkey:
|
||||
var version byte
|
||||
if contents, version, err = peekVersion(contents); err != nil {
|
||||
return
|
||||
}
|
||||
isSubkey := tag == packetTypePublicSubkey
|
||||
if version < 4 {
|
||||
p = &PublicKeyV3{IsSubkey: isSubkey}
|
||||
} else {
|
||||
p = &PublicKey{IsSubkey: isSubkey}
|
||||
}
|
||||
p = &PublicKey{IsSubkey: isSubkey}
|
||||
case packetTypeCompressed:
|
||||
p = new(Compressed)
|
||||
case packetTypeSymmetricallyEncrypted:
|
||||
|
|
@ -403,10 +361,12 @@ func Read(r io.Reader) (p Packet, err error) {
|
|||
p = new(UserId)
|
||||
case packetTypeUserAttribute:
|
||||
p = new(UserAttribute)
|
||||
case packetTypeSymmetricallyEncryptedMDC:
|
||||
case packetTypeSymmetricallyEncryptedIntegrityProtected:
|
||||
se := new(SymmetricallyEncrypted)
|
||||
se.MDC = true
|
||||
se.IntegrityProtected = true
|
||||
p = se
|
||||
case packetTypeAEADEncrypted:
|
||||
p = new(AEADEncrypted)
|
||||
default:
|
||||
err = errors.UnknownPacketTypeError(tag)
|
||||
}
|
||||
|
|
@ -424,8 +384,8 @@ func Read(r io.Reader) (p Packet, err error) {
|
|||
type SignatureType uint8
|
||||
|
||||
const (
|
||||
SigTypeBinary SignatureType = 0
|
||||
SigTypeText = 1
|
||||
SigTypeBinary SignatureType = 0x00
|
||||
SigTypeText = 0x01
|
||||
SigTypeGenericCert = 0x10
|
||||
SigTypePersonaCert = 0x11
|
||||
SigTypeCasualCert = 0x12
|
||||
|
|
@ -435,6 +395,7 @@ const (
|
|||
SigTypeDirectSignature = 0x1F
|
||||
SigTypeKeyRevocation = 0x20
|
||||
SigTypeSubkeyRevocation = 0x28
|
||||
SigTypeCertificationRevocation = 0x30
|
||||
)
|
||||
|
||||
// PublicKeyAlgorithm represents the different public key system specified for
|
||||
|
|
@ -449,6 +410,8 @@ const (
|
|||
// RFC 6637, Section 5.
|
||||
PubKeyAlgoECDH PublicKeyAlgorithm = 18
|
||||
PubKeyAlgoECDSA PublicKeyAlgorithm = 19
|
||||
// https://www.ietf.org/archive/id/draft-koch-eddsa-for-openpgp-04.txt
|
||||
PubKeyAlgoEdDSA PublicKeyAlgorithm = 22
|
||||
|
||||
// Deprecated in RFC 4880, Section 13.5. Use key flags instead.
|
||||
PubKeyAlgoRSAEncryptOnly PublicKeyAlgorithm = 2
|
||||
|
|
@ -459,7 +422,7 @@ const (
|
|||
// key of the given type.
|
||||
func (pka PublicKeyAlgorithm) CanEncrypt() bool {
|
||||
switch pka {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoElGamal:
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoElGamal, PubKeyAlgoECDH:
|
||||
return true
|
||||
}
|
||||
return false
|
||||
|
|
@ -469,7 +432,7 @@ func (pka PublicKeyAlgorithm) CanEncrypt() bool {
|
|||
// sign a message.
|
||||
func (pka PublicKeyAlgorithm) CanSign() bool {
|
||||
switch pka {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoDSA, PubKeyAlgoECDSA:
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoDSA, PubKeyAlgoECDSA, PubKeyAlgoEdDSA:
|
||||
return true
|
||||
}
|
||||
return false
|
||||
|
|
@ -477,7 +440,7 @@ func (pka PublicKeyAlgorithm) CanSign() bool {
|
|||
|
||||
// CipherFunction represents the different block ciphers specified for OpenPGP. See
|
||||
// http://www.iana.org/assignments/pgp-parameters/pgp-parameters.xhtml#pgp-parameters-13
|
||||
type CipherFunction uint8
|
||||
type CipherFunction algorithm.CipherFunction
|
||||
|
||||
const (
|
||||
Cipher3DES CipherFunction = 2
|
||||
|
|
@ -489,81 +452,22 @@ const (
|
|||
|
||||
// KeySize returns the key size, in bytes, of cipher.
|
||||
func (cipher CipherFunction) KeySize() int {
|
||||
switch cipher {
|
||||
case Cipher3DES:
|
||||
return 24
|
||||
case CipherCAST5:
|
||||
return cast5.KeySize
|
||||
case CipherAES128:
|
||||
return 16
|
||||
case CipherAES192:
|
||||
return 24
|
||||
case CipherAES256:
|
||||
return 32
|
||||
}
|
||||
return 0
|
||||
return algorithm.CipherFunction(cipher).KeySize()
|
||||
}
|
||||
|
||||
// IsSupported returns true if the cipher is supported from the library
|
||||
func (cipher CipherFunction) IsSupported() bool {
|
||||
return algorithm.CipherFunction(cipher).KeySize() > 0
|
||||
}
|
||||
|
||||
// blockSize returns the block size, in bytes, of cipher.
|
||||
func (cipher CipherFunction) blockSize() int {
|
||||
switch cipher {
|
||||
case Cipher3DES:
|
||||
return des.BlockSize
|
||||
case CipherCAST5:
|
||||
return 8
|
||||
case CipherAES128, CipherAES192, CipherAES256:
|
||||
return 16
|
||||
}
|
||||
return 0
|
||||
return algorithm.CipherFunction(cipher).BlockSize()
|
||||
}
|
||||
|
||||
// new returns a fresh instance of the given cipher.
|
||||
func (cipher CipherFunction) new(key []byte) (block cipher.Block) {
|
||||
switch cipher {
|
||||
case Cipher3DES:
|
||||
block, _ = des.NewTripleDESCipher(key)
|
||||
case CipherCAST5:
|
||||
block, _ = cast5.NewCipher(key)
|
||||
case CipherAES128, CipherAES192, CipherAES256:
|
||||
block, _ = aes.NewCipher(key)
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// readMPI reads a big integer from r. The bit length returned is the bit
|
||||
// length that was specified in r. This is preserved so that the integer can be
|
||||
// reserialized exactly.
|
||||
func readMPI(r io.Reader) (mpi []byte, bitLength uint16, err error) {
|
||||
var buf [2]byte
|
||||
_, err = readFull(r, buf[0:])
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
bitLength = uint16(buf[0])<<8 | uint16(buf[1])
|
||||
numBytes := (int(bitLength) + 7) / 8
|
||||
mpi = make([]byte, numBytes)
|
||||
_, err = readFull(r, mpi)
|
||||
// According to RFC 4880 3.2. we should check that the MPI has no leading
|
||||
// zeroes (at least when not an encrypted MPI?), but this implementation
|
||||
// does generate leading zeroes, so we keep accepting them.
|
||||
return
|
||||
}
|
||||
|
||||
// writeMPI serializes a big integer to w.
|
||||
func writeMPI(w io.Writer, bitLength uint16, mpiBytes []byte) (err error) {
|
||||
// Note that we can produce leading zeroes, in violation of RFC 4880 3.2.
|
||||
// Implementations seem to be tolerant of them, and stripping them would
|
||||
// make it complex to guarantee matching re-serialization.
|
||||
_, err = w.Write([]byte{byte(bitLength >> 8), byte(bitLength)})
|
||||
if err == nil {
|
||||
_, err = w.Write(mpiBytes)
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// writeBig serializes a *big.Int to w.
|
||||
func writeBig(w io.Writer, i *big.Int) error {
|
||||
return writeMPI(w, uint16(i.BitLen()), i.Bytes())
|
||||
return algorithm.CipherFunction(cipher).New(key)
|
||||
}
|
||||
|
||||
// padToKeySize left-pads a MPI with zeroes to match the length of the
|
||||
|
|
@ -588,3 +492,60 @@ const (
|
|||
CompressionZIP CompressionAlgo = 1
|
||||
CompressionZLIB CompressionAlgo = 2
|
||||
)
|
||||
|
||||
// AEADMode represents the different Authenticated Encryption with Associated
|
||||
// Data specified for OpenPGP.
|
||||
// See https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-9.6
|
||||
type AEADMode algorithm.AEADMode
|
||||
|
||||
const (
|
||||
AEADModeEAX AEADMode = 1
|
||||
AEADModeOCB AEADMode = 2
|
||||
AEADModeGCM AEADMode = 3
|
||||
)
|
||||
|
||||
func (mode AEADMode) IvLength() int {
|
||||
return algorithm.AEADMode(mode).NonceLength()
|
||||
}
|
||||
|
||||
func (mode AEADMode) TagLength() int {
|
||||
return algorithm.AEADMode(mode).TagLength()
|
||||
}
|
||||
|
||||
// new returns a fresh instance of the given mode.
|
||||
func (mode AEADMode) new(block cipher.Block) cipher.AEAD {
|
||||
return algorithm.AEADMode(mode).New(block)
|
||||
}
|
||||
|
||||
// ReasonForRevocation represents a revocation reason code as per RFC4880
|
||||
// section 5.2.3.23.
|
||||
type ReasonForRevocation uint8
|
||||
|
||||
const (
|
||||
NoReason ReasonForRevocation = 0
|
||||
KeySuperseded ReasonForRevocation = 1
|
||||
KeyCompromised ReasonForRevocation = 2
|
||||
KeyRetired ReasonForRevocation = 3
|
||||
)
|
||||
|
||||
// Curve is a mapping to supported ECC curves for key generation.
|
||||
// See https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-06.html#name-curve-specific-wire-formats
|
||||
type Curve string
|
||||
|
||||
const (
|
||||
Curve25519 Curve = "Curve25519"
|
||||
Curve448 Curve = "Curve448"
|
||||
CurveNistP256 Curve = "P256"
|
||||
CurveNistP384 Curve = "P384"
|
||||
CurveNistP521 Curve = "P521"
|
||||
CurveSecP256k1 Curve = "SecP256k1"
|
||||
CurveBrainpoolP256 Curve = "BrainpoolP256"
|
||||
CurveBrainpoolP384 Curve = "BrainpoolP384"
|
||||
CurveBrainpoolP512 Curve = "BrainpoolP512"
|
||||
)
|
||||
|
||||
// TrustLevel represents a trust level per RFC4880 5.2.3.13
|
||||
type TrustLevel uint8
|
||||
|
||||
// TrustAmount represents a trust amount per RFC4880 5.2.3.13
|
||||
type TrustAmount uint8
|
||||
739
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/private_key.go
generated
vendored
Normal file
739
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/private_key.go
generated
vendored
Normal file
|
|
@ -0,0 +1,739 @@
|
|||
// Copyright 2011 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package packet
|
||||
|
||||
import (
|
||||
"bytes"
|
||||
"crypto"
|
||||
"crypto/cipher"
|
||||
"crypto/dsa"
|
||||
"crypto/rand"
|
||||
"crypto/rsa"
|
||||
"crypto/sha1"
|
||||
"io"
|
||||
"io/ioutil"
|
||||
"math/big"
|
||||
"strconv"
|
||||
"time"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/ecdh"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/ecdsa"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/eddsa"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/elgamal"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/encoding"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/s2k"
|
||||
)
|
||||
|
||||
// PrivateKey represents a possibly encrypted private key. See RFC 4880,
|
||||
// section 5.5.3.
|
||||
type PrivateKey struct {
|
||||
PublicKey
|
||||
Encrypted bool // if true then the private key is unavailable until Decrypt has been called.
|
||||
encryptedData []byte
|
||||
cipher CipherFunction
|
||||
s2k func(out, in []byte)
|
||||
// An *{rsa|dsa|elgamal|ecdh|ecdsa|ed25519}.PrivateKey or
|
||||
// crypto.Signer/crypto.Decrypter (Decryptor RSA only).
|
||||
PrivateKey interface{}
|
||||
sha1Checksum bool
|
||||
iv []byte
|
||||
|
||||
// Type of encryption of the S2K packet
|
||||
// Allowed values are 0 (Not encrypted), 254 (SHA1), or
|
||||
// 255 (2-byte checksum)
|
||||
s2kType S2KType
|
||||
// Full parameters of the S2K packet
|
||||
s2kParams *s2k.Params
|
||||
}
|
||||
|
||||
//S2KType s2k packet type
|
||||
type S2KType uint8
|
||||
|
||||
const (
|
||||
// S2KNON unencrypt
|
||||
S2KNON S2KType = 0
|
||||
// S2KSHA1 sha1 sum check
|
||||
S2KSHA1 S2KType = 254
|
||||
// S2KCHECKSUM sum check
|
||||
S2KCHECKSUM S2KType = 255
|
||||
)
|
||||
|
||||
func NewRSAPrivateKey(creationTime time.Time, priv *rsa.PrivateKey) *PrivateKey {
|
||||
pk := new(PrivateKey)
|
||||
pk.PublicKey = *NewRSAPublicKey(creationTime, &priv.PublicKey)
|
||||
pk.PrivateKey = priv
|
||||
return pk
|
||||
}
|
||||
|
||||
func NewDSAPrivateKey(creationTime time.Time, priv *dsa.PrivateKey) *PrivateKey {
|
||||
pk := new(PrivateKey)
|
||||
pk.PublicKey = *NewDSAPublicKey(creationTime, &priv.PublicKey)
|
||||
pk.PrivateKey = priv
|
||||
return pk
|
||||
}
|
||||
|
||||
func NewElGamalPrivateKey(creationTime time.Time, priv *elgamal.PrivateKey) *PrivateKey {
|
||||
pk := new(PrivateKey)
|
||||
pk.PublicKey = *NewElGamalPublicKey(creationTime, &priv.PublicKey)
|
||||
pk.PrivateKey = priv
|
||||
return pk
|
||||
}
|
||||
|
||||
func NewECDSAPrivateKey(creationTime time.Time, priv *ecdsa.PrivateKey) *PrivateKey {
|
||||
pk := new(PrivateKey)
|
||||
pk.PublicKey = *NewECDSAPublicKey(creationTime, &priv.PublicKey)
|
||||
pk.PrivateKey = priv
|
||||
return pk
|
||||
}
|
||||
|
||||
func NewEdDSAPrivateKey(creationTime time.Time, priv *eddsa.PrivateKey) *PrivateKey {
|
||||
pk := new(PrivateKey)
|
||||
pk.PublicKey = *NewEdDSAPublicKey(creationTime, &priv.PublicKey)
|
||||
pk.PrivateKey = priv
|
||||
return pk
|
||||
}
|
||||
|
||||
func NewECDHPrivateKey(creationTime time.Time, priv *ecdh.PrivateKey) *PrivateKey {
|
||||
pk := new(PrivateKey)
|
||||
pk.PublicKey = *NewECDHPublicKey(creationTime, &priv.PublicKey)
|
||||
pk.PrivateKey = priv
|
||||
return pk
|
||||
}
|
||||
|
||||
// NewSignerPrivateKey creates a PrivateKey from a crypto.Signer that
|
||||
// implements RSA, ECDSA or EdDSA.
|
||||
func NewSignerPrivateKey(creationTime time.Time, signer interface{}) *PrivateKey {
|
||||
pk := new(PrivateKey)
|
||||
// In general, the public Keys should be used as pointers. We still
|
||||
// type-switch on the values, for backwards-compatibility.
|
||||
switch pubkey := signer.(type) {
|
||||
case *rsa.PrivateKey:
|
||||
pk.PublicKey = *NewRSAPublicKey(creationTime, &pubkey.PublicKey)
|
||||
case rsa.PrivateKey:
|
||||
pk.PublicKey = *NewRSAPublicKey(creationTime, &pubkey.PublicKey)
|
||||
case *ecdsa.PrivateKey:
|
||||
pk.PublicKey = *NewECDSAPublicKey(creationTime, &pubkey.PublicKey)
|
||||
case ecdsa.PrivateKey:
|
||||
pk.PublicKey = *NewECDSAPublicKey(creationTime, &pubkey.PublicKey)
|
||||
case *eddsa.PrivateKey:
|
||||
pk.PublicKey = *NewEdDSAPublicKey(creationTime, &pubkey.PublicKey)
|
||||
case eddsa.PrivateKey:
|
||||
pk.PublicKey = *NewEdDSAPublicKey(creationTime, &pubkey.PublicKey)
|
||||
default:
|
||||
panic("openpgp: unknown signer type in NewSignerPrivateKey")
|
||||
}
|
||||
pk.PrivateKey = signer
|
||||
return pk
|
||||
}
|
||||
|
||||
// NewDecrypterPrivateKey creates a PrivateKey from a *{rsa|elgamal|ecdh}.PrivateKey.
|
||||
func NewDecrypterPrivateKey(creationTime time.Time, decrypter interface{}) *PrivateKey {
|
||||
pk := new(PrivateKey)
|
||||
switch priv := decrypter.(type) {
|
||||
case *rsa.PrivateKey:
|
||||
pk.PublicKey = *NewRSAPublicKey(creationTime, &priv.PublicKey)
|
||||
case *elgamal.PrivateKey:
|
||||
pk.PublicKey = *NewElGamalPublicKey(creationTime, &priv.PublicKey)
|
||||
case *ecdh.PrivateKey:
|
||||
pk.PublicKey = *NewECDHPublicKey(creationTime, &priv.PublicKey)
|
||||
default:
|
||||
panic("openpgp: unknown decrypter type in NewDecrypterPrivateKey")
|
||||
}
|
||||
pk.PrivateKey = decrypter
|
||||
return pk
|
||||
}
|
||||
|
||||
func (pk *PrivateKey) parse(r io.Reader) (err error) {
|
||||
err = (&pk.PublicKey).parse(r)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
v5 := pk.PublicKey.Version == 5
|
||||
|
||||
var buf [1]byte
|
||||
_, err = readFull(r, buf[:])
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
pk.s2kType = S2KType(buf[0])
|
||||
var optCount [1]byte
|
||||
if v5 {
|
||||
if _, err = readFull(r, optCount[:]); err != nil {
|
||||
return
|
||||
}
|
||||
}
|
||||
|
||||
switch pk.s2kType {
|
||||
case S2KNON:
|
||||
pk.s2k = nil
|
||||
pk.Encrypted = false
|
||||
case S2KSHA1, S2KCHECKSUM:
|
||||
if v5 && pk.s2kType == S2KCHECKSUM {
|
||||
return errors.StructuralError("wrong s2k identifier for version 5")
|
||||
}
|
||||
_, err = readFull(r, buf[:])
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
pk.cipher = CipherFunction(buf[0])
|
||||
if pk.cipher != 0 && !pk.cipher.IsSupported() {
|
||||
return errors.UnsupportedError("unsupported cipher function in private key")
|
||||
}
|
||||
pk.s2kParams, err = s2k.ParseIntoParams(r)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
if pk.s2kParams.Dummy() {
|
||||
return
|
||||
}
|
||||
pk.s2k, err = pk.s2kParams.Function()
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
pk.Encrypted = true
|
||||
if pk.s2kType == S2KSHA1 {
|
||||
pk.sha1Checksum = true
|
||||
}
|
||||
default:
|
||||
return errors.UnsupportedError("deprecated s2k function in private key")
|
||||
}
|
||||
|
||||
if pk.Encrypted {
|
||||
blockSize := pk.cipher.blockSize()
|
||||
if blockSize == 0 {
|
||||
return errors.UnsupportedError("unsupported cipher in private key: " + strconv.Itoa(int(pk.cipher)))
|
||||
}
|
||||
pk.iv = make([]byte, blockSize)
|
||||
_, err = readFull(r, pk.iv)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
}
|
||||
|
||||
var privateKeyData []byte
|
||||
if v5 {
|
||||
var n [4]byte /* secret material four octet count */
|
||||
_, err = readFull(r, n[:])
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
count := uint32(uint32(n[0])<<24 | uint32(n[1])<<16 | uint32(n[2])<<8 | uint32(n[3]))
|
||||
if !pk.Encrypted {
|
||||
count = count + 2 /* two octet checksum */
|
||||
}
|
||||
privateKeyData = make([]byte, count)
|
||||
_, err = readFull(r, privateKeyData)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
} else {
|
||||
privateKeyData, err = ioutil.ReadAll(r)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
}
|
||||
if !pk.Encrypted {
|
||||
if len(privateKeyData) < 2 {
|
||||
return errors.StructuralError("truncated private key data")
|
||||
}
|
||||
var sum uint16
|
||||
for i := 0; i < len(privateKeyData)-2; i++ {
|
||||
sum += uint16(privateKeyData[i])
|
||||
}
|
||||
if privateKeyData[len(privateKeyData)-2] != uint8(sum>>8) ||
|
||||
privateKeyData[len(privateKeyData)-1] != uint8(sum) {
|
||||
return errors.StructuralError("private key checksum failure")
|
||||
}
|
||||
privateKeyData = privateKeyData[:len(privateKeyData)-2]
|
||||
return pk.parsePrivateKey(privateKeyData)
|
||||
}
|
||||
|
||||
pk.encryptedData = privateKeyData
|
||||
return
|
||||
}
|
||||
|
||||
// Dummy returns true if the private key is a dummy key. This is a GNU extension.
|
||||
func (pk *PrivateKey) Dummy() bool {
|
||||
return pk.s2kParams.Dummy()
|
||||
}
|
||||
|
||||
func mod64kHash(d []byte) uint16 {
|
||||
var h uint16
|
||||
for _, b := range d {
|
||||
h += uint16(b)
|
||||
}
|
||||
return h
|
||||
}
|
||||
|
||||
func (pk *PrivateKey) Serialize(w io.Writer) (err error) {
|
||||
contents := bytes.NewBuffer(nil)
|
||||
err = pk.PublicKey.serializeWithoutHeaders(contents)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
if _, err = contents.Write([]byte{uint8(pk.s2kType)}); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
optional := bytes.NewBuffer(nil)
|
||||
if pk.Encrypted || pk.Dummy() {
|
||||
optional.Write([]byte{uint8(pk.cipher)})
|
||||
if err := pk.s2kParams.Serialize(optional); err != nil {
|
||||
return err
|
||||
}
|
||||
if pk.Encrypted {
|
||||
optional.Write(pk.iv)
|
||||
}
|
||||
}
|
||||
if pk.Version == 5 {
|
||||
contents.Write([]byte{uint8(optional.Len())})
|
||||
}
|
||||
io.Copy(contents, optional)
|
||||
|
||||
if !pk.Dummy() {
|
||||
l := 0
|
||||
var priv []byte
|
||||
if !pk.Encrypted {
|
||||
buf := bytes.NewBuffer(nil)
|
||||
err = pk.serializePrivateKey(buf)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
l = buf.Len()
|
||||
checksum := mod64kHash(buf.Bytes())
|
||||
buf.Write([]byte{byte(checksum >> 8), byte(checksum)})
|
||||
priv = buf.Bytes()
|
||||
} else {
|
||||
priv, l = pk.encryptedData, len(pk.encryptedData)
|
||||
}
|
||||
|
||||
if pk.Version == 5 {
|
||||
contents.Write([]byte{byte(l >> 24), byte(l >> 16), byte(l >> 8), byte(l)})
|
||||
}
|
||||
contents.Write(priv)
|
||||
}
|
||||
|
||||
ptype := packetTypePrivateKey
|
||||
if pk.IsSubkey {
|
||||
ptype = packetTypePrivateSubkey
|
||||
}
|
||||
err = serializeHeader(w, ptype, contents.Len())
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
_, err = io.Copy(w, contents)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
func serializeRSAPrivateKey(w io.Writer, priv *rsa.PrivateKey) error {
|
||||
if _, err := w.Write(new(encoding.MPI).SetBig(priv.D).EncodedBytes()); err != nil {
|
||||
return err
|
||||
}
|
||||
if _, err := w.Write(new(encoding.MPI).SetBig(priv.Primes[1]).EncodedBytes()); err != nil {
|
||||
return err
|
||||
}
|
||||
if _, err := w.Write(new(encoding.MPI).SetBig(priv.Primes[0]).EncodedBytes()); err != nil {
|
||||
return err
|
||||
}
|
||||
_, err := w.Write(new(encoding.MPI).SetBig(priv.Precomputed.Qinv).EncodedBytes())
|
||||
return err
|
||||
}
|
||||
|
||||
func serializeDSAPrivateKey(w io.Writer, priv *dsa.PrivateKey) error {
|
||||
_, err := w.Write(new(encoding.MPI).SetBig(priv.X).EncodedBytes())
|
||||
return err
|
||||
}
|
||||
|
||||
func serializeElGamalPrivateKey(w io.Writer, priv *elgamal.PrivateKey) error {
|
||||
_, err := w.Write(new(encoding.MPI).SetBig(priv.X).EncodedBytes())
|
||||
return err
|
||||
}
|
||||
|
||||
func serializeECDSAPrivateKey(w io.Writer, priv *ecdsa.PrivateKey) error {
|
||||
_, err := w.Write(encoding.NewMPI(priv.MarshalIntegerSecret()).EncodedBytes())
|
||||
return err
|
||||
}
|
||||
|
||||
func serializeEdDSAPrivateKey(w io.Writer, priv *eddsa.PrivateKey) error {
|
||||
_, err := w.Write(encoding.NewMPI(priv.MarshalByteSecret()).EncodedBytes())
|
||||
return err
|
||||
}
|
||||
|
||||
func serializeECDHPrivateKey(w io.Writer, priv *ecdh.PrivateKey) error {
|
||||
_, err := w.Write(encoding.NewMPI(priv.MarshalByteSecret()).EncodedBytes())
|
||||
return err
|
||||
}
|
||||
|
||||
// Decrypt decrypts an encrypted private key using a passphrase.
|
||||
func (pk *PrivateKey) Decrypt(passphrase []byte) error {
|
||||
if pk.Dummy() {
|
||||
return errors.ErrDummyPrivateKey("dummy key found")
|
||||
}
|
||||
if !pk.Encrypted {
|
||||
return nil
|
||||
}
|
||||
|
||||
key := make([]byte, pk.cipher.KeySize())
|
||||
pk.s2k(key, passphrase)
|
||||
block := pk.cipher.new(key)
|
||||
cfb := cipher.NewCFBDecrypter(block, pk.iv)
|
||||
|
||||
data := make([]byte, len(pk.encryptedData))
|
||||
cfb.XORKeyStream(data, pk.encryptedData)
|
||||
|
||||
if pk.sha1Checksum {
|
||||
if len(data) < sha1.Size {
|
||||
return errors.StructuralError("truncated private key data")
|
||||
}
|
||||
h := sha1.New()
|
||||
h.Write(data[:len(data)-sha1.Size])
|
||||
sum := h.Sum(nil)
|
||||
if !bytes.Equal(sum, data[len(data)-sha1.Size:]) {
|
||||
return errors.StructuralError("private key checksum failure")
|
||||
}
|
||||
data = data[:len(data)-sha1.Size]
|
||||
} else {
|
||||
if len(data) < 2 {
|
||||
return errors.StructuralError("truncated private key data")
|
||||
}
|
||||
var sum uint16
|
||||
for i := 0; i < len(data)-2; i++ {
|
||||
sum += uint16(data[i])
|
||||
}
|
||||
if data[len(data)-2] != uint8(sum>>8) ||
|
||||
data[len(data)-1] != uint8(sum) {
|
||||
return errors.StructuralError("private key checksum failure")
|
||||
}
|
||||
data = data[:len(data)-2]
|
||||
}
|
||||
|
||||
err := pk.parsePrivateKey(data)
|
||||
if _, ok := err.(errors.KeyInvalidError); ok {
|
||||
return errors.KeyInvalidError("invalid key parameters")
|
||||
}
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
// Mark key as unencrypted
|
||||
pk.s2kType = S2KNON
|
||||
pk.s2k = nil
|
||||
pk.Encrypted = false
|
||||
pk.encryptedData = nil
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
// Encrypt encrypts an unencrypted private key using a passphrase.
|
||||
func (pk *PrivateKey) Encrypt(passphrase []byte) error {
|
||||
priv := bytes.NewBuffer(nil)
|
||||
err := pk.serializePrivateKey(priv)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
//Default config of private key encryption
|
||||
pk.cipher = CipherAES256
|
||||
s2kConfig := &s2k.Config{
|
||||
S2KMode: 3, //Iterated
|
||||
S2KCount: 65536,
|
||||
Hash: crypto.SHA256,
|
||||
}
|
||||
|
||||
pk.s2kParams, err = s2k.Generate(rand.Reader, s2kConfig)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
privateKeyBytes := priv.Bytes()
|
||||
key := make([]byte, pk.cipher.KeySize())
|
||||
|
||||
pk.sha1Checksum = true
|
||||
pk.s2k, err = pk.s2kParams.Function()
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
pk.s2k(key, passphrase)
|
||||
block := pk.cipher.new(key)
|
||||
pk.iv = make([]byte, pk.cipher.blockSize())
|
||||
_, err = rand.Read(pk.iv)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
cfb := cipher.NewCFBEncrypter(block, pk.iv)
|
||||
|
||||
if pk.sha1Checksum {
|
||||
pk.s2kType = S2KSHA1
|
||||
h := sha1.New()
|
||||
h.Write(privateKeyBytes)
|
||||
sum := h.Sum(nil)
|
||||
privateKeyBytes = append(privateKeyBytes, sum...)
|
||||
} else {
|
||||
pk.s2kType = S2KCHECKSUM
|
||||
var sum uint16
|
||||
for _, b := range privateKeyBytes {
|
||||
sum += uint16(b)
|
||||
}
|
||||
priv.Write([]byte{uint8(sum >> 8), uint8(sum)})
|
||||
}
|
||||
|
||||
pk.encryptedData = make([]byte, len(privateKeyBytes))
|
||||
cfb.XORKeyStream(pk.encryptedData, privateKeyBytes)
|
||||
pk.Encrypted = true
|
||||
pk.PrivateKey = nil
|
||||
return err
|
||||
}
|
||||
|
||||
func (pk *PrivateKey) serializePrivateKey(w io.Writer) (err error) {
|
||||
switch priv := pk.PrivateKey.(type) {
|
||||
case *rsa.PrivateKey:
|
||||
err = serializeRSAPrivateKey(w, priv)
|
||||
case *dsa.PrivateKey:
|
||||
err = serializeDSAPrivateKey(w, priv)
|
||||
case *elgamal.PrivateKey:
|
||||
err = serializeElGamalPrivateKey(w, priv)
|
||||
case *ecdsa.PrivateKey:
|
||||
err = serializeECDSAPrivateKey(w, priv)
|
||||
case *eddsa.PrivateKey:
|
||||
err = serializeEdDSAPrivateKey(w, priv)
|
||||
case *ecdh.PrivateKey:
|
||||
err = serializeECDHPrivateKey(w, priv)
|
||||
default:
|
||||
err = errors.InvalidArgumentError("unknown private key type")
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
func (pk *PrivateKey) parsePrivateKey(data []byte) (err error) {
|
||||
switch pk.PublicKey.PubKeyAlgo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoRSAEncryptOnly:
|
||||
return pk.parseRSAPrivateKey(data)
|
||||
case PubKeyAlgoDSA:
|
||||
return pk.parseDSAPrivateKey(data)
|
||||
case PubKeyAlgoElGamal:
|
||||
return pk.parseElGamalPrivateKey(data)
|
||||
case PubKeyAlgoECDSA:
|
||||
return pk.parseECDSAPrivateKey(data)
|
||||
case PubKeyAlgoECDH:
|
||||
return pk.parseECDHPrivateKey(data)
|
||||
case PubKeyAlgoEdDSA:
|
||||
return pk.parseEdDSAPrivateKey(data)
|
||||
}
|
||||
panic("impossible")
|
||||
}
|
||||
|
||||
func (pk *PrivateKey) parseRSAPrivateKey(data []byte) (err error) {
|
||||
rsaPub := pk.PublicKey.PublicKey.(*rsa.PublicKey)
|
||||
rsaPriv := new(rsa.PrivateKey)
|
||||
rsaPriv.PublicKey = *rsaPub
|
||||
|
||||
buf := bytes.NewBuffer(data)
|
||||
d := new(encoding.MPI)
|
||||
if _, err := d.ReadFrom(buf); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
p := new(encoding.MPI)
|
||||
if _, err := p.ReadFrom(buf); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
q := new(encoding.MPI)
|
||||
if _, err := q.ReadFrom(buf); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
rsaPriv.D = new(big.Int).SetBytes(d.Bytes())
|
||||
rsaPriv.Primes = make([]*big.Int, 2)
|
||||
rsaPriv.Primes[0] = new(big.Int).SetBytes(p.Bytes())
|
||||
rsaPriv.Primes[1] = new(big.Int).SetBytes(q.Bytes())
|
||||
if err := rsaPriv.Validate(); err != nil {
|
||||
return errors.KeyInvalidError(err.Error())
|
||||
}
|
||||
rsaPriv.Precompute()
|
||||
pk.PrivateKey = rsaPriv
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
func (pk *PrivateKey) parseDSAPrivateKey(data []byte) (err error) {
|
||||
dsaPub := pk.PublicKey.PublicKey.(*dsa.PublicKey)
|
||||
dsaPriv := new(dsa.PrivateKey)
|
||||
dsaPriv.PublicKey = *dsaPub
|
||||
|
||||
buf := bytes.NewBuffer(data)
|
||||
x := new(encoding.MPI)
|
||||
if _, err := x.ReadFrom(buf); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
dsaPriv.X = new(big.Int).SetBytes(x.Bytes())
|
||||
if err := validateDSAParameters(dsaPriv); err != nil {
|
||||
return err
|
||||
}
|
||||
pk.PrivateKey = dsaPriv
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
func (pk *PrivateKey) parseElGamalPrivateKey(data []byte) (err error) {
|
||||
pub := pk.PublicKey.PublicKey.(*elgamal.PublicKey)
|
||||
priv := new(elgamal.PrivateKey)
|
||||
priv.PublicKey = *pub
|
||||
|
||||
buf := bytes.NewBuffer(data)
|
||||
x := new(encoding.MPI)
|
||||
if _, err := x.ReadFrom(buf); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
priv.X = new(big.Int).SetBytes(x.Bytes())
|
||||
if err := validateElGamalParameters(priv); err != nil {
|
||||
return err
|
||||
}
|
||||
pk.PrivateKey = priv
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
func (pk *PrivateKey) parseECDSAPrivateKey(data []byte) (err error) {
|
||||
ecdsaPub := pk.PublicKey.PublicKey.(*ecdsa.PublicKey)
|
||||
ecdsaPriv := ecdsa.NewPrivateKey(*ecdsaPub)
|
||||
|
||||
buf := bytes.NewBuffer(data)
|
||||
d := new(encoding.MPI)
|
||||
if _, err := d.ReadFrom(buf); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
if err := ecdsaPriv.UnmarshalIntegerSecret(d.Bytes()); err != nil {
|
||||
return err
|
||||
}
|
||||
if err := ecdsa.Validate(ecdsaPriv); err != nil {
|
||||
return err
|
||||
}
|
||||
pk.PrivateKey = ecdsaPriv
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
func (pk *PrivateKey) parseECDHPrivateKey(data []byte) (err error) {
|
||||
ecdhPub := pk.PublicKey.PublicKey.(*ecdh.PublicKey)
|
||||
ecdhPriv := ecdh.NewPrivateKey(*ecdhPub)
|
||||
|
||||
buf := bytes.NewBuffer(data)
|
||||
d := new(encoding.MPI)
|
||||
if _, err := d.ReadFrom(buf); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
if err := ecdhPriv.UnmarshalByteSecret(d.Bytes()); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
if err := ecdh.Validate(ecdhPriv); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
pk.PrivateKey = ecdhPriv
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
func (pk *PrivateKey) parseEdDSAPrivateKey(data []byte) (err error) {
|
||||
eddsaPub := pk.PublicKey.PublicKey.(*eddsa.PublicKey)
|
||||
eddsaPriv := eddsa.NewPrivateKey(*eddsaPub)
|
||||
eddsaPriv.PublicKey = *eddsaPub
|
||||
|
||||
buf := bytes.NewBuffer(data)
|
||||
d := new(encoding.MPI)
|
||||
if _, err := d.ReadFrom(buf); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
if err = eddsaPriv.UnmarshalByteSecret(d.Bytes()); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
if err := eddsa.Validate(eddsaPriv); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
pk.PrivateKey = eddsaPriv
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
func validateDSAParameters(priv *dsa.PrivateKey) error {
|
||||
p := priv.P // group prime
|
||||
q := priv.Q // subgroup order
|
||||
g := priv.G // g has order q mod p
|
||||
x := priv.X // secret
|
||||
y := priv.Y // y == g**x mod p
|
||||
one := big.NewInt(1)
|
||||
// expect g, y >= 2 and g < p
|
||||
if g.Cmp(one) <= 0 || y.Cmp(one) <= 0 || g.Cmp(p) > 0 {
|
||||
return errors.KeyInvalidError("dsa: invalid group")
|
||||
}
|
||||
// expect p > q
|
||||
if p.Cmp(q) <= 0 {
|
||||
return errors.KeyInvalidError("dsa: invalid group prime")
|
||||
}
|
||||
// q should be large enough and divide p-1
|
||||
pSub1 := new(big.Int).Sub(p, one)
|
||||
if q.BitLen() < 150 || new(big.Int).Mod(pSub1, q).Cmp(big.NewInt(0)) != 0 {
|
||||
return errors.KeyInvalidError("dsa: invalid order")
|
||||
}
|
||||
// confirm that g has order q mod p
|
||||
if !q.ProbablyPrime(32) || new(big.Int).Exp(g, q, p).Cmp(one) != 0 {
|
||||
return errors.KeyInvalidError("dsa: invalid order")
|
||||
}
|
||||
// check y
|
||||
if new(big.Int).Exp(g, x, p).Cmp(y) != 0 {
|
||||
return errors.KeyInvalidError("dsa: mismatching values")
|
||||
}
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
func validateElGamalParameters(priv *elgamal.PrivateKey) error {
|
||||
p := priv.P // group prime
|
||||
g := priv.G // g has order p-1 mod p
|
||||
x := priv.X // secret
|
||||
y := priv.Y // y == g**x mod p
|
||||
one := big.NewInt(1)
|
||||
// Expect g, y >= 2 and g < p
|
||||
if g.Cmp(one) <= 0 || y.Cmp(one) <= 0 || g.Cmp(p) > 0 {
|
||||
return errors.KeyInvalidError("elgamal: invalid group")
|
||||
}
|
||||
if p.BitLen() < 1024 {
|
||||
return errors.KeyInvalidError("elgamal: group order too small")
|
||||
}
|
||||
pSub1 := new(big.Int).Sub(p, one)
|
||||
if new(big.Int).Exp(g, pSub1, p).Cmp(one) != 0 {
|
||||
return errors.KeyInvalidError("elgamal: invalid group")
|
||||
}
|
||||
// Since p-1 is not prime, g might have a smaller order that divides p-1.
|
||||
// We cannot confirm the exact order of g, but we make sure it is not too small.
|
||||
gExpI := new(big.Int).Set(g)
|
||||
i := 1
|
||||
threshold := 2 << 17 // we want order > threshold
|
||||
for i < threshold {
|
||||
i++ // we check every order to make sure key validation is not easily bypassed by guessing y'
|
||||
gExpI.Mod(new(big.Int).Mul(gExpI, g), p)
|
||||
if gExpI.Cmp(one) == 0 {
|
||||
return errors.KeyInvalidError("elgamal: order too small")
|
||||
}
|
||||
}
|
||||
// Check y
|
||||
if new(big.Int).Exp(g, x, p).Cmp(y) != 0 {
|
||||
return errors.KeyInvalidError("elgamal: mismatching values")
|
||||
}
|
||||
|
||||
return nil
|
||||
}
|
||||
12
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/private_key_test_data.go
generated
vendored
Normal file
12
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/private_key_test_data.go
generated
vendored
Normal file
|
|
@ -0,0 +1,12 @@
|
|||
package packet
|
||||
|
||||
// Generated with `gpg --export-secret-keys "Test Key 2"`
|
||||
const privKeyRSAHex = "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"
|
||||
|
||||
// Generated by `gpg --export-secret-keys` followed by a manual extraction of
|
||||
// the ElGamal subkey from the packets.
|
||||
const privKeyElGamalHex = "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"
|
||||
|
||||
// pkcs1PrivKeyHex is a PKCS#1, RSA private key.
|
||||
// Generated by `openssl genrsa 1024 | openssl rsa -outform DER | xxd -p`
|
||||
const pkcs1PrivKeyHex = "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"
|
||||
802
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/public_key.go
generated
vendored
Normal file
802
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/public_key.go
generated
vendored
Normal file
|
|
@ -0,0 +1,802 @@
|
|||
// Copyright 2011 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package packet
|
||||
|
||||
import (
|
||||
"crypto"
|
||||
"crypto/dsa"
|
||||
"crypto/rsa"
|
||||
"crypto/sha1"
|
||||
"crypto/sha256"
|
||||
_ "crypto/sha512"
|
||||
"encoding/binary"
|
||||
"fmt"
|
||||
"hash"
|
||||
"io"
|
||||
"math/big"
|
||||
"strconv"
|
||||
"time"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/ecdh"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/ecdsa"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/eddsa"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/elgamal"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/algorithm"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/ecc"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/encoding"
|
||||
)
|
||||
|
||||
type kdfHashFunction byte
|
||||
type kdfAlgorithm byte
|
||||
|
||||
// PublicKey represents an OpenPGP public key. See RFC 4880, section 5.5.2.
|
||||
type PublicKey struct {
|
||||
Version int
|
||||
CreationTime time.Time
|
||||
PubKeyAlgo PublicKeyAlgorithm
|
||||
PublicKey interface{} // *rsa.PublicKey, *dsa.PublicKey, *ecdsa.PublicKey or *eddsa.PublicKey
|
||||
Fingerprint []byte
|
||||
KeyId uint64
|
||||
IsSubkey bool
|
||||
|
||||
// RFC 4880 fields
|
||||
n, e, p, q, g, y encoding.Field
|
||||
|
||||
// RFC 6637 fields
|
||||
// oid contains the OID byte sequence identifying the elliptic curve used
|
||||
oid encoding.Field
|
||||
|
||||
// kdf stores key derivation function parameters
|
||||
// used for ECDH encryption. See RFC 6637, Section 9.
|
||||
kdf encoding.Field
|
||||
}
|
||||
|
||||
// UpgradeToV5 updates the version of the key to v5, and updates all necessary
|
||||
// fields.
|
||||
func (pk *PublicKey) UpgradeToV5() {
|
||||
pk.Version = 5
|
||||
pk.setFingerprintAndKeyId()
|
||||
}
|
||||
|
||||
// signingKey provides a convenient abstraction over signature verification
|
||||
// for v3 and v4 public keys.
|
||||
type signingKey interface {
|
||||
SerializeForHash(io.Writer) error
|
||||
SerializeSignaturePrefix(io.Writer)
|
||||
serializeWithoutHeaders(io.Writer) error
|
||||
}
|
||||
|
||||
// NewRSAPublicKey returns a PublicKey that wraps the given rsa.PublicKey.
|
||||
func NewRSAPublicKey(creationTime time.Time, pub *rsa.PublicKey) *PublicKey {
|
||||
pk := &PublicKey{
|
||||
Version: 4,
|
||||
CreationTime: creationTime,
|
||||
PubKeyAlgo: PubKeyAlgoRSA,
|
||||
PublicKey: pub,
|
||||
n: new(encoding.MPI).SetBig(pub.N),
|
||||
e: new(encoding.MPI).SetBig(big.NewInt(int64(pub.E))),
|
||||
}
|
||||
|
||||
pk.setFingerprintAndKeyId()
|
||||
return pk
|
||||
}
|
||||
|
||||
// NewDSAPublicKey returns a PublicKey that wraps the given dsa.PublicKey.
|
||||
func NewDSAPublicKey(creationTime time.Time, pub *dsa.PublicKey) *PublicKey {
|
||||
pk := &PublicKey{
|
||||
Version: 4,
|
||||
CreationTime: creationTime,
|
||||
PubKeyAlgo: PubKeyAlgoDSA,
|
||||
PublicKey: pub,
|
||||
p: new(encoding.MPI).SetBig(pub.P),
|
||||
q: new(encoding.MPI).SetBig(pub.Q),
|
||||
g: new(encoding.MPI).SetBig(pub.G),
|
||||
y: new(encoding.MPI).SetBig(pub.Y),
|
||||
}
|
||||
|
||||
pk.setFingerprintAndKeyId()
|
||||
return pk
|
||||
}
|
||||
|
||||
// NewElGamalPublicKey returns a PublicKey that wraps the given elgamal.PublicKey.
|
||||
func NewElGamalPublicKey(creationTime time.Time, pub *elgamal.PublicKey) *PublicKey {
|
||||
pk := &PublicKey{
|
||||
Version: 4,
|
||||
CreationTime: creationTime,
|
||||
PubKeyAlgo: PubKeyAlgoElGamal,
|
||||
PublicKey: pub,
|
||||
p: new(encoding.MPI).SetBig(pub.P),
|
||||
g: new(encoding.MPI).SetBig(pub.G),
|
||||
y: new(encoding.MPI).SetBig(pub.Y),
|
||||
}
|
||||
|
||||
pk.setFingerprintAndKeyId()
|
||||
return pk
|
||||
}
|
||||
|
||||
func NewECDSAPublicKey(creationTime time.Time, pub *ecdsa.PublicKey) *PublicKey {
|
||||
pk := &PublicKey{
|
||||
Version: 4,
|
||||
CreationTime: creationTime,
|
||||
PubKeyAlgo: PubKeyAlgoECDSA,
|
||||
PublicKey: pub,
|
||||
p: encoding.NewMPI(pub.MarshalPoint()),
|
||||
}
|
||||
|
||||
curveInfo := ecc.FindByCurve(pub.GetCurve())
|
||||
if curveInfo == nil {
|
||||
panic("unknown elliptic curve")
|
||||
}
|
||||
pk.oid = curveInfo.Oid
|
||||
pk.setFingerprintAndKeyId()
|
||||
return pk
|
||||
}
|
||||
|
||||
func NewECDHPublicKey(creationTime time.Time, pub *ecdh.PublicKey) *PublicKey {
|
||||
var pk *PublicKey
|
||||
var kdf = encoding.NewOID([]byte{0x1, pub.Hash.Id(), pub.Cipher.Id()})
|
||||
pk = &PublicKey{
|
||||
Version: 4,
|
||||
CreationTime: creationTime,
|
||||
PubKeyAlgo: PubKeyAlgoECDH,
|
||||
PublicKey: pub,
|
||||
p: encoding.NewMPI(pub.MarshalPoint()),
|
||||
kdf: kdf,
|
||||
}
|
||||
|
||||
curveInfo := ecc.FindByCurve(pub.GetCurve())
|
||||
|
||||
if curveInfo == nil {
|
||||
panic("unknown elliptic curve")
|
||||
}
|
||||
|
||||
pk.oid = curveInfo.Oid
|
||||
pk.setFingerprintAndKeyId()
|
||||
return pk
|
||||
}
|
||||
|
||||
func NewEdDSAPublicKey(creationTime time.Time, pub *eddsa.PublicKey) *PublicKey {
|
||||
curveInfo := ecc.FindByCurve(pub.GetCurve())
|
||||
pk := &PublicKey{
|
||||
Version: 4,
|
||||
CreationTime: creationTime,
|
||||
PubKeyAlgo: PubKeyAlgoEdDSA,
|
||||
PublicKey: pub,
|
||||
oid: curveInfo.Oid,
|
||||
// Native point format, see draft-koch-eddsa-for-openpgp-04, Appendix B
|
||||
p: encoding.NewMPI(pub.MarshalPoint()),
|
||||
}
|
||||
|
||||
pk.setFingerprintAndKeyId()
|
||||
return pk
|
||||
}
|
||||
|
||||
func (pk *PublicKey) parse(r io.Reader) (err error) {
|
||||
// RFC 4880, section 5.5.2
|
||||
var buf [6]byte
|
||||
_, err = readFull(r, buf[:])
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
if buf[0] != 4 && buf[0] != 5 {
|
||||
return errors.UnsupportedError("public key version " + strconv.Itoa(int(buf[0])))
|
||||
}
|
||||
|
||||
pk.Version = int(buf[0])
|
||||
if pk.Version == 5 {
|
||||
var n [4]byte
|
||||
_, err = readFull(r, n[:])
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
}
|
||||
pk.CreationTime = time.Unix(int64(uint32(buf[1])<<24|uint32(buf[2])<<16|uint32(buf[3])<<8|uint32(buf[4])), 0)
|
||||
pk.PubKeyAlgo = PublicKeyAlgorithm(buf[5])
|
||||
switch pk.PubKeyAlgo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly:
|
||||
err = pk.parseRSA(r)
|
||||
case PubKeyAlgoDSA:
|
||||
err = pk.parseDSA(r)
|
||||
case PubKeyAlgoElGamal:
|
||||
err = pk.parseElGamal(r)
|
||||
case PubKeyAlgoECDSA:
|
||||
err = pk.parseECDSA(r)
|
||||
case PubKeyAlgoECDH:
|
||||
err = pk.parseECDH(r)
|
||||
case PubKeyAlgoEdDSA:
|
||||
err = pk.parseEdDSA(r)
|
||||
default:
|
||||
err = errors.UnsupportedError("public key type: " + strconv.Itoa(int(pk.PubKeyAlgo)))
|
||||
}
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
pk.setFingerprintAndKeyId()
|
||||
return
|
||||
}
|
||||
|
||||
func (pk *PublicKey) setFingerprintAndKeyId() {
|
||||
// RFC 4880, section 12.2
|
||||
if pk.Version == 5 {
|
||||
fingerprint := sha256.New()
|
||||
pk.SerializeForHash(fingerprint)
|
||||
pk.Fingerprint = make([]byte, 32)
|
||||
copy(pk.Fingerprint, fingerprint.Sum(nil))
|
||||
pk.KeyId = binary.BigEndian.Uint64(pk.Fingerprint[:8])
|
||||
} else {
|
||||
fingerprint := sha1.New()
|
||||
pk.SerializeForHash(fingerprint)
|
||||
pk.Fingerprint = make([]byte, 20)
|
||||
copy(pk.Fingerprint, fingerprint.Sum(nil))
|
||||
pk.KeyId = binary.BigEndian.Uint64(pk.Fingerprint[12:20])
|
||||
}
|
||||
}
|
||||
|
||||
// parseRSA parses RSA public key material from the given Reader. See RFC 4880,
|
||||
// section 5.5.2.
|
||||
func (pk *PublicKey) parseRSA(r io.Reader) (err error) {
|
||||
pk.n = new(encoding.MPI)
|
||||
if _, err = pk.n.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
pk.e = new(encoding.MPI)
|
||||
if _, err = pk.e.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
if len(pk.e.Bytes()) > 3 {
|
||||
err = errors.UnsupportedError("large public exponent")
|
||||
return
|
||||
}
|
||||
rsa := &rsa.PublicKey{
|
||||
N: new(big.Int).SetBytes(pk.n.Bytes()),
|
||||
E: 0,
|
||||
}
|
||||
for i := 0; i < len(pk.e.Bytes()); i++ {
|
||||
rsa.E <<= 8
|
||||
rsa.E |= int(pk.e.Bytes()[i])
|
||||
}
|
||||
pk.PublicKey = rsa
|
||||
return
|
||||
}
|
||||
|
||||
// parseDSA parses DSA public key material from the given Reader. See RFC 4880,
|
||||
// section 5.5.2.
|
||||
func (pk *PublicKey) parseDSA(r io.Reader) (err error) {
|
||||
pk.p = new(encoding.MPI)
|
||||
if _, err = pk.p.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
pk.q = new(encoding.MPI)
|
||||
if _, err = pk.q.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
pk.g = new(encoding.MPI)
|
||||
if _, err = pk.g.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
pk.y = new(encoding.MPI)
|
||||
if _, err = pk.y.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
dsa := new(dsa.PublicKey)
|
||||
dsa.P = new(big.Int).SetBytes(pk.p.Bytes())
|
||||
dsa.Q = new(big.Int).SetBytes(pk.q.Bytes())
|
||||
dsa.G = new(big.Int).SetBytes(pk.g.Bytes())
|
||||
dsa.Y = new(big.Int).SetBytes(pk.y.Bytes())
|
||||
pk.PublicKey = dsa
|
||||
return
|
||||
}
|
||||
|
||||
// parseElGamal parses ElGamal public key material from the given Reader. See
|
||||
// RFC 4880, section 5.5.2.
|
||||
func (pk *PublicKey) parseElGamal(r io.Reader) (err error) {
|
||||
pk.p = new(encoding.MPI)
|
||||
if _, err = pk.p.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
pk.g = new(encoding.MPI)
|
||||
if _, err = pk.g.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
pk.y = new(encoding.MPI)
|
||||
if _, err = pk.y.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
elgamal := new(elgamal.PublicKey)
|
||||
elgamal.P = new(big.Int).SetBytes(pk.p.Bytes())
|
||||
elgamal.G = new(big.Int).SetBytes(pk.g.Bytes())
|
||||
elgamal.Y = new(big.Int).SetBytes(pk.y.Bytes())
|
||||
pk.PublicKey = elgamal
|
||||
return
|
||||
}
|
||||
|
||||
// parseECDSA parses ECDSA public key material from the given Reader. See
|
||||
// RFC 6637, Section 9.
|
||||
func (pk *PublicKey) parseECDSA(r io.Reader) (err error) {
|
||||
pk.oid = new(encoding.OID)
|
||||
if _, err = pk.oid.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
pk.p = new(encoding.MPI)
|
||||
if _, err = pk.p.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
curveInfo := ecc.FindByOid(pk.oid)
|
||||
if curveInfo == nil {
|
||||
return errors.UnsupportedError(fmt.Sprintf("unknown oid: %x", pk.oid))
|
||||
}
|
||||
|
||||
c, ok := curveInfo.Curve.(ecc.ECDSACurve)
|
||||
if !ok {
|
||||
return errors.UnsupportedError(fmt.Sprintf("unsupported oid: %x", pk.oid))
|
||||
}
|
||||
|
||||
ecdsaKey := ecdsa.NewPublicKey(c)
|
||||
err = ecdsaKey.UnmarshalPoint(pk.p.Bytes())
|
||||
pk.PublicKey = ecdsaKey
|
||||
|
||||
return
|
||||
}
|
||||
|
||||
// parseECDH parses ECDH public key material from the given Reader. See
|
||||
// RFC 6637, Section 9.
|
||||
func (pk *PublicKey) parseECDH(r io.Reader) (err error) {
|
||||
pk.oid = new(encoding.OID)
|
||||
if _, err = pk.oid.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
pk.p = new(encoding.MPI)
|
||||
if _, err = pk.p.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
pk.kdf = new(encoding.OID)
|
||||
if _, err = pk.kdf.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
curveInfo := ecc.FindByOid(pk.oid)
|
||||
|
||||
if curveInfo == nil {
|
||||
return errors.UnsupportedError(fmt.Sprintf("unknown oid: %x", pk.oid))
|
||||
}
|
||||
|
||||
c, ok := curveInfo.Curve.(ecc.ECDHCurve)
|
||||
if !ok {
|
||||
return errors.UnsupportedError(fmt.Sprintf("unsupported oid: %x", pk.oid))
|
||||
}
|
||||
|
||||
if kdfLen := len(pk.kdf.Bytes()); kdfLen < 3 {
|
||||
return errors.UnsupportedError("unsupported ECDH KDF length: " + strconv.Itoa(kdfLen))
|
||||
}
|
||||
if reserved := pk.kdf.Bytes()[0]; reserved != 0x01 {
|
||||
return errors.UnsupportedError("unsupported KDF reserved field: " + strconv.Itoa(int(reserved)))
|
||||
}
|
||||
kdfHash, ok := algorithm.HashById[pk.kdf.Bytes()[1]]
|
||||
if !ok {
|
||||
return errors.UnsupportedError("unsupported ECDH KDF hash: " + strconv.Itoa(int(pk.kdf.Bytes()[1])))
|
||||
}
|
||||
kdfCipher, ok := algorithm.CipherById[pk.kdf.Bytes()[2]]
|
||||
if !ok {
|
||||
return errors.UnsupportedError("unsupported ECDH KDF cipher: " + strconv.Itoa(int(pk.kdf.Bytes()[2])))
|
||||
}
|
||||
|
||||
ecdhKey := ecdh.NewPublicKey(c, kdfHash, kdfCipher)
|
||||
err = ecdhKey.UnmarshalPoint(pk.p.Bytes())
|
||||
pk.PublicKey = ecdhKey
|
||||
|
||||
return
|
||||
}
|
||||
|
||||
func (pk *PublicKey) parseEdDSA(r io.Reader) (err error) {
|
||||
pk.oid = new(encoding.OID)
|
||||
if _, err = pk.oid.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
curveInfo := ecc.FindByOid(pk.oid)
|
||||
if curveInfo == nil {
|
||||
return errors.UnsupportedError(fmt.Sprintf("unknown oid: %x", pk.oid))
|
||||
}
|
||||
|
||||
c, ok := curveInfo.Curve.(ecc.EdDSACurve)
|
||||
if !ok {
|
||||
return errors.UnsupportedError(fmt.Sprintf("unsupported oid: %x", pk.oid))
|
||||
}
|
||||
|
||||
pk.p = new(encoding.MPI)
|
||||
if _, err = pk.p.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
pub := eddsa.NewPublicKey(c)
|
||||
|
||||
switch flag := pk.p.Bytes()[0]; flag {
|
||||
case 0x04:
|
||||
// TODO: see _grcy_ecc_eddsa_ensure_compact in grcypt
|
||||
return errors.UnsupportedError("unsupported EdDSA compression: " + strconv.Itoa(int(flag)))
|
||||
case 0x40:
|
||||
err = pub.UnmarshalPoint(pk.p.Bytes())
|
||||
default:
|
||||
return errors.UnsupportedError("unsupported EdDSA compression: " + strconv.Itoa(int(flag)))
|
||||
}
|
||||
|
||||
pk.PublicKey = pub
|
||||
return
|
||||
}
|
||||
|
||||
// SerializeForHash serializes the PublicKey to w with the special packet
|
||||
// header format needed for hashing.
|
||||
func (pk *PublicKey) SerializeForHash(w io.Writer) error {
|
||||
pk.SerializeSignaturePrefix(w)
|
||||
return pk.serializeWithoutHeaders(w)
|
||||
}
|
||||
|
||||
// SerializeSignaturePrefix writes the prefix for this public key to the given Writer.
|
||||
// The prefix is used when calculating a signature over this public key. See
|
||||
// RFC 4880, section 5.2.4.
|
||||
func (pk *PublicKey) SerializeSignaturePrefix(w io.Writer) {
|
||||
var pLength = pk.algorithmSpecificByteCount()
|
||||
if pk.Version == 5 {
|
||||
pLength += 10 // version, timestamp (4), algorithm, key octet count (4).
|
||||
w.Write([]byte{
|
||||
0x9A,
|
||||
byte(pLength >> 24),
|
||||
byte(pLength >> 16),
|
||||
byte(pLength >> 8),
|
||||
byte(pLength),
|
||||
})
|
||||
return
|
||||
}
|
||||
pLength += 6
|
||||
w.Write([]byte{0x99, byte(pLength >> 8), byte(pLength)})
|
||||
}
|
||||
|
||||
func (pk *PublicKey) Serialize(w io.Writer) (err error) {
|
||||
length := 6 // 6 byte header
|
||||
length += pk.algorithmSpecificByteCount()
|
||||
if pk.Version == 5 {
|
||||
length += 4 // octet key count
|
||||
}
|
||||
packetType := packetTypePublicKey
|
||||
if pk.IsSubkey {
|
||||
packetType = packetTypePublicSubkey
|
||||
}
|
||||
err = serializeHeader(w, packetType, length)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
return pk.serializeWithoutHeaders(w)
|
||||
}
|
||||
|
||||
func (pk *PublicKey) algorithmSpecificByteCount() int {
|
||||
length := 0
|
||||
switch pk.PubKeyAlgo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly:
|
||||
length += int(pk.n.EncodedLength())
|
||||
length += int(pk.e.EncodedLength())
|
||||
case PubKeyAlgoDSA:
|
||||
length += int(pk.p.EncodedLength())
|
||||
length += int(pk.q.EncodedLength())
|
||||
length += int(pk.g.EncodedLength())
|
||||
length += int(pk.y.EncodedLength())
|
||||
case PubKeyAlgoElGamal:
|
||||
length += int(pk.p.EncodedLength())
|
||||
length += int(pk.g.EncodedLength())
|
||||
length += int(pk.y.EncodedLength())
|
||||
case PubKeyAlgoECDSA:
|
||||
length += int(pk.oid.EncodedLength())
|
||||
length += int(pk.p.EncodedLength())
|
||||
case PubKeyAlgoECDH:
|
||||
length += int(pk.oid.EncodedLength())
|
||||
length += int(pk.p.EncodedLength())
|
||||
length += int(pk.kdf.EncodedLength())
|
||||
case PubKeyAlgoEdDSA:
|
||||
length += int(pk.oid.EncodedLength())
|
||||
length += int(pk.p.EncodedLength())
|
||||
default:
|
||||
panic("unknown public key algorithm")
|
||||
}
|
||||
return length
|
||||
}
|
||||
|
||||
// serializeWithoutHeaders marshals the PublicKey to w in the form of an
|
||||
// OpenPGP public key packet, not including the packet header.
|
||||
func (pk *PublicKey) serializeWithoutHeaders(w io.Writer) (err error) {
|
||||
t := uint32(pk.CreationTime.Unix())
|
||||
if _, err = w.Write([]byte{
|
||||
byte(pk.Version),
|
||||
byte(t >> 24), byte(t >> 16), byte(t >> 8), byte(t),
|
||||
byte(pk.PubKeyAlgo),
|
||||
}); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
if pk.Version == 5 {
|
||||
n := pk.algorithmSpecificByteCount()
|
||||
if _, err = w.Write([]byte{
|
||||
byte(n >> 24), byte(n >> 16), byte(n >> 8), byte(n),
|
||||
}); err != nil {
|
||||
return
|
||||
}
|
||||
}
|
||||
|
||||
switch pk.PubKeyAlgo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly:
|
||||
if _, err = w.Write(pk.n.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
_, err = w.Write(pk.e.EncodedBytes())
|
||||
return
|
||||
case PubKeyAlgoDSA:
|
||||
if _, err = w.Write(pk.p.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
if _, err = w.Write(pk.q.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
if _, err = w.Write(pk.g.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
_, err = w.Write(pk.y.EncodedBytes())
|
||||
return
|
||||
case PubKeyAlgoElGamal:
|
||||
if _, err = w.Write(pk.p.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
if _, err = w.Write(pk.g.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
_, err = w.Write(pk.y.EncodedBytes())
|
||||
return
|
||||
case PubKeyAlgoECDSA:
|
||||
if _, err = w.Write(pk.oid.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
_, err = w.Write(pk.p.EncodedBytes())
|
||||
return
|
||||
case PubKeyAlgoECDH:
|
||||
if _, err = w.Write(pk.oid.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
if _, err = w.Write(pk.p.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
_, err = w.Write(pk.kdf.EncodedBytes())
|
||||
return
|
||||
case PubKeyAlgoEdDSA:
|
||||
if _, err = w.Write(pk.oid.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
_, err = w.Write(pk.p.EncodedBytes())
|
||||
return
|
||||
}
|
||||
return errors.InvalidArgumentError("bad public-key algorithm")
|
||||
}
|
||||
|
||||
// CanSign returns true iff this public key can generate signatures
|
||||
func (pk *PublicKey) CanSign() bool {
|
||||
return pk.PubKeyAlgo != PubKeyAlgoRSAEncryptOnly && pk.PubKeyAlgo != PubKeyAlgoElGamal && pk.PubKeyAlgo != PubKeyAlgoECDH
|
||||
}
|
||||
|
||||
// VerifySignature returns nil iff sig is a valid signature, made by this
|
||||
// public key, of the data hashed into signed. signed is mutated by this call.
|
||||
func (pk *PublicKey) VerifySignature(signed hash.Hash, sig *Signature) (err error) {
|
||||
if !pk.CanSign() {
|
||||
return errors.InvalidArgumentError("public key cannot generate signatures")
|
||||
}
|
||||
if sig.Version == 5 && (sig.SigType == 0x00 || sig.SigType == 0x01) {
|
||||
sig.AddMetadataToHashSuffix()
|
||||
}
|
||||
signed.Write(sig.HashSuffix)
|
||||
hashBytes := signed.Sum(nil)
|
||||
if hashBytes[0] != sig.HashTag[0] || hashBytes[1] != sig.HashTag[1] {
|
||||
return errors.SignatureError("hash tag doesn't match")
|
||||
}
|
||||
|
||||
if pk.PubKeyAlgo != sig.PubKeyAlgo {
|
||||
return errors.InvalidArgumentError("public key and signature use different algorithms")
|
||||
}
|
||||
|
||||
switch pk.PubKeyAlgo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly:
|
||||
rsaPublicKey, _ := pk.PublicKey.(*rsa.PublicKey)
|
||||
err = rsa.VerifyPKCS1v15(rsaPublicKey, sig.Hash, hashBytes, padToKeySize(rsaPublicKey, sig.RSASignature.Bytes()))
|
||||
if err != nil {
|
||||
return errors.SignatureError("RSA verification failure")
|
||||
}
|
||||
return nil
|
||||
case PubKeyAlgoDSA:
|
||||
dsaPublicKey, _ := pk.PublicKey.(*dsa.PublicKey)
|
||||
// Need to truncate hashBytes to match FIPS 186-3 section 4.6.
|
||||
subgroupSize := (dsaPublicKey.Q.BitLen() + 7) / 8
|
||||
if len(hashBytes) > subgroupSize {
|
||||
hashBytes = hashBytes[:subgroupSize]
|
||||
}
|
||||
if !dsa.Verify(dsaPublicKey, hashBytes, new(big.Int).SetBytes(sig.DSASigR.Bytes()), new(big.Int).SetBytes(sig.DSASigS.Bytes())) {
|
||||
return errors.SignatureError("DSA verification failure")
|
||||
}
|
||||
return nil
|
||||
case PubKeyAlgoECDSA:
|
||||
ecdsaPublicKey := pk.PublicKey.(*ecdsa.PublicKey)
|
||||
if !ecdsa.Verify(ecdsaPublicKey, hashBytes, new(big.Int).SetBytes(sig.ECDSASigR.Bytes()), new(big.Int).SetBytes(sig.ECDSASigS.Bytes())) {
|
||||
return errors.SignatureError("ECDSA verification failure")
|
||||
}
|
||||
return nil
|
||||
case PubKeyAlgoEdDSA:
|
||||
eddsaPublicKey := pk.PublicKey.(*eddsa.PublicKey)
|
||||
if !eddsa.Verify(eddsaPublicKey, hashBytes, sig.EdDSASigR.Bytes(), sig.EdDSASigS.Bytes()) {
|
||||
return errors.SignatureError("EdDSA verification failure")
|
||||
}
|
||||
return nil
|
||||
default:
|
||||
return errors.SignatureError("Unsupported public key algorithm used in signature")
|
||||
}
|
||||
}
|
||||
|
||||
// keySignatureHash returns a Hash of the message that needs to be signed for
|
||||
// pk to assert a subkey relationship to signed.
|
||||
func keySignatureHash(pk, signed signingKey, hashFunc crypto.Hash) (h hash.Hash, err error) {
|
||||
if !hashFunc.Available() {
|
||||
return nil, errors.UnsupportedError("hash function")
|
||||
}
|
||||
h = hashFunc.New()
|
||||
|
||||
// RFC 4880, section 5.2.4
|
||||
err = pk.SerializeForHash(h)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
err = signed.SerializeForHash(h)
|
||||
return
|
||||
}
|
||||
|
||||
// VerifyKeySignature returns nil iff sig is a valid signature, made by this
|
||||
// public key, of signed.
|
||||
func (pk *PublicKey) VerifyKeySignature(signed *PublicKey, sig *Signature) error {
|
||||
h, err := keySignatureHash(pk, signed, sig.Hash)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
if err = pk.VerifySignature(h, sig); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
if sig.FlagSign {
|
||||
// Signing subkeys must be cross-signed. See
|
||||
// https://www.gnupg.org/faq/subkey-cross-certify.html.
|
||||
if sig.EmbeddedSignature == nil {
|
||||
return errors.StructuralError("signing subkey is missing cross-signature")
|
||||
}
|
||||
// Verify the cross-signature. This is calculated over the same
|
||||
// data as the main signature, so we cannot just recursively
|
||||
// call signed.VerifyKeySignature(...)
|
||||
if h, err = keySignatureHash(pk, signed, sig.EmbeddedSignature.Hash); err != nil {
|
||||
return errors.StructuralError("error while hashing for cross-signature: " + err.Error())
|
||||
}
|
||||
if err := signed.VerifySignature(h, sig.EmbeddedSignature); err != nil {
|
||||
return errors.StructuralError("error while verifying cross-signature: " + err.Error())
|
||||
}
|
||||
}
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
func keyRevocationHash(pk signingKey, hashFunc crypto.Hash) (h hash.Hash, err error) {
|
||||
if !hashFunc.Available() {
|
||||
return nil, errors.UnsupportedError("hash function")
|
||||
}
|
||||
h = hashFunc.New()
|
||||
|
||||
// RFC 4880, section 5.2.4
|
||||
err = pk.SerializeForHash(h)
|
||||
|
||||
return
|
||||
}
|
||||
|
||||
// VerifyRevocationSignature returns nil iff sig is a valid signature, made by this
|
||||
// public key.
|
||||
func (pk *PublicKey) VerifyRevocationSignature(sig *Signature) (err error) {
|
||||
h, err := keyRevocationHash(pk, sig.Hash)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
return pk.VerifySignature(h, sig)
|
||||
}
|
||||
|
||||
// VerifySubkeyRevocationSignature returns nil iff sig is a valid subkey revocation signature,
|
||||
// made by this public key, of signed.
|
||||
func (pk *PublicKey) VerifySubkeyRevocationSignature(sig *Signature, signed *PublicKey) (err error) {
|
||||
h, err := keySignatureHash(pk, signed, sig.Hash)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
return pk.VerifySignature(h, sig)
|
||||
}
|
||||
|
||||
// userIdSignatureHash returns a Hash of the message that needs to be signed
|
||||
// to assert that pk is a valid key for id.
|
||||
func userIdSignatureHash(id string, pk *PublicKey, hashFunc crypto.Hash) (h hash.Hash, err error) {
|
||||
if !hashFunc.Available() {
|
||||
return nil, errors.UnsupportedError("hash function")
|
||||
}
|
||||
h = hashFunc.New()
|
||||
|
||||
// RFC 4880, section 5.2.4
|
||||
pk.SerializeSignaturePrefix(h)
|
||||
pk.serializeWithoutHeaders(h)
|
||||
|
||||
var buf [5]byte
|
||||
buf[0] = 0xb4
|
||||
buf[1] = byte(len(id) >> 24)
|
||||
buf[2] = byte(len(id) >> 16)
|
||||
buf[3] = byte(len(id) >> 8)
|
||||
buf[4] = byte(len(id))
|
||||
h.Write(buf[:])
|
||||
h.Write([]byte(id))
|
||||
|
||||
return
|
||||
}
|
||||
|
||||
// VerifyUserIdSignature returns nil iff sig is a valid signature, made by this
|
||||
// public key, that id is the identity of pub.
|
||||
func (pk *PublicKey) VerifyUserIdSignature(id string, pub *PublicKey, sig *Signature) (err error) {
|
||||
h, err := userIdSignatureHash(id, pub, sig.Hash)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
return pk.VerifySignature(h, sig)
|
||||
}
|
||||
|
||||
// KeyIdString returns the public key's fingerprint in capital hex
|
||||
// (e.g. "6C7EE1B8621CC013").
|
||||
func (pk *PublicKey) KeyIdString() string {
|
||||
return fmt.Sprintf("%X", pk.Fingerprint[12:20])
|
||||
}
|
||||
|
||||
// KeyIdShortString returns the short form of public key's fingerprint
|
||||
// in capital hex, as shown by gpg --list-keys (e.g. "621CC013").
|
||||
func (pk *PublicKey) KeyIdShortString() string {
|
||||
return fmt.Sprintf("%X", pk.Fingerprint[16:20])
|
||||
}
|
||||
|
||||
// BitLength returns the bit length for the given public key.
|
||||
func (pk *PublicKey) BitLength() (bitLength uint16, err error) {
|
||||
switch pk.PubKeyAlgo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly:
|
||||
bitLength = pk.n.BitLength()
|
||||
case PubKeyAlgoDSA:
|
||||
bitLength = pk.p.BitLength()
|
||||
case PubKeyAlgoElGamal:
|
||||
bitLength = pk.p.BitLength()
|
||||
case PubKeyAlgoECDSA:
|
||||
bitLength = pk.p.BitLength()
|
||||
case PubKeyAlgoECDH:
|
||||
bitLength = pk.p.BitLength()
|
||||
case PubKeyAlgoEdDSA:
|
||||
bitLength = pk.p.BitLength()
|
||||
default:
|
||||
err = errors.InvalidArgumentError("bad public-key algorithm")
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// KeyExpired returns whether sig is a self-signature of a key that has
|
||||
// expired or is created in the future.
|
||||
func (pk *PublicKey) KeyExpired(sig *Signature, currentTime time.Time) bool {
|
||||
if pk.CreationTime.After(currentTime) {
|
||||
return true
|
||||
}
|
||||
if sig.KeyLifetimeSecs == nil || *sig.KeyLifetimeSecs == 0 {
|
||||
return false
|
||||
}
|
||||
expiry := pk.CreationTime.Add(time.Duration(*sig.KeyLifetimeSecs) * time.Second)
|
||||
return currentTime.After(expiry)
|
||||
}
|
||||
24
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/public_key_test_data.go
generated
vendored
Normal file
24
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/public_key_test_data.go
generated
vendored
Normal file
|
|
@ -0,0 +1,24 @@
|
|||
package packet
|
||||
|
||||
const rsaFingerprintHex = "5fb74b1d03b1e3cb31bc2f8aa34d7e18c20c31bb"
|
||||
|
||||
const rsaPkDataHex = "988d044d3c5c10010400b1d13382944bd5aba23a4312968b5095d14f947f600eb478e14a6fcb16b0e0cac764884909c020bc495cfcc39a935387c661507bdb236a0612fb582cac3af9b29cc2c8c70090616c41b662f4da4c1201e195472eb7f4ae1ccbcbf9940fe21d985e379a5563dde5b9a23d35f1cfaa5790da3b79db26f23695107bfaca8e7b5bcd0011010001"
|
||||
|
||||
const dsaFingerprintHex = "eece4c094db002103714c63c8e8fbe54062f19ed"
|
||||
|
||||
const dsaPkDataHex = "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"
|
||||
|
||||
const ecdsaFingerprintHex = "9892270b38b8980b05c8d56d43fe956c542ca00b"
|
||||
|
||||
const ecdsaPkDataHex = "9893045071c29413052b8104002304230401f4867769cedfa52c325018896245443968e52e51d0c2df8d939949cb5b330f2921711fbee1c9b9dddb95d15cb0255e99badeddda7cc23d9ddcaacbc290969b9f24019375d61c2e4e3b36953a28d8b2bc95f78c3f1d592fb24499be348656a7b17e3963187b4361afe497bc5f9f81213f04069f8e1fb9e6a6290ae295ca1a92b894396cb4"
|
||||
|
||||
const ecdhFingerprintHex = "722354df2475a42164d1d49faa8b938f9a201946"
|
||||
|
||||
const ecdhPkDataHex = "b90073044d53059212052b810400220303042faa84024a20b6735c4897efa5bfb41bf85b7eefeab5ca0cb9ffc8ea04a46acb25534a577694f9e25340a4ab5223a9dd1eda530c8aa2e6718db10d7e672558c7736fe09369ea5739a2a3554bf16d41faa50562f11c6d39bbd5dffb6b9a9ec91803010909"
|
||||
|
||||
const eddsaFingerprintHex = "b2d5e5ec0e6deca6bc8eeeb00907e75e1dd99ad8"
|
||||
|
||||
const eddsaPkDataHex = "98330456e2132b16092b06010401da470f01010740bbda39266affa511a8c2d02edf690fb784b0499c4406185811a163539ef11dc1b41d74657374696e67203c74657374696e674074657374696e672e636f6d3e8879041316080021050256e2132b021b03050b09080702061508090a0b020416020301021e01021780000a09100907e75e1dd99ad86d0c00fe39d2008359352782bc9b61ac382584cd8eff3f57a18c2287e3afeeb05d1f04ba00fe2d0bc1ddf3ff8adb9afa3e7d9287244b4ec567f3db4d60b74a9b5465ed528203"
|
||||
|
||||
// Source: https://sites.google.com/site/brainhub/pgpecckeys#TOC-ECC-NIST-P-384-key
|
||||
const ecc384PubHex = `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`
|
||||
|
|
@ -5,8 +5,9 @@
|
|||
package packet
|
||||
|
||||
import (
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"io"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
)
|
||||
|
||||
// Reader reads packets from an io.Reader and allows packets to be 'unread' so
|
||||
|
|
@ -42,9 +43,18 @@ func (r *Reader) Next() (p Packet, err error) {
|
|||
r.readers = r.readers[:len(r.readers)-1]
|
||||
continue
|
||||
}
|
||||
if _, ok := err.(errors.UnknownPacketTypeError); !ok {
|
||||
return nil, err
|
||||
// TODO: Add strict mode that rejects unknown packets, instead of ignoring them.
|
||||
if _, ok := err.(errors.UnknownPacketTypeError); ok {
|
||||
continue
|
||||
}
|
||||
if _, ok := err.(errors.UnsupportedError); ok {
|
||||
switch p.(type) {
|
||||
case *SymmetricallyEncrypted, *AEADEncrypted, *Compressed, *LiteralData:
|
||||
return nil, err
|
||||
}
|
||||
continue
|
||||
}
|
||||
return nil, err
|
||||
}
|
||||
|
||||
return nil, io.EOF
|
||||
|
|
@ -8,17 +8,17 @@ import (
|
|||
"bytes"
|
||||
"crypto"
|
||||
"crypto/dsa"
|
||||
"crypto/ecdsa"
|
||||
"encoding/asn1"
|
||||
"encoding/binary"
|
||||
"hash"
|
||||
"io"
|
||||
"math/big"
|
||||
"strconv"
|
||||
"time"
|
||||
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"golang.org/x/crypto/openpgp/s2k"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/ecdsa"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/eddsa"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/algorithm"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/encoding"
|
||||
)
|
||||
|
||||
const (
|
||||
|
|
@ -27,10 +27,15 @@ const (
|
|||
KeyFlagSign
|
||||
KeyFlagEncryptCommunications
|
||||
KeyFlagEncryptStorage
|
||||
KeyFlagSplitKey
|
||||
KeyFlagAuthenticate
|
||||
_
|
||||
KeyFlagGroupKey
|
||||
)
|
||||
|
||||
// Signature represents a signature. See RFC 4880, section 5.2.
|
||||
type Signature struct {
|
||||
Version int
|
||||
SigType SignatureType
|
||||
PubKeyAlgo PublicKeyAlgorithm
|
||||
Hash crypto.Hash
|
||||
|
|
@ -39,12 +44,19 @@ type Signature struct {
|
|||
HashSuffix []byte
|
||||
// HashTag contains the first two bytes of the hash for fast rejection
|
||||
// of bad signed data.
|
||||
HashTag [2]byte
|
||||
HashTag [2]byte
|
||||
|
||||
// Metadata includes format, filename and time, and is protected by v5
|
||||
// signatures of type 0x00 or 0x01. This metadata is included into the hash
|
||||
// computation; if nil, six 0x00 bytes are used instead. See section 5.2.4.
|
||||
Metadata *LiteralData
|
||||
|
||||
CreationTime time.Time
|
||||
|
||||
RSASignature parsedMPI
|
||||
DSASigR, DSASigS parsedMPI
|
||||
ECDSASigR, ECDSASigS parsedMPI
|
||||
RSASignature encoding.Field
|
||||
DSASigR, DSASigS encoding.Field
|
||||
ECDSASigR, ECDSASigS encoding.Field
|
||||
EdDSASigR, EdDSASigS encoding.Field
|
||||
|
||||
// rawSubpackets contains the unparsed subpackets, in order.
|
||||
rawSubpackets []outputSubpacket
|
||||
|
|
@ -54,22 +66,44 @@ type Signature struct {
|
|||
|
||||
SigLifetimeSecs, KeyLifetimeSecs *uint32
|
||||
PreferredSymmetric, PreferredHash, PreferredCompression []uint8
|
||||
PreferredCipherSuites [][2]uint8
|
||||
IssuerKeyId *uint64
|
||||
IssuerFingerprint []byte
|
||||
SignerUserId *string
|
||||
IsPrimaryId *bool
|
||||
Notations []*Notation
|
||||
|
||||
// TrustLevel and TrustAmount can be set by the signer to assert that
|
||||
// the key is not only valid but also trustworthy at the specified
|
||||
// level.
|
||||
// See RFC 4880, section 5.2.3.13 for details.
|
||||
TrustLevel TrustLevel
|
||||
TrustAmount TrustAmount
|
||||
|
||||
// TrustRegularExpression can be used in conjunction with trust Signature
|
||||
// packets to limit the scope of the trust that is extended.
|
||||
// See RFC 4880, section 5.2.3.14 for details.
|
||||
TrustRegularExpression *string
|
||||
|
||||
// PolicyURI can be set to the URI of a document that describes the
|
||||
// policy under which the signature was issued. See RFC 4880, section
|
||||
// 5.2.3.20 for details.
|
||||
PolicyURI string
|
||||
|
||||
// FlagsValid is set if any flags were given. See RFC 4880, section
|
||||
// 5.2.3.21 for details.
|
||||
FlagsValid bool
|
||||
FlagCertify, FlagSign, FlagEncryptCommunications, FlagEncryptStorage bool
|
||||
FlagsValid bool
|
||||
FlagCertify, FlagSign, FlagEncryptCommunications, FlagEncryptStorage, FlagSplitKey, FlagAuthenticate, FlagGroupKey bool
|
||||
|
||||
// RevocationReason is set if this signature has been revoked.
|
||||
// See RFC 4880, section 5.2.3.23 for details.
|
||||
RevocationReason *uint8
|
||||
RevocationReason *ReasonForRevocation
|
||||
RevocationReasonText string
|
||||
|
||||
// MDC is set if this signature has a feature packet that indicates
|
||||
// support for MDC subpackets.
|
||||
MDC bool
|
||||
// In a self-signature, these flags are set there is a features subpacket
|
||||
// indicating that the issuer implementation supports these features
|
||||
// see https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh#features-subpacket
|
||||
SEIPDv1, SEIPDv2 bool
|
||||
|
||||
// EmbeddedSignature, if non-nil, is a signature of the parent key, by
|
||||
// this key. This prevents an attacker from claiming another's signing
|
||||
|
|
@ -86,11 +120,11 @@ func (sig *Signature) parse(r io.Reader) (err error) {
|
|||
if err != nil {
|
||||
return
|
||||
}
|
||||
if buf[0] != 4 {
|
||||
if buf[0] != 4 && buf[0] != 5 {
|
||||
err = errors.UnsupportedError("signature packet version " + strconv.Itoa(int(buf[0])))
|
||||
return
|
||||
}
|
||||
|
||||
sig.Version = int(buf[0])
|
||||
_, err = readFull(r, buf[:5])
|
||||
if err != nil {
|
||||
return
|
||||
|
|
@ -98,36 +132,34 @@ func (sig *Signature) parse(r io.Reader) (err error) {
|
|||
sig.SigType = SignatureType(buf[0])
|
||||
sig.PubKeyAlgo = PublicKeyAlgorithm(buf[1])
|
||||
switch sig.PubKeyAlgo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoDSA, PubKeyAlgoECDSA:
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoDSA, PubKeyAlgoECDSA, PubKeyAlgoEdDSA:
|
||||
default:
|
||||
err = errors.UnsupportedError("public key algorithm " + strconv.Itoa(int(sig.PubKeyAlgo)))
|
||||
return
|
||||
}
|
||||
|
||||
var ok bool
|
||||
sig.Hash, ok = s2k.HashIdToHash(buf[2])
|
||||
|
||||
if sig.Version < 5 {
|
||||
sig.Hash, ok = algorithm.HashIdToHashWithSha1(buf[2])
|
||||
} else {
|
||||
sig.Hash, ok = algorithm.HashIdToHash(buf[2])
|
||||
}
|
||||
|
||||
if !ok {
|
||||
return errors.UnsupportedError("hash function " + strconv.Itoa(int(buf[2])))
|
||||
}
|
||||
|
||||
hashedSubpacketsLength := int(buf[3])<<8 | int(buf[4])
|
||||
l := 6 + hashedSubpacketsLength
|
||||
sig.HashSuffix = make([]byte, l+6)
|
||||
sig.HashSuffix[0] = 4
|
||||
copy(sig.HashSuffix[1:], buf[:5])
|
||||
hashedSubpackets := sig.HashSuffix[6:l]
|
||||
hashedSubpackets := make([]byte, hashedSubpacketsLength)
|
||||
_, err = readFull(r, hashedSubpackets)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
// See RFC 4880, section 5.2.4
|
||||
trailer := sig.HashSuffix[l:]
|
||||
trailer[0] = 4
|
||||
trailer[1] = 0xff
|
||||
trailer[2] = uint8(l >> 24)
|
||||
trailer[3] = uint8(l >> 16)
|
||||
trailer[4] = uint8(l >> 8)
|
||||
trailer[5] = uint8(l)
|
||||
err = sig.buildHashSuffix(hashedSubpackets)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
err = parseSignatureSubpackets(sig, hashedSubpackets, true)
|
||||
if err != nil {
|
||||
|
|
@ -156,16 +188,33 @@ func (sig *Signature) parse(r io.Reader) (err error) {
|
|||
|
||||
switch sig.PubKeyAlgo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly:
|
||||
sig.RSASignature.bytes, sig.RSASignature.bitLength, err = readMPI(r)
|
||||
sig.RSASignature = new(encoding.MPI)
|
||||
_, err = sig.RSASignature.ReadFrom(r)
|
||||
case PubKeyAlgoDSA:
|
||||
sig.DSASigR.bytes, sig.DSASigR.bitLength, err = readMPI(r)
|
||||
if err == nil {
|
||||
sig.DSASigS.bytes, sig.DSASigS.bitLength, err = readMPI(r)
|
||||
sig.DSASigR = new(encoding.MPI)
|
||||
if _, err = sig.DSASigR.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
sig.DSASigS = new(encoding.MPI)
|
||||
_, err = sig.DSASigS.ReadFrom(r)
|
||||
case PubKeyAlgoECDSA:
|
||||
sig.ECDSASigR.bytes, sig.ECDSASigR.bitLength, err = readMPI(r)
|
||||
if err == nil {
|
||||
sig.ECDSASigS.bytes, sig.ECDSASigS.bitLength, err = readMPI(r)
|
||||
sig.ECDSASigR = new(encoding.MPI)
|
||||
if _, err = sig.ECDSASigR.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
sig.ECDSASigS = new(encoding.MPI)
|
||||
_, err = sig.ECDSASigS.ReadFrom(r)
|
||||
case PubKeyAlgoEdDSA:
|
||||
sig.EdDSASigR = new(encoding.MPI)
|
||||
if _, err = sig.EdDSASigR.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
sig.EdDSASigS = new(encoding.MPI)
|
||||
if _, err = sig.EdDSASigS.ReadFrom(r); err != nil {
|
||||
return
|
||||
}
|
||||
default:
|
||||
panic("unreachable")
|
||||
|
|
@ -195,16 +244,23 @@ type signatureSubpacketType uint8
|
|||
const (
|
||||
creationTimeSubpacket signatureSubpacketType = 2
|
||||
signatureExpirationSubpacket signatureSubpacketType = 3
|
||||
trustSubpacket signatureSubpacketType = 5
|
||||
regularExpressionSubpacket signatureSubpacketType = 6
|
||||
keyExpirationSubpacket signatureSubpacketType = 9
|
||||
prefSymmetricAlgosSubpacket signatureSubpacketType = 11
|
||||
issuerSubpacket signatureSubpacketType = 16
|
||||
notationDataSubpacket signatureSubpacketType = 20
|
||||
prefHashAlgosSubpacket signatureSubpacketType = 21
|
||||
prefCompressionSubpacket signatureSubpacketType = 22
|
||||
primaryUserIdSubpacket signatureSubpacketType = 25
|
||||
policyUriSubpacket signatureSubpacketType = 26
|
||||
keyFlagsSubpacket signatureSubpacketType = 27
|
||||
signerUserIdSubpacket signatureSubpacketType = 28
|
||||
reasonForRevocationSubpacket signatureSubpacketType = 29
|
||||
featuresSubpacket signatureSubpacketType = 30
|
||||
embeddedSignatureSubpacket signatureSubpacketType = 32
|
||||
issuerFingerprintSubpacket signatureSubpacketType = 33
|
||||
prefCipherSuitesSubpacket signatureSubpacketType = 39
|
||||
)
|
||||
|
||||
// parseSignatureSubpacket parses a single subpacket. len(subpacket) is >= 1.
|
||||
|
|
@ -248,12 +304,14 @@ func parseSignatureSubpacket(sig *Signature, subpacket []byte, isHashed bool) (r
|
|||
isCritical = subpacket[0]&0x80 == 0x80
|
||||
subpacket = subpacket[1:]
|
||||
sig.rawSubpackets = append(sig.rawSubpackets, outputSubpacket{isHashed, packetType, isCritical, subpacket})
|
||||
if !isHashed &&
|
||||
packetType != issuerSubpacket &&
|
||||
packetType != issuerFingerprintSubpacket &&
|
||||
packetType != embeddedSignatureSubpacket {
|
||||
return
|
||||
}
|
||||
switch packetType {
|
||||
case creationTimeSubpacket:
|
||||
if !isHashed {
|
||||
err = errors.StructuralError("signature creation time in non-hashed area")
|
||||
return
|
||||
}
|
||||
if len(subpacket) != 4 {
|
||||
err = errors.StructuralError("signature creation time not four bytes")
|
||||
return
|
||||
|
|
@ -262,20 +320,27 @@ func parseSignatureSubpacket(sig *Signature, subpacket []byte, isHashed bool) (r
|
|||
sig.CreationTime = time.Unix(int64(t), 0)
|
||||
case signatureExpirationSubpacket:
|
||||
// Signature expiration time, section 5.2.3.10
|
||||
if !isHashed {
|
||||
return
|
||||
}
|
||||
if len(subpacket) != 4 {
|
||||
err = errors.StructuralError("expiration subpacket with bad length")
|
||||
return
|
||||
}
|
||||
sig.SigLifetimeSecs = new(uint32)
|
||||
*sig.SigLifetimeSecs = binary.BigEndian.Uint32(subpacket)
|
||||
case keyExpirationSubpacket:
|
||||
// Key expiration time, section 5.2.3.6
|
||||
if !isHashed {
|
||||
case trustSubpacket:
|
||||
// Trust level and amount, section 5.2.3.13
|
||||
sig.TrustLevel = TrustLevel(subpacket[0])
|
||||
sig.TrustAmount = TrustAmount(subpacket[1])
|
||||
case regularExpressionSubpacket:
|
||||
// Trust regular expression, section 5.2.3.14
|
||||
// RFC specifies the string should be null-terminated; remove a null byte from the end
|
||||
if subpacket[len(subpacket)-1] != 0x00 {
|
||||
err = errors.StructuralError("expected regular expression to be null-terminated")
|
||||
return
|
||||
}
|
||||
trustRegularExpression := string(subpacket[:len(subpacket)-1])
|
||||
sig.TrustRegularExpression = &trustRegularExpression
|
||||
case keyExpirationSubpacket:
|
||||
// Key expiration time, section 5.2.3.6
|
||||
if len(subpacket) != 4 {
|
||||
err = errors.StructuralError("key expiration subpacket with bad length")
|
||||
return
|
||||
|
|
@ -284,38 +349,52 @@ func parseSignatureSubpacket(sig *Signature, subpacket []byte, isHashed bool) (r
|
|||
*sig.KeyLifetimeSecs = binary.BigEndian.Uint32(subpacket)
|
||||
case prefSymmetricAlgosSubpacket:
|
||||
// Preferred symmetric algorithms, section 5.2.3.7
|
||||
if !isHashed {
|
||||
return
|
||||
}
|
||||
sig.PreferredSymmetric = make([]byte, len(subpacket))
|
||||
copy(sig.PreferredSymmetric, subpacket)
|
||||
case issuerSubpacket:
|
||||
// Issuer, section 5.2.3.5
|
||||
if sig.Version > 4 {
|
||||
err = errors.StructuralError("issuer subpacket found in v5 key")
|
||||
return
|
||||
}
|
||||
if len(subpacket) != 8 {
|
||||
err = errors.StructuralError("issuer subpacket with bad length")
|
||||
return
|
||||
}
|
||||
sig.IssuerKeyId = new(uint64)
|
||||
*sig.IssuerKeyId = binary.BigEndian.Uint64(subpacket)
|
||||
case prefHashAlgosSubpacket:
|
||||
// Preferred hash algorithms, section 5.2.3.8
|
||||
if !isHashed {
|
||||
case notationDataSubpacket:
|
||||
// Notation data, section 5.2.3.16
|
||||
if len(subpacket) < 8 {
|
||||
err = errors.StructuralError("notation data subpacket with bad length")
|
||||
return
|
||||
}
|
||||
|
||||
nameLength := uint32(subpacket[4])<<8 | uint32(subpacket[5])
|
||||
valueLength := uint32(subpacket[6])<<8 | uint32(subpacket[7])
|
||||
if len(subpacket) != int(nameLength) + int(valueLength) + 8 {
|
||||
err = errors.StructuralError("notation data subpacket with bad length")
|
||||
return
|
||||
}
|
||||
|
||||
notation := Notation{
|
||||
IsHumanReadable: (subpacket[0] & 0x80) == 0x80,
|
||||
Name: string(subpacket[8: (nameLength + 8)]),
|
||||
Value: subpacket[(nameLength + 8) : (valueLength + nameLength + 8)],
|
||||
IsCritical: isCritical,
|
||||
}
|
||||
|
||||
sig.Notations = append(sig.Notations, ¬ation)
|
||||
case prefHashAlgosSubpacket:
|
||||
// Preferred hash algorithms, section 5.2.3.8
|
||||
sig.PreferredHash = make([]byte, len(subpacket))
|
||||
copy(sig.PreferredHash, subpacket)
|
||||
case prefCompressionSubpacket:
|
||||
// Preferred compression algorithms, section 5.2.3.9
|
||||
if !isHashed {
|
||||
return
|
||||
}
|
||||
sig.PreferredCompression = make([]byte, len(subpacket))
|
||||
copy(sig.PreferredCompression, subpacket)
|
||||
case primaryUserIdSubpacket:
|
||||
// Primary User ID, section 5.2.3.19
|
||||
if !isHashed {
|
||||
return
|
||||
}
|
||||
if len(subpacket) != 1 {
|
||||
err = errors.StructuralError("primary user id subpacket with bad length")
|
||||
return
|
||||
|
|
@ -326,9 +405,6 @@ func parseSignatureSubpacket(sig *Signature, subpacket []byte, isHashed bool) (r
|
|||
}
|
||||
case keyFlagsSubpacket:
|
||||
// Key flags, section 5.2.3.21
|
||||
if !isHashed {
|
||||
return
|
||||
}
|
||||
if len(subpacket) == 0 {
|
||||
err = errors.StructuralError("empty key flags subpacket")
|
||||
return
|
||||
|
|
@ -346,24 +422,40 @@ func parseSignatureSubpacket(sig *Signature, subpacket []byte, isHashed bool) (r
|
|||
if subpacket[0]&KeyFlagEncryptStorage != 0 {
|
||||
sig.FlagEncryptStorage = true
|
||||
}
|
||||
if subpacket[0]&KeyFlagSplitKey != 0 {
|
||||
sig.FlagSplitKey = true
|
||||
}
|
||||
if subpacket[0]&KeyFlagAuthenticate != 0 {
|
||||
sig.FlagAuthenticate = true
|
||||
}
|
||||
if subpacket[0]&KeyFlagGroupKey != 0 {
|
||||
sig.FlagGroupKey = true
|
||||
}
|
||||
case signerUserIdSubpacket:
|
||||
userId := string(subpacket)
|
||||
sig.SignerUserId = &userId
|
||||
case reasonForRevocationSubpacket:
|
||||
// Reason For Revocation, section 5.2.3.23
|
||||
if !isHashed {
|
||||
return
|
||||
}
|
||||
if len(subpacket) == 0 {
|
||||
err = errors.StructuralError("empty revocation reason subpacket")
|
||||
return
|
||||
}
|
||||
sig.RevocationReason = new(uint8)
|
||||
*sig.RevocationReason = subpacket[0]
|
||||
sig.RevocationReason = new(ReasonForRevocation)
|
||||
*sig.RevocationReason = ReasonForRevocation(subpacket[0])
|
||||
sig.RevocationReasonText = string(subpacket[1:])
|
||||
case featuresSubpacket:
|
||||
// Features subpacket, section 5.2.3.24 specifies a very general
|
||||
// mechanism for OpenPGP implementations to signal support for new
|
||||
// features. In practice, the subpacket is used exclusively to
|
||||
// indicate support for MDC-protected encryption.
|
||||
sig.MDC = len(subpacket) >= 1 && subpacket[0]&1 == 1
|
||||
// features.
|
||||
if len(subpacket) > 0 {
|
||||
if subpacket[0]&0x01 != 0 {
|
||||
sig.SEIPDv1 = true
|
||||
}
|
||||
// 0x02 and 0x04 are reserved
|
||||
if subpacket[0]&0x08 != 0 {
|
||||
sig.SEIPDv2 = true
|
||||
}
|
||||
}
|
||||
case embeddedSignatureSubpacket:
|
||||
// Only usage is in signatures that cross-certify
|
||||
// signing subkeys. section 5.2.3.26 describes the
|
||||
|
|
@ -382,6 +474,35 @@ func parseSignatureSubpacket(sig *Signature, subpacket []byte, isHashed bool) (r
|
|||
if sigType := sig.EmbeddedSignature.SigType; sigType != SigTypePrimaryKeyBinding {
|
||||
return nil, errors.StructuralError("cross-signature has unexpected type " + strconv.Itoa(int(sigType)))
|
||||
}
|
||||
case policyUriSubpacket:
|
||||
// Policy URI, section 5.2.3.20
|
||||
sig.PolicyURI = string(subpacket)
|
||||
case issuerFingerprintSubpacket:
|
||||
v, l := subpacket[0], len(subpacket[1:])
|
||||
if v == 5 && l != 32 || v != 5 && l != 20 {
|
||||
return nil, errors.StructuralError("bad fingerprint length")
|
||||
}
|
||||
sig.IssuerFingerprint = make([]byte, l)
|
||||
copy(sig.IssuerFingerprint, subpacket[1:])
|
||||
sig.IssuerKeyId = new(uint64)
|
||||
if v == 5 {
|
||||
*sig.IssuerKeyId = binary.BigEndian.Uint64(subpacket[1:9])
|
||||
} else {
|
||||
*sig.IssuerKeyId = binary.BigEndian.Uint64(subpacket[13:21])
|
||||
}
|
||||
case prefCipherSuitesSubpacket:
|
||||
// Preferred AEAD cipher suites
|
||||
// See https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#name-preferred-aead-ciphersuites
|
||||
if len(subpacket) % 2 != 0 {
|
||||
err = errors.StructuralError("invalid aead cipher suite length")
|
||||
return
|
||||
}
|
||||
|
||||
sig.PreferredCipherSuites = make([][2]byte, len(subpacket) / 2)
|
||||
|
||||
for i := 0; i < len(subpacket) / 2; i++ {
|
||||
sig.PreferredCipherSuites[i] = [2]uint8{subpacket[2*i], subpacket[2*i+1]}
|
||||
}
|
||||
default:
|
||||
if isCritical {
|
||||
err = errors.UnsupportedError("unknown critical signature subpacket type " + strconv.Itoa(int(packetType)))
|
||||
|
|
@ -406,6 +527,13 @@ func subpacketLengthLength(length int) int {
|
|||
return 5
|
||||
}
|
||||
|
||||
func (sig *Signature) CheckKeyIdOrFingerprint(pk *PublicKey) bool {
|
||||
if sig.IssuerFingerprint != nil && len(sig.IssuerFingerprint) >= 20 {
|
||||
return bytes.Equal(sig.IssuerFingerprint, pk.Fingerprint)
|
||||
}
|
||||
return sig.IssuerKeyId != nil && *sig.IssuerKeyId == pk.KeyId
|
||||
}
|
||||
|
||||
// serializeSubpacketLength marshals the given length into to.
|
||||
func serializeSubpacketLength(to []byte, length int) int {
|
||||
// RFC 4880, Section 4.2.2.
|
||||
|
|
@ -446,6 +574,9 @@ func serializeSubpackets(to []byte, subpackets []outputSubpacket, hashed bool) {
|
|||
if subpacket.hashed == hashed {
|
||||
n := serializeSubpacketLength(to, len(subpacket.contents)+1)
|
||||
to[n] = byte(subpacket.subpacketType)
|
||||
if subpacket.isCritical {
|
||||
to[n] |= 0x80
|
||||
}
|
||||
to = to[1+n:]
|
||||
n = copy(to, subpacket.contents)
|
||||
to = to[n:]
|
||||
|
|
@ -454,49 +585,74 @@ func serializeSubpackets(to []byte, subpackets []outputSubpacket, hashed bool) {
|
|||
return
|
||||
}
|
||||
|
||||
// KeyExpired returns whether sig is a self-signature of a key that has
|
||||
// expired.
|
||||
func (sig *Signature) KeyExpired(currentTime time.Time) bool {
|
||||
if sig.KeyLifetimeSecs == nil {
|
||||
// SigExpired returns whether sig is a signature that has expired or is created
|
||||
// in the future.
|
||||
func (sig *Signature) SigExpired(currentTime time.Time) bool {
|
||||
if sig.CreationTime.After(currentTime) {
|
||||
return true
|
||||
}
|
||||
if sig.SigLifetimeSecs == nil || *sig.SigLifetimeSecs == 0 {
|
||||
return false
|
||||
}
|
||||
expiry := sig.CreationTime.Add(time.Duration(*sig.KeyLifetimeSecs) * time.Second)
|
||||
expiry := sig.CreationTime.Add(time.Duration(*sig.SigLifetimeSecs) * time.Second)
|
||||
return currentTime.After(expiry)
|
||||
}
|
||||
|
||||
// buildHashSuffix constructs the HashSuffix member of sig in preparation for signing.
|
||||
func (sig *Signature) buildHashSuffix() (err error) {
|
||||
hashedSubpacketsLen := subpacketsLength(sig.outSubpackets, true)
|
||||
|
||||
func (sig *Signature) buildHashSuffix(hashedSubpackets []byte) (err error) {
|
||||
var hashId byte
|
||||
var ok bool
|
||||
l := 6 + hashedSubpacketsLen
|
||||
sig.HashSuffix = make([]byte, l+6)
|
||||
sig.HashSuffix[0] = 4
|
||||
sig.HashSuffix[1] = uint8(sig.SigType)
|
||||
sig.HashSuffix[2] = uint8(sig.PubKeyAlgo)
|
||||
sig.HashSuffix[3], ok = s2k.HashToHashId(sig.Hash)
|
||||
|
||||
if sig.Version < 5 {
|
||||
hashId, ok = algorithm.HashToHashIdWithSha1(sig.Hash)
|
||||
} else {
|
||||
hashId, ok = algorithm.HashToHashId(sig.Hash)
|
||||
}
|
||||
|
||||
if !ok {
|
||||
sig.HashSuffix = nil
|
||||
return errors.InvalidArgumentError("hash cannot be represented in OpenPGP: " + strconv.Itoa(int(sig.Hash)))
|
||||
}
|
||||
sig.HashSuffix[4] = byte(hashedSubpacketsLen >> 8)
|
||||
sig.HashSuffix[5] = byte(hashedSubpacketsLen)
|
||||
serializeSubpackets(sig.HashSuffix[6:l], sig.outSubpackets, true)
|
||||
trailer := sig.HashSuffix[l:]
|
||||
trailer[0] = 4
|
||||
trailer[1] = 0xff
|
||||
trailer[2] = byte(l >> 24)
|
||||
trailer[3] = byte(l >> 16)
|
||||
trailer[4] = byte(l >> 8)
|
||||
trailer[5] = byte(l)
|
||||
|
||||
hashedFields := bytes.NewBuffer([]byte{
|
||||
uint8(sig.Version),
|
||||
uint8(sig.SigType),
|
||||
uint8(sig.PubKeyAlgo),
|
||||
uint8(hashId),
|
||||
uint8(len(hashedSubpackets) >> 8),
|
||||
uint8(len(hashedSubpackets)),
|
||||
})
|
||||
hashedFields.Write(hashedSubpackets)
|
||||
|
||||
var l uint64 = uint64(6 + len(hashedSubpackets))
|
||||
if sig.Version == 5 {
|
||||
hashedFields.Write([]byte{0x05, 0xff})
|
||||
hashedFields.Write([]byte{
|
||||
uint8(l >> 56), uint8(l >> 48), uint8(l >> 40), uint8(l >> 32),
|
||||
uint8(l >> 24), uint8(l >> 16), uint8(l >> 8), uint8(l),
|
||||
})
|
||||
} else {
|
||||
hashedFields.Write([]byte{0x04, 0xff})
|
||||
hashedFields.Write([]byte{
|
||||
uint8(l >> 24), uint8(l >> 16), uint8(l >> 8), uint8(l),
|
||||
})
|
||||
}
|
||||
sig.HashSuffix = make([]byte, hashedFields.Len())
|
||||
copy(sig.HashSuffix, hashedFields.Bytes())
|
||||
return
|
||||
}
|
||||
|
||||
func (sig *Signature) signPrepareHash(h hash.Hash) (digest []byte, err error) {
|
||||
err = sig.buildHashSuffix()
|
||||
hashedSubpacketsLen := subpacketsLength(sig.outSubpackets, true)
|
||||
hashedSubpackets := make([]byte, hashedSubpacketsLen)
|
||||
serializeSubpackets(hashedSubpackets, sig.outSubpackets, true)
|
||||
err = sig.buildHashSuffix(hashedSubpackets)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
if sig.Version == 5 && (sig.SigType == 0x00 || sig.SigType == 0x01) {
|
||||
sig.AddMetadataToHashSuffix()
|
||||
}
|
||||
|
||||
h.Write(sig.HashSuffix)
|
||||
digest = h.Sum(nil)
|
||||
|
|
@ -509,17 +665,26 @@ func (sig *Signature) signPrepareHash(h hash.Hash) (digest []byte, err error) {
|
|||
// On success, the signature is stored in sig. Call Serialize to write it out.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (sig *Signature) Sign(h hash.Hash, priv *PrivateKey, config *Config) (err error) {
|
||||
sig.outSubpackets = sig.buildSubpackets()
|
||||
if priv.Dummy() {
|
||||
return errors.ErrDummyPrivateKey("dummy key found")
|
||||
}
|
||||
sig.Version = priv.PublicKey.Version
|
||||
sig.IssuerFingerprint = priv.PublicKey.Fingerprint
|
||||
sig.outSubpackets, err = sig.buildSubpackets(priv.PublicKey)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
digest, err := sig.signPrepareHash(h)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
switch priv.PubKeyAlgo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly:
|
||||
// supports both *rsa.PrivateKey and crypto.Signer
|
||||
sig.RSASignature.bytes, err = priv.PrivateKey.(crypto.Signer).Sign(config.Random(), digest, sig.Hash)
|
||||
sig.RSASignature.bitLength = uint16(8 * len(sig.RSASignature.bytes))
|
||||
sigdata, err := priv.PrivateKey.(crypto.Signer).Sign(config.Random(), digest, sig.Hash)
|
||||
if err == nil {
|
||||
sig.RSASignature = encoding.NewMPI(sigdata)
|
||||
}
|
||||
case PubKeyAlgoDSA:
|
||||
dsaPriv := priv.PrivateKey.(*dsa.PrivateKey)
|
||||
|
||||
|
|
@ -530,26 +695,23 @@ func (sig *Signature) Sign(h hash.Hash, priv *PrivateKey, config *Config) (err e
|
|||
}
|
||||
r, s, err := dsa.Sign(config.Random(), dsaPriv, digest)
|
||||
if err == nil {
|
||||
sig.DSASigR.bytes = r.Bytes()
|
||||
sig.DSASigR.bitLength = uint16(8 * len(sig.DSASigR.bytes))
|
||||
sig.DSASigS.bytes = s.Bytes()
|
||||
sig.DSASigS.bitLength = uint16(8 * len(sig.DSASigS.bytes))
|
||||
sig.DSASigR = new(encoding.MPI).SetBig(r)
|
||||
sig.DSASigS = new(encoding.MPI).SetBig(s)
|
||||
}
|
||||
case PubKeyAlgoECDSA:
|
||||
var r, s *big.Int
|
||||
if pk, ok := priv.PrivateKey.(*ecdsa.PrivateKey); ok {
|
||||
// direct support, avoid asn1 wrapping/unwrapping
|
||||
r, s, err = ecdsa.Sign(config.Random(), pk, digest)
|
||||
} else {
|
||||
var b []byte
|
||||
b, err = priv.PrivateKey.(crypto.Signer).Sign(config.Random(), digest, sig.Hash)
|
||||
if err == nil {
|
||||
r, s, err = unwrapECDSASig(b)
|
||||
}
|
||||
}
|
||||
sk := priv.PrivateKey.(*ecdsa.PrivateKey)
|
||||
r, s, err := ecdsa.Sign(config.Random(), sk, digest)
|
||||
|
||||
if err == nil {
|
||||
sig.ECDSASigR = fromBig(r)
|
||||
sig.ECDSASigS = fromBig(s)
|
||||
sig.ECDSASigR = new(encoding.MPI).SetBig(r)
|
||||
sig.ECDSASigS = new(encoding.MPI).SetBig(s)
|
||||
}
|
||||
case PubKeyAlgoEdDSA:
|
||||
sk := priv.PrivateKey.(*eddsa.PrivateKey)
|
||||
r, s, err := eddsa.Sign(sk, digest)
|
||||
if err == nil {
|
||||
sig.EdDSASigR = encoding.NewMPI(r)
|
||||
sig.EdDSASigS = encoding.NewMPI(s)
|
||||
}
|
||||
default:
|
||||
err = errors.UnsupportedError("public key algorithm: " + strconv.Itoa(int(sig.PubKeyAlgo)))
|
||||
|
|
@ -558,24 +720,14 @@ func (sig *Signature) Sign(h hash.Hash, priv *PrivateKey, config *Config) (err e
|
|||
return
|
||||
}
|
||||
|
||||
// unwrapECDSASig parses the two integer components of an ASN.1-encoded ECDSA
|
||||
// signature.
|
||||
func unwrapECDSASig(b []byte) (r, s *big.Int, err error) {
|
||||
var ecsdaSig struct {
|
||||
R, S *big.Int
|
||||
}
|
||||
_, err = asn1.Unmarshal(b, &ecsdaSig)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
return ecsdaSig.R, ecsdaSig.S, nil
|
||||
}
|
||||
|
||||
// SignUserId computes a signature from priv, asserting that pub is a valid
|
||||
// key for the identity id. On success, the signature is stored in sig. Call
|
||||
// Serialize to write it out.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (sig *Signature) SignUserId(id string, pub *PublicKey, priv *PrivateKey, config *Config) error {
|
||||
if priv.Dummy() {
|
||||
return errors.ErrDummyPrivateKey("dummy key found")
|
||||
}
|
||||
h, err := userIdSignatureHash(id, pub, sig.Hash)
|
||||
if err != nil {
|
||||
return err
|
||||
|
|
@ -583,10 +735,25 @@ func (sig *Signature) SignUserId(id string, pub *PublicKey, priv *PrivateKey, co
|
|||
return sig.Sign(h, priv, config)
|
||||
}
|
||||
|
||||
// CrossSignKey computes a signature from signingKey on pub hashed using hashKey. On success,
|
||||
// the signature is stored in sig. Call Serialize to write it out.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (sig *Signature) CrossSignKey(pub *PublicKey, hashKey *PublicKey, signingKey *PrivateKey,
|
||||
config *Config) error {
|
||||
h, err := keySignatureHash(hashKey, pub, sig.Hash)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
return sig.Sign(h, signingKey, config)
|
||||
}
|
||||
|
||||
// SignKey computes a signature from priv, asserting that pub is a subkey. On
|
||||
// success, the signature is stored in sig. Call Serialize to write it out.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (sig *Signature) SignKey(pub *PublicKey, priv *PrivateKey, config *Config) error {
|
||||
if priv.Dummy() {
|
||||
return errors.ErrDummyPrivateKey("dummy key found")
|
||||
}
|
||||
h, err := keySignatureHash(&priv.PublicKey, pub, sig.Hash)
|
||||
if err != nil {
|
||||
return err
|
||||
|
|
@ -594,26 +761,48 @@ func (sig *Signature) SignKey(pub *PublicKey, priv *PrivateKey, config *Config)
|
|||
return sig.Sign(h, priv, config)
|
||||
}
|
||||
|
||||
// RevokeKey computes a revocation signature of pub using priv. On success, the signature is
|
||||
// stored in sig. Call Serialize to write it out.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (sig *Signature) RevokeKey(pub *PublicKey, priv *PrivateKey, config *Config) error {
|
||||
h, err := keyRevocationHash(pub, sig.Hash)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
return sig.Sign(h, priv, config)
|
||||
}
|
||||
|
||||
// RevokeSubkey computes a subkey revocation signature of pub using priv.
|
||||
// On success, the signature is stored in sig. Call Serialize to write it out.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func (sig *Signature) RevokeSubkey(pub *PublicKey, priv *PrivateKey, config *Config) error {
|
||||
// Identical to a subkey binding signature
|
||||
return sig.SignKey(pub, priv, config)
|
||||
}
|
||||
|
||||
// Serialize marshals sig to w. Sign, SignUserId or SignKey must have been
|
||||
// called first.
|
||||
func (sig *Signature) Serialize(w io.Writer) (err error) {
|
||||
if len(sig.outSubpackets) == 0 {
|
||||
sig.outSubpackets = sig.rawSubpackets
|
||||
}
|
||||
if sig.RSASignature.bytes == nil && sig.DSASigR.bytes == nil && sig.ECDSASigR.bytes == nil {
|
||||
if sig.RSASignature == nil && sig.DSASigR == nil && sig.ECDSASigR == nil && sig.EdDSASigR == nil {
|
||||
return errors.InvalidArgumentError("Signature: need to call Sign, SignUserId or SignKey before Serialize")
|
||||
}
|
||||
|
||||
sigLength := 0
|
||||
switch sig.PubKeyAlgo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly:
|
||||
sigLength = 2 + len(sig.RSASignature.bytes)
|
||||
sigLength = int(sig.RSASignature.EncodedLength())
|
||||
case PubKeyAlgoDSA:
|
||||
sigLength = 2 + len(sig.DSASigR.bytes)
|
||||
sigLength += 2 + len(sig.DSASigS.bytes)
|
||||
sigLength = int(sig.DSASigR.EncodedLength())
|
||||
sigLength += int(sig.DSASigS.EncodedLength())
|
||||
case PubKeyAlgoECDSA:
|
||||
sigLength = 2 + len(sig.ECDSASigR.bytes)
|
||||
sigLength += 2 + len(sig.ECDSASigS.bytes)
|
||||
sigLength = int(sig.ECDSASigR.EncodedLength())
|
||||
sigLength += int(sig.ECDSASigS.EncodedLength())
|
||||
case PubKeyAlgoEdDSA:
|
||||
sigLength = int(sig.EdDSASigR.EncodedLength())
|
||||
sigLength += int(sig.EdDSASigS.EncodedLength())
|
||||
default:
|
||||
panic("impossible")
|
||||
}
|
||||
|
|
@ -622,16 +811,29 @@ func (sig *Signature) Serialize(w io.Writer) (err error) {
|
|||
length := len(sig.HashSuffix) - 6 /* trailer not included */ +
|
||||
2 /* length of unhashed subpackets */ + unhashedSubpacketsLen +
|
||||
2 /* hash tag */ + sigLength
|
||||
if sig.Version == 5 {
|
||||
length -= 4 // eight-octet instead of four-octet big endian
|
||||
}
|
||||
err = serializeHeader(w, packetTypeSignature, length)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
err = sig.serializeBody(w)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
_, err = w.Write(sig.HashSuffix[:len(sig.HashSuffix)-6])
|
||||
func (sig *Signature) serializeBody(w io.Writer) (err error) {
|
||||
hashedSubpacketsLen := uint16(uint16(sig.HashSuffix[4])<<8) | uint16(sig.HashSuffix[5])
|
||||
fields := sig.HashSuffix[:6+hashedSubpacketsLen]
|
||||
_, err = w.Write(fields)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
unhashedSubpacketsLen := subpacketsLength(sig.outSubpackets, false)
|
||||
unhashedSubpackets := make([]byte, 2+unhashedSubpacketsLen)
|
||||
unhashedSubpackets[0] = byte(unhashedSubpacketsLen >> 8)
|
||||
unhashedSubpackets[1] = byte(unhashedSubpacketsLen)
|
||||
|
|
@ -648,11 +850,22 @@ func (sig *Signature) Serialize(w io.Writer) (err error) {
|
|||
|
||||
switch sig.PubKeyAlgo {
|
||||
case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly:
|
||||
err = writeMPIs(w, sig.RSASignature)
|
||||
_, err = w.Write(sig.RSASignature.EncodedBytes())
|
||||
case PubKeyAlgoDSA:
|
||||
err = writeMPIs(w, sig.DSASigR, sig.DSASigS)
|
||||
if _, err = w.Write(sig.DSASigR.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
_, err = w.Write(sig.DSASigS.EncodedBytes())
|
||||
case PubKeyAlgoECDSA:
|
||||
err = writeMPIs(w, sig.ECDSASigR, sig.ECDSASigS)
|
||||
if _, err = w.Write(sig.ECDSASigR.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
_, err = w.Write(sig.ECDSASigS.EncodedBytes())
|
||||
case PubKeyAlgoEdDSA:
|
||||
if _, err = w.Write(sig.EdDSASigR.EncodedBytes()); err != nil {
|
||||
return
|
||||
}
|
||||
_, err = w.Write(sig.EdDSASigS.EncodedBytes())
|
||||
default:
|
||||
panic("impossible")
|
||||
}
|
||||
|
|
@ -667,17 +880,23 @@ type outputSubpacket struct {
|
|||
contents []byte
|
||||
}
|
||||
|
||||
func (sig *Signature) buildSubpackets() (subpackets []outputSubpacket) {
|
||||
func (sig *Signature) buildSubpackets(issuer PublicKey) (subpackets []outputSubpacket, err error) {
|
||||
creationTime := make([]byte, 4)
|
||||
binary.BigEndian.PutUint32(creationTime, uint32(sig.CreationTime.Unix()))
|
||||
subpackets = append(subpackets, outputSubpacket{true, creationTimeSubpacket, false, creationTime})
|
||||
|
||||
if sig.IssuerKeyId != nil {
|
||||
if sig.IssuerKeyId != nil && sig.Version == 4 {
|
||||
keyId := make([]byte, 8)
|
||||
binary.BigEndian.PutUint64(keyId, *sig.IssuerKeyId)
|
||||
subpackets = append(subpackets, outputSubpacket{true, issuerSubpacket, false, keyId})
|
||||
subpackets = append(subpackets, outputSubpacket{true, issuerSubpacket, true, keyId})
|
||||
}
|
||||
if sig.IssuerFingerprint != nil {
|
||||
contents := append([]uint8{uint8(issuer.Version)}, sig.IssuerFingerprint...)
|
||||
subpackets = append(subpackets, outputSubpacket{true, issuerFingerprintSubpacket, sig.Version == 5, contents})
|
||||
}
|
||||
if sig.SignerUserId != nil {
|
||||
subpackets = append(subpackets, outputSubpacket{true, signerUserIdSubpacket, false, []byte(*sig.SignerUserId)})
|
||||
}
|
||||
|
||||
if sig.SigLifetimeSecs != nil && *sig.SigLifetimeSecs != 0 {
|
||||
sigLifetime := make([]byte, 4)
|
||||
binary.BigEndian.PutUint32(sigLifetime, *sig.SigLifetimeSecs)
|
||||
|
|
@ -700,10 +919,51 @@ func (sig *Signature) buildSubpackets() (subpackets []outputSubpacket) {
|
|||
if sig.FlagEncryptStorage {
|
||||
flags |= KeyFlagEncryptStorage
|
||||
}
|
||||
if sig.FlagSplitKey {
|
||||
flags |= KeyFlagSplitKey
|
||||
}
|
||||
if sig.FlagAuthenticate {
|
||||
flags |= KeyFlagAuthenticate
|
||||
}
|
||||
if sig.FlagGroupKey {
|
||||
flags |= KeyFlagGroupKey
|
||||
}
|
||||
subpackets = append(subpackets, outputSubpacket{true, keyFlagsSubpacket, false, []byte{flags}})
|
||||
}
|
||||
|
||||
// The following subpackets may only appear in self-signatures
|
||||
for _, notation := range sig.Notations {
|
||||
subpackets = append(
|
||||
subpackets,
|
||||
outputSubpacket{
|
||||
true,
|
||||
notationDataSubpacket,
|
||||
notation.IsCritical,
|
||||
notation.getData(),
|
||||
})
|
||||
}
|
||||
|
||||
// The following subpackets may only appear in self-signatures.
|
||||
|
||||
var features = byte(0x00)
|
||||
if sig.SEIPDv1 {
|
||||
features |= 0x01
|
||||
}
|
||||
if sig.SEIPDv2 {
|
||||
features |= 0x08
|
||||
}
|
||||
|
||||
if features != 0x00 {
|
||||
subpackets = append(subpackets, outputSubpacket{true, featuresSubpacket, false, []byte{features}})
|
||||
}
|
||||
|
||||
if sig.TrustLevel != 0 {
|
||||
subpackets = append(subpackets, outputSubpacket{true, trustSubpacket, true, []byte{byte(sig.TrustLevel), byte(sig.TrustAmount)}})
|
||||
}
|
||||
|
||||
if sig.TrustRegularExpression != nil {
|
||||
// RFC specifies the string should be null-terminated; add a null byte to the end
|
||||
subpackets = append(subpackets, outputSubpacket{true, regularExpressionSubpacket, true, []byte(*sig.TrustRegularExpression + "\000")})
|
||||
}
|
||||
|
||||
if sig.KeyLifetimeSecs != nil && *sig.KeyLifetimeSecs != 0 {
|
||||
keyLifetime := make([]byte, 4)
|
||||
|
|
@ -727,5 +987,82 @@ func (sig *Signature) buildSubpackets() (subpackets []outputSubpacket) {
|
|||
subpackets = append(subpackets, outputSubpacket{true, prefCompressionSubpacket, false, sig.PreferredCompression})
|
||||
}
|
||||
|
||||
if len(sig.PolicyURI) > 0 {
|
||||
subpackets = append(subpackets, outputSubpacket{true, policyUriSubpacket, false, []uint8(sig.PolicyURI)})
|
||||
}
|
||||
|
||||
if len(sig.PreferredCipherSuites) > 0 {
|
||||
serialized := make([]byte, len(sig.PreferredCipherSuites)*2)
|
||||
for i, cipherSuite := range sig.PreferredCipherSuites {
|
||||
serialized[2*i] = cipherSuite[0]
|
||||
serialized[2*i+1] = cipherSuite[1]
|
||||
}
|
||||
subpackets = append(subpackets, outputSubpacket{true, prefCipherSuitesSubpacket, false, serialized})
|
||||
}
|
||||
|
||||
// Revocation reason appears only in revocation signatures and is serialized as per section 5.2.3.23.
|
||||
if sig.RevocationReason != nil {
|
||||
subpackets = append(subpackets, outputSubpacket{true, reasonForRevocationSubpacket, true,
|
||||
append([]uint8{uint8(*sig.RevocationReason)}, []uint8(sig.RevocationReasonText)...)})
|
||||
}
|
||||
|
||||
// EmbeddedSignature appears only in subkeys capable of signing and is serialized as per section 5.2.3.26.
|
||||
if sig.EmbeddedSignature != nil {
|
||||
var buf bytes.Buffer
|
||||
err = sig.EmbeddedSignature.serializeBody(&buf)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
subpackets = append(subpackets, outputSubpacket{true, embeddedSignatureSubpacket, true, buf.Bytes()})
|
||||
}
|
||||
|
||||
return
|
||||
}
|
||||
|
||||
// AddMetadataToHashSuffix modifies the current hash suffix to include metadata
|
||||
// (format, filename, and time). Version 5 keys protect this data including it
|
||||
// in the hash computation. See section 5.2.4.
|
||||
func (sig *Signature) AddMetadataToHashSuffix() {
|
||||
if sig == nil || sig.Version != 5 {
|
||||
return
|
||||
}
|
||||
if sig.SigType != 0x00 && sig.SigType != 0x01 {
|
||||
return
|
||||
}
|
||||
lit := sig.Metadata
|
||||
if lit == nil {
|
||||
// This will translate into six 0x00 bytes.
|
||||
lit = &LiteralData{}
|
||||
}
|
||||
|
||||
// Extract the current byte count
|
||||
n := sig.HashSuffix[len(sig.HashSuffix)-8:]
|
||||
l := uint64(
|
||||
uint64(n[0])<<56 | uint64(n[1])<<48 | uint64(n[2])<<40 | uint64(n[3])<<32 |
|
||||
uint64(n[4])<<24 | uint64(n[5])<<16 | uint64(n[6])<<8 | uint64(n[7]))
|
||||
|
||||
suffix := bytes.NewBuffer(nil)
|
||||
suffix.Write(sig.HashSuffix[:l])
|
||||
|
||||
// Add the metadata
|
||||
var buf [4]byte
|
||||
buf[0] = lit.Format
|
||||
fileName := lit.FileName
|
||||
if len(lit.FileName) > 255 {
|
||||
fileName = fileName[:255]
|
||||
}
|
||||
buf[1] = byte(len(fileName))
|
||||
suffix.Write(buf[:2])
|
||||
suffix.Write([]byte(lit.FileName))
|
||||
binary.BigEndian.PutUint32(buf[:], lit.Time)
|
||||
suffix.Write(buf[:])
|
||||
|
||||
// Update the counter and restore trailing bytes
|
||||
l = uint64(suffix.Len())
|
||||
suffix.Write([]byte{0x05, 0xff})
|
||||
suffix.Write([]byte{
|
||||
uint8(l >> 56), uint8(l >> 48), uint8(l >> 40), uint8(l >> 32),
|
||||
uint8(l >> 24), uint8(l >> 16), uint8(l >> 8), uint8(l),
|
||||
})
|
||||
sig.HashSuffix = suffix.Bytes()
|
||||
}
|
||||
303
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetric_key_encrypted.go
generated
vendored
Normal file
303
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetric_key_encrypted.go
generated
vendored
Normal file
|
|
@ -0,0 +1,303 @@
|
|||
// Copyright 2011 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package packet
|
||||
|
||||
import (
|
||||
"bytes"
|
||||
"crypto/cipher"
|
||||
"crypto/sha256"
|
||||
"io"
|
||||
"strconv"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/s2k"
|
||||
"golang.org/x/crypto/hkdf"
|
||||
)
|
||||
|
||||
// This is the largest session key that we'll support. Since at most 256-bit cipher
|
||||
// is supported in OpenPGP, this is large enough to contain also the auth tag.
|
||||
const maxSessionKeySizeInBytes = 64
|
||||
|
||||
// SymmetricKeyEncrypted represents a passphrase protected session key. See RFC
|
||||
// 4880, section 5.3.
|
||||
type SymmetricKeyEncrypted struct {
|
||||
Version int
|
||||
CipherFunc CipherFunction
|
||||
Mode AEADMode
|
||||
s2k func(out, in []byte)
|
||||
iv []byte
|
||||
encryptedKey []byte // Contains also the authentication tag for AEAD
|
||||
}
|
||||
|
||||
// parse parses an SymmetricKeyEncrypted packet as specified in
|
||||
// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#name-symmetric-key-encrypted-ses
|
||||
func (ske *SymmetricKeyEncrypted) parse(r io.Reader) error {
|
||||
var buf [1]byte
|
||||
|
||||
// Version
|
||||
if _, err := readFull(r, buf[:]); err != nil {
|
||||
return err
|
||||
}
|
||||
ske.Version = int(buf[0])
|
||||
if ske.Version != 4 && ske.Version != 5 {
|
||||
return errors.UnsupportedError("unknown SymmetricKeyEncrypted version")
|
||||
}
|
||||
|
||||
if ske.Version == 5 {
|
||||
// Scalar octet count
|
||||
if _, err := readFull(r, buf[:]); err != nil {
|
||||
return err
|
||||
}
|
||||
}
|
||||
|
||||
// Cipher function
|
||||
if _, err := readFull(r, buf[:]); err != nil {
|
||||
return err
|
||||
}
|
||||
ske.CipherFunc = CipherFunction(buf[0])
|
||||
if !ske.CipherFunc.IsSupported() {
|
||||
return errors.UnsupportedError("unknown cipher: " + strconv.Itoa(int(buf[0])))
|
||||
}
|
||||
|
||||
if ske.Version == 5 {
|
||||
// AEAD mode
|
||||
if _, err := readFull(r, buf[:]); err != nil {
|
||||
return errors.StructuralError("cannot read AEAD octet from packet")
|
||||
}
|
||||
ske.Mode = AEADMode(buf[0])
|
||||
|
||||
// Scalar octet count
|
||||
if _, err := readFull(r, buf[:]); err != nil {
|
||||
return err
|
||||
}
|
||||
}
|
||||
|
||||
var err error
|
||||
if ske.s2k, err = s2k.Parse(r); err != nil {
|
||||
if _, ok := err.(errors.ErrDummyPrivateKey); ok {
|
||||
return errors.UnsupportedError("missing key GNU extension in session key")
|
||||
}
|
||||
return err
|
||||
}
|
||||
|
||||
if ske.Version == 5 {
|
||||
// AEAD IV
|
||||
iv := make([]byte, ske.Mode.IvLength())
|
||||
_, err := readFull(r, iv)
|
||||
if err != nil {
|
||||
return errors.StructuralError("cannot read AEAD IV")
|
||||
}
|
||||
|
||||
ske.iv = iv
|
||||
}
|
||||
|
||||
encryptedKey := make([]byte, maxSessionKeySizeInBytes)
|
||||
// The session key may follow. We just have to try and read to find
|
||||
// out. If it exists then we limit it to maxSessionKeySizeInBytes.
|
||||
n, err := readFull(r, encryptedKey)
|
||||
if err != nil && err != io.ErrUnexpectedEOF {
|
||||
return err
|
||||
}
|
||||
|
||||
if n != 0 {
|
||||
if n == maxSessionKeySizeInBytes {
|
||||
return errors.UnsupportedError("oversized encrypted session key")
|
||||
}
|
||||
ske.encryptedKey = encryptedKey[:n]
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
// Decrypt attempts to decrypt an encrypted session key and returns the key and
|
||||
// the cipher to use when decrypting a subsequent Symmetrically Encrypted Data
|
||||
// packet.
|
||||
func (ske *SymmetricKeyEncrypted) Decrypt(passphrase []byte) ([]byte, CipherFunction, error) {
|
||||
key := make([]byte, ske.CipherFunc.KeySize())
|
||||
ske.s2k(key, passphrase)
|
||||
if len(ske.encryptedKey) == 0 {
|
||||
return key, ske.CipherFunc, nil
|
||||
}
|
||||
switch ske.Version {
|
||||
case 4:
|
||||
plaintextKey, cipherFunc, err := ske.decryptV4(key)
|
||||
return plaintextKey, cipherFunc, err
|
||||
case 5:
|
||||
plaintextKey, err := ske.decryptV5(key)
|
||||
return plaintextKey, CipherFunction(0), err
|
||||
}
|
||||
err := errors.UnsupportedError("unknown SymmetricKeyEncrypted version")
|
||||
return nil, CipherFunction(0), err
|
||||
}
|
||||
|
||||
func (ske *SymmetricKeyEncrypted) decryptV4(key []byte) ([]byte, CipherFunction, error) {
|
||||
// the IV is all zeros
|
||||
iv := make([]byte, ske.CipherFunc.blockSize())
|
||||
c := cipher.NewCFBDecrypter(ske.CipherFunc.new(key), iv)
|
||||
plaintextKey := make([]byte, len(ske.encryptedKey))
|
||||
c.XORKeyStream(plaintextKey, ske.encryptedKey)
|
||||
cipherFunc := CipherFunction(plaintextKey[0])
|
||||
if cipherFunc.blockSize() == 0 {
|
||||
return nil, ske.CipherFunc, errors.UnsupportedError(
|
||||
"unknown cipher: " + strconv.Itoa(int(cipherFunc)))
|
||||
}
|
||||
plaintextKey = plaintextKey[1:]
|
||||
if len(plaintextKey) != cipherFunc.KeySize() {
|
||||
return nil, cipherFunc, errors.StructuralError(
|
||||
"length of decrypted key not equal to cipher keysize")
|
||||
}
|
||||
return plaintextKey, cipherFunc, nil
|
||||
}
|
||||
|
||||
func (ske *SymmetricKeyEncrypted) decryptV5(key []byte) ([]byte, error) {
|
||||
adata := []byte{0xc3, byte(5), byte(ske.CipherFunc), byte(ske.Mode)}
|
||||
aead := getEncryptedKeyAeadInstance(ske.CipherFunc, ske.Mode, key, adata)
|
||||
|
||||
plaintextKey, err := aead.Open(nil, ske.iv, ske.encryptedKey, adata)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
return plaintextKey, nil
|
||||
}
|
||||
|
||||
// SerializeSymmetricKeyEncrypted serializes a symmetric key packet to w.
|
||||
// The packet contains a random session key, encrypted by a key derived from
|
||||
// the given passphrase. The session key is returned and must be passed to
|
||||
// SerializeSymmetricallyEncrypted.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func SerializeSymmetricKeyEncrypted(w io.Writer, passphrase []byte, config *Config) (key []byte, err error) {
|
||||
cipherFunc := config.Cipher()
|
||||
|
||||
sessionKey := make([]byte, cipherFunc.KeySize())
|
||||
_, err = io.ReadFull(config.Random(), sessionKey)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
err = SerializeSymmetricKeyEncryptedReuseKey(w, sessionKey, passphrase, config)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
key = sessionKey
|
||||
return
|
||||
}
|
||||
|
||||
// SerializeSymmetricKeyEncryptedReuseKey serializes a symmetric key packet to w.
|
||||
// The packet contains the given session key, encrypted by a key derived from
|
||||
// the given passphrase. The returned session key must be passed to
|
||||
// SerializeSymmetricallyEncrypted.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func SerializeSymmetricKeyEncryptedReuseKey(w io.Writer, sessionKey []byte, passphrase []byte, config *Config) (err error) {
|
||||
var version int
|
||||
if config.AEAD() != nil {
|
||||
version = 5
|
||||
} else {
|
||||
version = 4
|
||||
}
|
||||
cipherFunc := config.Cipher()
|
||||
// cipherFunc must be AES
|
||||
if !cipherFunc.IsSupported() || cipherFunc < CipherAES128 || cipherFunc > CipherAES256 {
|
||||
return errors.UnsupportedError("unsupported cipher: " + strconv.Itoa(int(cipherFunc)))
|
||||
}
|
||||
|
||||
keySize := cipherFunc.KeySize()
|
||||
s2kBuf := new(bytes.Buffer)
|
||||
keyEncryptingKey := make([]byte, keySize)
|
||||
// s2k.Serialize salts and stretches the passphrase, and writes the
|
||||
// resulting key to keyEncryptingKey and the s2k descriptor to s2kBuf.
|
||||
err = s2k.Serialize(s2kBuf, keyEncryptingKey, config.Random(), passphrase, &s2k.Config{Hash: config.Hash(), S2KCount: config.PasswordHashIterations()})
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
s2kBytes := s2kBuf.Bytes()
|
||||
|
||||
var packetLength int
|
||||
switch version {
|
||||
case 4:
|
||||
packetLength = 2 /* header */ + len(s2kBytes) + 1 /* cipher type */ + keySize
|
||||
case 5:
|
||||
ivLen := config.AEAD().Mode().IvLength()
|
||||
tagLen := config.AEAD().Mode().TagLength()
|
||||
packetLength = 5 + len(s2kBytes) + ivLen + keySize + tagLen
|
||||
}
|
||||
err = serializeHeader(w, packetTypeSymmetricKeyEncrypted, packetLength)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
// Symmetric Key Encrypted Version
|
||||
buf := []byte{byte(version)}
|
||||
|
||||
if version == 5 {
|
||||
// Scalar octet count
|
||||
buf = append(buf, byte(3 + len(s2kBytes) + config.AEAD().Mode().IvLength()))
|
||||
}
|
||||
|
||||
// Cipher function
|
||||
buf = append(buf, byte(cipherFunc))
|
||||
|
||||
if version == 5 {
|
||||
// AEAD mode
|
||||
buf = append(buf, byte(config.AEAD().Mode()))
|
||||
|
||||
// Scalar octet count
|
||||
buf = append(buf, byte(len(s2kBytes)))
|
||||
}
|
||||
_, err = w.Write(buf)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
_, err = w.Write(s2kBytes)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
switch version {
|
||||
case 4:
|
||||
iv := make([]byte, cipherFunc.blockSize())
|
||||
c := cipher.NewCFBEncrypter(cipherFunc.new(keyEncryptingKey), iv)
|
||||
encryptedCipherAndKey := make([]byte, keySize+1)
|
||||
c.XORKeyStream(encryptedCipherAndKey, buf[1:])
|
||||
c.XORKeyStream(encryptedCipherAndKey[1:], sessionKey)
|
||||
_, err = w.Write(encryptedCipherAndKey)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
case 5:
|
||||
mode := config.AEAD().Mode()
|
||||
adata := []byte{0xc3, byte(5), byte(cipherFunc), byte(mode)}
|
||||
aead := getEncryptedKeyAeadInstance(cipherFunc, mode, keyEncryptingKey, adata)
|
||||
|
||||
// Sample iv using random reader
|
||||
iv := make([]byte, config.AEAD().Mode().IvLength())
|
||||
_, err = io.ReadFull(config.Random(), iv)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
// Seal and write (encryptedData includes auth. tag)
|
||||
|
||||
encryptedData := aead.Seal(nil, iv, sessionKey, adata)
|
||||
_, err = w.Write(iv)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
_, err = w.Write(encryptedData)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
}
|
||||
|
||||
return
|
||||
}
|
||||
|
||||
func getEncryptedKeyAeadInstance(c CipherFunction, mode AEADMode, inputKey, associatedData []byte) (aead cipher.AEAD) {
|
||||
hkdfReader := hkdf.New(sha256.New, inputKey, []byte{}, associatedData)
|
||||
|
||||
encryptionKey := make([]byte, c.KeySize())
|
||||
_, _ = readFull(hkdfReader, encryptionKey)
|
||||
|
||||
blockCipher := c.new(encryptionKey)
|
||||
return mode.new(blockCipher)
|
||||
}
|
||||
91
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted.go
generated
vendored
Normal file
91
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted.go
generated
vendored
Normal file
|
|
@ -0,0 +1,91 @@
|
|||
// Copyright 2011 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package packet
|
||||
|
||||
import (
|
||||
"io"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
)
|
||||
|
||||
const aeadSaltSize = 32
|
||||
|
||||
// SymmetricallyEncrypted represents a symmetrically encrypted byte string. The
|
||||
// encrypted Contents will consist of more OpenPGP packets. See RFC 4880,
|
||||
// sections 5.7 and 5.13.
|
||||
type SymmetricallyEncrypted struct {
|
||||
Version int
|
||||
Contents io.Reader // contains tag for version 2
|
||||
IntegrityProtected bool // If true it is type 18 (with MDC or AEAD). False is packet type 9
|
||||
|
||||
// Specific to version 1
|
||||
prefix []byte
|
||||
|
||||
// Specific to version 2
|
||||
cipher CipherFunction
|
||||
mode AEADMode
|
||||
chunkSizeByte byte
|
||||
salt [aeadSaltSize]byte
|
||||
}
|
||||
|
||||
const (
|
||||
symmetricallyEncryptedVersionMdc = 1
|
||||
symmetricallyEncryptedVersionAead = 2
|
||||
)
|
||||
|
||||
|
||||
func (se *SymmetricallyEncrypted) parse(r io.Reader) error {
|
||||
if se.IntegrityProtected {
|
||||
// See RFC 4880, section 5.13.
|
||||
var buf [1]byte
|
||||
_, err := readFull(r, buf[:])
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
switch buf[0] {
|
||||
case symmetricallyEncryptedVersionMdc:
|
||||
se.Version = symmetricallyEncryptedVersionMdc
|
||||
case symmetricallyEncryptedVersionAead:
|
||||
se.Version = symmetricallyEncryptedVersionAead
|
||||
if err := se.parseAead(r); err != nil {
|
||||
return err
|
||||
}
|
||||
default:
|
||||
return errors.UnsupportedError("unknown SymmetricallyEncrypted version")
|
||||
}
|
||||
}
|
||||
se.Contents = r
|
||||
return nil
|
||||
}
|
||||
|
||||
// Decrypt returns a ReadCloser, from which the decrypted Contents of the
|
||||
// packet can be read. An incorrect key will only be detected after trying
|
||||
// to decrypt the entire data.
|
||||
func (se *SymmetricallyEncrypted) Decrypt(c CipherFunction, key []byte) (io.ReadCloser, error) {
|
||||
if se.Version == symmetricallyEncryptedVersionAead {
|
||||
return se.decryptAead(key)
|
||||
}
|
||||
|
||||
return se.decryptMdc(c, key)
|
||||
}
|
||||
|
||||
// SerializeSymmetricallyEncrypted serializes a symmetrically encrypted packet
|
||||
// to w and returns a WriteCloser to which the to-be-encrypted packets can be
|
||||
// written.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func SerializeSymmetricallyEncrypted(w io.Writer, c CipherFunction, aeadSupported bool, cipherSuite CipherSuite, key []byte, config *Config) (Contents io.WriteCloser, err error) {
|
||||
writeCloser := noOpCloser{w}
|
||||
ciphertext, err := serializeStreamHeader(writeCloser, packetTypeSymmetricallyEncryptedIntegrityProtected)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
if aeadSupported {
|
||||
return serializeSymmetricallyEncryptedAead(ciphertext, cipherSuite, config.AEADConfig.ChunkSizeByte(), config.Random(), key)
|
||||
}
|
||||
|
||||
return serializeSymmetricallyEncryptedMdc(ciphertext, c, key, config)
|
||||
}
|
||||
155
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted_aead.go
generated
vendored
Normal file
155
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted_aead.go
generated
vendored
Normal file
|
|
@ -0,0 +1,155 @@
|
|||
// Copyright 2023 Proton AG. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package packet
|
||||
|
||||
import (
|
||||
"crypto/cipher"
|
||||
"crypto/sha256"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"golang.org/x/crypto/hkdf"
|
||||
"io"
|
||||
)
|
||||
|
||||
// parseAead parses a V2 SEIPD packet (AEAD) as specified in
|
||||
// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-5.13.2
|
||||
func (se *SymmetricallyEncrypted) parseAead(r io.Reader) error {
|
||||
headerData := make([]byte, 3)
|
||||
if n, err := io.ReadFull(r, headerData); n < 3 {
|
||||
return errors.StructuralError("could not read aead header: " + err.Error())
|
||||
}
|
||||
|
||||
// Cipher
|
||||
se.cipher = CipherFunction(headerData[0])
|
||||
// cipherFunc must have block size 16 to use AEAD
|
||||
if se.cipher.blockSize() != 16 {
|
||||
return errors.UnsupportedError("invalid aead cipher: " + string(se.cipher))
|
||||
}
|
||||
|
||||
// Mode
|
||||
se.mode = AEADMode(headerData[1])
|
||||
if se.mode.TagLength() == 0 {
|
||||
return errors.UnsupportedError("unknown aead mode: " + string(se.mode))
|
||||
}
|
||||
|
||||
// Chunk size
|
||||
se.chunkSizeByte = headerData[2]
|
||||
if se.chunkSizeByte > 16 {
|
||||
return errors.UnsupportedError("invalid aead chunk size byte: " + string(se.chunkSizeByte))
|
||||
}
|
||||
|
||||
// Salt
|
||||
if n, err := io.ReadFull(r, se.salt[:]); n < aeadSaltSize {
|
||||
return errors.StructuralError("could not read aead salt: " + err.Error())
|
||||
}
|
||||
|
||||
return nil
|
||||
}
|
||||
|
||||
// associatedData for chunks: tag, version, cipher, mode, chunk size byte
|
||||
func (se *SymmetricallyEncrypted) associatedData() []byte {
|
||||
return []byte{
|
||||
0xD2,
|
||||
symmetricallyEncryptedVersionAead,
|
||||
byte(se.cipher),
|
||||
byte(se.mode),
|
||||
se.chunkSizeByte,
|
||||
}
|
||||
}
|
||||
|
||||
// decryptAead decrypts a V2 SEIPD packet (AEAD) as specified in
|
||||
// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-5.13.2
|
||||
func (se *SymmetricallyEncrypted) decryptAead(inputKey []byte) (io.ReadCloser, error) {
|
||||
aead, nonce := getSymmetricallyEncryptedAeadInstance(se.cipher, se.mode, inputKey, se.salt[:], se.associatedData())
|
||||
|
||||
// Carry the first tagLen bytes
|
||||
tagLen := se.mode.TagLength()
|
||||
peekedBytes := make([]byte, tagLen)
|
||||
n, err := io.ReadFull(se.Contents, peekedBytes)
|
||||
if n < tagLen || (err != nil && err != io.EOF) {
|
||||
return nil, errors.StructuralError("not enough data to decrypt:" + err.Error())
|
||||
}
|
||||
|
||||
return &aeadDecrypter{
|
||||
aeadCrypter: aeadCrypter{
|
||||
aead: aead,
|
||||
chunkSize: decodeAEADChunkSize(se.chunkSizeByte),
|
||||
initialNonce: nonce,
|
||||
associatedData: se.associatedData(),
|
||||
chunkIndex: make([]byte, 8),
|
||||
packetTag: packetTypeSymmetricallyEncryptedIntegrityProtected,
|
||||
},
|
||||
reader: se.Contents,
|
||||
peekedBytes: peekedBytes,
|
||||
}, nil
|
||||
}
|
||||
|
||||
// serializeSymmetricallyEncryptedAead encrypts to a writer a V2 SEIPD packet (AEAD) as specified in
|
||||
// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-5.13.2
|
||||
func serializeSymmetricallyEncryptedAead(ciphertext io.WriteCloser, cipherSuite CipherSuite, chunkSizeByte byte, rand io.Reader, inputKey []byte) (Contents io.WriteCloser, err error) {
|
||||
// cipherFunc must have block size 16 to use AEAD
|
||||
if cipherSuite.Cipher.blockSize() != 16 {
|
||||
return nil, errors.InvalidArgumentError("invalid aead cipher function")
|
||||
}
|
||||
|
||||
if cipherSuite.Cipher.KeySize() != len(inputKey) {
|
||||
return nil, errors.InvalidArgumentError("error in aead serialization: bad key length")
|
||||
}
|
||||
|
||||
// Data for en/decryption: tag, version, cipher, aead mode, chunk size
|
||||
prefix := []byte{
|
||||
0xD2,
|
||||
symmetricallyEncryptedVersionAead,
|
||||
byte(cipherSuite.Cipher),
|
||||
byte(cipherSuite.Mode),
|
||||
chunkSizeByte,
|
||||
}
|
||||
|
||||
// Write header (that correspond to prefix except first byte)
|
||||
n, err := ciphertext.Write(prefix[1:])
|
||||
if err != nil || n < 4 {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
// Random salt
|
||||
salt := make([]byte, aeadSaltSize)
|
||||
if _, err := rand.Read(salt); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
if _, err := ciphertext.Write(salt); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
aead, nonce := getSymmetricallyEncryptedAeadInstance(cipherSuite.Cipher, cipherSuite.Mode, inputKey, salt, prefix)
|
||||
|
||||
return &aeadEncrypter{
|
||||
aeadCrypter: aeadCrypter{
|
||||
aead: aead,
|
||||
chunkSize: decodeAEADChunkSize(chunkSizeByte),
|
||||
associatedData: prefix,
|
||||
chunkIndex: make([]byte, 8),
|
||||
initialNonce: nonce,
|
||||
packetTag: packetTypeSymmetricallyEncryptedIntegrityProtected,
|
||||
},
|
||||
writer: ciphertext,
|
||||
}, nil
|
||||
}
|
||||
|
||||
func getSymmetricallyEncryptedAeadInstance(c CipherFunction, mode AEADMode, inputKey, salt, associatedData []byte) (aead cipher.AEAD, nonce []byte) {
|
||||
hkdfReader := hkdf.New(sha256.New, inputKey, salt, associatedData)
|
||||
|
||||
encryptionKey := make([]byte, c.KeySize())
|
||||
_, _ = readFull(hkdfReader, encryptionKey)
|
||||
|
||||
// Last 64 bits of nonce are the counter
|
||||
nonce = make([]byte, mode.IvLength() - 8)
|
||||
|
||||
_, _ = readFull(hkdfReader, nonce)
|
||||
|
||||
blockCipher := c.new(encryptionKey)
|
||||
aead = mode.new(blockCipher)
|
||||
|
||||
return
|
||||
}
|
||||
|
|
@ -8,54 +8,38 @@ import (
|
|||
"crypto/cipher"
|
||||
"crypto/sha1"
|
||||
"crypto/subtle"
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"hash"
|
||||
"io"
|
||||
"strconv"
|
||||
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
)
|
||||
|
||||
// SymmetricallyEncrypted represents a symmetrically encrypted byte string. The
|
||||
// encrypted contents will consist of more OpenPGP packets. See RFC 4880,
|
||||
// sections 5.7 and 5.13.
|
||||
type SymmetricallyEncrypted struct {
|
||||
MDC bool // true iff this is a type 18 packet and thus has an embedded MAC.
|
||||
contents io.Reader
|
||||
prefix []byte
|
||||
// seMdcReader wraps an io.Reader with a no-op Close method.
|
||||
type seMdcReader struct {
|
||||
in io.Reader
|
||||
}
|
||||
|
||||
const symmetricallyEncryptedVersion = 1
|
||||
func (ser seMdcReader) Read(buf []byte) (int, error) {
|
||||
return ser.in.Read(buf)
|
||||
}
|
||||
|
||||
func (se *SymmetricallyEncrypted) parse(r io.Reader) error {
|
||||
if se.MDC {
|
||||
// See RFC 4880, section 5.13.
|
||||
var buf [1]byte
|
||||
_, err := readFull(r, buf[:])
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
if buf[0] != symmetricallyEncryptedVersion {
|
||||
return errors.UnsupportedError("unknown SymmetricallyEncrypted version")
|
||||
}
|
||||
}
|
||||
se.contents = r
|
||||
func (ser seMdcReader) Close() error {
|
||||
return nil
|
||||
}
|
||||
|
||||
// Decrypt returns a ReadCloser, from which the decrypted contents of the
|
||||
// packet can be read. An incorrect key can, with high probability, be detected
|
||||
// immediately and this will result in a KeyIncorrect error being returned.
|
||||
func (se *SymmetricallyEncrypted) Decrypt(c CipherFunction, key []byte) (io.ReadCloser, error) {
|
||||
keySize := c.KeySize()
|
||||
if keySize == 0 {
|
||||
return nil, errors.UnsupportedError("unknown cipher: " + strconv.Itoa(int(c)))
|
||||
func (se *SymmetricallyEncrypted) decryptMdc(c CipherFunction, key []byte) (io.ReadCloser, error) {
|
||||
if !c.IsSupported() {
|
||||
return nil, errors.UnsupportedError("unsupported cipher: " + strconv.Itoa(int(c)))
|
||||
}
|
||||
if len(key) != keySize {
|
||||
|
||||
if len(key) != c.KeySize() {
|
||||
return nil, errors.InvalidArgumentError("SymmetricallyEncrypted: incorrect key length")
|
||||
}
|
||||
|
||||
if se.prefix == nil {
|
||||
se.prefix = make([]byte, c.blockSize()+2)
|
||||
_, err := readFull(se.contents, se.prefix)
|
||||
_, err := readFull(se.Contents, se.prefix)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
|
@ -64,47 +48,31 @@ func (se *SymmetricallyEncrypted) Decrypt(c CipherFunction, key []byte) (io.Read
|
|||
}
|
||||
|
||||
ocfbResync := OCFBResync
|
||||
if se.MDC {
|
||||
if se.IntegrityProtected {
|
||||
// MDC packets use a different form of OCFB mode.
|
||||
ocfbResync = OCFBNoResync
|
||||
}
|
||||
|
||||
s := NewOCFBDecrypter(c.new(key), se.prefix, ocfbResync)
|
||||
if s == nil {
|
||||
return nil, errors.ErrKeyIncorrect
|
||||
}
|
||||
|
||||
plaintext := cipher.StreamReader{S: s, R: se.contents}
|
||||
plaintext := cipher.StreamReader{S: s, R: se.Contents}
|
||||
|
||||
if se.MDC {
|
||||
// MDC packets have an embedded hash that we need to check.
|
||||
if se.IntegrityProtected {
|
||||
// IntegrityProtected packets have an embedded hash that we need to check.
|
||||
h := sha1.New()
|
||||
h.Write(se.prefix)
|
||||
return &seMDCReader{in: plaintext, h: h}, nil
|
||||
}
|
||||
|
||||
// Otherwise, we just need to wrap plaintext so that it's a valid ReadCloser.
|
||||
return seReader{plaintext}, nil
|
||||
}
|
||||
|
||||
// seReader wraps an io.Reader with a no-op Close method.
|
||||
type seReader struct {
|
||||
in io.Reader
|
||||
}
|
||||
|
||||
func (ser seReader) Read(buf []byte) (int, error) {
|
||||
return ser.in.Read(buf)
|
||||
}
|
||||
|
||||
func (ser seReader) Close() error {
|
||||
return nil
|
||||
return seMdcReader{plaintext}, nil
|
||||
}
|
||||
|
||||
const mdcTrailerSize = 1 /* tag byte */ + 1 /* length byte */ + sha1.Size
|
||||
|
||||
// An seMDCReader wraps an io.Reader, maintains a running hash and keeps hold
|
||||
// of the most recent 22 bytes (mdcTrailerSize). Upon EOF, those bytes form an
|
||||
// MDC packet containing a hash of the previous contents which is checked
|
||||
// MDC packet containing a hash of the previous Contents which is checked
|
||||
// against the running hash. See RFC 4880, section 5.13.
|
||||
type seMDCReader struct {
|
||||
in io.Reader
|
||||
|
|
@ -175,12 +143,12 @@ func (ser *seMDCReader) Read(buf []byte) (n int, err error) {
|
|||
return
|
||||
}
|
||||
|
||||
// This is a new-format packet tag byte for a type 19 (MDC) packet.
|
||||
// This is a new-format packet tag byte for a type 19 (Integrity Protected) packet.
|
||||
const mdcPacketTagByte = byte(0x80) | 0x40 | 19
|
||||
|
||||
func (ser *seMDCReader) Close() error {
|
||||
if ser.error {
|
||||
return errors.SignatureError("error during reading")
|
||||
return errors.ErrMDCMissing
|
||||
}
|
||||
|
||||
for !ser.eof {
|
||||
|
|
@ -191,18 +159,20 @@ func (ser *seMDCReader) Close() error {
|
|||
break
|
||||
}
|
||||
if err != nil {
|
||||
return errors.SignatureError("error during reading")
|
||||
return errors.ErrMDCMissing
|
||||
}
|
||||
}
|
||||
|
||||
if ser.trailer[0] != mdcPacketTagByte || ser.trailer[1] != sha1.Size {
|
||||
return errors.SignatureError("MDC packet not found")
|
||||
}
|
||||
ser.h.Write(ser.trailer[:2])
|
||||
|
||||
final := ser.h.Sum(nil)
|
||||
if subtle.ConstantTimeCompare(final, ser.trailer[2:]) != 1 {
|
||||
return errors.SignatureError("hash mismatch")
|
||||
return errors.ErrMDCHashMismatch
|
||||
}
|
||||
// The hash already includes the MDC header, but we still check its value
|
||||
// to confirm encryption correctness
|
||||
if ser.trailer[0] != mdcPacketTagByte || ser.trailer[1] != sha1.Size {
|
||||
return errors.ErrMDCMissing
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
|
@ -236,7 +206,7 @@ func (w *seMDCWriter) Close() (err error) {
|
|||
return w.w.Close()
|
||||
}
|
||||
|
||||
// noOpCloser is like an io.NopCloser, but for an io.Writer.
|
||||
// noOpCloser is like an ioutil.NopCloser, but for an io.Writer.
|
||||
type noOpCloser struct {
|
||||
w io.Writer
|
||||
}
|
||||
|
|
@ -249,21 +219,17 @@ func (c noOpCloser) Close() error {
|
|||
return nil
|
||||
}
|
||||
|
||||
// SerializeSymmetricallyEncrypted serializes a symmetrically encrypted packet
|
||||
// to w and returns a WriteCloser to which the to-be-encrypted packets can be
|
||||
// written.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func SerializeSymmetricallyEncrypted(w io.Writer, c CipherFunction, key []byte, config *Config) (contents io.WriteCloser, err error) {
|
||||
if c.KeySize() != len(key) {
|
||||
return nil, errors.InvalidArgumentError("SymmetricallyEncrypted.Serialize: bad key length")
|
||||
}
|
||||
writeCloser := noOpCloser{w}
|
||||
ciphertext, err := serializeStreamHeader(writeCloser, packetTypeSymmetricallyEncryptedMDC)
|
||||
if err != nil {
|
||||
return
|
||||
func serializeSymmetricallyEncryptedMdc(ciphertext io.WriteCloser, c CipherFunction, key []byte, config *Config) (Contents io.WriteCloser, err error) {
|
||||
// Disallow old cipher suites
|
||||
if !c.IsSupported() || c < CipherAES128 {
|
||||
return nil, errors.InvalidArgumentError("invalid mdc cipher function")
|
||||
}
|
||||
|
||||
_, err = ciphertext.Write([]byte{symmetricallyEncryptedVersion})
|
||||
if c.KeySize() != len(key) {
|
||||
return nil, errors.InvalidArgumentError("error in mdc serialization: bad key length")
|
||||
}
|
||||
|
||||
_, err = ciphertext.Write([]byte{symmetricallyEncryptedVersionMdc})
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
|
@ -285,6 +251,6 @@ func SerializeSymmetricallyEncrypted(w io.Writer, c CipherFunction, key []byte,
|
|||
h := sha1.New()
|
||||
h.Write(iv)
|
||||
h.Write(iv[blockSize-2:])
|
||||
contents = &seMDCWriter{w: plaintext, h: h}
|
||||
Contents = &seMDCWriter{w: plaintext, h: h}
|
||||
return
|
||||
}
|
||||
|
|
@ -9,6 +9,7 @@ import (
|
|||
"image"
|
||||
"image/jpeg"
|
||||
"io"
|
||||
"io/ioutil"
|
||||
)
|
||||
|
||||
const UserAttrImageSubpacket = 1
|
||||
|
|
@ -41,9 +42,16 @@ func NewUserAttributePhoto(photos ...image.Image) (uat *UserAttribute, err error
|
|||
if err = jpeg.Encode(&buf, photo, nil); err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
lengthBuf := make([]byte, 5)
|
||||
n := serializeSubpacketLength(lengthBuf, len(buf.Bytes())+1)
|
||||
lengthBuf = lengthBuf[:n]
|
||||
|
||||
uat.Contents = append(uat.Contents, &OpaqueSubpacket{
|
||||
SubType: UserAttrImageSubpacket,
|
||||
Contents: buf.Bytes()})
|
||||
SubType: UserAttrImageSubpacket,
|
||||
EncodedLength: lengthBuf,
|
||||
Contents: buf.Bytes(),
|
||||
})
|
||||
}
|
||||
return
|
||||
}
|
||||
|
|
@ -55,7 +63,7 @@ func NewUserAttribute(contents ...*OpaqueSubpacket) *UserAttribute {
|
|||
|
||||
func (uat *UserAttribute) parse(r io.Reader) (err error) {
|
||||
// RFC 4880, section 5.13
|
||||
b, err := io.ReadAll(r)
|
||||
b, err := ioutil.ReadAll(r)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
|
@ -68,7 +76,10 @@ func (uat *UserAttribute) parse(r io.Reader) (err error) {
|
|||
func (uat *UserAttribute) Serialize(w io.Writer) (err error) {
|
||||
var buf bytes.Buffer
|
||||
for _, sp := range uat.Contents {
|
||||
sp.Serialize(&buf)
|
||||
err = sp.Serialize(&buf)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
}
|
||||
if err = serializeHeader(w, packetTypeUserAttribute, buf.Len()); err != nil {
|
||||
return err
|
||||
|
|
@ -6,6 +6,7 @@ package packet
|
|||
|
||||
import (
|
||||
"io"
|
||||
"io/ioutil"
|
||||
"strings"
|
||||
)
|
||||
|
||||
|
|
@ -65,7 +66,7 @@ func NewUserId(name, comment, email string) *UserId {
|
|||
|
||||
func (uid *UserId) parse(r io.Reader) (err error) {
|
||||
// RFC 4880, section 5.11
|
||||
b, err := io.ReadAll(r)
|
||||
b, err := ioutil.ReadAll(r)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
|
@ -155,5 +156,12 @@ func parseUserId(id string) (name, comment, email string) {
|
|||
name = strings.TrimSpace(id[n.start:n.end])
|
||||
comment = strings.TrimSpace(id[c.start:c.end])
|
||||
email = strings.TrimSpace(id[e.start:e.end])
|
||||
|
||||
// RFC 2822 3.4: alternate simple form of a mailbox
|
||||
if email == "" && strings.ContainsRune(name, '@') {
|
||||
email = name
|
||||
name = ""
|
||||
}
|
||||
|
||||
return
|
||||
}
|
||||
|
|
@ -3,24 +3,21 @@
|
|||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package openpgp implements high level operations on OpenPGP messages.
|
||||
//
|
||||
// Deprecated: this package is unmaintained except for security fixes. New
|
||||
// applications should consider a more focused, modern alternative to OpenPGP
|
||||
// for their specific task. If you are required to interoperate with OpenPGP
|
||||
// systems and need a maintained package, consider a community fork.
|
||||
// See https://golang.org/issue/44226.
|
||||
package openpgp // import "golang.org/x/crypto/openpgp"
|
||||
package openpgp // import "github.com/ProtonMail/go-crypto/openpgp"
|
||||
|
||||
import (
|
||||
"crypto"
|
||||
_ "crypto/sha256"
|
||||
_ "crypto/sha512"
|
||||
"hash"
|
||||
"io"
|
||||
"strconv"
|
||||
|
||||
"golang.org/x/crypto/openpgp/armor"
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"golang.org/x/crypto/openpgp/packet"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/armor"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/algorithm"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/packet"
|
||||
_ "golang.org/x/crypto/sha3"
|
||||
)
|
||||
|
||||
// SignatureType is the armor type for a PGP signature.
|
||||
|
|
@ -62,9 +59,9 @@ type MessageDetails struct {
|
|||
// been consumed. Once EOF has been seen, the following fields are
|
||||
// valid. (An authentication code failure is reported as a
|
||||
// SignatureError error when reading from UnverifiedBody.)
|
||||
SignatureError error // nil if the signature is good.
|
||||
Signature *packet.Signature // the signature packet itself, if v4 (default)
|
||||
SignatureV3 *packet.SignatureV3 // the signature packet if it is a v2 or v3 signature
|
||||
Signature *packet.Signature // the signature packet itself.
|
||||
SignatureError error // nil if the signature is good.
|
||||
UnverifiedSignatures []*packet.Signature // all other unverified signature packets.
|
||||
|
||||
decrypted io.ReadCloser
|
||||
}
|
||||
|
|
@ -94,7 +91,8 @@ func ReadMessage(r io.Reader, keyring KeyRing, prompt PromptFunction, config *pa
|
|||
|
||||
var symKeys []*packet.SymmetricKeyEncrypted
|
||||
var pubKeys []keyEnvelopePair
|
||||
var se *packet.SymmetricallyEncrypted
|
||||
// Integrity protected encrypted packet: SymmetricallyEncrypted or AEADEncrypted
|
||||
var edp packet.EncryptedDataPacket
|
||||
|
||||
packets := packet.NewReader(r)
|
||||
md = new(MessageDetails)
|
||||
|
|
@ -119,22 +117,30 @@ ParsePackets:
|
|||
// This packet contains the decryption key encrypted to a public key.
|
||||
md.EncryptedToKeyIds = append(md.EncryptedToKeyIds, p.KeyId)
|
||||
switch p.Algo {
|
||||
case packet.PubKeyAlgoRSA, packet.PubKeyAlgoRSAEncryptOnly, packet.PubKeyAlgoElGamal:
|
||||
case packet.PubKeyAlgoRSA, packet.PubKeyAlgoRSAEncryptOnly, packet.PubKeyAlgoElGamal, packet.PubKeyAlgoECDH:
|
||||
break
|
||||
default:
|
||||
continue
|
||||
}
|
||||
var keys []Key
|
||||
if p.KeyId == 0 {
|
||||
keys = keyring.DecryptionKeys()
|
||||
} else {
|
||||
keys = keyring.KeysById(p.KeyId)
|
||||
}
|
||||
for _, k := range keys {
|
||||
pubKeys = append(pubKeys, keyEnvelopePair{k, p})
|
||||
if keyring != nil {
|
||||
var keys []Key
|
||||
if p.KeyId == 0 {
|
||||
keys = keyring.DecryptionKeys()
|
||||
} else {
|
||||
keys = keyring.KeysById(p.KeyId)
|
||||
}
|
||||
for _, k := range keys {
|
||||
pubKeys = append(pubKeys, keyEnvelopePair{k, p})
|
||||
}
|
||||
}
|
||||
case *packet.SymmetricallyEncrypted:
|
||||
se = p
|
||||
if !p.IntegrityProtected && !config.AllowUnauthenticatedMessages() {
|
||||
return nil, errors.UnsupportedError("message is not integrity protected")
|
||||
}
|
||||
edp = p
|
||||
break ParsePackets
|
||||
case *packet.AEADEncrypted:
|
||||
edp = p
|
||||
break ParsePackets
|
||||
case *packet.Compressed, *packet.LiteralData, *packet.OnePassSignature:
|
||||
// This message isn't encrypted.
|
||||
|
|
@ -142,7 +148,7 @@ ParsePackets:
|
|||
return nil, errors.StructuralError("key material not followed by encrypted message")
|
||||
}
|
||||
packets.Unread(p)
|
||||
return readSignedMessage(packets, nil, keyring)
|
||||
return readSignedMessage(packets, nil, keyring, config)
|
||||
}
|
||||
}
|
||||
|
||||
|
|
@ -164,12 +170,13 @@ FindKey:
|
|||
}
|
||||
if !pk.key.PrivateKey.Encrypted {
|
||||
if len(pk.encryptedKey.Key) == 0 {
|
||||
pk.encryptedKey.Decrypt(pk.key.PrivateKey, config)
|
||||
errDec := pk.encryptedKey.Decrypt(pk.key.PrivateKey, config)
|
||||
if errDec != nil {
|
||||
continue
|
||||
}
|
||||
}
|
||||
if len(pk.encryptedKey.Key) == 0 {
|
||||
continue
|
||||
}
|
||||
decrypted, err = se.Decrypt(pk.encryptedKey.CipherFunc, pk.encryptedKey.Key)
|
||||
// Try to decrypt symmetrically encrypted
|
||||
decrypted, err = edp.Decrypt(pk.encryptedKey.CipherFunc, pk.encryptedKey.Key)
|
||||
if err != nil && err != errors.ErrKeyIncorrect {
|
||||
return nil, err
|
||||
}
|
||||
|
|
@ -204,16 +211,17 @@ FindKey:
|
|||
if len(symKeys) != 0 && passphrase != nil {
|
||||
for _, s := range symKeys {
|
||||
key, cipherFunc, err := s.Decrypt(passphrase)
|
||||
// In v4, on wrong passphrase, session key decryption is very likely to result in an invalid cipherFunc:
|
||||
// only for < 5% of cases we will proceed to decrypt the data
|
||||
if err == nil {
|
||||
decrypted, err = se.Decrypt(cipherFunc, key)
|
||||
if err != nil && err != errors.ErrKeyIncorrect {
|
||||
decrypted, err = edp.Decrypt(cipherFunc, key)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
if decrypted != nil {
|
||||
break FindKey
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
@ -222,13 +230,17 @@ FindKey:
|
|||
if err := packets.Push(decrypted); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
return readSignedMessage(packets, md, keyring)
|
||||
mdFinal, sensitiveParsingErr := readSignedMessage(packets, md, keyring, config)
|
||||
if sensitiveParsingErr != nil {
|
||||
return nil, errors.StructuralError("parsing error")
|
||||
}
|
||||
return mdFinal, nil
|
||||
}
|
||||
|
||||
// readSignedMessage reads a possibly signed message if mdin is non-zero then
|
||||
// that structure is updated and returned. Otherwise a fresh MessageDetails is
|
||||
// used.
|
||||
func readSignedMessage(packets *packet.Reader, mdin *MessageDetails, keyring KeyRing) (md *MessageDetails, err error) {
|
||||
func readSignedMessage(packets *packet.Reader, mdin *MessageDetails, keyring KeyRing, config *packet.Config) (md *MessageDetails, err error) {
|
||||
if mdin == nil {
|
||||
mdin = new(MessageDetails)
|
||||
}
|
||||
|
|
@ -237,6 +249,7 @@ func readSignedMessage(packets *packet.Reader, mdin *MessageDetails, keyring Key
|
|||
var p packet.Packet
|
||||
var h hash.Hash
|
||||
var wrappedHash hash.Hash
|
||||
var prevLast bool
|
||||
FindLiteralData:
|
||||
for {
|
||||
p, err = packets.Next()
|
||||
|
|
@ -249,21 +262,26 @@ FindLiteralData:
|
|||
return nil, err
|
||||
}
|
||||
case *packet.OnePassSignature:
|
||||
if !p.IsLast {
|
||||
return nil, errors.UnsupportedError("nested signatures")
|
||||
if prevLast {
|
||||
return nil, errors.UnsupportedError("nested signature packets")
|
||||
}
|
||||
|
||||
if p.IsLast {
|
||||
prevLast = true
|
||||
}
|
||||
|
||||
h, wrappedHash, err = hashForSignature(p.Hash, p.SigType)
|
||||
if err != nil {
|
||||
md = nil
|
||||
return
|
||||
md.SignatureError = err
|
||||
}
|
||||
|
||||
md.IsSigned = true
|
||||
md.SignedByKeyId = p.KeyId
|
||||
keys := keyring.KeysByIdUsage(p.KeyId, packet.KeyFlagSign)
|
||||
if len(keys) > 0 {
|
||||
md.SignedBy = &keys[0]
|
||||
if keyring != nil {
|
||||
keys := keyring.KeysByIdUsage(p.KeyId, packet.KeyFlagSign)
|
||||
if len(keys) > 0 {
|
||||
md.SignedBy = &keys[0]
|
||||
}
|
||||
}
|
||||
case *packet.LiteralData:
|
||||
md.LiteralData = p
|
||||
|
|
@ -271,8 +289,8 @@ FindLiteralData:
|
|||
}
|
||||
}
|
||||
|
||||
if md.SignedBy != nil {
|
||||
md.UnverifiedBody = &signatureCheckReader{packets, h, wrappedHash, md}
|
||||
if md.IsSigned && md.SignatureError == nil {
|
||||
md.UnverifiedBody = &signatureCheckReader{packets, h, wrappedHash, md, config}
|
||||
} else if md.decrypted != nil {
|
||||
md.UnverifiedBody = checkReader{md}
|
||||
} else {
|
||||
|
|
@ -287,11 +305,14 @@ FindLiteralData:
|
|||
// should be preprocessed (i.e. to normalize line endings). Thus this function
|
||||
// returns two hashes. The second should be used to hash the message itself and
|
||||
// performs any needed preprocessing.
|
||||
func hashForSignature(hashId crypto.Hash, sigType packet.SignatureType) (hash.Hash, hash.Hash, error) {
|
||||
if !hashId.Available() {
|
||||
return nil, nil, errors.UnsupportedError("hash not available: " + strconv.Itoa(int(hashId)))
|
||||
func hashForSignature(hashFunc crypto.Hash, sigType packet.SignatureType) (hash.Hash, hash.Hash, error) {
|
||||
if _, ok := algorithm.HashToHashIdWithSha1(hashFunc); !ok {
|
||||
return nil, nil, errors.UnsupportedError("unsupported hash function")
|
||||
}
|
||||
h := hashId.New()
|
||||
if !hashFunc.Available() {
|
||||
return nil, nil, errors.UnsupportedError("hash not available: " + strconv.Itoa(int(hashFunc)))
|
||||
}
|
||||
h := hashFunc.New()
|
||||
|
||||
switch sigType {
|
||||
case packet.SigTypeBinary:
|
||||
|
|
@ -310,15 +331,21 @@ type checkReader struct {
|
|||
md *MessageDetails
|
||||
}
|
||||
|
||||
func (cr checkReader) Read(buf []byte) (n int, err error) {
|
||||
n, err = cr.md.LiteralData.Body.Read(buf)
|
||||
if err == io.EOF {
|
||||
func (cr checkReader) Read(buf []byte) (int, error) {
|
||||
n, sensitiveParsingError := cr.md.LiteralData.Body.Read(buf)
|
||||
if sensitiveParsingError == io.EOF {
|
||||
mdcErr := cr.md.decrypted.Close()
|
||||
if mdcErr != nil {
|
||||
err = mdcErr
|
||||
return n, mdcErr
|
||||
}
|
||||
return n, io.EOF
|
||||
}
|
||||
return
|
||||
|
||||
if sensitiveParsingError != nil {
|
||||
return n, errors.StructuralError("parsing error")
|
||||
}
|
||||
|
||||
return n, nil
|
||||
}
|
||||
|
||||
// signatureCheckReader wraps an io.Reader from a LiteralData packet and hashes
|
||||
|
|
@ -328,26 +355,53 @@ type signatureCheckReader struct {
|
|||
packets *packet.Reader
|
||||
h, wrappedHash hash.Hash
|
||||
md *MessageDetails
|
||||
config *packet.Config
|
||||
}
|
||||
|
||||
func (scr *signatureCheckReader) Read(buf []byte) (n int, err error) {
|
||||
n, err = scr.md.LiteralData.Body.Read(buf)
|
||||
scr.wrappedHash.Write(buf[:n])
|
||||
if err == io.EOF {
|
||||
func (scr *signatureCheckReader) Read(buf []byte) (int, error) {
|
||||
n, sensitiveParsingError := scr.md.LiteralData.Body.Read(buf)
|
||||
|
||||
// Hash only if required
|
||||
if scr.md.SignedBy != nil {
|
||||
scr.wrappedHash.Write(buf[:n])
|
||||
}
|
||||
|
||||
if sensitiveParsingError == io.EOF {
|
||||
var p packet.Packet
|
||||
p, scr.md.SignatureError = scr.packets.Next()
|
||||
if scr.md.SignatureError != nil {
|
||||
return
|
||||
var readError error
|
||||
var sig *packet.Signature
|
||||
|
||||
p, readError = scr.packets.Next()
|
||||
for readError == nil {
|
||||
var ok bool
|
||||
if sig, ok = p.(*packet.Signature); ok {
|
||||
if sig.Version == 5 && (sig.SigType == 0x00 || sig.SigType == 0x01) {
|
||||
sig.Metadata = scr.md.LiteralData
|
||||
}
|
||||
|
||||
// If signature KeyID matches
|
||||
if scr.md.SignedBy != nil && *sig.IssuerKeyId == scr.md.SignedByKeyId {
|
||||
key := scr.md.SignedBy
|
||||
signatureError := key.PublicKey.VerifySignature(scr.h, sig)
|
||||
if signatureError == nil {
|
||||
signatureError = checkSignatureDetails(key, sig, scr.config)
|
||||
}
|
||||
scr.md.Signature = sig
|
||||
scr.md.SignatureError = signatureError
|
||||
} else {
|
||||
scr.md.UnverifiedSignatures = append(scr.md.UnverifiedSignatures, sig)
|
||||
}
|
||||
}
|
||||
|
||||
p, readError = scr.packets.Next()
|
||||
}
|
||||
|
||||
var ok bool
|
||||
if scr.md.Signature, ok = p.(*packet.Signature); ok {
|
||||
scr.md.SignatureError = scr.md.SignedBy.PublicKey.VerifySignature(scr.h, scr.md.Signature)
|
||||
} else if scr.md.SignatureV3, ok = p.(*packet.SignatureV3); ok {
|
||||
scr.md.SignatureError = scr.md.SignedBy.PublicKey.VerifySignatureV3(scr.h, scr.md.SignatureV3)
|
||||
} else {
|
||||
scr.md.SignatureError = errors.StructuralError("LiteralData not followed by Signature")
|
||||
return
|
||||
if scr.md.SignedBy != nil && scr.md.Signature == nil {
|
||||
if scr.md.UnverifiedSignatures == nil {
|
||||
scr.md.SignatureError = errors.StructuralError("LiteralData not followed by signature")
|
||||
} else {
|
||||
scr.md.SignatureError = errors.StructuralError("No matching signature found")
|
||||
}
|
||||
}
|
||||
|
||||
// The SymmetricallyEncrypted packet, if any, might have an
|
||||
|
|
@ -356,47 +410,87 @@ func (scr *signatureCheckReader) Read(buf []byte) (n int, err error) {
|
|||
if scr.md.decrypted != nil {
|
||||
mdcErr := scr.md.decrypted.Close()
|
||||
if mdcErr != nil {
|
||||
err = mdcErr
|
||||
return n, mdcErr
|
||||
}
|
||||
}
|
||||
return n, io.EOF
|
||||
}
|
||||
return
|
||||
|
||||
if sensitiveParsingError != nil {
|
||||
return n, errors.StructuralError("parsing error")
|
||||
}
|
||||
|
||||
return n, nil
|
||||
}
|
||||
|
||||
// VerifyDetachedSignature takes a signed file and a detached signature and
|
||||
// returns the signature packet and the entity the signature was signed by,
|
||||
// if any, and a possible signature verification error.
|
||||
// If the signer isn't known, ErrUnknownIssuer is returned.
|
||||
func VerifyDetachedSignature(keyring KeyRing, signed, signature io.Reader, config *packet.Config) (sig *packet.Signature, signer *Entity, err error) {
|
||||
var expectedHashes []crypto.Hash
|
||||
return verifyDetachedSignature(keyring, signed, signature, expectedHashes, config)
|
||||
}
|
||||
|
||||
// VerifyDetachedSignatureAndHash performs the same actions as
|
||||
// VerifyDetachedSignature and checks that the expected hash functions were used.
|
||||
func VerifyDetachedSignatureAndHash(keyring KeyRing, signed, signature io.Reader, expectedHashes []crypto.Hash, config *packet.Config) (sig *packet.Signature, signer *Entity, err error) {
|
||||
return verifyDetachedSignature(keyring, signed, signature, expectedHashes, config)
|
||||
}
|
||||
|
||||
// CheckDetachedSignature takes a signed file and a detached signature and
|
||||
// returns the signer if the signature is valid. If the signer isn't known,
|
||||
// returns the entity the signature was signed by, if any, and a possible
|
||||
// signature verification error. If the signer isn't known,
|
||||
// ErrUnknownIssuer is returned.
|
||||
func CheckDetachedSignature(keyring KeyRing, signed, signature io.Reader) (signer *Entity, err error) {
|
||||
func CheckDetachedSignature(keyring KeyRing, signed, signature io.Reader, config *packet.Config) (signer *Entity, err error) {
|
||||
var expectedHashes []crypto.Hash
|
||||
return CheckDetachedSignatureAndHash(keyring, signed, signature, expectedHashes, config)
|
||||
}
|
||||
|
||||
// CheckDetachedSignatureAndHash performs the same actions as
|
||||
// CheckDetachedSignature and checks that the expected hash functions were used.
|
||||
func CheckDetachedSignatureAndHash(keyring KeyRing, signed, signature io.Reader, expectedHashes []crypto.Hash, config *packet.Config) (signer *Entity, err error) {
|
||||
_, signer, err = verifyDetachedSignature(keyring, signed, signature, expectedHashes, config)
|
||||
return
|
||||
}
|
||||
|
||||
func verifyDetachedSignature(keyring KeyRing, signed, signature io.Reader, expectedHashes []crypto.Hash, config *packet.Config) (sig *packet.Signature, signer *Entity, err error) {
|
||||
var issuerKeyId uint64
|
||||
var hashFunc crypto.Hash
|
||||
var sigType packet.SignatureType
|
||||
var keys []Key
|
||||
var p packet.Packet
|
||||
|
||||
expectedHashesLen := len(expectedHashes)
|
||||
packets := packet.NewReader(signature)
|
||||
for {
|
||||
p, err = packets.Next()
|
||||
if err == io.EOF {
|
||||
return nil, errors.ErrUnknownIssuer
|
||||
return nil, nil, errors.ErrUnknownIssuer
|
||||
}
|
||||
if err != nil {
|
||||
return nil, err
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
switch sig := p.(type) {
|
||||
case *packet.Signature:
|
||||
if sig.IssuerKeyId == nil {
|
||||
return nil, errors.StructuralError("signature doesn't have an issuer")
|
||||
var ok bool
|
||||
sig, ok = p.(*packet.Signature)
|
||||
if !ok {
|
||||
return nil, nil, errors.StructuralError("non signature packet found")
|
||||
}
|
||||
if sig.IssuerKeyId == nil {
|
||||
return nil, nil, errors.StructuralError("signature doesn't have an issuer")
|
||||
}
|
||||
issuerKeyId = *sig.IssuerKeyId
|
||||
hashFunc = sig.Hash
|
||||
sigType = sig.SigType
|
||||
|
||||
for i, expectedHash := range expectedHashes {
|
||||
if hashFunc == expectedHash {
|
||||
break
|
||||
}
|
||||
if i+1 == expectedHashesLen {
|
||||
return nil, nil, errors.StructuralError("hash algorithm mismatch with cleartext message headers")
|
||||
}
|
||||
issuerKeyId = *sig.IssuerKeyId
|
||||
hashFunc = sig.Hash
|
||||
sigType = sig.SigType
|
||||
case *packet.SignatureV3:
|
||||
issuerKeyId = sig.IssuerKeyId
|
||||
hashFunc = sig.Hash
|
||||
sigType = sig.SigType
|
||||
default:
|
||||
return nil, errors.StructuralError("non signature packet found")
|
||||
}
|
||||
|
||||
keys = keyring.KeysByIdUsage(issuerKeyId, packet.KeyFlagSign)
|
||||
|
|
@ -411,38 +505,86 @@ func CheckDetachedSignature(keyring KeyRing, signed, signature io.Reader) (signe
|
|||
|
||||
h, wrappedHash, err := hashForSignature(hashFunc, sigType)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
if _, err := io.Copy(wrappedHash, signed); err != nil && err != io.EOF {
|
||||
return nil, err
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
for _, key := range keys {
|
||||
switch sig := p.(type) {
|
||||
case *packet.Signature:
|
||||
err = key.PublicKey.VerifySignature(h, sig)
|
||||
case *packet.SignatureV3:
|
||||
err = key.PublicKey.VerifySignatureV3(h, sig)
|
||||
default:
|
||||
panic("unreachable")
|
||||
}
|
||||
|
||||
err = key.PublicKey.VerifySignature(h, sig)
|
||||
if err == nil {
|
||||
return key.Entity, nil
|
||||
return sig, key.Entity, checkSignatureDetails(&key, sig, config)
|
||||
}
|
||||
}
|
||||
|
||||
return nil, err
|
||||
return nil, nil, err
|
||||
}
|
||||
|
||||
// CheckArmoredDetachedSignature performs the same actions as
|
||||
// CheckDetachedSignature but expects the signature to be armored.
|
||||
func CheckArmoredDetachedSignature(keyring KeyRing, signed, signature io.Reader) (signer *Entity, err error) {
|
||||
func CheckArmoredDetachedSignature(keyring KeyRing, signed, signature io.Reader, config *packet.Config) (signer *Entity, err error) {
|
||||
body, err := readArmored(signature, SignatureType)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
return CheckDetachedSignature(keyring, signed, body)
|
||||
return CheckDetachedSignature(keyring, signed, body, config)
|
||||
}
|
||||
|
||||
// checkSignatureDetails returns an error if:
|
||||
// - The signature (or one of the binding signatures mentioned below)
|
||||
// has a unknown critical notation data subpacket
|
||||
// - The primary key of the signing entity is revoked
|
||||
// The signature was signed by a subkey and:
|
||||
// - The signing subkey is revoked
|
||||
// - The primary identity is revoked
|
||||
// - The signature is expired
|
||||
// - The primary key of the signing entity is expired according to the
|
||||
// primary identity binding signature
|
||||
// The signature was signed by a subkey and:
|
||||
// - The signing subkey is expired according to the subkey binding signature
|
||||
// - The signing subkey binding signature is expired
|
||||
// - The signing subkey cross-signature is expired
|
||||
// NOTE: The order of these checks is important, as the caller may choose to
|
||||
// ignore ErrSignatureExpired or ErrKeyExpired errors, but should never
|
||||
// ignore any other errors.
|
||||
// TODO: Also return an error if:
|
||||
// - The primary key is expired according to a direct-key signature
|
||||
// - (For V5 keys only:) The direct-key signature (exists and) is expired
|
||||
func checkSignatureDetails(key *Key, signature *packet.Signature, config *packet.Config) error {
|
||||
now := config.Now()
|
||||
primaryIdentity := key.Entity.PrimaryIdentity()
|
||||
signedBySubKey := key.PublicKey != key.Entity.PrimaryKey
|
||||
sigsToCheck := []*packet.Signature{ signature, primaryIdentity.SelfSignature }
|
||||
if signedBySubKey {
|
||||
sigsToCheck = append(sigsToCheck, key.SelfSignature, key.SelfSignature.EmbeddedSignature)
|
||||
}
|
||||
for _, sig := range sigsToCheck {
|
||||
for _, notation := range sig.Notations {
|
||||
if notation.IsCritical && !config.KnownNotation(notation.Name) {
|
||||
return errors.SignatureError("unknown critical notation: " + notation.Name)
|
||||
}
|
||||
}
|
||||
}
|
||||
if key.Entity.Revoked(now) || // primary key is revoked
|
||||
(signedBySubKey && key.Revoked(now)) || // subkey is revoked
|
||||
primaryIdentity.Revoked(now) { // primary identity is revoked
|
||||
return errors.ErrKeyRevoked
|
||||
}
|
||||
if key.Entity.PrimaryKey.KeyExpired(primaryIdentity.SelfSignature, now) { // primary key is expired
|
||||
return errors.ErrKeyExpired
|
||||
}
|
||||
if signedBySubKey {
|
||||
if key.PublicKey.KeyExpired(key.SelfSignature, now) { // subkey is expired
|
||||
return errors.ErrKeyExpired
|
||||
}
|
||||
}
|
||||
for _, sig := range sigsToCheck {
|
||||
if sig.SigExpired(now) { // any of the relevant signatures are expired
|
||||
return errors.ErrSignatureExpired
|
||||
}
|
||||
}
|
||||
return nil
|
||||
}
|
||||
274
vendor/github.com/ProtonMail/go-crypto/openpgp/read_write_test_data.go
generated
vendored
Normal file
274
vendor/github.com/ProtonMail/go-crypto/openpgp/read_write_test_data.go
generated
vendored
Normal file
File diff suppressed because one or more lines are too long
|
|
@ -4,13 +4,7 @@
|
|||
|
||||
// Package s2k implements the various OpenPGP string-to-key transforms as
|
||||
// specified in RFC 4800 section 3.7.1.
|
||||
//
|
||||
// Deprecated: this package is unmaintained except for security fixes. New
|
||||
// applications should consider a more focused, modern alternative to OpenPGP
|
||||
// for their specific task. If you are required to interoperate with OpenPGP
|
||||
// systems and need a maintained package, consider a community fork.
|
||||
// See https://golang.org/issue/44226.
|
||||
package s2k // import "golang.org/x/crypto/openpgp/s2k"
|
||||
package s2k // import "github.com/ProtonMail/go-crypto/openpgp/s2k"
|
||||
|
||||
import (
|
||||
"crypto"
|
||||
|
|
@ -18,49 +12,67 @@ import (
|
|||
"io"
|
||||
"strconv"
|
||||
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/algorithm"
|
||||
)
|
||||
|
||||
// Config collects configuration parameters for s2k key-stretching
|
||||
// transformatioms. A nil *Config is valid and results in all default
|
||||
// transformations. A nil *Config is valid and results in all default
|
||||
// values. Currently, Config is used only by the Serialize function in
|
||||
// this package.
|
||||
type Config struct {
|
||||
// S2KMode is the mode of s2k function.
|
||||
// It can be 0 (simple), 1(salted), 3(iterated)
|
||||
// 2(reserved) 100-110(private/experimental).
|
||||
S2KMode uint8
|
||||
// Hash is the default hash function to be used. If
|
||||
// nil, SHA1 is used.
|
||||
// nil, SHA256 is used.
|
||||
Hash crypto.Hash
|
||||
// S2KCount is only used for symmetric encryption. It
|
||||
// determines the strength of the passphrase stretching when
|
||||
// the said passphrase is hashed to produce a key. S2KCount
|
||||
// should be between 1024 and 65011712, inclusive. If Config
|
||||
// is nil or S2KCount is 0, the value 65536 used. Not all
|
||||
// should be between 65536 and 65011712, inclusive. If Config
|
||||
// is nil or S2KCount is 0, the value 16777216 used. Not all
|
||||
// values in the above range can be represented. S2KCount will
|
||||
// be rounded up to the next representable value if it cannot
|
||||
// be encoded exactly. When set, it is strongly encrouraged to
|
||||
// use a value that is at least 65536. See RFC 4880 Section
|
||||
// 3.7.1.3.
|
||||
// be encoded exactly. See RFC 4880 Section 3.7.1.3.
|
||||
S2KCount int
|
||||
}
|
||||
|
||||
// Params contains all the parameters of the s2k packet
|
||||
type Params struct {
|
||||
// mode is the mode of s2k function.
|
||||
// It can be 0 (simple), 1(salted), 3(iterated)
|
||||
// 2(reserved) 100-110(private/experimental).
|
||||
mode uint8
|
||||
// hashId is the ID of the hash function used in any of the modes
|
||||
hashId byte
|
||||
// salt is a byte array to use as a salt in hashing process
|
||||
salt []byte
|
||||
// countByte is used to determine how many rounds of hashing are to
|
||||
// be performed in s2k mode 3. See RFC 4880 Section 3.7.1.3.
|
||||
countByte byte
|
||||
}
|
||||
|
||||
func (c *Config) hash() crypto.Hash {
|
||||
if c == nil || uint(c.Hash) == 0 {
|
||||
// SHA1 is the historical default in this package.
|
||||
return crypto.SHA1
|
||||
return crypto.SHA256
|
||||
}
|
||||
|
||||
return c.Hash
|
||||
}
|
||||
|
||||
func (c *Config) encodedCount() uint8 {
|
||||
// EncodedCount get encoded count
|
||||
func (c *Config) EncodedCount() uint8 {
|
||||
if c == nil || c.S2KCount == 0 {
|
||||
return 96 // The common case. Correspoding to 65536
|
||||
return 224 // The common case. Corresponding to 16777216
|
||||
}
|
||||
|
||||
i := c.S2KCount
|
||||
|
||||
switch {
|
||||
// Behave like GPG. Should we make 65536 the lowest value used?
|
||||
case i < 1024:
|
||||
i = 1024
|
||||
case i < 65536:
|
||||
i = 65536
|
||||
case i > 65011712:
|
||||
i = 65011712
|
||||
}
|
||||
|
|
@ -74,11 +86,11 @@ func (c *Config) encodedCount() uint8 {
|
|||
// if i is not in the above range (encodedCount above takes care to
|
||||
// pass i in the correct range). See RFC 4880 Section 3.7.7.1.
|
||||
func encodeCount(i int) uint8 {
|
||||
if i < 1024 || i > 65011712 {
|
||||
if i < 65536 || i > 65011712 {
|
||||
panic("count arg i outside the required range")
|
||||
}
|
||||
|
||||
for encoded := 0; encoded < 256; encoded++ {
|
||||
for encoded := 96; encoded < 256; encoded++ {
|
||||
count := decodeCount(uint8(encoded))
|
||||
if count >= i {
|
||||
return uint8(encoded)
|
||||
|
|
@ -157,9 +169,44 @@ func Iterated(out []byte, h hash.Hash, in []byte, salt []byte, count int) {
|
|||
}
|
||||
}
|
||||
|
||||
// Generate generates valid parameters from given configuration.
|
||||
// It will enforce salted + hashed s2k method
|
||||
func Generate(rand io.Reader, c *Config) (*Params, error) {
|
||||
hashId, ok := algorithm.HashToHashId(c.Hash)
|
||||
if !ok {
|
||||
return nil, errors.UnsupportedError("no such hash")
|
||||
}
|
||||
|
||||
params := &Params{
|
||||
mode: 3, // Enforce iterared + salted method
|
||||
hashId: hashId,
|
||||
salt: make([]byte, 8),
|
||||
countByte: c.EncodedCount(),
|
||||
}
|
||||
|
||||
if _, err := io.ReadFull(rand, params.salt); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
return params, nil
|
||||
}
|
||||
|
||||
// Parse reads a binary specification for a string-to-key transformation from r
|
||||
// and returns a function which performs that transform.
|
||||
// and returns a function which performs that transform. If the S2K is a special
|
||||
// GNU extension that indicates that the private key is missing, then the error
|
||||
// returned is errors.ErrDummyPrivateKey.
|
||||
func Parse(r io.Reader) (f func(out, in []byte), err error) {
|
||||
params, err := ParseIntoParams(r)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
return params.Function()
|
||||
}
|
||||
|
||||
// ParseIntoParams reads a binary specification for a string-to-key
|
||||
// transformation from r and returns a struct describing the s2k parameters.
|
||||
func ParseIntoParams(r io.Reader) (params *Params, err error) {
|
||||
var buf [9]byte
|
||||
|
||||
_, err = io.ReadFull(r, buf[:2])
|
||||
|
|
@ -167,113 +214,126 @@ func Parse(r io.Reader) (f func(out, in []byte), err error) {
|
|||
return
|
||||
}
|
||||
|
||||
hash, ok := HashIdToHash(buf[1])
|
||||
if !ok {
|
||||
return nil, errors.UnsupportedError("hash for S2K function: " + strconv.Itoa(int(buf[1])))
|
||||
params = &Params{
|
||||
mode: buf[0],
|
||||
hashId: buf[1],
|
||||
}
|
||||
if !hash.Available() {
|
||||
return nil, errors.UnsupportedError("hash not available: " + strconv.Itoa(int(hash)))
|
||||
}
|
||||
h := hash.New()
|
||||
|
||||
switch buf[0] {
|
||||
switch params.mode {
|
||||
case 0:
|
||||
f := func(out, in []byte) {
|
||||
Simple(out, h, in)
|
||||
}
|
||||
return f, nil
|
||||
return params, nil
|
||||
case 1:
|
||||
_, err = io.ReadFull(r, buf[:8])
|
||||
if err != nil {
|
||||
return
|
||||
return nil, err
|
||||
}
|
||||
f := func(out, in []byte) {
|
||||
Salted(out, h, in, buf[:8])
|
||||
}
|
||||
return f, nil
|
||||
|
||||
params.salt = buf[:8]
|
||||
return params, nil
|
||||
case 3:
|
||||
_, err = io.ReadFull(r, buf[:9])
|
||||
if err != nil {
|
||||
return
|
||||
return nil, err
|
||||
}
|
||||
count := decodeCount(buf[8])
|
||||
|
||||
params.salt = buf[:8]
|
||||
params.countByte = buf[8]
|
||||
return params, nil
|
||||
case 101:
|
||||
// This is a GNU extension. See
|
||||
// https://git.gnupg.org/cgi-bin/gitweb.cgi?p=gnupg.git;a=blob;f=doc/DETAILS;h=fe55ae16ab4e26d8356dc574c9e8bc935e71aef1;hb=23191d7851eae2217ecdac6484349849a24fd94a#l1109
|
||||
if _, err = io.ReadFull(r, buf[:4]); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
if buf[0] == 'G' && buf[1] == 'N' && buf[2] == 'U' && buf[3] == 1 {
|
||||
return params, nil
|
||||
}
|
||||
return nil, errors.UnsupportedError("GNU S2K extension")
|
||||
}
|
||||
|
||||
return nil, errors.UnsupportedError("S2K function")
|
||||
}
|
||||
|
||||
func (params *Params) Dummy() bool {
|
||||
return params != nil && params.mode == 101
|
||||
}
|
||||
|
||||
func (params *Params) Function() (f func(out, in []byte), err error) {
|
||||
if params.Dummy() {
|
||||
return nil, errors.ErrDummyPrivateKey("dummy key found")
|
||||
}
|
||||
hashObj, ok := algorithm.HashIdToHashWithSha1(params.hashId)
|
||||
if !ok {
|
||||
return nil, errors.UnsupportedError("hash for S2K function: " + strconv.Itoa(int(params.hashId)))
|
||||
}
|
||||
if !hashObj.Available() {
|
||||
return nil, errors.UnsupportedError("hash not available: " + strconv.Itoa(int(hashObj)))
|
||||
}
|
||||
|
||||
switch params.mode {
|
||||
case 0:
|
||||
f := func(out, in []byte) {
|
||||
Iterated(out, h, in, buf[:8], count)
|
||||
Simple(out, hashObj.New(), in)
|
||||
}
|
||||
|
||||
return f, nil
|
||||
case 1:
|
||||
f := func(out, in []byte) {
|
||||
Salted(out, hashObj.New(), in, params.salt)
|
||||
}
|
||||
|
||||
return f, nil
|
||||
case 3:
|
||||
f := func(out, in []byte) {
|
||||
Iterated(out, hashObj.New(), in, params.salt, decodeCount(params.countByte))
|
||||
}
|
||||
|
||||
return f, nil
|
||||
}
|
||||
|
||||
return nil, errors.UnsupportedError("S2K function")
|
||||
}
|
||||
|
||||
func (params *Params) Serialize(w io.Writer) (err error) {
|
||||
if _, err = w.Write([]byte{params.mode}); err != nil {
|
||||
return
|
||||
}
|
||||
if _, err = w.Write([]byte{params.hashId}); err != nil {
|
||||
return
|
||||
}
|
||||
if params.Dummy() {
|
||||
_, err = w.Write(append([]byte("GNU"), 1))
|
||||
return
|
||||
}
|
||||
if params.mode > 0 {
|
||||
if _, err = w.Write(params.salt); err != nil {
|
||||
return
|
||||
}
|
||||
if params.mode == 3 {
|
||||
_, err = w.Write([]byte{params.countByte})
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Serialize salts and stretches the given passphrase and writes the
|
||||
// resulting key into key. It also serializes an S2K descriptor to
|
||||
// w. The key stretching can be configured with c, which may be
|
||||
// nil. In that case, sensible defaults will be used.
|
||||
func Serialize(w io.Writer, key []byte, rand io.Reader, passphrase []byte, c *Config) error {
|
||||
var buf [11]byte
|
||||
buf[0] = 3 /* iterated and salted */
|
||||
buf[1], _ = HashToHashId(c.hash())
|
||||
salt := buf[2:10]
|
||||
if _, err := io.ReadFull(rand, salt); err != nil {
|
||||
params, err := Generate(rand, c)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
encodedCount := c.encodedCount()
|
||||
count := decodeCount(encodedCount)
|
||||
buf[10] = encodedCount
|
||||
if _, err := w.Write(buf[:]); err != nil {
|
||||
err = params.Serialize(w)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
Iterated(key, c.hash().New(), passphrase, salt, count)
|
||||
f, err := params.Function()
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
f(key, passphrase)
|
||||
return nil
|
||||
}
|
||||
|
||||
// hashToHashIdMapping contains pairs relating OpenPGP's hash identifier with
|
||||
// Go's crypto.Hash type. See RFC 4880, section 9.4.
|
||||
var hashToHashIdMapping = []struct {
|
||||
id byte
|
||||
hash crypto.Hash
|
||||
name string
|
||||
}{
|
||||
{1, crypto.MD5, "MD5"},
|
||||
{2, crypto.SHA1, "SHA1"},
|
||||
{3, crypto.RIPEMD160, "RIPEMD160"},
|
||||
{8, crypto.SHA256, "SHA256"},
|
||||
{9, crypto.SHA384, "SHA384"},
|
||||
{10, crypto.SHA512, "SHA512"},
|
||||
{11, crypto.SHA224, "SHA224"},
|
||||
}
|
||||
|
||||
// HashIdToHash returns a crypto.Hash which corresponds to the given OpenPGP
|
||||
// hash id.
|
||||
func HashIdToHash(id byte) (h crypto.Hash, ok bool) {
|
||||
for _, m := range hashToHashIdMapping {
|
||||
if m.id == id {
|
||||
return m.hash, true
|
||||
}
|
||||
}
|
||||
return 0, false
|
||||
}
|
||||
|
||||
// HashIdToString returns the name of the hash function corresponding to the
|
||||
// given OpenPGP hash id.
|
||||
func HashIdToString(id byte) (name string, ok bool) {
|
||||
for _, m := range hashToHashIdMapping {
|
||||
if m.id == id {
|
||||
return m.name, true
|
||||
}
|
||||
}
|
||||
|
||||
return "", false
|
||||
}
|
||||
|
||||
// HashToHashId returns an OpenPGP hash id which corresponds the given Hash.
|
||||
func HashToHashId(h crypto.Hash) (id byte, ok bool) {
|
||||
for _, m := range hashToHashIdMapping {
|
||||
if m.hash == h {
|
||||
return m.id, true
|
||||
}
|
||||
}
|
||||
return 0, false
|
||||
}
|
||||
|
|
@ -11,10 +11,10 @@ import (
|
|||
"strconv"
|
||||
"time"
|
||||
|
||||
"golang.org/x/crypto/openpgp/armor"
|
||||
"golang.org/x/crypto/openpgp/errors"
|
||||
"golang.org/x/crypto/openpgp/packet"
|
||||
"golang.org/x/crypto/openpgp/s2k"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/armor"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/errors"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/internal/algorithm"
|
||||
"github.com/ProtonMail/go-crypto/openpgp/packet"
|
||||
)
|
||||
|
||||
// DetachSign signs message with the private key from signer (which must
|
||||
|
|
@ -60,27 +60,31 @@ func armoredDetachSign(w io.Writer, signer *Entity, message io.Reader, sigType p
|
|||
}
|
||||
|
||||
func detachSign(w io.Writer, signer *Entity, message io.Reader, sigType packet.SignatureType, config *packet.Config) (err error) {
|
||||
if signer.PrivateKey == nil {
|
||||
signingKey, ok := signer.SigningKeyById(config.Now(), config.SigningKey())
|
||||
if !ok {
|
||||
return errors.InvalidArgumentError("no valid signing keys")
|
||||
}
|
||||
if signingKey.PrivateKey == nil {
|
||||
return errors.InvalidArgumentError("signing key doesn't have a private key")
|
||||
}
|
||||
if signer.PrivateKey.Encrypted {
|
||||
if signingKey.PrivateKey.Encrypted {
|
||||
return errors.InvalidArgumentError("signing key is encrypted")
|
||||
}
|
||||
if _, ok := algorithm.HashToHashId(config.Hash()); !ok {
|
||||
return errors.InvalidArgumentError("invalid hash function")
|
||||
}
|
||||
|
||||
sig := new(packet.Signature)
|
||||
sig.SigType = sigType
|
||||
sig.PubKeyAlgo = signer.PrivateKey.PubKeyAlgo
|
||||
sig.Hash = config.Hash()
|
||||
sig.CreationTime = config.Now()
|
||||
sig.IssuerKeyId = &signer.PrivateKey.KeyId
|
||||
sig := createSignaturePacket(signingKey.PublicKey, sigType, config)
|
||||
|
||||
h, wrappedHash, err := hashForSignature(sig.Hash, sig.SigType)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
io.Copy(wrappedHash, message)
|
||||
if _, err = io.Copy(wrappedHash, message); err != nil {
|
||||
return err
|
||||
}
|
||||
|
||||
err = sig.Sign(h, signer.PrivateKey, config)
|
||||
err = sig.Sign(h, signingKey.PrivateKey, config)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
|
@ -115,18 +119,24 @@ func SymmetricallyEncrypt(ciphertext io.Writer, passphrase []byte, hints *FileHi
|
|||
if err != nil {
|
||||
return
|
||||
}
|
||||
w, err := packet.SerializeSymmetricallyEncrypted(ciphertext, config.Cipher(), key, config)
|
||||
|
||||
var w io.WriteCloser
|
||||
cipherSuite := packet.CipherSuite{
|
||||
Cipher: config.Cipher(),
|
||||
Mode: config.AEAD().Mode(),
|
||||
}
|
||||
w, err = packet.SerializeSymmetricallyEncrypted(ciphertext, config.Cipher(), config.AEAD() != nil, cipherSuite, key, config)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
||||
literaldata := w
|
||||
literalData := w
|
||||
if algo := config.Compression(); algo != packet.CompressionNone {
|
||||
var compConfig *packet.CompressionConfig
|
||||
if config != nil {
|
||||
compConfig = config.CompressionConfig
|
||||
}
|
||||
literaldata, err = packet.SerializeCompressed(w, algo, compConfig)
|
||||
literalData, err = packet.SerializeCompressed(w, algo, compConfig)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
|
|
@ -136,7 +146,7 @@ func SymmetricallyEncrypt(ciphertext io.Writer, passphrase []byte, hints *FileHi
|
|||
if !hints.ModTime.IsZero() {
|
||||
epochSeconds = uint32(hints.ModTime.Unix())
|
||||
}
|
||||
return packet.SerializeLiteral(literaldata, hints.IsBinary, hints.FileName, epochSeconds)
|
||||
return packet.SerializeLiteral(literalData, hints.IsBinary, hints.FileName, epochSeconds)
|
||||
}
|
||||
|
||||
// intersectPreferences mutates and returns a prefix of a that contains only
|
||||
|
|
@ -156,23 +166,76 @@ func intersectPreferences(a []uint8, b []uint8) (intersection []uint8) {
|
|||
return a[:j]
|
||||
}
|
||||
|
||||
// intersectPreferences mutates and returns a prefix of a that contains only
|
||||
// the values in the intersection of a and b. The order of a is preserved.
|
||||
func intersectCipherSuites(a [][2]uint8, b [][2]uint8) (intersection [][2]uint8) {
|
||||
var j int
|
||||
for _, v := range a {
|
||||
for _, v2 := range b {
|
||||
if v[0] == v2[0] && v[1] == v2[1] {
|
||||
a[j] = v
|
||||
j++
|
||||
break
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return a[:j]
|
||||
}
|
||||
|
||||
func hashToHashId(h crypto.Hash) uint8 {
|
||||
v, ok := s2k.HashToHashId(h)
|
||||
v, ok := algorithm.HashToHashId(h)
|
||||
if !ok {
|
||||
panic("tried to convert unknown hash")
|
||||
}
|
||||
return v
|
||||
}
|
||||
|
||||
// EncryptText encrypts a message to a number of recipients and, optionally,
|
||||
// signs it. Optional information is contained in 'hints', also encrypted, that
|
||||
// aids the recipients in processing the message. The resulting WriteCloser
|
||||
// must be closed after the contents of the file have been written. If config
|
||||
// is nil, sensible defaults will be used. The signing is done in text mode.
|
||||
func EncryptText(ciphertext io.Writer, to []*Entity, signed *Entity, hints *FileHints, config *packet.Config) (plaintext io.WriteCloser, err error) {
|
||||
return encrypt(ciphertext, ciphertext, to, signed, hints, packet.SigTypeText, config)
|
||||
}
|
||||
|
||||
// Encrypt encrypts a message to a number of recipients and, optionally, signs
|
||||
// it. hints contains optional information, that is also encrypted, that aids
|
||||
// the recipients in processing the message. The resulting WriteCloser must
|
||||
// be closed after the contents of the file have been written.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func Encrypt(ciphertext io.Writer, to []*Entity, signed *Entity, hints *FileHints, config *packet.Config) (plaintext io.WriteCloser, err error) {
|
||||
return encrypt(ciphertext, ciphertext, to, signed, hints, packet.SigTypeBinary, config)
|
||||
}
|
||||
|
||||
// EncryptSplit encrypts a message to a number of recipients and, optionally, signs
|
||||
// it. hints contains optional information, that is also encrypted, that aids
|
||||
// the recipients in processing the message. The resulting WriteCloser must
|
||||
// be closed after the contents of the file have been written.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func EncryptSplit(keyWriter io.Writer, dataWriter io.Writer, to []*Entity, signed *Entity, hints *FileHints, config *packet.Config) (plaintext io.WriteCloser, err error) {
|
||||
return encrypt(keyWriter, dataWriter, to, signed, hints, packet.SigTypeBinary, config)
|
||||
}
|
||||
|
||||
// EncryptTextSplit encrypts a message to a number of recipients and, optionally, signs
|
||||
// it. hints contains optional information, that is also encrypted, that aids
|
||||
// the recipients in processing the message. The resulting WriteCloser must
|
||||
// be closed after the contents of the file have been written.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func EncryptTextSplit(keyWriter io.Writer, dataWriter io.Writer, to []*Entity, signed *Entity, hints *FileHints, config *packet.Config) (plaintext io.WriteCloser, err error) {
|
||||
return encrypt(keyWriter, dataWriter, to, signed, hints, packet.SigTypeText, config)
|
||||
}
|
||||
|
||||
// writeAndSign writes the data as a payload package and, optionally, signs
|
||||
// it. hints contains optional information, that is also encrypted,
|
||||
// that aids the recipients in processing the message. The resulting
|
||||
// WriteCloser must be closed after the contents of the file have been
|
||||
// written. If config is nil, sensible defaults will be used.
|
||||
func writeAndSign(payload io.WriteCloser, candidateHashes []uint8, signed *Entity, hints *FileHints, config *packet.Config) (plaintext io.WriteCloser, err error) {
|
||||
func writeAndSign(payload io.WriteCloser, candidateHashes []uint8, signed *Entity, hints *FileHints, sigType packet.SignatureType, config *packet.Config) (plaintext io.WriteCloser, err error) {
|
||||
var signer *packet.PrivateKey
|
||||
if signed != nil {
|
||||
signKey, ok := signed.signingKey(config.Now())
|
||||
signKey, ok := signed.SigningKeyById(config.Now(), config.SigningKey())
|
||||
if !ok {
|
||||
return nil, errors.InvalidArgumentError("no valid signing keys")
|
||||
}
|
||||
|
|
@ -187,7 +250,7 @@ func writeAndSign(payload io.WriteCloser, candidateHashes []uint8, signed *Entit
|
|||
|
||||
var hash crypto.Hash
|
||||
for _, hashId := range candidateHashes {
|
||||
if h, ok := s2k.HashIdToHash(hashId); ok && h.Available() {
|
||||
if h, ok := algorithm.HashIdToHash(hashId); ok && h.Available() {
|
||||
hash = h
|
||||
break
|
||||
}
|
||||
|
|
@ -196,7 +259,7 @@ func writeAndSign(payload io.WriteCloser, candidateHashes []uint8, signed *Entit
|
|||
// If the hash specified by config is a candidate, we'll use that.
|
||||
if configuredHash := config.Hash(); configuredHash.Available() {
|
||||
for _, hashId := range candidateHashes {
|
||||
if h, ok := s2k.HashIdToHash(hashId); ok && h == configuredHash {
|
||||
if h, ok := algorithm.HashIdToHash(hashId); ok && h == configuredHash {
|
||||
hash = h
|
||||
break
|
||||
}
|
||||
|
|
@ -205,7 +268,7 @@ func writeAndSign(payload io.WriteCloser, candidateHashes []uint8, signed *Entit
|
|||
|
||||
if hash == 0 {
|
||||
hashId := candidateHashes[0]
|
||||
name, ok := s2k.HashIdToString(hashId)
|
||||
name, ok := algorithm.HashIdToString(hashId)
|
||||
if !ok {
|
||||
name = "#" + strconv.Itoa(int(hashId))
|
||||
}
|
||||
|
|
@ -214,7 +277,7 @@ func writeAndSign(payload io.WriteCloser, candidateHashes []uint8, signed *Entit
|
|||
|
||||
if signer != nil {
|
||||
ops := &packet.OnePassSignature{
|
||||
SigType: packet.SigTypeBinary,
|
||||
SigType: sigType,
|
||||
Hash: hash,
|
||||
PubKeyAlgo: signer.PubKeyAlgo,
|
||||
KeyId: signer.KeyId,
|
||||
|
|
@ -247,68 +310,108 @@ func writeAndSign(payload io.WriteCloser, candidateHashes []uint8, signed *Entit
|
|||
}
|
||||
|
||||
if signer != nil {
|
||||
return signatureWriter{payload, literalData, hash, hash.New(), signer, config}, nil
|
||||
h, wrappedHash, err := hashForSignature(hash, sigType)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
metadata := &packet.LiteralData{
|
||||
Format: 't',
|
||||
FileName: hints.FileName,
|
||||
Time: epochSeconds,
|
||||
}
|
||||
if hints.IsBinary {
|
||||
metadata.Format = 'b'
|
||||
}
|
||||
return signatureWriter{payload, literalData, hash, wrappedHash, h, signer, sigType, config, metadata}, nil
|
||||
}
|
||||
return literalData, nil
|
||||
}
|
||||
|
||||
// Encrypt encrypts a message to a number of recipients and, optionally, signs
|
||||
// encrypt encrypts a message to a number of recipients and, optionally, signs
|
||||
// it. hints contains optional information, that is also encrypted, that aids
|
||||
// the recipients in processing the message. The resulting WriteCloser must
|
||||
// be closed after the contents of the file have been written.
|
||||
// If config is nil, sensible defaults will be used.
|
||||
func Encrypt(ciphertext io.Writer, to []*Entity, signed *Entity, hints *FileHints, config *packet.Config) (plaintext io.WriteCloser, err error) {
|
||||
func encrypt(keyWriter io.Writer, dataWriter io.Writer, to []*Entity, signed *Entity, hints *FileHints, sigType packet.SignatureType, config *packet.Config) (plaintext io.WriteCloser, err error) {
|
||||
if len(to) == 0 {
|
||||
return nil, errors.InvalidArgumentError("no encryption recipient provided")
|
||||
}
|
||||
|
||||
// These are the possible ciphers that we'll use for the message.
|
||||
candidateCiphers := []uint8{
|
||||
uint8(packet.CipherAES128),
|
||||
uint8(packet.CipherAES256),
|
||||
uint8(packet.CipherCAST5),
|
||||
uint8(packet.CipherAES128),
|
||||
}
|
||||
|
||||
// These are the possible hash functions that we'll use for the signature.
|
||||
candidateHashes := []uint8{
|
||||
hashToHashId(crypto.SHA256),
|
||||
hashToHashId(crypto.SHA384),
|
||||
hashToHashId(crypto.SHA512),
|
||||
hashToHashId(crypto.SHA1),
|
||||
hashToHashId(crypto.RIPEMD160),
|
||||
hashToHashId(crypto.SHA3_256),
|
||||
hashToHashId(crypto.SHA3_512),
|
||||
}
|
||||
|
||||
// Prefer GCM if everyone supports it
|
||||
candidateCipherSuites := [][2]uint8{
|
||||
{uint8(packet.CipherAES256), uint8(packet.AEADModeGCM)},
|
||||
{uint8(packet.CipherAES256), uint8(packet.AEADModeEAX)},
|
||||
{uint8(packet.CipherAES256), uint8(packet.AEADModeOCB)},
|
||||
{uint8(packet.CipherAES128), uint8(packet.AEADModeGCM)},
|
||||
{uint8(packet.CipherAES128), uint8(packet.AEADModeEAX)},
|
||||
{uint8(packet.CipherAES128), uint8(packet.AEADModeOCB)},
|
||||
}
|
||||
|
||||
candidateCompression := []uint8{
|
||||
uint8(packet.CompressionNone),
|
||||
uint8(packet.CompressionZIP),
|
||||
uint8(packet.CompressionZLIB),
|
||||
}
|
||||
// In the event that a recipient doesn't specify any supported ciphers
|
||||
// or hash functions, these are the ones that we assume that every
|
||||
// implementation supports.
|
||||
defaultCiphers := candidateCiphers[len(candidateCiphers)-1:]
|
||||
defaultHashes := candidateHashes[len(candidateHashes)-1:]
|
||||
|
||||
encryptKeys := make([]Key, len(to))
|
||||
|
||||
// AEAD is used only if config enables it and every key supports it
|
||||
aeadSupported := config.AEAD() != nil
|
||||
|
||||
for i := range to {
|
||||
var ok bool
|
||||
encryptKeys[i], ok = to[i].encryptionKey(config.Now())
|
||||
encryptKeys[i], ok = to[i].EncryptionKey(config.Now())
|
||||
if !ok {
|
||||
return nil, errors.InvalidArgumentError("cannot encrypt a message to key id " + strconv.FormatUint(to[i].PrimaryKey.KeyId, 16) + " because it has no encryption keys")
|
||||
return nil, errors.InvalidArgumentError("cannot encrypt a message to key id " + strconv.FormatUint(to[i].PrimaryKey.KeyId, 16) + " because it has no valid encryption keys")
|
||||
}
|
||||
|
||||
sig := to[i].primaryIdentity().SelfSignature
|
||||
sig := to[i].PrimaryIdentity().SelfSignature
|
||||
if sig.SEIPDv2 == false {
|
||||
aeadSupported = false
|
||||
}
|
||||
|
||||
preferredSymmetric := sig.PreferredSymmetric
|
||||
if len(preferredSymmetric) == 0 {
|
||||
preferredSymmetric = defaultCiphers
|
||||
}
|
||||
preferredHashes := sig.PreferredHash
|
||||
if len(preferredHashes) == 0 {
|
||||
preferredHashes = defaultHashes
|
||||
}
|
||||
candidateCiphers = intersectPreferences(candidateCiphers, preferredSymmetric)
|
||||
candidateHashes = intersectPreferences(candidateHashes, preferredHashes)
|
||||
candidateCiphers = intersectPreferences(candidateCiphers, sig.PreferredSymmetric)
|
||||
candidateHashes = intersectPreferences(candidateHashes, sig.PreferredHash)
|
||||
candidateCipherSuites = intersectCipherSuites(candidateCipherSuites, sig.PreferredCipherSuites)
|
||||
candidateCompression = intersectPreferences(candidateCompression, sig.PreferredCompression)
|
||||
}
|
||||
|
||||
if len(candidateCiphers) == 0 || len(candidateHashes) == 0 {
|
||||
return nil, errors.InvalidArgumentError("cannot encrypt because recipient set shares no common algorithms")
|
||||
// In the event that the intersection of supported algorithms is empty we use the ones
|
||||
// labelled as MUST that every implementation supports.
|
||||
if len(candidateCiphers) == 0 {
|
||||
// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-9.3
|
||||
candidateCiphers = []uint8{uint8(packet.CipherAES128)}
|
||||
}
|
||||
if len(candidateHashes) == 0 {
|
||||
// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#hash-algos
|
||||
candidateHashes = []uint8{hashToHashId(crypto.SHA256)}
|
||||
}
|
||||
if len(candidateCipherSuites) == 0 {
|
||||
// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-9.6
|
||||
candidateCipherSuites = [][2]uint8{{uint8(packet.CipherAES128), uint8(packet.AEADModeOCB)}}
|
||||
}
|
||||
|
||||
cipher := packet.CipherFunction(candidateCiphers[0])
|
||||
aeadCipherSuite := packet.CipherSuite{
|
||||
Cipher: packet.CipherFunction(candidateCipherSuites[0][0]),
|
||||
Mode: packet.AEADMode(candidateCipherSuites[0][1]),
|
||||
}
|
||||
|
||||
// If the cipher specified by config is a candidate, we'll use that.
|
||||
configuredCipher := config.Cipher()
|
||||
for _, c := range candidateCiphers {
|
||||
|
|
@ -325,17 +428,23 @@ func Encrypt(ciphertext io.Writer, to []*Entity, signed *Entity, hints *FileHint
|
|||
}
|
||||
|
||||
for _, key := range encryptKeys {
|
||||
if err := packet.SerializeEncryptedKey(ciphertext, key.PublicKey, cipher, symKey, config); err != nil {
|
||||
if err := packet.SerializeEncryptedKey(keyWriter, key.PublicKey, cipher, symKey, config); err != nil {
|
||||
return nil, err
|
||||
}
|
||||
}
|
||||
|
||||
payload, err := packet.SerializeSymmetricallyEncrypted(ciphertext, cipher, symKey, config)
|
||||
var payload io.WriteCloser
|
||||
payload, err = packet.SerializeSymmetricallyEncrypted(dataWriter, cipher, aeadSupported, aeadCipherSuite, symKey, config)
|
||||
if err != nil {
|
||||
return
|
||||
return
|
||||
}
|
||||
|
||||
payload, err = handleCompression(payload, candidateCompression, config)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
return writeAndSign(payload, candidateHashes, signed, hints, config)
|
||||
return writeAndSign(payload, candidateHashes, signed, hints, sigType, config)
|
||||
}
|
||||
|
||||
// Sign signs a message. The resulting WriteCloser must be closed after the
|
||||
|
|
@ -352,16 +461,20 @@ func Sign(output io.Writer, signed *Entity, hints *FileHints, config *packet.Con
|
|||
hashToHashId(crypto.SHA256),
|
||||
hashToHashId(crypto.SHA384),
|
||||
hashToHashId(crypto.SHA512),
|
||||
hashToHashId(crypto.SHA1),
|
||||
hashToHashId(crypto.RIPEMD160),
|
||||
hashToHashId(crypto.SHA3_256),
|
||||
hashToHashId(crypto.SHA3_512),
|
||||
}
|
||||
defaultHashes := candidateHashes[len(candidateHashes)-1:]
|
||||
preferredHashes := signed.primaryIdentity().SelfSignature.PreferredHash
|
||||
defaultHashes := candidateHashes[0:1]
|
||||
preferredHashes := signed.PrimaryIdentity().SelfSignature.PreferredHash
|
||||
if len(preferredHashes) == 0 {
|
||||
preferredHashes = defaultHashes
|
||||
}
|
||||
candidateHashes = intersectPreferences(candidateHashes, preferredHashes)
|
||||
return writeAndSign(noOpCloser{output}, candidateHashes, signed, hints, config)
|
||||
if len(candidateHashes) == 0 {
|
||||
return nil, errors.InvalidArgumentError("cannot sign because signing key shares no common algorithms with candidate hashes")
|
||||
}
|
||||
|
||||
return writeAndSign(noOpCloser{output}, candidateHashes, signed, hints, packet.SigTypeBinary, config)
|
||||
}
|
||||
|
||||
// signatureWriter hashes the contents of a message while passing it along to
|
||||
|
|
@ -371,24 +484,30 @@ type signatureWriter struct {
|
|||
encryptedData io.WriteCloser
|
||||
literalData io.WriteCloser
|
||||
hashType crypto.Hash
|
||||
wrappedHash hash.Hash
|
||||
h hash.Hash
|
||||
signer *packet.PrivateKey
|
||||
sigType packet.SignatureType
|
||||
config *packet.Config
|
||||
metadata *packet.LiteralData // V5 signatures protect document metadata
|
||||
}
|
||||
|
||||
func (s signatureWriter) Write(data []byte) (int, error) {
|
||||
s.h.Write(data)
|
||||
return s.literalData.Write(data)
|
||||
s.wrappedHash.Write(data)
|
||||
switch s.sigType {
|
||||
case packet.SigTypeBinary:
|
||||
return s.literalData.Write(data)
|
||||
case packet.SigTypeText:
|
||||
flag := 0
|
||||
return writeCanonical(s.literalData, data, &flag)
|
||||
}
|
||||
return 0, errors.UnsupportedError("unsupported signature type: " + strconv.Itoa(int(s.sigType)))
|
||||
}
|
||||
|
||||
func (s signatureWriter) Close() error {
|
||||
sig := &packet.Signature{
|
||||
SigType: packet.SigTypeBinary,
|
||||
PubKeyAlgo: s.signer.PubKeyAlgo,
|
||||
Hash: s.hashType,
|
||||
CreationTime: s.config.Now(),
|
||||
IssuerKeyId: &s.signer.KeyId,
|
||||
}
|
||||
sig := createSignaturePacket(&s.signer.PublicKey, s.sigType, s.config)
|
||||
sig.Hash = s.hashType
|
||||
sig.Metadata = s.metadata
|
||||
|
||||
if err := sig.Sign(s.h, s.signer, s.config); err != nil {
|
||||
return err
|
||||
|
|
@ -402,7 +521,22 @@ func (s signatureWriter) Close() error {
|
|||
return s.encryptedData.Close()
|
||||
}
|
||||
|
||||
// noOpCloser is like an io.NopCloser, but for an io.Writer.
|
||||
func createSignaturePacket(signer *packet.PublicKey, sigType packet.SignatureType, config *packet.Config) *packet.Signature {
|
||||
sigLifetimeSecs := config.SigLifetime()
|
||||
return &packet.Signature{
|
||||
Version: signer.Version,
|
||||
SigType: sigType,
|
||||
PubKeyAlgo: signer.PubKeyAlgo,
|
||||
Hash: config.Hash(),
|
||||
CreationTime: config.Now(),
|
||||
IssuerKeyId: &signer.KeyId,
|
||||
IssuerFingerprint: signer.Fingerprint,
|
||||
Notations: config.Notations(),
|
||||
SigLifetimeSecs: &sigLifetimeSecs,
|
||||
}
|
||||
}
|
||||
|
||||
// noOpCloser is like an ioutil.NopCloser, but for an io.Writer.
|
||||
// TODO: we have two of these in OpenPGP packages alone. This probably needs
|
||||
// to be promoted somewhere more common.
|
||||
type noOpCloser struct {
|
||||
|
|
@ -416,3 +550,34 @@ func (c noOpCloser) Write(data []byte) (n int, err error) {
|
|||
func (c noOpCloser) Close() error {
|
||||
return nil
|
||||
}
|
||||
|
||||
func handleCompression(compressed io.WriteCloser, candidateCompression []uint8, config *packet.Config) (data io.WriteCloser, err error) {
|
||||
data = compressed
|
||||
confAlgo := config.Compression()
|
||||
if confAlgo == packet.CompressionNone {
|
||||
return
|
||||
}
|
||||
|
||||
// Set algorithm labelled as MUST as fallback
|
||||
// https://www.ietf.org/archive/id/draft-ietf-openpgp-crypto-refresh-07.html#section-9.4
|
||||
finalAlgo := packet.CompressionNone
|
||||
// if compression specified by config available we will use it
|
||||
for _, c := range candidateCompression {
|
||||
if uint8(confAlgo) == c {
|
||||
finalAlgo = confAlgo
|
||||
break
|
||||
}
|
||||
}
|
||||
|
||||
if finalAlgo != packet.CompressionNone {
|
||||
var compConfig *packet.CompressionConfig
|
||||
if config != nil {
|
||||
compConfig = config.CompressionConfig
|
||||
}
|
||||
data, err = packet.SerializeCompressed(compressed, finalAlgo, compConfig)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
}
|
||||
return data, nil
|
||||
}
|
||||
|
|
@ -0,0 +1,57 @@
|
|||
Copyright (c) 2019 Cloudflare. All rights reserved.
|
||||
|
||||
Redistribution and use in source and binary forms, with or without
|
||||
modification, are permitted provided that the following conditions are
|
||||
met:
|
||||
|
||||
* Redistributions of source code must retain the above copyright
|
||||
notice, this list of conditions and the following disclaimer.
|
||||
* Redistributions in binary form must reproduce the above
|
||||
copyright notice, this list of conditions and the following disclaimer
|
||||
in the documentation and/or other materials provided with the
|
||||
distribution.
|
||||
* Neither the name of Cloudflare nor the names of its
|
||||
contributors may be used to endorse or promote products derived from
|
||||
this software without specific prior written permission.
|
||||
|
||||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||||
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
||||
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
|
||||
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
||||
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
||||
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
||||
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
||||
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||||
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
||||
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
|
||||
========================================================================
|
||||
|
||||
Copyright (c) 2009 The Go Authors. All rights reserved.
|
||||
|
||||
Redistribution and use in source and binary forms, with or without
|
||||
modification, are permitted provided that the following conditions are
|
||||
met:
|
||||
|
||||
* Redistributions of source code must retain the above copyright
|
||||
notice, this list of conditions and the following disclaimer.
|
||||
* Redistributions in binary form must reproduce the above
|
||||
copyright notice, this list of conditions and the following disclaimer
|
||||
in the documentation and/or other materials provided with the
|
||||
distribution.
|
||||
* Neither the name of Google Inc. nor the names of its
|
||||
contributors may be used to endorse or promote products derived from
|
||||
this software without specific prior written permission.
|
||||
|
||||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||||
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
||||
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
|
||||
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
||||
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
||||
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
||||
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
||||
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||||
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
||||
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
|
|
@ -0,0 +1,96 @@
|
|||
package x25519
|
||||
|
||||
import (
|
||||
fp "github.com/cloudflare/circl/math/fp25519"
|
||||
)
|
||||
|
||||
// ladderJoye calculates a fixed-point multiplication with the generator point.
|
||||
// The algorithm is the right-to-left Joye's ladder as described
|
||||
// in "How to precompute a ladder" in SAC'2017.
|
||||
func ladderJoye(k *Key) {
|
||||
w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved.
|
||||
fp.SetOne(&w[1]) // x1 = 1
|
||||
fp.SetOne(&w[2]) // z1 = 1
|
||||
w[3] = fp.Elt{ // x2 = G-S
|
||||
0xbd, 0xaa, 0x2f, 0xc8, 0xfe, 0xe1, 0x94, 0x7e,
|
||||
0xf8, 0xed, 0xb2, 0x14, 0xae, 0x95, 0xf0, 0xbb,
|
||||
0xe2, 0x48, 0x5d, 0x23, 0xb9, 0xa0, 0xc7, 0xad,
|
||||
0x34, 0xab, 0x7c, 0xe2, 0xee, 0xcd, 0xae, 0x1e,
|
||||
}
|
||||
fp.SetOne(&w[4]) // z2 = 1
|
||||
|
||||
const n = 255
|
||||
const h = 3
|
||||
swap := uint(1)
|
||||
for s := 0; s < n-h; s++ {
|
||||
i := (s + h) / 8
|
||||
j := (s + h) % 8
|
||||
bit := uint((k[i] >> uint(j)) & 1)
|
||||
copy(w[0][:], tableGenerator[s*Size:(s+1)*Size])
|
||||
diffAdd(&w, swap^bit)
|
||||
swap = bit
|
||||
}
|
||||
for s := 0; s < h; s++ {
|
||||
double(&w[1], &w[2])
|
||||
}
|
||||
toAffine((*[fp.Size]byte)(k), &w[1], &w[2])
|
||||
}
|
||||
|
||||
// ladderMontgomery calculates a generic scalar point multiplication
|
||||
// The algorithm implemented is the left-to-right Montgomery's ladder.
|
||||
func ladderMontgomery(k, xP *Key) {
|
||||
w := [5]fp.Elt{} // [x1, x2, z2, x3, z3] order must be preserved.
|
||||
w[0] = *(*fp.Elt)(xP) // x1 = xP
|
||||
fp.SetOne(&w[1]) // x2 = 1
|
||||
w[3] = *(*fp.Elt)(xP) // x3 = xP
|
||||
fp.SetOne(&w[4]) // z3 = 1
|
||||
|
||||
move := uint(0)
|
||||
for s := 255 - 1; s >= 0; s-- {
|
||||
i := s / 8
|
||||
j := s % 8
|
||||
bit := uint((k[i] >> uint(j)) & 1)
|
||||
ladderStep(&w, move^bit)
|
||||
move = bit
|
||||
}
|
||||
toAffine((*[fp.Size]byte)(k), &w[1], &w[2])
|
||||
}
|
||||
|
||||
func toAffine(k *[fp.Size]byte, x, z *fp.Elt) {
|
||||
fp.Inv(z, z)
|
||||
fp.Mul(x, x, z)
|
||||
_ = fp.ToBytes(k[:], x)
|
||||
}
|
||||
|
||||
var lowOrderPoints = [5]fp.Elt{
|
||||
{ /* (0,_,1) point of order 2 on Curve25519 */
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
},
|
||||
{ /* (1,_,1) point of order 4 on Curve25519 */
|
||||
0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
},
|
||||
{ /* (x,_,1) first point of order 8 on Curve25519 */
|
||||
0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae,
|
||||
0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a,
|
||||
0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd,
|
||||
0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00,
|
||||
},
|
||||
{ /* (x,_,1) second point of order 8 on Curve25519 */
|
||||
0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24,
|
||||
0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b,
|
||||
0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86,
|
||||
0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57,
|
||||
},
|
||||
{ /* (-1,_,1) a point of order 4 on the twist of Curve25519 */
|
||||
0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f,
|
||||
},
|
||||
}
|
||||
|
|
@ -0,0 +1,30 @@
|
|||
//go:build amd64 && !purego
|
||||
// +build amd64,!purego
|
||||
|
||||
package x25519
|
||||
|
||||
import (
|
||||
fp "github.com/cloudflare/circl/math/fp25519"
|
||||
"golang.org/x/sys/cpu"
|
||||
)
|
||||
|
||||
var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX
|
||||
|
||||
var _ = hasBmi2Adx
|
||||
|
||||
func double(x, z *fp.Elt) { doubleAmd64(x, z) }
|
||||
func diffAdd(w *[5]fp.Elt, b uint) { diffAddAmd64(w, b) }
|
||||
func ladderStep(w *[5]fp.Elt, b uint) { ladderStepAmd64(w, b) }
|
||||
func mulA24(z, x *fp.Elt) { mulA24Amd64(z, x) }
|
||||
|
||||
//go:noescape
|
||||
func ladderStepAmd64(w *[5]fp.Elt, b uint)
|
||||
|
||||
//go:noescape
|
||||
func diffAddAmd64(w *[5]fp.Elt, b uint)
|
||||
|
||||
//go:noescape
|
||||
func doubleAmd64(x, z *fp.Elt)
|
||||
|
||||
//go:noescape
|
||||
func mulA24Amd64(z, x *fp.Elt)
|
||||
|
|
@ -0,0 +1,111 @@
|
|||
#define ladderStepLeg \
|
||||
addSub(x2,z2) \
|
||||
addSub(x3,z3) \
|
||||
integerMulLeg(b0,x2,z3) \
|
||||
integerMulLeg(b1,x3,z2) \
|
||||
reduceFromDoubleLeg(t0,b0) \
|
||||
reduceFromDoubleLeg(t1,b1) \
|
||||
addSub(t0,t1) \
|
||||
cselect(x2,x3,regMove) \
|
||||
cselect(z2,z3,regMove) \
|
||||
integerSqrLeg(b0,t0) \
|
||||
integerSqrLeg(b1,t1) \
|
||||
reduceFromDoubleLeg(x3,b0) \
|
||||
reduceFromDoubleLeg(z3,b1) \
|
||||
integerMulLeg(b0,x1,z3) \
|
||||
reduceFromDoubleLeg(z3,b0) \
|
||||
integerSqrLeg(b0,x2) \
|
||||
integerSqrLeg(b1,z2) \
|
||||
reduceFromDoubleLeg(x2,b0) \
|
||||
reduceFromDoubleLeg(z2,b1) \
|
||||
subtraction(t0,x2,z2) \
|
||||
multiplyA24Leg(t1,t0) \
|
||||
additionLeg(t1,t1,z2) \
|
||||
integerMulLeg(b0,x2,z2) \
|
||||
integerMulLeg(b1,t0,t1) \
|
||||
reduceFromDoubleLeg(x2,b0) \
|
||||
reduceFromDoubleLeg(z2,b1)
|
||||
|
||||
#define ladderStepBmi2Adx \
|
||||
addSub(x2,z2) \
|
||||
addSub(x3,z3) \
|
||||
integerMulAdx(b0,x2,z3) \
|
||||
integerMulAdx(b1,x3,z2) \
|
||||
reduceFromDoubleAdx(t0,b0) \
|
||||
reduceFromDoubleAdx(t1,b1) \
|
||||
addSub(t0,t1) \
|
||||
cselect(x2,x3,regMove) \
|
||||
cselect(z2,z3,regMove) \
|
||||
integerSqrAdx(b0,t0) \
|
||||
integerSqrAdx(b1,t1) \
|
||||
reduceFromDoubleAdx(x3,b0) \
|
||||
reduceFromDoubleAdx(z3,b1) \
|
||||
integerMulAdx(b0,x1,z3) \
|
||||
reduceFromDoubleAdx(z3,b0) \
|
||||
integerSqrAdx(b0,x2) \
|
||||
integerSqrAdx(b1,z2) \
|
||||
reduceFromDoubleAdx(x2,b0) \
|
||||
reduceFromDoubleAdx(z2,b1) \
|
||||
subtraction(t0,x2,z2) \
|
||||
multiplyA24Adx(t1,t0) \
|
||||
additionAdx(t1,t1,z2) \
|
||||
integerMulAdx(b0,x2,z2) \
|
||||
integerMulAdx(b1,t0,t1) \
|
||||
reduceFromDoubleAdx(x2,b0) \
|
||||
reduceFromDoubleAdx(z2,b1)
|
||||
|
||||
#define difAddLeg \
|
||||
addSub(x1,z1) \
|
||||
integerMulLeg(b0,z1,ui) \
|
||||
reduceFromDoubleLeg(z1,b0) \
|
||||
addSub(x1,z1) \
|
||||
integerSqrLeg(b0,x1) \
|
||||
integerSqrLeg(b1,z1) \
|
||||
reduceFromDoubleLeg(x1,b0) \
|
||||
reduceFromDoubleLeg(z1,b1) \
|
||||
integerMulLeg(b0,x1,z2) \
|
||||
integerMulLeg(b1,z1,x2) \
|
||||
reduceFromDoubleLeg(x1,b0) \
|
||||
reduceFromDoubleLeg(z1,b1)
|
||||
|
||||
#define difAddBmi2Adx \
|
||||
addSub(x1,z1) \
|
||||
integerMulAdx(b0,z1,ui) \
|
||||
reduceFromDoubleAdx(z1,b0) \
|
||||
addSub(x1,z1) \
|
||||
integerSqrAdx(b0,x1) \
|
||||
integerSqrAdx(b1,z1) \
|
||||
reduceFromDoubleAdx(x1,b0) \
|
||||
reduceFromDoubleAdx(z1,b1) \
|
||||
integerMulAdx(b0,x1,z2) \
|
||||
integerMulAdx(b1,z1,x2) \
|
||||
reduceFromDoubleAdx(x1,b0) \
|
||||
reduceFromDoubleAdx(z1,b1)
|
||||
|
||||
#define doubleLeg \
|
||||
addSub(x1,z1) \
|
||||
integerSqrLeg(b0,x1) \
|
||||
integerSqrLeg(b1,z1) \
|
||||
reduceFromDoubleLeg(x1,b0) \
|
||||
reduceFromDoubleLeg(z1,b1) \
|
||||
subtraction(t0,x1,z1) \
|
||||
multiplyA24Leg(t1,t0) \
|
||||
additionLeg(t1,t1,z1) \
|
||||
integerMulLeg(b0,x1,z1) \
|
||||
integerMulLeg(b1,t0,t1) \
|
||||
reduceFromDoubleLeg(x1,b0) \
|
||||
reduceFromDoubleLeg(z1,b1)
|
||||
|
||||
#define doubleBmi2Adx \
|
||||
addSub(x1,z1) \
|
||||
integerSqrAdx(b0,x1) \
|
||||
integerSqrAdx(b1,z1) \
|
||||
reduceFromDoubleAdx(x1,b0) \
|
||||
reduceFromDoubleAdx(z1,b1) \
|
||||
subtraction(t0,x1,z1) \
|
||||
multiplyA24Adx(t1,t0) \
|
||||
additionAdx(t1,t1,z1) \
|
||||
integerMulAdx(b0,x1,z1) \
|
||||
integerMulAdx(b1,t0,t1) \
|
||||
reduceFromDoubleAdx(x1,b0) \
|
||||
reduceFromDoubleAdx(z1,b1)
|
||||
|
|
@ -0,0 +1,156 @@
|
|||
// +build amd64
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// Depends on circl/math/fp25519 package
|
||||
#include "../../math/fp25519/fp_amd64.h"
|
||||
#include "curve_amd64.h"
|
||||
|
||||
// CTE_A24 is (A+2)/4 from Curve25519
|
||||
#define CTE_A24 121666
|
||||
|
||||
#define Size 32
|
||||
|
||||
// multiplyA24Leg multiplies x times CTE_A24 and stores in z
|
||||
// Uses: AX, DX, R8-R13, FLAGS
|
||||
// Instr: x86_64, cmov
|
||||
#define multiplyA24Leg(z,x) \
|
||||
MOVL $CTE_A24, AX; MULQ 0+x; MOVQ AX, R8; MOVQ DX, R9; \
|
||||
MOVL $CTE_A24, AX; MULQ 8+x; MOVQ AX, R12; MOVQ DX, R10; \
|
||||
MOVL $CTE_A24, AX; MULQ 16+x; MOVQ AX, R13; MOVQ DX, R11; \
|
||||
MOVL $CTE_A24, AX; MULQ 24+x; \
|
||||
ADDQ R12, R9; \
|
||||
ADCQ R13, R10; \
|
||||
ADCQ AX, R11; \
|
||||
ADCQ $0, DX; \
|
||||
MOVL $38, AX; /* 2*C = 38 = 2^256 MOD 2^255-19*/ \
|
||||
IMULQ AX, DX; \
|
||||
ADDQ DX, R8; \
|
||||
ADCQ $0, R9; MOVQ R9, 8+z; \
|
||||
ADCQ $0, R10; MOVQ R10, 16+z; \
|
||||
ADCQ $0, R11; MOVQ R11, 24+z; \
|
||||
MOVQ $0, DX; \
|
||||
CMOVQCS AX, DX; \
|
||||
ADDQ DX, R8; MOVQ R8, 0+z;
|
||||
|
||||
// multiplyA24Adx multiplies x times CTE_A24 and stores in z
|
||||
// Uses: AX, DX, R8-R12, FLAGS
|
||||
// Instr: x86_64, cmov, bmi2
|
||||
#define multiplyA24Adx(z,x) \
|
||||
MOVQ $CTE_A24, DX; \
|
||||
MULXQ 0+x, R8, R10; \
|
||||
MULXQ 8+x, R9, R11; ADDQ R10, R9; \
|
||||
MULXQ 16+x, R10, AX; ADCQ R11, R10; \
|
||||
MULXQ 24+x, R11, R12; ADCQ AX, R11; \
|
||||
;;;;;;;;;;;;;;;;;;;;; ADCQ $0, R12; \
|
||||
MOVL $38, DX; /* 2*C = 38 = 2^256 MOD 2^255-19*/ \
|
||||
IMULQ DX, R12; \
|
||||
ADDQ R12, R8; \
|
||||
ADCQ $0, R9; MOVQ R9, 8+z; \
|
||||
ADCQ $0, R10; MOVQ R10, 16+z; \
|
||||
ADCQ $0, R11; MOVQ R11, 24+z; \
|
||||
MOVQ $0, R12; \
|
||||
CMOVQCS DX, R12; \
|
||||
ADDQ R12, R8; MOVQ R8, 0+z;
|
||||
|
||||
#define mulA24Legacy \
|
||||
multiplyA24Leg(0(DI),0(SI))
|
||||
#define mulA24Bmi2Adx \
|
||||
multiplyA24Adx(0(DI),0(SI))
|
||||
|
||||
// func mulA24Amd64(z, x *fp255.Elt)
|
||||
TEXT ·mulA24Amd64(SB),NOSPLIT,$0-16
|
||||
MOVQ z+0(FP), DI
|
||||
MOVQ x+8(FP), SI
|
||||
CHECK_BMI2ADX(LMA24, mulA24Legacy, mulA24Bmi2Adx)
|
||||
|
||||
|
||||
// func ladderStepAmd64(w *[5]fp255.Elt, b uint)
|
||||
// ladderStepAmd64 calculates a point addition and doubling as follows:
|
||||
// (x2,z2) = 2*(x2,z2) and (x3,z3) = (x2,z2)+(x3,z3) using as a difference (x1,-).
|
||||
// work = (x1,x2,z2,x3,z3) are five fp255.Elt of 32 bytes.
|
||||
// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and
|
||||
// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes.
|
||||
TEXT ·ladderStepAmd64(SB),NOSPLIT,$192-16
|
||||
// Parameters
|
||||
#define regWork DI
|
||||
#define regMove SI
|
||||
#define x1 0*Size(regWork)
|
||||
#define x2 1*Size(regWork)
|
||||
#define z2 2*Size(regWork)
|
||||
#define x3 3*Size(regWork)
|
||||
#define z3 4*Size(regWork)
|
||||
// Local variables
|
||||
#define t0 0*Size(SP)
|
||||
#define t1 1*Size(SP)
|
||||
#define b0 2*Size(SP)
|
||||
#define b1 4*Size(SP)
|
||||
MOVQ w+0(FP), regWork
|
||||
MOVQ b+8(FP), regMove
|
||||
CHECK_BMI2ADX(LLADSTEP, ladderStepLeg, ladderStepBmi2Adx)
|
||||
#undef regWork
|
||||
#undef regMove
|
||||
#undef x1
|
||||
#undef x2
|
||||
#undef z2
|
||||
#undef x3
|
||||
#undef z3
|
||||
#undef t0
|
||||
#undef t1
|
||||
#undef b0
|
||||
#undef b1
|
||||
|
||||
// func diffAddAmd64(w *[5]fp255.Elt, b uint)
|
||||
// diffAddAmd64 calculates a differential point addition using a precomputed point.
|
||||
// (x1,z1) = (x1,z1)+(mu) using a difference point (x2,z2)
|
||||
// w = (mu,x1,z1,x2,z2) are five fp.Elt, and
|
||||
// stack = (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes.
|
||||
TEXT ·diffAddAmd64(SB),NOSPLIT,$128-16
|
||||
// Parameters
|
||||
#define regWork DI
|
||||
#define regSwap SI
|
||||
#define ui 0*Size(regWork)
|
||||
#define x1 1*Size(regWork)
|
||||
#define z1 2*Size(regWork)
|
||||
#define x2 3*Size(regWork)
|
||||
#define z2 4*Size(regWork)
|
||||
// Local variables
|
||||
#define b0 0*Size(SP)
|
||||
#define b1 2*Size(SP)
|
||||
MOVQ w+0(FP), regWork
|
||||
MOVQ b+8(FP), regSwap
|
||||
cswap(x1,x2,regSwap)
|
||||
cswap(z1,z2,regSwap)
|
||||
CHECK_BMI2ADX(LDIFADD, difAddLeg, difAddBmi2Adx)
|
||||
#undef regWork
|
||||
#undef regSwap
|
||||
#undef ui
|
||||
#undef x1
|
||||
#undef z1
|
||||
#undef x2
|
||||
#undef z2
|
||||
#undef b0
|
||||
#undef b1
|
||||
|
||||
// func doubleAmd64(x, z *fp255.Elt)
|
||||
// doubleAmd64 calculates a point doubling (x1,z1) = 2*(x1,z1).
|
||||
// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and
|
||||
// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes.
|
||||
TEXT ·doubleAmd64(SB),NOSPLIT,$192-16
|
||||
// Parameters
|
||||
#define x1 0(DI)
|
||||
#define z1 0(SI)
|
||||
// Local variables
|
||||
#define t0 0*Size(SP)
|
||||
#define t1 1*Size(SP)
|
||||
#define b0 2*Size(SP)
|
||||
#define b1 4*Size(SP)
|
||||
MOVQ x+0(FP), DI
|
||||
MOVQ z+8(FP), SI
|
||||
CHECK_BMI2ADX(LDOUB,doubleLeg,doubleBmi2Adx)
|
||||
#undef x1
|
||||
#undef z1
|
||||
#undef t0
|
||||
#undef t1
|
||||
#undef b0
|
||||
#undef b1
|
||||
|
|
@ -0,0 +1,85 @@
|
|||
package x25519
|
||||
|
||||
import (
|
||||
"encoding/binary"
|
||||
"math/bits"
|
||||
|
||||
fp "github.com/cloudflare/circl/math/fp25519"
|
||||
)
|
||||
|
||||
func doubleGeneric(x, z *fp.Elt) {
|
||||
t0, t1 := &fp.Elt{}, &fp.Elt{}
|
||||
fp.AddSub(x, z)
|
||||
fp.Sqr(x, x)
|
||||
fp.Sqr(z, z)
|
||||
fp.Sub(t0, x, z)
|
||||
mulA24Generic(t1, t0)
|
||||
fp.Add(t1, t1, z)
|
||||
fp.Mul(x, x, z)
|
||||
fp.Mul(z, t0, t1)
|
||||
}
|
||||
|
||||
func diffAddGeneric(w *[5]fp.Elt, b uint) {
|
||||
mu, x1, z1, x2, z2 := &w[0], &w[1], &w[2], &w[3], &w[4]
|
||||
fp.Cswap(x1, x2, b)
|
||||
fp.Cswap(z1, z2, b)
|
||||
fp.AddSub(x1, z1)
|
||||
fp.Mul(z1, z1, mu)
|
||||
fp.AddSub(x1, z1)
|
||||
fp.Sqr(x1, x1)
|
||||
fp.Sqr(z1, z1)
|
||||
fp.Mul(x1, x1, z2)
|
||||
fp.Mul(z1, z1, x2)
|
||||
}
|
||||
|
||||
func ladderStepGeneric(w *[5]fp.Elt, b uint) {
|
||||
x1, x2, z2, x3, z3 := &w[0], &w[1], &w[2], &w[3], &w[4]
|
||||
t0 := &fp.Elt{}
|
||||
t1 := &fp.Elt{}
|
||||
fp.AddSub(x2, z2)
|
||||
fp.AddSub(x3, z3)
|
||||
fp.Mul(t0, x2, z3)
|
||||
fp.Mul(t1, x3, z2)
|
||||
fp.AddSub(t0, t1)
|
||||
fp.Cmov(x2, x3, b)
|
||||
fp.Cmov(z2, z3, b)
|
||||
fp.Sqr(x3, t0)
|
||||
fp.Sqr(z3, t1)
|
||||
fp.Mul(z3, x1, z3)
|
||||
fp.Sqr(x2, x2)
|
||||
fp.Sqr(z2, z2)
|
||||
fp.Sub(t0, x2, z2)
|
||||
mulA24Generic(t1, t0)
|
||||
fp.Add(t1, t1, z2)
|
||||
fp.Mul(x2, x2, z2)
|
||||
fp.Mul(z2, t0, t1)
|
||||
}
|
||||
|
||||
func mulA24Generic(z, x *fp.Elt) {
|
||||
const A24 = 121666
|
||||
const n = 8
|
||||
var xx [4]uint64
|
||||
for i := range xx {
|
||||
xx[i] = binary.LittleEndian.Uint64(x[i*n : (i+1)*n])
|
||||
}
|
||||
|
||||
h0, l0 := bits.Mul64(xx[0], A24)
|
||||
h1, l1 := bits.Mul64(xx[1], A24)
|
||||
h2, l2 := bits.Mul64(xx[2], A24)
|
||||
h3, l3 := bits.Mul64(xx[3], A24)
|
||||
|
||||
var c3 uint64
|
||||
l1, c0 := bits.Add64(h0, l1, 0)
|
||||
l2, c1 := bits.Add64(h1, l2, c0)
|
||||
l3, c2 := bits.Add64(h2, l3, c1)
|
||||
l4, _ := bits.Add64(h3, 0, c2)
|
||||
_, l4 = bits.Mul64(l4, 38)
|
||||
l0, c0 = bits.Add64(l0, l4, 0)
|
||||
xx[1], c1 = bits.Add64(l1, 0, c0)
|
||||
xx[2], c2 = bits.Add64(l2, 0, c1)
|
||||
xx[3], c3 = bits.Add64(l3, 0, c2)
|
||||
xx[0], _ = bits.Add64(l0, (-c3)&38, 0)
|
||||
for i := range xx {
|
||||
binary.LittleEndian.PutUint64(z[i*n:(i+1)*n], xx[i])
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,11 @@
|
|||
//go:build !amd64 || purego
|
||||
// +build !amd64 purego
|
||||
|
||||
package x25519
|
||||
|
||||
import fp "github.com/cloudflare/circl/math/fp25519"
|
||||
|
||||
func double(x, z *fp.Elt) { doubleGeneric(x, z) }
|
||||
func diffAdd(w *[5]fp.Elt, b uint) { diffAddGeneric(w, b) }
|
||||
func ladderStep(w *[5]fp.Elt, b uint) { ladderStepGeneric(w, b) }
|
||||
func mulA24(z, x *fp.Elt) { mulA24Generic(z, x) }
|
||||
|
|
@ -0,0 +1,19 @@
|
|||
/*
|
||||
Package x25519 provides Diffie-Hellman functions as specified in RFC-7748.
|
||||
|
||||
Validation of public keys.
|
||||
|
||||
The Diffie-Hellman function, as described in RFC-7748 [1], works for any
|
||||
public key. However, if a different protocol requires contributory
|
||||
behaviour [2,3], then the public keys must be validated against low-order
|
||||
points [3,4]. To do that, the Shared function performs this validation
|
||||
internally and returns false when the public key is invalid (i.e., it
|
||||
is a low-order point).
|
||||
|
||||
References:
|
||||
- [1] RFC7748 by Langley, Hamburg, Turner (https://rfc-editor.org/rfc/rfc7748.txt)
|
||||
- [2] Curve25519 by Bernstein (https://cr.yp.to/ecdh.html)
|
||||
- [3] Bernstein (https://cr.yp.to/ecdh.html#validate)
|
||||
- [4] Cremers&Jackson (https://eprint.iacr.org/2019/526)
|
||||
*/
|
||||
package x25519
|
||||
|
|
@ -0,0 +1,47 @@
|
|||
package x25519
|
||||
|
||||
import (
|
||||
"crypto/subtle"
|
||||
|
||||
fp "github.com/cloudflare/circl/math/fp25519"
|
||||
)
|
||||
|
||||
// Size is the length in bytes of a X25519 key.
|
||||
const Size = 32
|
||||
|
||||
// Key represents a X25519 key.
|
||||
type Key [Size]byte
|
||||
|
||||
func (k *Key) clamp(in *Key) *Key {
|
||||
*k = *in
|
||||
k[0] &= 248
|
||||
k[31] = (k[31] & 127) | 64
|
||||
return k
|
||||
}
|
||||
|
||||
// isValidPubKey verifies if the public key is not a low-order point.
|
||||
func (k *Key) isValidPubKey() bool {
|
||||
fp.Modp((*fp.Elt)(k))
|
||||
var isLowOrder int
|
||||
for _, P := range lowOrderPoints {
|
||||
isLowOrder |= subtle.ConstantTimeCompare(P[:], k[:])
|
||||
}
|
||||
return isLowOrder == 0
|
||||
}
|
||||
|
||||
// KeyGen obtains a public key given a secret key.
|
||||
func KeyGen(public, secret *Key) {
|
||||
ladderJoye(public.clamp(secret))
|
||||
}
|
||||
|
||||
// Shared calculates Alice's shared key from Alice's secret key and Bob's
|
||||
// public key returning true on success. A failure case happens when the public
|
||||
// key is a low-order point, thus the shared key is all-zeros and the function
|
||||
// returns false.
|
||||
func Shared(shared, secret, public *Key) bool {
|
||||
validPk := *public
|
||||
validPk[31] &= (1 << (255 % 8)) - 1
|
||||
ok := validPk.isValidPubKey()
|
||||
ladderMontgomery(shared.clamp(secret), &validPk)
|
||||
return ok
|
||||
}
|
||||
|
|
@ -0,0 +1,268 @@
|
|||
package x25519
|
||||
|
||||
import "github.com/cloudflare/circl/math/fp25519"
|
||||
|
||||
// tableGenerator contains the set of points:
|
||||
//
|
||||
// t[i] = (xi+1)/(xi-1),
|
||||
//
|
||||
// where (xi,yi) = 2^iG and G is the generator point
|
||||
// Size = (256)*(256/8) = 8192 bytes.
|
||||
var tableGenerator = [256 * fp25519.Size]byte{
|
||||
/* (2^ 0)P */ 0xf3, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x5f,
|
||||
/* (2^ 1)P */ 0x96, 0xfe, 0xaa, 0x16, 0xf4, 0x20, 0x82, 0x6b, 0x34, 0x6a, 0x56, 0x4f, 0x2b, 0xeb, 0xeb, 0x82, 0x0f, 0x95, 0xa5, 0x75, 0xb0, 0xa5, 0xa9, 0xd5, 0xf4, 0x88, 0x24, 0x4b, 0xcf, 0xb2, 0x42, 0x51,
|
||||
/* (2^ 2)P */ 0x0c, 0x68, 0x69, 0x00, 0x75, 0xbc, 0xae, 0x6a, 0x41, 0x9c, 0xf9, 0xa0, 0x20, 0x78, 0xcf, 0x89, 0xf4, 0xd0, 0x56, 0x3b, 0x18, 0xd9, 0x58, 0x2a, 0xa4, 0x11, 0x60, 0xe3, 0x80, 0xca, 0x5a, 0x4b,
|
||||
/* (2^ 3)P */ 0x5d, 0x74, 0x29, 0x8c, 0x34, 0x32, 0x91, 0x32, 0xd7, 0x2f, 0x64, 0xe1, 0x16, 0xe6, 0xa2, 0xf4, 0x34, 0xbc, 0x67, 0xff, 0x03, 0xbb, 0x45, 0x1e, 0x4a, 0x9b, 0x2a, 0xf4, 0xd0, 0x12, 0x69, 0x30,
|
||||
/* (2^ 4)P */ 0x54, 0x71, 0xaf, 0xe6, 0x07, 0x65, 0x88, 0xff, 0x2f, 0xc8, 0xee, 0xdf, 0x13, 0x0e, 0xf5, 0x04, 0xce, 0xb5, 0xba, 0x2a, 0xe8, 0x2f, 0x51, 0xaa, 0x22, 0xf2, 0xd5, 0x68, 0x1a, 0x25, 0x4e, 0x17,
|
||||
/* (2^ 5)P */ 0x98, 0x88, 0x02, 0x82, 0x0d, 0x70, 0x96, 0xcf, 0xc5, 0x02, 0x2c, 0x0a, 0x37, 0xe3, 0x43, 0x17, 0xaa, 0x6e, 0xe8, 0xb4, 0x98, 0xec, 0x9e, 0x37, 0x2e, 0x48, 0xe0, 0x51, 0x8a, 0x88, 0x59, 0x0c,
|
||||
/* (2^ 6)P */ 0x89, 0xd1, 0xb5, 0x99, 0xd6, 0xf1, 0xcb, 0xfb, 0x84, 0xdc, 0x9f, 0x8e, 0xd5, 0xf0, 0xae, 0xac, 0x14, 0x76, 0x1f, 0x23, 0x06, 0x0d, 0xc2, 0xc1, 0x72, 0xf9, 0x74, 0xa2, 0x8d, 0x21, 0x38, 0x29,
|
||||
/* (2^ 7)P */ 0x18, 0x7f, 0x1d, 0xff, 0xbe, 0x49, 0xaf, 0xf6, 0xc2, 0xc9, 0x7a, 0x38, 0x22, 0x1c, 0x54, 0xcc, 0x6b, 0xc5, 0x15, 0x40, 0xef, 0xc9, 0xfc, 0x96, 0xa9, 0x13, 0x09, 0x69, 0x7c, 0x62, 0xc1, 0x69,
|
||||
/* (2^ 8)P */ 0x0e, 0xdb, 0x33, 0x47, 0x2f, 0xfd, 0x86, 0x7a, 0xe9, 0x7d, 0x08, 0x9e, 0xf2, 0xc4, 0xb8, 0xfd, 0x29, 0xa2, 0xa2, 0x8e, 0x1a, 0x4b, 0x5e, 0x09, 0x79, 0x7a, 0xb3, 0x29, 0xc8, 0xa7, 0xd7, 0x1a,
|
||||
/* (2^ 9)P */ 0xc0, 0xa0, 0x7e, 0xd1, 0xca, 0x89, 0x2d, 0x34, 0x51, 0x20, 0xed, 0xcc, 0xa6, 0xdd, 0xbe, 0x67, 0x74, 0x2f, 0xb4, 0x2b, 0xbf, 0x31, 0xca, 0x19, 0xbb, 0xac, 0x80, 0x49, 0xc8, 0xb4, 0xf7, 0x3d,
|
||||
/* (2^ 10)P */ 0x83, 0xd8, 0x0a, 0xc8, 0x4d, 0x44, 0xc6, 0xa8, 0x85, 0xab, 0xe3, 0x66, 0x03, 0x44, 0x1e, 0xb9, 0xd8, 0xf6, 0x64, 0x01, 0xa0, 0xcd, 0x15, 0xc2, 0x68, 0xe6, 0x47, 0xf2, 0x6e, 0x7c, 0x86, 0x3d,
|
||||
/* (2^ 11)P */ 0x8c, 0x65, 0x3e, 0xcc, 0x2b, 0x58, 0xdd, 0xc7, 0x28, 0x55, 0x0e, 0xee, 0x48, 0x47, 0x2c, 0xfd, 0x71, 0x4f, 0x9f, 0xcc, 0x95, 0x9b, 0xfd, 0xa0, 0xdf, 0x5d, 0x67, 0xb0, 0x71, 0xd8, 0x29, 0x75,
|
||||
/* (2^ 12)P */ 0x78, 0xbd, 0x3c, 0x2d, 0xb4, 0x68, 0xf5, 0xb8, 0x82, 0xda, 0xf3, 0x91, 0x1b, 0x01, 0x33, 0x12, 0x62, 0x3b, 0x7c, 0x4a, 0xcd, 0x6c, 0xce, 0x2d, 0x03, 0x86, 0x49, 0x9e, 0x8e, 0xfc, 0xe7, 0x75,
|
||||
/* (2^ 13)P */ 0xec, 0xb6, 0xd0, 0xfc, 0xf1, 0x13, 0x4f, 0x2f, 0x45, 0x7a, 0xff, 0x29, 0x1f, 0xca, 0xa8, 0xf1, 0x9b, 0xe2, 0x81, 0x29, 0xa7, 0xc1, 0x49, 0xc2, 0x6a, 0xb5, 0x83, 0x8c, 0xbb, 0x0d, 0xbe, 0x6e,
|
||||
/* (2^ 14)P */ 0x22, 0xb2, 0x0b, 0x17, 0x8d, 0xfa, 0x14, 0x71, 0x5f, 0x93, 0x93, 0xbf, 0xd5, 0xdc, 0xa2, 0x65, 0x9a, 0x97, 0x9c, 0xb5, 0x68, 0x1f, 0xc4, 0xbd, 0x89, 0x92, 0xce, 0xa2, 0x79, 0xef, 0x0e, 0x2f,
|
||||
/* (2^ 15)P */ 0xce, 0x37, 0x3c, 0x08, 0x0c, 0xbf, 0xec, 0x42, 0x22, 0x63, 0x49, 0xec, 0x09, 0xbc, 0x30, 0x29, 0x0d, 0xac, 0xfe, 0x9c, 0xc1, 0xb0, 0x94, 0xf2, 0x80, 0xbb, 0xfa, 0xed, 0x4b, 0xaa, 0x80, 0x37,
|
||||
/* (2^ 16)P */ 0x29, 0xd9, 0xea, 0x7c, 0x3e, 0x7d, 0xc1, 0x56, 0xc5, 0x22, 0x57, 0x2e, 0xeb, 0x4b, 0xcb, 0xe7, 0x5a, 0xe1, 0xbf, 0x2d, 0x73, 0x31, 0xe9, 0x0c, 0xf8, 0x52, 0x10, 0x62, 0xc7, 0x83, 0xb8, 0x41,
|
||||
/* (2^ 17)P */ 0x50, 0x53, 0xd2, 0xc3, 0xa0, 0x5c, 0xf7, 0xdb, 0x51, 0xe3, 0xb1, 0x6e, 0x08, 0xbe, 0x36, 0x29, 0x12, 0xb2, 0xa9, 0xb4, 0x3c, 0xe0, 0x36, 0xc9, 0xaa, 0x25, 0x22, 0x32, 0x82, 0xbf, 0x45, 0x1d,
|
||||
/* (2^ 18)P */ 0xc5, 0x4c, 0x02, 0x6a, 0x03, 0xb1, 0x1a, 0xe8, 0x72, 0x9a, 0x4c, 0x30, 0x1c, 0x20, 0x12, 0xe2, 0xfc, 0xb1, 0x32, 0x68, 0xba, 0x3f, 0xd7, 0xc5, 0x81, 0x95, 0x83, 0x4d, 0x5a, 0xdb, 0xff, 0x20,
|
||||
/* (2^ 19)P */ 0xad, 0x0f, 0x5d, 0xbe, 0x67, 0xd3, 0x83, 0xa2, 0x75, 0x44, 0x16, 0x8b, 0xca, 0x25, 0x2b, 0x6c, 0x2e, 0xf2, 0xaa, 0x7c, 0x46, 0x35, 0x49, 0x9d, 0x49, 0xff, 0x85, 0xee, 0x8e, 0x40, 0x66, 0x51,
|
||||
/* (2^ 20)P */ 0x61, 0xe3, 0xb4, 0xfa, 0xa2, 0xba, 0x67, 0x3c, 0xef, 0x5c, 0xf3, 0x7e, 0xc6, 0x33, 0xe4, 0xb3, 0x1c, 0x9b, 0x15, 0x41, 0x92, 0x72, 0x59, 0x52, 0x33, 0xab, 0xb0, 0xd5, 0x92, 0x18, 0x62, 0x6a,
|
||||
/* (2^ 21)P */ 0xcb, 0xcd, 0x55, 0x75, 0x38, 0x4a, 0xb7, 0x20, 0x3f, 0x92, 0x08, 0x12, 0x0e, 0xa1, 0x2a, 0x53, 0xd1, 0x1d, 0x28, 0x62, 0x77, 0x7b, 0xa1, 0xea, 0xbf, 0x44, 0x5c, 0xf0, 0x43, 0x34, 0xab, 0x61,
|
||||
/* (2^ 22)P */ 0xf8, 0xde, 0x24, 0x23, 0x42, 0x6c, 0x7a, 0x25, 0x7f, 0xcf, 0xe3, 0x17, 0x10, 0x6c, 0x1c, 0x13, 0x57, 0xa2, 0x30, 0xf6, 0x39, 0x87, 0x75, 0x23, 0x80, 0x85, 0xa7, 0x01, 0x7a, 0x40, 0x5a, 0x29,
|
||||
/* (2^ 23)P */ 0xd9, 0xa8, 0x5d, 0x6d, 0x24, 0x43, 0xc4, 0xf8, 0x5d, 0xfa, 0x52, 0x0c, 0x45, 0x75, 0xd7, 0x19, 0x3d, 0xf8, 0x1b, 0x73, 0x92, 0xfc, 0xfc, 0x2a, 0x00, 0x47, 0x2b, 0x1b, 0xe8, 0xc8, 0x10, 0x7d,
|
||||
/* (2^ 24)P */ 0x0b, 0xa2, 0xba, 0x70, 0x1f, 0x27, 0xe0, 0xc8, 0x57, 0x39, 0xa6, 0x7c, 0x86, 0x48, 0x37, 0x99, 0xbb, 0xd4, 0x7e, 0xcb, 0xb3, 0xef, 0x12, 0x54, 0x75, 0x29, 0xe6, 0x73, 0x61, 0xd3, 0x96, 0x31,
|
||||
/* (2^ 25)P */ 0xfc, 0xdf, 0xc7, 0x41, 0xd1, 0xca, 0x5b, 0xde, 0x48, 0xc8, 0x95, 0xb3, 0xd2, 0x8c, 0xcc, 0x47, 0xcb, 0xf3, 0x1a, 0xe1, 0x42, 0xd9, 0x4c, 0xa3, 0xc2, 0xce, 0x4e, 0xd0, 0xf2, 0xdb, 0x56, 0x02,
|
||||
/* (2^ 26)P */ 0x7f, 0x66, 0x0e, 0x4b, 0xe9, 0xb7, 0x5a, 0x87, 0x10, 0x0d, 0x85, 0xc0, 0x83, 0xdd, 0xd4, 0xca, 0x9f, 0xc7, 0x72, 0x4e, 0x8f, 0x2e, 0xf1, 0x47, 0x9b, 0xb1, 0x85, 0x8c, 0xbb, 0x87, 0x1a, 0x5f,
|
||||
/* (2^ 27)P */ 0xb8, 0x51, 0x7f, 0x43, 0xb6, 0xd0, 0xe9, 0x7a, 0x65, 0x90, 0x87, 0x18, 0x55, 0xce, 0xc7, 0x12, 0xee, 0x7a, 0xf7, 0x5c, 0xfe, 0x09, 0xde, 0x2a, 0x27, 0x56, 0x2c, 0x7d, 0x2f, 0x5a, 0xa0, 0x23,
|
||||
/* (2^ 28)P */ 0x9a, 0x16, 0x7c, 0xf1, 0x28, 0xe1, 0x08, 0x59, 0x2d, 0x85, 0xd0, 0x8a, 0xdd, 0x98, 0x74, 0xf7, 0x64, 0x2f, 0x10, 0xab, 0xce, 0xc4, 0xb4, 0x74, 0x45, 0x98, 0x13, 0x10, 0xdd, 0xba, 0x3a, 0x18,
|
||||
/* (2^ 29)P */ 0xac, 0xaa, 0x92, 0xaa, 0x8d, 0xba, 0x65, 0xb1, 0x05, 0x67, 0x38, 0x99, 0x95, 0xef, 0xc5, 0xd5, 0xd1, 0x40, 0xfc, 0xf8, 0x0c, 0x8f, 0x2f, 0xbe, 0x14, 0x45, 0x20, 0xee, 0x35, 0xe6, 0x01, 0x27,
|
||||
/* (2^ 30)P */ 0x14, 0x65, 0x15, 0x20, 0x00, 0xa8, 0x9f, 0x62, 0xce, 0xc1, 0xa8, 0x64, 0x87, 0x86, 0x23, 0xf2, 0x0e, 0x06, 0x3f, 0x0b, 0xff, 0x4f, 0x89, 0x5b, 0xfa, 0xa3, 0x08, 0xf7, 0x4c, 0x94, 0xd9, 0x60,
|
||||
/* (2^ 31)P */ 0x1f, 0x20, 0x7a, 0x1c, 0x1a, 0x00, 0xea, 0xae, 0x63, 0xce, 0xe2, 0x3e, 0x63, 0x6a, 0xf1, 0xeb, 0xe1, 0x07, 0x7a, 0x4c, 0x59, 0x09, 0x77, 0x6f, 0xcb, 0x08, 0x02, 0x0d, 0x15, 0x58, 0xb9, 0x79,
|
||||
/* (2^ 32)P */ 0xe7, 0x10, 0xd4, 0x01, 0x53, 0x5e, 0xb5, 0x24, 0x4d, 0xc8, 0xfd, 0xf3, 0xdf, 0x4e, 0xa3, 0xe3, 0xd8, 0x32, 0x40, 0x90, 0xe4, 0x68, 0x87, 0xd8, 0xec, 0xae, 0x3a, 0x7b, 0x42, 0x84, 0x13, 0x13,
|
||||
/* (2^ 33)P */ 0x14, 0x4f, 0x23, 0x86, 0x12, 0xe5, 0x05, 0x84, 0x29, 0xc5, 0xb4, 0xad, 0x39, 0x47, 0xdc, 0x14, 0xfd, 0x4f, 0x63, 0x50, 0xb2, 0xb5, 0xa2, 0xb8, 0x93, 0xff, 0xa7, 0xd8, 0x4a, 0xa9, 0xe2, 0x2f,
|
||||
/* (2^ 34)P */ 0xdd, 0xfa, 0x43, 0xe8, 0xef, 0x57, 0x5c, 0xec, 0x18, 0x99, 0xbb, 0xf0, 0x40, 0xce, 0x43, 0x28, 0x05, 0x63, 0x3d, 0xcf, 0xd6, 0x61, 0xb5, 0xa4, 0x7e, 0x77, 0xfb, 0xe8, 0xbd, 0x29, 0x36, 0x74,
|
||||
/* (2^ 35)P */ 0x8f, 0x73, 0xaf, 0xbb, 0x46, 0xdd, 0x3e, 0x34, 0x51, 0xa6, 0x01, 0xb1, 0x28, 0x18, 0x98, 0xed, 0x7a, 0x79, 0x2c, 0x88, 0x0b, 0x76, 0x01, 0xa4, 0x30, 0x87, 0xc8, 0x8d, 0xe2, 0x23, 0xc2, 0x1f,
|
||||
/* (2^ 36)P */ 0x0e, 0xba, 0x0f, 0xfc, 0x91, 0x4e, 0x60, 0x48, 0xa4, 0x6f, 0x2c, 0x05, 0x8f, 0xf7, 0x37, 0xb6, 0x9c, 0x23, 0xe9, 0x09, 0x3d, 0xac, 0xcc, 0x91, 0x7c, 0x68, 0x7a, 0x43, 0xd4, 0xee, 0xf7, 0x23,
|
||||
/* (2^ 37)P */ 0x00, 0xd8, 0x9b, 0x8d, 0x11, 0xb1, 0x73, 0x51, 0xa7, 0xd4, 0x89, 0x31, 0xb6, 0x41, 0xd6, 0x29, 0x86, 0xc5, 0xbb, 0x88, 0x79, 0x17, 0xbf, 0xfd, 0xf5, 0x1d, 0xd8, 0xca, 0x4f, 0x89, 0x59, 0x29,
|
||||
/* (2^ 38)P */ 0x99, 0xc8, 0xbb, 0xb4, 0xf3, 0x8e, 0xbc, 0xae, 0xb9, 0x92, 0x69, 0xb2, 0x5a, 0x99, 0x48, 0x41, 0xfb, 0x2c, 0xf9, 0x34, 0x01, 0x0b, 0xe2, 0x24, 0xe8, 0xde, 0x05, 0x4a, 0x89, 0x58, 0xd1, 0x40,
|
||||
/* (2^ 39)P */ 0xf6, 0x76, 0xaf, 0x85, 0x11, 0x0b, 0xb0, 0x46, 0x79, 0x7a, 0x18, 0x73, 0x78, 0xc7, 0xba, 0x26, 0x5f, 0xff, 0x8f, 0xab, 0x95, 0xbf, 0xc0, 0x3d, 0xd7, 0x24, 0x55, 0x94, 0xd8, 0x8b, 0x60, 0x2a,
|
||||
/* (2^ 40)P */ 0x02, 0x63, 0x44, 0xbd, 0x88, 0x95, 0x44, 0x26, 0x9c, 0x43, 0x88, 0x03, 0x1c, 0xc2, 0x4b, 0x7c, 0xb2, 0x11, 0xbd, 0x83, 0xf3, 0xa4, 0x98, 0x8e, 0xb9, 0x76, 0xd8, 0xc9, 0x7b, 0x8d, 0x21, 0x26,
|
||||
/* (2^ 41)P */ 0x8a, 0x17, 0x7c, 0x99, 0x42, 0x15, 0x08, 0xe3, 0x6f, 0x60, 0xb6, 0x6f, 0xa8, 0x29, 0x2d, 0x3c, 0x74, 0x93, 0x27, 0xfa, 0x36, 0x77, 0x21, 0x5c, 0xfa, 0xb1, 0xfe, 0x4a, 0x73, 0x05, 0xde, 0x7d,
|
||||
/* (2^ 42)P */ 0xab, 0x2b, 0xd4, 0x06, 0x39, 0x0e, 0xf1, 0x3b, 0x9c, 0x64, 0x80, 0x19, 0x3e, 0x80, 0xf7, 0xe4, 0x7a, 0xbf, 0x95, 0x95, 0xf8, 0x3b, 0x05, 0xe6, 0x30, 0x55, 0x24, 0xda, 0x38, 0xaf, 0x4f, 0x39,
|
||||
/* (2^ 43)P */ 0xf4, 0x28, 0x69, 0x89, 0x58, 0xfb, 0x8e, 0x7a, 0x3c, 0x11, 0x6a, 0xcc, 0xe9, 0x78, 0xc7, 0xfb, 0x6f, 0x59, 0xaf, 0x30, 0xe3, 0x0c, 0x67, 0x72, 0xf7, 0x6c, 0x3d, 0x1d, 0xa8, 0x22, 0xf2, 0x48,
|
||||
/* (2^ 44)P */ 0xa7, 0xca, 0x72, 0x0d, 0x41, 0xce, 0x1f, 0xf0, 0x95, 0x55, 0x3b, 0x21, 0xc7, 0xec, 0x20, 0x5a, 0x83, 0x14, 0xfa, 0xc1, 0x65, 0x11, 0xc2, 0x7b, 0x41, 0xa7, 0xa8, 0x1d, 0xe3, 0x9a, 0xf8, 0x07,
|
||||
/* (2^ 45)P */ 0xf9, 0x0f, 0x83, 0xc6, 0xb4, 0xc2, 0xd2, 0x05, 0x93, 0x62, 0x31, 0xc6, 0x0f, 0x33, 0x3e, 0xd4, 0x04, 0xa9, 0xd3, 0x96, 0x0a, 0x59, 0xa5, 0xa5, 0xb6, 0x33, 0x53, 0xa6, 0x91, 0xdb, 0x5e, 0x70,
|
||||
/* (2^ 46)P */ 0xf7, 0xa5, 0xb9, 0x0b, 0x5e, 0xe1, 0x8e, 0x04, 0x5d, 0xaf, 0x0a, 0x9e, 0xca, 0xcf, 0x40, 0x32, 0x0b, 0xa4, 0xc4, 0xed, 0xce, 0x71, 0x4b, 0x8f, 0x6d, 0x4a, 0x54, 0xde, 0xa3, 0x0d, 0x1c, 0x62,
|
||||
/* (2^ 47)P */ 0x91, 0x40, 0x8c, 0xa0, 0x36, 0x28, 0x87, 0x92, 0x45, 0x14, 0xc9, 0x10, 0xb0, 0x75, 0x83, 0xce, 0x94, 0x63, 0x27, 0x4f, 0x52, 0xeb, 0x72, 0x8a, 0x35, 0x36, 0xc8, 0x7e, 0xfa, 0xfc, 0x67, 0x26,
|
||||
/* (2^ 48)P */ 0x2a, 0x75, 0xe8, 0x45, 0x33, 0x17, 0x4c, 0x7f, 0xa5, 0x79, 0x70, 0xee, 0xfe, 0x47, 0x1b, 0x06, 0x34, 0xff, 0x86, 0x9f, 0xfa, 0x9a, 0xdd, 0x25, 0x9c, 0xc8, 0x5d, 0x42, 0xf5, 0xce, 0x80, 0x37,
|
||||
/* (2^ 49)P */ 0xe9, 0xb4, 0x3b, 0x51, 0x5a, 0x03, 0x46, 0x1a, 0xda, 0x5a, 0x57, 0xac, 0x79, 0xf3, 0x1e, 0x3e, 0x50, 0x4b, 0xa2, 0x5f, 0x1c, 0x5f, 0x8c, 0xc7, 0x22, 0x9f, 0xfd, 0x34, 0x76, 0x96, 0x1a, 0x32,
|
||||
/* (2^ 50)P */ 0xfa, 0x27, 0x6e, 0x82, 0xb8, 0x07, 0x67, 0x94, 0xd0, 0x6f, 0x50, 0x4c, 0xd6, 0x84, 0xca, 0x3d, 0x36, 0x14, 0xe9, 0x75, 0x80, 0x21, 0x89, 0xc1, 0x84, 0x84, 0x3b, 0x9b, 0x16, 0x84, 0x92, 0x6d,
|
||||
/* (2^ 51)P */ 0xdf, 0x2d, 0x3f, 0x38, 0x40, 0xe8, 0x67, 0x3a, 0x75, 0x9b, 0x4f, 0x0c, 0xa3, 0xc9, 0xee, 0x33, 0x47, 0xef, 0x83, 0xa7, 0x6f, 0xc8, 0xc7, 0x3e, 0xc4, 0xfb, 0xc9, 0xba, 0x9f, 0x44, 0xec, 0x26,
|
||||
/* (2^ 52)P */ 0x7d, 0x9e, 0x9b, 0xa0, 0xcb, 0x38, 0x0f, 0x5c, 0x8c, 0x47, 0xa3, 0x62, 0xc7, 0x8c, 0x16, 0x81, 0x1c, 0x12, 0xfc, 0x06, 0xd3, 0xb0, 0x23, 0x3e, 0xdd, 0xdc, 0xef, 0xa5, 0xa0, 0x8a, 0x23, 0x5a,
|
||||
/* (2^ 53)P */ 0xff, 0x43, 0xea, 0xc4, 0x21, 0x61, 0xa2, 0x1b, 0xb5, 0x32, 0x88, 0x7c, 0x7f, 0xc7, 0xf8, 0x36, 0x9a, 0xf9, 0xdc, 0x0a, 0x0b, 0xea, 0xfb, 0x88, 0xf9, 0xeb, 0x5b, 0xc2, 0x8e, 0x93, 0xa9, 0x5c,
|
||||
/* (2^ 54)P */ 0xa0, 0xcd, 0xfc, 0x51, 0x5e, 0x6a, 0x43, 0xd5, 0x3b, 0x89, 0xcd, 0xc2, 0x97, 0x47, 0xbc, 0x1d, 0x08, 0x4a, 0x22, 0xd3, 0x65, 0x6a, 0x34, 0x19, 0x66, 0xf4, 0x9a, 0x9b, 0xe4, 0x34, 0x50, 0x0f,
|
||||
/* (2^ 55)P */ 0x6e, 0xb9, 0xe0, 0xa1, 0x67, 0x39, 0x3c, 0xf2, 0x88, 0x4d, 0x7a, 0x86, 0xfa, 0x08, 0x8b, 0xe5, 0x79, 0x16, 0x34, 0xa7, 0xc6, 0xab, 0x2f, 0xfb, 0x46, 0x69, 0x02, 0xb6, 0x1e, 0x38, 0x75, 0x2a,
|
||||
/* (2^ 56)P */ 0xac, 0x20, 0x94, 0xc1, 0xe4, 0x3b, 0x0a, 0xc8, 0xdc, 0xb6, 0xf2, 0x81, 0xc6, 0xf6, 0xb1, 0x66, 0x88, 0x33, 0xe9, 0x61, 0x67, 0x03, 0xf7, 0x7c, 0xc4, 0xa4, 0x60, 0xa6, 0xd8, 0xbb, 0xab, 0x25,
|
||||
/* (2^ 57)P */ 0x98, 0x51, 0xfd, 0x14, 0xba, 0x12, 0xea, 0x91, 0xa9, 0xff, 0x3c, 0x4a, 0xfc, 0x50, 0x49, 0x68, 0x28, 0xad, 0xf5, 0x30, 0x21, 0x84, 0x26, 0xf8, 0x41, 0xa4, 0x01, 0x53, 0xf7, 0x88, 0xa9, 0x3e,
|
||||
/* (2^ 58)P */ 0x6f, 0x8c, 0x5f, 0x69, 0x9a, 0x10, 0x78, 0xc9, 0xf3, 0xc3, 0x30, 0x05, 0x4a, 0xeb, 0x46, 0x17, 0x95, 0x99, 0x45, 0xb4, 0x77, 0x6d, 0x4d, 0x44, 0xc7, 0x5c, 0x4e, 0x05, 0x8c, 0x2b, 0x95, 0x75,
|
||||
/* (2^ 59)P */ 0xaa, 0xd6, 0xf4, 0x15, 0x79, 0x3f, 0x70, 0xa3, 0xd8, 0x47, 0x26, 0x2f, 0x20, 0x46, 0xc3, 0x66, 0x4b, 0x64, 0x1d, 0x81, 0xdf, 0x69, 0x14, 0xd0, 0x1f, 0xd7, 0xa5, 0x81, 0x7d, 0xa4, 0xfe, 0x77,
|
||||
/* (2^ 60)P */ 0x81, 0xa3, 0x7c, 0xf5, 0x9e, 0x52, 0xe9, 0xc5, 0x1a, 0x88, 0x2f, 0xce, 0xb9, 0xb4, 0xee, 0x6e, 0xd6, 0x9b, 0x00, 0xe8, 0x28, 0x1a, 0xe9, 0xb6, 0xec, 0x3f, 0xfc, 0x9a, 0x3e, 0xbe, 0x80, 0x4b,
|
||||
/* (2^ 61)P */ 0xc5, 0xd2, 0xae, 0x26, 0xc5, 0x73, 0x37, 0x7e, 0x9d, 0xa4, 0xc9, 0x53, 0xb4, 0xfc, 0x4a, 0x1b, 0x4d, 0xb2, 0xff, 0xba, 0xd7, 0xbd, 0x20, 0xa9, 0x0e, 0x40, 0x2d, 0x12, 0x9f, 0x69, 0x54, 0x7c,
|
||||
/* (2^ 62)P */ 0xc8, 0x4b, 0xa9, 0x4f, 0xe1, 0xc8, 0x46, 0xef, 0x5e, 0xed, 0x52, 0x29, 0xce, 0x74, 0xb0, 0xe0, 0xd5, 0x85, 0xd8, 0xdb, 0xe1, 0x50, 0xa4, 0xbe, 0x2c, 0x71, 0x0f, 0x32, 0x49, 0x86, 0xb6, 0x61,
|
||||
/* (2^ 63)P */ 0xd1, 0xbd, 0xcc, 0x09, 0x73, 0x5f, 0x48, 0x8a, 0x2d, 0x1a, 0x4d, 0x7d, 0x0d, 0x32, 0x06, 0xbd, 0xf4, 0xbe, 0x2d, 0x32, 0x73, 0x29, 0x23, 0x25, 0x70, 0xf7, 0x17, 0x8c, 0x75, 0xc4, 0x5d, 0x44,
|
||||
/* (2^ 64)P */ 0x3c, 0x93, 0xc8, 0x7c, 0x17, 0x34, 0x04, 0xdb, 0x9f, 0x05, 0xea, 0x75, 0x21, 0xe8, 0x6f, 0xed, 0x34, 0xdb, 0x53, 0xc0, 0xfd, 0xbe, 0xfe, 0x1e, 0x99, 0xaf, 0x5d, 0xc6, 0x67, 0xe8, 0xdb, 0x4a,
|
||||
/* (2^ 65)P */ 0xdf, 0x09, 0x06, 0xa9, 0xa2, 0x71, 0xcd, 0x3a, 0x50, 0x40, 0xd0, 0x6d, 0x85, 0x91, 0xe9, 0xe5, 0x3c, 0xc2, 0x57, 0x81, 0x68, 0x9b, 0xc6, 0x1e, 0x4d, 0xfe, 0x5c, 0x88, 0xf6, 0x27, 0x74, 0x69,
|
||||
/* (2^ 66)P */ 0x51, 0xa8, 0xe1, 0x65, 0x9b, 0x7b, 0xbe, 0xd7, 0xdd, 0x36, 0xc5, 0x22, 0xd5, 0x28, 0x3d, 0xa0, 0x45, 0xb6, 0xd2, 0x8f, 0x65, 0x9d, 0x39, 0x28, 0xe1, 0x41, 0x26, 0x7c, 0xe1, 0xb7, 0xe5, 0x49,
|
||||
/* (2^ 67)P */ 0xa4, 0x57, 0x04, 0x70, 0x98, 0x3a, 0x8c, 0x6f, 0x78, 0x67, 0xbb, 0x5e, 0xa2, 0xf0, 0x78, 0x50, 0x0f, 0x96, 0x82, 0xc3, 0xcb, 0x3c, 0x3c, 0xd1, 0xb1, 0x84, 0xdf, 0xa7, 0x58, 0x32, 0x00, 0x2e,
|
||||
/* (2^ 68)P */ 0x1c, 0x6a, 0x29, 0xe6, 0x9b, 0xf3, 0xd1, 0x8a, 0xb2, 0xbf, 0x5f, 0x2a, 0x65, 0xaa, 0xee, 0xc1, 0xcb, 0xf3, 0x26, 0xfd, 0x73, 0x06, 0xee, 0x33, 0xcc, 0x2c, 0x9d, 0xa6, 0x73, 0x61, 0x25, 0x59,
|
||||
/* (2^ 69)P */ 0x41, 0xfc, 0x18, 0x4e, 0xaa, 0x07, 0xea, 0x41, 0x1e, 0xa5, 0x87, 0x7c, 0x52, 0x19, 0xfc, 0xd9, 0x6f, 0xca, 0x31, 0x58, 0x80, 0xcb, 0xaa, 0xbd, 0x4f, 0x69, 0x16, 0xc9, 0x2d, 0x65, 0x5b, 0x44,
|
||||
/* (2^ 70)P */ 0x15, 0x23, 0x17, 0xf2, 0xa7, 0xa3, 0x92, 0xce, 0x64, 0x99, 0x1b, 0xe1, 0x2d, 0x28, 0xdc, 0x1e, 0x4a, 0x31, 0x4c, 0xe0, 0xaf, 0x3a, 0x82, 0xa1, 0x86, 0xf5, 0x7c, 0x43, 0x94, 0x2d, 0x0a, 0x79,
|
||||
/* (2^ 71)P */ 0x09, 0xe0, 0xf6, 0x93, 0xfb, 0x47, 0xc4, 0x71, 0x76, 0x52, 0x84, 0x22, 0x67, 0xa5, 0x22, 0x89, 0x69, 0x51, 0x4f, 0x20, 0x3b, 0x90, 0x70, 0xbf, 0xfe, 0x19, 0xa3, 0x1b, 0x89, 0x89, 0x7a, 0x2f,
|
||||
/* (2^ 72)P */ 0x0c, 0x14, 0xe2, 0x77, 0xb5, 0x8e, 0xa0, 0x02, 0xf4, 0xdc, 0x7b, 0x42, 0xd4, 0x4e, 0x9a, 0xed, 0xd1, 0x3c, 0x32, 0xe4, 0x44, 0xec, 0x53, 0x52, 0x5b, 0x35, 0xe9, 0x14, 0x3c, 0x36, 0x88, 0x3e,
|
||||
/* (2^ 73)P */ 0x8c, 0x0b, 0x11, 0x77, 0x42, 0xc1, 0x66, 0xaa, 0x90, 0x33, 0xa2, 0x10, 0x16, 0x39, 0xe0, 0x1a, 0xa2, 0xc2, 0x3f, 0xc9, 0x12, 0xbd, 0x30, 0x20, 0xab, 0xc7, 0x55, 0x95, 0x57, 0x41, 0xe1, 0x3e,
|
||||
/* (2^ 74)P */ 0x41, 0x7d, 0x6e, 0x6d, 0x3a, 0xde, 0x14, 0x92, 0xfe, 0x7e, 0xf1, 0x07, 0x86, 0xd8, 0xcd, 0x3c, 0x17, 0x12, 0xe1, 0xf8, 0x88, 0x12, 0x4f, 0x67, 0xd0, 0x93, 0x9f, 0x32, 0x0f, 0x25, 0x82, 0x56,
|
||||
/* (2^ 75)P */ 0x6e, 0x39, 0x2e, 0x6d, 0x13, 0x0b, 0xf0, 0x6c, 0xbf, 0xde, 0x14, 0x10, 0x6f, 0xf8, 0x4c, 0x6e, 0x83, 0x4e, 0xcc, 0xbf, 0xb5, 0xb1, 0x30, 0x59, 0xb6, 0x16, 0xba, 0x8a, 0xb4, 0x69, 0x70, 0x04,
|
||||
/* (2^ 76)P */ 0x93, 0x07, 0xb2, 0x69, 0xab, 0xe4, 0x4c, 0x0d, 0x9e, 0xfb, 0xd0, 0x97, 0x1a, 0xb9, 0x4d, 0xb2, 0x1d, 0xd0, 0x00, 0x4e, 0xf5, 0x50, 0xfa, 0xcd, 0xb5, 0xdd, 0x8b, 0x36, 0x85, 0x10, 0x1b, 0x22,
|
||||
/* (2^ 77)P */ 0xd2, 0xd8, 0xe3, 0xb1, 0x68, 0x94, 0xe5, 0xe7, 0x93, 0x2f, 0x12, 0xbd, 0x63, 0x65, 0xc5, 0x53, 0x09, 0x3f, 0x66, 0xe0, 0x03, 0xa9, 0xe8, 0xee, 0x42, 0x3d, 0xbe, 0xcb, 0x62, 0xa6, 0xef, 0x61,
|
||||
/* (2^ 78)P */ 0x2a, 0xab, 0x6e, 0xde, 0xdd, 0xdd, 0xf8, 0x2c, 0x31, 0xf2, 0x35, 0x14, 0xd5, 0x0a, 0xf8, 0x9b, 0x73, 0x49, 0xf0, 0xc9, 0xce, 0xda, 0xea, 0x5d, 0x27, 0x9b, 0xd2, 0x41, 0x5d, 0x5b, 0x27, 0x29,
|
||||
/* (2^ 79)P */ 0x4f, 0xf1, 0xeb, 0x95, 0x08, 0x0f, 0xde, 0xcf, 0xa7, 0x05, 0x49, 0x05, 0x6b, 0xb9, 0xaa, 0xb9, 0xfd, 0x20, 0xc4, 0xa1, 0xd9, 0x0d, 0xe8, 0xca, 0xc7, 0xbb, 0x73, 0x16, 0x2f, 0xbf, 0x63, 0x0a,
|
||||
/* (2^ 80)P */ 0x8c, 0xbc, 0x8f, 0x95, 0x11, 0x6e, 0x2f, 0x09, 0xad, 0x2f, 0x82, 0x04, 0xe8, 0x81, 0x2a, 0x67, 0x17, 0x25, 0xd5, 0x60, 0x15, 0x35, 0xc8, 0xca, 0xf8, 0x92, 0xf1, 0xc8, 0x22, 0x77, 0x3f, 0x6f,
|
||||
/* (2^ 81)P */ 0xb7, 0x94, 0xe8, 0xc2, 0xcc, 0x90, 0xba, 0xf8, 0x0d, 0x9f, 0xff, 0x38, 0xa4, 0x57, 0x75, 0x2c, 0x59, 0x23, 0xe5, 0x5a, 0x85, 0x1d, 0x4d, 0x89, 0x69, 0x3d, 0x74, 0x7b, 0x15, 0x22, 0xe1, 0x68,
|
||||
/* (2^ 82)P */ 0xf3, 0x19, 0xb9, 0xcf, 0x70, 0x55, 0x7e, 0xd8, 0xb9, 0x8d, 0x79, 0x95, 0xcd, 0xde, 0x2c, 0x3f, 0xce, 0xa2, 0xc0, 0x10, 0x47, 0x15, 0x21, 0x21, 0xb2, 0xc5, 0x6d, 0x24, 0x15, 0xa1, 0x66, 0x3c,
|
||||
/* (2^ 83)P */ 0x72, 0xcb, 0x4e, 0x29, 0x62, 0xc5, 0xed, 0xcb, 0x16, 0x0b, 0x28, 0x6a, 0xc3, 0x43, 0x71, 0xba, 0x67, 0x8b, 0x07, 0xd4, 0xef, 0xc2, 0x10, 0x96, 0x1e, 0x4b, 0x6a, 0x94, 0x5d, 0x73, 0x44, 0x61,
|
||||
/* (2^ 84)P */ 0x50, 0x33, 0x5b, 0xd7, 0x1e, 0x11, 0x6f, 0x53, 0x1b, 0xd8, 0x41, 0x20, 0x8c, 0xdb, 0x11, 0x02, 0x3c, 0x41, 0x10, 0x0e, 0x00, 0xb1, 0x3c, 0xf9, 0x76, 0x88, 0x9e, 0x03, 0x3c, 0xfd, 0x9d, 0x14,
|
||||
/* (2^ 85)P */ 0x5b, 0x15, 0x63, 0x6b, 0xe4, 0xdd, 0x79, 0xd4, 0x76, 0x79, 0x83, 0x3c, 0xe9, 0x15, 0x6e, 0xb6, 0x38, 0xe0, 0x13, 0x1f, 0x3b, 0xe4, 0xfd, 0xda, 0x35, 0x0b, 0x4b, 0x2e, 0x1a, 0xda, 0xaf, 0x5f,
|
||||
/* (2^ 86)P */ 0x81, 0x75, 0x19, 0x17, 0xdf, 0xbb, 0x00, 0x36, 0xc2, 0xd2, 0x3c, 0xbe, 0x0b, 0x05, 0x72, 0x39, 0x86, 0xbe, 0xd5, 0xbd, 0x6d, 0x90, 0x38, 0x59, 0x0f, 0x86, 0x9b, 0x3f, 0xe4, 0xe5, 0xfc, 0x34,
|
||||
/* (2^ 87)P */ 0x02, 0x4d, 0xd1, 0x42, 0xcd, 0xa4, 0xa8, 0x75, 0x65, 0xdf, 0x41, 0x34, 0xc5, 0xab, 0x8d, 0x82, 0xd3, 0x31, 0xe1, 0xd2, 0xed, 0xab, 0xdc, 0x33, 0x5f, 0xd2, 0x14, 0xb8, 0x6f, 0xd7, 0xba, 0x3e,
|
||||
/* (2^ 88)P */ 0x0f, 0xe1, 0x70, 0x6f, 0x56, 0x6f, 0x90, 0xd4, 0x5a, 0x0f, 0x69, 0x51, 0xaa, 0xf7, 0x12, 0x5d, 0xf2, 0xfc, 0xce, 0x76, 0x6e, 0xb1, 0xad, 0x45, 0x99, 0x29, 0x23, 0xad, 0xae, 0x68, 0xf7, 0x01,
|
||||
/* (2^ 89)P */ 0xbd, 0xfe, 0x48, 0x62, 0x7b, 0xc7, 0x6c, 0x2b, 0xfd, 0xaf, 0x3a, 0xec, 0x28, 0x06, 0xd3, 0x3c, 0x6a, 0x48, 0xef, 0xd4, 0x80, 0x0b, 0x1c, 0xce, 0x23, 0x6c, 0xf6, 0xa6, 0x2e, 0xff, 0x3b, 0x4c,
|
||||
/* (2^ 90)P */ 0x5f, 0xeb, 0xea, 0x4a, 0x09, 0xc4, 0x2e, 0x3f, 0xa7, 0x2c, 0x37, 0x6e, 0x28, 0x9b, 0xb1, 0x61, 0x1d, 0x70, 0x2a, 0xde, 0x66, 0xa9, 0xef, 0x5e, 0xef, 0xe3, 0x55, 0xde, 0x65, 0x05, 0xb2, 0x23,
|
||||
/* (2^ 91)P */ 0x57, 0x85, 0xd5, 0x79, 0x52, 0xca, 0x01, 0xe3, 0x4f, 0x87, 0xc2, 0x27, 0xce, 0xd4, 0xb2, 0x07, 0x67, 0x1d, 0xcf, 0x9d, 0x8a, 0xcd, 0x32, 0xa5, 0x56, 0xff, 0x2b, 0x3f, 0xe2, 0xfe, 0x52, 0x2a,
|
||||
/* (2^ 92)P */ 0x3d, 0x66, 0xd8, 0x7c, 0xb3, 0xef, 0x24, 0x86, 0x94, 0x75, 0xbd, 0xff, 0x20, 0xac, 0xc7, 0xbb, 0x45, 0x74, 0xd3, 0x82, 0x9c, 0x5e, 0xb8, 0x57, 0x66, 0xec, 0xa6, 0x86, 0xcb, 0x52, 0x30, 0x7b,
|
||||
/* (2^ 93)P */ 0x1e, 0xe9, 0x25, 0x25, 0xad, 0xf0, 0x82, 0x34, 0xa0, 0xdc, 0x8e, 0xd2, 0x43, 0x80, 0xb6, 0x2c, 0x3a, 0x00, 0x1b, 0x2e, 0x05, 0x6d, 0x4f, 0xaf, 0x0a, 0x1b, 0x78, 0x29, 0x25, 0x8c, 0x5f, 0x18,
|
||||
/* (2^ 94)P */ 0xd6, 0xe0, 0x0c, 0xd8, 0x5b, 0xde, 0x41, 0xaa, 0xd6, 0xe9, 0x53, 0x68, 0x41, 0xb2, 0x07, 0x94, 0x3a, 0x4c, 0x7f, 0x35, 0x6e, 0xc3, 0x3e, 0x56, 0xce, 0x7b, 0x29, 0x0e, 0xdd, 0xb8, 0xc4, 0x4c,
|
||||
/* (2^ 95)P */ 0x0e, 0x73, 0xb8, 0xff, 0x52, 0x1a, 0xfc, 0xa2, 0x37, 0x8e, 0x05, 0x67, 0x6e, 0xf1, 0x11, 0x18, 0xe1, 0x4e, 0xdf, 0xcd, 0x66, 0xa3, 0xf9, 0x10, 0x99, 0xf0, 0xb9, 0xa0, 0xc4, 0xa0, 0xf4, 0x72,
|
||||
/* (2^ 96)P */ 0xa7, 0x4e, 0x3f, 0x66, 0x6f, 0xc0, 0x16, 0x8c, 0xba, 0x0f, 0x97, 0x4e, 0xf7, 0x3a, 0x3b, 0x69, 0x45, 0xc3, 0x9e, 0xd6, 0xf1, 0xe7, 0x02, 0x21, 0x89, 0x80, 0x8a, 0x96, 0xbc, 0x3c, 0xa5, 0x0b,
|
||||
/* (2^ 97)P */ 0x37, 0x55, 0xa1, 0xfe, 0xc7, 0x9d, 0x3d, 0xca, 0x93, 0x64, 0x53, 0x51, 0xbb, 0x24, 0x68, 0x4c, 0xb1, 0x06, 0x40, 0x84, 0x14, 0x63, 0x88, 0xb9, 0x60, 0xcc, 0x54, 0xb4, 0x2a, 0xa7, 0xd2, 0x40,
|
||||
/* (2^ 98)P */ 0x75, 0x09, 0x57, 0x12, 0xb7, 0xa1, 0x36, 0x59, 0x57, 0xa6, 0xbd, 0xde, 0x48, 0xd6, 0xb9, 0x91, 0xea, 0x30, 0x43, 0xb6, 0x4b, 0x09, 0x44, 0x33, 0xd0, 0x51, 0xee, 0x12, 0x0d, 0xa1, 0x6b, 0x00,
|
||||
/* (2^ 99)P */ 0x58, 0x5d, 0xde, 0xf5, 0x68, 0x84, 0x22, 0x19, 0xb0, 0x05, 0xcc, 0x38, 0x4c, 0x2f, 0xb1, 0x0e, 0x90, 0x19, 0x60, 0xd5, 0x9d, 0x9f, 0x03, 0xa1, 0x0b, 0x0e, 0xff, 0x4f, 0xce, 0xd4, 0x02, 0x45,
|
||||
/* (2^100)P */ 0x89, 0xc1, 0x37, 0x68, 0x10, 0x54, 0x20, 0xeb, 0x3c, 0xb9, 0xd3, 0x6d, 0x4c, 0x54, 0xf6, 0xd0, 0x4f, 0xd7, 0x16, 0xc4, 0x64, 0x70, 0x72, 0x40, 0xf0, 0x2e, 0x50, 0x4b, 0x11, 0xc6, 0x15, 0x6e,
|
||||
/* (2^101)P */ 0x6b, 0xa7, 0xb1, 0xcf, 0x98, 0xa3, 0xf2, 0x4d, 0xb1, 0xf6, 0xf2, 0x19, 0x74, 0x6c, 0x25, 0x11, 0x43, 0x60, 0x6e, 0x06, 0x62, 0x79, 0x49, 0x4a, 0x44, 0x5b, 0x35, 0x41, 0xab, 0x3a, 0x5b, 0x70,
|
||||
/* (2^102)P */ 0xd8, 0xb1, 0x97, 0xd7, 0x36, 0xf5, 0x5e, 0x36, 0xdb, 0xf0, 0xdd, 0x22, 0xd6, 0x6b, 0x07, 0x00, 0x88, 0x5a, 0x57, 0xe0, 0xb0, 0x33, 0xbf, 0x3b, 0x4d, 0xca, 0xe4, 0xc8, 0x05, 0xaa, 0x77, 0x37,
|
||||
/* (2^103)P */ 0x5f, 0xdb, 0x78, 0x55, 0xc8, 0x45, 0x27, 0x39, 0xe2, 0x5a, 0xae, 0xdb, 0x49, 0x41, 0xda, 0x6f, 0x67, 0x98, 0xdc, 0x8a, 0x0b, 0xb0, 0xf0, 0xb1, 0xa3, 0x1d, 0x6f, 0xd3, 0x37, 0x34, 0x96, 0x09,
|
||||
/* (2^104)P */ 0x53, 0x38, 0xdc, 0xa5, 0x90, 0x4e, 0x82, 0x7e, 0xbd, 0x5c, 0x13, 0x1f, 0x64, 0xf6, 0xb5, 0xcc, 0xcc, 0x8f, 0xce, 0x87, 0x6c, 0xd8, 0x36, 0x67, 0x9f, 0x24, 0x04, 0x66, 0xe2, 0x3c, 0x5f, 0x62,
|
||||
/* (2^105)P */ 0x3f, 0xf6, 0x02, 0x95, 0x05, 0xc8, 0x8a, 0xaf, 0x69, 0x14, 0x35, 0x2e, 0x0a, 0xe7, 0x05, 0x0c, 0x05, 0x63, 0x4b, 0x76, 0x9c, 0x2e, 0x29, 0x35, 0xc3, 0x3a, 0xe2, 0xc7, 0x60, 0x43, 0x39, 0x1a,
|
||||
/* (2^106)P */ 0x64, 0x32, 0x18, 0x51, 0x32, 0xd5, 0xc6, 0xd5, 0x4f, 0xb7, 0xc2, 0x43, 0xbd, 0x5a, 0x06, 0x62, 0x9b, 0x3f, 0x97, 0x3b, 0xd0, 0xf5, 0xfb, 0xb5, 0x5e, 0x6e, 0x20, 0x61, 0x36, 0xda, 0xa3, 0x13,
|
||||
/* (2^107)P */ 0xe5, 0x94, 0x5d, 0x72, 0x37, 0x58, 0xbd, 0xc6, 0xc5, 0x16, 0x50, 0x20, 0x12, 0x09, 0xe3, 0x18, 0x68, 0x3c, 0x03, 0x70, 0x15, 0xce, 0x88, 0x20, 0x87, 0x79, 0x83, 0x5c, 0x49, 0x1f, 0xba, 0x7f,
|
||||
/* (2^108)P */ 0x9d, 0x07, 0xf9, 0xf2, 0x23, 0x74, 0x8c, 0x5a, 0xc5, 0x3f, 0x02, 0x34, 0x7b, 0x15, 0x35, 0x17, 0x51, 0xb3, 0xfa, 0xd2, 0x9a, 0xb4, 0xf9, 0xe4, 0x3c, 0xe3, 0x78, 0xc8, 0x72, 0xff, 0x91, 0x66,
|
||||
/* (2^109)P */ 0x3e, 0xff, 0x5e, 0xdc, 0xde, 0x2a, 0x2c, 0x12, 0xf4, 0x6c, 0x95, 0xd8, 0xf1, 0x4b, 0xdd, 0xf8, 0xda, 0x5b, 0x9e, 0x9e, 0x5d, 0x20, 0x86, 0xeb, 0x43, 0xc7, 0x75, 0xd9, 0xb9, 0x92, 0x9b, 0x04,
|
||||
/* (2^110)P */ 0x5a, 0xc0, 0xf6, 0xb0, 0x30, 0x97, 0x37, 0xa5, 0x53, 0xa5, 0xf3, 0xc6, 0xac, 0xff, 0xa0, 0x72, 0x6d, 0xcd, 0x0d, 0xb2, 0x34, 0x2c, 0x03, 0xb0, 0x4a, 0x16, 0xd5, 0x88, 0xbc, 0x9d, 0x0e, 0x47,
|
||||
/* (2^111)P */ 0x47, 0xc0, 0x37, 0xa2, 0x0c, 0xf1, 0x9c, 0xb1, 0xa2, 0x81, 0x6c, 0x1f, 0x71, 0x66, 0x54, 0xb6, 0x43, 0x0b, 0xd8, 0x6d, 0xd1, 0x1b, 0x32, 0xb3, 0x8e, 0xbe, 0x5f, 0x0c, 0x60, 0x4f, 0xc1, 0x48,
|
||||
/* (2^112)P */ 0x03, 0xc8, 0xa6, 0x4a, 0x26, 0x1c, 0x45, 0x66, 0xa6, 0x7d, 0xfa, 0xa4, 0x04, 0x39, 0x6e, 0xb6, 0x95, 0x83, 0x12, 0xb3, 0xb0, 0x19, 0x5f, 0xd4, 0x10, 0xbc, 0xc9, 0xc3, 0x27, 0x26, 0x60, 0x31,
|
||||
/* (2^113)P */ 0x0d, 0xe1, 0xe4, 0x32, 0x48, 0xdc, 0x20, 0x31, 0xf7, 0x17, 0xc7, 0x56, 0x67, 0xc4, 0x20, 0xeb, 0x94, 0x02, 0x28, 0x67, 0x3f, 0x2e, 0xf5, 0x00, 0x09, 0xc5, 0x30, 0x47, 0xc1, 0x4f, 0x6d, 0x56,
|
||||
/* (2^114)P */ 0x06, 0x72, 0x83, 0xfd, 0x40, 0x5d, 0x3a, 0x7e, 0x7a, 0x54, 0x59, 0x71, 0xdc, 0x26, 0xe9, 0xc1, 0x95, 0x60, 0x8d, 0xa6, 0xfb, 0x30, 0x67, 0x21, 0xa7, 0xce, 0x69, 0x3f, 0x84, 0xc3, 0xe8, 0x22,
|
||||
/* (2^115)P */ 0x2b, 0x4b, 0x0e, 0x93, 0xe8, 0x74, 0xd0, 0x33, 0x16, 0x58, 0xd1, 0x84, 0x0e, 0x35, 0xe4, 0xb6, 0x65, 0x23, 0xba, 0xd6, 0x6a, 0xc2, 0x34, 0x55, 0xf3, 0xf3, 0xf1, 0x89, 0x2f, 0xc1, 0x73, 0x77,
|
||||
/* (2^116)P */ 0xaa, 0x62, 0x79, 0xa5, 0x4d, 0x40, 0xba, 0x8c, 0x56, 0xce, 0x99, 0x19, 0xa8, 0x97, 0x98, 0x5b, 0xfc, 0x92, 0x16, 0x12, 0x2f, 0x86, 0x8e, 0x50, 0x91, 0xc2, 0x93, 0xa0, 0x7f, 0x90, 0x81, 0x3a,
|
||||
/* (2^117)P */ 0x10, 0xa5, 0x25, 0x47, 0xff, 0xd0, 0xde, 0x0d, 0x03, 0xc5, 0x3f, 0x67, 0x10, 0xcc, 0xd8, 0x10, 0x89, 0x4e, 0x1f, 0x9f, 0x1c, 0x15, 0x9d, 0x5b, 0x4c, 0xa4, 0x09, 0xcb, 0xd5, 0xc1, 0xa5, 0x32,
|
||||
/* (2^118)P */ 0xfb, 0x41, 0x05, 0xb9, 0x42, 0xa4, 0x0a, 0x1e, 0xdb, 0x85, 0xb4, 0xc1, 0x7c, 0xeb, 0x85, 0x5f, 0xe5, 0xf2, 0x9d, 0x8a, 0xce, 0x95, 0xe5, 0xbe, 0x36, 0x22, 0x42, 0x22, 0xc7, 0x96, 0xe4, 0x25,
|
||||
/* (2^119)P */ 0xb9, 0xe5, 0x0f, 0xcd, 0x46, 0x3c, 0xdf, 0x5e, 0x88, 0x33, 0xa4, 0xd2, 0x7e, 0x5a, 0xe7, 0x34, 0x52, 0xe3, 0x61, 0xd7, 0x11, 0xde, 0x88, 0xe4, 0x5c, 0x54, 0x85, 0xa0, 0x01, 0x8a, 0x87, 0x0e,
|
||||
/* (2^120)P */ 0x04, 0xbb, 0x21, 0xe0, 0x77, 0x3c, 0x49, 0xba, 0x9a, 0x89, 0xdf, 0xc7, 0x43, 0x18, 0x4d, 0x2b, 0x67, 0x0d, 0xe8, 0x7a, 0x48, 0x7a, 0xa3, 0x9e, 0x94, 0x17, 0xe4, 0x11, 0x80, 0x95, 0xa9, 0x67,
|
||||
/* (2^121)P */ 0x65, 0xb0, 0x97, 0x66, 0x1a, 0x05, 0x58, 0x4b, 0xd4, 0xa6, 0x6b, 0x8d, 0x7d, 0x3f, 0xe3, 0x47, 0xc1, 0x46, 0xca, 0x83, 0xd4, 0xa8, 0x4d, 0xbb, 0x0d, 0xdb, 0xc2, 0x81, 0xa1, 0xca, 0xbe, 0x68,
|
||||
/* (2^122)P */ 0xa5, 0x9a, 0x98, 0x0b, 0xe9, 0x80, 0x89, 0x8d, 0x9b, 0xc9, 0x93, 0x2c, 0x4a, 0xb1, 0x5e, 0xf9, 0xa2, 0x73, 0x6e, 0x79, 0xc4, 0xc7, 0xc6, 0x51, 0x69, 0xb5, 0xef, 0xb5, 0x63, 0x83, 0x22, 0x6e,
|
||||
/* (2^123)P */ 0xc8, 0x24, 0xd6, 0x2d, 0xb0, 0xc0, 0xbb, 0xc6, 0xee, 0x70, 0x81, 0xec, 0x7d, 0xb4, 0x7e, 0x77, 0xa9, 0xaf, 0xcf, 0x04, 0xa0, 0x15, 0xde, 0x3c, 0x9b, 0xbf, 0x60, 0x71, 0x08, 0xbc, 0xc6, 0x1d,
|
||||
/* (2^124)P */ 0x02, 0x40, 0xc3, 0xee, 0x43, 0xe0, 0x07, 0x2e, 0x7f, 0xdc, 0x68, 0x7a, 0x67, 0xfc, 0xe9, 0x18, 0x9a, 0x5b, 0xd1, 0x8b, 0x18, 0x03, 0xda, 0xd8, 0x53, 0x82, 0x56, 0x00, 0xbb, 0xc3, 0xfb, 0x48,
|
||||
/* (2^125)P */ 0xe1, 0x4c, 0x65, 0xfb, 0x4c, 0x7d, 0x54, 0x57, 0xad, 0xe2, 0x58, 0xa0, 0x82, 0x5b, 0x56, 0xd3, 0x78, 0x44, 0x15, 0xbf, 0x0b, 0xaf, 0x3e, 0xf6, 0x18, 0xbb, 0xdf, 0x14, 0xf1, 0x1e, 0x53, 0x47,
|
||||
/* (2^126)P */ 0x87, 0xc5, 0x78, 0x42, 0x0a, 0x63, 0xec, 0xe1, 0xf3, 0x83, 0x8e, 0xca, 0x46, 0xd5, 0x07, 0x55, 0x2b, 0x0c, 0xdc, 0x3a, 0xc6, 0x35, 0xe1, 0x85, 0x4e, 0x84, 0x82, 0x56, 0xa8, 0xef, 0xa7, 0x0a,
|
||||
/* (2^127)P */ 0x15, 0xf6, 0xe1, 0xb3, 0xa8, 0x1b, 0x69, 0x72, 0xfa, 0x3f, 0xbe, 0x1f, 0x70, 0xe9, 0xb4, 0x32, 0x68, 0x78, 0xbb, 0x39, 0x2e, 0xd9, 0xb6, 0x97, 0xe8, 0x39, 0x2e, 0xa0, 0xde, 0x53, 0xfe, 0x2c,
|
||||
/* (2^128)P */ 0xb0, 0x52, 0xcd, 0x85, 0xcd, 0x92, 0x73, 0x68, 0x31, 0x98, 0xe2, 0x10, 0xc9, 0x66, 0xff, 0x27, 0x06, 0x2d, 0x83, 0xa9, 0x56, 0x45, 0x13, 0x97, 0xa0, 0xf8, 0x84, 0x0a, 0x36, 0xb0, 0x9b, 0x26,
|
||||
/* (2^129)P */ 0x5c, 0xf8, 0x43, 0x76, 0x45, 0x55, 0x6e, 0x70, 0x1b, 0x7d, 0x59, 0x9b, 0x8c, 0xa4, 0x34, 0x37, 0x72, 0xa4, 0xef, 0xc6, 0xe8, 0x91, 0xee, 0x7a, 0xe0, 0xd9, 0xa9, 0x98, 0xc1, 0xab, 0xd6, 0x5c,
|
||||
/* (2^130)P */ 0x1a, 0xe4, 0x3c, 0xcb, 0x06, 0xde, 0x04, 0x0e, 0x38, 0xe1, 0x02, 0x34, 0x89, 0xeb, 0xc6, 0xd8, 0x72, 0x37, 0x6e, 0x68, 0xbb, 0x59, 0x46, 0x90, 0xc8, 0xa8, 0x6b, 0x74, 0x71, 0xc3, 0x15, 0x72,
|
||||
/* (2^131)P */ 0xd9, 0xa2, 0xe4, 0xea, 0x7e, 0xa9, 0x12, 0xfd, 0xc5, 0xf2, 0x94, 0x63, 0x51, 0xb7, 0x14, 0x95, 0x94, 0xf2, 0x08, 0x92, 0x80, 0xd5, 0x6f, 0x26, 0xb9, 0x26, 0x9a, 0x61, 0x85, 0x70, 0x84, 0x5c,
|
||||
/* (2^132)P */ 0xea, 0x94, 0xd6, 0xfe, 0x10, 0x54, 0x98, 0x52, 0x54, 0xd2, 0x2e, 0x4a, 0x93, 0x5b, 0x90, 0x3c, 0x67, 0xe4, 0x3b, 0x2d, 0x69, 0x47, 0xbb, 0x10, 0xe1, 0xe9, 0xe5, 0x69, 0x2d, 0x3d, 0x3b, 0x06,
|
||||
/* (2^133)P */ 0xeb, 0x7d, 0xa5, 0xdd, 0xee, 0x26, 0x27, 0x47, 0x91, 0x18, 0xf4, 0x10, 0xae, 0xc4, 0xb6, 0xef, 0x14, 0x76, 0x30, 0x7b, 0x91, 0x41, 0x16, 0x2b, 0x7c, 0x5b, 0xf4, 0xc4, 0x4f, 0x55, 0x7c, 0x11,
|
||||
/* (2^134)P */ 0x12, 0x88, 0x9d, 0x8f, 0x11, 0xf3, 0x7c, 0xc0, 0x39, 0x79, 0x01, 0x50, 0x20, 0xd8, 0xdb, 0x01, 0x27, 0x28, 0x1b, 0x17, 0xf4, 0x03, 0xe8, 0xd7, 0xea, 0x25, 0xd2, 0x87, 0x74, 0xe8, 0x15, 0x10,
|
||||
/* (2^135)P */ 0x4d, 0xcc, 0x3a, 0xd2, 0xfe, 0xe3, 0x8d, 0xc5, 0x2d, 0xbe, 0xa7, 0x94, 0xc2, 0x91, 0xdb, 0x50, 0x57, 0xf4, 0x9c, 0x1c, 0x3d, 0xd4, 0x94, 0x0b, 0x4a, 0x52, 0x37, 0x6e, 0xfa, 0x40, 0x16, 0x6b,
|
||||
/* (2^136)P */ 0x09, 0x0d, 0xda, 0x5f, 0x6c, 0x34, 0x2f, 0x69, 0x51, 0x31, 0x4d, 0xfa, 0x59, 0x1c, 0x0b, 0x20, 0x96, 0xa2, 0x77, 0x07, 0x76, 0x6f, 0xc4, 0xb8, 0xcf, 0xfb, 0xfd, 0x3f, 0x5f, 0x39, 0x38, 0x4b,
|
||||
/* (2^137)P */ 0x71, 0xd6, 0x54, 0xbe, 0x00, 0x5e, 0xd2, 0x18, 0xa6, 0xab, 0xc8, 0xbe, 0x82, 0x05, 0xd5, 0x60, 0x82, 0xb9, 0x78, 0x3b, 0x26, 0x8f, 0xad, 0x87, 0x32, 0x04, 0xda, 0x9c, 0x4e, 0xf6, 0xfd, 0x50,
|
||||
/* (2^138)P */ 0xf0, 0xdc, 0x78, 0xc5, 0xaa, 0x67, 0xf5, 0x90, 0x3b, 0x13, 0xa3, 0xf2, 0x0e, 0x9b, 0x1e, 0xef, 0x71, 0xde, 0xd9, 0x42, 0x92, 0xba, 0xeb, 0x0e, 0xc7, 0x01, 0x31, 0xf0, 0x9b, 0x3c, 0x47, 0x15,
|
||||
/* (2^139)P */ 0x95, 0x80, 0xb7, 0x56, 0xae, 0xe8, 0x77, 0x7c, 0x8e, 0x07, 0x6f, 0x6e, 0x66, 0xe7, 0x78, 0xb6, 0x1f, 0xba, 0x48, 0x53, 0x61, 0xb9, 0xa0, 0x2d, 0x0b, 0x3f, 0x73, 0xff, 0xc1, 0x31, 0xf9, 0x7c,
|
||||
/* (2^140)P */ 0x6c, 0x36, 0x0a, 0x0a, 0xf5, 0x57, 0xb3, 0x26, 0x32, 0xd7, 0x87, 0x2b, 0xf4, 0x8c, 0x70, 0xe9, 0xc0, 0xb2, 0x1c, 0xf9, 0xa5, 0xee, 0x3a, 0xc1, 0x4c, 0xbb, 0x43, 0x11, 0x99, 0x0c, 0xd9, 0x35,
|
||||
/* (2^141)P */ 0xdc, 0xd9, 0xa0, 0xa9, 0x04, 0xc4, 0xc1, 0x47, 0x51, 0xd2, 0x72, 0x19, 0x45, 0x58, 0x9e, 0x65, 0x31, 0x8c, 0xb3, 0x73, 0xc4, 0xa8, 0x75, 0x38, 0x24, 0x1f, 0x56, 0x79, 0xd3, 0x9e, 0xbd, 0x1f,
|
||||
/* (2^142)P */ 0x8d, 0xc2, 0x1e, 0xd4, 0x6f, 0xbc, 0xfa, 0x11, 0xca, 0x2d, 0x2a, 0xcd, 0xe3, 0xdf, 0xf8, 0x7e, 0x95, 0x45, 0x40, 0x8c, 0x5d, 0x3b, 0xe7, 0x72, 0x27, 0x2f, 0xb7, 0x54, 0x49, 0xfa, 0x35, 0x61,
|
||||
/* (2^143)P */ 0x9c, 0xb6, 0x24, 0xde, 0xa2, 0x32, 0xfc, 0xcc, 0x88, 0x5d, 0x09, 0x1f, 0x8c, 0x69, 0x55, 0x3f, 0x29, 0xf9, 0xc3, 0x5a, 0xed, 0x50, 0x33, 0xbe, 0xeb, 0x7e, 0x47, 0xca, 0x06, 0xf8, 0x9b, 0x5e,
|
||||
/* (2^144)P */ 0x68, 0x9f, 0x30, 0x3c, 0xb6, 0x8f, 0xce, 0xe9, 0xf4, 0xf9, 0xe1, 0x65, 0x35, 0xf6, 0x76, 0x53, 0xf1, 0x93, 0x63, 0x5a, 0xb3, 0xcf, 0xaf, 0xd1, 0x06, 0x35, 0x62, 0xe5, 0xed, 0xa1, 0x32, 0x66,
|
||||
/* (2^145)P */ 0x4c, 0xed, 0x2d, 0x0c, 0x39, 0x6c, 0x7d, 0x0b, 0x1f, 0xcb, 0x04, 0xdf, 0x81, 0x32, 0xcb, 0x56, 0xc7, 0xc3, 0xec, 0x49, 0x12, 0x5a, 0x30, 0x66, 0x2a, 0xa7, 0x8c, 0xa3, 0x60, 0x8b, 0x58, 0x5d,
|
||||
/* (2^146)P */ 0x2d, 0xf4, 0xe5, 0xe8, 0x78, 0xbf, 0xec, 0xa6, 0xec, 0x3e, 0x8a, 0x3c, 0x4b, 0xb4, 0xee, 0x86, 0x04, 0x16, 0xd2, 0xfb, 0x48, 0x9c, 0x21, 0xec, 0x31, 0x67, 0xc3, 0x17, 0xf5, 0x1a, 0xaf, 0x1a,
|
||||
/* (2^147)P */ 0xe7, 0xbd, 0x69, 0x67, 0x83, 0xa2, 0x06, 0xc3, 0xdb, 0x2a, 0x1e, 0x2b, 0x62, 0x80, 0x82, 0x20, 0xa6, 0x94, 0xff, 0xfb, 0x1f, 0xf5, 0x27, 0x80, 0x6b, 0xf2, 0x24, 0x11, 0xce, 0xa1, 0xcf, 0x76,
|
||||
/* (2^148)P */ 0xb6, 0xab, 0x22, 0x24, 0x56, 0x00, 0xeb, 0x18, 0xc3, 0x29, 0x8c, 0x8f, 0xd5, 0xc4, 0x77, 0xf3, 0x1a, 0x56, 0x31, 0xf5, 0x07, 0xc2, 0xbb, 0x4d, 0x27, 0x8a, 0x12, 0x82, 0xf0, 0xb7, 0x53, 0x02,
|
||||
/* (2^149)P */ 0xe0, 0x17, 0x2c, 0xb6, 0x1c, 0x09, 0x1f, 0x3d, 0xa9, 0x28, 0x46, 0xd6, 0xab, 0xe1, 0x60, 0x48, 0x53, 0x42, 0x9d, 0x30, 0x36, 0x74, 0xd1, 0x52, 0x76, 0xe5, 0xfa, 0x3e, 0xe1, 0x97, 0x6f, 0x35,
|
||||
/* (2^150)P */ 0x5b, 0x53, 0x50, 0xa1, 0x1a, 0xe1, 0x51, 0xd3, 0xcc, 0x78, 0xd8, 0x1d, 0xbb, 0x45, 0x6b, 0x3e, 0x98, 0x2c, 0xd9, 0xbe, 0x28, 0x61, 0x77, 0x0c, 0xb8, 0x85, 0x28, 0x03, 0x93, 0xae, 0x34, 0x1d,
|
||||
/* (2^151)P */ 0xc3, 0xa4, 0x5b, 0xa8, 0x8c, 0x48, 0xa0, 0x4b, 0xce, 0xe6, 0x9c, 0x3c, 0xc3, 0x48, 0x53, 0x98, 0x70, 0xa7, 0xbd, 0x97, 0x6f, 0x4c, 0x12, 0x66, 0x4a, 0x12, 0x54, 0x06, 0x29, 0xa0, 0x81, 0x0f,
|
||||
/* (2^152)P */ 0xfd, 0x86, 0x9b, 0x56, 0xa6, 0x9c, 0xd0, 0x9e, 0x2d, 0x9a, 0xaf, 0x18, 0xfd, 0x09, 0x10, 0x81, 0x0a, 0xc2, 0xd8, 0x93, 0x3f, 0xd0, 0x08, 0xff, 0x6b, 0xf2, 0xae, 0x9f, 0x19, 0x48, 0xa1, 0x52,
|
||||
/* (2^153)P */ 0x73, 0x1b, 0x8d, 0x2d, 0xdc, 0xf9, 0x03, 0x3e, 0x70, 0x1a, 0x96, 0x73, 0x18, 0x80, 0x05, 0x42, 0x70, 0x59, 0xa3, 0x41, 0xf0, 0x87, 0xd9, 0xc0, 0x49, 0xd5, 0xc0, 0xa1, 0x15, 0x1f, 0xaa, 0x07,
|
||||
/* (2^154)P */ 0x24, 0x72, 0xd2, 0x8c, 0xe0, 0x6c, 0xd4, 0xdf, 0x39, 0x42, 0x4e, 0x93, 0x4f, 0x02, 0x0a, 0x6d, 0x59, 0x7b, 0x89, 0x99, 0x63, 0x7a, 0x8a, 0x80, 0xa2, 0x95, 0x3d, 0xe1, 0xe9, 0x56, 0x45, 0x0a,
|
||||
/* (2^155)P */ 0x45, 0x30, 0xc1, 0xe9, 0x1f, 0x99, 0x1a, 0xd2, 0xb8, 0x51, 0x77, 0xfe, 0x48, 0x85, 0x0e, 0x9b, 0x35, 0x00, 0xf3, 0x4b, 0xcb, 0x43, 0xa6, 0x5d, 0x21, 0xf7, 0x40, 0x39, 0xd6, 0x28, 0xdb, 0x77,
|
||||
/* (2^156)P */ 0x11, 0x90, 0xdc, 0x4a, 0x61, 0xeb, 0x5e, 0xfc, 0xeb, 0x11, 0xc4, 0xe8, 0x9a, 0x41, 0x29, 0x52, 0x74, 0xcf, 0x1d, 0x7d, 0x78, 0xe7, 0xc3, 0x9e, 0xb5, 0x4c, 0x6e, 0x21, 0x3e, 0x05, 0x0d, 0x34,
|
||||
/* (2^157)P */ 0xb4, 0xf2, 0x8d, 0xb4, 0x39, 0xaf, 0xc7, 0xca, 0x94, 0x0a, 0xa1, 0x71, 0x28, 0xec, 0xfa, 0xc0, 0xed, 0x75, 0xa5, 0x5c, 0x24, 0x69, 0x0a, 0x14, 0x4c, 0x3a, 0x27, 0x34, 0x71, 0xc3, 0xf1, 0x0c,
|
||||
/* (2^158)P */ 0xa5, 0xb8, 0x24, 0xc2, 0x6a, 0x30, 0xee, 0xc8, 0xb0, 0x30, 0x49, 0xcb, 0x7c, 0xee, 0xea, 0x57, 0x4f, 0xe7, 0xcb, 0xaa, 0xbd, 0x06, 0xe8, 0xa1, 0x7d, 0x65, 0xeb, 0x2e, 0x74, 0x62, 0x9a, 0x7d,
|
||||
/* (2^159)P */ 0x30, 0x48, 0x6c, 0x54, 0xef, 0xb6, 0xb6, 0x9e, 0x2e, 0x6e, 0xb3, 0xdd, 0x1f, 0xca, 0x5c, 0x88, 0x05, 0x71, 0x0d, 0xef, 0x83, 0xf3, 0xb9, 0xe6, 0x12, 0x04, 0x2e, 0x9d, 0xef, 0x4f, 0x65, 0x58,
|
||||
/* (2^160)P */ 0x26, 0x8e, 0x0e, 0xbe, 0xff, 0xc4, 0x05, 0xa9, 0x6e, 0x81, 0x31, 0x9b, 0xdf, 0xe5, 0x2d, 0x94, 0xe1, 0x88, 0x2e, 0x80, 0x3f, 0x72, 0x7d, 0x49, 0x8d, 0x40, 0x2f, 0x60, 0xea, 0x4d, 0x68, 0x30,
|
||||
/* (2^161)P */ 0x34, 0xcb, 0xe6, 0xa3, 0x78, 0xa2, 0xe5, 0x21, 0xc4, 0x1d, 0x15, 0x5b, 0x6f, 0x6e, 0xfb, 0xae, 0x15, 0xca, 0x77, 0x9d, 0x04, 0x8e, 0x0b, 0xb3, 0x81, 0x89, 0xb9, 0x53, 0xcf, 0xc9, 0xc3, 0x28,
|
||||
/* (2^162)P */ 0x2a, 0xdd, 0x6c, 0x55, 0x21, 0xb7, 0x7f, 0x28, 0x74, 0x22, 0x02, 0x97, 0xa8, 0x7c, 0x31, 0x0d, 0x58, 0x32, 0x54, 0x3a, 0x42, 0xc7, 0x68, 0x74, 0x2f, 0x64, 0xb5, 0x4e, 0x46, 0x11, 0x7f, 0x4a,
|
||||
/* (2^163)P */ 0xa6, 0x3a, 0x19, 0x4d, 0x77, 0xa4, 0x37, 0xa2, 0xa1, 0x29, 0x21, 0xa9, 0x6e, 0x98, 0x65, 0xd8, 0x88, 0x1a, 0x7c, 0xf8, 0xec, 0x15, 0xc5, 0x24, 0xeb, 0xf5, 0x39, 0x5f, 0x57, 0x03, 0x40, 0x60,
|
||||
/* (2^164)P */ 0x27, 0x9b, 0x0a, 0x57, 0x89, 0xf1, 0xb9, 0x47, 0x78, 0x4b, 0x5e, 0x46, 0xde, 0xce, 0x98, 0x2b, 0x20, 0x5c, 0xb8, 0xdb, 0x51, 0xf5, 0x6d, 0x02, 0x01, 0x19, 0xe2, 0x47, 0x10, 0xd9, 0xfc, 0x74,
|
||||
/* (2^165)P */ 0xa3, 0xbf, 0xc1, 0x23, 0x0a, 0xa9, 0xe2, 0x13, 0xf6, 0x19, 0x85, 0x47, 0x4e, 0x07, 0xb0, 0x0c, 0x44, 0xcf, 0xf6, 0x3a, 0xbe, 0xcb, 0xf1, 0x5f, 0xbe, 0x2d, 0x81, 0xbe, 0x38, 0x54, 0xfe, 0x67,
|
||||
/* (2^166)P */ 0xb0, 0x05, 0x0f, 0xa4, 0x4f, 0xf6, 0x3c, 0xd1, 0x87, 0x37, 0x28, 0x32, 0x2f, 0xfb, 0x4d, 0x05, 0xea, 0x2a, 0x0d, 0x7f, 0x5b, 0x91, 0x73, 0x41, 0x4e, 0x0d, 0x61, 0x1f, 0x4f, 0x14, 0x2f, 0x48,
|
||||
/* (2^167)P */ 0x34, 0x82, 0x7f, 0xb4, 0x01, 0x02, 0x21, 0xf6, 0x90, 0xb9, 0x70, 0x9e, 0x92, 0xe1, 0x0a, 0x5d, 0x7c, 0x56, 0x49, 0xb0, 0x55, 0xf4, 0xd7, 0xdc, 0x01, 0x6f, 0x91, 0xf0, 0xf1, 0xd0, 0x93, 0x7e,
|
||||
/* (2^168)P */ 0xfa, 0xb4, 0x7d, 0x8a, 0xf1, 0xcb, 0x79, 0xdd, 0x2f, 0xc6, 0x74, 0x6f, 0xbf, 0x91, 0x83, 0xbe, 0xbd, 0x91, 0x82, 0x4b, 0xd1, 0x45, 0x71, 0x02, 0x05, 0x17, 0xbf, 0x2c, 0xea, 0x73, 0x5a, 0x58,
|
||||
/* (2^169)P */ 0xb2, 0x0d, 0x8a, 0x92, 0x3e, 0xa0, 0x5c, 0x48, 0xe7, 0x57, 0x28, 0x74, 0xa5, 0x01, 0xfc, 0x10, 0xa7, 0x51, 0xd5, 0xd6, 0xdb, 0x2e, 0x48, 0x2f, 0x8a, 0xdb, 0x8f, 0x04, 0xb5, 0x33, 0x04, 0x0f,
|
||||
/* (2^170)P */ 0x47, 0x62, 0xdc, 0xd7, 0x8d, 0x2e, 0xda, 0x60, 0x9a, 0x81, 0xd4, 0x8c, 0xd3, 0xc9, 0xb4, 0x88, 0x97, 0x66, 0xf6, 0x01, 0xc0, 0x3a, 0x03, 0x13, 0x75, 0x7d, 0x36, 0x3b, 0xfe, 0x24, 0x3b, 0x27,
|
||||
/* (2^171)P */ 0xd4, 0xb9, 0xb3, 0x31, 0x6a, 0xf6, 0xe8, 0xc6, 0xd5, 0x49, 0xdf, 0x94, 0xa4, 0x14, 0x15, 0x28, 0xa7, 0x3d, 0xb2, 0xc8, 0xdf, 0x6f, 0x72, 0xd1, 0x48, 0xe5, 0xde, 0x03, 0xd1, 0xe7, 0x3a, 0x4b,
|
||||
/* (2^172)P */ 0x7e, 0x9d, 0x4b, 0xce, 0x19, 0x6e, 0x25, 0xc6, 0x1c, 0xc6, 0xe3, 0x86, 0xf1, 0x5c, 0x5c, 0xff, 0x45, 0xc1, 0x8e, 0x4b, 0xa3, 0x3c, 0xc6, 0xac, 0x74, 0x65, 0xe6, 0xfe, 0x88, 0x18, 0x62, 0x74,
|
||||
/* (2^173)P */ 0x1e, 0x0a, 0x29, 0x45, 0x96, 0x40, 0x6f, 0x95, 0x2e, 0x96, 0x3a, 0x26, 0xe3, 0xf8, 0x0b, 0xef, 0x7b, 0x64, 0xc2, 0x5e, 0xeb, 0x50, 0x6a, 0xed, 0x02, 0x75, 0xca, 0x9d, 0x3a, 0x28, 0x94, 0x06,
|
||||
/* (2^174)P */ 0xd1, 0xdc, 0xa2, 0x43, 0x36, 0x96, 0x9b, 0x76, 0x53, 0x53, 0xfc, 0x09, 0xea, 0xc8, 0xb7, 0x42, 0xab, 0x7e, 0x39, 0x13, 0xee, 0x2a, 0x00, 0x4f, 0x3a, 0xd6, 0xb7, 0x19, 0x2c, 0x5e, 0x00, 0x63,
|
||||
/* (2^175)P */ 0xea, 0x3b, 0x02, 0x63, 0xda, 0x36, 0x67, 0xca, 0xb7, 0x99, 0x2a, 0xb1, 0x6d, 0x7f, 0x6c, 0x96, 0xe1, 0xc5, 0x37, 0xc5, 0x90, 0x93, 0xe0, 0xac, 0xee, 0x89, 0xaa, 0xa1, 0x63, 0x60, 0x69, 0x0b,
|
||||
/* (2^176)P */ 0xe5, 0x56, 0x8c, 0x28, 0x97, 0x3e, 0xb0, 0xeb, 0xe8, 0x8b, 0x8c, 0x93, 0x9f, 0x9f, 0x2a, 0x43, 0x71, 0x7f, 0x71, 0x5b, 0x3d, 0xa9, 0xa5, 0xa6, 0x97, 0x9d, 0x8f, 0xe1, 0xc3, 0xb4, 0x5f, 0x1a,
|
||||
/* (2^177)P */ 0xce, 0xcd, 0x60, 0x1c, 0xad, 0xe7, 0x94, 0x1c, 0xa0, 0xc4, 0x02, 0xfc, 0x43, 0x2a, 0x20, 0xee, 0x20, 0x6a, 0xc4, 0x67, 0xd8, 0xe4, 0xaf, 0x8d, 0x58, 0x7b, 0xc2, 0x8a, 0x3c, 0x26, 0x10, 0x0a,
|
||||
/* (2^178)P */ 0x4a, 0x2a, 0x43, 0xe4, 0xdf, 0xa9, 0xde, 0xd0, 0xc5, 0x77, 0x92, 0xbe, 0x7b, 0xf8, 0x6a, 0x85, 0x1a, 0xc7, 0x12, 0xc2, 0xac, 0x72, 0x84, 0xce, 0x91, 0x1e, 0xbb, 0x9b, 0x6d, 0x1b, 0x15, 0x6f,
|
||||
/* (2^179)P */ 0x6a, 0xd5, 0xee, 0x7c, 0x52, 0x6c, 0x77, 0x26, 0xec, 0xfa, 0xf8, 0xfb, 0xb7, 0x1c, 0x21, 0x7d, 0xcc, 0x09, 0x46, 0xfd, 0xa6, 0x66, 0xae, 0x37, 0x42, 0x0c, 0x77, 0xd2, 0x02, 0xb7, 0x81, 0x1f,
|
||||
/* (2^180)P */ 0x92, 0x83, 0xc5, 0xea, 0x57, 0xb0, 0xb0, 0x2f, 0x9d, 0x4e, 0x74, 0x29, 0xfe, 0x89, 0xdd, 0xe1, 0xf8, 0xb4, 0xbe, 0x17, 0xeb, 0xf8, 0x64, 0xc9, 0x1e, 0xd4, 0xa2, 0xc9, 0x73, 0x10, 0x57, 0x29,
|
||||
/* (2^181)P */ 0x54, 0xe2, 0xc0, 0x81, 0x89, 0xa1, 0x48, 0xa9, 0x30, 0x28, 0xb2, 0x65, 0x9b, 0x36, 0xf6, 0x2d, 0xc6, 0xd3, 0xcf, 0x5f, 0xd7, 0xb2, 0x3e, 0xa3, 0x1f, 0xa0, 0x99, 0x41, 0xec, 0xd6, 0x8c, 0x07,
|
||||
/* (2^182)P */ 0x2f, 0x0d, 0x90, 0xad, 0x41, 0x4a, 0x58, 0x4a, 0x52, 0x4c, 0xc7, 0xe2, 0x78, 0x2b, 0x14, 0x32, 0x78, 0xc9, 0x31, 0x84, 0x33, 0xe8, 0xc4, 0x68, 0xc2, 0x9f, 0x68, 0x08, 0x90, 0xea, 0x69, 0x7f,
|
||||
/* (2^183)P */ 0x65, 0x82, 0xa3, 0x46, 0x1e, 0xc8, 0xf2, 0x52, 0xfd, 0x32, 0xa8, 0x04, 0x2d, 0x07, 0x78, 0xfd, 0x94, 0x9e, 0x35, 0x25, 0xfa, 0xd5, 0xd7, 0x8c, 0xd2, 0x29, 0xcc, 0x54, 0x74, 0x1b, 0xe7, 0x4d,
|
||||
/* (2^184)P */ 0xc9, 0x6a, 0xda, 0x1e, 0xad, 0x60, 0xeb, 0x42, 0x3a, 0x9c, 0xc0, 0xdb, 0xdf, 0x37, 0xad, 0x0a, 0x91, 0xc1, 0x3c, 0xe3, 0x71, 0x4b, 0x00, 0x81, 0x3c, 0x80, 0x22, 0x51, 0x34, 0xbe, 0xe6, 0x44,
|
||||
/* (2^185)P */ 0xdb, 0x20, 0x19, 0xba, 0x88, 0x83, 0xfe, 0x03, 0x08, 0xb0, 0x0d, 0x15, 0x32, 0x7c, 0xd5, 0xf5, 0x29, 0x0c, 0xf6, 0x1a, 0x28, 0xc4, 0xc8, 0x49, 0xee, 0x1a, 0x70, 0xde, 0x18, 0xb5, 0xed, 0x21,
|
||||
/* (2^186)P */ 0x99, 0xdc, 0x06, 0x8f, 0x41, 0x3e, 0xb6, 0x7f, 0xb8, 0xd7, 0x66, 0xc1, 0x99, 0x0d, 0x46, 0xa4, 0x83, 0x0a, 0x52, 0xce, 0x48, 0x52, 0xdd, 0x24, 0x58, 0x83, 0x92, 0x2b, 0x71, 0xad, 0xc3, 0x5e,
|
||||
/* (2^187)P */ 0x0f, 0x93, 0x17, 0xbd, 0x5f, 0x2a, 0x02, 0x15, 0xe3, 0x70, 0x25, 0xd8, 0x77, 0x4a, 0xf6, 0xa4, 0x12, 0x37, 0x78, 0x15, 0x69, 0x8d, 0xbc, 0x12, 0xbb, 0x0a, 0x62, 0xfc, 0xc0, 0x94, 0x81, 0x49,
|
||||
/* (2^188)P */ 0x82, 0x6c, 0x68, 0x55, 0xd2, 0xd9, 0xa2, 0x38, 0xf0, 0x21, 0x3e, 0x19, 0xd9, 0x6b, 0x5c, 0x78, 0x84, 0x54, 0x4a, 0xb2, 0x1a, 0xc8, 0xd5, 0xe4, 0x89, 0x09, 0xe2, 0xb2, 0x60, 0x78, 0x30, 0x56,
|
||||
/* (2^189)P */ 0xc4, 0x74, 0x4d, 0x8b, 0xf7, 0x55, 0x9d, 0x42, 0x31, 0x01, 0x35, 0x43, 0x46, 0x83, 0xf1, 0x22, 0xff, 0x1f, 0xc7, 0x98, 0x45, 0xc2, 0x60, 0x1e, 0xef, 0x83, 0x99, 0x97, 0x14, 0xf0, 0xf2, 0x59,
|
||||
/* (2^190)P */ 0x44, 0x4a, 0x49, 0xeb, 0x56, 0x7d, 0xa4, 0x46, 0x8e, 0xa1, 0x36, 0xd6, 0x54, 0xa8, 0x22, 0x3e, 0x3b, 0x1c, 0x49, 0x74, 0x52, 0xe1, 0x46, 0xb3, 0xe7, 0xcd, 0x90, 0x53, 0x4e, 0xfd, 0xea, 0x2c,
|
||||
/* (2^191)P */ 0x75, 0x66, 0x0d, 0xbe, 0x38, 0x85, 0x8a, 0xba, 0x23, 0x8e, 0x81, 0x50, 0xbb, 0x74, 0x90, 0x4b, 0xc3, 0x04, 0xd3, 0x85, 0x90, 0xb8, 0xda, 0xcb, 0xc4, 0x92, 0x61, 0xe5, 0xe0, 0x4f, 0xa2, 0x61,
|
||||
/* (2^192)P */ 0xcb, 0x5b, 0x52, 0xdb, 0xe6, 0x15, 0x76, 0xcb, 0xca, 0xe4, 0x67, 0xa5, 0x35, 0x8c, 0x7d, 0xdd, 0x69, 0xdd, 0xfc, 0xca, 0x3a, 0x15, 0xb4, 0xe6, 0x66, 0x97, 0x3c, 0x7f, 0x09, 0x8e, 0x66, 0x2d,
|
||||
/* (2^193)P */ 0xf0, 0x5e, 0xe5, 0x5c, 0x26, 0x7e, 0x7e, 0xa5, 0x67, 0xb9, 0xd4, 0x7c, 0x52, 0x4e, 0x9f, 0x5d, 0xe5, 0xd1, 0x2f, 0x49, 0x06, 0x36, 0xc8, 0xfb, 0xae, 0xf7, 0xc3, 0xb7, 0xbe, 0x52, 0x0d, 0x09,
|
||||
/* (2^194)P */ 0x7c, 0x4d, 0x7b, 0x1e, 0x5a, 0x51, 0xb9, 0x09, 0xc0, 0x44, 0xda, 0x99, 0x25, 0x6a, 0x26, 0x1f, 0x04, 0x55, 0xc5, 0xe2, 0x48, 0x95, 0xc4, 0xa1, 0xcc, 0x15, 0x6f, 0x12, 0x87, 0x42, 0xf0, 0x7e,
|
||||
/* (2^195)P */ 0x15, 0xef, 0x30, 0xbd, 0x9d, 0x65, 0xd1, 0xfe, 0x7b, 0x27, 0xe0, 0xc4, 0xee, 0xb9, 0x4a, 0x8b, 0x91, 0x32, 0xdf, 0xa5, 0x36, 0x62, 0x4d, 0x88, 0x88, 0xf7, 0x5c, 0xbf, 0xa6, 0x6e, 0xd9, 0x1f,
|
||||
/* (2^196)P */ 0x9a, 0x0d, 0x19, 0x1f, 0x98, 0x61, 0xa1, 0x42, 0xc1, 0x52, 0x60, 0x7e, 0x50, 0x49, 0xd8, 0x61, 0xd5, 0x2c, 0x5a, 0x28, 0xbf, 0x13, 0xe1, 0x9f, 0xd8, 0x85, 0xad, 0xdb, 0x76, 0xd6, 0x22, 0x7c,
|
||||
/* (2^197)P */ 0x7d, 0xd2, 0xfb, 0x2b, 0xed, 0x70, 0xe7, 0x82, 0xa5, 0xf5, 0x96, 0xe9, 0xec, 0xb2, 0x05, 0x4c, 0x50, 0x01, 0x90, 0xb0, 0xc2, 0xa9, 0x40, 0xcd, 0x64, 0xbf, 0xd9, 0x13, 0x92, 0x31, 0x95, 0x58,
|
||||
/* (2^198)P */ 0x08, 0x2e, 0xea, 0x3f, 0x70, 0x5d, 0xcc, 0xe7, 0x8c, 0x18, 0xe2, 0x58, 0x12, 0x49, 0x0c, 0xb5, 0xf0, 0x5b, 0x20, 0x48, 0xaa, 0x0b, 0xe3, 0xcc, 0x62, 0x2d, 0xa3, 0xcf, 0x9c, 0x65, 0x7c, 0x53,
|
||||
/* (2^199)P */ 0x88, 0xc0, 0xcf, 0x98, 0x3a, 0x62, 0xb6, 0x37, 0xa4, 0xac, 0xd6, 0xa4, 0x1f, 0xed, 0x9b, 0xfe, 0xb0, 0xd1, 0xa8, 0x56, 0x8e, 0x9b, 0xd2, 0x04, 0x75, 0x95, 0x51, 0x0b, 0xc4, 0x71, 0x5f, 0x72,
|
||||
/* (2^200)P */ 0xe6, 0x9c, 0x33, 0xd0, 0x9c, 0xf8, 0xc7, 0x28, 0x8b, 0xc1, 0xdd, 0x69, 0x44, 0xb1, 0x67, 0x83, 0x2c, 0x65, 0xa1, 0xa6, 0x83, 0xda, 0x3a, 0x88, 0x17, 0x6c, 0x4d, 0x03, 0x74, 0x19, 0x5f, 0x58,
|
||||
/* (2^201)P */ 0x88, 0x91, 0xb1, 0xf1, 0x66, 0xb2, 0xcf, 0x89, 0x17, 0x52, 0xc3, 0xe7, 0x63, 0x48, 0x3b, 0xe6, 0x6a, 0x52, 0xc0, 0xb4, 0xa6, 0x9d, 0x8c, 0xd8, 0x35, 0x46, 0x95, 0xf0, 0x9d, 0x5c, 0x03, 0x3e,
|
||||
/* (2^202)P */ 0x9d, 0xde, 0x45, 0xfb, 0x12, 0x54, 0x9d, 0xdd, 0x0d, 0xf4, 0xcf, 0xe4, 0x32, 0x45, 0x68, 0xdd, 0x1c, 0x67, 0x1d, 0x15, 0x9b, 0x99, 0x5c, 0x4b, 0x90, 0xf6, 0xe7, 0x11, 0xc8, 0x2c, 0x8c, 0x2d,
|
||||
/* (2^203)P */ 0x40, 0x5d, 0x05, 0x90, 0x1d, 0xbe, 0x54, 0x7f, 0x40, 0xaf, 0x4a, 0x46, 0xdf, 0xc5, 0x64, 0xa4, 0xbe, 0x17, 0xe9, 0xf0, 0x24, 0x96, 0x97, 0x33, 0x30, 0x6b, 0x35, 0x27, 0xc5, 0x8d, 0x01, 0x2c,
|
||||
/* (2^204)P */ 0xd4, 0xb3, 0x30, 0xe3, 0x24, 0x50, 0x41, 0xa5, 0xd3, 0x52, 0x16, 0x69, 0x96, 0x3d, 0xff, 0x73, 0xf1, 0x59, 0x9b, 0xef, 0xc4, 0x42, 0xec, 0x94, 0x5a, 0x8e, 0xd0, 0x18, 0x16, 0x20, 0x47, 0x07,
|
||||
/* (2^205)P */ 0x53, 0x1c, 0x41, 0xca, 0x8a, 0xa4, 0x6c, 0x4d, 0x19, 0x61, 0xa6, 0xcf, 0x2f, 0x5f, 0x41, 0x66, 0xff, 0x27, 0xe2, 0x51, 0x00, 0xd4, 0x4d, 0x9c, 0xeb, 0xf7, 0x02, 0x9a, 0xc0, 0x0b, 0x81, 0x59,
|
||||
/* (2^206)P */ 0x1d, 0x10, 0xdc, 0xb3, 0x71, 0xb1, 0x7e, 0x2a, 0x8e, 0xf6, 0xfe, 0x9f, 0xb9, 0x5a, 0x1c, 0x44, 0xea, 0x59, 0xb3, 0x93, 0x9b, 0x5c, 0x02, 0x32, 0x2f, 0x11, 0x9d, 0x1e, 0xa7, 0xe0, 0x8c, 0x5e,
|
||||
/* (2^207)P */ 0xfd, 0x03, 0x95, 0x42, 0x92, 0xcb, 0xcc, 0xbf, 0x55, 0x5d, 0x09, 0x2f, 0x75, 0xba, 0x71, 0xd2, 0x1e, 0x09, 0x2d, 0x97, 0x5e, 0xad, 0x5e, 0x34, 0xba, 0x03, 0x31, 0xa8, 0x11, 0xdf, 0xc8, 0x18,
|
||||
/* (2^208)P */ 0x4c, 0x0f, 0xed, 0x9a, 0x9a, 0x94, 0xcd, 0x90, 0x7e, 0xe3, 0x60, 0x66, 0xcb, 0xf4, 0xd1, 0xc5, 0x0b, 0x2e, 0xc5, 0x56, 0x2d, 0xc5, 0xca, 0xb8, 0x0d, 0x8e, 0x80, 0xc5, 0x00, 0xe4, 0x42, 0x6e,
|
||||
/* (2^209)P */ 0x23, 0xfd, 0xae, 0xee, 0x66, 0x69, 0xb4, 0xa3, 0xca, 0xcd, 0x9e, 0xe3, 0x0b, 0x1f, 0x4f, 0x0c, 0x1d, 0xa5, 0x83, 0xd6, 0xc9, 0xc8, 0x9d, 0x18, 0x1b, 0x35, 0x09, 0x4c, 0x05, 0x7f, 0xf2, 0x51,
|
||||
/* (2^210)P */ 0x82, 0x06, 0x32, 0x2a, 0xcd, 0x7c, 0x48, 0x4c, 0x96, 0x1c, 0xdf, 0xb3, 0x5b, 0xa9, 0x7e, 0x58, 0xe8, 0xb8, 0x5c, 0x55, 0x9e, 0xf7, 0xcc, 0xc8, 0x3d, 0xd7, 0x06, 0xa2, 0x29, 0xc8, 0x7d, 0x54,
|
||||
/* (2^211)P */ 0x06, 0x9b, 0xc3, 0x80, 0xcd, 0xa6, 0x22, 0xb8, 0xc6, 0xd4, 0x00, 0x20, 0x73, 0x54, 0x6d, 0xe9, 0x4d, 0x3b, 0x46, 0x91, 0x6f, 0x5b, 0x53, 0x28, 0x1d, 0x6e, 0x48, 0xe2, 0x60, 0x46, 0x8f, 0x22,
|
||||
/* (2^212)P */ 0xbf, 0x3a, 0x8d, 0xde, 0x38, 0x95, 0x79, 0x98, 0x6e, 0xca, 0xeb, 0x45, 0x00, 0x33, 0xd8, 0x8c, 0x38, 0xe7, 0x21, 0x82, 0x00, 0x2a, 0x95, 0x79, 0xbb, 0xd2, 0x5c, 0x53, 0xa7, 0xe1, 0x22, 0x43,
|
||||
/* (2^213)P */ 0x1c, 0x80, 0xd1, 0x19, 0x18, 0xc1, 0x14, 0xb1, 0xc7, 0x5e, 0x3f, 0x4f, 0xd8, 0xe4, 0x16, 0x20, 0x4c, 0x0f, 0x26, 0x09, 0xf4, 0x2d, 0x0e, 0xdd, 0x66, 0x72, 0x5f, 0xae, 0xc0, 0x62, 0xc3, 0x5e,
|
||||
/* (2^214)P */ 0xee, 0xb4, 0xb2, 0xb8, 0x18, 0x2b, 0x46, 0xc0, 0xfb, 0x1a, 0x4d, 0x27, 0x50, 0xd9, 0xc8, 0x7c, 0xd2, 0x02, 0x6b, 0x43, 0x05, 0x71, 0x5f, 0xf2, 0xd3, 0xcc, 0xf9, 0xbf, 0xdc, 0xf8, 0xbb, 0x43,
|
||||
/* (2^215)P */ 0xdf, 0xe9, 0x39, 0xa0, 0x67, 0x17, 0xad, 0xb6, 0x83, 0x35, 0x9d, 0xf6, 0xa8, 0x4d, 0x71, 0xb0, 0xf5, 0x31, 0x29, 0xb4, 0x18, 0xfa, 0x55, 0x5e, 0x61, 0x09, 0xc6, 0x33, 0x8f, 0x55, 0xd5, 0x4e,
|
||||
/* (2^216)P */ 0xdd, 0xa5, 0x47, 0xc6, 0x01, 0x79, 0xe3, 0x1f, 0x57, 0xd3, 0x81, 0x80, 0x1f, 0xdf, 0x3d, 0x59, 0xa6, 0xd7, 0x3f, 0x81, 0xfd, 0xa4, 0x49, 0x02, 0x61, 0xaf, 0x9c, 0x4e, 0x27, 0xca, 0xac, 0x69,
|
||||
/* (2^217)P */ 0xc9, 0x21, 0x07, 0x33, 0xea, 0xa3, 0x7b, 0x04, 0xa0, 0x1e, 0x7e, 0x0e, 0xc2, 0x3f, 0x42, 0x83, 0x60, 0x4a, 0x31, 0x01, 0xaf, 0xc0, 0xf4, 0x1d, 0x27, 0x95, 0x28, 0x89, 0xab, 0x2d, 0xa6, 0x09,
|
||||
/* (2^218)P */ 0x00, 0xcb, 0xc6, 0x9c, 0xa4, 0x25, 0xb3, 0xa5, 0xb6, 0x6c, 0xb5, 0x54, 0xc6, 0x5d, 0x4b, 0xe9, 0xa0, 0x94, 0xc9, 0xad, 0x79, 0x87, 0xe2, 0x3b, 0xad, 0x4a, 0x3a, 0xba, 0xf8, 0xe8, 0x96, 0x42,
|
||||
/* (2^219)P */ 0xab, 0x1e, 0x45, 0x1e, 0x76, 0x89, 0x86, 0x32, 0x4a, 0x59, 0x59, 0xff, 0x8b, 0x59, 0x4d, 0x2e, 0x4a, 0x08, 0xa7, 0xd7, 0x53, 0x68, 0xb9, 0x49, 0xa8, 0x20, 0x14, 0x60, 0x19, 0xa3, 0x80, 0x49,
|
||||
/* (2^220)P */ 0x42, 0x2c, 0x55, 0x2f, 0xe1, 0xb9, 0x65, 0x95, 0x96, 0xfe, 0x00, 0x71, 0xdb, 0x18, 0x53, 0x8a, 0xd7, 0xd0, 0xad, 0x43, 0x4d, 0x0b, 0xc9, 0x05, 0xda, 0x4e, 0x5d, 0x6a, 0xd6, 0x4c, 0x8b, 0x53,
|
||||
/* (2^221)P */ 0x9f, 0x03, 0x9f, 0xe8, 0xc3, 0x4f, 0xe9, 0xf4, 0x45, 0x80, 0x61, 0x6f, 0xf2, 0x9a, 0x2c, 0x59, 0x50, 0x95, 0x4b, 0xfd, 0xb5, 0x6e, 0xa3, 0x08, 0x19, 0x14, 0xed, 0xc2, 0xf6, 0xfa, 0xff, 0x25,
|
||||
/* (2^222)P */ 0x54, 0xd3, 0x79, 0xcc, 0x59, 0x44, 0x43, 0x34, 0x6b, 0x47, 0xd5, 0xb1, 0xb4, 0xbf, 0xec, 0xee, 0x99, 0x5d, 0x61, 0x61, 0xa0, 0x34, 0xeb, 0xdd, 0x73, 0xb7, 0x64, 0xeb, 0xcc, 0xce, 0x29, 0x51,
|
||||
/* (2^223)P */ 0x20, 0x35, 0x99, 0x94, 0x58, 0x21, 0x43, 0xee, 0x3b, 0x0b, 0x4c, 0xf1, 0x7c, 0x9c, 0x2f, 0x77, 0xd5, 0xda, 0xbe, 0x06, 0xe3, 0xfc, 0xe2, 0xd2, 0x97, 0x6a, 0xf0, 0x46, 0xb5, 0x42, 0x5f, 0x71,
|
||||
/* (2^224)P */ 0x1a, 0x5f, 0x5b, 0xda, 0xce, 0xcd, 0x4e, 0x43, 0xa9, 0x41, 0x97, 0xa4, 0x15, 0x71, 0xa1, 0x0d, 0x2e, 0xad, 0xed, 0x73, 0x7c, 0xd7, 0x0b, 0x68, 0x41, 0x90, 0xdd, 0x4e, 0x35, 0x02, 0x7c, 0x48,
|
||||
/* (2^225)P */ 0xc4, 0xd9, 0x0e, 0xa7, 0xf3, 0xef, 0xef, 0xb8, 0x02, 0xe3, 0x57, 0xe8, 0xa3, 0x2a, 0xa3, 0x56, 0xa0, 0xa5, 0xa2, 0x48, 0xbd, 0x68, 0x3a, 0xdf, 0x44, 0xc4, 0x76, 0x31, 0xb7, 0x50, 0xf6, 0x07,
|
||||
/* (2^226)P */ 0xb1, 0xcc, 0xe0, 0x26, 0x16, 0x9b, 0x8b, 0xe3, 0x36, 0xfb, 0x09, 0x8b, 0xc1, 0x53, 0xe0, 0x79, 0x64, 0x49, 0xf9, 0xc9, 0x19, 0x03, 0xd9, 0x56, 0xc4, 0xf5, 0x9f, 0xac, 0xe7, 0x41, 0xa9, 0x1c,
|
||||
/* (2^227)P */ 0xbb, 0xa0, 0x2f, 0x16, 0x29, 0xdf, 0xc4, 0x49, 0x05, 0x33, 0xb3, 0x82, 0x32, 0xcf, 0x88, 0x84, 0x7d, 0x43, 0xbb, 0xca, 0x14, 0xda, 0xdf, 0x95, 0x86, 0xad, 0xd5, 0x64, 0x82, 0xf7, 0x91, 0x33,
|
||||
/* (2^228)P */ 0x5d, 0x09, 0xb5, 0xe2, 0x6a, 0xe0, 0x9a, 0x72, 0x46, 0xa9, 0x59, 0x32, 0xd7, 0x58, 0x8a, 0xd5, 0xed, 0x21, 0x39, 0xd1, 0x62, 0x42, 0x83, 0xe9, 0x92, 0xb5, 0x4b, 0xa5, 0xfa, 0xda, 0xfe, 0x27,
|
||||
/* (2^229)P */ 0xbb, 0x48, 0xad, 0x29, 0xb8, 0xc5, 0x9d, 0xa9, 0x60, 0xe2, 0x9e, 0x49, 0x42, 0x57, 0x02, 0x5f, 0xfd, 0x13, 0x75, 0x5d, 0xcd, 0x8e, 0x2c, 0x80, 0x38, 0xd9, 0x6d, 0x3f, 0xef, 0xb3, 0xce, 0x78,
|
||||
/* (2^230)P */ 0x94, 0x5d, 0x13, 0x8a, 0x4f, 0xf4, 0x42, 0xc3, 0xa3, 0xdd, 0x8c, 0x82, 0x44, 0xdb, 0x9e, 0x7b, 0xe7, 0xcf, 0x37, 0x05, 0x1a, 0xd1, 0x36, 0x94, 0xc8, 0xb4, 0x1a, 0xec, 0x64, 0xb1, 0x64, 0x50,
|
||||
/* (2^231)P */ 0xfc, 0xb2, 0x7e, 0xd3, 0xcf, 0xec, 0x20, 0x70, 0xfc, 0x25, 0x0d, 0xd9, 0x3e, 0xea, 0x31, 0x1f, 0x34, 0xbb, 0xa1, 0xdf, 0x7b, 0x0d, 0x93, 0x1b, 0x44, 0x30, 0x11, 0x48, 0x7a, 0x46, 0x44, 0x53,
|
||||
/* (2^232)P */ 0xfb, 0x6d, 0x5e, 0xf2, 0x70, 0x31, 0x07, 0x70, 0xc8, 0x4c, 0x11, 0x50, 0x1a, 0xdc, 0x85, 0xe3, 0x00, 0x4f, 0xfc, 0xc8, 0x8a, 0x69, 0x48, 0x23, 0xd8, 0x40, 0xdd, 0x84, 0x52, 0xa5, 0x77, 0x2a,
|
||||
/* (2^233)P */ 0xe4, 0x6c, 0x8c, 0xc9, 0xe0, 0xaf, 0x06, 0xfe, 0xe4, 0xd6, 0xdf, 0xdd, 0x96, 0xdf, 0x35, 0xc2, 0xd3, 0x1e, 0xbf, 0x33, 0x1e, 0xd0, 0x28, 0x14, 0xaf, 0xbd, 0x00, 0x93, 0xec, 0x68, 0x57, 0x78,
|
||||
/* (2^234)P */ 0x3b, 0xb6, 0xde, 0x91, 0x7a, 0xe5, 0x02, 0x97, 0x80, 0x8b, 0xce, 0xe5, 0xbf, 0xb8, 0xbd, 0x61, 0xac, 0x58, 0x1d, 0x3d, 0x6f, 0x42, 0x5b, 0x64, 0xbc, 0x57, 0xa5, 0x27, 0x22, 0xa8, 0x04, 0x48,
|
||||
/* (2^235)P */ 0x01, 0x26, 0x4d, 0xb4, 0x8a, 0x04, 0x57, 0x8e, 0x35, 0x69, 0x3a, 0x4b, 0x1a, 0x50, 0xd6, 0x68, 0x93, 0xc2, 0xe1, 0xf9, 0xc3, 0x9e, 0x9c, 0xc3, 0xe2, 0x63, 0xde, 0xd4, 0x57, 0xf2, 0x72, 0x41,
|
||||
/* (2^236)P */ 0x01, 0x64, 0x0c, 0x33, 0x50, 0xb4, 0x68, 0xd3, 0x91, 0x23, 0x8f, 0x41, 0x17, 0x30, 0x0d, 0x04, 0x0d, 0xd9, 0xb7, 0x90, 0x60, 0xbb, 0x34, 0x2c, 0x1f, 0xd5, 0xdf, 0x8f, 0x22, 0x49, 0xf6, 0x16,
|
||||
/* (2^237)P */ 0xf5, 0x8e, 0x92, 0x2b, 0x8e, 0x81, 0xa6, 0xbe, 0x72, 0x1e, 0xc1, 0xcd, 0x91, 0xcf, 0x8c, 0xe2, 0xcd, 0x36, 0x7a, 0xe7, 0x68, 0xaa, 0x4a, 0x59, 0x0f, 0xfd, 0x7f, 0x6c, 0x80, 0x34, 0x30, 0x31,
|
||||
/* (2^238)P */ 0x65, 0xbd, 0x49, 0x22, 0xac, 0x27, 0x9d, 0x8a, 0x12, 0x95, 0x8e, 0x01, 0x64, 0xb4, 0xa3, 0x19, 0xc7, 0x7e, 0xb3, 0x52, 0xf3, 0xcf, 0x6c, 0xc2, 0x21, 0x7b, 0x79, 0x1d, 0x34, 0x68, 0x6f, 0x05,
|
||||
/* (2^239)P */ 0x27, 0x23, 0xfd, 0x7e, 0x75, 0xd6, 0x79, 0x5e, 0x15, 0xfe, 0x3a, 0x55, 0xb6, 0xbc, 0xbd, 0xfa, 0x60, 0x5a, 0xaf, 0x6e, 0x2c, 0x22, 0xe7, 0xd3, 0x3b, 0x74, 0xae, 0x4d, 0x6d, 0xc7, 0x46, 0x70,
|
||||
/* (2^240)P */ 0x55, 0x4a, 0x8d, 0xb1, 0x72, 0xe8, 0x0b, 0x66, 0x96, 0x14, 0x4e, 0x57, 0x18, 0x25, 0x99, 0x19, 0xbb, 0xdc, 0x2b, 0x30, 0x3a, 0x05, 0x03, 0xc1, 0x8e, 0x8e, 0x21, 0x0b, 0x80, 0xe9, 0xd8, 0x3e,
|
||||
/* (2^241)P */ 0x3e, 0xe0, 0x75, 0xfa, 0x39, 0x92, 0x0b, 0x7b, 0x83, 0xc0, 0x33, 0x46, 0x68, 0xfb, 0xe9, 0xef, 0x93, 0x77, 0x1a, 0x39, 0xbe, 0x5f, 0xa3, 0x98, 0x34, 0xfe, 0xd0, 0xe2, 0x0f, 0x51, 0x65, 0x60,
|
||||
/* (2^242)P */ 0x0c, 0xad, 0xab, 0x48, 0x85, 0x66, 0xcb, 0x55, 0x27, 0xe5, 0x87, 0xda, 0x48, 0x45, 0x58, 0xb4, 0xdd, 0xc1, 0x07, 0x01, 0xea, 0xec, 0x43, 0x2c, 0x35, 0xde, 0x72, 0x93, 0x80, 0x28, 0x60, 0x52,
|
||||
/* (2^243)P */ 0x1f, 0x3b, 0x21, 0xf9, 0x6a, 0xc5, 0x15, 0x34, 0xdb, 0x98, 0x7e, 0x01, 0x4d, 0x1a, 0xee, 0x5b, 0x9b, 0x70, 0xcf, 0xb5, 0x05, 0xb1, 0xf6, 0x13, 0xb6, 0x9a, 0xb2, 0x82, 0x34, 0x0e, 0xf2, 0x5f,
|
||||
/* (2^244)P */ 0x90, 0x6c, 0x2e, 0xcc, 0x75, 0x9c, 0xa2, 0x0a, 0x06, 0xe2, 0x70, 0x3a, 0xca, 0x73, 0x7d, 0xfc, 0x15, 0xc5, 0xb5, 0xc4, 0x8f, 0xc3, 0x9f, 0x89, 0x07, 0xc2, 0xff, 0x24, 0xb1, 0x86, 0x03, 0x25,
|
||||
/* (2^245)P */ 0x56, 0x2b, 0x3d, 0xae, 0xd5, 0x28, 0xea, 0x54, 0xce, 0x60, 0xde, 0xd6, 0x9d, 0x14, 0x13, 0x99, 0xc1, 0xd6, 0x06, 0x8f, 0xc5, 0x4f, 0x69, 0x16, 0xc7, 0x8f, 0x01, 0xeb, 0x75, 0x39, 0xb2, 0x46,
|
||||
/* (2^246)P */ 0xe2, 0xb4, 0xb7, 0xb4, 0x0f, 0x6a, 0x0a, 0x47, 0xde, 0x53, 0x72, 0x8f, 0x5a, 0x47, 0x92, 0x5d, 0xdb, 0x3a, 0xbd, 0x2f, 0xb5, 0xe5, 0xee, 0xab, 0x68, 0x69, 0x80, 0xa0, 0x01, 0x08, 0xa2, 0x7f,
|
||||
/* (2^247)P */ 0xd2, 0x14, 0x77, 0x9f, 0xf1, 0xfa, 0xf3, 0x76, 0xc3, 0x60, 0x46, 0x2f, 0xc1, 0x40, 0xe8, 0xb3, 0x4e, 0x74, 0x12, 0xf2, 0x8d, 0xcd, 0xb4, 0x0f, 0xd2, 0x2d, 0x3a, 0x1d, 0x25, 0x5a, 0x06, 0x4b,
|
||||
/* (2^248)P */ 0x4a, 0xcd, 0x77, 0x3d, 0x38, 0xde, 0xeb, 0x5c, 0xb1, 0x9c, 0x2c, 0x88, 0xdf, 0x39, 0xdf, 0x6a, 0x59, 0xf7, 0x9a, 0xb0, 0x2e, 0x24, 0xdd, 0xa2, 0x22, 0x64, 0x5f, 0x0e, 0xe5, 0xc0, 0x47, 0x31,
|
||||
/* (2^249)P */ 0xdb, 0x50, 0x13, 0x1d, 0x10, 0xa5, 0x4c, 0x16, 0x62, 0xc9, 0x3f, 0xc3, 0x79, 0x34, 0xd1, 0xf8, 0x08, 0xda, 0xe5, 0x13, 0x4d, 0xce, 0x40, 0xe6, 0xba, 0xf8, 0x61, 0x50, 0xc4, 0xe0, 0xde, 0x4b,
|
||||
/* (2^250)P */ 0xc9, 0xb1, 0xed, 0xa4, 0xc1, 0x6d, 0xc4, 0xd7, 0x8a, 0xd9, 0x7f, 0x43, 0xb6, 0xd7, 0x14, 0x55, 0x0b, 0xc0, 0xa1, 0xb2, 0x6b, 0x2f, 0x94, 0x58, 0x0e, 0x71, 0x70, 0x1d, 0xab, 0xb2, 0xff, 0x2d,
|
||||
/* (2^251)P */ 0x68, 0x6d, 0x8b, 0xc1, 0x2f, 0xcf, 0xdf, 0xcc, 0x67, 0x61, 0x80, 0xb7, 0xa8, 0xcb, 0xeb, 0xa8, 0xe3, 0x37, 0x29, 0x5e, 0xf9, 0x97, 0x06, 0x98, 0x8c, 0x6e, 0x12, 0xd0, 0x1c, 0xba, 0xfb, 0x02,
|
||||
/* (2^252)P */ 0x65, 0x45, 0xff, 0xad, 0x60, 0xc3, 0x98, 0xcb, 0x19, 0x15, 0xdb, 0x4b, 0xd2, 0x01, 0x71, 0x44, 0xd5, 0x15, 0xfb, 0x75, 0x74, 0xc8, 0xc4, 0x98, 0x7d, 0xa2, 0x22, 0x6e, 0x6d, 0xc7, 0xf8, 0x05,
|
||||
/* (2^253)P */ 0x94, 0xf4, 0xb9, 0xfe, 0xdf, 0xe5, 0x69, 0xab, 0x75, 0x6b, 0x40, 0x18, 0x9d, 0xc7, 0x09, 0xae, 0x1d, 0x2d, 0xa4, 0x94, 0xfb, 0x45, 0x9b, 0x19, 0x84, 0xfa, 0x2a, 0xae, 0xeb, 0x0a, 0x71, 0x79,
|
||||
/* (2^254)P */ 0xdf, 0xd2, 0x34, 0xf3, 0xa7, 0xed, 0xad, 0xa6, 0xb4, 0x57, 0x2a, 0xaf, 0x51, 0x9c, 0xde, 0x7b, 0xa8, 0xea, 0xdc, 0x86, 0x4f, 0xc6, 0x8f, 0xa9, 0x7b, 0xd0, 0x0e, 0xc2, 0x35, 0x03, 0xbe, 0x6b,
|
||||
/* (2^255)P */ 0x44, 0x43, 0x98, 0x53, 0xbe, 0xdc, 0x7f, 0x66, 0xa8, 0x49, 0x59, 0x00, 0x1c, 0xbc, 0x72, 0x07, 0x8e, 0xd6, 0xbe, 0x4e, 0x9f, 0xa4, 0x07, 0xba, 0xbf, 0x30, 0xdf, 0xba, 0x85, 0xb0, 0xa7, 0x1f,
|
||||
}
|
||||
|
|
@ -0,0 +1,104 @@
|
|||
package x448
|
||||
|
||||
import (
|
||||
fp "github.com/cloudflare/circl/math/fp448"
|
||||
)
|
||||
|
||||
// ladderJoye calculates a fixed-point multiplication with the generator point.
|
||||
// The algorithm is the right-to-left Joye's ladder as described
|
||||
// in "How to precompute a ladder" in SAC'2017.
|
||||
func ladderJoye(k *Key) {
|
||||
w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved.
|
||||
w[1] = fp.Elt{ // x1 = S
|
||||
0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
}
|
||||
fp.SetOne(&w[2]) // z1 = 1
|
||||
w[3] = fp.Elt{ // x2 = G-S
|
||||
0x20, 0x27, 0x9d, 0xc9, 0x7d, 0x19, 0xb1, 0xac,
|
||||
0xf8, 0xba, 0x69, 0x1c, 0xff, 0x33, 0xac, 0x23,
|
||||
0x51, 0x1b, 0xce, 0x3a, 0x64, 0x65, 0xbd, 0xf1,
|
||||
0x23, 0xf8, 0xc1, 0x84, 0x9d, 0x45, 0x54, 0x29,
|
||||
0x67, 0xb9, 0x81, 0x1c, 0x03, 0xd1, 0xcd, 0xda,
|
||||
0x7b, 0xeb, 0xff, 0x1a, 0x88, 0x03, 0xcf, 0x3a,
|
||||
0x42, 0x44, 0x32, 0x01, 0x25, 0xb7, 0xfa, 0xf0,
|
||||
}
|
||||
fp.SetOne(&w[4]) // z2 = 1
|
||||
|
||||
const n = 448
|
||||
const h = 2
|
||||
swap := uint(1)
|
||||
for s := 0; s < n-h; s++ {
|
||||
i := (s + h) / 8
|
||||
j := (s + h) % 8
|
||||
bit := uint((k[i] >> uint(j)) & 1)
|
||||
copy(w[0][:], tableGenerator[s*Size:(s+1)*Size])
|
||||
diffAdd(&w, swap^bit)
|
||||
swap = bit
|
||||
}
|
||||
for s := 0; s < h; s++ {
|
||||
double(&w[1], &w[2])
|
||||
}
|
||||
toAffine((*[fp.Size]byte)(k), &w[1], &w[2])
|
||||
}
|
||||
|
||||
// ladderMontgomery calculates a generic scalar point multiplication
|
||||
// The algorithm implemented is the left-to-right Montgomery's ladder.
|
||||
func ladderMontgomery(k, xP *Key) {
|
||||
w := [5]fp.Elt{} // [x1, x2, z2, x3, z3] order must be preserved.
|
||||
w[0] = *(*fp.Elt)(xP) // x1 = xP
|
||||
fp.SetOne(&w[1]) // x2 = 1
|
||||
w[3] = *(*fp.Elt)(xP) // x3 = xP
|
||||
fp.SetOne(&w[4]) // z3 = 1
|
||||
|
||||
move := uint(0)
|
||||
for s := 448 - 1; s >= 0; s-- {
|
||||
i := s / 8
|
||||
j := s % 8
|
||||
bit := uint((k[i] >> uint(j)) & 1)
|
||||
ladderStep(&w, move^bit)
|
||||
move = bit
|
||||
}
|
||||
toAffine((*[fp.Size]byte)(k), &w[1], &w[2])
|
||||
}
|
||||
|
||||
func toAffine(k *[fp.Size]byte, x, z *fp.Elt) {
|
||||
fp.Inv(z, z)
|
||||
fp.Mul(x, x, z)
|
||||
_ = fp.ToBytes(k[:], x)
|
||||
}
|
||||
|
||||
var lowOrderPoints = [3]fp.Elt{
|
||||
{ /* (0,_,1) point of order 2 on Curve448 */
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
},
|
||||
{ /* (1,_,1) a point of order 4 on the twist of Curve448 */
|
||||
0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
|
||||
},
|
||||
{ /* (-1,_,1) point of order 4 on Curve448 */
|
||||
0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
},
|
||||
}
|
||||
|
|
@ -0,0 +1,30 @@
|
|||
//go:build amd64 && !purego
|
||||
// +build amd64,!purego
|
||||
|
||||
package x448
|
||||
|
||||
import (
|
||||
fp "github.com/cloudflare/circl/math/fp448"
|
||||
"golang.org/x/sys/cpu"
|
||||
)
|
||||
|
||||
var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX
|
||||
|
||||
var _ = hasBmi2Adx
|
||||
|
||||
func double(x, z *fp.Elt) { doubleAmd64(x, z) }
|
||||
func diffAdd(w *[5]fp.Elt, b uint) { diffAddAmd64(w, b) }
|
||||
func ladderStep(w *[5]fp.Elt, b uint) { ladderStepAmd64(w, b) }
|
||||
func mulA24(z, x *fp.Elt) { mulA24Amd64(z, x) }
|
||||
|
||||
//go:noescape
|
||||
func doubleAmd64(x, z *fp.Elt)
|
||||
|
||||
//go:noescape
|
||||
func diffAddAmd64(w *[5]fp.Elt, b uint)
|
||||
|
||||
//go:noescape
|
||||
func ladderStepAmd64(w *[5]fp.Elt, b uint)
|
||||
|
||||
//go:noescape
|
||||
func mulA24Amd64(z, x *fp.Elt)
|
||||
|
|
@ -0,0 +1,111 @@
|
|||
#define ladderStepLeg \
|
||||
addSub(x2,z2) \
|
||||
addSub(x3,z3) \
|
||||
integerMulLeg(b0,x2,z3) \
|
||||
integerMulLeg(b1,x3,z2) \
|
||||
reduceFromDoubleLeg(t0,b0) \
|
||||
reduceFromDoubleLeg(t1,b1) \
|
||||
addSub(t0,t1) \
|
||||
cselect(x2,x3,regMove) \
|
||||
cselect(z2,z3,regMove) \
|
||||
integerSqrLeg(b0,t0) \
|
||||
integerSqrLeg(b1,t1) \
|
||||
reduceFromDoubleLeg(x3,b0) \
|
||||
reduceFromDoubleLeg(z3,b1) \
|
||||
integerMulLeg(b0,x1,z3) \
|
||||
reduceFromDoubleLeg(z3,b0) \
|
||||
integerSqrLeg(b0,x2) \
|
||||
integerSqrLeg(b1,z2) \
|
||||
reduceFromDoubleLeg(x2,b0) \
|
||||
reduceFromDoubleLeg(z2,b1) \
|
||||
subtraction(t0,x2,z2) \
|
||||
multiplyA24Leg(t1,t0) \
|
||||
additionLeg(t1,t1,z2) \
|
||||
integerMulLeg(b0,x2,z2) \
|
||||
integerMulLeg(b1,t0,t1) \
|
||||
reduceFromDoubleLeg(x2,b0) \
|
||||
reduceFromDoubleLeg(z2,b1)
|
||||
|
||||
#define ladderStepBmi2Adx \
|
||||
addSub(x2,z2) \
|
||||
addSub(x3,z3) \
|
||||
integerMulAdx(b0,x2,z3) \
|
||||
integerMulAdx(b1,x3,z2) \
|
||||
reduceFromDoubleAdx(t0,b0) \
|
||||
reduceFromDoubleAdx(t1,b1) \
|
||||
addSub(t0,t1) \
|
||||
cselect(x2,x3,regMove) \
|
||||
cselect(z2,z3,regMove) \
|
||||
integerSqrAdx(b0,t0) \
|
||||
integerSqrAdx(b1,t1) \
|
||||
reduceFromDoubleAdx(x3,b0) \
|
||||
reduceFromDoubleAdx(z3,b1) \
|
||||
integerMulAdx(b0,x1,z3) \
|
||||
reduceFromDoubleAdx(z3,b0) \
|
||||
integerSqrAdx(b0,x2) \
|
||||
integerSqrAdx(b1,z2) \
|
||||
reduceFromDoubleAdx(x2,b0) \
|
||||
reduceFromDoubleAdx(z2,b1) \
|
||||
subtraction(t0,x2,z2) \
|
||||
multiplyA24Adx(t1,t0) \
|
||||
additionAdx(t1,t1,z2) \
|
||||
integerMulAdx(b0,x2,z2) \
|
||||
integerMulAdx(b1,t0,t1) \
|
||||
reduceFromDoubleAdx(x2,b0) \
|
||||
reduceFromDoubleAdx(z2,b1)
|
||||
|
||||
#define difAddLeg \
|
||||
addSub(x1,z1) \
|
||||
integerMulLeg(b0,z1,ui) \
|
||||
reduceFromDoubleLeg(z1,b0) \
|
||||
addSub(x1,z1) \
|
||||
integerSqrLeg(b0,x1) \
|
||||
integerSqrLeg(b1,z1) \
|
||||
reduceFromDoubleLeg(x1,b0) \
|
||||
reduceFromDoubleLeg(z1,b1) \
|
||||
integerMulLeg(b0,x1,z2) \
|
||||
integerMulLeg(b1,z1,x2) \
|
||||
reduceFromDoubleLeg(x1,b0) \
|
||||
reduceFromDoubleLeg(z1,b1)
|
||||
|
||||
#define difAddBmi2Adx \
|
||||
addSub(x1,z1) \
|
||||
integerMulAdx(b0,z1,ui) \
|
||||
reduceFromDoubleAdx(z1,b0) \
|
||||
addSub(x1,z1) \
|
||||
integerSqrAdx(b0,x1) \
|
||||
integerSqrAdx(b1,z1) \
|
||||
reduceFromDoubleAdx(x1,b0) \
|
||||
reduceFromDoubleAdx(z1,b1) \
|
||||
integerMulAdx(b0,x1,z2) \
|
||||
integerMulAdx(b1,z1,x2) \
|
||||
reduceFromDoubleAdx(x1,b0) \
|
||||
reduceFromDoubleAdx(z1,b1)
|
||||
|
||||
#define doubleLeg \
|
||||
addSub(x1,z1) \
|
||||
integerSqrLeg(b0,x1) \
|
||||
integerSqrLeg(b1,z1) \
|
||||
reduceFromDoubleLeg(x1,b0) \
|
||||
reduceFromDoubleLeg(z1,b1) \
|
||||
subtraction(t0,x1,z1) \
|
||||
multiplyA24Leg(t1,t0) \
|
||||
additionLeg(t1,t1,z1) \
|
||||
integerMulLeg(b0,x1,z1) \
|
||||
integerMulLeg(b1,t0,t1) \
|
||||
reduceFromDoubleLeg(x1,b0) \
|
||||
reduceFromDoubleLeg(z1,b1)
|
||||
|
||||
#define doubleBmi2Adx \
|
||||
addSub(x1,z1) \
|
||||
integerSqrAdx(b0,x1) \
|
||||
integerSqrAdx(b1,z1) \
|
||||
reduceFromDoubleAdx(x1,b0) \
|
||||
reduceFromDoubleAdx(z1,b1) \
|
||||
subtraction(t0,x1,z1) \
|
||||
multiplyA24Adx(t1,t0) \
|
||||
additionAdx(t1,t1,z1) \
|
||||
integerMulAdx(b0,x1,z1) \
|
||||
integerMulAdx(b1,t0,t1) \
|
||||
reduceFromDoubleAdx(x1,b0) \
|
||||
reduceFromDoubleAdx(z1,b1)
|
||||
|
|
@ -0,0 +1,193 @@
|
|||
// +build amd64
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// Depends on circl/math/fp448 package
|
||||
#include "../../math/fp448/fp_amd64.h"
|
||||
#include "curve_amd64.h"
|
||||
|
||||
// CTE_A24 is (A+2)/4 from Curve448
|
||||
#define CTE_A24 39082
|
||||
|
||||
#define Size 56
|
||||
|
||||
// multiplyA24Leg multiplies x times CTE_A24 and stores in z
|
||||
// Uses: AX, DX, R8-R15, FLAGS
|
||||
// Instr: x86_64, cmov, adx
|
||||
#define multiplyA24Leg(z,x) \
|
||||
MOVQ $CTE_A24, R15; \
|
||||
MOVQ 0+x, AX; MULQ R15; MOVQ AX, R8; ;;;;;;;;;;;; MOVQ DX, R9; \
|
||||
MOVQ 8+x, AX; MULQ R15; ADDQ AX, R9; ADCQ $0, DX; MOVQ DX, R10; \
|
||||
MOVQ 16+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX; MOVQ DX, R11; \
|
||||
MOVQ 24+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX; MOVQ DX, R12; \
|
||||
MOVQ 32+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX; MOVQ DX, R13; \
|
||||
MOVQ 40+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX; MOVQ DX, R14; \
|
||||
MOVQ 48+x, AX; MULQ R15; ADDQ AX, R14; ADCQ $0, DX; \
|
||||
MOVQ DX, AX; \
|
||||
SHLQ $32, AX; \
|
||||
ADDQ DX, R8; MOVQ $0, DX; \
|
||||
ADCQ $0, R9; \
|
||||
ADCQ $0, R10; \
|
||||
ADCQ AX, R11; \
|
||||
ADCQ $0, R12; \
|
||||
ADCQ $0, R13; \
|
||||
ADCQ $0, R14; \
|
||||
ADCQ $0, DX; \
|
||||
MOVQ DX, AX; \
|
||||
SHLQ $32, AX; \
|
||||
ADDQ DX, R8; \
|
||||
ADCQ $0, R9; \
|
||||
ADCQ $0, R10; \
|
||||
ADCQ AX, R11; \
|
||||
ADCQ $0, R12; \
|
||||
ADCQ $0, R13; \
|
||||
ADCQ $0, R14; \
|
||||
MOVQ R8, 0+z; \
|
||||
MOVQ R9, 8+z; \
|
||||
MOVQ R10, 16+z; \
|
||||
MOVQ R11, 24+z; \
|
||||
MOVQ R12, 32+z; \
|
||||
MOVQ R13, 40+z; \
|
||||
MOVQ R14, 48+z;
|
||||
|
||||
// multiplyA24Adx multiplies x times CTE_A24 and stores in z
|
||||
// Uses: AX, DX, R8-R14, FLAGS
|
||||
// Instr: x86_64, bmi2
|
||||
#define multiplyA24Adx(z,x) \
|
||||
MOVQ $CTE_A24, DX; \
|
||||
MULXQ 0+x, R8, R9; \
|
||||
MULXQ 8+x, AX, R10; ADDQ AX, R9; \
|
||||
MULXQ 16+x, AX, R11; ADCQ AX, R10; \
|
||||
MULXQ 24+x, AX, R12; ADCQ AX, R11; \
|
||||
MULXQ 32+x, AX, R13; ADCQ AX, R12; \
|
||||
MULXQ 40+x, AX, R14; ADCQ AX, R13; \
|
||||
MULXQ 48+x, AX, DX; ADCQ AX, R14; \
|
||||
;;;;;;;;;;;;;;;;;;;; ADCQ $0, DX; \
|
||||
MOVQ DX, AX; \
|
||||
SHLQ $32, AX; \
|
||||
ADDQ DX, R8; MOVQ $0, DX; \
|
||||
ADCQ $0, R9; \
|
||||
ADCQ $0, R10; \
|
||||
ADCQ AX, R11; \
|
||||
ADCQ $0, R12; \
|
||||
ADCQ $0, R13; \
|
||||
ADCQ $0, R14; \
|
||||
ADCQ $0, DX; \
|
||||
MOVQ DX, AX; \
|
||||
SHLQ $32, AX; \
|
||||
ADDQ DX, R8; \
|
||||
ADCQ $0, R9; \
|
||||
ADCQ $0, R10; \
|
||||
ADCQ AX, R11; \
|
||||
ADCQ $0, R12; \
|
||||
ADCQ $0, R13; \
|
||||
ADCQ $0, R14; \
|
||||
MOVQ R8, 0+z; \
|
||||
MOVQ R9, 8+z; \
|
||||
MOVQ R10, 16+z; \
|
||||
MOVQ R11, 24+z; \
|
||||
MOVQ R12, 32+z; \
|
||||
MOVQ R13, 40+z; \
|
||||
MOVQ R14, 48+z;
|
||||
|
||||
#define mulA24Legacy \
|
||||
multiplyA24Leg(0(DI),0(SI))
|
||||
#define mulA24Bmi2Adx \
|
||||
multiplyA24Adx(0(DI),0(SI))
|
||||
|
||||
// func mulA24Amd64(z, x *fp448.Elt)
|
||||
TEXT ·mulA24Amd64(SB),NOSPLIT,$0-16
|
||||
MOVQ z+0(FP), DI
|
||||
MOVQ x+8(FP), SI
|
||||
CHECK_BMI2ADX(LMA24, mulA24Legacy, mulA24Bmi2Adx)
|
||||
|
||||
// func ladderStepAmd64(w *[5]fp448.Elt, b uint)
|
||||
// ladderStepAmd64 calculates a point addition and doubling as follows:
|
||||
// (x2,z2) = 2*(x2,z2) and (x3,z3) = (x2,z2)+(x3,z3) using as a difference (x1,-).
|
||||
// w = {x1,x2,z2,x3,z4} are five fp255.Elt of 56 bytes.
|
||||
// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and
|
||||
// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes.
|
||||
TEXT ·ladderStepAmd64(SB),NOSPLIT,$336-16
|
||||
// Parameters
|
||||
#define regWork DI
|
||||
#define regMove SI
|
||||
#define x1 0*Size(regWork)
|
||||
#define x2 1*Size(regWork)
|
||||
#define z2 2*Size(regWork)
|
||||
#define x3 3*Size(regWork)
|
||||
#define z3 4*Size(regWork)
|
||||
// Local variables
|
||||
#define t0 0*Size(SP)
|
||||
#define t1 1*Size(SP)
|
||||
#define b0 2*Size(SP)
|
||||
#define b1 4*Size(SP)
|
||||
MOVQ w+0(FP), regWork
|
||||
MOVQ b+8(FP), regMove
|
||||
CHECK_BMI2ADX(LLADSTEP, ladderStepLeg, ladderStepBmi2Adx)
|
||||
#undef regWork
|
||||
#undef regMove
|
||||
#undef x1
|
||||
#undef x2
|
||||
#undef z2
|
||||
#undef x3
|
||||
#undef z3
|
||||
#undef t0
|
||||
#undef t1
|
||||
#undef b0
|
||||
#undef b1
|
||||
|
||||
// func diffAddAmd64(work *[5]fp.Elt, swap uint)
|
||||
// diffAddAmd64 calculates a differential point addition using a precomputed point.
|
||||
// (x1,z1) = (x1,z1)+(mu) using a difference point (x2,z2)
|
||||
// work = {mu,x1,z1,x2,z2} are five fp448.Elt of 56 bytes, and
|
||||
// stack = (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes.
|
||||
// This is Equation 7 at https://eprint.iacr.org/2017/264.
|
||||
TEXT ·diffAddAmd64(SB),NOSPLIT,$224-16
|
||||
// Parameters
|
||||
#define regWork DI
|
||||
#define regSwap SI
|
||||
#define ui 0*Size(regWork)
|
||||
#define x1 1*Size(regWork)
|
||||
#define z1 2*Size(regWork)
|
||||
#define x2 3*Size(regWork)
|
||||
#define z2 4*Size(regWork)
|
||||
// Local variables
|
||||
#define b0 0*Size(SP)
|
||||
#define b1 2*Size(SP)
|
||||
MOVQ w+0(FP), regWork
|
||||
MOVQ b+8(FP), regSwap
|
||||
cswap(x1,x2,regSwap)
|
||||
cswap(z1,z2,regSwap)
|
||||
CHECK_BMI2ADX(LDIFADD, difAddLeg, difAddBmi2Adx)
|
||||
#undef regWork
|
||||
#undef regSwap
|
||||
#undef ui
|
||||
#undef x1
|
||||
#undef z1
|
||||
#undef x2
|
||||
#undef z2
|
||||
#undef b0
|
||||
#undef b1
|
||||
|
||||
// func doubleAmd64(x, z *fp448.Elt)
|
||||
// doubleAmd64 calculates a point doubling (x1,z1) = 2*(x1,z1).
|
||||
// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and
|
||||
// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes.
|
||||
TEXT ·doubleAmd64(SB),NOSPLIT,$336-16
|
||||
// Parameters
|
||||
#define x1 0(DI)
|
||||
#define z1 0(SI)
|
||||
// Local variables
|
||||
#define t0 0*Size(SP)
|
||||
#define t1 1*Size(SP)
|
||||
#define b0 2*Size(SP)
|
||||
#define b1 4*Size(SP)
|
||||
MOVQ x+0(FP), DI
|
||||
MOVQ z+8(FP), SI
|
||||
CHECK_BMI2ADX(LDOUB,doubleLeg,doubleBmi2Adx)
|
||||
#undef x1
|
||||
#undef z1
|
||||
#undef t0
|
||||
#undef t1
|
||||
#undef b0
|
||||
#undef b1
|
||||
|
|
@ -0,0 +1,100 @@
|
|||
package x448
|
||||
|
||||
import (
|
||||
"encoding/binary"
|
||||
"math/bits"
|
||||
|
||||
"github.com/cloudflare/circl/math/fp448"
|
||||
)
|
||||
|
||||
func doubleGeneric(x, z *fp448.Elt) {
|
||||
t0, t1 := &fp448.Elt{}, &fp448.Elt{}
|
||||
fp448.AddSub(x, z)
|
||||
fp448.Sqr(x, x)
|
||||
fp448.Sqr(z, z)
|
||||
fp448.Sub(t0, x, z)
|
||||
mulA24Generic(t1, t0)
|
||||
fp448.Add(t1, t1, z)
|
||||
fp448.Mul(x, x, z)
|
||||
fp448.Mul(z, t0, t1)
|
||||
}
|
||||
|
||||
func diffAddGeneric(w *[5]fp448.Elt, b uint) {
|
||||
mu, x1, z1, x2, z2 := &w[0], &w[1], &w[2], &w[3], &w[4]
|
||||
fp448.Cswap(x1, x2, b)
|
||||
fp448.Cswap(z1, z2, b)
|
||||
fp448.AddSub(x1, z1)
|
||||
fp448.Mul(z1, z1, mu)
|
||||
fp448.AddSub(x1, z1)
|
||||
fp448.Sqr(x1, x1)
|
||||
fp448.Sqr(z1, z1)
|
||||
fp448.Mul(x1, x1, z2)
|
||||
fp448.Mul(z1, z1, x2)
|
||||
}
|
||||
|
||||
func ladderStepGeneric(w *[5]fp448.Elt, b uint) {
|
||||
x1, x2, z2, x3, z3 := &w[0], &w[1], &w[2], &w[3], &w[4]
|
||||
t0 := &fp448.Elt{}
|
||||
t1 := &fp448.Elt{}
|
||||
fp448.AddSub(x2, z2)
|
||||
fp448.AddSub(x3, z3)
|
||||
fp448.Mul(t0, x2, z3)
|
||||
fp448.Mul(t1, x3, z2)
|
||||
fp448.AddSub(t0, t1)
|
||||
fp448.Cmov(x2, x3, b)
|
||||
fp448.Cmov(z2, z3, b)
|
||||
fp448.Sqr(x3, t0)
|
||||
fp448.Sqr(z3, t1)
|
||||
fp448.Mul(z3, x1, z3)
|
||||
fp448.Sqr(x2, x2)
|
||||
fp448.Sqr(z2, z2)
|
||||
fp448.Sub(t0, x2, z2)
|
||||
mulA24Generic(t1, t0)
|
||||
fp448.Add(t1, t1, z2)
|
||||
fp448.Mul(x2, x2, z2)
|
||||
fp448.Mul(z2, t0, t1)
|
||||
}
|
||||
|
||||
func mulA24Generic(z, x *fp448.Elt) {
|
||||
const A24 = 39082
|
||||
const n = 8
|
||||
var xx [7]uint64
|
||||
for i := range xx {
|
||||
xx[i] = binary.LittleEndian.Uint64(x[i*n : (i+1)*n])
|
||||
}
|
||||
h0, l0 := bits.Mul64(xx[0], A24)
|
||||
h1, l1 := bits.Mul64(xx[1], A24)
|
||||
h2, l2 := bits.Mul64(xx[2], A24)
|
||||
h3, l3 := bits.Mul64(xx[3], A24)
|
||||
h4, l4 := bits.Mul64(xx[4], A24)
|
||||
h5, l5 := bits.Mul64(xx[5], A24)
|
||||
h6, l6 := bits.Mul64(xx[6], A24)
|
||||
|
||||
l1, c0 := bits.Add64(h0, l1, 0)
|
||||
l2, c1 := bits.Add64(h1, l2, c0)
|
||||
l3, c2 := bits.Add64(h2, l3, c1)
|
||||
l4, c3 := bits.Add64(h3, l4, c2)
|
||||
l5, c4 := bits.Add64(h4, l5, c3)
|
||||
l6, c5 := bits.Add64(h5, l6, c4)
|
||||
l7, _ := bits.Add64(h6, 0, c5)
|
||||
|
||||
l0, c0 = bits.Add64(l0, l7, 0)
|
||||
l1, c1 = bits.Add64(l1, 0, c0)
|
||||
l2, c2 = bits.Add64(l2, 0, c1)
|
||||
l3, c3 = bits.Add64(l3, l7<<32, c2)
|
||||
l4, c4 = bits.Add64(l4, 0, c3)
|
||||
l5, c5 = bits.Add64(l5, 0, c4)
|
||||
l6, l7 = bits.Add64(l6, 0, c5)
|
||||
|
||||
xx[0], c0 = bits.Add64(l0, l7, 0)
|
||||
xx[1], c1 = bits.Add64(l1, 0, c0)
|
||||
xx[2], c2 = bits.Add64(l2, 0, c1)
|
||||
xx[3], c3 = bits.Add64(l3, l7<<32, c2)
|
||||
xx[4], c4 = bits.Add64(l4, 0, c3)
|
||||
xx[5], c5 = bits.Add64(l5, 0, c4)
|
||||
xx[6], _ = bits.Add64(l6, 0, c5)
|
||||
|
||||
for i := range xx {
|
||||
binary.LittleEndian.PutUint64(z[i*n:(i+1)*n], xx[i])
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,11 @@
|
|||
//go:build !amd64 || purego
|
||||
// +build !amd64 purego
|
||||
|
||||
package x448
|
||||
|
||||
import fp "github.com/cloudflare/circl/math/fp448"
|
||||
|
||||
func double(x, z *fp.Elt) { doubleGeneric(x, z) }
|
||||
func diffAdd(w *[5]fp.Elt, b uint) { diffAddGeneric(w, b) }
|
||||
func ladderStep(w *[5]fp.Elt, b uint) { ladderStepGeneric(w, b) }
|
||||
func mulA24(z, x *fp.Elt) { mulA24Generic(z, x) }
|
||||
|
|
@ -0,0 +1,19 @@
|
|||
/*
|
||||
Package x448 provides Diffie-Hellman functions as specified in RFC-7748.
|
||||
|
||||
Validation of public keys.
|
||||
|
||||
The Diffie-Hellman function, as described in RFC-7748 [1], works for any
|
||||
public key. However, if a different protocol requires contributory
|
||||
behaviour [2,3], then the public keys must be validated against low-order
|
||||
points [3,4]. To do that, the Shared function performs this validation
|
||||
internally and returns false when the public key is invalid (i.e., it
|
||||
is a low-order point).
|
||||
|
||||
References:
|
||||
- [1] RFC7748 by Langley, Hamburg, Turner (https://rfc-editor.org/rfc/rfc7748.txt)
|
||||
- [2] Curve25519 by Bernstein (https://cr.yp.to/ecdh.html)
|
||||
- [3] Bernstein (https://cr.yp.to/ecdh.html#validate)
|
||||
- [4] Cremers&Jackson (https://eprint.iacr.org/2019/526)
|
||||
*/
|
||||
package x448
|
||||
|
|
@ -0,0 +1,46 @@
|
|||
package x448
|
||||
|
||||
import (
|
||||
"crypto/subtle"
|
||||
|
||||
fp "github.com/cloudflare/circl/math/fp448"
|
||||
)
|
||||
|
||||
// Size is the length in bytes of a X448 key.
|
||||
const Size = 56
|
||||
|
||||
// Key represents a X448 key.
|
||||
type Key [Size]byte
|
||||
|
||||
func (k *Key) clamp(in *Key) *Key {
|
||||
*k = *in
|
||||
k[0] &= 252
|
||||
k[55] |= 128
|
||||
return k
|
||||
}
|
||||
|
||||
// isValidPubKey verifies if the public key is not a low-order point.
|
||||
func (k *Key) isValidPubKey() bool {
|
||||
fp.Modp((*fp.Elt)(k))
|
||||
var isLowOrder int
|
||||
for _, P := range lowOrderPoints {
|
||||
isLowOrder |= subtle.ConstantTimeCompare(P[:], k[:])
|
||||
}
|
||||
return isLowOrder == 0
|
||||
}
|
||||
|
||||
// KeyGen obtains a public key given a secret key.
|
||||
func KeyGen(public, secret *Key) {
|
||||
ladderJoye(public.clamp(secret))
|
||||
}
|
||||
|
||||
// Shared calculates Alice's shared key from Alice's secret key and Bob's
|
||||
// public key returning true on success. A failure case happens when the public
|
||||
// key is a low-order point, thus the shared key is all-zeros and the function
|
||||
// returns false.
|
||||
func Shared(shared, secret, public *Key) bool {
|
||||
validPk := *public
|
||||
ok := validPk.isValidPubKey()
|
||||
ladderMontgomery(shared.clamp(secret), &validPk)
|
||||
return ok
|
||||
}
|
||||
|
|
@ -0,0 +1,460 @@
|
|||
package x448
|
||||
|
||||
import fp "github.com/cloudflare/circl/math/fp448"
|
||||
|
||||
// tableGenerator contains the set of points:
|
||||
//
|
||||
// t[i] = (xi+1)/(xi-1),
|
||||
//
|
||||
// where (xi,yi) = 2^iG and G is the generator point
|
||||
// Size = (448)*(448/8) = 25088 bytes.
|
||||
var tableGenerator = [448 * fp.Size]byte{
|
||||
/* (2^ 0)P */ 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f,
|
||||
/* (2^ 1)P */ 0x37, 0xfa, 0xaa, 0x0d, 0x86, 0xa6, 0x24, 0xe9, 0x6c, 0x95, 0x08, 0x34, 0xba, 0x1a, 0x81, 0x3a, 0xae, 0x01, 0xa5, 0xa7, 0x05, 0x85, 0x96, 0x00, 0x06, 0x5a, 0xd7, 0xff, 0xee, 0x8e, 0x8f, 0x94, 0xd2, 0xdc, 0xd7, 0xfc, 0xe7, 0xe5, 0x99, 0x1d, 0x05, 0x46, 0x43, 0xe8, 0xbc, 0x12, 0xb7, 0xeb, 0x30, 0x5e, 0x7a, 0x85, 0x68, 0xed, 0x9d, 0x28,
|
||||
/* (2^ 2)P */ 0xf1, 0x7d, 0x08, 0x2b, 0x32, 0x4a, 0x62, 0x80, 0x36, 0xe7, 0xa4, 0x76, 0x5a, 0x2a, 0x1e, 0xf7, 0x9e, 0x3c, 0x40, 0x46, 0x9a, 0x1b, 0x61, 0xc1, 0xbf, 0x1a, 0x1b, 0xae, 0x91, 0x80, 0xa3, 0x76, 0x6c, 0xd4, 0x8f, 0xa4, 0xee, 0x26, 0x39, 0x23, 0xa4, 0x80, 0xf4, 0x66, 0x92, 0xe4, 0xe1, 0x18, 0x76, 0xc5, 0xe2, 0x19, 0x87, 0xd5, 0xc3, 0xe8,
|
||||
/* (2^ 3)P */ 0xfb, 0xc9, 0xf0, 0x07, 0xf2, 0x93, 0xd8, 0x50, 0x36, 0xed, 0xfb, 0xbd, 0xb2, 0xd3, 0xfc, 0xdf, 0xd5, 0x2a, 0x6e, 0x26, 0x09, 0xce, 0xd4, 0x07, 0x64, 0x9f, 0x40, 0x74, 0xad, 0x98, 0x2f, 0x1c, 0xb6, 0xdc, 0x2d, 0x42, 0xff, 0xbf, 0x97, 0xd8, 0xdb, 0xef, 0x99, 0xca, 0x73, 0x99, 0x1a, 0x04, 0x3b, 0x56, 0x2c, 0x1f, 0x87, 0x9d, 0x9f, 0x03,
|
||||
/* (2^ 4)P */ 0x4c, 0x35, 0x97, 0xf7, 0x81, 0x2c, 0x84, 0xa6, 0xe0, 0xcb, 0xce, 0x37, 0x4c, 0x21, 0x1c, 0x67, 0xfa, 0xab, 0x18, 0x4d, 0xef, 0xd0, 0xf0, 0x44, 0xa9, 0xfb, 0xc0, 0x8e, 0xda, 0x57, 0xa1, 0xd8, 0xeb, 0x87, 0xf4, 0x17, 0xea, 0x66, 0x0f, 0x16, 0xea, 0xcd, 0x5f, 0x3e, 0x88, 0xea, 0x09, 0x68, 0x40, 0xdf, 0x43, 0xcc, 0x54, 0x61, 0x58, 0xaa,
|
||||
/* (2^ 5)P */ 0x8d, 0xe7, 0x59, 0xd7, 0x5e, 0x63, 0x37, 0xa7, 0x3f, 0xd1, 0x49, 0x85, 0x01, 0xdd, 0x5e, 0xb3, 0xe6, 0x29, 0xcb, 0x25, 0x93, 0xdd, 0x08, 0x96, 0x83, 0x52, 0x76, 0x85, 0xf5, 0x5d, 0x02, 0xbf, 0xe9, 0x6d, 0x15, 0x27, 0xc1, 0x09, 0xd1, 0x14, 0x4d, 0x6e, 0xe8, 0xaf, 0x59, 0x58, 0x34, 0x9d, 0x2a, 0x99, 0x85, 0x26, 0xbe, 0x4b, 0x1e, 0xb9,
|
||||
/* (2^ 6)P */ 0x8d, 0xce, 0x94, 0xe2, 0x18, 0x56, 0x0d, 0x82, 0x8e, 0xdf, 0x85, 0x01, 0x8f, 0x93, 0x3c, 0xc6, 0xbd, 0x61, 0xfb, 0xf4, 0x22, 0xc5, 0x16, 0x87, 0xd1, 0xb1, 0x9e, 0x09, 0xc5, 0x83, 0x2e, 0x4a, 0x07, 0x88, 0xee, 0xe0, 0x29, 0x8d, 0x2e, 0x1f, 0x88, 0xad, 0xfd, 0x18, 0x93, 0xb7, 0xed, 0x42, 0x86, 0x78, 0xf0, 0xb8, 0x70, 0xbe, 0x01, 0x67,
|
||||
/* (2^ 7)P */ 0xdf, 0x62, 0x2d, 0x94, 0xc7, 0x35, 0x23, 0xda, 0x27, 0xbb, 0x2b, 0xdb, 0x30, 0x80, 0x68, 0x16, 0xa3, 0xae, 0xd7, 0xd2, 0xa7, 0x7c, 0xbf, 0x6a, 0x1d, 0x83, 0xde, 0x96, 0x0a, 0x43, 0xb6, 0x30, 0x37, 0xd6, 0xee, 0x63, 0x59, 0x9a, 0xbf, 0xa3, 0x30, 0x6c, 0xaf, 0x0c, 0xee, 0x3d, 0xcb, 0x35, 0x4b, 0x55, 0x5f, 0x84, 0x85, 0xcb, 0x4f, 0x1e,
|
||||
/* (2^ 8)P */ 0x9d, 0x04, 0x68, 0x89, 0xa4, 0xa9, 0x0d, 0x87, 0xc1, 0x70, 0xf1, 0xeb, 0xfb, 0x47, 0x0a, 0xf0, 0xde, 0x67, 0xb7, 0x94, 0xcd, 0x36, 0x43, 0xa5, 0x49, 0x43, 0x67, 0xc3, 0xee, 0x3c, 0x6b, 0xec, 0xd0, 0x1a, 0xf4, 0xad, 0xef, 0x06, 0x4a, 0xe8, 0x46, 0x24, 0xd7, 0x93, 0xbf, 0xf0, 0xe3, 0x81, 0x61, 0xec, 0xea, 0x64, 0xfe, 0x67, 0xeb, 0xc7,
|
||||
/* (2^ 9)P */ 0x95, 0x45, 0x79, 0xcf, 0x2c, 0xfd, 0x9b, 0xfe, 0x84, 0x46, 0x4b, 0x8f, 0xa1, 0xcf, 0xc3, 0x04, 0x94, 0x78, 0xdb, 0xc9, 0xa6, 0x01, 0x75, 0xa4, 0xb4, 0x93, 0x72, 0x43, 0xa7, 0x7d, 0xda, 0x31, 0x38, 0x54, 0xab, 0x4e, 0x3f, 0x89, 0xa6, 0xab, 0x57, 0xc0, 0x16, 0x65, 0xdb, 0x92, 0x96, 0xe4, 0xc8, 0xae, 0xe7, 0x4c, 0x7a, 0xeb, 0xbb, 0x5a,
|
||||
/* (2^ 10)P */ 0xbe, 0xfe, 0x86, 0xc3, 0x97, 0xe0, 0x6a, 0x18, 0x20, 0x21, 0xca, 0x22, 0x55, 0xa1, 0xeb, 0xf5, 0x74, 0xe5, 0xc9, 0x59, 0xa7, 0x92, 0x65, 0x15, 0x08, 0x71, 0xd1, 0x09, 0x7e, 0x83, 0xfc, 0xbc, 0x5a, 0x93, 0x38, 0x0d, 0x43, 0x42, 0xfd, 0x76, 0x30, 0xe8, 0x63, 0x60, 0x09, 0x8d, 0x6c, 0xd3, 0xf8, 0x56, 0x3d, 0x68, 0x47, 0xab, 0xa0, 0x1d,
|
||||
/* (2^ 11)P */ 0x38, 0x50, 0x1c, 0xb1, 0xac, 0x88, 0x8f, 0x38, 0xe3, 0x69, 0xe6, 0xfc, 0x4f, 0x8f, 0xe1, 0x9b, 0xb1, 0x1a, 0x09, 0x39, 0x19, 0xdf, 0xcd, 0x98, 0x7b, 0x64, 0x42, 0xf6, 0x11, 0xea, 0xc7, 0xe8, 0x92, 0x65, 0x00, 0x2c, 0x75, 0xb5, 0x94, 0x1e, 0x5b, 0xa6, 0x66, 0x81, 0x77, 0xf3, 0x39, 0x94, 0xac, 0xbd, 0xe4, 0x2a, 0x66, 0x84, 0x9c, 0x60,
|
||||
/* (2^ 12)P */ 0xb5, 0xb6, 0xd9, 0x03, 0x67, 0xa4, 0xa8, 0x0a, 0x4a, 0x2b, 0x9d, 0xfa, 0x13, 0xe1, 0x99, 0x25, 0x4a, 0x5c, 0x67, 0xb9, 0xb2, 0xb7, 0xdd, 0x1e, 0xaf, 0xeb, 0x63, 0x41, 0xb6, 0xb9, 0xa0, 0x87, 0x0a, 0xe0, 0x06, 0x07, 0xaa, 0x97, 0xf8, 0xf9, 0x38, 0x4f, 0xdf, 0x0c, 0x40, 0x7c, 0xc3, 0x98, 0xa9, 0x74, 0xf1, 0x5d, 0xda, 0xd1, 0xc0, 0x0a,
|
||||
/* (2^ 13)P */ 0xf2, 0x0a, 0xab, 0xab, 0x94, 0x50, 0xf0, 0xa3, 0x6f, 0xc6, 0x66, 0xba, 0xa6, 0xdc, 0x44, 0xdd, 0xd6, 0x08, 0xf4, 0xd3, 0xed, 0xb1, 0x40, 0x93, 0xee, 0xf6, 0xb8, 0x8e, 0xb4, 0x7c, 0xb9, 0x82, 0xc9, 0x9d, 0x45, 0x3b, 0x8e, 0x10, 0xcb, 0x70, 0x1e, 0xba, 0x3c, 0x62, 0x50, 0xda, 0xa9, 0x93, 0xb5, 0xd7, 0xd0, 0x6f, 0x29, 0x52, 0x95, 0xae,
|
||||
/* (2^ 14)P */ 0x14, 0x68, 0x69, 0x23, 0xa8, 0x44, 0x87, 0x9e, 0x22, 0x91, 0xe8, 0x92, 0xdf, 0xf7, 0xae, 0xba, 0x1c, 0x96, 0xe1, 0xc3, 0x94, 0xed, 0x6c, 0x95, 0xae, 0x96, 0xa7, 0x15, 0x9f, 0xf1, 0x17, 0x11, 0x92, 0x42, 0xd5, 0xcd, 0x18, 0xe7, 0xa9, 0xb5, 0x2f, 0xcd, 0xde, 0x6c, 0xc9, 0x7d, 0xfc, 0x7e, 0xbd, 0x7f, 0x10, 0x3d, 0x01, 0x00, 0x8d, 0x95,
|
||||
/* (2^ 15)P */ 0x3b, 0x76, 0x72, 0xae, 0xaf, 0x84, 0xf2, 0xf7, 0xd1, 0x6d, 0x13, 0x9c, 0x47, 0xe1, 0xb7, 0xa3, 0x19, 0x16, 0xee, 0x75, 0x45, 0xf6, 0x1a, 0x7b, 0x78, 0x49, 0x79, 0x05, 0x86, 0xf0, 0x7f, 0x9f, 0xfc, 0xc4, 0xbd, 0x86, 0xf3, 0x41, 0xa7, 0xfe, 0x01, 0xd5, 0x67, 0x16, 0x10, 0x5b, 0xa5, 0x16, 0xf3, 0x7f, 0x60, 0xce, 0xd2, 0x0c, 0x8e, 0x4b,
|
||||
/* (2^ 16)P */ 0x4a, 0x07, 0x99, 0x4a, 0x0f, 0x74, 0x91, 0x14, 0x68, 0xb9, 0x48, 0xb7, 0x44, 0x77, 0x9b, 0x4a, 0xe0, 0x68, 0x0e, 0x43, 0x4d, 0x98, 0x98, 0xbf, 0xa8, 0x3a, 0xb7, 0x6d, 0x2a, 0x9a, 0x77, 0x5f, 0x62, 0xf5, 0x6b, 0x4a, 0xb7, 0x7d, 0xe5, 0x09, 0x6b, 0xc0, 0x8b, 0x9c, 0x88, 0x37, 0x33, 0xf2, 0x41, 0xac, 0x22, 0x1f, 0xcf, 0x3b, 0x82, 0x34,
|
||||
/* (2^ 17)P */ 0x00, 0xc3, 0x78, 0x42, 0x32, 0x2e, 0xdc, 0xda, 0xb1, 0x96, 0x21, 0xa4, 0xe4, 0xbb, 0xe9, 0x9d, 0xbb, 0x0f, 0x93, 0xed, 0x26, 0x3d, 0xb5, 0xdb, 0x94, 0x31, 0x37, 0x07, 0xa2, 0xb2, 0xd5, 0x99, 0x0d, 0x93, 0xe1, 0xce, 0x3f, 0x0b, 0x96, 0x82, 0x47, 0xfe, 0x60, 0x6f, 0x8f, 0x61, 0x88, 0xd7, 0x05, 0x95, 0x0b, 0x46, 0x06, 0xb7, 0x32, 0x06,
|
||||
/* (2^ 18)P */ 0x44, 0xf5, 0x34, 0xdf, 0x2f, 0x9c, 0x5d, 0x9f, 0x53, 0x5c, 0x42, 0x8f, 0xc9, 0xdc, 0xd8, 0x40, 0xa2, 0xe7, 0x6a, 0x4a, 0x05, 0xf7, 0x86, 0x77, 0x2b, 0xae, 0x37, 0xed, 0x48, 0xfb, 0xf7, 0x62, 0x7c, 0x17, 0x59, 0x92, 0x41, 0x61, 0x93, 0x38, 0x30, 0xd1, 0xef, 0x54, 0x54, 0x03, 0x17, 0x57, 0x91, 0x15, 0x11, 0x33, 0xb5, 0xfa, 0xfb, 0x17,
|
||||
/* (2^ 19)P */ 0x29, 0xbb, 0xd4, 0xb4, 0x9c, 0xf1, 0x72, 0x94, 0xce, 0x6a, 0x29, 0xa8, 0x89, 0x18, 0x19, 0xf7, 0xb7, 0xcc, 0xee, 0x9a, 0x02, 0xe3, 0xc0, 0xb1, 0xe0, 0xee, 0x83, 0x78, 0xb4, 0x9e, 0x07, 0x87, 0xdf, 0xb0, 0x82, 0x26, 0x4e, 0xa4, 0x0c, 0x33, 0xaf, 0x40, 0x59, 0xb6, 0xdd, 0x52, 0x45, 0xf0, 0xb4, 0xf6, 0xe8, 0x4e, 0x4e, 0x79, 0x1a, 0x5d,
|
||||
/* (2^ 20)P */ 0x27, 0x33, 0x4d, 0x4c, 0x6b, 0x4f, 0x75, 0xb1, 0xbc, 0x1f, 0xab, 0x5b, 0x2b, 0xf0, 0x1c, 0x57, 0x86, 0xdd, 0xfd, 0x60, 0xb0, 0x8c, 0xe7, 0x9a, 0xe5, 0x5c, 0xeb, 0x11, 0x3a, 0xda, 0x22, 0x25, 0x99, 0x06, 0x8d, 0xf4, 0xaf, 0x29, 0x7a, 0xc9, 0xe5, 0xd2, 0x16, 0x9e, 0xd4, 0x63, 0x1d, 0x64, 0xa6, 0x47, 0x96, 0x37, 0x6f, 0x93, 0x2c, 0xcc,
|
||||
/* (2^ 21)P */ 0xc1, 0x94, 0x74, 0x86, 0x75, 0xf2, 0x91, 0x58, 0x23, 0x85, 0x63, 0x76, 0x54, 0xc7, 0xb4, 0x8c, 0xbc, 0x4e, 0xc4, 0xa7, 0xba, 0xa0, 0x55, 0x26, 0x71, 0xd5, 0x33, 0x72, 0xc9, 0xad, 0x1e, 0xf9, 0x5d, 0x78, 0x70, 0x93, 0x4e, 0x85, 0xfc, 0x39, 0x06, 0x73, 0x76, 0xff, 0xe8, 0x64, 0x69, 0x42, 0x45, 0xb2, 0x69, 0xb5, 0x32, 0xe7, 0x2c, 0xde,
|
||||
/* (2^ 22)P */ 0xde, 0x16, 0xd8, 0x33, 0x49, 0x32, 0xe9, 0x0e, 0x3a, 0x60, 0xee, 0x2e, 0x24, 0x75, 0xe3, 0x9c, 0x92, 0x07, 0xdb, 0xad, 0x92, 0xf5, 0x11, 0xdf, 0xdb, 0xb0, 0x17, 0x5c, 0xd6, 0x1a, 0x70, 0x00, 0xb7, 0xe2, 0x18, 0xec, 0xdc, 0xc2, 0x02, 0x93, 0xb3, 0xc8, 0x3f, 0x4f, 0x1b, 0x96, 0xe6, 0x33, 0x8c, 0xfb, 0xcc, 0xa5, 0x4e, 0xe8, 0xe7, 0x11,
|
||||
/* (2^ 23)P */ 0x05, 0x7a, 0x74, 0x52, 0xf8, 0xdf, 0x0d, 0x7c, 0x6a, 0x1a, 0x4e, 0x9a, 0x02, 0x1d, 0xae, 0x77, 0xf8, 0x8e, 0xf9, 0xa2, 0x38, 0x54, 0x50, 0xb2, 0x2c, 0x08, 0x9d, 0x9b, 0x9f, 0xfb, 0x2b, 0x06, 0xde, 0x9d, 0xc2, 0x03, 0x0b, 0x22, 0x2b, 0x10, 0x5b, 0x3a, 0x73, 0x29, 0x8e, 0x3e, 0x37, 0x08, 0x2c, 0x3b, 0xf8, 0x80, 0xc1, 0x66, 0x1e, 0x98,
|
||||
/* (2^ 24)P */ 0xd8, 0xd6, 0x3e, 0xcd, 0x63, 0x8c, 0x2b, 0x41, 0x81, 0xc0, 0x0c, 0x06, 0x87, 0xd6, 0xe7, 0x92, 0xfe, 0xf1, 0x0c, 0x4a, 0x84, 0x5b, 0xaf, 0x40, 0x53, 0x6f, 0x60, 0xd6, 0x6b, 0x76, 0x4b, 0xc2, 0xad, 0xc9, 0xb6, 0xb6, 0x6a, 0xa2, 0xb3, 0xf5, 0xf5, 0xc2, 0x55, 0x83, 0xb2, 0xd3, 0xe9, 0x41, 0x6c, 0x63, 0x51, 0xb8, 0x81, 0x74, 0xc8, 0x2c,
|
||||
/* (2^ 25)P */ 0xb2, 0xaf, 0x1c, 0xee, 0x07, 0xb0, 0x58, 0xa8, 0x2c, 0x6a, 0xc9, 0x2d, 0x62, 0x28, 0x75, 0x0c, 0x40, 0xb6, 0x11, 0x33, 0x96, 0x80, 0x28, 0x6d, 0xd5, 0x9e, 0x87, 0x90, 0x01, 0x66, 0x1d, 0x1c, 0xf8, 0xb4, 0x92, 0xac, 0x38, 0x18, 0x05, 0xc2, 0x4c, 0x4b, 0x54, 0x7d, 0x80, 0x46, 0x87, 0x2d, 0x99, 0x8e, 0x70, 0x80, 0x69, 0x71, 0x8b, 0xed,
|
||||
/* (2^ 26)P */ 0x37, 0xa7, 0x6b, 0x71, 0x36, 0x75, 0x8e, 0xff, 0x0f, 0x42, 0xda, 0x5a, 0x46, 0xa6, 0x97, 0x79, 0x7e, 0x30, 0xb3, 0x8f, 0xc7, 0x3a, 0xa0, 0xcb, 0x1d, 0x9c, 0x78, 0x77, 0x36, 0xc2, 0xe7, 0xf4, 0x2f, 0x29, 0x07, 0xb1, 0x07, 0xfd, 0xed, 0x1b, 0x39, 0x77, 0x06, 0x38, 0x77, 0x0f, 0x50, 0x31, 0x12, 0xbf, 0x92, 0xbf, 0x72, 0x79, 0x54, 0xa9,
|
||||
/* (2^ 27)P */ 0xbd, 0x4d, 0x46, 0x6b, 0x1a, 0x80, 0x46, 0x2d, 0xed, 0xfd, 0x64, 0x6d, 0x94, 0xbc, 0x4a, 0x6e, 0x0c, 0x12, 0xf6, 0x12, 0xab, 0x54, 0x88, 0xd3, 0x85, 0xac, 0x51, 0xae, 0x6f, 0xca, 0xc4, 0xb7, 0xec, 0x22, 0x54, 0x6d, 0x80, 0xb2, 0x1c, 0x63, 0x33, 0x76, 0x6b, 0x8e, 0x6d, 0x59, 0xcd, 0x73, 0x92, 0x5f, 0xff, 0xad, 0x10, 0x35, 0x70, 0x5f,
|
||||
/* (2^ 28)P */ 0xb3, 0x84, 0xde, 0xc8, 0x04, 0x43, 0x63, 0xfa, 0x29, 0xd9, 0xf0, 0x69, 0x65, 0x5a, 0x0c, 0xe8, 0x2e, 0x0b, 0xfe, 0xb0, 0x7a, 0x42, 0xb3, 0xc3, 0xfc, 0xe6, 0xb8, 0x92, 0x29, 0xae, 0xed, 0xec, 0xd5, 0xe8, 0x4a, 0xa1, 0xbd, 0x3b, 0xd3, 0xc0, 0x07, 0xab, 0x65, 0x65, 0x35, 0x9a, 0xa6, 0x5e, 0x78, 0x18, 0x76, 0x1c, 0x15, 0x49, 0xe6, 0x75,
|
||||
/* (2^ 29)P */ 0x45, 0xb3, 0x92, 0xa9, 0xc3, 0xb8, 0x11, 0x68, 0x64, 0x3a, 0x83, 0x5d, 0xa8, 0x94, 0x6a, 0x9d, 0xaa, 0x27, 0x9f, 0x98, 0x5d, 0xc0, 0x29, 0xf0, 0xc0, 0x4b, 0x14, 0x3c, 0x05, 0xe7, 0xf8, 0xbd, 0x38, 0x22, 0x96, 0x75, 0x65, 0x5e, 0x0d, 0x3f, 0xbb, 0x6f, 0xe8, 0x3f, 0x96, 0x76, 0x9f, 0xba, 0xd9, 0x44, 0x92, 0x96, 0x22, 0xe7, 0x52, 0xe7,
|
||||
/* (2^ 30)P */ 0xf4, 0xa3, 0x95, 0x90, 0x47, 0xdf, 0x7d, 0xdc, 0xf4, 0x13, 0x87, 0x67, 0x7d, 0x4f, 0x9d, 0xa0, 0x00, 0x46, 0x72, 0x08, 0xc3, 0xa2, 0x7a, 0x3e, 0xe7, 0x6d, 0x52, 0x7c, 0x11, 0x36, 0x50, 0x83, 0x89, 0x64, 0xcb, 0x1f, 0x08, 0x83, 0x46, 0xcb, 0xac, 0xa6, 0xd8, 0x9c, 0x1b, 0xe8, 0x05, 0x47, 0xc7, 0x26, 0x06, 0x83, 0x39, 0xe9, 0xb1, 0x1c,
|
||||
/* (2^ 31)P */ 0x11, 0xe8, 0xc8, 0x42, 0xbf, 0x30, 0x9c, 0xa3, 0xf1, 0x85, 0x96, 0x95, 0x4f, 0x4f, 0x52, 0xa2, 0xf5, 0x8b, 0x68, 0x24, 0x16, 0xac, 0x9b, 0xa9, 0x27, 0x28, 0x0e, 0x84, 0x03, 0x46, 0x22, 0x5f, 0xf7, 0x0d, 0xa6, 0x85, 0x88, 0xc1, 0x45, 0x4b, 0x85, 0x1a, 0x10, 0x7f, 0xc9, 0x94, 0x20, 0xb0, 0x04, 0x28, 0x12, 0x30, 0xb9, 0xe6, 0x40, 0x6b,
|
||||
/* (2^ 32)P */ 0xac, 0x1b, 0x57, 0xb6, 0x42, 0xdb, 0x81, 0x8d, 0x76, 0xfd, 0x9b, 0x1c, 0x29, 0x30, 0xd5, 0x3a, 0xcc, 0x53, 0xd9, 0x26, 0x7a, 0x0f, 0x9c, 0x2e, 0x79, 0xf5, 0x62, 0xeb, 0x61, 0x9d, 0x9b, 0x80, 0x39, 0xcd, 0x60, 0x2e, 0x1f, 0x08, 0x22, 0xbc, 0x19, 0xb3, 0x2a, 0x43, 0x44, 0xf2, 0x4e, 0x66, 0xf4, 0x36, 0xa6, 0xa7, 0xbc, 0xa4, 0x15, 0x7e,
|
||||
/* (2^ 33)P */ 0xc1, 0x90, 0x8a, 0xde, 0xff, 0x78, 0xc3, 0x73, 0x16, 0xee, 0x76, 0xa0, 0x84, 0x60, 0x8d, 0xe6, 0x82, 0x0f, 0xde, 0x4e, 0xc5, 0x99, 0x34, 0x06, 0x90, 0x44, 0x55, 0xf8, 0x91, 0xd8, 0xe1, 0xe4, 0x2c, 0x8a, 0xde, 0x94, 0x1e, 0x78, 0x25, 0x3d, 0xfd, 0xd8, 0x59, 0x7d, 0xaf, 0x6e, 0xbe, 0x96, 0xbe, 0x3c, 0x16, 0x23, 0x0f, 0x4c, 0xa4, 0x28,
|
||||
/* (2^ 34)P */ 0xba, 0x11, 0x35, 0x57, 0x03, 0xb6, 0xf4, 0x24, 0x89, 0xb8, 0x5a, 0x0d, 0x50, 0x9c, 0xaa, 0x51, 0x7f, 0xa4, 0x0e, 0xfc, 0x71, 0xb3, 0x3b, 0xf1, 0x96, 0x50, 0x23, 0x15, 0xf5, 0xf5, 0xd4, 0x23, 0xdc, 0x8b, 0x26, 0x9e, 0xae, 0xb7, 0x50, 0xcd, 0xc4, 0x25, 0xf6, 0x75, 0x40, 0x9c, 0x37, 0x79, 0x33, 0x60, 0xd4, 0x4b, 0x13, 0x32, 0xee, 0xe2,
|
||||
/* (2^ 35)P */ 0x43, 0xb8, 0x56, 0x59, 0xf0, 0x68, 0x23, 0xb3, 0xea, 0x70, 0x58, 0x4c, 0x1e, 0x5a, 0x16, 0x54, 0x03, 0xb2, 0xf4, 0x73, 0xb6, 0xd9, 0x5c, 0x9c, 0x6f, 0xcf, 0x82, 0x2e, 0x54, 0x15, 0x46, 0x2c, 0xa3, 0xda, 0x4e, 0x87, 0xf5, 0x2b, 0xba, 0x91, 0xa3, 0xa0, 0x89, 0xba, 0x48, 0x2b, 0xfa, 0x64, 0x02, 0x7f, 0x78, 0x03, 0xd1, 0xe8, 0x3b, 0xe9,
|
||||
/* (2^ 36)P */ 0x15, 0xa4, 0x71, 0xd4, 0x0c, 0x24, 0xe9, 0x07, 0xa1, 0x43, 0xf4, 0x7f, 0xbb, 0xa2, 0xa6, 0x6b, 0xfa, 0xb7, 0xea, 0x58, 0xd1, 0x96, 0xb0, 0x24, 0x5c, 0xc7, 0x37, 0x4e, 0x60, 0x0f, 0x40, 0xf2, 0x2f, 0x44, 0x70, 0xea, 0x80, 0x63, 0xfe, 0xfc, 0x46, 0x59, 0x12, 0x27, 0xb5, 0x27, 0xfd, 0xb7, 0x73, 0x0b, 0xca, 0x8b, 0xc2, 0xd3, 0x71, 0x08,
|
||||
/* (2^ 37)P */ 0x26, 0x0e, 0xd7, 0x52, 0x6f, 0xf1, 0xf2, 0x9d, 0xb8, 0x3d, 0xbd, 0xd4, 0x75, 0x97, 0xd8, 0xbf, 0xa8, 0x86, 0x96, 0xa5, 0x80, 0xa0, 0x45, 0x75, 0xf6, 0x77, 0x71, 0xdb, 0x77, 0x96, 0x55, 0x99, 0x31, 0xd0, 0x4f, 0x34, 0xf4, 0x35, 0x39, 0x41, 0xd3, 0x7d, 0xf7, 0xe2, 0x74, 0xde, 0xbe, 0x5b, 0x1f, 0x39, 0x10, 0x21, 0xa3, 0x4d, 0x3b, 0xc8,
|
||||
/* (2^ 38)P */ 0x04, 0x00, 0x2a, 0x45, 0xb2, 0xaf, 0x9b, 0x18, 0x6a, 0xeb, 0x96, 0x28, 0xa4, 0x77, 0xd0, 0x13, 0xcf, 0x17, 0x65, 0xe8, 0xc5, 0x81, 0x28, 0xad, 0x39, 0x7a, 0x0b, 0xaa, 0x55, 0x2b, 0xf3, 0xfc, 0x86, 0x40, 0xad, 0x0d, 0x1e, 0x28, 0xa2, 0x2d, 0xc5, 0xd6, 0x04, 0x15, 0xa2, 0x30, 0x3d, 0x12, 0x8e, 0xd6, 0xb5, 0xf7, 0x69, 0xbb, 0x84, 0x20,
|
||||
/* (2^ 39)P */ 0xd7, 0x7a, 0x77, 0x2c, 0xfb, 0x81, 0x80, 0xe9, 0x1e, 0xc6, 0x36, 0x31, 0x79, 0xc3, 0x7c, 0xa9, 0x57, 0x6b, 0xb5, 0x70, 0xfb, 0xe4, 0xa1, 0xff, 0xfd, 0x21, 0xa5, 0x7c, 0xfa, 0x44, 0xba, 0x0d, 0x96, 0x3d, 0xc4, 0x5c, 0x39, 0x52, 0x87, 0xd7, 0x22, 0x0f, 0x52, 0x88, 0x91, 0x87, 0x96, 0xac, 0xfa, 0x3b, 0xdf, 0xdc, 0x83, 0x8c, 0x99, 0x29,
|
||||
/* (2^ 40)P */ 0x98, 0x6b, 0x3a, 0x8d, 0x83, 0x17, 0xe1, 0x62, 0xd8, 0x80, 0x4c, 0x97, 0xce, 0x6b, 0xaa, 0x10, 0xa7, 0xc4, 0xe9, 0xeb, 0xa5, 0xfb, 0xc9, 0xdd, 0x2d, 0xeb, 0xfc, 0x9a, 0x71, 0xcd, 0x68, 0x6e, 0xc0, 0x35, 0x64, 0x62, 0x1b, 0x95, 0x12, 0xe8, 0x53, 0xec, 0xf0, 0xf4, 0x86, 0x86, 0x78, 0x18, 0xc4, 0xc6, 0xbc, 0x5a, 0x59, 0x8f, 0x7c, 0x7e,
|
||||
/* (2^ 41)P */ 0x7f, 0xd7, 0x1e, 0xc5, 0x83, 0xdc, 0x1f, 0xbe, 0x0b, 0xcf, 0x2e, 0x01, 0x01, 0xed, 0xac, 0x17, 0x3b, 0xed, 0xa4, 0x30, 0x96, 0x0e, 0x14, 0x7e, 0x19, 0x2b, 0xa5, 0x67, 0x1e, 0xb3, 0x34, 0x03, 0xa8, 0xbb, 0x0a, 0x7d, 0x08, 0x2d, 0xd5, 0x53, 0x19, 0x6f, 0x13, 0xd5, 0xc0, 0x90, 0x8a, 0xcc, 0xc9, 0x5c, 0xab, 0x24, 0xd7, 0x03, 0xf6, 0x57,
|
||||
/* (2^ 42)P */ 0x49, 0xcb, 0xb4, 0x96, 0x5f, 0xa6, 0xf8, 0x71, 0x6f, 0x59, 0xad, 0x05, 0x24, 0x2d, 0xaf, 0x67, 0xa8, 0xbe, 0x95, 0xdf, 0x0d, 0x28, 0x5a, 0x7f, 0x6e, 0x87, 0x8c, 0x6e, 0x67, 0x0c, 0xf4, 0xe0, 0x1c, 0x30, 0xc2, 0x66, 0xae, 0x20, 0xa1, 0x34, 0xec, 0x9c, 0xbc, 0xae, 0x3d, 0xa1, 0x28, 0x28, 0x95, 0x1d, 0xc9, 0x3a, 0xa8, 0xfd, 0xfc, 0xa1,
|
||||
/* (2^ 43)P */ 0xe2, 0x2b, 0x9d, 0xed, 0x02, 0x99, 0x67, 0xbb, 0x2e, 0x16, 0x62, 0x05, 0x70, 0xc7, 0x27, 0xb9, 0x1c, 0x3f, 0xf2, 0x11, 0x01, 0xd8, 0x51, 0xa4, 0x18, 0x92, 0xa9, 0x5d, 0xfb, 0xa9, 0xe4, 0x42, 0xba, 0x38, 0x34, 0x1a, 0x4a, 0xc5, 0x6a, 0x37, 0xde, 0xa7, 0x0c, 0xb4, 0x7e, 0x7f, 0xde, 0xa6, 0xee, 0xcd, 0x55, 0x57, 0x05, 0x06, 0xfd, 0x5d,
|
||||
/* (2^ 44)P */ 0x2f, 0x32, 0xcf, 0x2e, 0x2c, 0x7b, 0xbe, 0x9a, 0x0c, 0x57, 0x35, 0xf8, 0x87, 0xda, 0x9c, 0xec, 0x48, 0xf2, 0xbb, 0xe2, 0xda, 0x10, 0x58, 0x20, 0xc6, 0xd3, 0x87, 0xe9, 0xc7, 0x26, 0xd1, 0x9a, 0x46, 0x87, 0x90, 0xda, 0xdc, 0xde, 0xc3, 0xb3, 0xf2, 0xe8, 0x6f, 0x4a, 0xe6, 0xe8, 0x9d, 0x98, 0x36, 0x20, 0x03, 0x47, 0x15, 0x3f, 0x64, 0x59,
|
||||
/* (2^ 45)P */ 0xd4, 0x71, 0x49, 0x0a, 0x67, 0x97, 0xaa, 0x3f, 0xf4, 0x1b, 0x3a, 0x6e, 0x5e, 0x17, 0xcc, 0x0a, 0x8f, 0x81, 0x6a, 0x41, 0x38, 0x77, 0x40, 0x8a, 0x11, 0x42, 0x62, 0xd2, 0x50, 0x32, 0x79, 0x78, 0x28, 0xc2, 0x2e, 0x10, 0x01, 0x94, 0x30, 0x4f, 0x7f, 0x18, 0x17, 0x56, 0x85, 0x4e, 0xad, 0xf7, 0xcb, 0x87, 0x3c, 0x3f, 0x50, 0x2c, 0xc0, 0xba,
|
||||
/* (2^ 46)P */ 0xbc, 0x30, 0x8e, 0x65, 0x8e, 0x57, 0x5b, 0x38, 0x7a, 0xd4, 0x95, 0x52, 0x7a, 0x32, 0x59, 0x69, 0xcd, 0x9d, 0x47, 0x34, 0x5b, 0x55, 0xa5, 0x24, 0x60, 0xdd, 0xc0, 0xc1, 0x62, 0x73, 0x44, 0xae, 0x4c, 0x9c, 0x65, 0x55, 0x1b, 0x9d, 0x8a, 0x29, 0xb0, 0x1a, 0x52, 0xa8, 0xf1, 0xe6, 0x9a, 0xb3, 0xf6, 0xa3, 0xc9, 0x0a, 0x70, 0x7d, 0x0f, 0xee,
|
||||
/* (2^ 47)P */ 0x77, 0xd3, 0xe5, 0x8e, 0xfa, 0x00, 0xeb, 0x1b, 0x7f, 0xdc, 0x68, 0x3f, 0x92, 0xbd, 0xb7, 0x0b, 0xb7, 0xb5, 0x24, 0xdf, 0xc5, 0x67, 0x53, 0xd4, 0x36, 0x79, 0xc4, 0x7b, 0x57, 0xbc, 0x99, 0x97, 0x60, 0xef, 0xe4, 0x01, 0xa1, 0xa7, 0xaa, 0x12, 0x36, 0x29, 0xb1, 0x03, 0xc2, 0x83, 0x1c, 0x2b, 0x83, 0xef, 0x2e, 0x2c, 0x23, 0x92, 0xfd, 0xd1,
|
||||
/* (2^ 48)P */ 0x94, 0xef, 0x03, 0x59, 0xfa, 0x8a, 0x18, 0x76, 0xee, 0x58, 0x08, 0x4d, 0x44, 0xce, 0xf1, 0x52, 0x33, 0x49, 0xf6, 0x69, 0x71, 0xe3, 0xa9, 0xbc, 0x86, 0xe3, 0x43, 0xde, 0x33, 0x7b, 0x90, 0x8b, 0x3e, 0x7d, 0xd5, 0x4a, 0xf0, 0x23, 0x99, 0xa6, 0xea, 0x5f, 0x08, 0xe5, 0xb9, 0x49, 0x8b, 0x0d, 0x6a, 0x21, 0xab, 0x07, 0x62, 0xcd, 0xc4, 0xbe,
|
||||
/* (2^ 49)P */ 0x61, 0xbf, 0x70, 0x14, 0xfa, 0x4e, 0x9e, 0x7c, 0x0c, 0xf8, 0xb2, 0x48, 0x71, 0x62, 0x83, 0xd6, 0xd1, 0xdc, 0x9c, 0x29, 0x66, 0xb1, 0x34, 0x9c, 0x8d, 0xe6, 0x88, 0xaf, 0xbe, 0xdc, 0x4d, 0xeb, 0xb0, 0xe7, 0x28, 0xae, 0xb2, 0x05, 0x56, 0xc6, 0x0e, 0x10, 0x26, 0xab, 0x2c, 0x59, 0x72, 0x03, 0x66, 0xfe, 0x8f, 0x2c, 0x51, 0x2d, 0xdc, 0xae,
|
||||
/* (2^ 50)P */ 0xdc, 0x63, 0xf1, 0x8b, 0x5c, 0x65, 0x0b, 0xf1, 0xa6, 0x22, 0xe2, 0xd9, 0xdb, 0x49, 0xb1, 0x3c, 0x47, 0xc2, 0xfe, 0xac, 0x86, 0x07, 0x52, 0xec, 0xb0, 0x08, 0x69, 0xfb, 0xd1, 0x06, 0xdc, 0x48, 0x5c, 0x3d, 0xb2, 0x4d, 0xb8, 0x1a, 0x4e, 0xda, 0xb9, 0xc1, 0x2b, 0xab, 0x4b, 0x62, 0x81, 0x21, 0x9a, 0xfc, 0x3d, 0x39, 0x83, 0x11, 0x36, 0xeb,
|
||||
/* (2^ 51)P */ 0x94, 0xf3, 0x17, 0xef, 0xf9, 0x60, 0x54, 0xc3, 0xd7, 0x27, 0x35, 0xc5, 0x98, 0x5e, 0xf6, 0x63, 0x6c, 0xa0, 0x4a, 0xd3, 0xa3, 0x98, 0xd9, 0x42, 0xe3, 0xf1, 0xf8, 0x81, 0x96, 0xa9, 0xea, 0x6d, 0x4b, 0x8e, 0x33, 0xca, 0x94, 0x0d, 0xa0, 0xf7, 0xbb, 0x64, 0xa3, 0x36, 0x6f, 0xdc, 0x5a, 0x94, 0x42, 0xca, 0x06, 0xb2, 0x2b, 0x9a, 0x9f, 0x71,
|
||||
/* (2^ 52)P */ 0xec, 0xdb, 0xa6, 0x1f, 0xdf, 0x15, 0x36, 0xa3, 0xda, 0x8a, 0x7a, 0xb6, 0xa7, 0xe3, 0xaf, 0x52, 0xe0, 0x8d, 0xe8, 0xf2, 0x44, 0x20, 0xeb, 0xa1, 0x20, 0xc4, 0x65, 0x3c, 0x7c, 0x6c, 0x49, 0xed, 0x2f, 0x66, 0x23, 0x68, 0x61, 0x91, 0x40, 0x9f, 0x50, 0x19, 0xd1, 0x84, 0xa7, 0xe2, 0xed, 0x34, 0x37, 0xe3, 0xe4, 0x11, 0x7f, 0x87, 0x55, 0x0f,
|
||||
/* (2^ 53)P */ 0xb3, 0xa1, 0x0f, 0xb0, 0x48, 0xc0, 0x4d, 0x96, 0xa7, 0xcf, 0x5a, 0x81, 0xb8, 0x4a, 0x46, 0xef, 0x0a, 0xd3, 0x40, 0x7e, 0x02, 0xe3, 0x63, 0xaa, 0x50, 0xd1, 0x2a, 0x37, 0x22, 0x4a, 0x7f, 0x4f, 0xb6, 0xf9, 0x01, 0x82, 0x78, 0x3d, 0x93, 0x14, 0x11, 0x8a, 0x90, 0x60, 0xcd, 0x45, 0x4e, 0x7b, 0x42, 0xb9, 0x3e, 0x6e, 0x68, 0x1f, 0x36, 0x41,
|
||||
/* (2^ 54)P */ 0x13, 0x73, 0x0e, 0x4f, 0x79, 0x93, 0x9e, 0x29, 0x70, 0x7b, 0x4a, 0x59, 0x1a, 0x9a, 0xf4, 0x55, 0x08, 0xf0, 0xdb, 0x17, 0x58, 0xec, 0x64, 0xad, 0x7f, 0x29, 0xeb, 0x3f, 0x85, 0x4e, 0x60, 0x28, 0x98, 0x1f, 0x73, 0x4e, 0xe6, 0xa8, 0xab, 0xd5, 0xd6, 0xfc, 0xa1, 0x36, 0x6d, 0x15, 0xc6, 0x13, 0x83, 0xa0, 0xc2, 0x6e, 0xd9, 0xdb, 0xc9, 0xcc,
|
||||
/* (2^ 55)P */ 0xff, 0xd8, 0x52, 0xa3, 0xdc, 0x99, 0xcf, 0x3e, 0x19, 0xb3, 0x68, 0xd0, 0xb5, 0x0d, 0xb8, 0xee, 0x3f, 0xef, 0x6e, 0xc0, 0x38, 0x28, 0x44, 0x92, 0x78, 0x91, 0x1a, 0x08, 0x78, 0x6c, 0x65, 0x24, 0xf3, 0xa2, 0x3d, 0xf2, 0xe5, 0x79, 0x62, 0x69, 0x29, 0xf4, 0x22, 0xc5, 0xdb, 0x6a, 0xae, 0xf4, 0x44, 0xa3, 0x6f, 0xc7, 0x86, 0xab, 0xef, 0xef,
|
||||
/* (2^ 56)P */ 0xbf, 0x54, 0x9a, 0x09, 0x5d, 0x17, 0xd0, 0xde, 0xfb, 0xf5, 0xca, 0xff, 0x13, 0x20, 0x88, 0x82, 0x3a, 0xe2, 0xd0, 0x3b, 0xfb, 0x05, 0x76, 0xd1, 0xc0, 0x02, 0x71, 0x3b, 0x94, 0xe8, 0xc9, 0x84, 0xcf, 0xa4, 0xe9, 0x28, 0x7b, 0xf5, 0x09, 0xc3, 0x2b, 0x22, 0x40, 0xf1, 0x68, 0x24, 0x24, 0x7d, 0x9f, 0x6e, 0xcd, 0xfe, 0xb0, 0x19, 0x61, 0xf5,
|
||||
/* (2^ 57)P */ 0xe8, 0x63, 0x51, 0xb3, 0x95, 0x6b, 0x7b, 0x74, 0x92, 0x52, 0x45, 0xa4, 0xed, 0xea, 0x0e, 0x0d, 0x2b, 0x01, 0x1e, 0x2c, 0xbc, 0x91, 0x06, 0x69, 0xdb, 0x1f, 0xb5, 0x77, 0x1d, 0x56, 0xf5, 0xb4, 0x02, 0x80, 0x49, 0x56, 0x12, 0xce, 0x86, 0x05, 0xc9, 0xd9, 0xae, 0xf3, 0x6d, 0xe6, 0x3f, 0x40, 0x52, 0xe9, 0x49, 0x2b, 0x31, 0x06, 0x86, 0x14,
|
||||
/* (2^ 58)P */ 0xf5, 0x09, 0x3b, 0xd2, 0xff, 0xdf, 0x11, 0xa5, 0x1c, 0x99, 0xe8, 0x1b, 0xa4, 0x2c, 0x7d, 0x8e, 0xc8, 0xf7, 0x03, 0x46, 0xfa, 0xb6, 0xde, 0x73, 0x91, 0x7e, 0x5a, 0x7a, 0xd7, 0x9a, 0x5b, 0x80, 0x24, 0x62, 0x5e, 0x92, 0xf1, 0xa3, 0x45, 0xa3, 0x43, 0x92, 0x8a, 0x2a, 0x5b, 0x0c, 0xb4, 0xc8, 0xad, 0x1c, 0xb6, 0x6c, 0x5e, 0x81, 0x18, 0x91,
|
||||
/* (2^ 59)P */ 0x96, 0xb3, 0xca, 0x2b, 0xe3, 0x7a, 0x59, 0x72, 0x17, 0x74, 0x29, 0x21, 0xe7, 0x78, 0x07, 0xad, 0xda, 0xb6, 0xcd, 0xf9, 0x27, 0x4d, 0xc8, 0xf2, 0x98, 0x22, 0xca, 0xf2, 0x33, 0x74, 0x7a, 0xdd, 0x1e, 0x71, 0xec, 0xe3, 0x3f, 0xe2, 0xa2, 0xd2, 0x38, 0x75, 0xb0, 0xd0, 0x0a, 0xcf, 0x7d, 0x36, 0xdc, 0x49, 0x38, 0x25, 0x34, 0x4f, 0x20, 0x9a,
|
||||
/* (2^ 60)P */ 0x2b, 0x6e, 0x04, 0x0d, 0x4f, 0x3d, 0x3b, 0x24, 0xf6, 0x4e, 0x5e, 0x0a, 0xbd, 0x48, 0x96, 0xba, 0x81, 0x8f, 0x39, 0x82, 0x13, 0xe6, 0x72, 0xf3, 0x0f, 0xb6, 0x94, 0xf4, 0xc5, 0x90, 0x74, 0x91, 0xa8, 0xf2, 0xc9, 0xca, 0x9a, 0x4d, 0x98, 0xf2, 0xdf, 0x52, 0x4e, 0x97, 0x2f, 0xeb, 0x84, 0xd3, 0xaf, 0xc2, 0xcc, 0xfb, 0x4c, 0x26, 0x4b, 0xe4,
|
||||
/* (2^ 61)P */ 0x12, 0x9e, 0xfb, 0x9d, 0x78, 0x79, 0x99, 0xdd, 0xb3, 0x0b, 0x2e, 0x56, 0x41, 0x8e, 0x3f, 0x39, 0xb8, 0x97, 0x89, 0x53, 0x9b, 0x8a, 0x3c, 0x40, 0x9d, 0xa4, 0x6c, 0x2e, 0x31, 0x71, 0xc6, 0x0a, 0x41, 0xd4, 0x95, 0x06, 0x5e, 0xc1, 0xab, 0xc2, 0x14, 0xc4, 0xc7, 0x15, 0x08, 0x3a, 0xad, 0x7a, 0xb4, 0x62, 0xa3, 0x0c, 0x90, 0xf4, 0x47, 0x08,
|
||||
/* (2^ 62)P */ 0x7f, 0xec, 0x09, 0x82, 0xf5, 0x94, 0x09, 0x93, 0x32, 0xd3, 0xdc, 0x56, 0x80, 0x7b, 0x5b, 0x22, 0x80, 0x6a, 0x96, 0x72, 0xb1, 0xc2, 0xd9, 0xa1, 0x8b, 0x66, 0x42, 0x16, 0xe2, 0x07, 0xb3, 0x2d, 0xf1, 0x75, 0x35, 0x72, 0xc7, 0x98, 0xbe, 0x63, 0x3b, 0x20, 0x75, 0x05, 0xc1, 0x3e, 0x31, 0x5a, 0xf7, 0xaa, 0xae, 0x4b, 0xdb, 0x1d, 0xd0, 0x74,
|
||||
/* (2^ 63)P */ 0x36, 0x5c, 0x74, 0xe6, 0x5d, 0x59, 0x3f, 0x15, 0x4b, 0x4d, 0x4e, 0x67, 0x41, 0xfe, 0x98, 0x1f, 0x49, 0x76, 0x91, 0x0f, 0x9b, 0xf4, 0xaf, 0x86, 0xaf, 0x66, 0x19, 0xed, 0x46, 0xf1, 0x05, 0x9a, 0xcc, 0xd1, 0x14, 0x1f, 0x82, 0x12, 0x8e, 0xe6, 0xf4, 0xc3, 0x42, 0x5c, 0x4e, 0x33, 0x93, 0xbe, 0x30, 0xe7, 0x64, 0xa9, 0x35, 0x00, 0x4d, 0xf9,
|
||||
/* (2^ 64)P */ 0x1f, 0xc1, 0x1e, 0xb7, 0xe3, 0x7c, 0xfa, 0xa3, 0x6b, 0x76, 0xaf, 0x9c, 0x05, 0x85, 0x4a, 0xa9, 0xfb, 0xe3, 0x7e, 0xf2, 0x49, 0x56, 0xdc, 0x2f, 0x57, 0x10, 0xba, 0x37, 0xb2, 0x62, 0xf5, 0x6b, 0xe5, 0x8f, 0x0a, 0x87, 0xd1, 0x6a, 0xcb, 0x9d, 0x07, 0xd0, 0xf6, 0x38, 0x99, 0x2c, 0x61, 0x4a, 0x4e, 0xd8, 0xd2, 0x88, 0x29, 0x99, 0x11, 0x95,
|
||||
/* (2^ 65)P */ 0x6f, 0xdc, 0xd5, 0xd6, 0xd6, 0xa7, 0x4c, 0x46, 0x93, 0x65, 0x62, 0x23, 0x95, 0x32, 0x9c, 0xde, 0x40, 0x41, 0x68, 0x2c, 0x18, 0x4e, 0x5a, 0x8c, 0xc0, 0xc5, 0xc5, 0xea, 0x5c, 0x45, 0x0f, 0x60, 0x78, 0x39, 0xb6, 0x36, 0x23, 0x12, 0xbc, 0x21, 0x9a, 0xf8, 0x91, 0xac, 0xc4, 0x70, 0xdf, 0x85, 0x8e, 0x3c, 0xec, 0x22, 0x04, 0x98, 0xa8, 0xaa,
|
||||
/* (2^ 66)P */ 0xcc, 0x52, 0x10, 0x5b, 0x4b, 0x6c, 0xc5, 0xfa, 0x3e, 0xd4, 0xf8, 0x1c, 0x04, 0x14, 0x48, 0x33, 0xd9, 0xfc, 0x5f, 0xb0, 0xa5, 0x48, 0x8c, 0x45, 0x8a, 0xee, 0x3e, 0xa7, 0xc1, 0x2e, 0x34, 0xca, 0xf6, 0xc9, 0xeb, 0x10, 0xbb, 0xe1, 0x59, 0x84, 0x25, 0xe8, 0x81, 0x70, 0xc0, 0x09, 0x42, 0xa7, 0x3b, 0x0d, 0x33, 0x00, 0xb5, 0x77, 0xbe, 0x25,
|
||||
/* (2^ 67)P */ 0xcd, 0x1f, 0xbc, 0x7d, 0xef, 0xe5, 0xca, 0x91, 0xaf, 0xa9, 0x59, 0x6a, 0x09, 0xca, 0xd6, 0x1b, 0x3d, 0x55, 0xde, 0xa2, 0x6a, 0x80, 0xd6, 0x95, 0x47, 0xe4, 0x5f, 0x68, 0x54, 0x08, 0xdf, 0x29, 0xba, 0x2a, 0x02, 0x84, 0xe8, 0xe9, 0x00, 0x77, 0x99, 0x36, 0x03, 0xf6, 0x4a, 0x3e, 0x21, 0x81, 0x7d, 0xb8, 0xa4, 0x8a, 0xa2, 0x05, 0xef, 0xbc,
|
||||
/* (2^ 68)P */ 0x7c, 0x59, 0x5f, 0x66, 0xd9, 0xb7, 0x83, 0x43, 0x8a, 0xa1, 0x8d, 0x51, 0x70, 0xba, 0xf2, 0x9b, 0x95, 0xc0, 0x4b, 0x4c, 0xa0, 0x14, 0xd3, 0xa4, 0x5d, 0x4a, 0x37, 0x36, 0x97, 0x31, 0x1e, 0x12, 0xe7, 0xbb, 0x08, 0x67, 0xa5, 0x23, 0xd7, 0xfb, 0x97, 0xd8, 0x6a, 0x03, 0xb1, 0xf8, 0x7f, 0xda, 0x58, 0xd9, 0x3f, 0x73, 0x4a, 0x53, 0xe1, 0x7b,
|
||||
/* (2^ 69)P */ 0x55, 0x83, 0x98, 0x78, 0x6c, 0x56, 0x5e, 0xed, 0xf7, 0x23, 0x3e, 0x4c, 0x7d, 0x09, 0x2d, 0x09, 0x9c, 0x58, 0x8b, 0x32, 0xca, 0xfe, 0xbf, 0x47, 0x03, 0xeb, 0x4d, 0xe7, 0xeb, 0x9c, 0x83, 0x05, 0x68, 0xaa, 0x80, 0x89, 0x44, 0xf9, 0xd4, 0xdc, 0xdb, 0xb1, 0xdb, 0x77, 0xac, 0xf9, 0x2a, 0xae, 0x35, 0xac, 0x74, 0xb5, 0x95, 0x62, 0x18, 0x85,
|
||||
/* (2^ 70)P */ 0xab, 0x82, 0x7e, 0x10, 0xd7, 0xe6, 0x57, 0xd1, 0x66, 0x12, 0x31, 0x9c, 0x9c, 0xa6, 0x27, 0x59, 0x71, 0x2e, 0xeb, 0xa0, 0x68, 0xc5, 0x87, 0x51, 0xf4, 0xca, 0x3f, 0x98, 0x56, 0xb0, 0x89, 0xb1, 0xc7, 0x7b, 0x46, 0xb3, 0xae, 0x36, 0xf2, 0xee, 0x15, 0x1a, 0x60, 0xf4, 0x50, 0x76, 0x4f, 0xc4, 0x53, 0x0d, 0x36, 0x4d, 0x31, 0xb1, 0x20, 0x51,
|
||||
/* (2^ 71)P */ 0xf7, 0x1d, 0x8c, 0x1b, 0x5e, 0xe5, 0x02, 0x6f, 0xc5, 0xa5, 0xe0, 0x5f, 0xc6, 0xb6, 0x63, 0x43, 0xaf, 0x3c, 0x19, 0x6c, 0xf4, 0xaf, 0xa4, 0x33, 0xb1, 0x0a, 0x37, 0x3d, 0xd9, 0x4d, 0xe2, 0x29, 0x24, 0x26, 0x94, 0x7c, 0x02, 0xe4, 0xe2, 0xf2, 0xbe, 0xbd, 0xac, 0x1b, 0x48, 0xb8, 0xdd, 0xe9, 0x0d, 0x9a, 0x50, 0x1a, 0x98, 0x71, 0x6e, 0xdc,
|
||||
/* (2^ 72)P */ 0x9f, 0x40, 0xb1, 0xb3, 0x66, 0x28, 0x6c, 0xfe, 0xa6, 0x7d, 0xf8, 0x3e, 0xb8, 0xf3, 0xde, 0x52, 0x76, 0x52, 0xa3, 0x92, 0x98, 0x23, 0xab, 0x4f, 0x88, 0x97, 0xfc, 0x22, 0xe1, 0x6b, 0x67, 0xcd, 0x13, 0x95, 0xda, 0x65, 0xdd, 0x3b, 0x67, 0x3f, 0x5f, 0x4c, 0xf2, 0x8a, 0xad, 0x98, 0xa7, 0x94, 0x24, 0x45, 0x87, 0x11, 0x7c, 0x75, 0x79, 0x85,
|
||||
/* (2^ 73)P */ 0x70, 0xbf, 0xf9, 0x3b, 0xa9, 0x44, 0x57, 0x72, 0x96, 0xc9, 0xa4, 0x98, 0x65, 0xbf, 0x87, 0xb3, 0x3a, 0x39, 0x12, 0xde, 0xe5, 0x39, 0x01, 0x4f, 0xf7, 0xc0, 0x71, 0x52, 0x36, 0x85, 0xb3, 0x18, 0xf8, 0x14, 0xc0, 0x6d, 0xae, 0x9e, 0x4f, 0xb0, 0x72, 0x87, 0xac, 0x5c, 0xd1, 0x6c, 0x41, 0x6c, 0x90, 0x9d, 0x22, 0x81, 0xe4, 0x2b, 0xea, 0xe5,
|
||||
/* (2^ 74)P */ 0xfc, 0xea, 0x1a, 0x65, 0xd9, 0x49, 0x6a, 0x39, 0xb5, 0x96, 0x72, 0x7b, 0x32, 0xf1, 0xd0, 0xe9, 0x45, 0xd9, 0x31, 0x55, 0xc7, 0x34, 0xe9, 0x5a, 0xec, 0x73, 0x0b, 0x03, 0xc4, 0xb3, 0xe6, 0xc9, 0x5e, 0x0a, 0x17, 0xfe, 0x53, 0x66, 0x7f, 0x21, 0x18, 0x74, 0x54, 0x1b, 0xc9, 0x49, 0x16, 0xd2, 0x48, 0xaf, 0x5b, 0x47, 0x7b, 0xeb, 0xaa, 0xc9,
|
||||
/* (2^ 75)P */ 0x47, 0x04, 0xf5, 0x5a, 0x87, 0x77, 0x9e, 0x21, 0x34, 0x4e, 0x83, 0x88, 0xaf, 0x02, 0x1d, 0xb0, 0x5a, 0x1d, 0x1d, 0x7d, 0x8d, 0x2c, 0xd3, 0x8d, 0x63, 0xa9, 0x45, 0xfb, 0x15, 0x6d, 0x86, 0x45, 0xcd, 0x38, 0x0e, 0xf7, 0x37, 0x79, 0xed, 0x6d, 0x5a, 0xbc, 0x32, 0xcc, 0x66, 0xf1, 0x3a, 0xb2, 0x87, 0x6f, 0x70, 0x71, 0xd9, 0xf2, 0xfa, 0x7b,
|
||||
/* (2^ 76)P */ 0x68, 0x07, 0xdc, 0x61, 0x40, 0xe4, 0xec, 0x32, 0xc8, 0xbe, 0x66, 0x30, 0x54, 0x80, 0xfd, 0x13, 0x7a, 0xef, 0xae, 0xed, 0x2e, 0x00, 0x6d, 0x3f, 0xbd, 0xfc, 0x91, 0x24, 0x53, 0x7f, 0x63, 0x9d, 0x2e, 0xe3, 0x76, 0xe0, 0xf3, 0xe1, 0x8f, 0x7a, 0xc4, 0x77, 0x0c, 0x91, 0xc0, 0xc2, 0x18, 0x6b, 0x04, 0xad, 0xb6, 0x70, 0x9a, 0x64, 0xc5, 0x82,
|
||||
/* (2^ 77)P */ 0x7f, 0xea, 0x13, 0xd8, 0x9e, 0xfc, 0x5b, 0x06, 0xb5, 0x4f, 0xda, 0x38, 0xe0, 0x9c, 0xd2, 0x3a, 0xc1, 0x1c, 0x62, 0x70, 0x7f, 0xc6, 0x24, 0x0a, 0x47, 0x04, 0x01, 0xc4, 0x55, 0x09, 0xd1, 0x7a, 0x07, 0xba, 0xa3, 0x80, 0x4f, 0xc1, 0x65, 0x36, 0x6d, 0xc0, 0x10, 0xcf, 0x94, 0xa9, 0xa2, 0x01, 0x44, 0xd1, 0xf9, 0x1c, 0x4c, 0xfb, 0xf8, 0x99,
|
||||
/* (2^ 78)P */ 0x6c, 0xb9, 0x6b, 0xee, 0x43, 0x5b, 0xb9, 0xbb, 0xee, 0x2e, 0x52, 0xc1, 0xc6, 0xb9, 0x61, 0xd2, 0x93, 0xa5, 0xaf, 0x52, 0xf4, 0xa4, 0x1a, 0x51, 0x61, 0xa7, 0xcb, 0x9e, 0xbb, 0x56, 0x65, 0xe2, 0xbf, 0x75, 0xb9, 0x9c, 0x50, 0x96, 0x60, 0x81, 0x74, 0x47, 0xc0, 0x04, 0x88, 0x71, 0x76, 0x39, 0x9a, 0xa7, 0xb1, 0x4e, 0x43, 0x15, 0xe0, 0xbb,
|
||||
/* (2^ 79)P */ 0xbb, 0xce, 0xe2, 0xbb, 0xf9, 0x17, 0x0f, 0x82, 0x40, 0xad, 0x73, 0xe3, 0xeb, 0x3b, 0x06, 0x1a, 0xcf, 0x8e, 0x6e, 0x28, 0xb8, 0x26, 0xd9, 0x5b, 0xb7, 0xb3, 0xcf, 0xb4, 0x6a, 0x1c, 0xbf, 0x7f, 0xb8, 0xb5, 0x79, 0xcf, 0x45, 0x68, 0x7d, 0xc5, 0xeb, 0xf3, 0xbe, 0x39, 0x40, 0xfc, 0x07, 0x90, 0x7a, 0x62, 0xad, 0x86, 0x08, 0x71, 0x25, 0xe1,
|
||||
/* (2^ 80)P */ 0x9b, 0x46, 0xac, 0xef, 0xc1, 0x4e, 0xa1, 0x97, 0x95, 0x76, 0xf9, 0x1b, 0xc2, 0xb2, 0x6a, 0x41, 0xea, 0x80, 0x3d, 0xe9, 0x08, 0x52, 0x5a, 0xe3, 0xf2, 0x08, 0xc5, 0xea, 0x39, 0x3f, 0x44, 0x71, 0x4d, 0xea, 0x0d, 0x05, 0x23, 0xe4, 0x2e, 0x3c, 0x89, 0xfe, 0x12, 0x8a, 0x95, 0x42, 0x0a, 0x68, 0xea, 0x5a, 0x28, 0x06, 0x9e, 0xe3, 0x5f, 0xe0,
|
||||
/* (2^ 81)P */ 0x00, 0x61, 0x6c, 0x98, 0x9b, 0xe7, 0xb9, 0x06, 0x1c, 0xc5, 0x1b, 0xed, 0xbe, 0xc8, 0xb3, 0xea, 0x87, 0xf0, 0xc4, 0x24, 0x7d, 0xbb, 0x5d, 0xa4, 0x1d, 0x7a, 0x16, 0x00, 0x55, 0x94, 0x67, 0x78, 0xbd, 0x58, 0x02, 0x82, 0x90, 0x53, 0x76, 0xd4, 0x72, 0x99, 0x51, 0x6f, 0x7b, 0xcf, 0x80, 0x30, 0x31, 0x3b, 0x01, 0xc7, 0xc1, 0xef, 0xe6, 0x42,
|
||||
/* (2^ 82)P */ 0xe2, 0x35, 0xaf, 0x4b, 0x79, 0xc6, 0x12, 0x24, 0x99, 0xc0, 0x68, 0xb0, 0x43, 0x3e, 0xe5, 0xef, 0xe2, 0x29, 0xea, 0xb8, 0xb3, 0xbc, 0x6a, 0x53, 0x2c, 0x69, 0x18, 0x5a, 0xf9, 0x15, 0xae, 0x66, 0x58, 0x18, 0xd3, 0x2d, 0x4b, 0x00, 0xfd, 0x84, 0xab, 0x4f, 0xae, 0x70, 0x6b, 0x9e, 0x9a, 0xdf, 0x83, 0xfd, 0x2e, 0x3c, 0xcf, 0xf8, 0x88, 0x5b,
|
||||
/* (2^ 83)P */ 0xa4, 0x90, 0x31, 0x85, 0x13, 0xcd, 0xdf, 0x64, 0xc9, 0xa1, 0x0b, 0xe7, 0xb6, 0x73, 0x8a, 0x1b, 0x22, 0x78, 0x4c, 0xd4, 0xae, 0x48, 0x18, 0x00, 0x00, 0xa8, 0x9f, 0x06, 0xf9, 0xfb, 0x2d, 0xc3, 0xb1, 0x2a, 0xbc, 0x13, 0x99, 0x57, 0xaf, 0xf0, 0x8d, 0x61, 0x54, 0x29, 0xd5, 0xf2, 0x72, 0x00, 0x96, 0xd1, 0x85, 0x12, 0x8a, 0xf0, 0x23, 0xfb,
|
||||
/* (2^ 84)P */ 0x69, 0xc7, 0xdb, 0xd9, 0x92, 0x75, 0x08, 0x9b, 0xeb, 0xa5, 0x93, 0xd1, 0x1a, 0xf4, 0xf5, 0xaf, 0xe6, 0xc4, 0x4a, 0x0d, 0x35, 0x26, 0x39, 0x9d, 0xd3, 0x17, 0x3e, 0xae, 0x2d, 0xbf, 0x73, 0x9f, 0xb7, 0x74, 0x91, 0xd1, 0xd8, 0x5c, 0x14, 0xf9, 0x75, 0xdf, 0xeb, 0xc2, 0x22, 0xd8, 0x14, 0x8d, 0x86, 0x23, 0x4d, 0xd1, 0x2d, 0xdb, 0x6b, 0x42,
|
||||
/* (2^ 85)P */ 0x8c, 0xda, 0xc6, 0xf8, 0x71, 0xba, 0x2b, 0x06, 0x78, 0xae, 0xcc, 0x3a, 0xe3, 0xe3, 0xa1, 0x8b, 0xe2, 0x34, 0x6d, 0x28, 0x9e, 0x46, 0x13, 0x4d, 0x9e, 0xa6, 0x73, 0x49, 0x65, 0x79, 0x88, 0xb9, 0x3a, 0xd1, 0x6d, 0x2f, 0x48, 0x2b, 0x0a, 0x7f, 0x58, 0x20, 0x37, 0xf4, 0x0e, 0xbb, 0x4a, 0x95, 0x58, 0x0c, 0x88, 0x30, 0xc4, 0x74, 0xdd, 0xfd,
|
||||
/* (2^ 86)P */ 0x6d, 0x13, 0x4e, 0x89, 0x2d, 0xa9, 0xa3, 0xed, 0x09, 0xe3, 0x0e, 0x71, 0x3e, 0x4a, 0xab, 0x90, 0xde, 0x03, 0xeb, 0x56, 0x46, 0x60, 0x06, 0xf5, 0x71, 0xe5, 0xee, 0x9b, 0xef, 0xff, 0xc4, 0x2c, 0x9f, 0x37, 0x48, 0x45, 0x94, 0x12, 0x41, 0x81, 0x15, 0x70, 0x91, 0x99, 0x5e, 0x56, 0x6b, 0xf4, 0xa6, 0xc9, 0xf5, 0x69, 0x9d, 0x78, 0x37, 0x57,
|
||||
/* (2^ 87)P */ 0xf3, 0x51, 0x57, 0x7e, 0x43, 0x6f, 0xc6, 0x67, 0x59, 0x0c, 0xcf, 0x94, 0xe6, 0x3d, 0xb5, 0x07, 0xc9, 0x77, 0x48, 0xc9, 0x68, 0x0d, 0x98, 0x36, 0x62, 0x35, 0x38, 0x1c, 0xf5, 0xc5, 0xec, 0x66, 0x78, 0xfe, 0x47, 0xab, 0x26, 0xd6, 0x44, 0xb6, 0x06, 0x0f, 0x89, 0xe3, 0x19, 0x40, 0x1a, 0xe7, 0xd8, 0x65, 0x55, 0xf7, 0x1a, 0xfc, 0xa3, 0x0e,
|
||||
/* (2^ 88)P */ 0x0e, 0x30, 0xa6, 0xb7, 0x58, 0x60, 0x62, 0x2a, 0x6c, 0x13, 0xa8, 0x14, 0x9b, 0xb8, 0xf2, 0x70, 0xd8, 0xb1, 0x71, 0x88, 0x8c, 0x18, 0x31, 0x25, 0x93, 0x90, 0xb4, 0xc7, 0x49, 0xd8, 0xd4, 0xdb, 0x1e, 0x1e, 0x7f, 0xaa, 0xba, 0xc9, 0xf2, 0x5d, 0xa9, 0x3a, 0x43, 0xb4, 0x5c, 0xee, 0x7b, 0xc7, 0x97, 0xb7, 0x66, 0xd7, 0x23, 0xd9, 0x22, 0x59,
|
||||
/* (2^ 89)P */ 0x28, 0x19, 0xa6, 0xf9, 0x89, 0x20, 0x78, 0xd4, 0x6d, 0xcb, 0x79, 0x8f, 0x61, 0x6f, 0xb2, 0x5c, 0x4f, 0xa6, 0x54, 0x84, 0x95, 0x24, 0x36, 0x64, 0xcb, 0x39, 0xe7, 0x8f, 0x97, 0x9c, 0x5c, 0x3c, 0xfb, 0x51, 0x11, 0x01, 0x17, 0xdb, 0xc9, 0x9b, 0x51, 0x03, 0x9a, 0xe9, 0xe5, 0x24, 0x1e, 0xf5, 0xda, 0xe0, 0x48, 0x02, 0x23, 0xd0, 0x2c, 0x81,
|
||||
/* (2^ 90)P */ 0x42, 0x1b, 0xe4, 0x91, 0x85, 0x2a, 0x0c, 0xd2, 0x28, 0x66, 0x57, 0x9e, 0x33, 0x8d, 0x25, 0x71, 0x10, 0x65, 0x76, 0xa2, 0x8c, 0x21, 0x86, 0x81, 0x15, 0xc2, 0x27, 0xeb, 0x54, 0x2d, 0x4f, 0x6c, 0xe6, 0xd6, 0x24, 0x9c, 0x1a, 0x12, 0xb8, 0x81, 0xe2, 0x0a, 0xf3, 0xd3, 0xf0, 0xd3, 0xe1, 0x74, 0x1f, 0x9b, 0x11, 0x47, 0xd0, 0xcf, 0xb6, 0x54,
|
||||
/* (2^ 91)P */ 0x26, 0x45, 0xa2, 0x10, 0xd4, 0x2d, 0xae, 0xc0, 0xb0, 0xe8, 0x86, 0xb3, 0xc7, 0xea, 0x70, 0x87, 0x61, 0xb5, 0xa5, 0x55, 0xbe, 0x88, 0x1d, 0x7a, 0xd9, 0x6f, 0xeb, 0x83, 0xe2, 0x44, 0x7f, 0x98, 0x04, 0xd6, 0x50, 0x9d, 0xa7, 0x86, 0x66, 0x09, 0x63, 0xe1, 0xed, 0x72, 0xb1, 0xe4, 0x1d, 0x3a, 0xfd, 0x47, 0xce, 0x1c, 0xaa, 0x3b, 0x8f, 0x1b,
|
||||
/* (2^ 92)P */ 0xf4, 0x3c, 0x4a, 0xb6, 0xc2, 0x9c, 0xe0, 0x2e, 0xb7, 0x38, 0xea, 0x61, 0x35, 0x97, 0x10, 0x90, 0xae, 0x22, 0x48, 0xb3, 0xa9, 0xc6, 0x7a, 0xbb, 0x23, 0xf2, 0xf8, 0x1b, 0xa7, 0xa1, 0x79, 0xcc, 0xc4, 0xf8, 0x08, 0x76, 0x8a, 0x5a, 0x1c, 0x1b, 0xc5, 0x33, 0x91, 0xa9, 0xb8, 0xb9, 0xd3, 0xf8, 0x49, 0xcd, 0xe5, 0x82, 0x43, 0xf7, 0xca, 0x68,
|
||||
/* (2^ 93)P */ 0x38, 0xba, 0xae, 0x44, 0xfe, 0x57, 0x64, 0x56, 0x7c, 0x0e, 0x9c, 0xca, 0xff, 0xa9, 0x82, 0xbb, 0x38, 0x4a, 0xa7, 0xf7, 0x47, 0xab, 0xbe, 0x6d, 0x23, 0x0b, 0x8a, 0xed, 0xc2, 0xb9, 0x8f, 0xf1, 0xec, 0x91, 0x44, 0x73, 0x64, 0xba, 0xd5, 0x8f, 0x37, 0x38, 0x0d, 0xd5, 0xf8, 0x73, 0x57, 0xb6, 0xc2, 0x45, 0xdc, 0x25, 0xb2, 0xb6, 0xea, 0xd9,
|
||||
/* (2^ 94)P */ 0xbf, 0xe9, 0x1a, 0x40, 0x4d, 0xcc, 0xe6, 0x1d, 0x70, 0x1a, 0x65, 0xcc, 0x34, 0x2c, 0x37, 0x2c, 0x2d, 0x6b, 0x6d, 0xe5, 0x2f, 0x19, 0x9e, 0xe4, 0xe1, 0xaa, 0xd4, 0xab, 0x54, 0xf4, 0xa8, 0xe4, 0x69, 0x2d, 0x8e, 0x4d, 0xd7, 0xac, 0xb0, 0x5b, 0xfe, 0xe3, 0x26, 0x07, 0xc3, 0xf8, 0x1b, 0x43, 0xa8, 0x1d, 0x64, 0xa5, 0x25, 0x88, 0xbb, 0x77,
|
||||
/* (2^ 95)P */ 0x92, 0xcd, 0x6e, 0xa0, 0x79, 0x04, 0x18, 0xf4, 0x11, 0x58, 0x48, 0xb5, 0x3c, 0x7b, 0xd1, 0xcc, 0xd3, 0x14, 0x2c, 0xa0, 0xdd, 0x04, 0x44, 0x11, 0xb3, 0x6d, 0x2f, 0x0d, 0xf5, 0x2a, 0x75, 0x5d, 0x1d, 0xda, 0x86, 0x8d, 0x7d, 0x6b, 0x32, 0x68, 0xb6, 0x6c, 0x64, 0x9e, 0xde, 0x80, 0x88, 0xce, 0x08, 0xbf, 0x0b, 0xe5, 0x8e, 0x4f, 0x1d, 0xfb,
|
||||
/* (2^ 96)P */ 0xaf, 0xe8, 0x85, 0xbf, 0x7f, 0x37, 0x8d, 0x66, 0x7c, 0xd5, 0xd3, 0x96, 0xa5, 0x81, 0x67, 0x95, 0xff, 0x48, 0xde, 0xde, 0xd7, 0x7a, 0x46, 0x34, 0xb1, 0x13, 0x70, 0x29, 0xed, 0x87, 0x90, 0xb0, 0x40, 0x2c, 0xa6, 0x43, 0x6e, 0xb6, 0xbc, 0x48, 0x8a, 0xc1, 0xae, 0xb8, 0xd4, 0xe2, 0xc0, 0x32, 0xb2, 0xa6, 0x2a, 0x8f, 0xb5, 0x16, 0x9e, 0xc3,
|
||||
/* (2^ 97)P */ 0xff, 0x4d, 0xd2, 0xd6, 0x74, 0xef, 0x2c, 0x96, 0xc1, 0x11, 0xa8, 0xb8, 0xfe, 0x94, 0x87, 0x3e, 0xa0, 0xfb, 0x57, 0xa3, 0xfc, 0x7a, 0x7e, 0x6a, 0x59, 0x6c, 0x54, 0xbb, 0xbb, 0xa2, 0x25, 0x38, 0x1b, 0xdf, 0x5d, 0x7b, 0x94, 0x14, 0xde, 0x07, 0x6e, 0xd3, 0xab, 0x02, 0x26, 0x74, 0x16, 0x12, 0xdf, 0x2e, 0x2a, 0xa7, 0xb0, 0xe8, 0x29, 0xc0,
|
||||
/* (2^ 98)P */ 0x6a, 0x38, 0x0b, 0xd3, 0xba, 0x45, 0x23, 0xe0, 0x04, 0x3b, 0x83, 0x39, 0xc5, 0x11, 0xe6, 0xcf, 0x39, 0x0a, 0xb3, 0xb0, 0x3b, 0x27, 0x29, 0x63, 0x1c, 0xf3, 0x00, 0xe6, 0xd2, 0x55, 0x21, 0x1f, 0x84, 0x97, 0x9f, 0x01, 0x49, 0x43, 0x30, 0x5f, 0xe0, 0x1d, 0x24, 0xc4, 0x4e, 0xa0, 0x2b, 0x0b, 0x12, 0x55, 0xc3, 0x27, 0xae, 0x08, 0x83, 0x7c,
|
||||
/* (2^ 99)P */ 0x5d, 0x1a, 0xb7, 0xa9, 0xf5, 0xfd, 0xec, 0xad, 0xb7, 0x87, 0x02, 0x5f, 0x0d, 0x30, 0x4d, 0xe2, 0x65, 0x87, 0xa4, 0x41, 0x45, 0x1d, 0x67, 0xe0, 0x30, 0x5c, 0x13, 0x87, 0xf6, 0x2e, 0x08, 0xc1, 0xc7, 0x12, 0x45, 0xc8, 0x9b, 0xad, 0xb8, 0xd5, 0x57, 0xbb, 0x5c, 0x48, 0x3a, 0xe1, 0x91, 0x5e, 0xf6, 0x4d, 0x8a, 0x63, 0x75, 0x69, 0x0c, 0x01,
|
||||
/* (2^100)P */ 0x8f, 0x53, 0x2d, 0xa0, 0x71, 0x3d, 0xfc, 0x45, 0x10, 0x96, 0xcf, 0x56, 0xf9, 0xbb, 0x40, 0x3c, 0x86, 0x52, 0x76, 0xbe, 0x84, 0xf9, 0xa6, 0x9d, 0x3d, 0x27, 0xbe, 0xb4, 0x00, 0x49, 0x94, 0xf5, 0x5d, 0xe1, 0x62, 0x85, 0x66, 0xe5, 0xb8, 0x20, 0x2c, 0x09, 0x7d, 0x9d, 0x3d, 0x6e, 0x74, 0x39, 0xab, 0xad, 0xa0, 0x90, 0x97, 0x5f, 0xbb, 0xa7,
|
||||
/* (2^101)P */ 0xdb, 0x2d, 0x99, 0x08, 0x16, 0x46, 0x83, 0x7a, 0xa8, 0xea, 0x3d, 0x28, 0x5b, 0x49, 0xfc, 0xb9, 0x6d, 0x00, 0x9e, 0x54, 0x4f, 0x47, 0x64, 0x9b, 0x58, 0x4d, 0x07, 0x0c, 0x6f, 0x29, 0x56, 0x0b, 0x00, 0x14, 0x85, 0x96, 0x41, 0x04, 0xb9, 0x5c, 0xa4, 0xf6, 0x16, 0x73, 0x6a, 0xc7, 0x62, 0x0c, 0x65, 0x2f, 0x93, 0xbf, 0xf7, 0xb9, 0xb7, 0xf1,
|
||||
/* (2^102)P */ 0xeb, 0x6d, 0xb3, 0x46, 0x32, 0xd2, 0xcb, 0x08, 0x94, 0x14, 0xbf, 0x3f, 0xc5, 0xcb, 0x5f, 0x9f, 0x8a, 0x89, 0x0c, 0x1b, 0x45, 0xad, 0x4c, 0x50, 0xb4, 0xe1, 0xa0, 0x6b, 0x11, 0x92, 0xaf, 0x1f, 0x00, 0xcc, 0xe5, 0x13, 0x7e, 0xe4, 0x2e, 0xa0, 0x57, 0xf3, 0xa7, 0x84, 0x79, 0x7a, 0xc2, 0xb7, 0xb7, 0xfc, 0x5d, 0xa5, 0xa9, 0x64, 0xcc, 0xd8,
|
||||
/* (2^103)P */ 0xa9, 0xc4, 0x12, 0x8b, 0x34, 0x78, 0x3e, 0x38, 0xfd, 0x3f, 0x87, 0xfa, 0x88, 0x94, 0xd5, 0xd9, 0x7f, 0xeb, 0x58, 0xff, 0xb9, 0x45, 0xdb, 0xa1, 0xed, 0x22, 0x28, 0x1d, 0x00, 0x6d, 0x79, 0x85, 0x7a, 0x75, 0x5d, 0xf0, 0xb1, 0x9e, 0x47, 0x28, 0x8c, 0x62, 0xdf, 0xfb, 0x4c, 0x7b, 0xc5, 0x1a, 0x42, 0x95, 0xef, 0x9a, 0xb7, 0x27, 0x7e, 0xda,
|
||||
/* (2^104)P */ 0xca, 0xd5, 0xc0, 0x17, 0xa1, 0x66, 0x79, 0x9c, 0x2a, 0xb7, 0x0a, 0xfe, 0x62, 0xe4, 0x26, 0x78, 0x90, 0xa7, 0xcb, 0xb0, 0x4f, 0x6d, 0xf9, 0x8f, 0xf7, 0x7d, 0xac, 0xb8, 0x78, 0x1f, 0x41, 0xea, 0x97, 0x1e, 0x62, 0x97, 0x43, 0x80, 0x58, 0x80, 0xb6, 0x69, 0x7d, 0xee, 0x16, 0xd2, 0xa1, 0x81, 0xd7, 0xb1, 0x27, 0x03, 0x48, 0xda, 0xab, 0xec,
|
||||
/* (2^105)P */ 0x5b, 0xed, 0x40, 0x8e, 0x8c, 0xc1, 0x66, 0x90, 0x7f, 0x0c, 0xb2, 0xfc, 0xbd, 0x16, 0xac, 0x7d, 0x4c, 0x6a, 0xf9, 0xae, 0xe7, 0x4e, 0x11, 0x12, 0xe9, 0xbe, 0x17, 0x09, 0xc6, 0xc1, 0x5e, 0xb5, 0x7b, 0x50, 0x5c, 0x27, 0xfb, 0x80, 0xab, 0x01, 0xfa, 0x5b, 0x9b, 0x75, 0x16, 0x6e, 0xb2, 0x5c, 0x8c, 0x2f, 0xa5, 0x6a, 0x1a, 0x68, 0xa6, 0x90,
|
||||
/* (2^106)P */ 0x75, 0xfe, 0xb6, 0x96, 0x96, 0x87, 0x4c, 0x12, 0xa9, 0xd1, 0xd8, 0x03, 0xa3, 0xc1, 0x15, 0x96, 0xe8, 0xa0, 0x75, 0x82, 0xa0, 0x6d, 0xea, 0x54, 0xdc, 0x5f, 0x0d, 0x7e, 0xf6, 0x70, 0xb5, 0xdc, 0x7a, 0xf6, 0xc4, 0xd4, 0x21, 0x49, 0xf5, 0xd4, 0x14, 0x6d, 0x48, 0x1d, 0x7c, 0x99, 0x42, 0xdf, 0x78, 0x6b, 0x9d, 0xb9, 0x30, 0x3c, 0xd0, 0x29,
|
||||
/* (2^107)P */ 0x85, 0xd6, 0xd8, 0xf3, 0x91, 0x74, 0xdd, 0xbd, 0x72, 0x96, 0x10, 0xe4, 0x76, 0x02, 0x5a, 0x72, 0x67, 0xd3, 0x17, 0x72, 0x14, 0x9a, 0x20, 0x5b, 0x0f, 0x8d, 0xed, 0x6d, 0x4e, 0xe3, 0xd9, 0x82, 0xc2, 0x99, 0xee, 0x39, 0x61, 0x69, 0x8a, 0x24, 0x01, 0x92, 0x15, 0xe7, 0xfc, 0xf9, 0x4d, 0xac, 0xf1, 0x30, 0x49, 0x01, 0x0b, 0x6e, 0x0f, 0x20,
|
||||
/* (2^108)P */ 0xd8, 0x25, 0x94, 0x5e, 0x43, 0x29, 0xf5, 0xcc, 0xe8, 0xe3, 0x55, 0x41, 0x3c, 0x9f, 0x58, 0x5b, 0x00, 0xeb, 0xc5, 0xdf, 0xcf, 0xfb, 0xfd, 0x6e, 0x92, 0xec, 0x99, 0x30, 0xd6, 0x05, 0xdd, 0x80, 0x7a, 0x5d, 0x6d, 0x16, 0x85, 0xd8, 0x9d, 0x43, 0x65, 0xd8, 0x2c, 0x33, 0x2f, 0x5c, 0x41, 0xea, 0xb7, 0x95, 0x77, 0xf2, 0x9e, 0x59, 0x09, 0xe8,
|
||||
/* (2^109)P */ 0x00, 0xa0, 0x03, 0x80, 0xcd, 0x60, 0xe5, 0x17, 0xd4, 0x15, 0x99, 0xdd, 0x4f, 0xbf, 0x66, 0xb8, 0xc0, 0xf5, 0xf9, 0xfc, 0x6d, 0x42, 0x18, 0x34, 0x1c, 0x7d, 0x5b, 0xb5, 0x09, 0xd0, 0x99, 0x57, 0x81, 0x0b, 0x62, 0xb3, 0xa2, 0xf9, 0x0b, 0xae, 0x95, 0xb8, 0xc2, 0x3b, 0x0d, 0x5b, 0x00, 0xf1, 0xed, 0xbc, 0x05, 0x9d, 0x61, 0xbc, 0x73, 0x9d,
|
||||
/* (2^110)P */ 0xd4, 0xdb, 0x29, 0xe5, 0x85, 0xe9, 0xc6, 0x89, 0x2a, 0xa8, 0x54, 0xab, 0xb3, 0x7f, 0x88, 0xc0, 0x4d, 0xe0, 0xd1, 0x74, 0x6e, 0xa3, 0xa7, 0x39, 0xd5, 0xcc, 0xa1, 0x8a, 0xcb, 0x5b, 0x34, 0xad, 0x92, 0xb4, 0xd8, 0xd5, 0x17, 0xf6, 0x77, 0x18, 0x9e, 0xaf, 0x45, 0x3b, 0x03, 0xe2, 0xf8, 0x52, 0x60, 0xdc, 0x15, 0x20, 0x9e, 0xdf, 0xd8, 0x5d,
|
||||
/* (2^111)P */ 0x02, 0xc1, 0xac, 0x1a, 0x15, 0x8e, 0x6c, 0xf5, 0x1e, 0x1e, 0xba, 0x7e, 0xc2, 0xda, 0x7d, 0x02, 0xda, 0x43, 0xae, 0x04, 0x70, 0x28, 0x54, 0x78, 0x94, 0xf5, 0x4f, 0x07, 0x84, 0x8f, 0xed, 0xaa, 0xc0, 0xb8, 0xcd, 0x7f, 0x7e, 0x33, 0xa3, 0xbe, 0x21, 0x29, 0xc8, 0x56, 0x34, 0xc0, 0x76, 0x87, 0x8f, 0xc7, 0x73, 0x58, 0x90, 0x16, 0xfc, 0xd6,
|
||||
/* (2^112)P */ 0xb8, 0x3f, 0xe1, 0xdf, 0x3a, 0x91, 0x25, 0x0c, 0xf6, 0x47, 0xa8, 0x89, 0xc4, 0xc6, 0x61, 0xec, 0x86, 0x2c, 0xfd, 0xbe, 0xa4, 0x6f, 0xc2, 0xd4, 0x46, 0x19, 0x70, 0x5d, 0x09, 0x02, 0x86, 0xd3, 0x4b, 0xe9, 0x16, 0x7b, 0xf0, 0x0d, 0x6c, 0xff, 0x91, 0x05, 0xbf, 0x55, 0xb4, 0x00, 0x8d, 0xe5, 0x6d, 0x68, 0x20, 0x90, 0x12, 0xb5, 0x5c, 0x32,
|
||||
/* (2^113)P */ 0x80, 0x45, 0xc8, 0x51, 0x87, 0xba, 0x1c, 0x5c, 0xcf, 0x5f, 0x4b, 0x3c, 0x9e, 0x3b, 0x36, 0xd2, 0x26, 0xa2, 0x7f, 0xab, 0xb7, 0xbf, 0xda, 0x68, 0x23, 0x8f, 0xc3, 0xa0, 0xfd, 0xad, 0xf1, 0x56, 0x3b, 0xd0, 0x75, 0x2b, 0x44, 0x61, 0xd8, 0xf4, 0xf1, 0x05, 0x49, 0x53, 0x07, 0xee, 0x47, 0xef, 0xc0, 0x7c, 0x9d, 0xe4, 0x15, 0x88, 0xc5, 0x47,
|
||||
/* (2^114)P */ 0x2d, 0xb5, 0x09, 0x80, 0xb9, 0xd3, 0xd8, 0xfe, 0x4c, 0xd2, 0xa6, 0x6e, 0xd3, 0x75, 0xcf, 0xb0, 0x99, 0xcb, 0x50, 0x8d, 0xe9, 0x67, 0x9b, 0x20, 0xe8, 0x57, 0xd8, 0x14, 0x85, 0x73, 0x6a, 0x74, 0xe0, 0x99, 0xf0, 0x6b, 0x6e, 0x59, 0x30, 0x31, 0x33, 0x96, 0x5f, 0xa1, 0x0c, 0x1b, 0xf4, 0xca, 0x09, 0xe1, 0x9b, 0xb5, 0xcf, 0x6d, 0x0b, 0xeb,
|
||||
/* (2^115)P */ 0x1a, 0xde, 0x50, 0xa9, 0xac, 0x3e, 0x10, 0x43, 0x4f, 0x82, 0x4f, 0xc0, 0xfe, 0x3f, 0x33, 0xd2, 0x64, 0x86, 0x50, 0xa9, 0x51, 0x76, 0x5e, 0x50, 0x97, 0x6c, 0x73, 0x8d, 0x77, 0xa3, 0x75, 0x03, 0xbc, 0xc9, 0xfb, 0x50, 0xd9, 0x6d, 0x16, 0xad, 0x5d, 0x32, 0x3d, 0xac, 0x44, 0xdf, 0x51, 0xf7, 0x19, 0xd4, 0x0b, 0x57, 0x78, 0x0b, 0x81, 0x4e,
|
||||
/* (2^116)P */ 0x32, 0x24, 0xf1, 0x6c, 0x55, 0x62, 0x1d, 0xb3, 0x1f, 0xda, 0xfa, 0x6a, 0x8f, 0x98, 0x01, 0x16, 0xde, 0x44, 0x50, 0x0d, 0x2e, 0x6c, 0x0b, 0xa2, 0xd3, 0x74, 0x0e, 0xa9, 0xbf, 0x8d, 0xa9, 0xc8, 0xc8, 0x2f, 0x62, 0xc1, 0x35, 0x5e, 0xfd, 0x3a, 0xb3, 0x83, 0x2d, 0xee, 0x4e, 0xfd, 0x5c, 0x5e, 0xad, 0x85, 0xa5, 0x10, 0xb5, 0x4f, 0x34, 0xa7,
|
||||
/* (2^117)P */ 0xd1, 0x58, 0x6f, 0xe6, 0x54, 0x2c, 0xc2, 0xcd, 0xcf, 0x83, 0xdc, 0x88, 0x0c, 0xb9, 0xb4, 0x62, 0x18, 0x89, 0x65, 0x28, 0xe9, 0x72, 0x4b, 0x65, 0xcf, 0xd6, 0x90, 0x88, 0xd7, 0x76, 0x17, 0x4f, 0x74, 0x64, 0x1e, 0xcb, 0xd3, 0xf5, 0x4b, 0xaa, 0x2e, 0x4d, 0x2d, 0x7c, 0x13, 0x1f, 0xfd, 0xd9, 0x60, 0x83, 0x7e, 0xda, 0x64, 0x1c, 0xdc, 0x9f,
|
||||
/* (2^118)P */ 0xad, 0xef, 0xac, 0x1b, 0xc1, 0x30, 0x5a, 0x15, 0xc9, 0x1f, 0xac, 0xf1, 0xca, 0x44, 0x95, 0x95, 0xea, 0xf2, 0x22, 0xe7, 0x8d, 0x25, 0xf0, 0xff, 0xd8, 0x71, 0xf7, 0xf8, 0x8f, 0x8f, 0xcd, 0xf4, 0x1e, 0xfe, 0x6c, 0x68, 0x04, 0xb8, 0x78, 0xa1, 0x5f, 0xa6, 0x5d, 0x5e, 0xf9, 0x8d, 0xea, 0x80, 0xcb, 0xf3, 0x17, 0xa6, 0x03, 0xc9, 0x38, 0xd5,
|
||||
/* (2^119)P */ 0x79, 0x14, 0x31, 0xc3, 0x38, 0xe5, 0xaa, 0xbf, 0x17, 0xa3, 0x04, 0x4e, 0x80, 0x59, 0x9c, 0x9f, 0x19, 0x39, 0xe4, 0x2d, 0x23, 0x54, 0x4a, 0x7f, 0x3e, 0xf3, 0xd9, 0xc7, 0xba, 0x6c, 0x8f, 0x6b, 0xfa, 0x34, 0xb5, 0x23, 0x17, 0x1d, 0xff, 0x1d, 0xea, 0x1f, 0xd7, 0xba, 0x61, 0xb2, 0xe0, 0x38, 0x6a, 0xe9, 0xcf, 0x48, 0x5d, 0x6a, 0x10, 0x9c,
|
||||
/* (2^120)P */ 0xc8, 0xbb, 0x13, 0x1c, 0x3f, 0x3c, 0x34, 0xfd, 0xac, 0x37, 0x52, 0x44, 0x25, 0xa8, 0xde, 0x1d, 0x63, 0xf4, 0x81, 0x9a, 0xbe, 0x0b, 0x74, 0x2e, 0xc8, 0x51, 0x16, 0xd3, 0xac, 0x4a, 0xaf, 0xe2, 0x5f, 0x3a, 0x89, 0x32, 0xd1, 0x9b, 0x7c, 0x90, 0x0d, 0xac, 0xdc, 0x8b, 0x73, 0x45, 0x45, 0x97, 0xb1, 0x90, 0x2c, 0x1b, 0x31, 0xca, 0xb1, 0x94,
|
||||
/* (2^121)P */ 0x07, 0x28, 0xdd, 0x10, 0x14, 0xa5, 0x95, 0x7e, 0xf3, 0xe4, 0xd4, 0x14, 0xb4, 0x7e, 0x76, 0xdb, 0x42, 0xd6, 0x94, 0x3e, 0xeb, 0x44, 0x64, 0x88, 0x0d, 0xec, 0xc1, 0x21, 0xf0, 0x79, 0xe0, 0x83, 0x67, 0x55, 0x53, 0xc2, 0xf6, 0xc5, 0xc5, 0x89, 0x39, 0xe8, 0x42, 0xd0, 0x17, 0xbd, 0xff, 0x35, 0x59, 0x0e, 0xc3, 0x06, 0x86, 0xd4, 0x64, 0xcf,
|
||||
/* (2^122)P */ 0x91, 0xa8, 0xdb, 0x57, 0x9b, 0xe2, 0x96, 0x31, 0x10, 0x6e, 0xd7, 0x9a, 0x97, 0xb3, 0xab, 0xb5, 0x15, 0x66, 0xbe, 0xcc, 0x6d, 0x9a, 0xac, 0x06, 0xb3, 0x0d, 0xaa, 0x4b, 0x9c, 0x96, 0x79, 0x6c, 0x34, 0xee, 0x9e, 0x53, 0x4d, 0x6e, 0xbd, 0x88, 0x02, 0xbf, 0x50, 0x54, 0x12, 0x5d, 0x01, 0x02, 0x46, 0xc6, 0x74, 0x02, 0x8c, 0x24, 0xae, 0xb1,
|
||||
/* (2^123)P */ 0xf5, 0x22, 0xea, 0xac, 0x7d, 0x9c, 0x33, 0x8a, 0xa5, 0x36, 0x79, 0x6a, 0x4f, 0xa4, 0xdc, 0xa5, 0x73, 0x64, 0xc4, 0x6f, 0x43, 0x02, 0x3b, 0x94, 0x66, 0xd2, 0x4b, 0x4f, 0xf6, 0x45, 0x33, 0x5d, 0x10, 0x33, 0x18, 0x1e, 0xa3, 0xfc, 0xf7, 0xd2, 0xb8, 0xc8, 0xa7, 0xe0, 0x76, 0x8a, 0xcd, 0xff, 0x4f, 0x99, 0x34, 0x47, 0x84, 0x91, 0x96, 0x9f,
|
||||
/* (2^124)P */ 0x8a, 0x48, 0x3b, 0x48, 0x4a, 0xbc, 0xac, 0xe2, 0x80, 0xd6, 0xd2, 0x35, 0xde, 0xd0, 0x56, 0x42, 0x33, 0xb3, 0x56, 0x5a, 0xcd, 0xb8, 0x3d, 0xb5, 0x25, 0xc1, 0xed, 0xff, 0x87, 0x0b, 0x79, 0xff, 0xf2, 0x62, 0xe1, 0x76, 0xc6, 0xa2, 0x0f, 0xa8, 0x9b, 0x0d, 0xcc, 0x3f, 0x3d, 0x35, 0x27, 0x8d, 0x0b, 0x74, 0xb0, 0xc3, 0x78, 0x8c, 0xcc, 0xc8,
|
||||
/* (2^125)P */ 0xfc, 0x9a, 0x0c, 0xa8, 0x49, 0x42, 0xb8, 0xdf, 0xcf, 0xb3, 0x19, 0xa6, 0x64, 0x57, 0xfe, 0xe8, 0xf8, 0xa6, 0x4b, 0x86, 0xa1, 0xd5, 0x83, 0x7f, 0x14, 0x99, 0x18, 0x0c, 0x7d, 0x5b, 0xf7, 0x3d, 0xf9, 0x4b, 0x79, 0xb1, 0x86, 0x30, 0xb4, 0x5e, 0x6a, 0xe8, 0x9d, 0xfa, 0x8a, 0x41, 0xc4, 0x30, 0xfc, 0x56, 0x74, 0x14, 0x42, 0xc8, 0x96, 0x0e,
|
||||
/* (2^126)P */ 0xdf, 0x66, 0xec, 0xbc, 0x44, 0xdb, 0x19, 0xce, 0xd4, 0xb5, 0x49, 0x40, 0x07, 0x49, 0xe0, 0x3a, 0x61, 0x10, 0xfb, 0x7d, 0xba, 0xb1, 0xe0, 0x28, 0x5b, 0x99, 0x59, 0x96, 0xa2, 0xee, 0xe0, 0x23, 0x37, 0x39, 0x1f, 0xe6, 0x57, 0x9f, 0xf8, 0xf8, 0xdc, 0x74, 0xf6, 0x8f, 0x4f, 0x5e, 0x51, 0xa4, 0x12, 0xac, 0xbe, 0xe4, 0xf3, 0xd1, 0xf0, 0x24,
|
||||
/* (2^127)P */ 0x1e, 0x3e, 0x9a, 0x5f, 0xdf, 0x9f, 0xd6, 0x4e, 0x8a, 0x28, 0xc3, 0xcd, 0x96, 0x9d, 0x57, 0xc7, 0x61, 0x81, 0x90, 0xff, 0xae, 0xb1, 0x4f, 0xc2, 0x96, 0x8b, 0x1a, 0x18, 0xf4, 0x50, 0xcb, 0x31, 0xe1, 0x57, 0xf4, 0x90, 0xa8, 0xea, 0xac, 0xe7, 0x61, 0x98, 0xb6, 0x15, 0xc1, 0x7b, 0x29, 0xa4, 0xc3, 0x18, 0xef, 0xb9, 0xd8, 0xdf, 0xf6, 0xac,
|
||||
/* (2^128)P */ 0xca, 0xa8, 0x6c, 0xf1, 0xb4, 0xca, 0xfe, 0x31, 0xee, 0x48, 0x38, 0x8b, 0x0e, 0xbb, 0x7a, 0x30, 0xaa, 0xf9, 0xee, 0x27, 0x53, 0x24, 0xdc, 0x2e, 0x15, 0xa6, 0x48, 0x8f, 0xa0, 0x7e, 0xf1, 0xdc, 0x93, 0x87, 0x39, 0xeb, 0x7f, 0x38, 0x92, 0x92, 0x4c, 0x29, 0xe9, 0x57, 0xd8, 0x59, 0xfc, 0xe9, 0x9c, 0x44, 0xc0, 0x65, 0xcf, 0xac, 0x4b, 0xdc,
|
||||
/* (2^129)P */ 0xa3, 0xd0, 0x37, 0x8f, 0x86, 0x2f, 0xc6, 0x47, 0x55, 0x46, 0x65, 0x26, 0x4b, 0x91, 0xe2, 0x18, 0x5c, 0x4f, 0x23, 0xc1, 0x37, 0x29, 0xb9, 0xc1, 0x27, 0xc5, 0x3c, 0xbf, 0x7e, 0x23, 0xdb, 0x73, 0x99, 0xbd, 0x1b, 0xb2, 0x31, 0x68, 0x3a, 0xad, 0xb7, 0xb0, 0x10, 0xc5, 0xe5, 0x11, 0x51, 0xba, 0xa7, 0x60, 0x66, 0x54, 0xf0, 0x08, 0xd7, 0x69,
|
||||
/* (2^130)P */ 0x89, 0x41, 0x79, 0xcc, 0xeb, 0x0a, 0xf5, 0x4b, 0xa3, 0x4c, 0xce, 0x52, 0xb0, 0xa7, 0xe4, 0x41, 0x75, 0x7d, 0x04, 0xbb, 0x09, 0x4c, 0x50, 0x9f, 0xdf, 0xea, 0x74, 0x61, 0x02, 0xad, 0xb4, 0x9d, 0xb7, 0x05, 0xb9, 0xea, 0xeb, 0x91, 0x35, 0xe7, 0x49, 0xea, 0xd3, 0x4f, 0x3c, 0x60, 0x21, 0x7a, 0xde, 0xc7, 0xe2, 0x5a, 0xee, 0x8e, 0x93, 0xc7,
|
||||
/* (2^131)P */ 0x00, 0xe8, 0xed, 0xd0, 0xb3, 0x0d, 0xaf, 0xb2, 0xde, 0x2c, 0xf6, 0x00, 0xe2, 0xea, 0x6d, 0xf8, 0x0e, 0xd9, 0x67, 0x59, 0xa9, 0x50, 0xbb, 0x17, 0x8f, 0xff, 0xb1, 0x9f, 0x17, 0xb6, 0xf2, 0xb5, 0xba, 0x80, 0xf7, 0x0f, 0xba, 0xd5, 0x09, 0x43, 0xaa, 0x4e, 0x3a, 0x67, 0x6a, 0x89, 0x9b, 0x18, 0x65, 0x35, 0xf8, 0x3a, 0x49, 0x91, 0x30, 0x51,
|
||||
/* (2^132)P */ 0x8d, 0x25, 0xe9, 0x0e, 0x7d, 0x50, 0x76, 0xe4, 0x58, 0x7e, 0xb9, 0x33, 0xe6, 0x65, 0x90, 0xc2, 0x50, 0x9d, 0x50, 0x2e, 0x11, 0xad, 0xd5, 0x43, 0x52, 0x32, 0x41, 0x4f, 0x7b, 0xb6, 0xa0, 0xec, 0x81, 0x75, 0x36, 0x7c, 0x77, 0x85, 0x59, 0x70, 0xe4, 0xf9, 0xef, 0x66, 0x8d, 0x35, 0xc8, 0x2a, 0x6e, 0x5b, 0xc6, 0x0d, 0x0b, 0x29, 0x60, 0x68,
|
||||
/* (2^133)P */ 0xf8, 0xce, 0xb0, 0x3a, 0x56, 0x7d, 0x51, 0x9a, 0x25, 0x73, 0xea, 0xdd, 0xe4, 0xe0, 0x0e, 0xf0, 0x07, 0xc0, 0x31, 0x00, 0x73, 0x35, 0xd0, 0x39, 0xc4, 0x9b, 0xb7, 0x95, 0xe0, 0x62, 0x70, 0x36, 0x0b, 0xcb, 0xa0, 0x42, 0xde, 0x51, 0xcf, 0x41, 0xe0, 0xb8, 0xb4, 0xc0, 0xe5, 0x46, 0x99, 0x9f, 0x02, 0x7f, 0x14, 0x8c, 0xc1, 0x4e, 0xef, 0xe8,
|
||||
/* (2^134)P */ 0x10, 0x01, 0x57, 0x0a, 0xbe, 0x8b, 0x18, 0xc8, 0xca, 0x00, 0x28, 0x77, 0x4a, 0x9a, 0xc7, 0x55, 0x2a, 0xcc, 0x0c, 0x7b, 0xb9, 0xe9, 0xc8, 0x97, 0x7c, 0x02, 0xe3, 0x09, 0x2f, 0x62, 0x30, 0xb8, 0x40, 0x09, 0x65, 0xe9, 0x55, 0x63, 0xb5, 0x07, 0xca, 0x9f, 0x00, 0xdf, 0x9d, 0x5c, 0xc7, 0xee, 0x57, 0xa5, 0x90, 0x15, 0x1e, 0x22, 0xa0, 0x12,
|
||||
/* (2^135)P */ 0x71, 0x2d, 0xc9, 0xef, 0x27, 0xb9, 0xd8, 0x12, 0x43, 0x6b, 0xa8, 0xce, 0x3b, 0x6d, 0x6e, 0x91, 0x43, 0x23, 0xbc, 0x32, 0xb3, 0xbf, 0xe1, 0xc7, 0x39, 0xcf, 0x7c, 0x42, 0x4c, 0xb1, 0x30, 0xe2, 0xdd, 0x69, 0x06, 0xe5, 0xea, 0xf0, 0x2a, 0x16, 0x50, 0x71, 0xca, 0x92, 0xdf, 0xc1, 0xcc, 0xec, 0xe6, 0x54, 0x07, 0xf3, 0x18, 0x8d, 0xd8, 0x29,
|
||||
/* (2^136)P */ 0x98, 0x51, 0x48, 0x8f, 0xfa, 0x2e, 0x5e, 0x67, 0xb0, 0xc6, 0x17, 0x12, 0xb6, 0x7d, 0xc9, 0xad, 0x81, 0x11, 0xad, 0x0c, 0x1c, 0x2d, 0x45, 0xdf, 0xac, 0x66, 0xbd, 0x08, 0x6f, 0x7c, 0xc7, 0x06, 0x6e, 0x19, 0x08, 0x39, 0x64, 0xd7, 0xe4, 0xd1, 0x11, 0x5f, 0x1c, 0xf4, 0x67, 0xc3, 0x88, 0x6a, 0xe6, 0x07, 0xa3, 0x83, 0xd7, 0xfd, 0x2a, 0xf9,
|
||||
/* (2^137)P */ 0x87, 0xed, 0xeb, 0xd9, 0xdf, 0xff, 0x43, 0x8b, 0xaa, 0x20, 0x58, 0xb0, 0xb4, 0x6b, 0x14, 0xb8, 0x02, 0xc5, 0x40, 0x20, 0x22, 0xbb, 0xf7, 0xb4, 0xf3, 0x05, 0x1e, 0x4d, 0x94, 0xff, 0xe3, 0xc5, 0x22, 0x82, 0xfe, 0xaf, 0x90, 0x42, 0x98, 0x6b, 0x76, 0x8b, 0x3e, 0x89, 0x3f, 0x42, 0x2a, 0xa7, 0x26, 0x00, 0xda, 0x5c, 0xa2, 0x2b, 0xec, 0xdd,
|
||||
/* (2^138)P */ 0x5c, 0x21, 0x16, 0x0d, 0x46, 0xb8, 0xd0, 0xa7, 0x88, 0xe7, 0x25, 0xcb, 0x3e, 0x50, 0x73, 0x61, 0xe7, 0xaf, 0x5a, 0x3f, 0x47, 0x8b, 0x3d, 0x97, 0x79, 0x2c, 0xe6, 0x6d, 0x95, 0x74, 0x65, 0x70, 0x36, 0xfd, 0xd1, 0x9e, 0x13, 0x18, 0x63, 0xb1, 0x2d, 0x0b, 0xb5, 0x36, 0x3e, 0xe7, 0x35, 0x42, 0x3b, 0xe6, 0x1f, 0x4d, 0x9d, 0x59, 0xa2, 0x43,
|
||||
/* (2^139)P */ 0x8c, 0x0c, 0x7c, 0x24, 0x9e, 0xe0, 0xf8, 0x05, 0x1c, 0x9e, 0x1f, 0x31, 0xc0, 0x70, 0xb3, 0xfb, 0x4e, 0xf8, 0x0a, 0x57, 0xb7, 0x49, 0xb5, 0x73, 0xa1, 0x5f, 0x9b, 0x6a, 0x07, 0x6c, 0x87, 0x71, 0x87, 0xd4, 0xbe, 0x98, 0x1e, 0x98, 0xee, 0x52, 0xc1, 0x7b, 0x95, 0x0f, 0x28, 0x32, 0x36, 0x28, 0xd0, 0x3a, 0x0f, 0x7d, 0x2a, 0xa9, 0x62, 0xb9,
|
||||
/* (2^140)P */ 0x97, 0xe6, 0x18, 0x77, 0xf9, 0x34, 0xac, 0xbc, 0xe0, 0x62, 0x9f, 0x42, 0xde, 0xbd, 0x2f, 0xf7, 0x1f, 0xb7, 0x14, 0x52, 0x8a, 0x79, 0xb2, 0x3f, 0xd2, 0x95, 0x71, 0x01, 0xe8, 0xaf, 0x8c, 0xa4, 0xa4, 0xa7, 0x27, 0xf3, 0x5c, 0xdf, 0x3e, 0x57, 0x7a, 0xf1, 0x76, 0x49, 0xe6, 0x42, 0x3f, 0x8f, 0x1e, 0x63, 0x4a, 0x65, 0xb5, 0x41, 0xf5, 0x02,
|
||||
/* (2^141)P */ 0x72, 0x85, 0xc5, 0x0b, 0xe1, 0x47, 0x64, 0x02, 0xc5, 0x4d, 0x81, 0x69, 0xb2, 0xcf, 0x0f, 0x6c, 0xd4, 0x6d, 0xd0, 0xc7, 0xb4, 0x1c, 0xd0, 0x32, 0x59, 0x89, 0xe2, 0xe0, 0x96, 0x8b, 0x12, 0x98, 0xbf, 0x63, 0x7a, 0x4c, 0x76, 0x7e, 0x58, 0x17, 0x8f, 0x5b, 0x0a, 0x59, 0x65, 0x75, 0xbc, 0x61, 0x1f, 0xbe, 0xc5, 0x6e, 0x0a, 0x57, 0x52, 0x70,
|
||||
/* (2^142)P */ 0x92, 0x1c, 0x77, 0xbb, 0x62, 0x02, 0x6c, 0x25, 0x9c, 0x66, 0x07, 0x83, 0xab, 0xcc, 0x80, 0x5d, 0xd2, 0x76, 0x0c, 0xa4, 0xc5, 0xb4, 0x8a, 0x68, 0x23, 0x31, 0x32, 0x29, 0x8a, 0x47, 0x92, 0x12, 0x80, 0xb3, 0xfa, 0x18, 0xe4, 0x8d, 0xc0, 0x4d, 0xfe, 0x97, 0x5f, 0x72, 0x41, 0xb5, 0x5c, 0x7a, 0xbd, 0xf0, 0xcf, 0x5e, 0x97, 0xaa, 0x64, 0x32,
|
||||
/* (2^143)P */ 0x35, 0x3f, 0x75, 0xc1, 0x7a, 0x75, 0x7e, 0xa9, 0xc6, 0x0b, 0x4e, 0x32, 0x62, 0xec, 0xe3, 0x5c, 0xfb, 0x01, 0x43, 0xb6, 0xd4, 0x5b, 0x75, 0xd2, 0xee, 0x7f, 0x5d, 0x23, 0x2b, 0xb3, 0x54, 0x34, 0x4c, 0xd3, 0xb4, 0x32, 0x84, 0x81, 0xb5, 0x09, 0x76, 0x19, 0xda, 0x58, 0xda, 0x7c, 0xdb, 0x2e, 0xdd, 0x4c, 0x8e, 0xdd, 0x5d, 0x89, 0x10, 0x10,
|
||||
/* (2^144)P */ 0x57, 0x25, 0x6a, 0x08, 0x37, 0x92, 0xa8, 0xdf, 0x24, 0xef, 0x8f, 0x33, 0x34, 0x52, 0xa4, 0x4c, 0xf0, 0x77, 0x9f, 0x69, 0x77, 0xd5, 0x8f, 0xd2, 0x9a, 0xb3, 0xb6, 0x1d, 0x2d, 0xa6, 0xf7, 0x1f, 0xda, 0xd7, 0xcb, 0x75, 0x11, 0xc3, 0x6b, 0xc0, 0x38, 0xb1, 0xd5, 0x2d, 0x96, 0x84, 0x16, 0xfa, 0x26, 0xb9, 0xcc, 0x3f, 0x16, 0x47, 0x23, 0x74,
|
||||
/* (2^145)P */ 0x9b, 0x61, 0x2a, 0x1c, 0xdd, 0x39, 0xa5, 0xfa, 0x1c, 0x7d, 0x63, 0x50, 0xca, 0xe6, 0x9d, 0xfa, 0xb7, 0xc4, 0x4c, 0x6a, 0x97, 0x5f, 0x36, 0x4e, 0x47, 0xdd, 0x17, 0xf7, 0xf9, 0x19, 0xce, 0x75, 0x17, 0xad, 0xce, 0x2a, 0xf3, 0xfe, 0x27, 0x8f, 0x3e, 0x48, 0xc0, 0x60, 0x87, 0x24, 0x19, 0xae, 0x59, 0xe4, 0x5a, 0x00, 0x2a, 0xba, 0xa2, 0x1f,
|
||||
/* (2^146)P */ 0x26, 0x88, 0x42, 0x60, 0x9f, 0x6e, 0x2c, 0x7c, 0x39, 0x0f, 0x47, 0x6a, 0x0e, 0x02, 0xbb, 0x4b, 0x34, 0x29, 0x55, 0x18, 0x36, 0xcf, 0x3b, 0x47, 0xf1, 0x2e, 0xfc, 0x6e, 0x94, 0xff, 0xe8, 0x6b, 0x06, 0xd2, 0xba, 0x77, 0x5e, 0x60, 0xd7, 0x19, 0xef, 0x02, 0x9d, 0x3a, 0xc2, 0xb7, 0xa9, 0xd8, 0x57, 0xee, 0x7e, 0x2b, 0xf2, 0x6d, 0x28, 0xda,
|
||||
/* (2^147)P */ 0xdf, 0xd9, 0x92, 0x11, 0x98, 0x23, 0xe2, 0x45, 0x2f, 0x74, 0x70, 0xee, 0x0e, 0x55, 0x65, 0x79, 0x86, 0x38, 0x17, 0x92, 0x85, 0x87, 0x99, 0x50, 0xd9, 0x7c, 0xdb, 0xa1, 0x10, 0xec, 0x30, 0xb7, 0x40, 0xa3, 0x23, 0x9b, 0x0e, 0x27, 0x49, 0x29, 0x03, 0x94, 0xff, 0x53, 0xdc, 0xd7, 0xed, 0x49, 0xa9, 0x5a, 0x3b, 0xee, 0xd7, 0xc7, 0x65, 0xaf,
|
||||
/* (2^148)P */ 0xa0, 0xbd, 0xbe, 0x03, 0xee, 0x0c, 0xbe, 0x32, 0x00, 0x7b, 0x52, 0xcb, 0x92, 0x29, 0xbf, 0xa0, 0xc6, 0xd9, 0xd2, 0xd6, 0x15, 0xe8, 0x3a, 0x75, 0x61, 0x65, 0x56, 0xae, 0xad, 0x3c, 0x2a, 0x64, 0x14, 0x3f, 0x8e, 0xc1, 0x2d, 0x0c, 0x8d, 0x20, 0xdb, 0x58, 0x4b, 0xe5, 0x40, 0x15, 0x4b, 0xdc, 0xa8, 0xbd, 0xef, 0x08, 0xa7, 0xd1, 0xf4, 0xb0,
|
||||
/* (2^149)P */ 0xa9, 0x0f, 0x05, 0x94, 0x66, 0xac, 0x1f, 0x65, 0x3f, 0xe1, 0xb8, 0xe1, 0x34, 0x5e, 0x1d, 0x8f, 0xe3, 0x93, 0x03, 0x15, 0xff, 0xb6, 0x65, 0xb6, 0x6e, 0xc0, 0x2f, 0xd4, 0x2e, 0xb9, 0x2c, 0x13, 0x3c, 0x99, 0x1c, 0xb5, 0x87, 0xba, 0x79, 0xcb, 0xf0, 0x18, 0x06, 0x86, 0x04, 0x14, 0x25, 0x09, 0xcd, 0x1c, 0x14, 0xda, 0x35, 0xd0, 0x38, 0x3b,
|
||||
/* (2^150)P */ 0x1b, 0x04, 0xa3, 0x27, 0xb4, 0xd3, 0x37, 0x48, 0x1e, 0x8f, 0x69, 0xd3, 0x5a, 0x2f, 0x20, 0x02, 0x36, 0xbe, 0x06, 0x7b, 0x6b, 0x6c, 0x12, 0x5b, 0x80, 0x74, 0x44, 0xe6, 0xf8, 0xf5, 0x95, 0x59, 0x29, 0xab, 0x51, 0x47, 0x83, 0x28, 0xe0, 0xad, 0xde, 0xaa, 0xd3, 0xb1, 0x1a, 0xcb, 0xa3, 0xcd, 0x8b, 0x6a, 0xb1, 0xa7, 0x0a, 0xd1, 0xf9, 0xbe,
|
||||
/* (2^151)P */ 0xce, 0x2f, 0x85, 0xca, 0x74, 0x6d, 0x49, 0xb8, 0xce, 0x80, 0x44, 0xe0, 0xda, 0x5b, 0xcf, 0x2f, 0x79, 0x74, 0xfe, 0xb4, 0x2c, 0x99, 0x20, 0x6e, 0x09, 0x04, 0xfb, 0x6d, 0x57, 0x5b, 0x95, 0x0c, 0x45, 0xda, 0x4f, 0x7f, 0x63, 0xcc, 0x85, 0x5a, 0x67, 0x50, 0x68, 0x71, 0xb4, 0x67, 0xb1, 0x2e, 0xc1, 0x1c, 0xdc, 0xff, 0x2a, 0x7c, 0x10, 0x5e,
|
||||
/* (2^152)P */ 0xa6, 0xde, 0xf3, 0xd4, 0x22, 0x30, 0x24, 0x9e, 0x0b, 0x30, 0x54, 0x59, 0x7e, 0xa2, 0xeb, 0x89, 0x54, 0x65, 0x3e, 0x40, 0xd1, 0xde, 0xe6, 0xee, 0x4d, 0xbf, 0x5e, 0x40, 0x1d, 0xee, 0x4f, 0x68, 0xd9, 0xa7, 0x2f, 0xb3, 0x64, 0xb3, 0xf5, 0xc8, 0xd3, 0xaa, 0x70, 0x70, 0x3d, 0xef, 0xd3, 0x95, 0x54, 0xdb, 0x3e, 0x94, 0x95, 0x92, 0x1f, 0x45,
|
||||
/* (2^153)P */ 0x22, 0x80, 0x1d, 0x9d, 0x96, 0xa5, 0x78, 0x6f, 0xe0, 0x1e, 0x1b, 0x66, 0x42, 0xc8, 0xae, 0x9e, 0x46, 0x45, 0x08, 0x41, 0xdf, 0x80, 0xae, 0x6f, 0xdb, 0x15, 0x5a, 0x21, 0x31, 0x7a, 0xd0, 0xf2, 0x54, 0x15, 0x88, 0xd3, 0x0f, 0x7f, 0x14, 0x5a, 0x14, 0x97, 0xab, 0xf4, 0x58, 0x6a, 0x9f, 0xea, 0x74, 0xe5, 0x6b, 0x90, 0x59, 0x2b, 0x48, 0xd9,
|
||||
/* (2^154)P */ 0x12, 0x24, 0x04, 0xf5, 0x50, 0xc2, 0x8c, 0xb0, 0x7c, 0x46, 0x98, 0xd5, 0x24, 0xad, 0xf6, 0x72, 0xdc, 0x82, 0x1a, 0x60, 0xc1, 0xeb, 0x48, 0xef, 0x7f, 0x6e, 0xe6, 0xcc, 0xdb, 0x7b, 0xae, 0xbe, 0x5e, 0x1e, 0x5c, 0xe6, 0x0a, 0x70, 0xdf, 0xa4, 0xa3, 0x85, 0x1b, 0x1b, 0x7f, 0x72, 0xb9, 0x96, 0x6f, 0xdc, 0x03, 0x76, 0x66, 0xfb, 0xa0, 0x33,
|
||||
/* (2^155)P */ 0x37, 0x40, 0xbb, 0xbc, 0x68, 0x58, 0x86, 0xca, 0xbb, 0xa5, 0x24, 0x76, 0x3d, 0x48, 0xd1, 0xad, 0xb4, 0xa8, 0xcf, 0xc3, 0xb6, 0xa8, 0xba, 0x1a, 0x3a, 0xbe, 0x33, 0x75, 0x04, 0x5c, 0x13, 0x8c, 0x0d, 0x70, 0x8d, 0xa6, 0x4e, 0x2a, 0xeb, 0x17, 0x3c, 0x22, 0xdd, 0x3e, 0x96, 0x40, 0x11, 0x9e, 0x4e, 0xae, 0x3d, 0xf8, 0x91, 0xd7, 0x50, 0xc8,
|
||||
/* (2^156)P */ 0xd8, 0xca, 0xde, 0x19, 0xcf, 0x00, 0xe4, 0x73, 0x18, 0x7f, 0x9b, 0x9f, 0xf4, 0x5b, 0x49, 0x49, 0x99, 0xdc, 0xa4, 0x46, 0x21, 0xb5, 0xd7, 0x3e, 0xb7, 0x47, 0x1b, 0xa9, 0x9f, 0x4c, 0x69, 0x7d, 0xec, 0x33, 0xd6, 0x1c, 0x51, 0x7f, 0x47, 0x74, 0x7a, 0x6c, 0xf3, 0xd2, 0x2e, 0xbf, 0xdf, 0x6c, 0x9e, 0x77, 0x3b, 0x34, 0xf6, 0x73, 0x80, 0xed,
|
||||
/* (2^157)P */ 0x16, 0xfb, 0x16, 0xc3, 0xc2, 0x83, 0xe4, 0xf4, 0x03, 0x7f, 0x52, 0xb0, 0x67, 0x51, 0x7b, 0x24, 0x5a, 0x51, 0xd3, 0xb6, 0x4e, 0x59, 0x76, 0xcd, 0x08, 0x7b, 0x1d, 0x7a, 0x9c, 0x65, 0xae, 0xce, 0xaa, 0xd2, 0x1c, 0x85, 0x66, 0x68, 0x06, 0x15, 0xa8, 0x06, 0xe6, 0x16, 0x37, 0xf4, 0x49, 0x9e, 0x0f, 0x50, 0x37, 0xb1, 0xb2, 0x93, 0x70, 0x43,
|
||||
/* (2^158)P */ 0x18, 0x3a, 0x16, 0xe5, 0x8d, 0xc8, 0x35, 0xd6, 0x7b, 0x09, 0xec, 0x61, 0x5f, 0x5c, 0x2a, 0x19, 0x96, 0x2e, 0xc3, 0xfd, 0xab, 0xe6, 0x23, 0xae, 0xab, 0xc5, 0xcb, 0xb9, 0x7b, 0x2d, 0x34, 0x51, 0xb9, 0x41, 0x9e, 0x7d, 0xca, 0xda, 0x25, 0x45, 0x14, 0xb0, 0xc7, 0x4d, 0x26, 0x2b, 0xfe, 0x43, 0xb0, 0x21, 0x5e, 0xfa, 0xdc, 0x7c, 0xf9, 0x5a,
|
||||
/* (2^159)P */ 0x94, 0xad, 0x42, 0x17, 0xf5, 0xcd, 0x1c, 0x0d, 0xf6, 0x41, 0xd2, 0x55, 0xbb, 0x50, 0xf1, 0xc6, 0xbc, 0xa6, 0xc5, 0x3a, 0xfd, 0x9b, 0x75, 0x3e, 0xf6, 0x1a, 0xa7, 0xb2, 0x6e, 0x64, 0x12, 0xdc, 0x3c, 0xe5, 0xf6, 0xfc, 0x3b, 0xfa, 0x43, 0x81, 0xd4, 0xa5, 0xee, 0xf5, 0x9c, 0x47, 0x2f, 0xd0, 0x9c, 0xde, 0xa1, 0x48, 0x91, 0x9a, 0x34, 0xc1,
|
||||
/* (2^160)P */ 0x37, 0x1b, 0xb3, 0x88, 0xc9, 0x98, 0x4e, 0xfb, 0x84, 0x4f, 0x2b, 0x0a, 0xb6, 0x8f, 0x35, 0x15, 0xcd, 0x61, 0x7a, 0x5f, 0x5c, 0xa0, 0xca, 0x23, 0xa0, 0x93, 0x1f, 0xcc, 0x3c, 0x39, 0x3a, 0x24, 0xa7, 0x49, 0xad, 0x8d, 0x59, 0xcc, 0x94, 0x5a, 0x16, 0xf5, 0x70, 0xe8, 0x52, 0x1e, 0xee, 0x20, 0x30, 0x17, 0x7e, 0xf0, 0x4c, 0x93, 0x06, 0x5a,
|
||||
/* (2^161)P */ 0x81, 0xba, 0x3b, 0xd7, 0x3e, 0xb4, 0x32, 0x3a, 0x22, 0x39, 0x2a, 0xfc, 0x19, 0xd9, 0xd2, 0xf6, 0xc5, 0x79, 0x6c, 0x0e, 0xde, 0xda, 0x01, 0xff, 0x52, 0xfb, 0xb6, 0x95, 0x4e, 0x7a, 0x10, 0xb8, 0x06, 0x86, 0x3c, 0xcd, 0x56, 0xd6, 0x15, 0xbf, 0x6e, 0x3e, 0x4f, 0x35, 0x5e, 0xca, 0xbc, 0xa5, 0x95, 0xa2, 0xdf, 0x2d, 0x1d, 0xaf, 0x59, 0xf9,
|
||||
/* (2^162)P */ 0x69, 0xe5, 0xe2, 0xfa, 0xc9, 0x7f, 0xdd, 0x09, 0xf5, 0x6b, 0x4e, 0x2e, 0xbe, 0xb4, 0xbf, 0x3e, 0xb2, 0xf2, 0x81, 0x30, 0xe1, 0x07, 0xa8, 0x0d, 0x2b, 0xd2, 0x5a, 0x55, 0xbe, 0x4b, 0x86, 0x5d, 0xb0, 0x5e, 0x7c, 0x8f, 0xc1, 0x3c, 0x81, 0x4c, 0xf7, 0x6d, 0x7d, 0xe6, 0x4f, 0x8a, 0x85, 0xc2, 0x2f, 0x28, 0xef, 0x8c, 0x69, 0xc2, 0xc2, 0x1a,
|
||||
/* (2^163)P */ 0xd9, 0xe4, 0x0e, 0x1e, 0xc2, 0xf7, 0x2f, 0x9f, 0xa1, 0x40, 0xfe, 0x46, 0x16, 0xaf, 0x2e, 0xd1, 0xec, 0x15, 0x9b, 0x61, 0x92, 0xce, 0xfc, 0x10, 0x43, 0x1d, 0x00, 0xf6, 0xbe, 0x20, 0x80, 0x80, 0x6f, 0x3c, 0x16, 0x94, 0x59, 0xba, 0x03, 0x53, 0x6e, 0xb6, 0xdd, 0x25, 0x7b, 0x86, 0xbf, 0x96, 0xf4, 0x2f, 0xa1, 0x96, 0x8d, 0xf9, 0xb3, 0x29,
|
||||
/* (2^164)P */ 0x3b, 0x04, 0x60, 0x6e, 0xce, 0xab, 0xd2, 0x63, 0x18, 0x53, 0x88, 0x16, 0x4a, 0x6a, 0xab, 0x72, 0x03, 0x68, 0xa5, 0xd4, 0x0d, 0xb2, 0x82, 0x81, 0x1f, 0x2b, 0x5c, 0x75, 0xe8, 0xd2, 0x1d, 0x7f, 0xe7, 0x1b, 0x35, 0x02, 0xde, 0xec, 0xbd, 0xcb, 0xc7, 0x01, 0xd3, 0x95, 0x61, 0xfe, 0xb2, 0x7a, 0x66, 0x09, 0x4c, 0x6d, 0xfd, 0x39, 0xf7, 0x52,
|
||||
/* (2^165)P */ 0x42, 0xc1, 0x5f, 0xf8, 0x35, 0x52, 0xc1, 0xfe, 0xc5, 0x11, 0x80, 0x1c, 0x11, 0x46, 0x31, 0x11, 0xbe, 0xd0, 0xc4, 0xb6, 0x07, 0x13, 0x38, 0xa0, 0x8d, 0x65, 0xf0, 0x56, 0x9e, 0x16, 0xbf, 0x9d, 0xcd, 0x51, 0x34, 0xf9, 0x08, 0x48, 0x7b, 0x76, 0x0c, 0x7b, 0x30, 0x07, 0xa8, 0x76, 0xaf, 0xa3, 0x29, 0x38, 0xb0, 0x58, 0xde, 0x72, 0x4b, 0x45,
|
||||
/* (2^166)P */ 0xd4, 0x16, 0xa7, 0xc0, 0xb4, 0x9f, 0xdf, 0x1a, 0x37, 0xc8, 0x35, 0xed, 0xc5, 0x85, 0x74, 0x64, 0x09, 0x22, 0xef, 0xe9, 0x0c, 0xaf, 0x12, 0x4c, 0x9e, 0xf8, 0x47, 0x56, 0xe0, 0x7f, 0x4e, 0x24, 0x6b, 0x0c, 0xe7, 0xad, 0xc6, 0x47, 0x1d, 0xa4, 0x0d, 0x86, 0x89, 0x65, 0xe8, 0x5f, 0x71, 0xc7, 0xe9, 0xcd, 0xec, 0x6c, 0x62, 0xc7, 0xe3, 0xb3,
|
||||
/* (2^167)P */ 0xb5, 0xea, 0x86, 0xe3, 0x15, 0x18, 0x3f, 0x6d, 0x7b, 0x05, 0x95, 0x15, 0x53, 0x26, 0x1c, 0xeb, 0xbe, 0x7e, 0x16, 0x42, 0x4b, 0xa2, 0x3d, 0xdd, 0x0e, 0xff, 0xba, 0x67, 0xb5, 0xae, 0x7a, 0x17, 0xde, 0x23, 0xad, 0x14, 0xcc, 0xd7, 0xaf, 0x57, 0x01, 0xe0, 0xdd, 0x48, 0xdd, 0xd7, 0xe3, 0xdf, 0xe9, 0x2d, 0xda, 0x67, 0xa4, 0x9f, 0x29, 0x04,
|
||||
/* (2^168)P */ 0x16, 0x53, 0xe6, 0x9c, 0x4e, 0xe5, 0x1e, 0x70, 0x81, 0x25, 0x02, 0x9b, 0x47, 0x6d, 0xd2, 0x08, 0x73, 0xbe, 0x0a, 0xf1, 0x7b, 0xeb, 0x24, 0xeb, 0x38, 0x23, 0x5c, 0xb6, 0x3e, 0xce, 0x1e, 0xe3, 0xbc, 0x82, 0x35, 0x1f, 0xaf, 0x3a, 0x3a, 0xe5, 0x4e, 0xc1, 0xca, 0xbf, 0x47, 0xb4, 0xbb, 0xbc, 0x5f, 0xea, 0xc6, 0xca, 0xf3, 0xa0, 0xa2, 0x73,
|
||||
/* (2^169)P */ 0xef, 0xa4, 0x7a, 0x4e, 0xe4, 0xc7, 0xb6, 0x43, 0x2e, 0xa5, 0xe4, 0xa5, 0xba, 0x1e, 0xa5, 0xfe, 0x9e, 0xce, 0xa9, 0x80, 0x04, 0xcb, 0x4f, 0xd8, 0x74, 0x05, 0x48, 0xfa, 0x99, 0x11, 0x5d, 0x97, 0x3b, 0x07, 0x0d, 0xdd, 0xe6, 0xb1, 0x74, 0x87, 0x1a, 0xd3, 0x26, 0xb7, 0x8f, 0xe1, 0x63, 0x3d, 0xec, 0x53, 0x93, 0xb0, 0x81, 0x78, 0x34, 0xa4,
|
||||
/* (2^170)P */ 0xe1, 0xe7, 0xd4, 0x58, 0x9d, 0x0e, 0x8b, 0x65, 0x66, 0x37, 0x16, 0x48, 0x6f, 0xaa, 0x42, 0x37, 0x77, 0xad, 0xb1, 0x56, 0x48, 0xdf, 0x65, 0x36, 0x30, 0xb8, 0x00, 0x12, 0xd8, 0x32, 0x28, 0x7f, 0xc1, 0x71, 0xeb, 0x93, 0x0f, 0x48, 0x04, 0xe1, 0x5a, 0x6a, 0x96, 0xc1, 0xca, 0x89, 0x6d, 0x1b, 0x82, 0x4c, 0x18, 0x6d, 0x55, 0x4b, 0xea, 0xfd,
|
||||
/* (2^171)P */ 0x62, 0x1a, 0x53, 0xb4, 0xb1, 0xbe, 0x6f, 0x15, 0x18, 0x88, 0xd4, 0x66, 0x61, 0xc7, 0x12, 0x69, 0x02, 0xbd, 0x03, 0x23, 0x2b, 0xef, 0xf9, 0x54, 0xa4, 0x85, 0xa8, 0xe3, 0xb7, 0xbd, 0xa9, 0xa3, 0xf3, 0x2a, 0xdd, 0xf1, 0xd4, 0x03, 0x0f, 0xa9, 0xa1, 0xd8, 0xa3, 0xcd, 0xb2, 0x71, 0x90, 0x4b, 0x35, 0x62, 0xf2, 0x2f, 0xce, 0x67, 0x1f, 0xaa,
|
||||
/* (2^172)P */ 0x9e, 0x1e, 0xcd, 0x43, 0x7e, 0x87, 0x37, 0x94, 0x3a, 0x97, 0x4c, 0x7e, 0xee, 0xc9, 0x37, 0x85, 0xf1, 0xd9, 0x4f, 0xbf, 0xf9, 0x6f, 0x39, 0x9a, 0x39, 0x87, 0x2e, 0x25, 0x84, 0x42, 0xc3, 0x80, 0xcb, 0x07, 0x22, 0xae, 0x30, 0xd5, 0x50, 0xa1, 0x23, 0xcc, 0x31, 0x81, 0x9d, 0xf1, 0x30, 0xd9, 0x2b, 0x73, 0x41, 0x16, 0x50, 0xab, 0x2d, 0xa2,
|
||||
/* (2^173)P */ 0xa4, 0x69, 0x4f, 0xa1, 0x4e, 0xb9, 0xbf, 0x14, 0xe8, 0x2b, 0x04, 0x93, 0xb7, 0x6e, 0x9f, 0x7d, 0x73, 0x0a, 0xc5, 0x14, 0xb8, 0xde, 0x8c, 0xc1, 0xfe, 0xc0, 0xa7, 0xa4, 0xcc, 0x42, 0x42, 0x81, 0x15, 0x65, 0x8a, 0x80, 0xb9, 0xde, 0x1f, 0x60, 0x33, 0x0e, 0xcb, 0xfc, 0xe0, 0xdb, 0x83, 0xa1, 0xe5, 0xd0, 0x16, 0x86, 0x2c, 0xe2, 0x87, 0xed,
|
||||
/* (2^174)P */ 0x7a, 0xc0, 0xeb, 0x6b, 0xf6, 0x0d, 0x4c, 0x6d, 0x1e, 0xdb, 0xab, 0xe7, 0x19, 0x45, 0xc6, 0xe3, 0xb2, 0x06, 0xbb, 0xbc, 0x70, 0x99, 0x83, 0x33, 0xeb, 0x28, 0xc8, 0x77, 0xf6, 0x4d, 0x01, 0xb7, 0x59, 0xa0, 0xd2, 0xb3, 0x2a, 0x72, 0x30, 0xe7, 0x11, 0x39, 0xb6, 0x41, 0x29, 0x65, 0x5a, 0x14, 0xb9, 0x86, 0x08, 0xe0, 0x7d, 0x32, 0x8c, 0xf0,
|
||||
/* (2^175)P */ 0x5c, 0x11, 0x30, 0x9e, 0x05, 0x27, 0xf5, 0x45, 0x0f, 0xb3, 0xc9, 0x75, 0xc3, 0xd7, 0xe1, 0x82, 0x3b, 0x8e, 0x87, 0x23, 0x00, 0x15, 0x19, 0x07, 0xd9, 0x21, 0x53, 0xc7, 0xf1, 0xa3, 0xbf, 0x70, 0x64, 0x15, 0x18, 0xca, 0x23, 0x9e, 0xd3, 0x08, 0xc3, 0x2a, 0x8b, 0xe5, 0x83, 0x04, 0x89, 0x14, 0xfd, 0x28, 0x25, 0x1c, 0xe3, 0x26, 0xa7, 0x22,
|
||||
/* (2^176)P */ 0xdc, 0xd4, 0x75, 0x60, 0x99, 0x94, 0xea, 0x09, 0x8e, 0x8a, 0x3c, 0x1b, 0xf9, 0xbd, 0x33, 0x0d, 0x51, 0x3d, 0x12, 0x6f, 0x4e, 0x72, 0xe0, 0x17, 0x20, 0xe9, 0x75, 0xe6, 0x3a, 0xb2, 0x13, 0x83, 0x4e, 0x7a, 0x08, 0x9e, 0xd1, 0x04, 0x5f, 0x6b, 0x42, 0x0b, 0x76, 0x2a, 0x2d, 0x77, 0x53, 0x6c, 0x65, 0x6d, 0x8e, 0x25, 0x3c, 0xb6, 0x8b, 0x69,
|
||||
/* (2^177)P */ 0xb9, 0x49, 0x28, 0xd0, 0xdc, 0x6c, 0x8f, 0x4c, 0xc9, 0x14, 0x8a, 0x38, 0xa3, 0xcb, 0xc4, 0x9d, 0x53, 0xcf, 0xe9, 0xe3, 0xcf, 0xe0, 0xb1, 0xf2, 0x1b, 0x4c, 0x7f, 0x83, 0x2a, 0x7a, 0xe9, 0x8b, 0x3b, 0x86, 0x61, 0x30, 0xe9, 0x99, 0xbd, 0xba, 0x19, 0x6e, 0x65, 0x2a, 0x12, 0x3e, 0x9c, 0xa8, 0xaf, 0xc3, 0xcf, 0xf8, 0x1f, 0x77, 0x86, 0xea,
|
||||
/* (2^178)P */ 0x30, 0xde, 0xe7, 0xff, 0x54, 0xf7, 0xa2, 0x59, 0xf6, 0x0b, 0xfb, 0x7a, 0xf2, 0x39, 0xf0, 0xdb, 0x39, 0xbc, 0xf0, 0xfa, 0x60, 0xeb, 0x6b, 0x4f, 0x47, 0x17, 0xc8, 0x00, 0x65, 0x6d, 0x25, 0x1c, 0xd0, 0x48, 0x56, 0x53, 0x45, 0x11, 0x30, 0x02, 0x49, 0x20, 0x27, 0xac, 0xf2, 0x4c, 0xac, 0x64, 0x3d, 0x52, 0xb8, 0x89, 0xe0, 0x93, 0x16, 0x0f,
|
||||
/* (2^179)P */ 0x84, 0x09, 0xba, 0x40, 0xb2, 0x2f, 0xa3, 0xa8, 0xc2, 0xba, 0x46, 0x33, 0x05, 0x9d, 0x62, 0xad, 0xa1, 0x3c, 0x33, 0xef, 0x0d, 0xeb, 0xf0, 0x77, 0x11, 0x5a, 0xb0, 0x21, 0x9c, 0xdf, 0x55, 0x24, 0x25, 0x35, 0x51, 0x61, 0x92, 0xf0, 0xb1, 0xce, 0xf5, 0xd4, 0x7b, 0x6c, 0x21, 0x9d, 0x56, 0x52, 0xf8, 0xa1, 0x4c, 0xe9, 0x27, 0x55, 0xac, 0x91,
|
||||
/* (2^180)P */ 0x03, 0x3e, 0x30, 0xd2, 0x0a, 0xfa, 0x7d, 0x82, 0x3d, 0x1f, 0x8b, 0xcb, 0xb6, 0x04, 0x5c, 0xcc, 0x8b, 0xda, 0xe2, 0x68, 0x74, 0x08, 0x8c, 0x44, 0x83, 0x57, 0x6d, 0x6f, 0x80, 0xb0, 0x7e, 0xa9, 0x82, 0x91, 0x7b, 0x4c, 0x37, 0x97, 0xd1, 0x63, 0xd1, 0xbd, 0x45, 0xe6, 0x8a, 0x86, 0xd6, 0x89, 0x54, 0xfd, 0xd2, 0xb1, 0xd7, 0x54, 0xad, 0xaf,
|
||||
/* (2^181)P */ 0x8b, 0x33, 0x62, 0x49, 0x9f, 0x63, 0xf9, 0x87, 0x42, 0x58, 0xbf, 0xb3, 0xe6, 0x68, 0x02, 0x60, 0x5c, 0x76, 0x62, 0xf7, 0x61, 0xd7, 0x36, 0x31, 0xf7, 0x9c, 0xb5, 0xe5, 0x13, 0x6c, 0xea, 0x78, 0xae, 0xcf, 0xde, 0xbf, 0xb6, 0xeb, 0x4f, 0xc8, 0x2a, 0xb4, 0x9a, 0x9f, 0xf3, 0xd1, 0x6a, 0xec, 0x0c, 0xbd, 0x85, 0x98, 0x40, 0x06, 0x1c, 0x2a,
|
||||
/* (2^182)P */ 0x74, 0x3b, 0xe7, 0x81, 0xd5, 0xae, 0x54, 0x56, 0x03, 0xe8, 0x97, 0x16, 0x76, 0xcf, 0x24, 0x96, 0x96, 0x5b, 0xcc, 0x09, 0xab, 0x23, 0x6f, 0x54, 0xae, 0x8f, 0xe4, 0x12, 0xcb, 0xfd, 0xbc, 0xac, 0x93, 0x45, 0x3d, 0x68, 0x08, 0x22, 0x59, 0xc6, 0xf0, 0x47, 0x19, 0x8c, 0x79, 0x93, 0x1e, 0x0e, 0x30, 0xb0, 0x94, 0xfb, 0x17, 0x1d, 0x5a, 0x12,
|
||||
/* (2^183)P */ 0x85, 0xff, 0x40, 0x18, 0x85, 0xff, 0x44, 0x37, 0x69, 0x23, 0x4d, 0x34, 0xe1, 0xeb, 0xa3, 0x1b, 0x55, 0x40, 0xc1, 0x64, 0xf4, 0xd4, 0x13, 0x0a, 0x9f, 0xb9, 0x19, 0xfc, 0x88, 0x7d, 0xc0, 0x72, 0xcf, 0x69, 0x2f, 0xd2, 0x0c, 0x82, 0x0f, 0xda, 0x08, 0xba, 0x0f, 0xaa, 0x3b, 0xe9, 0xe5, 0x83, 0x7a, 0x06, 0xe8, 0x1b, 0x38, 0x43, 0xc3, 0x54,
|
||||
/* (2^184)P */ 0x14, 0xaa, 0xb3, 0x6e, 0xe6, 0x28, 0xee, 0xc5, 0x22, 0x6c, 0x7c, 0xf9, 0xa8, 0x71, 0xcc, 0xfe, 0x68, 0x7e, 0xd3, 0xb8, 0x37, 0x96, 0xca, 0x0b, 0xd9, 0xb6, 0x06, 0xa9, 0xf6, 0x71, 0xe8, 0x31, 0xf7, 0xd8, 0xf1, 0x5d, 0xab, 0xb9, 0xf0, 0x5c, 0x98, 0xcf, 0x22, 0xa2, 0x2a, 0xf6, 0xd0, 0x59, 0xf0, 0x9d, 0xd9, 0x6a, 0x4f, 0x59, 0x57, 0xad,
|
||||
/* (2^185)P */ 0xd7, 0x2b, 0x3d, 0x38, 0x4c, 0x2e, 0x23, 0x4d, 0x49, 0xa2, 0x62, 0x62, 0xf9, 0x0f, 0xde, 0x08, 0xf3, 0x86, 0x71, 0xb6, 0xc7, 0xf9, 0x85, 0x9c, 0x33, 0xa1, 0xcf, 0x16, 0xaa, 0x60, 0xb9, 0xb7, 0xea, 0xed, 0x01, 0x1c, 0x59, 0xdb, 0x3f, 0x3f, 0x97, 0x2e, 0xf0, 0x09, 0x9f, 0x10, 0x85, 0x5f, 0x53, 0x39, 0xf3, 0x13, 0x40, 0x56, 0x95, 0xf9,
|
||||
/* (2^186)P */ 0xb4, 0xe3, 0xda, 0xc6, 0x1f, 0x78, 0x8e, 0xac, 0xd4, 0x20, 0x1d, 0xa0, 0xbf, 0x4c, 0x09, 0x16, 0xa7, 0x30, 0xb5, 0x8d, 0x9e, 0xa1, 0x5f, 0x6d, 0x52, 0xf4, 0x71, 0xb6, 0x32, 0x2d, 0x21, 0x51, 0xc6, 0xfc, 0x2f, 0x08, 0xf4, 0x13, 0x6c, 0x55, 0xba, 0x72, 0x81, 0x24, 0x49, 0x0e, 0x4f, 0x06, 0x36, 0x39, 0x6a, 0xc5, 0x81, 0xfc, 0xeb, 0xb2,
|
||||
/* (2^187)P */ 0x7d, 0x8d, 0xc8, 0x6c, 0xea, 0xb4, 0xb9, 0xe8, 0x40, 0xc9, 0x69, 0xc9, 0x30, 0x05, 0xfd, 0x34, 0x46, 0xfd, 0x94, 0x05, 0x16, 0xf5, 0x4b, 0x13, 0x3d, 0x24, 0x1a, 0xd6, 0x64, 0x2b, 0x9c, 0xe2, 0xa5, 0xd9, 0x98, 0xe0, 0xe8, 0xf4, 0xbc, 0x2c, 0xbd, 0xa2, 0x56, 0xe3, 0x9e, 0x14, 0xdb, 0xbf, 0x05, 0xbf, 0x9a, 0x13, 0x5d, 0xf7, 0x91, 0xa3,
|
||||
/* (2^188)P */ 0x8b, 0xcb, 0x27, 0xf3, 0x15, 0x26, 0x05, 0x40, 0x0f, 0xa6, 0x15, 0x13, 0x71, 0x95, 0xa2, 0xc6, 0x38, 0x04, 0x67, 0xf8, 0x9a, 0x83, 0x06, 0xaa, 0x25, 0x36, 0x72, 0x01, 0x6f, 0x74, 0x5f, 0xe5, 0x6e, 0x44, 0x99, 0xce, 0x13, 0xbc, 0x82, 0xc2, 0x0d, 0xa4, 0x98, 0x50, 0x38, 0xf3, 0xa2, 0xc5, 0xe5, 0x24, 0x1f, 0x6f, 0x56, 0x3e, 0x07, 0xb2,
|
||||
/* (2^189)P */ 0xbd, 0x0f, 0x32, 0x60, 0x07, 0xb1, 0xd7, 0x0b, 0x11, 0x07, 0x57, 0x02, 0x89, 0xe8, 0x8b, 0xe8, 0x5a, 0x1f, 0xee, 0x54, 0x6b, 0xff, 0xb3, 0x04, 0x07, 0x57, 0x13, 0x0b, 0x94, 0xa8, 0x4d, 0x81, 0xe2, 0x17, 0x16, 0x45, 0xd4, 0x4b, 0xf7, 0x7e, 0x64, 0x66, 0x20, 0xe8, 0x0b, 0x26, 0xfd, 0xa9, 0x8a, 0x47, 0x52, 0x89, 0x14, 0xd0, 0xd1, 0xa1,
|
||||
/* (2^190)P */ 0xdc, 0x03, 0xe6, 0x20, 0x44, 0x47, 0x8f, 0x04, 0x16, 0x24, 0x22, 0xc1, 0x55, 0x5c, 0xbe, 0x43, 0xc3, 0x92, 0xc5, 0x54, 0x3d, 0x5d, 0xd1, 0x05, 0x9c, 0xc6, 0x7c, 0xbf, 0x23, 0x84, 0x1a, 0xba, 0x4f, 0x1f, 0xfc, 0xa1, 0xae, 0x1a, 0x64, 0x02, 0x51, 0xf1, 0xcb, 0x7a, 0x20, 0xce, 0xb2, 0x34, 0x3c, 0xca, 0xe0, 0xe4, 0xba, 0x22, 0xd4, 0x7b,
|
||||
/* (2^191)P */ 0xca, 0xfd, 0xca, 0xd7, 0xde, 0x61, 0xae, 0xf0, 0x79, 0x0c, 0x20, 0xab, 0xbc, 0x6f, 0x4d, 0x61, 0xf0, 0xc7, 0x9c, 0x8d, 0x4b, 0x52, 0xf3, 0xb9, 0x48, 0x63, 0x0b, 0xb6, 0xd2, 0x25, 0x9a, 0x96, 0x72, 0xc1, 0x6b, 0x0c, 0xb5, 0xfb, 0x71, 0xaa, 0xad, 0x47, 0x5b, 0xe7, 0xc0, 0x0a, 0x55, 0xb2, 0xd4, 0x16, 0x2f, 0xb1, 0x01, 0xfd, 0xce, 0x27,
|
||||
/* (2^192)P */ 0x64, 0x11, 0x4b, 0xab, 0x57, 0x09, 0xc6, 0x49, 0x4a, 0x37, 0xc3, 0x36, 0xc4, 0x7b, 0x81, 0x1f, 0x42, 0xed, 0xbb, 0xe0, 0xa0, 0x8d, 0x51, 0xe6, 0xca, 0x8b, 0xb9, 0xcd, 0x99, 0x2d, 0x91, 0x53, 0xa9, 0x47, 0xcb, 0x32, 0xc7, 0xa4, 0x92, 0xec, 0x46, 0x74, 0x44, 0x6d, 0x71, 0x9f, 0x6d, 0x0c, 0x69, 0xa4, 0xf8, 0xbe, 0x9f, 0x7f, 0xa0, 0xd7,
|
||||
/* (2^193)P */ 0x5f, 0x33, 0xb6, 0x91, 0xc8, 0xa5, 0x3f, 0x5d, 0x7f, 0x38, 0x6e, 0x74, 0x20, 0x4a, 0xd6, 0x2b, 0x98, 0x2a, 0x41, 0x4b, 0x83, 0x64, 0x0b, 0x92, 0x7a, 0x06, 0x1e, 0xc6, 0x2c, 0xf6, 0xe4, 0x91, 0xe5, 0xb1, 0x2e, 0x6e, 0x4e, 0xa8, 0xc8, 0x14, 0x32, 0x57, 0x44, 0x1c, 0xe4, 0xb9, 0x7f, 0x54, 0x51, 0x08, 0x81, 0xaa, 0x4e, 0xce, 0xa1, 0x5d,
|
||||
/* (2^194)P */ 0x5c, 0xd5, 0x9b, 0x5e, 0x7c, 0xb5, 0xb1, 0x52, 0x73, 0x00, 0x41, 0x56, 0x79, 0x08, 0x7e, 0x07, 0x28, 0x06, 0xa6, 0xfb, 0x7f, 0x69, 0xbd, 0x7a, 0x3c, 0xae, 0x9f, 0x39, 0xbb, 0x54, 0xa2, 0x79, 0xb9, 0x0e, 0x7f, 0xbb, 0xe0, 0xe6, 0xb7, 0x27, 0x64, 0x38, 0x45, 0xdb, 0x84, 0xe4, 0x61, 0x72, 0x3f, 0xe2, 0x24, 0xfe, 0x7a, 0x31, 0x9a, 0xc9,
|
||||
/* (2^195)P */ 0xa1, 0xd2, 0xa4, 0xee, 0x24, 0x96, 0xe5, 0x5b, 0x79, 0x78, 0x3c, 0x7b, 0x82, 0x3b, 0x8b, 0x58, 0x0b, 0xa3, 0x63, 0x2d, 0xbc, 0x75, 0x46, 0xe8, 0x83, 0x1a, 0xc0, 0x2a, 0x92, 0x61, 0xa8, 0x75, 0x37, 0x3c, 0xbf, 0x0f, 0xef, 0x8f, 0x6c, 0x97, 0x75, 0x10, 0x05, 0x7a, 0xde, 0x23, 0xe8, 0x2a, 0x35, 0xeb, 0x41, 0x64, 0x7d, 0xcf, 0xe0, 0x52,
|
||||
/* (2^196)P */ 0x4a, 0xd0, 0x49, 0x93, 0xae, 0xf3, 0x24, 0x8c, 0xe1, 0x09, 0x98, 0x45, 0xd8, 0xb9, 0xfe, 0x8e, 0x8c, 0xa8, 0x2c, 0xc9, 0x9f, 0xce, 0x01, 0xdc, 0x38, 0x11, 0xab, 0x85, 0xb9, 0xe8, 0x00, 0x51, 0xfd, 0x82, 0xe1, 0x9b, 0x4e, 0xfc, 0xb5, 0x2a, 0x0f, 0x8b, 0xda, 0x4e, 0x02, 0xca, 0xcc, 0xe3, 0x91, 0xc4, 0xe0, 0xcf, 0x7b, 0xd6, 0xe6, 0x6a,
|
||||
/* (2^197)P */ 0xfe, 0x11, 0xd7, 0xaa, 0xe3, 0x0c, 0x52, 0x2e, 0x04, 0xe0, 0xe0, 0x61, 0xc8, 0x05, 0xd7, 0x31, 0x4c, 0xc3, 0x9b, 0x2d, 0xce, 0x59, 0xbe, 0x12, 0xb7, 0x30, 0x21, 0xfc, 0x81, 0xb8, 0x5e, 0x57, 0x73, 0xd0, 0xad, 0x8e, 0x9e, 0xe4, 0xeb, 0xcd, 0xcf, 0xd2, 0x0f, 0x01, 0x35, 0x16, 0xed, 0x7a, 0x43, 0x8e, 0x42, 0xdc, 0xea, 0x4c, 0xa8, 0x7c,
|
||||
/* (2^198)P */ 0x37, 0x26, 0xcc, 0x76, 0x0b, 0xe5, 0x76, 0xdd, 0x3e, 0x19, 0x3c, 0xc4, 0x6c, 0x7f, 0xd0, 0x03, 0xc1, 0xb8, 0x59, 0x82, 0xca, 0x36, 0xc1, 0xe4, 0xc8, 0xb2, 0x83, 0x69, 0x9c, 0xc5, 0x9d, 0x12, 0x82, 0x1c, 0xea, 0xb2, 0x84, 0x9f, 0xf3, 0x52, 0x6b, 0xbb, 0xd8, 0x81, 0x56, 0x83, 0x04, 0x66, 0x05, 0x22, 0x49, 0x37, 0x93, 0xb1, 0xfd, 0xd5,
|
||||
/* (2^199)P */ 0xaf, 0x96, 0xbf, 0x03, 0xbe, 0xe6, 0x5d, 0x78, 0x19, 0xba, 0x37, 0x46, 0x0a, 0x2b, 0x52, 0x7c, 0xd8, 0x51, 0x9e, 0x3d, 0x29, 0x42, 0xdb, 0x0e, 0x31, 0x20, 0x94, 0xf8, 0x43, 0x9a, 0x2d, 0x22, 0xd3, 0xe3, 0xa1, 0x79, 0x68, 0xfb, 0x2d, 0x7e, 0xd6, 0x79, 0xda, 0x0b, 0xc6, 0x5b, 0x76, 0x68, 0xf0, 0xfe, 0x72, 0x59, 0xbb, 0xa1, 0x9c, 0x74,
|
||||
/* (2^200)P */ 0x0a, 0xd9, 0xec, 0xc5, 0xbd, 0xf0, 0xda, 0xcf, 0x82, 0xab, 0x46, 0xc5, 0x32, 0x13, 0xdc, 0x5b, 0xac, 0xc3, 0x53, 0x9a, 0x7f, 0xef, 0xa5, 0x40, 0x5a, 0x1f, 0xc1, 0x12, 0x91, 0x54, 0x83, 0x6a, 0xb0, 0x9a, 0x85, 0x4d, 0xbf, 0x36, 0x8e, 0xd3, 0xa2, 0x2b, 0xe5, 0xd6, 0xc6, 0xe1, 0x58, 0x5b, 0x82, 0x9b, 0xc8, 0xf2, 0x03, 0xba, 0xf5, 0x92,
|
||||
/* (2^201)P */ 0xfb, 0x21, 0x7e, 0xde, 0xe7, 0xb4, 0xc0, 0x56, 0x86, 0x3a, 0x5b, 0x78, 0xf8, 0xf0, 0xf4, 0xe7, 0x5c, 0x00, 0xd2, 0xd7, 0xd6, 0xf8, 0x75, 0x5e, 0x0f, 0x3e, 0xd1, 0x4b, 0x77, 0xd8, 0xad, 0xb0, 0xc9, 0x8b, 0x59, 0x7d, 0x30, 0x76, 0x64, 0x7a, 0x76, 0xd9, 0x51, 0x69, 0xfc, 0xbd, 0x8e, 0xb5, 0x55, 0xe0, 0xd2, 0x07, 0x15, 0xa9, 0xf7, 0xa4,
|
||||
/* (2^202)P */ 0xaa, 0x2d, 0x2f, 0x2b, 0x3c, 0x15, 0xdd, 0xcd, 0xe9, 0x28, 0x82, 0x4f, 0xa2, 0xaa, 0x31, 0x48, 0xcc, 0xfa, 0x07, 0x73, 0x8a, 0x34, 0x74, 0x0d, 0xab, 0x1a, 0xca, 0xd2, 0xbf, 0x3a, 0xdb, 0x1a, 0x5f, 0x50, 0x62, 0xf4, 0x6b, 0x83, 0x38, 0x43, 0x96, 0xee, 0x6b, 0x39, 0x1e, 0xf0, 0x17, 0x80, 0x1e, 0x9b, 0xed, 0x2b, 0x2f, 0xcc, 0x65, 0xf7,
|
||||
/* (2^203)P */ 0x03, 0xb3, 0x23, 0x9c, 0x0d, 0xd1, 0xeb, 0x7e, 0x34, 0x17, 0x8a, 0x4c, 0xde, 0x54, 0x39, 0xc4, 0x11, 0x82, 0xd3, 0xa4, 0x00, 0x32, 0x95, 0x9c, 0xa6, 0x64, 0x76, 0x6e, 0xd6, 0x53, 0x27, 0xb4, 0x6a, 0x14, 0x8c, 0x54, 0xf6, 0x58, 0x9e, 0x22, 0x4a, 0x55, 0x18, 0x77, 0xd0, 0x08, 0x6b, 0x19, 0x8a, 0xb5, 0xe7, 0x19, 0xb8, 0x60, 0x92, 0xb1,
|
||||
/* (2^204)P */ 0x66, 0xec, 0xf3, 0x12, 0xde, 0x67, 0x7f, 0xd4, 0x5b, 0xf6, 0x70, 0x64, 0x0a, 0xb5, 0xc2, 0xf9, 0xb3, 0x64, 0xab, 0x56, 0x46, 0xc7, 0x93, 0xc2, 0x8b, 0x2d, 0xd0, 0xd6, 0x39, 0x3b, 0x1f, 0xcd, 0xb3, 0xac, 0xcc, 0x2c, 0x27, 0x6a, 0xbc, 0xb3, 0x4b, 0xa8, 0x3c, 0x69, 0x20, 0xe2, 0x18, 0x35, 0x17, 0xe1, 0x8a, 0xd3, 0x11, 0x74, 0xaa, 0x4d,
|
||||
/* (2^205)P */ 0x96, 0xc4, 0x16, 0x7e, 0xfd, 0xf5, 0xd0, 0x7d, 0x1f, 0x32, 0x1b, 0xdb, 0xa6, 0xfd, 0x51, 0x75, 0x4d, 0xd7, 0x00, 0xe5, 0x7f, 0x58, 0x5b, 0xeb, 0x4b, 0x6a, 0x78, 0xfe, 0xe5, 0xd6, 0x8f, 0x99, 0x17, 0xca, 0x96, 0x45, 0xf7, 0x52, 0xdf, 0x84, 0x06, 0x77, 0xb9, 0x05, 0x63, 0x5d, 0xe9, 0x91, 0xb1, 0x4b, 0x82, 0x5a, 0xdb, 0xd7, 0xca, 0x69,
|
||||
/* (2^206)P */ 0x02, 0xd3, 0x38, 0x38, 0x87, 0xea, 0xbd, 0x9f, 0x11, 0xca, 0xf3, 0x21, 0xf1, 0x9b, 0x35, 0x97, 0x98, 0xff, 0x8e, 0x6d, 0x3d, 0xd6, 0xb2, 0xfa, 0x68, 0xcb, 0x7e, 0x62, 0x85, 0xbb, 0xc7, 0x5d, 0xee, 0x32, 0x30, 0x2e, 0x71, 0x96, 0x63, 0x43, 0x98, 0xc4, 0xa7, 0xde, 0x60, 0xb2, 0xd9, 0x43, 0x4a, 0xfa, 0x97, 0x2d, 0x5f, 0x21, 0xd4, 0xfe,
|
||||
/* (2^207)P */ 0x3b, 0x20, 0x29, 0x07, 0x07, 0xb5, 0x78, 0xc3, 0xc7, 0xab, 0x56, 0xba, 0x40, 0xde, 0x1d, 0xcf, 0xc3, 0x00, 0x56, 0x21, 0x0c, 0xc8, 0x42, 0xd9, 0x0e, 0xcd, 0x02, 0x7c, 0x07, 0xb9, 0x11, 0xd7, 0x96, 0xaf, 0xff, 0xad, 0xc5, 0xba, 0x30, 0x6d, 0x82, 0x3a, 0xbf, 0xef, 0x7b, 0xf7, 0x0a, 0x74, 0xbd, 0x31, 0x0c, 0xe4, 0xec, 0x1a, 0xe5, 0xc5,
|
||||
/* (2^208)P */ 0xcc, 0xf2, 0x28, 0x16, 0x12, 0xbf, 0xef, 0x85, 0xbc, 0xf7, 0xcb, 0x9f, 0xdb, 0xa8, 0xb2, 0x49, 0x53, 0x48, 0xa8, 0x24, 0xa8, 0x68, 0x8d, 0xbb, 0x21, 0x0a, 0x5a, 0xbd, 0xb2, 0x91, 0x61, 0x47, 0xc4, 0x43, 0x08, 0xa6, 0x19, 0xef, 0x8e, 0x88, 0x39, 0xc6, 0x33, 0x30, 0xf3, 0x0e, 0xc5, 0x92, 0x66, 0xd6, 0xfe, 0xc5, 0x12, 0xd9, 0x4c, 0x2d,
|
||||
/* (2^209)P */ 0x30, 0x34, 0x07, 0xbf, 0x9c, 0x5a, 0x4e, 0x65, 0xf1, 0x39, 0x35, 0x38, 0xae, 0x7b, 0x55, 0xac, 0x6a, 0x92, 0x24, 0x7e, 0x50, 0xd3, 0xba, 0x78, 0x51, 0xfe, 0x4d, 0x32, 0x05, 0x11, 0xf5, 0x52, 0xf1, 0x31, 0x45, 0x39, 0x98, 0x7b, 0x28, 0x56, 0xc3, 0x5d, 0x4f, 0x07, 0x6f, 0x84, 0xb8, 0x1a, 0x58, 0x0b, 0xc4, 0x7c, 0xc4, 0x8d, 0x32, 0x8e,
|
||||
/* (2^210)P */ 0x7e, 0xaf, 0x98, 0xce, 0xc5, 0x2b, 0x9d, 0xf6, 0xfa, 0x2c, 0xb6, 0x2a, 0x5a, 0x1d, 0xc0, 0x24, 0x8d, 0xa4, 0xce, 0xb1, 0x12, 0x01, 0xf9, 0x79, 0xc6, 0x79, 0x38, 0x0c, 0xd4, 0x07, 0xc9, 0xf7, 0x37, 0xa1, 0x0b, 0xfe, 0x72, 0xec, 0x5d, 0xd6, 0xb0, 0x1c, 0x70, 0xbe, 0x70, 0x01, 0x13, 0xe0, 0x86, 0x95, 0xc7, 0x2e, 0x12, 0x3b, 0xe6, 0xa6,
|
||||
/* (2^211)P */ 0x24, 0x82, 0x67, 0xe0, 0x14, 0x7b, 0x56, 0x08, 0x38, 0x44, 0xdb, 0xa0, 0x3a, 0x05, 0x47, 0xb2, 0xc0, 0xac, 0xd1, 0xcc, 0x3f, 0x82, 0xb8, 0x8a, 0x88, 0xbc, 0xf5, 0x33, 0xa1, 0x35, 0x0f, 0xf6, 0xe2, 0xef, 0x6c, 0xf7, 0x37, 0x9e, 0xe8, 0x10, 0xca, 0xb0, 0x8e, 0x80, 0x86, 0x00, 0x23, 0xd0, 0x4a, 0x76, 0x9f, 0xf7, 0x2c, 0x52, 0x15, 0x0e,
|
||||
/* (2^212)P */ 0x5e, 0x49, 0xe1, 0x2c, 0x9a, 0x01, 0x76, 0xa6, 0xb3, 0x07, 0x5b, 0xa4, 0x07, 0xef, 0x1d, 0xc3, 0x6a, 0xbb, 0x64, 0xbe, 0x71, 0x15, 0x6e, 0x32, 0x31, 0x46, 0x9a, 0x9e, 0x8f, 0x45, 0x73, 0xce, 0x0b, 0x94, 0x1a, 0x52, 0x07, 0xf4, 0x50, 0x30, 0x49, 0x53, 0x50, 0xfb, 0x71, 0x1f, 0x5a, 0x03, 0xa9, 0x76, 0xf2, 0x8f, 0x42, 0xff, 0xed, 0xed,
|
||||
/* (2^213)P */ 0xed, 0x08, 0xdb, 0x91, 0x1c, 0xee, 0xa2, 0xb4, 0x47, 0xa2, 0xfa, 0xcb, 0x03, 0xd1, 0xff, 0x8c, 0xad, 0x64, 0x50, 0x61, 0xcd, 0xfc, 0x88, 0xa0, 0x31, 0x95, 0x30, 0xb9, 0x58, 0xdd, 0xd7, 0x43, 0xe4, 0x46, 0xc2, 0x16, 0xd9, 0x72, 0x4a, 0x56, 0x51, 0x70, 0x85, 0xf1, 0xa1, 0x80, 0x40, 0xd5, 0xba, 0x67, 0x81, 0xda, 0xcd, 0x03, 0xea, 0x51,
|
||||
/* (2^214)P */ 0x42, 0x50, 0xf0, 0xef, 0x37, 0x61, 0x72, 0x85, 0xe1, 0xf1, 0xff, 0x6f, 0x3d, 0xe8, 0x7b, 0x21, 0x5c, 0xe5, 0x50, 0x03, 0xde, 0x00, 0xc1, 0xf7, 0x3a, 0x55, 0x12, 0x1c, 0x9e, 0x1e, 0xce, 0xd1, 0x2f, 0xaf, 0x05, 0x70, 0x5b, 0x47, 0xf2, 0x04, 0x7a, 0x89, 0xbc, 0x78, 0xa6, 0x65, 0x6c, 0xaa, 0x3c, 0xa2, 0x3c, 0x8b, 0x5c, 0xa9, 0x22, 0x48,
|
||||
/* (2^215)P */ 0x7e, 0x8c, 0x8f, 0x2f, 0x60, 0xe3, 0x5a, 0x94, 0xd4, 0xce, 0xdd, 0x9d, 0x83, 0x3b, 0x77, 0x78, 0x43, 0x1d, 0xfd, 0x8f, 0xc8, 0xe8, 0x02, 0x90, 0xab, 0xf6, 0xc9, 0xfc, 0xf1, 0x63, 0xaa, 0x5f, 0x42, 0xf1, 0x78, 0x34, 0x64, 0x16, 0x75, 0x9c, 0x7d, 0xd0, 0xe4, 0x74, 0x5a, 0xa8, 0xfb, 0xcb, 0xac, 0x20, 0xa3, 0xc2, 0xa6, 0x20, 0xf8, 0x1b,
|
||||
/* (2^216)P */ 0x00, 0x4f, 0x1e, 0x56, 0xb5, 0x34, 0xb2, 0x87, 0x31, 0xe5, 0xee, 0x8d, 0xf1, 0x41, 0x67, 0xb7, 0x67, 0x3a, 0x54, 0x86, 0x5c, 0xf0, 0x0b, 0x37, 0x2f, 0x1b, 0x92, 0x5d, 0x58, 0x93, 0xdc, 0xd8, 0x58, 0xcc, 0x9e, 0x67, 0xd0, 0x97, 0x3a, 0xaf, 0x49, 0x39, 0x2d, 0x3b, 0xd8, 0x98, 0xfb, 0x76, 0x6b, 0xe7, 0xaf, 0xc3, 0x45, 0x44, 0x53, 0x94,
|
||||
/* (2^217)P */ 0x30, 0xbd, 0x90, 0x75, 0xd3, 0xbd, 0x3b, 0x58, 0x27, 0x14, 0x9f, 0x6b, 0xd4, 0x31, 0x99, 0xcd, 0xde, 0x3a, 0x21, 0x1e, 0xb4, 0x02, 0xe4, 0x33, 0x04, 0x02, 0xb0, 0x50, 0x66, 0x68, 0x90, 0xdd, 0x7b, 0x69, 0x31, 0xd9, 0xcf, 0x68, 0x73, 0xf1, 0x60, 0xdd, 0xc8, 0x1d, 0x5d, 0xe3, 0xd6, 0x5b, 0x2a, 0xa4, 0xea, 0xc4, 0x3f, 0x08, 0xcd, 0x9c,
|
||||
/* (2^218)P */ 0x6b, 0x1a, 0xbf, 0x55, 0xc1, 0x1b, 0x0c, 0x05, 0x09, 0xdf, 0xf5, 0x5e, 0xa3, 0x77, 0x95, 0xe9, 0xdf, 0x19, 0xdd, 0xc7, 0x94, 0xcb, 0x06, 0x73, 0xd0, 0x88, 0x02, 0x33, 0x94, 0xca, 0x7a, 0x2f, 0x8e, 0x3d, 0x72, 0x61, 0x2d, 0x4d, 0xa6, 0x61, 0x1f, 0x32, 0x5e, 0x87, 0x53, 0x36, 0x11, 0x15, 0x20, 0xb3, 0x5a, 0x57, 0x51, 0x93, 0x20, 0xd8,
|
||||
/* (2^219)P */ 0xb7, 0x56, 0xf4, 0xab, 0x7d, 0x0c, 0xfb, 0x99, 0x1a, 0x30, 0x29, 0xb0, 0x75, 0x2a, 0xf8, 0x53, 0x71, 0x23, 0xbd, 0xa7, 0xd8, 0x0a, 0xe2, 0x27, 0x65, 0xe9, 0x74, 0x26, 0x98, 0x4a, 0x69, 0x19, 0xb2, 0x4d, 0x0a, 0x17, 0x98, 0xb2, 0xa9, 0x57, 0x4e, 0xf6, 0x86, 0xc8, 0x01, 0xa4, 0xc6, 0x98, 0xad, 0x5a, 0x90, 0x2c, 0x05, 0x46, 0x64, 0xb7,
|
||||
/* (2^220)P */ 0x7b, 0x91, 0xdf, 0xfc, 0xf8, 0x1c, 0x8c, 0x15, 0x9e, 0xf7, 0xd5, 0xa8, 0xe8, 0xe7, 0xe3, 0xa3, 0xb0, 0x04, 0x74, 0xfa, 0x78, 0xfb, 0x26, 0xbf, 0x67, 0x42, 0xf9, 0x8c, 0x9b, 0xb4, 0x69, 0x5b, 0x02, 0x13, 0x6d, 0x09, 0x6c, 0xd6, 0x99, 0x61, 0x7b, 0x89, 0x4a, 0x67, 0x75, 0xa3, 0x98, 0x13, 0x23, 0x1d, 0x18, 0x24, 0x0e, 0xef, 0x41, 0x79,
|
||||
/* (2^221)P */ 0x86, 0x33, 0xab, 0x08, 0xcb, 0xbf, 0x1e, 0x76, 0x3c, 0x0b, 0xbd, 0x30, 0xdb, 0xe9, 0xa3, 0x35, 0x87, 0x1b, 0xe9, 0x07, 0x00, 0x66, 0x7f, 0x3b, 0x35, 0x0c, 0x8a, 0x3f, 0x61, 0xbc, 0xe0, 0xae, 0xf6, 0xcc, 0x54, 0xe1, 0x72, 0x36, 0x2d, 0xee, 0x93, 0x24, 0xf8, 0xd7, 0xc5, 0xf9, 0xcb, 0xb0, 0xe5, 0x88, 0x0d, 0x23, 0x4b, 0x76, 0x15, 0xa2,
|
||||
/* (2^222)P */ 0x37, 0xdb, 0x83, 0xd5, 0x6d, 0x06, 0x24, 0x37, 0x1b, 0x15, 0x85, 0x15, 0xe2, 0xc0, 0x4e, 0x02, 0xa9, 0x6d, 0x0a, 0x3a, 0x94, 0x4a, 0x6f, 0x49, 0x00, 0x01, 0x72, 0xbb, 0x60, 0x14, 0x35, 0xae, 0xb4, 0xc6, 0x01, 0x0a, 0x00, 0x9e, 0xc3, 0x58, 0xc5, 0xd1, 0x5e, 0x30, 0x73, 0x96, 0x24, 0x85, 0x9d, 0xf0, 0xf9, 0xec, 0x09, 0xd3, 0xe7, 0x70,
|
||||
/* (2^223)P */ 0xf3, 0xbd, 0x96, 0x87, 0xe9, 0x71, 0xbd, 0xd6, 0xa2, 0x45, 0xeb, 0x0a, 0xcd, 0x2c, 0xf1, 0x72, 0xa6, 0x31, 0xa9, 0x6f, 0x09, 0xa1, 0x5e, 0xdd, 0xc8, 0x8d, 0x0d, 0xbc, 0x5a, 0x8d, 0xb1, 0x2c, 0x9a, 0xcc, 0x37, 0x74, 0xc2, 0xa9, 0x4e, 0xd6, 0xc0, 0x3c, 0xa0, 0x23, 0xb0, 0xa0, 0x77, 0x14, 0x80, 0x45, 0x71, 0x6a, 0x2d, 0x41, 0xc3, 0x82,
|
||||
/* (2^224)P */ 0x37, 0x44, 0xec, 0x8a, 0x3e, 0xc1, 0x0c, 0xa9, 0x12, 0x9c, 0x08, 0x88, 0xcb, 0xd9, 0xf8, 0xba, 0x00, 0xd6, 0xc3, 0xdf, 0xef, 0x7a, 0x44, 0x7e, 0x25, 0x69, 0xc9, 0xc1, 0x46, 0xe5, 0x20, 0x9e, 0xcc, 0x0b, 0x05, 0x3e, 0xf4, 0x78, 0x43, 0x0c, 0xa6, 0x2f, 0xc1, 0xfa, 0x70, 0xb2, 0x3c, 0x31, 0x7a, 0x63, 0x58, 0xab, 0x17, 0xcf, 0x4c, 0x4f,
|
||||
/* (2^225)P */ 0x2b, 0x08, 0x31, 0x59, 0x75, 0x8b, 0xec, 0x0a, 0xa9, 0x79, 0x70, 0xdd, 0xf1, 0x11, 0xc3, 0x11, 0x1f, 0xab, 0x37, 0xaa, 0x26, 0xea, 0x53, 0xc4, 0x79, 0xa7, 0x91, 0x00, 0xaa, 0x08, 0x42, 0xeb, 0x8b, 0x8b, 0xe8, 0xc3, 0x2f, 0xb8, 0x78, 0x90, 0x38, 0x0e, 0x8a, 0x42, 0x0c, 0x0f, 0xbf, 0x3e, 0xf8, 0xd8, 0x07, 0xcf, 0x6a, 0x34, 0xc9, 0xfa,
|
||||
/* (2^226)P */ 0x11, 0xe0, 0x76, 0x4d, 0x23, 0xc5, 0xa6, 0xcc, 0x9f, 0x9a, 0x2a, 0xde, 0x3a, 0xb5, 0x92, 0x39, 0x19, 0x8a, 0xf1, 0x8d, 0xf9, 0x4d, 0xc9, 0xb4, 0x39, 0x9f, 0x57, 0xd8, 0x72, 0xab, 0x1d, 0x61, 0x6a, 0xb2, 0xff, 0x52, 0xba, 0x54, 0x0e, 0xfb, 0x83, 0x30, 0x8a, 0xf7, 0x3b, 0xf4, 0xd8, 0xae, 0x1a, 0x94, 0x3a, 0xec, 0x63, 0xfe, 0x6e, 0x7c,
|
||||
/* (2^227)P */ 0xdc, 0x70, 0x8e, 0x55, 0x44, 0xbf, 0xd2, 0x6a, 0xa0, 0x14, 0x61, 0x89, 0xd5, 0x55, 0x45, 0x3c, 0xf6, 0x40, 0x0d, 0x83, 0x85, 0x44, 0xb4, 0x62, 0x56, 0xfe, 0x60, 0xd7, 0x07, 0x1d, 0x47, 0x30, 0x3b, 0x73, 0xa4, 0xb5, 0xb7, 0xea, 0xac, 0xda, 0xf1, 0x17, 0xaa, 0x60, 0xdf, 0xe9, 0x84, 0xda, 0x31, 0x32, 0x61, 0xbf, 0xd0, 0x7e, 0x8a, 0x02,
|
||||
/* (2^228)P */ 0xb9, 0x51, 0xb3, 0x89, 0x21, 0x5d, 0xa2, 0xfe, 0x79, 0x2a, 0xb3, 0x2a, 0x3b, 0xe6, 0x6f, 0x2b, 0x22, 0x03, 0xea, 0x7b, 0x1f, 0xaf, 0x85, 0xc3, 0x38, 0x55, 0x5b, 0x8e, 0xb4, 0xaa, 0x77, 0xfe, 0x03, 0x6e, 0xda, 0x91, 0x24, 0x0c, 0x48, 0x39, 0x27, 0x43, 0x16, 0xd2, 0x0a, 0x0d, 0x43, 0xa3, 0x0e, 0xca, 0x45, 0xd1, 0x7f, 0xf5, 0xd3, 0x16,
|
||||
/* (2^229)P */ 0x3d, 0x32, 0x9b, 0x38, 0xf8, 0x06, 0x93, 0x78, 0x5b, 0x50, 0x2b, 0x06, 0xd8, 0x66, 0xfe, 0xab, 0x9b, 0x58, 0xc7, 0xd1, 0x4d, 0xd5, 0xf8, 0x3b, 0x10, 0x7e, 0x85, 0xde, 0x58, 0x4e, 0xdf, 0x53, 0xd9, 0x58, 0xe0, 0x15, 0x81, 0x9f, 0x1a, 0x78, 0xfc, 0x9f, 0x10, 0xc2, 0x23, 0xd6, 0x78, 0xd1, 0x9d, 0xd2, 0xd5, 0x1c, 0x53, 0xe2, 0xc9, 0x76,
|
||||
/* (2^230)P */ 0x98, 0x1e, 0x38, 0x7b, 0x71, 0x18, 0x4b, 0x15, 0xaf, 0xa1, 0xa6, 0x98, 0xcb, 0x26, 0xa3, 0xc8, 0x07, 0x46, 0xda, 0x3b, 0x70, 0x65, 0xec, 0x7a, 0x2b, 0x34, 0x94, 0xa8, 0xb6, 0x14, 0xf8, 0x1a, 0xce, 0xf7, 0xc8, 0x60, 0xf3, 0x88, 0xf4, 0x33, 0x60, 0x7b, 0xd1, 0x02, 0xe7, 0xda, 0x00, 0x4a, 0xea, 0xd2, 0xfd, 0x88, 0xd2, 0x99, 0x28, 0xf3,
|
||||
/* (2^231)P */ 0x28, 0x24, 0x1d, 0x26, 0xc2, 0xeb, 0x8b, 0x3b, 0xb4, 0x6b, 0xbe, 0x6b, 0x77, 0xff, 0xf3, 0x21, 0x3b, 0x26, 0x6a, 0x8c, 0x8e, 0x2a, 0x44, 0xa8, 0x01, 0x2b, 0x71, 0xea, 0x64, 0x30, 0xfd, 0xfd, 0x95, 0xcb, 0x39, 0x38, 0x48, 0xfa, 0x96, 0x97, 0x8c, 0x2f, 0x33, 0xca, 0x03, 0xe6, 0xd7, 0x94, 0x55, 0x6c, 0xc3, 0xb3, 0xa8, 0xf7, 0xae, 0x8c,
|
||||
/* (2^232)P */ 0xea, 0x62, 0x8a, 0xb4, 0xeb, 0x74, 0xf7, 0xb8, 0xae, 0xc5, 0x20, 0x71, 0x06, 0xd6, 0x7c, 0x62, 0x9b, 0x69, 0x74, 0xef, 0xa7, 0x6d, 0xd6, 0x8c, 0x37, 0xb9, 0xbf, 0xcf, 0xeb, 0xe4, 0x2f, 0x04, 0x02, 0x21, 0x7d, 0x75, 0x6b, 0x92, 0x48, 0xf8, 0x70, 0xad, 0x69, 0xe2, 0xea, 0x0e, 0x88, 0x67, 0x72, 0xcc, 0x2d, 0x10, 0xce, 0x2d, 0xcf, 0x65,
|
||||
/* (2^233)P */ 0x49, 0xf3, 0x57, 0x64, 0xe5, 0x5c, 0xc5, 0x65, 0x49, 0x97, 0xc4, 0x8a, 0xcc, 0xa9, 0xca, 0x94, 0x7b, 0x86, 0x88, 0xb6, 0x51, 0x27, 0x69, 0xa5, 0x0f, 0x8b, 0x06, 0x59, 0xa0, 0x94, 0xef, 0x63, 0x1a, 0x01, 0x9e, 0x4f, 0xd2, 0x5a, 0x93, 0xc0, 0x7c, 0xe6, 0x61, 0x77, 0xb6, 0xf5, 0x40, 0xd9, 0x98, 0x43, 0x5b, 0x56, 0x68, 0xe9, 0x37, 0x8f,
|
||||
/* (2^234)P */ 0xee, 0x87, 0xd2, 0x05, 0x1b, 0x39, 0x89, 0x10, 0x07, 0x6d, 0xe8, 0xfd, 0x8b, 0x4d, 0xb2, 0xa7, 0x7b, 0x1e, 0xa0, 0x6c, 0x0d, 0x3d, 0x3d, 0x49, 0xba, 0x61, 0x36, 0x1f, 0xc2, 0x84, 0x4a, 0xcc, 0x87, 0xa9, 0x1b, 0x23, 0x04, 0xe2, 0x3e, 0x97, 0xe1, 0xdb, 0xd5, 0x5a, 0xe8, 0x41, 0x6b, 0xe5, 0x5a, 0xa1, 0x99, 0xe5, 0x7b, 0xa7, 0xe0, 0x3b,
|
||||
/* (2^235)P */ 0xea, 0xa3, 0x6a, 0xdd, 0x77, 0x7f, 0x77, 0x41, 0xc5, 0x6a, 0xe4, 0xaf, 0x11, 0x5f, 0x88, 0xa5, 0x10, 0xee, 0xd0, 0x8c, 0x0c, 0xb4, 0xa5, 0x2a, 0xd0, 0xd8, 0x1d, 0x47, 0x06, 0xc0, 0xd5, 0xce, 0x51, 0x54, 0x9b, 0x2b, 0xe6, 0x2f, 0xe7, 0xe7, 0x31, 0x5f, 0x5c, 0x23, 0x81, 0x3e, 0x03, 0x93, 0xaa, 0x2d, 0x71, 0x84, 0xa0, 0x89, 0x32, 0xa6,
|
||||
/* (2^236)P */ 0x55, 0xa3, 0x13, 0x92, 0x4e, 0x93, 0x7d, 0xec, 0xca, 0x57, 0xfb, 0x37, 0xae, 0xd2, 0x18, 0x2e, 0x54, 0x05, 0x6c, 0xd1, 0x28, 0xca, 0x90, 0x40, 0x82, 0x2e, 0x79, 0xc6, 0x5a, 0xc7, 0xdd, 0x84, 0x93, 0xdf, 0x15, 0xb8, 0x1f, 0xb1, 0xf9, 0xaf, 0x2c, 0xe5, 0x32, 0xcd, 0xc2, 0x99, 0x6d, 0xac, 0x85, 0x5c, 0x63, 0xd3, 0xe2, 0xff, 0x24, 0xda,
|
||||
/* (2^237)P */ 0x2d, 0x8d, 0xfd, 0x65, 0xcc, 0xe5, 0x02, 0xa0, 0xe5, 0xb9, 0xec, 0x59, 0x09, 0x50, 0x27, 0xb7, 0x3d, 0x2a, 0x79, 0xb2, 0x76, 0x5d, 0x64, 0x95, 0xf8, 0xc5, 0xaf, 0x8a, 0x62, 0x11, 0x5c, 0x56, 0x1c, 0x05, 0x64, 0x9e, 0x5e, 0xbd, 0x54, 0x04, 0xe6, 0x9e, 0xab, 0xe6, 0x22, 0x7e, 0x42, 0x54, 0xb5, 0xa5, 0xd0, 0x8d, 0x28, 0x6b, 0x0f, 0x0b,
|
||||
/* (2^238)P */ 0x2d, 0xb2, 0x8c, 0x59, 0x10, 0x37, 0x84, 0x3b, 0x9b, 0x65, 0x1b, 0x0f, 0x10, 0xf9, 0xea, 0x60, 0x1b, 0x02, 0xf5, 0xee, 0x8b, 0xe6, 0x32, 0x7d, 0x10, 0x7f, 0x5f, 0x8c, 0x72, 0x09, 0x4e, 0x1f, 0x29, 0xff, 0x65, 0xcb, 0x3e, 0x3a, 0xd2, 0x96, 0x50, 0x1e, 0xea, 0x64, 0x99, 0xb5, 0x4c, 0x7a, 0x69, 0xb8, 0x95, 0xae, 0x48, 0xc0, 0x7c, 0xb1,
|
||||
/* (2^239)P */ 0xcd, 0x7c, 0x4f, 0x3e, 0xea, 0xf3, 0x90, 0xcb, 0x12, 0x76, 0xd1, 0x17, 0xdc, 0x0d, 0x13, 0x0f, 0xfd, 0x4d, 0xb5, 0x1f, 0xe4, 0xdd, 0xf2, 0x4d, 0x58, 0xea, 0xa5, 0x66, 0x92, 0xcf, 0xe5, 0x54, 0xea, 0x9b, 0x35, 0x83, 0x1a, 0x44, 0x8e, 0x62, 0x73, 0x45, 0x98, 0xa3, 0x89, 0x95, 0x52, 0x93, 0x1a, 0x8d, 0x63, 0x0f, 0xc2, 0x57, 0x3c, 0xb1,
|
||||
/* (2^240)P */ 0x72, 0xb4, 0xdf, 0x51, 0xb7, 0xf6, 0x52, 0xa2, 0x14, 0x56, 0xe5, 0x0a, 0x2e, 0x75, 0x81, 0x02, 0xee, 0x93, 0x48, 0x0a, 0x92, 0x4e, 0x0c, 0x0f, 0xdf, 0x09, 0x89, 0x99, 0xf6, 0xf9, 0x22, 0xa2, 0x32, 0xf8, 0xb0, 0x76, 0x0c, 0xb2, 0x4d, 0x6e, 0xbe, 0x83, 0x35, 0x61, 0x44, 0xd2, 0x58, 0xc7, 0xdd, 0x14, 0xcf, 0xc3, 0x4b, 0x7c, 0x07, 0xee,
|
||||
/* (2^241)P */ 0x8b, 0x03, 0xee, 0xcb, 0xa7, 0x2e, 0x28, 0xbd, 0x97, 0xd1, 0x4c, 0x2b, 0xd1, 0x92, 0x67, 0x5b, 0x5a, 0x12, 0xbf, 0x29, 0x17, 0xfc, 0x50, 0x09, 0x74, 0x76, 0xa2, 0xd4, 0x82, 0xfd, 0x2c, 0x0c, 0x90, 0xf7, 0xe7, 0xe5, 0x9a, 0x2c, 0x16, 0x40, 0xb9, 0x6c, 0xd9, 0xe0, 0x22, 0x9e, 0xf8, 0xdd, 0x73, 0xe4, 0x7b, 0x9e, 0xbe, 0x4f, 0x66, 0x22,
|
||||
/* (2^242)P */ 0xa4, 0x10, 0xbe, 0xb8, 0x83, 0x3a, 0x77, 0x8e, 0xea, 0x0a, 0xc4, 0x97, 0x3e, 0xb6, 0x6c, 0x81, 0xd7, 0x65, 0xd9, 0xf7, 0xae, 0xe6, 0xbe, 0xab, 0x59, 0x81, 0x29, 0x4b, 0xff, 0xe1, 0x0f, 0xc3, 0x2b, 0xad, 0x4b, 0xef, 0xc4, 0x50, 0x9f, 0x88, 0x31, 0xf2, 0xde, 0x80, 0xd6, 0xf4, 0x20, 0x9c, 0x77, 0x9b, 0xbe, 0xbe, 0x08, 0xf5, 0xf0, 0x95,
|
||||
/* (2^243)P */ 0x0e, 0x7c, 0x7b, 0x7c, 0xb3, 0xd8, 0x83, 0xfc, 0x8c, 0x75, 0x51, 0x74, 0x1b, 0xe1, 0x6d, 0x11, 0x05, 0x46, 0x24, 0x0d, 0xa4, 0x2b, 0x32, 0xfd, 0x2c, 0x4e, 0x21, 0xdf, 0x39, 0x6b, 0x96, 0xfc, 0xff, 0x92, 0xfc, 0x35, 0x0d, 0x9a, 0x4b, 0xc0, 0x70, 0x46, 0x32, 0x7d, 0xc0, 0xc4, 0x04, 0xe0, 0x2d, 0x83, 0xa7, 0x00, 0xc7, 0xcb, 0xb4, 0x8f,
|
||||
/* (2^244)P */ 0xa9, 0x5a, 0x7f, 0x0e, 0xdd, 0x2c, 0x85, 0xaa, 0x4d, 0xac, 0xde, 0xb3, 0xb6, 0xaf, 0xe6, 0xd1, 0x06, 0x7b, 0x2c, 0xa4, 0x01, 0x19, 0x22, 0x7d, 0x78, 0xf0, 0x3a, 0xea, 0x89, 0xfe, 0x21, 0x61, 0x6d, 0xb8, 0xfe, 0xa5, 0x2a, 0xab, 0x0d, 0x7b, 0x51, 0x39, 0xb6, 0xde, 0xbc, 0xf0, 0xc5, 0x48, 0xd7, 0x09, 0x82, 0x6e, 0x66, 0x75, 0xc5, 0xcd,
|
||||
/* (2^245)P */ 0xee, 0xdf, 0x2b, 0x6c, 0xa8, 0xde, 0x61, 0xe1, 0x27, 0xfa, 0x2a, 0x0f, 0x68, 0xe7, 0x7a, 0x9b, 0x13, 0xe9, 0x56, 0xd2, 0x1c, 0x3d, 0x2f, 0x3c, 0x7a, 0xf6, 0x6f, 0x45, 0xee, 0xe8, 0xf4, 0xa0, 0xa6, 0xe8, 0xa5, 0x27, 0xee, 0xf2, 0x85, 0xa9, 0xd5, 0x0e, 0xa9, 0x26, 0x60, 0xfe, 0xee, 0xc7, 0x59, 0x99, 0x5e, 0xa3, 0xdf, 0x23, 0x36, 0xd5,
|
||||
/* (2^246)P */ 0x15, 0x66, 0x6f, 0xd5, 0x78, 0xa4, 0x0a, 0xf7, 0xb1, 0xe8, 0x75, 0x6b, 0x48, 0x7d, 0xa6, 0x4d, 0x3d, 0x36, 0x9b, 0xc7, 0xcc, 0x68, 0x9a, 0xfe, 0x2f, 0x39, 0x2a, 0x51, 0x31, 0x39, 0x7d, 0x73, 0x6f, 0xc8, 0x74, 0x72, 0x6f, 0x6e, 0xda, 0x5f, 0xad, 0x48, 0xc8, 0x40, 0xe1, 0x06, 0x01, 0x36, 0xa1, 0x88, 0xc8, 0x99, 0x9c, 0xd1, 0x11, 0x8f,
|
||||
/* (2^247)P */ 0xab, 0xc5, 0xcb, 0xcf, 0xbd, 0x73, 0x21, 0xd0, 0x82, 0xb1, 0x2e, 0x2d, 0xd4, 0x36, 0x1b, 0xed, 0xa9, 0x8a, 0x26, 0x79, 0xc4, 0x17, 0xae, 0xe5, 0x09, 0x0a, 0x0c, 0xa4, 0x21, 0xa0, 0x6e, 0xdd, 0x62, 0x8e, 0x44, 0x62, 0xcc, 0x50, 0xff, 0x93, 0xb3, 0x9a, 0x72, 0x8c, 0x3f, 0xa1, 0xa6, 0x4d, 0x87, 0xd5, 0x1c, 0x5a, 0xc0, 0x0b, 0x1a, 0xd6,
|
||||
/* (2^248)P */ 0x67, 0x36, 0x6a, 0x1f, 0x96, 0xe5, 0x80, 0x20, 0xa9, 0xe8, 0x0b, 0x0e, 0x21, 0x29, 0x3f, 0xc8, 0x0a, 0x6d, 0x27, 0x47, 0xca, 0xd9, 0x05, 0x55, 0xbf, 0x11, 0xcf, 0x31, 0x7a, 0x37, 0xc7, 0x90, 0xa9, 0xf4, 0x07, 0x5e, 0xd5, 0xc3, 0x92, 0xaa, 0x95, 0xc8, 0x23, 0x2a, 0x53, 0x45, 0xe3, 0x3a, 0x24, 0xe9, 0x67, 0x97, 0x3a, 0x82, 0xf9, 0xa6,
|
||||
/* (2^249)P */ 0x92, 0x9e, 0x6d, 0x82, 0x67, 0xe9, 0xf9, 0x17, 0x96, 0x2c, 0xa7, 0xd3, 0x89, 0xf9, 0xdb, 0xd8, 0x20, 0xc6, 0x2e, 0xec, 0x4a, 0x76, 0x64, 0xbf, 0x27, 0x40, 0xe2, 0xb4, 0xdf, 0x1f, 0xa0, 0xef, 0x07, 0x80, 0xfb, 0x8e, 0x12, 0xf8, 0xb8, 0xe1, 0xc6, 0xdf, 0x7c, 0x69, 0x35, 0x5a, 0xe1, 0x8e, 0x5d, 0x69, 0x84, 0x56, 0xb6, 0x31, 0x1c, 0x0b,
|
||||
/* (2^250)P */ 0xd6, 0x94, 0x5c, 0xef, 0xbb, 0x46, 0x45, 0x44, 0x5b, 0xa1, 0xae, 0x03, 0x65, 0xdd, 0xb5, 0x66, 0x88, 0x35, 0x29, 0x95, 0x16, 0x54, 0xa6, 0xf5, 0xc9, 0x78, 0x34, 0xe6, 0x0f, 0xc4, 0x2b, 0x5b, 0x79, 0x51, 0x68, 0x48, 0x3a, 0x26, 0x87, 0x05, 0x70, 0xaf, 0x8b, 0xa6, 0xc7, 0x2e, 0xb3, 0xa9, 0x10, 0x01, 0xb0, 0xb9, 0x31, 0xfd, 0xdc, 0x80,
|
||||
/* (2^251)P */ 0x25, 0xf2, 0xad, 0xd6, 0x75, 0xa3, 0x04, 0x05, 0x64, 0x8a, 0x97, 0x60, 0x27, 0x2a, 0xe5, 0x6d, 0xb0, 0x73, 0xf4, 0x07, 0x2a, 0x9d, 0xe9, 0x46, 0xb4, 0x1c, 0x51, 0xf8, 0x63, 0x98, 0x7e, 0xe5, 0x13, 0x51, 0xed, 0x98, 0x65, 0x98, 0x4f, 0x8f, 0xe7, 0x7e, 0x72, 0xd7, 0x64, 0x11, 0x2f, 0xcd, 0x12, 0xf8, 0xc4, 0x63, 0x52, 0x0f, 0x7f, 0xc4,
|
||||
/* (2^252)P */ 0x5c, 0xd9, 0x85, 0x63, 0xc7, 0x8a, 0x65, 0x9a, 0x25, 0x83, 0x31, 0x73, 0x49, 0xf0, 0x93, 0x96, 0x70, 0x67, 0x6d, 0xb1, 0xff, 0x95, 0x54, 0xe4, 0xf8, 0x15, 0x6c, 0x5f, 0xbd, 0xf6, 0x0f, 0x38, 0x7b, 0x68, 0x7d, 0xd9, 0x3d, 0xf0, 0xa9, 0xa0, 0xe4, 0xd1, 0xb6, 0x34, 0x6d, 0x14, 0x16, 0xc2, 0x4c, 0x30, 0x0e, 0x67, 0xd3, 0xbe, 0x2e, 0xc0,
|
||||
/* (2^253)P */ 0x06, 0x6b, 0x52, 0xc8, 0x14, 0xcd, 0xae, 0x03, 0x93, 0xea, 0xc1, 0xf2, 0xf6, 0x8b, 0xc5, 0xb6, 0xdc, 0x82, 0x42, 0x29, 0x94, 0xe0, 0x25, 0x6c, 0x3f, 0x9f, 0x5d, 0xe4, 0x96, 0xf6, 0x8e, 0x3f, 0xf9, 0x72, 0xc4, 0x77, 0x60, 0x8b, 0xa4, 0xf9, 0xa8, 0xc3, 0x0a, 0x81, 0xb1, 0x97, 0x70, 0x18, 0xab, 0xea, 0x37, 0x8a, 0x08, 0xc7, 0xe2, 0x95,
|
||||
/* (2^254)P */ 0x94, 0x49, 0xd9, 0x5f, 0x76, 0x72, 0x82, 0xad, 0x2d, 0x50, 0x1a, 0x7a, 0x5b, 0xe6, 0x95, 0x1e, 0x95, 0x65, 0x87, 0x1c, 0x52, 0xd7, 0x44, 0xe6, 0x9b, 0x56, 0xcd, 0x6f, 0x05, 0xff, 0x67, 0xc5, 0xdb, 0xa2, 0xac, 0xe4, 0xa2, 0x28, 0x63, 0x5f, 0xfb, 0x0c, 0x3b, 0xf1, 0x87, 0xc3, 0x36, 0x78, 0x3f, 0x77, 0xfa, 0x50, 0x85, 0xf9, 0xd7, 0x82,
|
||||
/* (2^255)P */ 0x64, 0xc0, 0xe0, 0xd8, 0x2d, 0xed, 0xcb, 0x6a, 0xfd, 0xcd, 0xbc, 0x7e, 0x9f, 0xc8, 0x85, 0xe9, 0xc1, 0x7c, 0x0f, 0xe5, 0x18, 0xea, 0xd4, 0x51, 0xad, 0x59, 0x13, 0x75, 0xd9, 0x3d, 0xd4, 0x8a, 0xb2, 0xbe, 0x78, 0x52, 0x2b, 0x52, 0x94, 0x37, 0x41, 0xd6, 0xb4, 0xb6, 0x45, 0x20, 0x76, 0xe0, 0x1f, 0x31, 0xdb, 0xb1, 0xa1, 0x43, 0xf0, 0x18,
|
||||
/* (2^256)P */ 0x74, 0xa9, 0xa4, 0xa9, 0xdd, 0x6e, 0x3e, 0x68, 0xe5, 0xc3, 0x2e, 0x92, 0x17, 0xa4, 0xcb, 0x80, 0xb1, 0xf0, 0x06, 0x93, 0xef, 0xe6, 0x00, 0xe6, 0x3b, 0xb1, 0x32, 0x65, 0x7b, 0x83, 0xb6, 0x8a, 0x49, 0x1b, 0x14, 0x89, 0xee, 0xba, 0xf5, 0x6a, 0x8d, 0x36, 0xef, 0xb0, 0xd8, 0xb2, 0x16, 0x99, 0x17, 0x35, 0x02, 0x16, 0x55, 0x58, 0xdd, 0x82,
|
||||
/* (2^257)P */ 0x36, 0x95, 0xe8, 0xf4, 0x36, 0x42, 0xbb, 0xc5, 0x3e, 0xfa, 0x30, 0x84, 0x9e, 0x59, 0xfd, 0xd2, 0x95, 0x42, 0xf8, 0x64, 0xd9, 0xb9, 0x0e, 0x9f, 0xfa, 0xd0, 0x7b, 0x20, 0x31, 0x77, 0x48, 0x29, 0x4d, 0xd0, 0x32, 0x57, 0x56, 0x30, 0xa6, 0x17, 0x53, 0x04, 0xbf, 0x08, 0x28, 0xec, 0xb8, 0x46, 0xc1, 0x03, 0x89, 0xdc, 0xed, 0xa0, 0x35, 0x53,
|
||||
/* (2^258)P */ 0xc5, 0x7f, 0x9e, 0xd8, 0xc5, 0xba, 0x5f, 0x68, 0xc8, 0x23, 0x75, 0xea, 0x0d, 0xd9, 0x5a, 0xfd, 0x61, 0x1a, 0xa3, 0x2e, 0x45, 0x63, 0x14, 0x55, 0x86, 0x21, 0x29, 0xbe, 0xef, 0x5e, 0x50, 0xe5, 0x18, 0x59, 0xe7, 0xe3, 0xce, 0x4d, 0x8c, 0x15, 0x8f, 0x89, 0x66, 0x44, 0x52, 0x3d, 0xfa, 0xc7, 0x9a, 0x59, 0x90, 0x8e, 0xc0, 0x06, 0x3f, 0xc9,
|
||||
/* (2^259)P */ 0x8e, 0x04, 0xd9, 0x16, 0x50, 0x1d, 0x8c, 0x9f, 0xd5, 0xe3, 0xce, 0xfd, 0x47, 0x04, 0x27, 0x4d, 0xc2, 0xfa, 0x71, 0xd9, 0x0b, 0xb8, 0x65, 0xf4, 0x11, 0xf3, 0x08, 0xee, 0x81, 0xc8, 0x67, 0x99, 0x0b, 0x8d, 0x77, 0xa3, 0x4f, 0xb5, 0x9b, 0xdb, 0x26, 0xf1, 0x97, 0xeb, 0x04, 0x54, 0xeb, 0x80, 0x08, 0x1d, 0x1d, 0xf6, 0x3d, 0x1f, 0x5a, 0xb8,
|
||||
/* (2^260)P */ 0xb7, 0x9c, 0x9d, 0xee, 0xb9, 0x5c, 0xad, 0x0d, 0x9e, 0xfd, 0x60, 0x3c, 0x27, 0x4e, 0xa2, 0x95, 0xfb, 0x64, 0x7e, 0x79, 0x64, 0x87, 0x10, 0xb4, 0x73, 0xe0, 0x9d, 0x46, 0x4d, 0x3d, 0xee, 0x83, 0xe4, 0x16, 0x88, 0x97, 0xe6, 0x4d, 0xba, 0x70, 0xb6, 0x96, 0x7b, 0xff, 0x4b, 0xc8, 0xcf, 0x72, 0x83, 0x3e, 0x5b, 0x24, 0x2e, 0x57, 0xf1, 0x82,
|
||||
/* (2^261)P */ 0x30, 0x71, 0x40, 0x51, 0x4f, 0x44, 0xbb, 0xc7, 0xf0, 0x54, 0x6e, 0x9d, 0xeb, 0x15, 0xad, 0xf8, 0x61, 0x43, 0x5a, 0xef, 0xc0, 0xb1, 0x57, 0xae, 0x03, 0x40, 0xe8, 0x68, 0x6f, 0x03, 0x20, 0x4f, 0x8a, 0x51, 0x2a, 0x9e, 0xd2, 0x45, 0xaf, 0xb4, 0xf5, 0xd4, 0x95, 0x7f, 0x3d, 0x3d, 0xb7, 0xb6, 0x28, 0xc5, 0x08, 0x8b, 0x44, 0xd6, 0x3f, 0xe7,
|
||||
/* (2^262)P */ 0xa9, 0x52, 0x04, 0x67, 0xcb, 0x20, 0x63, 0xf8, 0x18, 0x01, 0x44, 0x21, 0x6a, 0x8a, 0x83, 0x48, 0xd4, 0xaf, 0x23, 0x0f, 0x35, 0x8d, 0xe5, 0x5a, 0xc4, 0x7c, 0x55, 0x46, 0x19, 0x5f, 0x35, 0xe0, 0x5d, 0x97, 0x4c, 0x2d, 0x04, 0xed, 0x59, 0xd4, 0xb0, 0xb2, 0xc6, 0xe3, 0x51, 0xe1, 0x38, 0xc6, 0x30, 0x49, 0x8f, 0xae, 0x61, 0x64, 0xce, 0xa8,
|
||||
/* (2^263)P */ 0x9b, 0x64, 0x83, 0x3c, 0xd3, 0xdf, 0xb9, 0x27, 0xe7, 0x5b, 0x7f, 0xeb, 0xf3, 0x26, 0xcf, 0xb1, 0x8f, 0xaf, 0x26, 0xc8, 0x48, 0xce, 0xa1, 0xac, 0x7d, 0x10, 0x34, 0x28, 0xe1, 0x1f, 0x69, 0x03, 0x64, 0x77, 0x61, 0xdd, 0x4a, 0x9b, 0x18, 0x47, 0xf8, 0xca, 0x63, 0xc9, 0x03, 0x2d, 0x20, 0x2a, 0x69, 0x6e, 0x42, 0xd0, 0xe7, 0xaa, 0xb5, 0xf3,
|
||||
/* (2^264)P */ 0xea, 0x31, 0x0c, 0x57, 0x0f, 0x3e, 0xe3, 0x35, 0xd8, 0x30, 0xa5, 0x6f, 0xdd, 0x95, 0x43, 0xc6, 0x66, 0x07, 0x4f, 0x34, 0xc3, 0x7e, 0x04, 0x10, 0x2d, 0xc4, 0x1c, 0x94, 0x52, 0x2e, 0x5b, 0x9a, 0x65, 0x2f, 0x91, 0xaa, 0x4f, 0x3c, 0xdc, 0x23, 0x18, 0xe1, 0x4f, 0x85, 0xcd, 0xf4, 0x8c, 0x51, 0xf7, 0xab, 0x4f, 0xdc, 0x15, 0x5c, 0x9e, 0xc5,
|
||||
/* (2^265)P */ 0x54, 0x57, 0x23, 0x17, 0xe7, 0x82, 0x2f, 0x04, 0x7d, 0xfe, 0xe7, 0x1f, 0xa2, 0x57, 0x79, 0xe9, 0x58, 0x9b, 0xbe, 0xc6, 0x16, 0x4a, 0x17, 0x50, 0x90, 0x4a, 0x34, 0x70, 0x87, 0x37, 0x01, 0x26, 0xd8, 0xa3, 0x5f, 0x07, 0x7c, 0xd0, 0x7d, 0x05, 0x8a, 0x93, 0x51, 0x2f, 0x99, 0xea, 0xcf, 0x00, 0xd8, 0xc7, 0xe6, 0x9b, 0x8c, 0x62, 0x45, 0x87,
|
||||
/* (2^266)P */ 0xc3, 0xfd, 0x29, 0x66, 0xe7, 0x30, 0x29, 0x77, 0xe0, 0x0d, 0x63, 0x5b, 0xe6, 0x90, 0x1a, 0x1e, 0x99, 0xc2, 0xa7, 0xab, 0xff, 0xa7, 0xbd, 0x79, 0x01, 0x97, 0xfd, 0x27, 0x1b, 0x43, 0x2b, 0xe6, 0xfe, 0x5e, 0xf1, 0xb9, 0x35, 0x38, 0x08, 0x25, 0x55, 0x90, 0x68, 0x2e, 0xc3, 0x67, 0x39, 0x9f, 0x2b, 0x2c, 0x70, 0x48, 0x8c, 0x47, 0xee, 0x56,
|
||||
/* (2^267)P */ 0xf7, 0x32, 0x70, 0xb5, 0xe6, 0x42, 0xfd, 0x0a, 0x39, 0x9b, 0x07, 0xfe, 0x0e, 0xf4, 0x47, 0xba, 0x6a, 0x3f, 0xf5, 0x2c, 0x15, 0xf3, 0x60, 0x3f, 0xb1, 0x83, 0x7b, 0x2e, 0x34, 0x58, 0x1a, 0x6e, 0x4a, 0x49, 0x05, 0x45, 0xca, 0xdb, 0x00, 0x01, 0x0c, 0x42, 0x5e, 0x60, 0x40, 0x5f, 0xd9, 0xc7, 0x3a, 0x9e, 0x1c, 0x8d, 0xab, 0x11, 0x55, 0x65,
|
||||
/* (2^268)P */ 0x87, 0x40, 0xb7, 0x0d, 0xaa, 0x34, 0x89, 0x90, 0x75, 0x6d, 0xa2, 0xfe, 0x3b, 0x6d, 0x5c, 0x39, 0x98, 0x10, 0x9e, 0x15, 0xc5, 0x35, 0xa2, 0x27, 0x23, 0x0a, 0x2d, 0x60, 0xe2, 0xa8, 0x7f, 0x3e, 0x77, 0x8f, 0xcc, 0x44, 0xcc, 0x30, 0x28, 0xe2, 0xf0, 0x04, 0x8c, 0xee, 0xe4, 0x5f, 0x68, 0x8c, 0xdf, 0x70, 0xbf, 0x31, 0xee, 0x2a, 0xfc, 0xce,
|
||||
/* (2^269)P */ 0x92, 0xf2, 0xa0, 0xd9, 0x58, 0x3b, 0x7c, 0x1a, 0x99, 0x46, 0x59, 0x54, 0x60, 0x06, 0x8d, 0x5e, 0xf0, 0x22, 0xa1, 0xed, 0x92, 0x8a, 0x4d, 0x76, 0x95, 0x05, 0x0b, 0xff, 0xfc, 0x9a, 0xd1, 0xcc, 0x05, 0xb9, 0x5e, 0x99, 0xe8, 0x2a, 0x76, 0x7b, 0xfd, 0xa6, 0xe2, 0xd1, 0x1a, 0xd6, 0x76, 0x9f, 0x2f, 0x0e, 0xd1, 0xa8, 0x77, 0x5a, 0x40, 0x5a,
|
||||
/* (2^270)P */ 0xff, 0xf9, 0x3f, 0xa9, 0xa6, 0x6c, 0x6d, 0x03, 0x8b, 0xa7, 0x10, 0x5d, 0x3f, 0xec, 0x3e, 0x1c, 0x0b, 0x6b, 0xa2, 0x6a, 0x22, 0xa9, 0x28, 0xd0, 0x66, 0xc9, 0xc2, 0x3d, 0x47, 0x20, 0x7d, 0xa6, 0x1d, 0xd8, 0x25, 0xb5, 0xf2, 0xf9, 0x70, 0x19, 0x6b, 0xf8, 0x43, 0x36, 0xc5, 0x1f, 0xe4, 0x5a, 0x4c, 0x13, 0xe4, 0x6d, 0x08, 0x0b, 0x1d, 0xb1,
|
||||
/* (2^271)P */ 0x3f, 0x20, 0x9b, 0xfb, 0xec, 0x7d, 0x31, 0xc5, 0xfc, 0x88, 0x0b, 0x30, 0xed, 0x36, 0xc0, 0x63, 0xb1, 0x7d, 0x10, 0xda, 0xb6, 0x2e, 0xad, 0xf3, 0xec, 0x94, 0xe7, 0xec, 0xb5, 0x9c, 0xfe, 0xf5, 0x35, 0xf0, 0xa2, 0x2d, 0x7f, 0xca, 0x6b, 0x67, 0x1a, 0xf6, 0xb3, 0xda, 0x09, 0x2a, 0xaa, 0xdf, 0xb1, 0xca, 0x9b, 0xfb, 0xeb, 0xb3, 0xcd, 0xc0,
|
||||
/* (2^272)P */ 0xcd, 0x4d, 0x89, 0x00, 0xa4, 0x3b, 0x48, 0xf0, 0x76, 0x91, 0x35, 0xa5, 0xf8, 0xc9, 0xb6, 0x46, 0xbc, 0xf6, 0x9a, 0x45, 0x47, 0x17, 0x96, 0x80, 0x5b, 0x3a, 0x28, 0x33, 0xf9, 0x5a, 0xef, 0x43, 0x07, 0xfe, 0x3b, 0xf4, 0x8e, 0x19, 0xce, 0xd2, 0x94, 0x4b, 0x6d, 0x8e, 0x67, 0x20, 0xc7, 0x4f, 0x2f, 0x59, 0x8e, 0xe1, 0xa1, 0xa9, 0xf9, 0x0e,
|
||||
/* (2^273)P */ 0xdc, 0x7b, 0xb5, 0x50, 0x2e, 0xe9, 0x7e, 0x8b, 0x78, 0xa1, 0x38, 0x96, 0x22, 0xc3, 0x61, 0x67, 0x6d, 0xc8, 0x58, 0xed, 0x41, 0x1d, 0x5d, 0x86, 0x98, 0x7f, 0x2f, 0x1b, 0x8d, 0x3e, 0xaa, 0xc1, 0xd2, 0x0a, 0xf3, 0xbf, 0x95, 0x04, 0xf3, 0x10, 0x3c, 0x2b, 0x7f, 0x90, 0x46, 0x04, 0xaa, 0x6a, 0xa9, 0x35, 0x76, 0xac, 0x49, 0xb5, 0x00, 0x45,
|
||||
/* (2^274)P */ 0xb1, 0x93, 0x79, 0x84, 0x4a, 0x2a, 0x30, 0x78, 0x16, 0xaa, 0xc5, 0x74, 0x06, 0xce, 0xa5, 0xa7, 0x32, 0x86, 0xe0, 0xf9, 0x10, 0xd2, 0x58, 0x76, 0xfb, 0x66, 0x49, 0x76, 0x3a, 0x90, 0xba, 0xb5, 0xcc, 0x99, 0xcd, 0x09, 0xc1, 0x9a, 0x74, 0x23, 0xdf, 0x0c, 0xfe, 0x99, 0x52, 0x80, 0xa3, 0x7c, 0x1c, 0x71, 0x5f, 0x2c, 0x49, 0x57, 0xf4, 0xf9,
|
||||
/* (2^275)P */ 0x6d, 0xbf, 0x52, 0xe6, 0x25, 0x98, 0xed, 0xcf, 0xe3, 0xbc, 0x08, 0xa2, 0x1a, 0x90, 0xae, 0xa0, 0xbf, 0x07, 0x15, 0xad, 0x0a, 0x9f, 0x3e, 0x47, 0x44, 0xc2, 0x10, 0x46, 0xa6, 0x7a, 0x9e, 0x2f, 0x57, 0xbc, 0xe2, 0xf0, 0x1d, 0xd6, 0x9a, 0x06, 0xed, 0xfc, 0x54, 0x95, 0x92, 0x15, 0xa2, 0xf7, 0x8d, 0x6b, 0xef, 0xb2, 0x05, 0xed, 0x5c, 0x63,
|
||||
/* (2^276)P */ 0xbc, 0x0b, 0x27, 0x3a, 0x3a, 0xf8, 0xe1, 0x48, 0x02, 0x7e, 0x27, 0xe6, 0x81, 0x62, 0x07, 0x73, 0x74, 0xe5, 0x52, 0xd7, 0xf8, 0x26, 0xca, 0x93, 0x4d, 0x3e, 0x9b, 0x55, 0x09, 0x8e, 0xe3, 0xd7, 0xa6, 0xe3, 0xb6, 0x2a, 0xa9, 0xb3, 0xb0, 0xa0, 0x8c, 0x01, 0xbb, 0x07, 0x90, 0x78, 0x6d, 0x6d, 0xe9, 0xf0, 0x7a, 0x90, 0xbd, 0xdc, 0x0c, 0x36,
|
||||
/* (2^277)P */ 0x7f, 0x20, 0x12, 0x0f, 0x40, 0x00, 0x53, 0xd8, 0x0c, 0x27, 0x47, 0x47, 0x22, 0x80, 0xfb, 0x62, 0xe4, 0xa7, 0xf7, 0xbd, 0x42, 0xa5, 0xc3, 0x2b, 0xb2, 0x7f, 0x50, 0xcc, 0xe2, 0xfb, 0xd5, 0xc0, 0x63, 0xdd, 0x24, 0x5f, 0x7c, 0x08, 0x91, 0xbf, 0x6e, 0x47, 0x44, 0xd4, 0x6a, 0xc0, 0xc3, 0x09, 0x39, 0x27, 0xdd, 0xc7, 0xca, 0x06, 0x29, 0x55,
|
||||
/* (2^278)P */ 0x76, 0x28, 0x58, 0xb0, 0xd2, 0xf3, 0x0f, 0x04, 0xe9, 0xc9, 0xab, 0x66, 0x5b, 0x75, 0x51, 0xdc, 0xe5, 0x8f, 0xe8, 0x1f, 0xdb, 0x03, 0x0f, 0xb0, 0x7d, 0xf9, 0x20, 0x64, 0x89, 0xe9, 0xdc, 0xe6, 0x24, 0xc3, 0xd5, 0xd2, 0x41, 0xa6, 0xe4, 0xe3, 0xc4, 0x79, 0x7c, 0x0f, 0xa1, 0x61, 0x2f, 0xda, 0xa4, 0xc9, 0xfd, 0xad, 0x5c, 0x65, 0x6a, 0xf3,
|
||||
/* (2^279)P */ 0xd5, 0xab, 0x72, 0x7a, 0x3b, 0x59, 0xea, 0xcf, 0xd5, 0x17, 0xd2, 0xb2, 0x5f, 0x2d, 0xab, 0xad, 0x9e, 0x88, 0x64, 0x55, 0x96, 0x6e, 0xf3, 0x44, 0xa9, 0x11, 0xf5, 0xf8, 0x3a, 0xf1, 0xcd, 0x79, 0x4c, 0x99, 0x6d, 0x23, 0x6a, 0xa0, 0xc2, 0x1a, 0x19, 0x45, 0xb5, 0xd8, 0x95, 0x2f, 0x49, 0xe9, 0x46, 0x39, 0x26, 0x60, 0x04, 0x15, 0x8b, 0xcc,
|
||||
/* (2^280)P */ 0x66, 0x0c, 0xf0, 0x54, 0x41, 0x02, 0x91, 0xab, 0xe5, 0x85, 0x8a, 0x44, 0xa6, 0x34, 0x96, 0x32, 0xc0, 0xdf, 0x6c, 0x41, 0x39, 0xd4, 0xc6, 0xe1, 0xe3, 0x81, 0xb0, 0x4c, 0x34, 0x4f, 0xe5, 0xf4, 0x35, 0x46, 0x1f, 0xeb, 0x75, 0xfd, 0x43, 0x37, 0x50, 0x99, 0xab, 0xad, 0xb7, 0x8c, 0xa1, 0x57, 0xcb, 0xe6, 0xce, 0x16, 0x2e, 0x85, 0xcc, 0xf9,
|
||||
/* (2^281)P */ 0x63, 0xd1, 0x3f, 0x9e, 0xa2, 0x17, 0x2e, 0x1d, 0x3e, 0xce, 0x48, 0x2d, 0xbb, 0x8f, 0x69, 0xc9, 0xa6, 0x3d, 0x4e, 0xfe, 0x09, 0x56, 0xb3, 0x02, 0x5f, 0x99, 0x97, 0x0c, 0x54, 0xda, 0x32, 0x97, 0x9b, 0xf4, 0x95, 0xf1, 0xad, 0xe3, 0x2b, 0x04, 0xa7, 0x9b, 0x3f, 0xbb, 0xe7, 0x87, 0x2e, 0x1f, 0x8b, 0x4b, 0x7a, 0xa4, 0x43, 0x0c, 0x0f, 0x35,
|
||||
/* (2^282)P */ 0x05, 0xdc, 0xe0, 0x2c, 0xa1, 0xc1, 0xd0, 0xf1, 0x1f, 0x4e, 0xc0, 0x6c, 0x35, 0x7b, 0xca, 0x8f, 0x8b, 0x02, 0xb1, 0xf7, 0xd6, 0x2e, 0xe7, 0x93, 0x80, 0x85, 0x18, 0x88, 0x19, 0xb9, 0xb4, 0x4a, 0xbc, 0xeb, 0x5a, 0x78, 0x38, 0xed, 0xc6, 0x27, 0x2a, 0x74, 0x76, 0xf0, 0x1b, 0x79, 0x92, 0x2f, 0xd2, 0x81, 0x98, 0xdf, 0xa9, 0x50, 0x19, 0xeb,
|
||||
/* (2^283)P */ 0xb5, 0xe7, 0xb4, 0x11, 0x3a, 0x81, 0xb6, 0xb4, 0xf8, 0xa2, 0xb3, 0x6c, 0xfc, 0x9d, 0xe0, 0xc0, 0xe0, 0x59, 0x7f, 0x05, 0x37, 0xef, 0x2c, 0xa9, 0x3a, 0x24, 0xac, 0x7b, 0x25, 0xa0, 0x55, 0xd2, 0x44, 0x82, 0x82, 0x6e, 0x64, 0xa3, 0x58, 0xc8, 0x67, 0xae, 0x26, 0xa7, 0x0f, 0x42, 0x63, 0xe1, 0x93, 0x01, 0x52, 0x19, 0xaf, 0x49, 0x3e, 0x33,
|
||||
/* (2^284)P */ 0x05, 0x85, 0xe6, 0x66, 0xaf, 0x5f, 0xdf, 0xbf, 0x9d, 0x24, 0x62, 0x60, 0x90, 0xe2, 0x4c, 0x7d, 0x4e, 0xc3, 0x74, 0x5d, 0x4f, 0x53, 0xf3, 0x63, 0x13, 0xf4, 0x74, 0x28, 0x6b, 0x7d, 0x57, 0x0c, 0x9d, 0x84, 0xa7, 0x1a, 0xff, 0xa0, 0x79, 0xdf, 0xfc, 0x65, 0x98, 0x8e, 0x22, 0x0d, 0x62, 0x7e, 0xf2, 0x34, 0x60, 0x83, 0x05, 0x14, 0xb1, 0xc1,
|
||||
/* (2^285)P */ 0x64, 0x22, 0xcc, 0xdf, 0x5c, 0xbc, 0x88, 0x68, 0x4c, 0xd9, 0xbc, 0x0e, 0xc9, 0x8b, 0xb4, 0x23, 0x52, 0xad, 0xb0, 0xb3, 0xf1, 0x17, 0xd8, 0x15, 0x04, 0x6b, 0x99, 0xf0, 0xc4, 0x7d, 0x48, 0x22, 0x4a, 0xf8, 0x6f, 0xaa, 0x88, 0x0d, 0xc5, 0x5e, 0xa9, 0x1c, 0x61, 0x3d, 0x95, 0xa9, 0x7b, 0x6a, 0x79, 0x33, 0x0a, 0x2b, 0x99, 0xe3, 0x4e, 0x48,
|
||||
/* (2^286)P */ 0x6b, 0x9b, 0x6a, 0x2a, 0xf1, 0x60, 0x31, 0xb4, 0x73, 0xd1, 0x87, 0x45, 0x9c, 0x15, 0x58, 0x4b, 0x91, 0x6d, 0x94, 0x1c, 0x41, 0x11, 0x4a, 0x83, 0xec, 0xaf, 0x65, 0xbc, 0x34, 0xaa, 0x26, 0xe2, 0xaf, 0xed, 0x46, 0x05, 0x4e, 0xdb, 0xc6, 0x4e, 0x10, 0x28, 0x4e, 0x72, 0xe5, 0x31, 0xa3, 0x20, 0xd7, 0xb1, 0x96, 0x64, 0xf6, 0xce, 0x08, 0x08,
|
||||
/* (2^287)P */ 0x16, 0xa9, 0x5c, 0x9f, 0x9a, 0xb4, 0xb8, 0xc8, 0x32, 0x78, 0xc0, 0x3a, 0xd9, 0x5f, 0x94, 0xac, 0x3a, 0x42, 0x1f, 0x43, 0xd6, 0x80, 0x47, 0x2c, 0xdc, 0x76, 0x27, 0xfa, 0x50, 0xe5, 0xa1, 0xe4, 0xc3, 0xcb, 0x61, 0x31, 0xe1, 0x2e, 0xde, 0x81, 0x3b, 0x77, 0x1c, 0x39, 0x3c, 0xdb, 0xda, 0x87, 0x4b, 0x84, 0x12, 0xeb, 0xdd, 0x54, 0xbf, 0xe7,
|
||||
/* (2^288)P */ 0xbf, 0xcb, 0x73, 0x21, 0x3d, 0x7e, 0x13, 0x8c, 0xa6, 0x34, 0x21, 0x2b, 0xa5, 0xe4, 0x9f, 0x8e, 0x9c, 0x01, 0x9c, 0x43, 0xd9, 0xc7, 0xb9, 0xf1, 0xbe, 0x7f, 0x45, 0x51, 0x97, 0xa1, 0x8e, 0x01, 0xf8, 0xbd, 0xd2, 0xbf, 0x81, 0x3a, 0x8b, 0xab, 0xe4, 0x89, 0xb7, 0xbd, 0xf2, 0xcd, 0xa9, 0x8a, 0x8a, 0xde, 0xfb, 0x8a, 0x55, 0x12, 0x7b, 0x17,
|
||||
/* (2^289)P */ 0x1b, 0x95, 0x58, 0x4d, 0xe6, 0x51, 0x31, 0x52, 0x1c, 0xd8, 0x15, 0x84, 0xb1, 0x0d, 0x36, 0x25, 0x88, 0x91, 0x46, 0x71, 0x42, 0x56, 0xe2, 0x90, 0x08, 0x9e, 0x77, 0x1b, 0xee, 0x22, 0x3f, 0xec, 0xee, 0x8c, 0x7b, 0x2e, 0x79, 0xc4, 0x6c, 0x07, 0xa1, 0x7e, 0x52, 0xf5, 0x26, 0x5c, 0x84, 0x2a, 0x50, 0x6e, 0x82, 0xb3, 0x76, 0xda, 0x35, 0x16,
|
||||
/* (2^290)P */ 0x0a, 0x6f, 0x99, 0x87, 0xc0, 0x7d, 0x8a, 0xb2, 0xca, 0xae, 0xe8, 0x65, 0x98, 0x0f, 0xb3, 0x44, 0xe1, 0xdc, 0x52, 0x79, 0x75, 0xec, 0x8f, 0x95, 0x87, 0x45, 0xd1, 0x32, 0x18, 0x55, 0x15, 0xce, 0x64, 0x9b, 0x08, 0x4f, 0x2c, 0xea, 0xba, 0x1c, 0x57, 0x06, 0x63, 0xc8, 0xb1, 0xfd, 0xc5, 0x67, 0xe7, 0x1f, 0x87, 0x9e, 0xde, 0x72, 0x7d, 0xec,
|
||||
/* (2^291)P */ 0x36, 0x8b, 0x4d, 0x2c, 0xc2, 0x46, 0xe8, 0x96, 0xac, 0x0b, 0x8c, 0xc5, 0x09, 0x10, 0xfc, 0xf2, 0xda, 0xea, 0x22, 0xb2, 0xd3, 0x89, 0xeb, 0xb2, 0x85, 0x0f, 0xff, 0x59, 0x50, 0x2c, 0x99, 0x5a, 0x1f, 0xec, 0x2a, 0x6f, 0xec, 0xcf, 0xe9, 0xce, 0x12, 0x6b, 0x19, 0xd8, 0xde, 0x9b, 0xce, 0x0e, 0x6a, 0xaa, 0xe1, 0x32, 0xea, 0x4c, 0xfe, 0x92,
|
||||
/* (2^292)P */ 0x5f, 0x17, 0x70, 0x53, 0x26, 0x03, 0x0b, 0xab, 0xd1, 0xc1, 0x42, 0x0b, 0xab, 0x2b, 0x3d, 0x31, 0xa4, 0xd5, 0x2b, 0x5e, 0x00, 0xd5, 0x9a, 0x22, 0x34, 0xe0, 0x53, 0x3f, 0x59, 0x7f, 0x2c, 0x6d, 0x72, 0x9a, 0xa4, 0xbe, 0x3d, 0x42, 0x05, 0x1b, 0xf2, 0x7f, 0x88, 0x56, 0xd1, 0x7c, 0x7d, 0x6b, 0x9f, 0x43, 0xfe, 0x65, 0x19, 0xae, 0x9c, 0x4c,
|
||||
/* (2^293)P */ 0xf3, 0x7c, 0x20, 0xa9, 0xfc, 0xf2, 0xf2, 0x3b, 0x3c, 0x57, 0x41, 0x94, 0xe5, 0xcc, 0x6a, 0x37, 0x5d, 0x09, 0xf2, 0xab, 0xc2, 0xca, 0x60, 0x38, 0x6b, 0x7a, 0xe1, 0x78, 0x2b, 0xc1, 0x1d, 0xe8, 0xfd, 0xbc, 0x3d, 0x5c, 0xa2, 0xdb, 0x49, 0x20, 0x79, 0xe6, 0x1b, 0x9b, 0x65, 0xd9, 0x6d, 0xec, 0x57, 0x1d, 0xd2, 0xe9, 0x90, 0xeb, 0x43, 0x7b,
|
||||
/* (2^294)P */ 0x2a, 0x8b, 0x2e, 0x19, 0x18, 0x10, 0xb8, 0x83, 0xe7, 0x7d, 0x2d, 0x9a, 0x3a, 0xe5, 0xd1, 0xe4, 0x7c, 0x38, 0xe5, 0x59, 0x2a, 0x6e, 0xd9, 0x01, 0x29, 0x3d, 0x23, 0xf7, 0x52, 0xba, 0x61, 0x04, 0x9a, 0xde, 0xc4, 0x31, 0x50, 0xeb, 0x1b, 0xaa, 0xde, 0x39, 0x58, 0xd8, 0x1b, 0x1e, 0xfc, 0x57, 0x9a, 0x28, 0x43, 0x9e, 0x97, 0x5e, 0xaa, 0xa3,
|
||||
/* (2^295)P */ 0x97, 0x0a, 0x74, 0xc4, 0x39, 0x99, 0x6b, 0x40, 0xc7, 0x3e, 0x8c, 0xa7, 0xb1, 0x4e, 0x9a, 0x59, 0x6e, 0x1c, 0xfe, 0xfc, 0x2a, 0x5e, 0x73, 0x2b, 0x8c, 0xa9, 0x71, 0xf5, 0xda, 0x6b, 0x15, 0xab, 0xf7, 0xbe, 0x2a, 0x44, 0x5f, 0xba, 0xae, 0x67, 0x93, 0xc5, 0x86, 0xc1, 0xb8, 0xdf, 0xdc, 0xcb, 0xd7, 0xff, 0xb1, 0x71, 0x7c, 0x6f, 0x88, 0xf8,
|
||||
/* (2^296)P */ 0x3f, 0x89, 0xb1, 0xbf, 0x24, 0x16, 0xac, 0x56, 0xfe, 0xdf, 0x94, 0x71, 0xbf, 0xd6, 0x57, 0x0c, 0xb4, 0x77, 0x37, 0xaa, 0x2a, 0x70, 0x76, 0x49, 0xaf, 0x0c, 0x97, 0x8e, 0x78, 0x2a, 0x67, 0xc9, 0x3b, 0x3d, 0x5b, 0x01, 0x2f, 0xda, 0xd5, 0xa8, 0xde, 0x02, 0xa9, 0xac, 0x76, 0x00, 0x0b, 0x46, 0xc6, 0x2d, 0xdc, 0x08, 0xf4, 0x10, 0x2c, 0xbe,
|
||||
/* (2^297)P */ 0xcb, 0x07, 0xf9, 0x91, 0xc6, 0xd5, 0x3e, 0x54, 0x63, 0xae, 0xfc, 0x10, 0xbe, 0x3a, 0x20, 0x73, 0x4e, 0x65, 0x0e, 0x2d, 0x86, 0x77, 0x83, 0x9d, 0xe2, 0x0a, 0xe9, 0xac, 0x22, 0x52, 0x76, 0xd4, 0x6e, 0xfa, 0xe0, 0x09, 0xef, 0x78, 0x82, 0x9f, 0x26, 0xf9, 0x06, 0xb5, 0xe7, 0x05, 0x0e, 0xf2, 0x46, 0x72, 0x93, 0xd3, 0x24, 0xbd, 0x87, 0x60,
|
||||
/* (2^298)P */ 0x14, 0x55, 0x84, 0x7b, 0x6c, 0x60, 0x80, 0x73, 0x8c, 0xbe, 0x2d, 0xd6, 0x69, 0xd6, 0x17, 0x26, 0x44, 0x9f, 0x88, 0xa2, 0x39, 0x7c, 0x89, 0xbc, 0x6d, 0x9e, 0x46, 0xb6, 0x68, 0x66, 0xea, 0xdc, 0x31, 0xd6, 0x21, 0x51, 0x9f, 0x28, 0x28, 0xaf, 0x9e, 0x47, 0x2c, 0x4c, 0x8f, 0xf3, 0xaf, 0x1f, 0xe4, 0xab, 0xac, 0xe9, 0x0c, 0x91, 0x3a, 0x61,
|
||||
/* (2^299)P */ 0xb0, 0x37, 0x55, 0x4b, 0xe9, 0xc3, 0xb1, 0xce, 0x42, 0xe6, 0xc5, 0x11, 0x7f, 0x2c, 0x11, 0xfc, 0x4e, 0x71, 0x17, 0x00, 0x74, 0x7f, 0xbf, 0x07, 0x4d, 0xfd, 0x40, 0xb2, 0x87, 0xb0, 0xef, 0x1f, 0x35, 0x2c, 0x2d, 0xd7, 0xe1, 0xe4, 0xad, 0x0e, 0x7f, 0x63, 0x66, 0x62, 0x23, 0x41, 0xf6, 0xc1, 0x14, 0xa6, 0xd7, 0xa9, 0x11, 0x56, 0x9d, 0x1b,
|
||||
/* (2^300)P */ 0x02, 0x82, 0x42, 0x18, 0x4f, 0x1b, 0xc9, 0x5d, 0x78, 0x5f, 0xee, 0xed, 0x01, 0x49, 0x8f, 0xf2, 0xa0, 0xe2, 0x6e, 0xbb, 0x6b, 0x04, 0x8d, 0xb2, 0x41, 0xae, 0xc8, 0x1b, 0x59, 0x34, 0xb8, 0x2a, 0xdb, 0x1f, 0xd2, 0x52, 0xdf, 0x3f, 0x35, 0x00, 0x8b, 0x61, 0xbc, 0x97, 0xa0, 0xc4, 0x77, 0xd1, 0xe4, 0x2c, 0x59, 0x68, 0xff, 0x30, 0xf2, 0xe2,
|
||||
/* (2^301)P */ 0x79, 0x08, 0xb1, 0xdb, 0x55, 0xae, 0xd0, 0xed, 0xda, 0xa0, 0xec, 0x6c, 0xae, 0x68, 0xf2, 0x0b, 0x61, 0xb3, 0xf5, 0x21, 0x69, 0x87, 0x0b, 0x03, 0xea, 0x8a, 0x15, 0xd9, 0x7e, 0xca, 0xf7, 0xcd, 0xf3, 0x33, 0xb3, 0x4c, 0x5b, 0x23, 0x4e, 0x6f, 0x90, 0xad, 0x91, 0x4b, 0x4f, 0x46, 0x37, 0xe5, 0xe8, 0xb7, 0xeb, 0xd5, 0xca, 0x34, 0x4e, 0x23,
|
||||
/* (2^302)P */ 0x09, 0x02, 0xdd, 0xfd, 0x70, 0xac, 0x56, 0x80, 0x36, 0x5e, 0x49, 0xd0, 0x3f, 0xc2, 0xe0, 0xba, 0x46, 0x7f, 0x5c, 0xf7, 0xc5, 0xbd, 0xd5, 0x55, 0x7d, 0x3f, 0xd5, 0x7d, 0x06, 0xdf, 0x27, 0x20, 0x4f, 0xe9, 0x30, 0xec, 0x1b, 0xa0, 0x0c, 0xd4, 0x2c, 0xe1, 0x2b, 0x65, 0x73, 0xea, 0x75, 0x35, 0xe8, 0xe6, 0x56, 0xd6, 0x07, 0x15, 0x99, 0xdf,
|
||||
/* (2^303)P */ 0x4e, 0x10, 0xb7, 0xd0, 0x63, 0x8c, 0xcf, 0x16, 0x00, 0x7c, 0x58, 0xdf, 0x86, 0xdc, 0x4e, 0xca, 0x9c, 0x40, 0x5a, 0x42, 0xfd, 0xec, 0x98, 0xa4, 0x42, 0x53, 0xae, 0x16, 0x9d, 0xfd, 0x75, 0x5a, 0x12, 0x56, 0x1e, 0xc6, 0x57, 0xcc, 0x79, 0x27, 0x96, 0x00, 0xcf, 0x80, 0x4f, 0x8a, 0x36, 0x5c, 0xbb, 0xe9, 0x12, 0xdb, 0xb6, 0x2b, 0xad, 0x96,
|
||||
/* (2^304)P */ 0x92, 0x32, 0x1f, 0xfd, 0xc6, 0x02, 0x94, 0x08, 0x1b, 0x60, 0x6a, 0x9f, 0x8b, 0xd6, 0xc8, 0xad, 0xd5, 0x1b, 0x27, 0x4e, 0xa4, 0x4d, 0x4a, 0x00, 0x10, 0x5f, 0x86, 0x11, 0xf5, 0xe3, 0x14, 0x32, 0x43, 0xee, 0xb9, 0xc7, 0xab, 0xf4, 0x6f, 0xe5, 0x66, 0x0c, 0x06, 0x0d, 0x96, 0x79, 0x28, 0xaf, 0x45, 0x2b, 0x56, 0xbe, 0xe4, 0x4a, 0x52, 0xd6,
|
||||
/* (2^305)P */ 0x15, 0x16, 0x69, 0xef, 0x60, 0xca, 0x82, 0x25, 0x0f, 0xc6, 0x30, 0xa0, 0x0a, 0xd1, 0x83, 0x29, 0xcd, 0xb6, 0x89, 0x6c, 0xf5, 0xb2, 0x08, 0x38, 0xe6, 0xca, 0x6b, 0x19, 0x93, 0xc6, 0x5f, 0x75, 0x8e, 0x60, 0x34, 0x23, 0xc4, 0x13, 0x17, 0x69, 0x55, 0xcc, 0x72, 0x9c, 0x2b, 0x6c, 0x80, 0xf4, 0x4b, 0x8b, 0xb6, 0x97, 0x65, 0x07, 0xb6, 0xfb,
|
||||
/* (2^306)P */ 0x01, 0x99, 0x74, 0x28, 0xa6, 0x67, 0xa3, 0xe5, 0x25, 0xfb, 0xdf, 0x82, 0x93, 0xe7, 0x35, 0x74, 0xce, 0xe3, 0x15, 0x1c, 0x1d, 0x79, 0x52, 0x84, 0x08, 0x04, 0x2f, 0x5c, 0xb8, 0xcd, 0x7f, 0x89, 0xb0, 0x39, 0x93, 0x63, 0xc9, 0x5d, 0x06, 0x01, 0x59, 0xf7, 0x7e, 0xf1, 0x4c, 0x3d, 0x12, 0x8d, 0x69, 0x1d, 0xb7, 0x21, 0x5e, 0x88, 0x82, 0xa2,
|
||||
/* (2^307)P */ 0x8e, 0x69, 0xaf, 0x9a, 0x41, 0x0d, 0x9d, 0xcf, 0x8e, 0x8d, 0x5c, 0x51, 0x6e, 0xde, 0x0e, 0x48, 0x23, 0x89, 0xe5, 0x37, 0x80, 0xd6, 0x9d, 0x72, 0x32, 0x26, 0x38, 0x2d, 0x63, 0xa0, 0xfa, 0xd3, 0x40, 0xc0, 0x8c, 0x68, 0x6f, 0x2b, 0x1e, 0x9a, 0x39, 0x51, 0x78, 0x74, 0x9a, 0x7b, 0x4a, 0x8f, 0x0c, 0xa0, 0x88, 0x60, 0xa5, 0x21, 0xcd, 0xc7,
|
||||
/* (2^308)P */ 0x3a, 0x7f, 0x73, 0x14, 0xbf, 0x89, 0x6a, 0x4c, 0x09, 0x5d, 0xf2, 0x93, 0x20, 0x2d, 0xc4, 0x29, 0x86, 0x06, 0x95, 0xab, 0x22, 0x76, 0x4c, 0x54, 0xe1, 0x7e, 0x80, 0x6d, 0xab, 0x29, 0x61, 0x87, 0x77, 0xf6, 0xc0, 0x3e, 0xda, 0xab, 0x65, 0x7e, 0x39, 0x12, 0xa1, 0x6b, 0x42, 0xf7, 0xc5, 0x97, 0x77, 0xec, 0x6f, 0x22, 0xbe, 0x44, 0xc7, 0x03,
|
||||
/* (2^309)P */ 0xa5, 0x23, 0x90, 0x41, 0xa3, 0xc5, 0x3e, 0xe0, 0xa5, 0x32, 0x49, 0x1f, 0x39, 0x78, 0xb1, 0xd8, 0x24, 0xea, 0xd4, 0x87, 0x53, 0x42, 0x51, 0xf4, 0xd9, 0x46, 0x25, 0x2f, 0x62, 0xa9, 0x90, 0x9a, 0x4a, 0x25, 0x8a, 0xd2, 0x10, 0xe7, 0x3c, 0xbc, 0x58, 0x8d, 0x16, 0x14, 0x96, 0xa4, 0x6f, 0xf8, 0x12, 0x69, 0x91, 0x73, 0xe2, 0xfa, 0xf4, 0x57,
|
||||
/* (2^310)P */ 0x51, 0x45, 0x3f, 0x96, 0xdc, 0x97, 0x38, 0xa6, 0x01, 0x63, 0x09, 0xea, 0xc2, 0x13, 0x30, 0xb0, 0x00, 0xb8, 0x0a, 0xce, 0xd1, 0x8f, 0x3e, 0x69, 0x62, 0x46, 0x33, 0x9c, 0xbf, 0x4b, 0xcb, 0x0c, 0x90, 0x1c, 0x45, 0xcf, 0x37, 0x5b, 0xf7, 0x4b, 0x5e, 0x95, 0xc3, 0x28, 0x9f, 0x08, 0x83, 0x53, 0x74, 0xab, 0x0c, 0xb4, 0xc0, 0xa1, 0xbc, 0x89,
|
||||
/* (2^311)P */ 0x06, 0xb1, 0x51, 0x15, 0x65, 0x60, 0x21, 0x17, 0x7a, 0x20, 0x65, 0xee, 0x12, 0x35, 0x4d, 0x46, 0xf4, 0xf8, 0xd0, 0xb1, 0xca, 0x09, 0x30, 0x08, 0x89, 0x23, 0x3b, 0xe7, 0xab, 0x8b, 0x77, 0xa6, 0xad, 0x25, 0xdd, 0xea, 0x3c, 0x7d, 0xa5, 0x24, 0xb3, 0xe8, 0xfa, 0xfb, 0xc9, 0xf2, 0x71, 0xe9, 0xfa, 0xf2, 0xdc, 0x54, 0xdd, 0x55, 0x2e, 0x2f,
|
||||
/* (2^312)P */ 0x7f, 0x96, 0x96, 0xfb, 0x52, 0x86, 0xcf, 0xea, 0x62, 0x18, 0xf1, 0x53, 0x1f, 0x61, 0x2a, 0x9f, 0x8c, 0x51, 0xca, 0x2c, 0xde, 0x6d, 0xce, 0xab, 0x58, 0x32, 0x0b, 0x33, 0x9b, 0x99, 0xb4, 0x5c, 0x88, 0x2a, 0x76, 0xcc, 0x3e, 0x54, 0x1e, 0x9d, 0xa2, 0x89, 0xe4, 0x19, 0xba, 0x80, 0xc8, 0x39, 0x32, 0x7f, 0x0f, 0xc7, 0x84, 0xbb, 0x43, 0x56,
|
||||
/* (2^313)P */ 0x9b, 0x07, 0xb4, 0x42, 0xa9, 0xa0, 0x78, 0x4f, 0x28, 0x70, 0x2b, 0x7e, 0x61, 0xe0, 0xdd, 0x02, 0x98, 0xfc, 0xed, 0x31, 0x80, 0xf1, 0x15, 0x52, 0x89, 0x23, 0xcd, 0x5d, 0x2b, 0xc5, 0x19, 0x32, 0xfb, 0x70, 0x50, 0x7a, 0x97, 0x6b, 0x42, 0xdb, 0xca, 0xdb, 0xc4, 0x59, 0x99, 0xe0, 0x12, 0x1f, 0x17, 0xba, 0x8b, 0xf0, 0xc4, 0x38, 0x5d, 0x27,
|
||||
/* (2^314)P */ 0x29, 0x1d, 0xdc, 0x2b, 0xf6, 0x5b, 0x04, 0x61, 0x36, 0x76, 0xa0, 0x56, 0x36, 0x6e, 0xd7, 0x24, 0x4d, 0xe7, 0xef, 0x44, 0xd2, 0xd5, 0x07, 0xcd, 0xc4, 0x9d, 0x80, 0x48, 0xc3, 0x38, 0xcf, 0xd8, 0xa3, 0xdd, 0xb2, 0x5e, 0xb5, 0x70, 0x15, 0xbb, 0x36, 0x85, 0x8a, 0xd7, 0xfb, 0x56, 0x94, 0x73, 0x9c, 0x81, 0xbe, 0xb1, 0x44, 0x28, 0xf1, 0x37,
|
||||
/* (2^315)P */ 0xbf, 0xcf, 0x5c, 0xd2, 0xe2, 0xea, 0xc2, 0xcd, 0x70, 0x7a, 0x9d, 0xcb, 0x81, 0xc1, 0xe9, 0xf1, 0x56, 0x71, 0x52, 0xf7, 0x1b, 0x87, 0xc6, 0xd8, 0xcc, 0xb2, 0x69, 0xf3, 0xb0, 0xbd, 0xba, 0x83, 0x12, 0x26, 0xc4, 0xce, 0x72, 0xde, 0x3b, 0x21, 0x28, 0x9e, 0x5a, 0x94, 0xf5, 0x04, 0xa3, 0xc8, 0x0f, 0x5e, 0xbc, 0x71, 0xf9, 0x0d, 0xce, 0xf5,
|
||||
/* (2^316)P */ 0x93, 0x97, 0x00, 0x85, 0xf4, 0xb4, 0x40, 0xec, 0xd9, 0x2b, 0x6c, 0xd6, 0x63, 0x9e, 0x93, 0x0a, 0x5a, 0xf4, 0xa7, 0x9a, 0xe3, 0x3c, 0xf0, 0x55, 0xd1, 0x96, 0x6c, 0xf5, 0x2a, 0xce, 0xd7, 0x95, 0x72, 0xbf, 0xc5, 0x0c, 0xce, 0x79, 0xa2, 0x0a, 0x78, 0xe0, 0x72, 0xd0, 0x66, 0x28, 0x05, 0x75, 0xd3, 0x23, 0x09, 0x91, 0xed, 0x7e, 0xc4, 0xbc,
|
||||
/* (2^317)P */ 0x77, 0xc2, 0x9a, 0xf7, 0xa6, 0xe6, 0x18, 0xb4, 0xe7, 0xf6, 0xda, 0xec, 0x44, 0x6d, 0xfb, 0x08, 0xee, 0x65, 0xa8, 0x92, 0x85, 0x1f, 0xba, 0x38, 0x93, 0x20, 0x5c, 0x4d, 0xd2, 0x18, 0x0f, 0x24, 0xbe, 0x1a, 0x96, 0x44, 0x7d, 0xeb, 0xb3, 0xda, 0x95, 0xf4, 0xaf, 0x6c, 0x06, 0x0f, 0x47, 0x37, 0xc8, 0x77, 0x63, 0xe1, 0x29, 0xef, 0xff, 0xa5,
|
||||
/* (2^318)P */ 0x16, 0x12, 0xd9, 0x47, 0x90, 0x22, 0x9b, 0x05, 0xf2, 0xa5, 0x9a, 0xae, 0x83, 0x98, 0xb5, 0xac, 0xab, 0x29, 0xaa, 0xdc, 0x5f, 0xde, 0xcd, 0xf7, 0x42, 0xad, 0x3b, 0x96, 0xd6, 0x3e, 0x6e, 0x52, 0x47, 0xb1, 0xab, 0x51, 0xde, 0x49, 0x7c, 0x87, 0x8d, 0x86, 0xe2, 0x70, 0x13, 0x21, 0x51, 0x1c, 0x0c, 0x25, 0xc1, 0xb0, 0xe6, 0x19, 0xcf, 0x12,
|
||||
/* (2^319)P */ 0xf0, 0xbc, 0x97, 0x8f, 0x4b, 0x2f, 0xd1, 0x1f, 0x8c, 0x57, 0xed, 0x3c, 0xf4, 0x26, 0x19, 0xbb, 0x60, 0xca, 0x24, 0xc5, 0xd9, 0x97, 0xe2, 0x5f, 0x76, 0x49, 0x39, 0x7e, 0x2d, 0x12, 0x21, 0x98, 0xda, 0xe6, 0xdb, 0xd2, 0xd8, 0x9f, 0x18, 0xd8, 0x83, 0x6c, 0xba, 0x89, 0x8d, 0x29, 0xfa, 0x46, 0x33, 0x8c, 0x28, 0xdf, 0x6a, 0xb3, 0x69, 0x28,
|
||||
/* (2^320)P */ 0x86, 0x17, 0xbc, 0xd6, 0x7c, 0xba, 0x1e, 0x83, 0xbb, 0x84, 0xb5, 0x8c, 0xad, 0xdf, 0xa1, 0x24, 0x81, 0x70, 0x40, 0x0f, 0xad, 0xad, 0x3b, 0x23, 0xd0, 0x93, 0xa0, 0x49, 0x5c, 0x4b, 0x51, 0xbe, 0x20, 0x49, 0x4e, 0xda, 0x2d, 0xd3, 0xad, 0x1b, 0x74, 0x08, 0x41, 0xf0, 0xef, 0x19, 0xe9, 0x45, 0x5d, 0x02, 0xae, 0x26, 0x25, 0xd9, 0xd1, 0xc2,
|
||||
/* (2^321)P */ 0x48, 0x81, 0x3e, 0xb2, 0x83, 0xf8, 0x4d, 0xb3, 0xd0, 0x4c, 0x75, 0xb3, 0xa0, 0x52, 0x26, 0xf2, 0xaf, 0x5d, 0x36, 0x70, 0x72, 0xd6, 0xb7, 0x88, 0x08, 0x69, 0xbd, 0x15, 0x25, 0xb1, 0x45, 0x1b, 0xb7, 0x0b, 0x5f, 0x71, 0x5d, 0x83, 0x49, 0xb9, 0x84, 0x3b, 0x7c, 0xc1, 0x50, 0x93, 0x05, 0x53, 0xe0, 0x61, 0xea, 0xc1, 0xef, 0xdb, 0x82, 0x97,
|
||||
/* (2^322)P */ 0x00, 0xd5, 0xc3, 0x3a, 0x4d, 0x8a, 0x23, 0x7a, 0xef, 0xff, 0x37, 0xef, 0xf3, 0xbc, 0xa9, 0xb6, 0xae, 0xd7, 0x3a, 0x7b, 0xfd, 0x3e, 0x8e, 0x9b, 0xab, 0x44, 0x54, 0x60, 0x28, 0x6c, 0xbf, 0x15, 0x24, 0x4a, 0x56, 0x60, 0x7f, 0xa9, 0x7a, 0x28, 0x59, 0x2c, 0x8a, 0xd1, 0x7d, 0x6b, 0x00, 0xfd, 0xa5, 0xad, 0xbc, 0x19, 0x3f, 0xcb, 0x73, 0xe0,
|
||||
/* (2^323)P */ 0xcf, 0x9e, 0x66, 0x06, 0x4d, 0x2b, 0xf5, 0x9c, 0xc2, 0x9d, 0x9e, 0xed, 0x5a, 0x5c, 0x2d, 0x00, 0xbf, 0x29, 0x90, 0x88, 0xe4, 0x5d, 0xfd, 0xe2, 0xf0, 0x38, 0xec, 0x4d, 0x26, 0xea, 0x54, 0xf0, 0x3c, 0x84, 0x10, 0x6a, 0xf9, 0x66, 0x9c, 0xe7, 0x21, 0xfd, 0x0f, 0xc7, 0x13, 0x50, 0x81, 0xb6, 0x50, 0xf9, 0x04, 0x7f, 0xa4, 0x37, 0x85, 0x14,
|
||||
/* (2^324)P */ 0xdb, 0x87, 0x49, 0xc7, 0xa8, 0x39, 0x0c, 0x32, 0x98, 0x0c, 0xb9, 0x1a, 0x1b, 0x4d, 0xe0, 0x8a, 0x9a, 0x8e, 0x8f, 0xab, 0x5a, 0x17, 0x3d, 0x04, 0x21, 0xce, 0x3e, 0x2c, 0xf9, 0xa3, 0x97, 0xe4, 0x77, 0x95, 0x0e, 0xb6, 0xa5, 0x15, 0xad, 0x3a, 0x1e, 0x46, 0x53, 0x17, 0x09, 0x83, 0x71, 0x4e, 0x86, 0x38, 0xd5, 0x23, 0x44, 0x16, 0x8d, 0xc8,
|
||||
/* (2^325)P */ 0x05, 0x5e, 0x99, 0x08, 0xbb, 0xc3, 0xc0, 0xb7, 0x6c, 0x12, 0xf2, 0xf3, 0xf4, 0x7c, 0x6a, 0x4d, 0x9e, 0xeb, 0x3d, 0xb9, 0x63, 0x94, 0xce, 0x81, 0xd8, 0x11, 0xcb, 0x55, 0x69, 0x4a, 0x20, 0x0b, 0x4c, 0x2e, 0x14, 0xb8, 0xd4, 0x6a, 0x7c, 0xf0, 0xed, 0xfc, 0x8f, 0xef, 0xa0, 0xeb, 0x6c, 0x01, 0xe2, 0xdc, 0x10, 0x22, 0xa2, 0x01, 0x85, 0x64,
|
||||
/* (2^326)P */ 0x58, 0xe1, 0x9c, 0x27, 0x55, 0xc6, 0x25, 0xa6, 0x7d, 0x67, 0x88, 0x65, 0x99, 0x6c, 0xcb, 0xdb, 0x27, 0x4f, 0x44, 0x29, 0xf5, 0x4a, 0x23, 0x10, 0xbc, 0x03, 0x3f, 0x36, 0x1e, 0xef, 0xb0, 0xba, 0x75, 0xe8, 0x74, 0x5f, 0x69, 0x3e, 0x26, 0x40, 0xb4, 0x2f, 0xdc, 0x43, 0xbf, 0xa1, 0x8b, 0xbd, 0xca, 0x6e, 0xc1, 0x6e, 0x21, 0x79, 0xa0, 0xd0,
|
||||
/* (2^327)P */ 0x78, 0x93, 0x4a, 0x2d, 0x22, 0x6e, 0x6e, 0x7d, 0x74, 0xd2, 0x66, 0x58, 0xce, 0x7b, 0x1d, 0x97, 0xb1, 0xf2, 0xda, 0x1c, 0x79, 0xfb, 0xba, 0xd1, 0xc0, 0xc5, 0x6e, 0xc9, 0x11, 0x89, 0xd2, 0x41, 0x8d, 0x70, 0xb9, 0xcc, 0xea, 0x6a, 0xb3, 0x45, 0xb6, 0x05, 0x2e, 0xf2, 0x17, 0xf1, 0x27, 0xb8, 0xed, 0x06, 0x1f, 0xdb, 0x9d, 0x1f, 0x69, 0x28,
|
||||
/* (2^328)P */ 0x93, 0x12, 0xa8, 0x11, 0xe1, 0x92, 0x30, 0x8d, 0xac, 0xe1, 0x1c, 0x60, 0x7c, 0xed, 0x2d, 0x2e, 0xd3, 0x03, 0x5c, 0x9c, 0xc5, 0xbd, 0x64, 0x4a, 0x8c, 0xba, 0x76, 0xfe, 0xc6, 0xc1, 0xea, 0xc2, 0x4f, 0xbe, 0x70, 0x3d, 0x64, 0xcf, 0x8e, 0x18, 0xcb, 0xcd, 0x57, 0xa7, 0xf7, 0x36, 0xa9, 0x6b, 0x3e, 0xb8, 0x69, 0xee, 0x47, 0xa2, 0x7e, 0xb2,
|
||||
/* (2^329)P */ 0x96, 0xaf, 0x3a, 0xf5, 0xed, 0xcd, 0xaf, 0xf7, 0x82, 0xaf, 0x59, 0x62, 0x0b, 0x36, 0x85, 0xf9, 0xaf, 0xd6, 0x38, 0xff, 0x87, 0x2e, 0x1d, 0x6c, 0x8b, 0xaf, 0x3b, 0xdf, 0x28, 0xa2, 0xd6, 0x4d, 0x80, 0x92, 0xc3, 0x0f, 0x34, 0xa8, 0xae, 0x69, 0x5d, 0x7b, 0x9d, 0xbc, 0xf5, 0xfd, 0x1d, 0xb1, 0x96, 0x55, 0x86, 0xe1, 0x5c, 0xb6, 0xac, 0xb9,
|
||||
/* (2^330)P */ 0x50, 0x9e, 0x37, 0x28, 0x7d, 0xa8, 0x33, 0x63, 0xda, 0x3f, 0x20, 0x98, 0x0e, 0x09, 0xa8, 0x77, 0x3b, 0x7a, 0xfc, 0x16, 0x85, 0x44, 0x64, 0x77, 0x65, 0x68, 0x92, 0x41, 0xc6, 0x1f, 0xdf, 0x27, 0xf9, 0xec, 0xa0, 0x61, 0x22, 0xea, 0x19, 0xe7, 0x75, 0x8b, 0x4e, 0xe5, 0x0f, 0xb7, 0xf7, 0xd2, 0x53, 0xf4, 0xdd, 0x4a, 0xaa, 0x78, 0x40, 0xb7,
|
||||
/* (2^331)P */ 0xd4, 0x89, 0xe3, 0x79, 0xba, 0xb6, 0xc3, 0xda, 0xe6, 0x78, 0x65, 0x7d, 0x6e, 0x22, 0x62, 0xb1, 0x3d, 0xea, 0x90, 0x84, 0x30, 0x5e, 0xd4, 0x39, 0x84, 0x78, 0xd9, 0x75, 0xd6, 0xce, 0x2a, 0x11, 0x29, 0x69, 0xa4, 0x5e, 0xaa, 0x2a, 0x98, 0x5a, 0xe5, 0x91, 0x8f, 0xb2, 0xfb, 0xda, 0x97, 0xe8, 0x83, 0x6f, 0x04, 0xb9, 0x5d, 0xaf, 0xe1, 0x9b,
|
||||
/* (2^332)P */ 0x8b, 0xe4, 0xe1, 0x48, 0x9c, 0xc4, 0x83, 0x89, 0xdf, 0x65, 0xd3, 0x35, 0x55, 0x13, 0xf4, 0x1f, 0x36, 0x92, 0x33, 0x38, 0xcb, 0xed, 0x15, 0xe6, 0x60, 0x2d, 0x25, 0xf5, 0x36, 0x60, 0x3a, 0x37, 0x9b, 0x71, 0x9d, 0x42, 0xb0, 0x14, 0xc8, 0xba, 0x62, 0xa3, 0x49, 0xb0, 0x88, 0xc1, 0x72, 0x73, 0xdd, 0x62, 0x40, 0xa9, 0x62, 0x88, 0x99, 0xca,
|
||||
/* (2^333)P */ 0x47, 0x7b, 0xea, 0xda, 0x46, 0x2f, 0x45, 0xc6, 0xe3, 0xb4, 0x4d, 0x8d, 0xac, 0x0b, 0x54, 0x22, 0x06, 0x31, 0x16, 0x66, 0x3e, 0xe4, 0x38, 0x12, 0xcd, 0xf3, 0xe7, 0x99, 0x37, 0xd9, 0x62, 0x24, 0x4b, 0x05, 0xf2, 0x58, 0xe6, 0x29, 0x4b, 0x0d, 0xf6, 0xc1, 0xba, 0xa0, 0x1e, 0x0f, 0xcb, 0x1f, 0xc6, 0x2b, 0x19, 0xfc, 0x82, 0x01, 0xd0, 0x86,
|
||||
/* (2^334)P */ 0xa2, 0xae, 0x77, 0x20, 0xfb, 0xa8, 0x18, 0xb4, 0x61, 0xef, 0xe8, 0x52, 0x79, 0xbb, 0x86, 0x90, 0x5d, 0x2e, 0x76, 0xed, 0x66, 0x60, 0x5d, 0x00, 0xb5, 0xa4, 0x00, 0x40, 0x89, 0xec, 0xd1, 0xd2, 0x0d, 0x26, 0xb9, 0x30, 0xb2, 0xd2, 0xb8, 0xe8, 0x0e, 0x56, 0xf9, 0x67, 0x94, 0x2e, 0x62, 0xe1, 0x79, 0x48, 0x2b, 0xa9, 0xfa, 0xea, 0xdb, 0x28,
|
||||
/* (2^335)P */ 0x35, 0xf1, 0xb0, 0x43, 0xbd, 0x27, 0xef, 0x18, 0x44, 0xa2, 0x04, 0xb4, 0x69, 0xa1, 0x97, 0x1f, 0x8c, 0x04, 0x82, 0x9b, 0x00, 0x6d, 0xf8, 0xbf, 0x7d, 0xc1, 0x5b, 0xab, 0xe8, 0xb2, 0x34, 0xbd, 0xaf, 0x7f, 0xb2, 0x0d, 0xf3, 0xed, 0xfc, 0x5b, 0x50, 0xee, 0xe7, 0x4a, 0x20, 0xd9, 0xf5, 0xc6, 0x9a, 0x97, 0x6d, 0x07, 0x2f, 0xb9, 0x31, 0x02,
|
||||
/* (2^336)P */ 0xf9, 0x54, 0x4a, 0xc5, 0x61, 0x7e, 0x1d, 0xa6, 0x0e, 0x1a, 0xa8, 0xd3, 0x8c, 0x36, 0x7d, 0xf1, 0x06, 0xb1, 0xac, 0x93, 0xcd, 0xe9, 0x8f, 0x61, 0x6c, 0x5d, 0x03, 0x23, 0xdf, 0x85, 0x53, 0x39, 0x63, 0x5e, 0xeb, 0xf3, 0xd3, 0xd3, 0x75, 0x97, 0x9b, 0x62, 0x9b, 0x01, 0xb3, 0x19, 0xd8, 0x2b, 0x36, 0xf2, 0x2c, 0x2c, 0x6f, 0x36, 0xc6, 0x3c,
|
||||
/* (2^337)P */ 0x05, 0x74, 0x43, 0x10, 0xb6, 0xb0, 0xf8, 0xbf, 0x02, 0x46, 0x9a, 0xee, 0xc1, 0xaf, 0xc1, 0xe5, 0x5a, 0x2e, 0xbb, 0xe1, 0xdc, 0xc6, 0xce, 0x51, 0x29, 0x50, 0xbf, 0x1b, 0xde, 0xff, 0xba, 0x4d, 0x8d, 0x8b, 0x7e, 0xe7, 0xbd, 0x5b, 0x8f, 0xbe, 0xe3, 0x75, 0x71, 0xff, 0x37, 0x05, 0x5a, 0x10, 0xeb, 0x54, 0x7e, 0x44, 0x72, 0x2c, 0xd4, 0xfc,
|
||||
/* (2^338)P */ 0x03, 0x12, 0x1c, 0xb2, 0x08, 0x90, 0xa1, 0x2d, 0x50, 0xa0, 0xad, 0x7f, 0x8d, 0xa6, 0x97, 0xc1, 0xbd, 0xdc, 0xc3, 0xa7, 0xad, 0x31, 0xdf, 0xb8, 0x03, 0x84, 0xc3, 0xb9, 0x29, 0x3d, 0x92, 0x2e, 0xc3, 0x90, 0x07, 0xe8, 0xa7, 0xc7, 0xbc, 0x61, 0xe9, 0x3e, 0xa0, 0x35, 0xda, 0x1d, 0xab, 0x48, 0xfe, 0x50, 0xc9, 0x25, 0x59, 0x23, 0x69, 0x3f,
|
||||
/* (2^339)P */ 0x8e, 0x91, 0xab, 0x6b, 0x91, 0x4f, 0x89, 0x76, 0x67, 0xad, 0xb2, 0x65, 0x9d, 0xad, 0x02, 0x36, 0xdc, 0xac, 0x96, 0x93, 0x97, 0x21, 0x14, 0xd0, 0xe8, 0x11, 0x60, 0x1e, 0xeb, 0x96, 0x06, 0xf2, 0x53, 0xf2, 0x6d, 0xb7, 0x93, 0x6f, 0x26, 0x91, 0x23, 0xe3, 0x34, 0x04, 0x92, 0x91, 0x37, 0x08, 0x50, 0xd6, 0x28, 0x09, 0x27, 0xa1, 0x0c, 0x00,
|
||||
/* (2^340)P */ 0x1f, 0xbb, 0x21, 0x26, 0x33, 0xcb, 0xa4, 0xd1, 0xee, 0x85, 0xf9, 0xd9, 0x3c, 0x90, 0xc3, 0xd1, 0x26, 0xa2, 0x25, 0x93, 0x43, 0x61, 0xed, 0x91, 0x6e, 0x54, 0x03, 0x2e, 0x42, 0x9d, 0xf7, 0xa6, 0x02, 0x0f, 0x2f, 0x9c, 0x7a, 0x8d, 0x12, 0xc2, 0x18, 0xfc, 0x41, 0xff, 0x85, 0x26, 0x1a, 0x44, 0x55, 0x0b, 0x89, 0xab, 0x6f, 0x62, 0x33, 0x8c,
|
||||
/* (2^341)P */ 0xe0, 0x3c, 0x5d, 0x70, 0x64, 0x87, 0x81, 0x35, 0xf2, 0x37, 0xa6, 0x24, 0x3e, 0xe0, 0x62, 0xd5, 0x71, 0xe7, 0x93, 0xfb, 0xac, 0xc3, 0xe7, 0xc7, 0x04, 0xe2, 0x70, 0xd3, 0x29, 0x5b, 0x21, 0xbf, 0xf4, 0x26, 0x5d, 0xf3, 0x95, 0xb4, 0x2a, 0x6a, 0x07, 0x55, 0xa6, 0x4b, 0x3b, 0x15, 0xf2, 0x25, 0x8a, 0x95, 0x3f, 0x63, 0x2f, 0x7a, 0x23, 0x96,
|
||||
/* (2^342)P */ 0x0d, 0x3d, 0xd9, 0x13, 0xa7, 0xb3, 0x5e, 0x67, 0xf7, 0x02, 0x23, 0xee, 0x84, 0xff, 0x99, 0xda, 0xb9, 0x53, 0xf8, 0xf0, 0x0e, 0x39, 0x2f, 0x3c, 0x64, 0x34, 0xe3, 0x09, 0xfd, 0x2b, 0x33, 0xc7, 0xfe, 0x62, 0x2b, 0x84, 0xdf, 0x2b, 0xd2, 0x7c, 0x26, 0x01, 0x70, 0x66, 0x5b, 0x85, 0xc2, 0xbe, 0x88, 0x37, 0xf1, 0x30, 0xac, 0xb8, 0x76, 0xa3,
|
||||
/* (2^343)P */ 0x6e, 0x01, 0xf0, 0x55, 0x35, 0xe4, 0xbd, 0x43, 0x62, 0x9d, 0xd6, 0x11, 0xef, 0x6f, 0xb8, 0x8c, 0xaa, 0x98, 0x87, 0xc6, 0x6d, 0xc4, 0xcc, 0x74, 0x92, 0x53, 0x4a, 0xdf, 0xe4, 0x08, 0x89, 0x17, 0xd0, 0x0f, 0xf4, 0x00, 0x60, 0x78, 0x08, 0x44, 0xb5, 0xda, 0x18, 0xed, 0x98, 0xc8, 0x61, 0x3d, 0x39, 0xdb, 0xcf, 0x1d, 0x49, 0x40, 0x65, 0x75,
|
||||
/* (2^344)P */ 0x8e, 0x10, 0xae, 0x5f, 0x06, 0xd2, 0x95, 0xfd, 0x20, 0x16, 0x49, 0x5b, 0x57, 0xbe, 0x22, 0x8b, 0x43, 0xfb, 0xe6, 0xcc, 0x26, 0xa5, 0x5d, 0xd3, 0x68, 0xc5, 0xf9, 0x5a, 0x86, 0x24, 0x87, 0x27, 0x05, 0xfd, 0xe2, 0xff, 0xb3, 0xa3, 0x7b, 0x37, 0x59, 0xc5, 0x4e, 0x14, 0x94, 0xf9, 0x3b, 0xcb, 0x7c, 0xed, 0xca, 0x1d, 0xb2, 0xac, 0x05, 0x4a,
|
||||
/* (2^345)P */ 0xf4, 0xd1, 0x81, 0xeb, 0x89, 0xbf, 0xfe, 0x1e, 0x41, 0x92, 0x29, 0xee, 0xe1, 0x43, 0xf5, 0x86, 0x1d, 0x2f, 0xbb, 0x1e, 0x84, 0x5d, 0x7b, 0x8d, 0xd5, 0xda, 0xee, 0x1e, 0x8a, 0xd0, 0x27, 0xf2, 0x60, 0x51, 0x59, 0x82, 0xf4, 0x84, 0x2b, 0x5b, 0x14, 0x2d, 0x81, 0x82, 0x3e, 0x2b, 0xb4, 0x6d, 0x51, 0x4f, 0xc5, 0xcb, 0xbf, 0x74, 0xe3, 0xb4,
|
||||
/* (2^346)P */ 0x19, 0x2f, 0x22, 0xb3, 0x04, 0x5f, 0x81, 0xca, 0x05, 0x60, 0xb9, 0xaa, 0xee, 0x0e, 0x2f, 0x48, 0x38, 0xf9, 0x91, 0xb4, 0x66, 0xe4, 0x57, 0x28, 0x54, 0x10, 0xe9, 0x61, 0x9d, 0xd4, 0x90, 0x75, 0xb1, 0x39, 0x23, 0xb6, 0xfc, 0x82, 0xe0, 0xfa, 0xbb, 0x5c, 0x6e, 0xc3, 0x44, 0x13, 0x00, 0x83, 0x55, 0x9e, 0x8e, 0x10, 0x61, 0x81, 0x91, 0x04,
|
||||
/* (2^347)P */ 0x5f, 0x2a, 0xd7, 0x81, 0xd9, 0x9c, 0xbb, 0x79, 0xbc, 0x62, 0x56, 0x98, 0x03, 0x5a, 0x18, 0x85, 0x2a, 0x9c, 0xd0, 0xfb, 0xd2, 0xb1, 0xaf, 0xef, 0x0d, 0x24, 0xc5, 0xfa, 0x39, 0xbb, 0x6b, 0xed, 0xa4, 0xdf, 0xe4, 0x87, 0xcd, 0x41, 0xd3, 0x72, 0x32, 0xc6, 0x28, 0x21, 0xb1, 0xba, 0x8b, 0xa3, 0x91, 0x79, 0x76, 0x22, 0x25, 0x10, 0x61, 0xd1,
|
||||
/* (2^348)P */ 0x73, 0xb5, 0x32, 0x97, 0xdd, 0xeb, 0xdd, 0x22, 0x22, 0xf1, 0x33, 0x3c, 0x77, 0x56, 0x7d, 0x6b, 0x48, 0x2b, 0x05, 0x81, 0x03, 0x03, 0x91, 0x9a, 0xe3, 0x5e, 0xd4, 0xee, 0x3f, 0xf8, 0xbb, 0x50, 0x21, 0x32, 0x4c, 0x4a, 0x58, 0x49, 0xde, 0x0c, 0xde, 0x30, 0x82, 0x3d, 0x92, 0xf0, 0x6c, 0xcc, 0x32, 0x3e, 0xd2, 0x78, 0x8a, 0x6e, 0x2c, 0xd0,
|
||||
/* (2^349)P */ 0xf0, 0xf7, 0xa1, 0x0b, 0xc1, 0x74, 0x85, 0xa8, 0xe9, 0xdd, 0x48, 0xa1, 0xc0, 0x16, 0xd8, 0x2b, 0x61, 0x08, 0xc2, 0x2b, 0x30, 0x26, 0x79, 0xce, 0x9e, 0xfd, 0x39, 0xd7, 0x81, 0xa4, 0x63, 0x8c, 0xd5, 0x74, 0xa0, 0x88, 0xfa, 0x03, 0x30, 0xe9, 0x7f, 0x2b, 0xc6, 0x02, 0xc9, 0x5e, 0xe4, 0xd5, 0x4d, 0x92, 0xd0, 0xf6, 0xf2, 0x5b, 0x79, 0x08,
|
||||
/* (2^350)P */ 0x34, 0x89, 0x81, 0x43, 0xd1, 0x94, 0x2c, 0x10, 0x54, 0x9b, 0xa0, 0xe5, 0x44, 0xe8, 0xc2, 0x2f, 0x3e, 0x0e, 0x74, 0xae, 0xba, 0xe2, 0xac, 0x85, 0x6b, 0xd3, 0x5c, 0x97, 0xf7, 0x90, 0xf1, 0x12, 0xc0, 0x03, 0xc8, 0x1f, 0x37, 0x72, 0x8c, 0x9b, 0x9c, 0x17, 0x96, 0x9d, 0xc7, 0xbf, 0xa3, 0x3f, 0x44, 0x3d, 0x87, 0x81, 0xbd, 0x81, 0xa6, 0x5f,
|
||||
/* (2^351)P */ 0xe4, 0xff, 0x78, 0x62, 0x82, 0x5b, 0x76, 0x58, 0xf5, 0x5b, 0xa6, 0xc4, 0x53, 0x11, 0x3b, 0x7b, 0xaa, 0x67, 0xf8, 0xea, 0x3b, 0x5d, 0x9a, 0x2e, 0x04, 0xeb, 0x4a, 0x24, 0xfb, 0x56, 0xf0, 0xa8, 0xd4, 0x14, 0xed, 0x0f, 0xfd, 0xc5, 0x26, 0x17, 0x2a, 0xf0, 0xb9, 0x13, 0x8c, 0xbd, 0x65, 0x14, 0x24, 0x95, 0x27, 0x12, 0x63, 0x2a, 0x09, 0x18,
|
||||
/* (2^352)P */ 0xe1, 0x5c, 0xe7, 0xe0, 0x00, 0x6a, 0x96, 0xf2, 0x49, 0x6a, 0x39, 0xa5, 0xe0, 0x17, 0x79, 0x4a, 0x63, 0x07, 0x62, 0x09, 0x61, 0x1b, 0x6e, 0xa9, 0xb5, 0x62, 0xb7, 0xde, 0xdf, 0x80, 0x4c, 0x5a, 0x99, 0x73, 0x59, 0x9d, 0xfb, 0xb1, 0x5e, 0xbe, 0xb8, 0xb7, 0x63, 0x93, 0xe8, 0xad, 0x5e, 0x1f, 0xae, 0x59, 0x1c, 0xcd, 0xb4, 0xc2, 0xb3, 0x8a,
|
||||
/* (2^353)P */ 0x78, 0x53, 0xa1, 0x4c, 0x70, 0x9c, 0x63, 0x7e, 0xb3, 0x12, 0x40, 0x5f, 0xbb, 0x23, 0xa7, 0xf7, 0x77, 0x96, 0x5b, 0x4d, 0x91, 0x10, 0x52, 0x85, 0x9e, 0xa5, 0x38, 0x0b, 0xfd, 0x25, 0x01, 0x4b, 0xfa, 0x4d, 0xd3, 0x3f, 0x78, 0x74, 0x42, 0xff, 0x62, 0x2d, 0x27, 0xdc, 0x9d, 0xd1, 0x29, 0x76, 0x2e, 0x78, 0xb3, 0x35, 0xfa, 0x15, 0xd5, 0x38,
|
||||
/* (2^354)P */ 0x8b, 0xc7, 0x43, 0xce, 0xf0, 0x5e, 0xf1, 0x0d, 0x02, 0x38, 0xe8, 0x82, 0xc9, 0x25, 0xad, 0x2d, 0x27, 0xa4, 0x54, 0x18, 0xb2, 0x30, 0x73, 0xa4, 0x41, 0x08, 0xe4, 0x86, 0xe6, 0x8c, 0xe9, 0x2a, 0x34, 0xb3, 0xd6, 0x61, 0x8f, 0x66, 0x26, 0x08, 0xb6, 0x06, 0x33, 0xaa, 0x12, 0xac, 0x72, 0xec, 0x2e, 0x52, 0xa3, 0x25, 0x3e, 0xd7, 0x62, 0xe8,
|
||||
/* (2^355)P */ 0xc4, 0xbb, 0x89, 0xc8, 0x40, 0xcc, 0x84, 0xec, 0x4a, 0xd9, 0xc4, 0x55, 0x78, 0x00, 0xcf, 0xd8, 0xe9, 0x24, 0x59, 0xdc, 0x5e, 0xf0, 0x66, 0xa1, 0x83, 0xae, 0x97, 0x18, 0xc5, 0x54, 0x27, 0xa2, 0x21, 0x52, 0x03, 0x31, 0x5b, 0x11, 0x67, 0xf6, 0x12, 0x00, 0x87, 0x2f, 0xff, 0x59, 0x70, 0x8f, 0x6d, 0x71, 0xab, 0xab, 0x24, 0xb8, 0xba, 0x35,
|
||||
/* (2^356)P */ 0x69, 0x43, 0xa7, 0x14, 0x06, 0x96, 0xe9, 0xc2, 0xe3, 0x2b, 0x45, 0x22, 0xc0, 0xd0, 0x2f, 0x34, 0xd1, 0x01, 0x99, 0xfc, 0x99, 0x38, 0xa1, 0x25, 0x2e, 0x59, 0x6c, 0x27, 0xc9, 0xeb, 0x7b, 0xdc, 0x4e, 0x26, 0x68, 0xba, 0xfa, 0xec, 0x02, 0x05, 0x64, 0x80, 0x30, 0x20, 0x5c, 0x26, 0x7f, 0xaf, 0x95, 0x17, 0x3d, 0x5c, 0x9e, 0x96, 0x96, 0xaf,
|
||||
/* (2^357)P */ 0xa6, 0xba, 0x21, 0x29, 0x32, 0xe2, 0x98, 0xde, 0x9b, 0x6d, 0x0b, 0x44, 0x91, 0xa8, 0x3e, 0xd4, 0xb8, 0x04, 0x6c, 0xf6, 0x04, 0x39, 0xbd, 0x52, 0x05, 0x15, 0x27, 0x78, 0x8e, 0x55, 0xac, 0x79, 0xc5, 0xe6, 0x00, 0x7f, 0x90, 0xa2, 0xdd, 0x07, 0x13, 0xe0, 0x24, 0x70, 0x5c, 0x0f, 0x4d, 0xa9, 0xf9, 0xae, 0xcb, 0x34, 0x10, 0x9d, 0x89, 0x9d,
|
||||
/* (2^358)P */ 0x12, 0xe0, 0xb3, 0x9f, 0xc4, 0x96, 0x1d, 0xcf, 0xed, 0x99, 0x64, 0x28, 0x8d, 0xc7, 0x31, 0x82, 0xee, 0x5e, 0x75, 0x48, 0xff, 0x3a, 0xf2, 0x09, 0x34, 0x03, 0x93, 0x52, 0x19, 0xb2, 0xc5, 0x81, 0x93, 0x45, 0x5e, 0x59, 0x21, 0x2b, 0xec, 0x89, 0xba, 0x36, 0x6e, 0xf9, 0x82, 0x75, 0x7e, 0x82, 0x3f, 0xaa, 0xe2, 0xe3, 0x3b, 0x94, 0xfd, 0x98,
|
||||
/* (2^359)P */ 0x7c, 0xdb, 0x75, 0x31, 0x61, 0xfb, 0x15, 0x28, 0x94, 0xd7, 0xc3, 0x5a, 0xa9, 0xa1, 0x0a, 0x66, 0x0f, 0x2b, 0x13, 0x3e, 0x42, 0xb5, 0x28, 0x3a, 0xca, 0x83, 0xf3, 0x61, 0x22, 0xf4, 0x40, 0xc5, 0xdf, 0xe7, 0x31, 0x9f, 0x7e, 0x51, 0x75, 0x06, 0x9d, 0x51, 0xc8, 0xe7, 0x9f, 0xc3, 0x71, 0x4f, 0x3d, 0x5b, 0xfb, 0xe9, 0x8e, 0x08, 0x40, 0x8e,
|
||||
/* (2^360)P */ 0xf7, 0x31, 0xad, 0x50, 0x5d, 0x25, 0x93, 0x73, 0x68, 0xf6, 0x7c, 0x89, 0x5a, 0x3d, 0x9f, 0x9b, 0x05, 0x82, 0xe7, 0x70, 0x4b, 0x19, 0xaa, 0xcf, 0xff, 0xde, 0x50, 0x8f, 0x2f, 0x69, 0xd3, 0xf0, 0x99, 0x51, 0x6b, 0x9d, 0xb6, 0x56, 0x6f, 0xf8, 0x4c, 0x74, 0x8b, 0x4c, 0x91, 0xf9, 0xa9, 0xb1, 0x3e, 0x07, 0xdf, 0x0b, 0x27, 0x8a, 0xb1, 0xed,
|
||||
/* (2^361)P */ 0xfb, 0x67, 0xd9, 0x48, 0xd2, 0xe4, 0x44, 0x9b, 0x43, 0x15, 0x8a, 0xeb, 0x00, 0x53, 0xad, 0x25, 0xc7, 0x7e, 0x19, 0x30, 0x87, 0xb7, 0xd5, 0x5f, 0x04, 0xf8, 0xaa, 0xdd, 0x57, 0xae, 0x34, 0x75, 0xe2, 0x84, 0x4b, 0x54, 0x60, 0x37, 0x95, 0xe4, 0xd3, 0xec, 0xac, 0xef, 0x47, 0x31, 0xa3, 0xc8, 0x31, 0x22, 0xdb, 0x26, 0xe7, 0x6a, 0xb5, 0xad,
|
||||
/* (2^362)P */ 0x44, 0x09, 0x5c, 0x95, 0xe4, 0x72, 0x3c, 0x1a, 0xd1, 0xac, 0x42, 0x51, 0x99, 0x6f, 0xfa, 0x1f, 0xf2, 0x22, 0xbe, 0xff, 0x7b, 0x66, 0xf5, 0x6c, 0xb3, 0x66, 0xc7, 0x4d, 0x78, 0x31, 0x83, 0x80, 0xf5, 0x41, 0xe9, 0x7f, 0xbe, 0xf7, 0x23, 0x49, 0x6b, 0x84, 0x4e, 0x7e, 0x47, 0x07, 0x6e, 0x74, 0xdf, 0xe5, 0x9d, 0x9e, 0x56, 0x2a, 0xc0, 0xbc,
|
||||
/* (2^363)P */ 0xac, 0x10, 0x80, 0x8c, 0x7c, 0xfa, 0x83, 0xdf, 0xb3, 0xd0, 0xc4, 0xbe, 0xfb, 0x9f, 0xac, 0xc9, 0xc3, 0x40, 0x95, 0x0b, 0x09, 0x23, 0xda, 0x63, 0x67, 0xcf, 0xe7, 0x9f, 0x7d, 0x7b, 0x6b, 0xe2, 0xe6, 0x6d, 0xdb, 0x87, 0x9e, 0xa6, 0xff, 0x6d, 0xab, 0xbd, 0xfb, 0x54, 0x84, 0x68, 0xcf, 0x89, 0xf1, 0xd0, 0xe2, 0x85, 0x61, 0xdc, 0x22, 0xd1,
|
||||
/* (2^364)P */ 0xa8, 0x48, 0xfb, 0x8c, 0x6a, 0x63, 0x01, 0x72, 0x43, 0x43, 0xeb, 0x21, 0xa3, 0x00, 0x8a, 0xc0, 0x87, 0x51, 0x9e, 0x86, 0x75, 0x16, 0x79, 0xf9, 0x6b, 0x11, 0x80, 0x62, 0xc2, 0x9d, 0xb8, 0x8c, 0x30, 0x8e, 0x8d, 0x03, 0x52, 0x7e, 0x31, 0x59, 0x38, 0xf9, 0x25, 0xc7, 0x0f, 0xc7, 0xa8, 0x2b, 0x5c, 0x80, 0xfa, 0x90, 0xa2, 0x63, 0xca, 0xe7,
|
||||
/* (2^365)P */ 0xf1, 0x5d, 0xb5, 0xd9, 0x20, 0x10, 0x7d, 0x0f, 0xc5, 0x50, 0x46, 0x07, 0xff, 0x02, 0x75, 0x2b, 0x4a, 0xf3, 0x39, 0x91, 0x72, 0xb7, 0xd5, 0xcc, 0x38, 0xb8, 0xe7, 0x36, 0x26, 0x5e, 0x11, 0x97, 0x25, 0xfb, 0x49, 0x68, 0xdc, 0xb4, 0x46, 0x87, 0x5c, 0xc2, 0x7f, 0xaa, 0x7d, 0x36, 0x23, 0xa6, 0xc6, 0x53, 0xec, 0xbc, 0x57, 0x47, 0xc1, 0x2b,
|
||||
/* (2^366)P */ 0x25, 0x5d, 0x7d, 0x95, 0xda, 0x0b, 0x8f, 0x78, 0x1e, 0x19, 0x09, 0xfa, 0x67, 0xe0, 0xa0, 0x17, 0x24, 0x76, 0x6c, 0x30, 0x1f, 0x62, 0x3d, 0xbe, 0x45, 0x70, 0xcc, 0xb6, 0x1e, 0x68, 0x06, 0x25, 0x68, 0x16, 0x1a, 0x33, 0x3f, 0x90, 0xc7, 0x78, 0x2d, 0x98, 0x3c, 0x2f, 0xb9, 0x2d, 0x94, 0x0b, 0xfb, 0x49, 0x56, 0x30, 0xd7, 0xc1, 0xe6, 0x48,
|
||||
/* (2^367)P */ 0x7a, 0xd1, 0xe0, 0x8e, 0x67, 0xfc, 0x0b, 0x50, 0x1f, 0x84, 0x98, 0xfa, 0xaf, 0xae, 0x2e, 0x31, 0x27, 0xcf, 0x3f, 0xf2, 0x6e, 0x8d, 0x81, 0x8f, 0xd2, 0x5f, 0xde, 0xd3, 0x5e, 0xe9, 0xe7, 0x13, 0x48, 0x83, 0x5a, 0x4e, 0x84, 0xd1, 0x58, 0xcf, 0x6b, 0x84, 0xdf, 0x13, 0x1d, 0x91, 0x85, 0xe8, 0xcb, 0x29, 0x79, 0xd2, 0xca, 0xac, 0x6a, 0x93,
|
||||
/* (2^368)P */ 0x53, 0x82, 0xce, 0x61, 0x96, 0x88, 0x6f, 0xe1, 0x4a, 0x4c, 0x1e, 0x30, 0x73, 0xe8, 0x74, 0xde, 0x40, 0x2b, 0xe0, 0xc4, 0xb5, 0xd8, 0x7c, 0x15, 0xe7, 0xe1, 0xb1, 0xe0, 0xd6, 0x88, 0xb1, 0x6a, 0x57, 0x19, 0x6a, 0x22, 0x66, 0x57, 0xf6, 0x8d, 0xfd, 0xc0, 0xf2, 0xa3, 0x03, 0x56, 0xfb, 0x2e, 0x75, 0x5e, 0xc7, 0x8e, 0x22, 0x96, 0x5c, 0x06,
|
||||
/* (2^369)P */ 0x98, 0x7e, 0xbf, 0x3e, 0xbf, 0x24, 0x9d, 0x15, 0xd3, 0xf6, 0xd3, 0xd2, 0xf0, 0x11, 0xf2, 0xdb, 0x36, 0x23, 0x38, 0xf7, 0x1d, 0x71, 0x20, 0xd2, 0x54, 0x7f, 0x1e, 0x24, 0x8f, 0xe2, 0xaa, 0xf7, 0x3f, 0x6b, 0x41, 0x4e, 0xdc, 0x0e, 0xec, 0xe8, 0x35, 0x0a, 0x08, 0x6d, 0x89, 0x5b, 0x32, 0x91, 0x01, 0xb6, 0xe0, 0x2c, 0xc6, 0xa1, 0xbe, 0xb4,
|
||||
/* (2^370)P */ 0x29, 0xf2, 0x1e, 0x1c, 0xdc, 0x68, 0x8a, 0x43, 0x87, 0x2c, 0x48, 0xb3, 0x9e, 0xed, 0xd2, 0x82, 0x46, 0xac, 0x2f, 0xef, 0x93, 0x34, 0x37, 0xca, 0x64, 0x8d, 0xc9, 0x06, 0x90, 0xbb, 0x78, 0x0a, 0x3c, 0x4c, 0xcf, 0x35, 0x7a, 0x0f, 0xf7, 0xa7, 0xf4, 0x2f, 0x45, 0x69, 0x3f, 0xa9, 0x5d, 0xce, 0x7b, 0x8a, 0x84, 0xc3, 0xae, 0xf4, 0xda, 0xd5,
|
||||
/* (2^371)P */ 0xca, 0xba, 0x95, 0x43, 0x05, 0x7b, 0x06, 0xd9, 0x5c, 0x0a, 0x18, 0x5f, 0x6a, 0x6a, 0xce, 0xc0, 0x3d, 0x95, 0x51, 0x0e, 0x1a, 0xbe, 0x85, 0x7a, 0xf2, 0x69, 0xec, 0xc0, 0x8c, 0xca, 0xa3, 0x32, 0x0a, 0x76, 0x50, 0xc6, 0x76, 0x61, 0x00, 0x89, 0xbf, 0x6e, 0x0f, 0x48, 0x90, 0x31, 0x93, 0xec, 0x34, 0x70, 0xf0, 0xc3, 0x8d, 0xf0, 0x0f, 0xb5,
|
||||
/* (2^372)P */ 0xbe, 0x23, 0xe2, 0x18, 0x99, 0xf1, 0xed, 0x8a, 0xf6, 0xc9, 0xac, 0xb8, 0x1e, 0x9a, 0x3c, 0x15, 0xae, 0xd7, 0x6d, 0xb3, 0x04, 0xee, 0x5b, 0x0d, 0x1e, 0x79, 0xb7, 0xf9, 0xf9, 0x8d, 0xad, 0xf9, 0x8f, 0x5a, 0x6a, 0x7b, 0xd7, 0x9b, 0xca, 0x62, 0xfe, 0x9c, 0xc0, 0x6f, 0x6d, 0x9d, 0x76, 0xa3, 0x69, 0xb9, 0x4c, 0xa1, 0xc4, 0x0c, 0x76, 0xaa,
|
||||
/* (2^373)P */ 0x1c, 0x06, 0xfe, 0x3f, 0x45, 0x70, 0xcd, 0x97, 0xa9, 0xa2, 0xb1, 0xd3, 0xf2, 0xa5, 0x0c, 0x49, 0x2c, 0x75, 0x73, 0x1f, 0xcf, 0x00, 0xaf, 0xd5, 0x2e, 0xde, 0x0d, 0x8f, 0x8f, 0x7c, 0xc4, 0x58, 0xce, 0xd4, 0xf6, 0x24, 0x19, 0x2e, 0xd8, 0xc5, 0x1d, 0x1a, 0x3f, 0xb8, 0x4f, 0xbc, 0x7d, 0xbd, 0x68, 0xe3, 0x81, 0x98, 0x1b, 0xa8, 0xc9, 0xd9,
|
||||
/* (2^374)P */ 0x39, 0x95, 0x78, 0x24, 0x6c, 0x38, 0xe4, 0xe7, 0xd0, 0x8d, 0xb9, 0x38, 0x71, 0x5e, 0xc1, 0x62, 0x80, 0xcc, 0xcb, 0x8c, 0x97, 0xca, 0xf8, 0xb9, 0xd9, 0x9c, 0xce, 0x72, 0x7b, 0x70, 0xee, 0x5f, 0xea, 0xa2, 0xdf, 0xa9, 0x14, 0x10, 0xf9, 0x6e, 0x59, 0x9f, 0x9c, 0xe0, 0x0c, 0xb2, 0x07, 0x97, 0xcd, 0xd2, 0x89, 0x16, 0xfd, 0x9c, 0xa8, 0xa5,
|
||||
/* (2^375)P */ 0x5a, 0x61, 0xf1, 0x59, 0x7c, 0x38, 0xda, 0xe2, 0x85, 0x99, 0x68, 0xe9, 0xc9, 0xf7, 0x32, 0x7e, 0xc4, 0xca, 0xb7, 0x11, 0x08, 0x69, 0x2b, 0x66, 0x02, 0xf7, 0x2e, 0x18, 0xc3, 0x8e, 0xe1, 0xf9, 0xc5, 0x19, 0x9a, 0x0a, 0x9c, 0x07, 0xba, 0xc7, 0x9c, 0x03, 0x34, 0x89, 0x99, 0x67, 0x0b, 0x16, 0x4b, 0x07, 0x36, 0x16, 0x36, 0x2c, 0xe2, 0xa1,
|
||||
/* (2^376)P */ 0x70, 0x10, 0x91, 0x27, 0xa8, 0x24, 0x8e, 0x29, 0x04, 0x6f, 0x79, 0x1f, 0xd3, 0xa5, 0x68, 0xd3, 0x0b, 0x7d, 0x56, 0x4d, 0x14, 0x57, 0x7b, 0x2e, 0x00, 0x9f, 0x9a, 0xfd, 0x6c, 0x63, 0x18, 0x81, 0xdb, 0x9d, 0xb7, 0xd7, 0xa4, 0x1e, 0xe8, 0x40, 0xf1, 0x4c, 0xa3, 0x01, 0xd5, 0x4b, 0x75, 0xea, 0xdd, 0x97, 0xfd, 0x5b, 0xb2, 0x66, 0x6a, 0x24,
|
||||
/* (2^377)P */ 0x72, 0x11, 0xfe, 0x73, 0x1b, 0xd3, 0xea, 0x7f, 0x93, 0x15, 0x15, 0x05, 0xfe, 0x40, 0xe8, 0x28, 0xd8, 0x50, 0x47, 0x66, 0xfa, 0xb7, 0xb5, 0x04, 0xba, 0x35, 0x1e, 0x32, 0x9f, 0x5f, 0x32, 0xba, 0x3d, 0xd1, 0xed, 0x9a, 0x76, 0xca, 0xa3, 0x3e, 0x77, 0xd8, 0xd8, 0x7c, 0x5f, 0x68, 0x42, 0xb5, 0x86, 0x7f, 0x3b, 0xc9, 0xc1, 0x89, 0x64, 0xda,
|
||||
/* (2^378)P */ 0xd5, 0xd4, 0x17, 0x31, 0xfc, 0x6a, 0xfd, 0xb8, 0xe8, 0xe5, 0x3e, 0x39, 0x06, 0xe4, 0xd1, 0x90, 0x2a, 0xca, 0xf6, 0x54, 0x6c, 0x1b, 0x2f, 0x49, 0x97, 0xb1, 0x2a, 0x82, 0x43, 0x3d, 0x1f, 0x8b, 0xe2, 0x47, 0xc5, 0x24, 0xa8, 0xd5, 0x53, 0x29, 0x7d, 0xc6, 0x87, 0xa6, 0x25, 0x3a, 0x64, 0xdd, 0x71, 0x08, 0x9e, 0xcd, 0xe9, 0x45, 0xc7, 0xba,
|
||||
/* (2^379)P */ 0x37, 0x72, 0x6d, 0x13, 0x7a, 0x8d, 0x04, 0x31, 0xe6, 0xe3, 0x9e, 0x36, 0x71, 0x3e, 0xc0, 0x1e, 0xe3, 0x71, 0xd3, 0x49, 0x4e, 0x4a, 0x36, 0x42, 0x68, 0x68, 0x61, 0xc7, 0x3c, 0xdb, 0x81, 0x49, 0xf7, 0x91, 0x4d, 0xea, 0x4c, 0x4f, 0x98, 0xc6, 0x7e, 0x60, 0x84, 0x4b, 0x6a, 0x37, 0xbb, 0x52, 0xf7, 0xce, 0x02, 0xe4, 0xad, 0xd1, 0x3c, 0xa7,
|
||||
/* (2^380)P */ 0x51, 0x06, 0x2d, 0xf8, 0x08, 0xe8, 0xf1, 0x0c, 0xe5, 0xa9, 0xac, 0x29, 0x73, 0x3b, 0xed, 0x98, 0x5f, 0x55, 0x08, 0x38, 0x51, 0x44, 0x36, 0x5d, 0xea, 0xc3, 0xb8, 0x0e, 0xa0, 0x4f, 0xd2, 0x79, 0xe9, 0x98, 0xc3, 0xf5, 0x00, 0xb9, 0x26, 0x27, 0x42, 0xa8, 0x07, 0xc1, 0x12, 0x31, 0xc1, 0xc3, 0x3c, 0x3b, 0x7a, 0x72, 0x97, 0xc2, 0x70, 0x3a,
|
||||
/* (2^381)P */ 0xf4, 0xb2, 0xba, 0x32, 0xbc, 0xa9, 0x2f, 0x87, 0xc7, 0x3c, 0x45, 0xcd, 0xae, 0xe2, 0x13, 0x6d, 0x3a, 0xf2, 0xf5, 0x66, 0x97, 0x29, 0xaf, 0x53, 0x9f, 0xda, 0xea, 0x14, 0xdf, 0x04, 0x98, 0x19, 0x95, 0x9e, 0x2a, 0x00, 0x5c, 0x9d, 0x1d, 0xf0, 0x39, 0x23, 0xff, 0xfc, 0xca, 0x36, 0xb7, 0xde, 0xdf, 0x37, 0x78, 0x52, 0x21, 0xfa, 0x19, 0x10,
|
||||
/* (2^382)P */ 0x50, 0x20, 0x73, 0x74, 0x62, 0x21, 0xf2, 0xf7, 0x9b, 0x66, 0x85, 0x34, 0x74, 0xd4, 0x9d, 0x60, 0xd7, 0xbc, 0xc8, 0x46, 0x3b, 0xb8, 0x80, 0x42, 0x15, 0x0a, 0x6c, 0x35, 0x1a, 0x69, 0xf0, 0x1d, 0x4b, 0x29, 0x54, 0x5a, 0x9a, 0x48, 0xec, 0x9f, 0x37, 0x74, 0x91, 0xd0, 0xd1, 0x9e, 0x00, 0xc2, 0x76, 0x56, 0xd6, 0xa0, 0x15, 0x14, 0x83, 0x59,
|
||||
/* (2^383)P */ 0xc2, 0xf8, 0x22, 0x20, 0x23, 0x07, 0xbd, 0x1d, 0x6f, 0x1e, 0x8c, 0x56, 0x06, 0x6a, 0x4b, 0x9f, 0xe2, 0xa9, 0x92, 0x46, 0x4b, 0x46, 0x59, 0xd7, 0xe1, 0xda, 0x14, 0x98, 0x07, 0x65, 0x7e, 0x28, 0x20, 0xf2, 0x9d, 0x4f, 0x36, 0x5c, 0x92, 0xe0, 0x9d, 0xfe, 0x3e, 0xda, 0xe4, 0x47, 0x19, 0x3c, 0x00, 0x7f, 0x22, 0xf2, 0x9e, 0x51, 0xae, 0x4d,
|
||||
/* (2^384)P */ 0xbe, 0x8c, 0x1b, 0x10, 0xb6, 0xad, 0xcc, 0xcc, 0xd8, 0x5e, 0x21, 0xa6, 0xfb, 0xf1, 0xf6, 0xbd, 0x0a, 0x24, 0x67, 0xb4, 0x57, 0x7a, 0xbc, 0xe8, 0xe9, 0xff, 0xee, 0x0a, 0x1f, 0xee, 0xbd, 0xc8, 0x44, 0xed, 0x2b, 0xbb, 0x55, 0x1f, 0xdd, 0x7c, 0xb3, 0xeb, 0x3f, 0x63, 0xa1, 0x28, 0x91, 0x21, 0xab, 0x71, 0xc6, 0x4c, 0xd0, 0xe9, 0xb0, 0x21,
|
||||
/* (2^385)P */ 0xad, 0xc9, 0x77, 0x2b, 0xee, 0x89, 0xa4, 0x7b, 0xfd, 0xf9, 0xf6, 0x14, 0xe4, 0xed, 0x1a, 0x16, 0x9b, 0x78, 0x41, 0x43, 0xa8, 0x83, 0x72, 0x06, 0x2e, 0x7c, 0xdf, 0xeb, 0x7e, 0xdd, 0xd7, 0x8b, 0xea, 0x9a, 0x2b, 0x03, 0xba, 0x57, 0xf3, 0xf1, 0xd9, 0xe5, 0x09, 0xc5, 0x98, 0x61, 0x1c, 0x51, 0x6d, 0x5d, 0x6e, 0xfb, 0x5e, 0x95, 0x9f, 0xb5,
|
||||
/* (2^386)P */ 0x23, 0xe2, 0x1e, 0x95, 0xa3, 0x5e, 0x42, 0x10, 0xc7, 0xc3, 0x70, 0xbf, 0x4b, 0x6b, 0x83, 0x36, 0x93, 0xb7, 0x68, 0x47, 0x88, 0x3a, 0x10, 0x88, 0x48, 0x7f, 0x8c, 0xae, 0x54, 0x10, 0x02, 0xa4, 0x52, 0x8f, 0x8d, 0xf7, 0x26, 0x4f, 0x50, 0xc3, 0x6a, 0xe2, 0x4e, 0x3b, 0x4c, 0xb9, 0x8a, 0x14, 0x15, 0x6d, 0x21, 0x29, 0xb3, 0x6e, 0x4e, 0xd0,
|
||||
/* (2^387)P */ 0x4c, 0x8a, 0x18, 0x3f, 0xb7, 0x20, 0xfd, 0x3e, 0x54, 0xca, 0x68, 0x3c, 0xea, 0x6f, 0xf4, 0x6b, 0xa2, 0xbd, 0x01, 0xbd, 0xfe, 0x08, 0xa8, 0xd8, 0xc2, 0x20, 0x36, 0x05, 0xcd, 0xe9, 0xf3, 0x9e, 0xfa, 0x85, 0x66, 0x8f, 0x4b, 0x1d, 0x8c, 0x64, 0x4f, 0xb8, 0xc6, 0x0f, 0x5b, 0x57, 0xd8, 0x24, 0x19, 0x5a, 0x14, 0x4b, 0x92, 0xd3, 0x96, 0xbc,
|
||||
/* (2^388)P */ 0xa9, 0x3f, 0xc9, 0x6c, 0xca, 0x64, 0x1e, 0x6f, 0xdf, 0x65, 0x7f, 0x9a, 0x47, 0x6b, 0x8a, 0x60, 0x31, 0xa6, 0x06, 0xac, 0x69, 0x30, 0xe6, 0xea, 0x63, 0x42, 0x26, 0x5f, 0xdb, 0xd0, 0xf2, 0x8e, 0x34, 0x0a, 0x3a, 0xeb, 0xf3, 0x79, 0xc8, 0xb7, 0x60, 0x56, 0x5c, 0x37, 0x95, 0x71, 0xf8, 0x7f, 0x49, 0x3e, 0x9e, 0x01, 0x26, 0x1e, 0x80, 0x9f,
|
||||
/* (2^389)P */ 0xf8, 0x16, 0x9a, 0xaa, 0xb0, 0x28, 0xb5, 0x8e, 0xd0, 0x60, 0xe5, 0x26, 0xa9, 0x47, 0xc4, 0x5c, 0xa9, 0x39, 0xfe, 0x0a, 0xd8, 0x07, 0x2b, 0xb3, 0xce, 0xf1, 0xea, 0x1a, 0xf4, 0x7b, 0x98, 0x31, 0x3d, 0x13, 0x29, 0x80, 0xe8, 0x0d, 0xcf, 0x56, 0x39, 0x86, 0x50, 0x0c, 0xb3, 0x18, 0xf4, 0xc5, 0xca, 0xf2, 0x6f, 0xcd, 0x8d, 0xd5, 0x02, 0xb0,
|
||||
/* (2^390)P */ 0xbf, 0x39, 0x3f, 0xac, 0x6d, 0x1a, 0x6a, 0xe4, 0x42, 0x24, 0xd6, 0x41, 0x9d, 0xb9, 0x5b, 0x46, 0x73, 0x93, 0x76, 0xaa, 0xb7, 0x37, 0x36, 0xa6, 0x09, 0xe5, 0x04, 0x3b, 0x66, 0xc4, 0x29, 0x3e, 0x41, 0xc2, 0xcb, 0xe5, 0x17, 0xd7, 0x34, 0x67, 0x1d, 0x2c, 0x12, 0xec, 0x24, 0x7a, 0x40, 0xa2, 0x45, 0x41, 0xf0, 0x75, 0xed, 0x43, 0x30, 0xc9,
|
||||
/* (2^391)P */ 0x80, 0xf6, 0x47, 0x5b, 0xad, 0x54, 0x02, 0xbc, 0xdd, 0xa4, 0xb2, 0xd7, 0x42, 0x95, 0xf2, 0x0d, 0x1b, 0xef, 0x37, 0xa7, 0xb4, 0x34, 0x04, 0x08, 0x71, 0x1b, 0xd3, 0xdf, 0xa1, 0xf0, 0x2b, 0xfa, 0xc0, 0x1f, 0xf3, 0x44, 0xb5, 0xc6, 0x47, 0x3d, 0x65, 0x67, 0x45, 0x4d, 0x2f, 0xde, 0x52, 0x73, 0xfc, 0x30, 0x01, 0x6b, 0xc1, 0x03, 0xd8, 0xd7,
|
||||
/* (2^392)P */ 0x1c, 0x67, 0x55, 0x3e, 0x01, 0x17, 0x0f, 0x3e, 0xe5, 0x34, 0x58, 0xfc, 0xcb, 0x71, 0x24, 0x74, 0x5d, 0x36, 0x1e, 0x89, 0x2a, 0x63, 0xf8, 0xf8, 0x9f, 0x50, 0x9f, 0x32, 0x92, 0x29, 0xd8, 0x1a, 0xec, 0x76, 0x57, 0x6c, 0x67, 0x12, 0x6a, 0x6e, 0xef, 0x97, 0x1f, 0xc3, 0x77, 0x60, 0x3c, 0x22, 0xcb, 0xc7, 0x04, 0x1a, 0x89, 0x2d, 0x10, 0xa6,
|
||||
/* (2^393)P */ 0x12, 0xf5, 0xa9, 0x26, 0x16, 0xd9, 0x3c, 0x65, 0x5d, 0x83, 0xab, 0xd1, 0x70, 0x6b, 0x1c, 0xdb, 0xe7, 0x86, 0x0d, 0xfb, 0xe7, 0xf8, 0x2a, 0x58, 0x6e, 0x7a, 0x66, 0x13, 0x53, 0x3a, 0x6f, 0x8d, 0x43, 0x5f, 0x14, 0x23, 0x14, 0xff, 0x3d, 0x52, 0x7f, 0xee, 0xbd, 0x7a, 0x34, 0x8b, 0x35, 0x24, 0xc3, 0x7a, 0xdb, 0xcf, 0x22, 0x74, 0x9a, 0x8f,
|
||||
/* (2^394)P */ 0xdb, 0x20, 0xfc, 0xe5, 0x39, 0x4e, 0x7d, 0x78, 0xee, 0x0b, 0xbf, 0x1d, 0x80, 0xd4, 0x05, 0x4f, 0xb9, 0xd7, 0x4e, 0x94, 0x88, 0x9a, 0x50, 0x78, 0x1a, 0x70, 0x8c, 0xcc, 0x25, 0xb6, 0x61, 0x09, 0xdc, 0x7b, 0xea, 0x3f, 0x7f, 0xea, 0x2a, 0x0d, 0x47, 0x1c, 0x8e, 0xa6, 0x5b, 0xd2, 0xa3, 0x61, 0x93, 0x3c, 0x68, 0x9f, 0x8b, 0xea, 0xb0, 0xcb,
|
||||
/* (2^395)P */ 0xff, 0x54, 0x02, 0x19, 0xae, 0x8b, 0x4c, 0x2c, 0x3a, 0xe0, 0xe4, 0xac, 0x87, 0xf7, 0x51, 0x45, 0x41, 0x43, 0xdc, 0xaa, 0xcd, 0xcb, 0xdc, 0x40, 0xe3, 0x44, 0x3b, 0x1d, 0x9e, 0x3d, 0xb9, 0x82, 0xcc, 0x7a, 0xc5, 0x12, 0xf8, 0x1e, 0xdd, 0xdb, 0x8d, 0xb0, 0x2a, 0xe8, 0xe6, 0x6c, 0x94, 0x3b, 0xb7, 0x2d, 0xba, 0x79, 0x3b, 0xb5, 0x86, 0xfb,
|
||||
/* (2^396)P */ 0x82, 0x88, 0x13, 0xdd, 0x6c, 0xcd, 0x85, 0x2b, 0x90, 0x86, 0xb7, 0xac, 0x16, 0xa6, 0x6e, 0x6a, 0x94, 0xd8, 0x1e, 0x4e, 0x41, 0x0f, 0xce, 0x81, 0x6a, 0xa8, 0x26, 0x56, 0x43, 0x52, 0x52, 0xe6, 0xff, 0x88, 0xcf, 0x47, 0x05, 0x1d, 0xff, 0xf3, 0xa0, 0x10, 0xb2, 0x97, 0x87, 0xeb, 0x47, 0xbb, 0xfa, 0x1f, 0xe8, 0x4c, 0xce, 0xc4, 0xcd, 0x93,
|
||||
/* (2^397)P */ 0xf4, 0x11, 0xf5, 0x8d, 0x89, 0x29, 0x79, 0xb3, 0x59, 0x0b, 0x29, 0x7d, 0x9c, 0x12, 0x4a, 0x65, 0x72, 0x3a, 0xf9, 0xec, 0x37, 0x18, 0x86, 0xef, 0x44, 0x07, 0x25, 0x74, 0x76, 0x53, 0xed, 0x51, 0x01, 0xc6, 0x28, 0xc5, 0xc3, 0x4a, 0x0f, 0x99, 0xec, 0xc8, 0x40, 0x5a, 0x83, 0x30, 0x79, 0xa2, 0x3e, 0x63, 0x09, 0x2d, 0x6f, 0x23, 0x54, 0x1c,
|
||||
/* (2^398)P */ 0x5c, 0x6f, 0x3b, 0x1c, 0x30, 0x77, 0x7e, 0x87, 0x66, 0x83, 0x2e, 0x7e, 0x85, 0x50, 0xfd, 0xa0, 0x7a, 0xc2, 0xf5, 0x0f, 0xc1, 0x64, 0xe7, 0x0b, 0xbd, 0x59, 0xa7, 0xe7, 0x65, 0x53, 0xc3, 0xf5, 0x55, 0x5b, 0xe1, 0x82, 0x30, 0x5a, 0x61, 0xcd, 0xa0, 0x89, 0x32, 0xdb, 0x87, 0xfc, 0x21, 0x8a, 0xab, 0x6d, 0x82, 0xa8, 0x42, 0x81, 0x4f, 0xf2,
|
||||
/* (2^399)P */ 0xb3, 0xeb, 0x88, 0x18, 0xf6, 0x56, 0x96, 0xbf, 0xba, 0x5d, 0x71, 0xa1, 0x5a, 0xd1, 0x04, 0x7b, 0xd5, 0x46, 0x01, 0x74, 0xfe, 0x15, 0x25, 0xb7, 0xff, 0x0c, 0x24, 0x47, 0xac, 0xfd, 0xab, 0x47, 0x32, 0xe1, 0x6a, 0x4e, 0xca, 0xcf, 0x7f, 0xdd, 0xf8, 0xd2, 0x4b, 0x3b, 0xf5, 0x17, 0xba, 0xba, 0x8b, 0xa1, 0xec, 0x28, 0x3f, 0x97, 0xab, 0x2a,
|
||||
/* (2^400)P */ 0x51, 0x38, 0xc9, 0x5e, 0xc6, 0xb3, 0x64, 0xf2, 0x24, 0x4d, 0x04, 0x7d, 0xc8, 0x39, 0x0c, 0x4a, 0xc9, 0x73, 0x74, 0x1b, 0x5c, 0xb2, 0xc5, 0x41, 0x62, 0xa0, 0x4c, 0x6d, 0x8d, 0x91, 0x9a, 0x7b, 0x88, 0xab, 0x9c, 0x7e, 0x23, 0xdb, 0x6f, 0xb5, 0x72, 0xd6, 0x47, 0x40, 0xef, 0x22, 0x58, 0x62, 0x19, 0x6c, 0x38, 0xba, 0x5b, 0x00, 0x30, 0x9f,
|
||||
/* (2^401)P */ 0x65, 0xbb, 0x3b, 0x9b, 0xe9, 0xae, 0xbf, 0xbe, 0xe4, 0x13, 0x95, 0xf3, 0xe3, 0x77, 0xcb, 0xe4, 0x9a, 0x22, 0xb5, 0x4a, 0x08, 0x9d, 0xb3, 0x9e, 0x27, 0xe0, 0x15, 0x6c, 0x9f, 0x7e, 0x9a, 0x5e, 0x15, 0x45, 0x25, 0x8d, 0x01, 0x0a, 0xd2, 0x2b, 0xbd, 0x48, 0x06, 0x0d, 0x18, 0x97, 0x4b, 0xdc, 0xbc, 0xf0, 0xcd, 0xb2, 0x52, 0x3c, 0xac, 0xf5,
|
||||
/* (2^402)P */ 0x3e, 0xed, 0x47, 0x6b, 0x5c, 0xf6, 0x76, 0xd0, 0xe9, 0x15, 0xa3, 0xcb, 0x36, 0x00, 0x21, 0xa3, 0x79, 0x20, 0xa5, 0x3e, 0x88, 0x03, 0xcb, 0x7e, 0x63, 0xbb, 0xed, 0xa9, 0x13, 0x35, 0x16, 0xaf, 0x2e, 0xb4, 0x70, 0x14, 0x93, 0xfb, 0xc4, 0x9b, 0xd8, 0xb1, 0xbe, 0x43, 0xd1, 0x85, 0xb8, 0x97, 0xef, 0xea, 0x88, 0xa1, 0x25, 0x52, 0x62, 0x75,
|
||||
/* (2^403)P */ 0x8e, 0x4f, 0xaa, 0x23, 0x62, 0x7e, 0x2b, 0x37, 0x89, 0x00, 0x11, 0x30, 0xc5, 0x33, 0x4a, 0x89, 0x8a, 0xe2, 0xfc, 0x5c, 0x6a, 0x75, 0xe5, 0xf7, 0x02, 0x4a, 0x9b, 0xf7, 0xb5, 0x6a, 0x85, 0x31, 0xd3, 0x5a, 0xcf, 0xc3, 0xf8, 0xde, 0x2f, 0xcf, 0xb5, 0x24, 0xf4, 0xe3, 0xa1, 0xad, 0x42, 0xae, 0x09, 0xb9, 0x2e, 0x04, 0x2d, 0x01, 0x22, 0x3f,
|
||||
/* (2^404)P */ 0x41, 0x16, 0xfb, 0x7d, 0x50, 0xfd, 0xb5, 0xba, 0x88, 0x24, 0xba, 0xfd, 0x3d, 0xb2, 0x90, 0x15, 0xb7, 0xfa, 0xa2, 0xe1, 0x4c, 0x7d, 0xb9, 0xc6, 0xff, 0x81, 0x57, 0xb6, 0xc2, 0x9e, 0xcb, 0xc4, 0x35, 0xbd, 0x01, 0xb7, 0xaa, 0xce, 0xd0, 0xe9, 0xb5, 0xd6, 0x72, 0xbf, 0xd2, 0xee, 0xc7, 0xac, 0x94, 0xff, 0x29, 0x57, 0x02, 0x49, 0x09, 0xad,
|
||||
/* (2^405)P */ 0x27, 0xa5, 0x78, 0x1b, 0xbf, 0x6b, 0xaf, 0x0b, 0x8c, 0xd9, 0xa8, 0x37, 0xb0, 0x67, 0x18, 0xb6, 0xc7, 0x05, 0x8a, 0x67, 0x03, 0x30, 0x62, 0x6e, 0x56, 0x82, 0xa9, 0x54, 0x3e, 0x0c, 0x4e, 0x07, 0xe1, 0x5a, 0x38, 0xed, 0xfa, 0xc8, 0x55, 0x6b, 0x08, 0xa3, 0x6b, 0x64, 0x2a, 0x15, 0xd6, 0x39, 0x6f, 0x47, 0x99, 0x42, 0x3f, 0x33, 0x84, 0x8f,
|
||||
/* (2^406)P */ 0xbc, 0x45, 0x29, 0x81, 0x0e, 0xa4, 0xc5, 0x72, 0x3a, 0x10, 0xe1, 0xc4, 0x1e, 0xda, 0xc3, 0xfe, 0xb0, 0xce, 0xd2, 0x13, 0x34, 0x67, 0x21, 0xc6, 0x7e, 0xf9, 0x8c, 0xff, 0x39, 0x50, 0xae, 0x92, 0x60, 0x35, 0x2f, 0x8b, 0x6e, 0xc9, 0xc1, 0x27, 0x3a, 0x94, 0x66, 0x3e, 0x26, 0x84, 0x93, 0xc8, 0x6c, 0xcf, 0xd2, 0x03, 0xa1, 0x10, 0xcf, 0xb7,
|
||||
/* (2^407)P */ 0x64, 0xda, 0x19, 0xf6, 0xc5, 0x73, 0x17, 0x44, 0x88, 0x81, 0x07, 0x0d, 0x34, 0xb2, 0x75, 0xf9, 0xd9, 0xe2, 0xe0, 0x8b, 0x71, 0xcf, 0x72, 0x34, 0x83, 0xb4, 0xce, 0xfc, 0xd7, 0x29, 0x09, 0x5a, 0x98, 0xbf, 0x14, 0xac, 0x77, 0x55, 0x38, 0x47, 0x5b, 0x0f, 0x40, 0x24, 0xe5, 0xa5, 0xa6, 0xac, 0x2d, 0xa6, 0xff, 0x9c, 0x73, 0xfe, 0x5c, 0x7e,
|
||||
/* (2^408)P */ 0x1e, 0x33, 0xcc, 0x68, 0xb2, 0xbc, 0x8c, 0x93, 0xaf, 0xcc, 0x38, 0xf8, 0xd9, 0x16, 0x72, 0x50, 0xac, 0xd9, 0xb5, 0x0b, 0x9a, 0xbe, 0x46, 0x7a, 0xf1, 0xee, 0xf1, 0xad, 0xec, 0x5b, 0x59, 0x27, 0x9c, 0x05, 0xa3, 0x87, 0xe0, 0x37, 0x2c, 0x83, 0xce, 0xb3, 0x65, 0x09, 0x8e, 0xc3, 0x9c, 0xbf, 0x6a, 0xa2, 0x00, 0xcc, 0x12, 0x36, 0xc5, 0x95,
|
||||
/* (2^409)P */ 0x36, 0x11, 0x02, 0x14, 0x9c, 0x3c, 0xeb, 0x2f, 0x23, 0x5b, 0x6b, 0x2b, 0x08, 0x54, 0x53, 0xac, 0xb2, 0xa3, 0xe0, 0x26, 0x62, 0x3c, 0xe4, 0xe1, 0x81, 0xee, 0x13, 0x3e, 0xa4, 0x97, 0xef, 0xf9, 0x92, 0x27, 0x01, 0xce, 0x54, 0x8b, 0x3e, 0x31, 0xbe, 0xa7, 0x88, 0xcf, 0x47, 0x99, 0x3c, 0x10, 0x6f, 0x60, 0xb3, 0x06, 0x4e, 0xee, 0x1b, 0xf0,
|
||||
/* (2^410)P */ 0x59, 0x49, 0x66, 0xcf, 0x22, 0xe6, 0xf6, 0x73, 0xfe, 0xa3, 0x1c, 0x09, 0xfa, 0x5f, 0x65, 0xa8, 0xf0, 0x82, 0xc2, 0xef, 0x16, 0x63, 0x6e, 0x79, 0x69, 0x51, 0x39, 0x07, 0x65, 0xc4, 0x81, 0xec, 0x73, 0x0f, 0x15, 0x93, 0xe1, 0x30, 0x33, 0xe9, 0x37, 0x86, 0x42, 0x4c, 0x1f, 0x9b, 0xad, 0xee, 0x3f, 0xf1, 0x2a, 0x8e, 0x6a, 0xa3, 0xc8, 0x35,
|
||||
/* (2^411)P */ 0x1e, 0x49, 0xf1, 0xdd, 0xd2, 0x9c, 0x8e, 0x78, 0xb2, 0x06, 0xe4, 0x6a, 0xab, 0x3a, 0xdc, 0xcd, 0xf4, 0xeb, 0xe1, 0xe7, 0x2f, 0xaa, 0xeb, 0x40, 0x31, 0x9f, 0xb9, 0xab, 0x13, 0xa9, 0x78, 0xbf, 0x38, 0x89, 0x0e, 0x85, 0x14, 0x8b, 0x46, 0x76, 0x14, 0xda, 0xcf, 0x33, 0xc8, 0x79, 0xd3, 0xd5, 0xa3, 0x6a, 0x69, 0x45, 0x70, 0x34, 0xc3, 0xe9,
|
||||
/* (2^412)P */ 0x5e, 0xe7, 0x78, 0xe9, 0x24, 0xcc, 0xe9, 0xf4, 0xc8, 0x6b, 0xe0, 0xfb, 0x3a, 0xbe, 0xcc, 0x42, 0x4a, 0x00, 0x22, 0xf8, 0xe6, 0x32, 0xbe, 0x6d, 0x18, 0x55, 0x60, 0xe9, 0x72, 0x69, 0x50, 0x56, 0xca, 0x04, 0x18, 0x38, 0xa1, 0xee, 0xd8, 0x38, 0x3c, 0xa7, 0x70, 0xe2, 0xb9, 0x4c, 0xa0, 0xc8, 0x89, 0x72, 0xcf, 0x49, 0x7f, 0xdf, 0xbc, 0x67,
|
||||
/* (2^413)P */ 0x1d, 0x17, 0xcb, 0x0b, 0xbd, 0xb2, 0x36, 0xe3, 0xa8, 0x99, 0x31, 0xb6, 0x26, 0x9c, 0x0c, 0x74, 0xaf, 0x4d, 0x24, 0x61, 0xcf, 0x31, 0x7b, 0xed, 0xdd, 0xc3, 0xf6, 0x32, 0x70, 0xfe, 0x17, 0xf6, 0x51, 0x37, 0x65, 0xce, 0x5d, 0xaf, 0xa5, 0x2f, 0x2a, 0xfe, 0x00, 0x71, 0x7c, 0x50, 0xbe, 0x21, 0xc7, 0xed, 0xc6, 0xfc, 0x67, 0xcf, 0x9c, 0xdd,
|
||||
/* (2^414)P */ 0x26, 0x3e, 0xf8, 0xbb, 0xd0, 0xb1, 0x01, 0xd8, 0xeb, 0x0b, 0x62, 0x87, 0x35, 0x4c, 0xde, 0xca, 0x99, 0x9c, 0x6d, 0xf7, 0xb6, 0xf0, 0x57, 0x0a, 0x52, 0x29, 0x6a, 0x3f, 0x26, 0x31, 0x04, 0x07, 0x2a, 0xc9, 0xfa, 0x9b, 0x0e, 0x62, 0x8e, 0x72, 0xf2, 0xad, 0xce, 0xb6, 0x35, 0x7a, 0xc1, 0xae, 0x35, 0xc7, 0xa3, 0x14, 0xcf, 0x0c, 0x28, 0xb7,
|
||||
/* (2^415)P */ 0xa6, 0xf1, 0x32, 0x3a, 0x20, 0xd2, 0x24, 0x97, 0xcf, 0x5d, 0x37, 0x99, 0xaf, 0x33, 0x7a, 0x5b, 0x7a, 0xcc, 0x4e, 0x41, 0x38, 0xb1, 0x4e, 0xad, 0xc9, 0xd9, 0x71, 0x7e, 0xb2, 0xf5, 0xd5, 0x01, 0x6c, 0x4d, 0xfd, 0xa1, 0xda, 0x03, 0x38, 0x9b, 0x3d, 0x92, 0x92, 0xf2, 0xca, 0xbf, 0x1f, 0x24, 0xa4, 0xbb, 0x30, 0x6a, 0x74, 0x56, 0xc8, 0xce,
|
||||
/* (2^416)P */ 0x27, 0xf4, 0xed, 0xc9, 0xc3, 0xb1, 0x79, 0x85, 0xbe, 0xf6, 0xeb, 0xf3, 0x55, 0xc7, 0xaa, 0xa6, 0xe9, 0x07, 0x5d, 0xf4, 0xeb, 0xa6, 0x81, 0xe3, 0x0e, 0xcf, 0xa3, 0xc1, 0xef, 0xe7, 0x34, 0xb2, 0x03, 0x73, 0x8a, 0x91, 0xf1, 0xad, 0x05, 0xc7, 0x0b, 0x43, 0x99, 0x12, 0x31, 0xc8, 0xc7, 0xc5, 0xa4, 0x3d, 0xcd, 0xe5, 0x4e, 0x6d, 0x24, 0xdd,
|
||||
/* (2^417)P */ 0x61, 0x54, 0xd0, 0x95, 0x2c, 0x45, 0x75, 0xac, 0xb5, 0x1a, 0x9d, 0x11, 0xeb, 0xed, 0x6b, 0x57, 0xa3, 0xe6, 0xcd, 0x77, 0xd4, 0x83, 0x8e, 0x39, 0xf1, 0x0f, 0x98, 0xcb, 0x40, 0x02, 0x6e, 0x10, 0x82, 0x9e, 0xb4, 0x93, 0x76, 0xd7, 0x97, 0xa3, 0x53, 0x12, 0x86, 0xc6, 0x15, 0x78, 0x73, 0x93, 0xe7, 0x7f, 0xcf, 0x1f, 0xbf, 0xcd, 0xd2, 0x7a,
|
||||
/* (2^418)P */ 0xc2, 0x21, 0xdc, 0xd5, 0x69, 0xff, 0xca, 0x49, 0x3a, 0xe1, 0xc3, 0x69, 0x41, 0x56, 0xc1, 0x76, 0x63, 0x24, 0xbd, 0x64, 0x1b, 0x3d, 0x92, 0xf9, 0x13, 0x04, 0x25, 0xeb, 0x27, 0xa6, 0xef, 0x39, 0x3a, 0x80, 0xe0, 0xf8, 0x27, 0xee, 0xc9, 0x49, 0x77, 0xef, 0x3f, 0x29, 0x3d, 0x5e, 0xe6, 0x66, 0x83, 0xd1, 0xf6, 0xfe, 0x9d, 0xbc, 0xf1, 0x96,
|
||||
/* (2^419)P */ 0x6b, 0xc6, 0x99, 0x26, 0x3c, 0xf3, 0x63, 0xf9, 0xc7, 0x29, 0x8c, 0x52, 0x62, 0x2d, 0xdc, 0x8a, 0x66, 0xce, 0x2c, 0xa7, 0xe4, 0xf0, 0xd7, 0x37, 0x17, 0x1e, 0xe4, 0xa3, 0x53, 0x7b, 0x29, 0x8e, 0x60, 0x99, 0xf9, 0x0c, 0x7c, 0x6f, 0xa2, 0xcc, 0x9f, 0x80, 0xdd, 0x5e, 0x46, 0xaa, 0x0d, 0x6c, 0xc9, 0x6c, 0xf7, 0x78, 0x5b, 0x38, 0xe3, 0x24,
|
||||
/* (2^420)P */ 0x4b, 0x75, 0x6a, 0x2f, 0x08, 0xe1, 0x72, 0x76, 0xab, 0x82, 0x96, 0xdf, 0x3b, 0x1f, 0x9b, 0xd8, 0xed, 0xdb, 0xcd, 0x15, 0x09, 0x5a, 0x1e, 0xb7, 0xc5, 0x26, 0x72, 0x07, 0x0c, 0x50, 0xcd, 0x3b, 0x4d, 0x3f, 0xa2, 0x67, 0xc2, 0x02, 0x61, 0x2e, 0x68, 0xe9, 0x6f, 0xf0, 0x21, 0x2a, 0xa7, 0x3b, 0x88, 0x04, 0x11, 0x64, 0x49, 0x0d, 0xb4, 0x46,
|
||||
/* (2^421)P */ 0x63, 0x85, 0xf3, 0xc5, 0x2b, 0x5a, 0x9f, 0xf0, 0x17, 0xcb, 0x45, 0x0a, 0xf3, 0x6e, 0x7e, 0xb0, 0x7c, 0xbc, 0xf0, 0x4f, 0x3a, 0xb0, 0xbc, 0x36, 0x36, 0x52, 0x51, 0xcb, 0xfe, 0x9a, 0xcb, 0xe8, 0x7e, 0x4b, 0x06, 0x7f, 0xaa, 0x35, 0xc8, 0x0e, 0x7a, 0x30, 0xa3, 0xb1, 0x09, 0xbb, 0x86, 0x4c, 0xbe, 0xb8, 0xbd, 0xe0, 0x32, 0xa5, 0xd4, 0xf7,
|
||||
/* (2^422)P */ 0x7d, 0x50, 0x37, 0x68, 0x4e, 0x22, 0xb2, 0x2c, 0xd5, 0x0f, 0x2b, 0x6d, 0xb1, 0x51, 0xf2, 0x82, 0xe9, 0x98, 0x7c, 0x50, 0xc7, 0x96, 0x7e, 0x0e, 0xdc, 0xb1, 0x0e, 0xb2, 0x63, 0x8c, 0x30, 0x37, 0x72, 0x21, 0x9c, 0x61, 0xc2, 0xa7, 0x33, 0xd9, 0xb2, 0x63, 0x93, 0xd1, 0x6b, 0x6a, 0x73, 0xa5, 0x58, 0x80, 0xff, 0x04, 0xc7, 0x83, 0x21, 0x29,
|
||||
/* (2^423)P */ 0x29, 0x04, 0xbc, 0x99, 0x39, 0xc9, 0x58, 0xc9, 0x6b, 0x17, 0xe8, 0x90, 0xb3, 0xe6, 0xa9, 0xb6, 0x28, 0x9b, 0xcb, 0x3b, 0x28, 0x90, 0x68, 0x71, 0xff, 0xcf, 0x08, 0x78, 0xc9, 0x8d, 0xa8, 0x4e, 0x43, 0xd1, 0x1c, 0x9e, 0xa4, 0xe3, 0xdf, 0xbf, 0x92, 0xf4, 0xf9, 0x41, 0xba, 0x4d, 0x1c, 0xf9, 0xdd, 0x74, 0x76, 0x1c, 0x6e, 0x3e, 0x94, 0x87,
|
||||
/* (2^424)P */ 0xe4, 0xda, 0xc5, 0xd7, 0xfb, 0x87, 0xc5, 0x4d, 0x6b, 0x19, 0xaa, 0xb9, 0xbc, 0x8c, 0xf2, 0x8a, 0xd8, 0x5d, 0xdb, 0x4d, 0xef, 0xa6, 0xf2, 0x65, 0xf1, 0x22, 0x9c, 0xf1, 0x46, 0x30, 0x71, 0x7c, 0xe4, 0x53, 0x8e, 0x55, 0x2e, 0x9c, 0x9a, 0x31, 0x2a, 0xc3, 0xab, 0x0f, 0xde, 0xe4, 0xbe, 0xd8, 0x96, 0x50, 0x6e, 0x0c, 0x54, 0x49, 0xe6, 0xec,
|
||||
/* (2^425)P */ 0x3c, 0x1d, 0x5a, 0xa5, 0xda, 0xad, 0xdd, 0xc2, 0xae, 0xac, 0x6f, 0x86, 0x75, 0x31, 0x91, 0x64, 0x45, 0x9d, 0xa4, 0xf0, 0x81, 0xf1, 0x0e, 0xba, 0x74, 0xaf, 0x7b, 0xcd, 0x6f, 0xfe, 0xac, 0x4e, 0xdb, 0x4e, 0x45, 0x35, 0x36, 0xc5, 0xc0, 0x6c, 0x3d, 0x64, 0xf4, 0xd8, 0x07, 0x62, 0xd1, 0xec, 0xf3, 0xfc, 0x93, 0xc9, 0x28, 0x0c, 0x2c, 0xf3,
|
||||
/* (2^426)P */ 0x0c, 0x69, 0x2b, 0x5c, 0xb6, 0x41, 0x69, 0xf1, 0xa4, 0xf1, 0x5b, 0x75, 0x4c, 0x42, 0x8b, 0x47, 0xeb, 0x69, 0xfb, 0xa8, 0xe6, 0xf9, 0x7b, 0x48, 0x50, 0xaf, 0xd3, 0xda, 0xb2, 0x35, 0x10, 0xb5, 0x5b, 0x40, 0x90, 0x39, 0xc9, 0x07, 0x06, 0x73, 0x26, 0x20, 0x95, 0x01, 0xa4, 0x2d, 0xf0, 0xe7, 0x2e, 0x00, 0x7d, 0x41, 0x09, 0x68, 0x13, 0xc4,
|
||||
/* (2^427)P */ 0xbe, 0x38, 0x78, 0xcf, 0xc9, 0x4f, 0x36, 0xca, 0x09, 0x61, 0x31, 0x3c, 0x57, 0x2e, 0xec, 0x17, 0xa4, 0x7d, 0x19, 0x2b, 0x9b, 0x5b, 0xbe, 0x8f, 0xd6, 0xc5, 0x2f, 0x86, 0xf2, 0x64, 0x76, 0x17, 0x00, 0x6e, 0x1a, 0x8c, 0x67, 0x1b, 0x68, 0xeb, 0x15, 0xa2, 0xd6, 0x09, 0x91, 0xdd, 0x23, 0x0d, 0x98, 0xb2, 0x10, 0x19, 0x55, 0x9b, 0x63, 0xf2,
|
||||
/* (2^428)P */ 0x51, 0x1f, 0x93, 0xea, 0x2a, 0x3a, 0xfa, 0x41, 0xc0, 0x57, 0xfb, 0x74, 0xa6, 0x65, 0x09, 0x56, 0x14, 0xb6, 0x12, 0xaa, 0xb3, 0x1a, 0x8d, 0x3b, 0x76, 0x91, 0x7a, 0x23, 0x56, 0x9c, 0x6a, 0xc0, 0xe0, 0x3c, 0x3f, 0xb5, 0x1a, 0xf4, 0x57, 0x71, 0x93, 0x2b, 0xb1, 0xa7, 0x70, 0x57, 0x22, 0x80, 0xf5, 0xb8, 0x07, 0x77, 0x87, 0x0c, 0xbe, 0x83,
|
||||
/* (2^429)P */ 0x07, 0x9b, 0x0e, 0x52, 0x38, 0x63, 0x13, 0x86, 0x6a, 0xa6, 0xb4, 0xd2, 0x60, 0x68, 0x9a, 0x99, 0x82, 0x0a, 0x04, 0x5f, 0x89, 0x7a, 0x1a, 0x2a, 0xae, 0x2d, 0x35, 0x0c, 0x1e, 0xad, 0xef, 0x4f, 0x9a, 0xfc, 0xc8, 0xd9, 0xcf, 0x9d, 0x48, 0x71, 0xa5, 0x55, 0x79, 0x73, 0x39, 0x1b, 0xd8, 0x73, 0xec, 0x9b, 0x03, 0x16, 0xd8, 0x82, 0xf7, 0x67,
|
||||
/* (2^430)P */ 0x52, 0x67, 0x42, 0x21, 0xc9, 0x40, 0x78, 0x82, 0x2b, 0x95, 0x2d, 0x20, 0x92, 0xd1, 0xe2, 0x61, 0x25, 0xb0, 0xc6, 0x9c, 0x20, 0x59, 0x8e, 0x28, 0x6f, 0xf3, 0xfd, 0xd3, 0xc1, 0x32, 0x43, 0xc9, 0xa6, 0x08, 0x7a, 0x77, 0x9c, 0x4c, 0x8c, 0x33, 0x71, 0x13, 0x69, 0xe3, 0x52, 0x30, 0xa7, 0xf5, 0x07, 0x67, 0xac, 0xad, 0x46, 0x8a, 0x26, 0x25,
|
||||
/* (2^431)P */ 0xda, 0x86, 0xc4, 0xa2, 0x71, 0x56, 0xdd, 0xd2, 0x48, 0xd3, 0xde, 0x42, 0x63, 0x01, 0xa7, 0x2c, 0x92, 0x83, 0x6f, 0x2e, 0xd8, 0x1e, 0x3f, 0xc1, 0xc5, 0x42, 0x4e, 0x34, 0x19, 0x54, 0x6e, 0x35, 0x2c, 0x51, 0x2e, 0xfd, 0x0f, 0x9a, 0x45, 0x66, 0x5e, 0x4a, 0x83, 0xda, 0x0a, 0x53, 0x68, 0x63, 0xfa, 0xce, 0x47, 0x20, 0xd3, 0x34, 0xba, 0x0d,
|
||||
/* (2^432)P */ 0xd0, 0xe9, 0x64, 0xa4, 0x61, 0x4b, 0x86, 0xe5, 0x93, 0x6f, 0xda, 0x0e, 0x31, 0x7e, 0x6e, 0xe3, 0xc6, 0x73, 0xd8, 0xa3, 0x08, 0x57, 0x52, 0xcd, 0x51, 0x63, 0x1d, 0x9f, 0x93, 0x00, 0x62, 0x91, 0x26, 0x21, 0xa7, 0xdd, 0x25, 0x0f, 0x09, 0x0d, 0x35, 0xad, 0xcf, 0x11, 0x8e, 0x6e, 0xe8, 0xae, 0x1d, 0x95, 0xcb, 0x88, 0xf8, 0x70, 0x7b, 0x91,
|
||||
/* (2^433)P */ 0x0c, 0x19, 0x5c, 0xd9, 0x8d, 0xda, 0x9d, 0x2c, 0x90, 0x54, 0x65, 0xe8, 0xb6, 0x35, 0x50, 0xae, 0xea, 0xae, 0x43, 0xb7, 0x1e, 0x99, 0x8b, 0x4c, 0x36, 0x4e, 0xe4, 0x1e, 0xc4, 0x64, 0x43, 0xb6, 0xeb, 0xd4, 0xe9, 0x60, 0x22, 0xee, 0xcf, 0xb8, 0x52, 0x1b, 0xf0, 0x04, 0xce, 0xbc, 0x2b, 0xf0, 0xbe, 0xcd, 0x44, 0x74, 0x1e, 0x1f, 0x63, 0xf9,
|
||||
/* (2^434)P */ 0xe1, 0x3f, 0x95, 0x94, 0xb2, 0xb6, 0x31, 0xa9, 0x1b, 0xdb, 0xfd, 0x0e, 0xdb, 0xdd, 0x1a, 0x22, 0x78, 0x60, 0x9f, 0x75, 0x5f, 0x93, 0x06, 0x0c, 0xd8, 0xbb, 0xa2, 0x85, 0x2b, 0x5e, 0xc0, 0x9b, 0xa8, 0x5d, 0xaf, 0x93, 0x91, 0x91, 0x47, 0x41, 0x1a, 0xfc, 0xb4, 0x51, 0x85, 0xad, 0x69, 0x4d, 0x73, 0x69, 0xd5, 0x4e, 0x82, 0xfb, 0x66, 0xcb,
|
||||
/* (2^435)P */ 0x7c, 0xbe, 0xc7, 0x51, 0xc4, 0x74, 0x6e, 0xab, 0xfd, 0x41, 0x4f, 0x76, 0x4f, 0x24, 0x03, 0xd6, 0x2a, 0xb7, 0x42, 0xb4, 0xda, 0x41, 0x2c, 0x82, 0x48, 0x4c, 0x7f, 0x6f, 0x25, 0x5d, 0x36, 0xd4, 0x69, 0xf5, 0xef, 0x02, 0x81, 0xea, 0x6f, 0x19, 0x69, 0xe8, 0x6f, 0x5b, 0x2f, 0x14, 0x0e, 0x6f, 0x89, 0xb4, 0xb5, 0xd8, 0xae, 0xef, 0x7b, 0x87,
|
||||
/* (2^436)P */ 0xe9, 0x91, 0xa0, 0x8b, 0xc9, 0xe0, 0x01, 0x90, 0x37, 0xc1, 0x6f, 0xdc, 0x5e, 0xf7, 0xbf, 0x43, 0x00, 0xaa, 0x10, 0x76, 0x76, 0x18, 0x6e, 0x19, 0x1e, 0x94, 0x50, 0x11, 0x0a, 0xd1, 0xe2, 0xdb, 0x08, 0x21, 0xa0, 0x1f, 0xdb, 0x54, 0xfe, 0xea, 0x6e, 0xa3, 0x68, 0x56, 0x87, 0x0b, 0x22, 0x4e, 0x66, 0xf3, 0x82, 0x82, 0x00, 0xcd, 0xd4, 0x12,
|
||||
/* (2^437)P */ 0x25, 0x8e, 0x24, 0x77, 0x64, 0x4c, 0xe0, 0xf8, 0x18, 0xc0, 0xdc, 0xc7, 0x1b, 0x35, 0x65, 0xde, 0x67, 0x41, 0x5e, 0x6f, 0x90, 0x82, 0xa7, 0x2e, 0x6d, 0xf1, 0x47, 0xb4, 0x92, 0x9c, 0xfd, 0x6a, 0x9a, 0x41, 0x36, 0x20, 0x24, 0x58, 0xc3, 0x59, 0x07, 0x9a, 0xfa, 0x9f, 0x03, 0xcb, 0xc7, 0x69, 0x37, 0x60, 0xe1, 0xab, 0x13, 0x72, 0xee, 0xa2,
|
||||
/* (2^438)P */ 0x74, 0x78, 0xfb, 0x13, 0xcb, 0x8e, 0x37, 0x1a, 0xf6, 0x1d, 0x17, 0x83, 0x06, 0xd4, 0x27, 0x06, 0x21, 0xe8, 0xda, 0xdf, 0x6b, 0xf3, 0x83, 0x6b, 0x34, 0x8a, 0x8c, 0xee, 0x01, 0x05, 0x5b, 0xed, 0xd3, 0x1b, 0xc9, 0x64, 0x83, 0xc9, 0x49, 0xc2, 0x57, 0x1b, 0xdd, 0xcf, 0xf1, 0x9d, 0x63, 0xee, 0x1c, 0x0d, 0xa0, 0x0a, 0x73, 0x1f, 0x5b, 0x32,
|
||||
/* (2^439)P */ 0x29, 0xce, 0x1e, 0xc0, 0x6a, 0xf5, 0xeb, 0x99, 0x5a, 0x39, 0x23, 0xe9, 0xdd, 0xac, 0x44, 0x88, 0xbc, 0x80, 0x22, 0xde, 0x2c, 0xcb, 0xa8, 0x3b, 0xff, 0xf7, 0x6f, 0xc7, 0x71, 0x72, 0xa8, 0xa3, 0xf6, 0x4d, 0xc6, 0x75, 0xda, 0x80, 0xdc, 0xd9, 0x30, 0xd9, 0x07, 0x50, 0x5a, 0x54, 0x7d, 0xda, 0x39, 0x6f, 0x78, 0x94, 0xbf, 0x25, 0x98, 0xdc,
|
||||
/* (2^440)P */ 0x01, 0x26, 0x62, 0x44, 0xfb, 0x0f, 0x11, 0x72, 0x73, 0x0a, 0x16, 0xc7, 0x16, 0x9c, 0x9b, 0x37, 0xd8, 0xff, 0x4f, 0xfe, 0x57, 0xdb, 0xae, 0xef, 0x7d, 0x94, 0x30, 0x04, 0x70, 0x83, 0xde, 0x3c, 0xd4, 0xb5, 0x70, 0xda, 0xa7, 0x55, 0xc8, 0x19, 0xe1, 0x36, 0x15, 0x61, 0xe7, 0x3b, 0x7d, 0x85, 0xbb, 0xf3, 0x42, 0x5a, 0x94, 0xf4, 0x53, 0x2a,
|
||||
/* (2^441)P */ 0x14, 0x60, 0xa6, 0x0b, 0x83, 0xe1, 0x23, 0x77, 0xc0, 0xce, 0x50, 0xed, 0x35, 0x8d, 0x98, 0x99, 0x7d, 0xf5, 0x8d, 0xce, 0x94, 0x25, 0xc8, 0x0f, 0x6d, 0xfa, 0x4a, 0xa4, 0x3a, 0x1f, 0x66, 0xfb, 0x5a, 0x64, 0xaf, 0x8b, 0x54, 0x54, 0x44, 0x3f, 0x5b, 0x88, 0x61, 0xe4, 0x48, 0x45, 0x26, 0x20, 0xbe, 0x0d, 0x06, 0xbb, 0x65, 0x59, 0xe1, 0x36,
|
||||
/* (2^442)P */ 0xb7, 0x98, 0xce, 0xa3, 0xe3, 0xee, 0x11, 0x1b, 0x9e, 0x24, 0x59, 0x75, 0x31, 0x37, 0x44, 0x6f, 0x6b, 0x9e, 0xec, 0xb7, 0x44, 0x01, 0x7e, 0xab, 0xbb, 0x69, 0x5d, 0x11, 0xb0, 0x30, 0x64, 0xea, 0x91, 0xb4, 0x7a, 0x8c, 0x02, 0x4c, 0xb9, 0x10, 0xa7, 0xc7, 0x79, 0xe6, 0xdc, 0x77, 0xe3, 0xc8, 0xef, 0x3e, 0xf9, 0x38, 0x81, 0xce, 0x9a, 0xb2,
|
||||
/* (2^443)P */ 0x91, 0x12, 0x76, 0xd0, 0x10, 0xb4, 0xaf, 0xe1, 0x89, 0x3a, 0x93, 0x6b, 0x5c, 0x19, 0x5f, 0x24, 0xed, 0x04, 0x92, 0xc7, 0xf0, 0x00, 0x08, 0xc1, 0x92, 0xff, 0x90, 0xdb, 0xb2, 0xbf, 0xdf, 0x49, 0xcd, 0xbd, 0x5c, 0x6e, 0xbf, 0x16, 0xbb, 0x61, 0xf9, 0x20, 0x33, 0x35, 0x93, 0x11, 0xbc, 0x59, 0x69, 0xce, 0x18, 0x9f, 0xf8, 0x7b, 0xa1, 0x6e,
|
||||
/* (2^444)P */ 0xa1, 0xf4, 0xaf, 0xad, 0xf8, 0xe6, 0x99, 0xd2, 0xa1, 0x4d, 0xde, 0x56, 0xc9, 0x7b, 0x0b, 0x11, 0x3e, 0xbf, 0x89, 0x1a, 0x9a, 0x90, 0xe5, 0xe2, 0xa6, 0x37, 0x88, 0xa1, 0x68, 0x59, 0xae, 0x8c, 0xec, 0x02, 0x14, 0x8d, 0xb7, 0x2e, 0x25, 0x75, 0x7f, 0x76, 0x1a, 0xd3, 0x4d, 0xad, 0x8a, 0x00, 0x6c, 0x96, 0x49, 0xa4, 0xc3, 0x2e, 0x5c, 0x7b,
|
||||
/* (2^445)P */ 0x26, 0x53, 0xf7, 0xda, 0xa8, 0x01, 0x14, 0xb1, 0x63, 0xe3, 0xc3, 0x89, 0x88, 0xb0, 0x85, 0x40, 0x2b, 0x26, 0x9a, 0x10, 0x1a, 0x70, 0x33, 0xf4, 0x50, 0x9d, 0x4d, 0xd8, 0x64, 0xc6, 0x0f, 0xe1, 0x17, 0xc8, 0x10, 0x4b, 0xfc, 0xa0, 0xc9, 0xba, 0x2c, 0x98, 0x09, 0xf5, 0x84, 0xb6, 0x7c, 0x4e, 0xa3, 0xe3, 0x81, 0x1b, 0x32, 0x60, 0x02, 0xdd,
|
||||
/* (2^446)P */ 0xa3, 0xe5, 0x86, 0xd4, 0x43, 0xa8, 0xd1, 0x98, 0x9d, 0x9d, 0xdb, 0x04, 0xcf, 0x6e, 0x35, 0x05, 0x30, 0x53, 0x3b, 0xbc, 0x90, 0x00, 0x4a, 0xc5, 0x40, 0x2a, 0x0f, 0xde, 0x1a, 0xd7, 0x36, 0x27, 0x44, 0x62, 0xa6, 0xac, 0x9d, 0xd2, 0x70, 0x69, 0x14, 0x39, 0x9b, 0xd1, 0xc3, 0x0a, 0x3a, 0x82, 0x0e, 0xf1, 0x94, 0xd7, 0x42, 0x94, 0xd5, 0x7d,
|
||||
/* (2^447)P */ 0x04, 0xc0, 0x6e, 0x12, 0x90, 0x70, 0xf9, 0xdf, 0xf7, 0xc9, 0x86, 0xc0, 0xe6, 0x92, 0x8b, 0x0a, 0xa1, 0xc1, 0x3b, 0xcc, 0x33, 0xb7, 0xf0, 0xeb, 0x51, 0x50, 0x80, 0x20, 0x69, 0x1c, 0x4f, 0x89, 0x05, 0x1e, 0xe4, 0x7a, 0x0a, 0xc2, 0xf0, 0xf5, 0x78, 0x91, 0x76, 0x34, 0x45, 0xdc, 0x24, 0x53, 0x24, 0x98, 0xe2, 0x73, 0x6f, 0xe6, 0x46, 0x67,
|
||||
}
|
||||
|
|
@ -0,0 +1,71 @@
|
|||
package goldilocks
|
||||
|
||||
import fp "github.com/cloudflare/circl/math/fp448"
|
||||
|
||||
var (
|
||||
// genX is the x-coordinate of the generator of Goldilocks curve.
|
||||
genX = fp.Elt{
|
||||
0x5e, 0xc0, 0x0c, 0xc7, 0x2b, 0xa8, 0x26, 0x26,
|
||||
0x8e, 0x93, 0x00, 0x8b, 0xe1, 0x80, 0x3b, 0x43,
|
||||
0x11, 0x65, 0xb6, 0x2a, 0xf7, 0x1a, 0xae, 0x12,
|
||||
0x64, 0xa4, 0xd3, 0xa3, 0x24, 0xe3, 0x6d, 0xea,
|
||||
0x67, 0x17, 0x0f, 0x47, 0x70, 0x65, 0x14, 0x9e,
|
||||
0xda, 0x36, 0xbf, 0x22, 0xa6, 0x15, 0x1d, 0x22,
|
||||
0xed, 0x0d, 0xed, 0x6b, 0xc6, 0x70, 0x19, 0x4f,
|
||||
}
|
||||
// genY is the y-coordinate of the generator of Goldilocks curve.
|
||||
genY = fp.Elt{
|
||||
0x14, 0xfa, 0x30, 0xf2, 0x5b, 0x79, 0x08, 0x98,
|
||||
0xad, 0xc8, 0xd7, 0x4e, 0x2c, 0x13, 0xbd, 0xfd,
|
||||
0xc4, 0x39, 0x7c, 0xe6, 0x1c, 0xff, 0xd3, 0x3a,
|
||||
0xd7, 0xc2, 0xa0, 0x05, 0x1e, 0x9c, 0x78, 0x87,
|
||||
0x40, 0x98, 0xa3, 0x6c, 0x73, 0x73, 0xea, 0x4b,
|
||||
0x62, 0xc7, 0xc9, 0x56, 0x37, 0x20, 0x76, 0x88,
|
||||
0x24, 0xbc, 0xb6, 0x6e, 0x71, 0x46, 0x3f, 0x69,
|
||||
}
|
||||
// paramD is -39081 in Fp.
|
||||
paramD = fp.Elt{
|
||||
0x56, 0x67, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
}
|
||||
// order is 2^446-0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d,
|
||||
// which is the number of points in the prime subgroup.
|
||||
order = Scalar{
|
||||
0xf3, 0x44, 0x58, 0xab, 0x92, 0xc2, 0x78, 0x23,
|
||||
0x55, 0x8f, 0xc5, 0x8d, 0x72, 0xc2, 0x6c, 0x21,
|
||||
0x90, 0x36, 0xd6, 0xae, 0x49, 0xdb, 0x4e, 0xc4,
|
||||
0xe9, 0x23, 0xca, 0x7c, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f,
|
||||
}
|
||||
// residue448 is 2^448 mod order.
|
||||
residue448 = [4]uint64{
|
||||
0x721cf5b5529eec34, 0x7a4cf635c8e9c2ab, 0xeec492d944a725bf, 0x20cd77058,
|
||||
}
|
||||
// invFour is 1/4 mod order.
|
||||
invFour = Scalar{
|
||||
0x3d, 0x11, 0xd6, 0xaa, 0xa4, 0x30, 0xde, 0x48,
|
||||
0xd5, 0x63, 0x71, 0xa3, 0x9c, 0x30, 0x5b, 0x08,
|
||||
0xa4, 0x8d, 0xb5, 0x6b, 0xd2, 0xb6, 0x13, 0x71,
|
||||
0xfa, 0x88, 0x32, 0xdf, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f,
|
||||
}
|
||||
// paramDTwist is -39082 in Fp. The D parameter of the twist curve.
|
||||
paramDTwist = fp.Elt{
|
||||
0x55, 0x67, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
|
||||
}
|
||||
)
|
||||
|
|
@ -0,0 +1,80 @@
|
|||
// Package goldilocks provides elliptic curve operations over the goldilocks curve.
|
||||
package goldilocks
|
||||
|
||||
import fp "github.com/cloudflare/circl/math/fp448"
|
||||
|
||||
// Curve is the Goldilocks curve x^2+y^2=z^2-39081x^2y^2.
|
||||
type Curve struct{}
|
||||
|
||||
// Identity returns the identity point.
|
||||
func (Curve) Identity() *Point {
|
||||
return &Point{
|
||||
y: fp.One(),
|
||||
z: fp.One(),
|
||||
}
|
||||
}
|
||||
|
||||
// IsOnCurve returns true if the point lies on the curve.
|
||||
func (Curve) IsOnCurve(P *Point) bool {
|
||||
x2, y2, t, t2, z2 := &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{}
|
||||
rhs, lhs := &fp.Elt{}, &fp.Elt{}
|
||||
fp.Mul(t, &P.ta, &P.tb) // t = ta*tb
|
||||
fp.Sqr(x2, &P.x) // x^2
|
||||
fp.Sqr(y2, &P.y) // y^2
|
||||
fp.Sqr(z2, &P.z) // z^2
|
||||
fp.Sqr(t2, t) // t^2
|
||||
fp.Add(lhs, x2, y2) // x^2 + y^2
|
||||
fp.Mul(rhs, t2, ¶mD) // dt^2
|
||||
fp.Add(rhs, rhs, z2) // z^2 + dt^2
|
||||
fp.Sub(lhs, lhs, rhs) // x^2 + y^2 - (z^2 + dt^2)
|
||||
eq0 := fp.IsZero(lhs)
|
||||
|
||||
fp.Mul(lhs, &P.x, &P.y) // xy
|
||||
fp.Mul(rhs, t, &P.z) // tz
|
||||
fp.Sub(lhs, lhs, rhs) // xy - tz
|
||||
eq1 := fp.IsZero(lhs)
|
||||
return eq0 && eq1
|
||||
}
|
||||
|
||||
// Generator returns the generator point.
|
||||
func (Curve) Generator() *Point {
|
||||
return &Point{
|
||||
x: genX,
|
||||
y: genY,
|
||||
z: fp.One(),
|
||||
ta: genX,
|
||||
tb: genY,
|
||||
}
|
||||
}
|
||||
|
||||
// Order returns the number of points in the prime subgroup.
|
||||
func (Curve) Order() Scalar { return order }
|
||||
|
||||
// Double returns 2P.
|
||||
func (Curve) Double(P *Point) *Point { R := *P; R.Double(); return &R }
|
||||
|
||||
// Add returns P+Q.
|
||||
func (Curve) Add(P, Q *Point) *Point { R := *P; R.Add(Q); return &R }
|
||||
|
||||
// ScalarMult returns kP. This function runs in constant time.
|
||||
func (e Curve) ScalarMult(k *Scalar, P *Point) *Point {
|
||||
k4 := &Scalar{}
|
||||
k4.divBy4(k)
|
||||
return e.pull(twistCurve{}.ScalarMult(k4, e.push(P)))
|
||||
}
|
||||
|
||||
// ScalarBaseMult returns kG where G is the generator point. This function runs in constant time.
|
||||
func (e Curve) ScalarBaseMult(k *Scalar) *Point {
|
||||
k4 := &Scalar{}
|
||||
k4.divBy4(k)
|
||||
return e.pull(twistCurve{}.ScalarBaseMult(k4))
|
||||
}
|
||||
|
||||
// CombinedMult returns mG+nP, where G is the generator point. This function is non-constant time.
|
||||
func (e Curve) CombinedMult(m, n *Scalar, P *Point) *Point {
|
||||
m4 := &Scalar{}
|
||||
n4 := &Scalar{}
|
||||
m4.divBy4(m)
|
||||
n4.divBy4(n)
|
||||
return e.pull(twistCurve{}.CombinedMult(m4, n4, twistCurve{}.pull(P)))
|
||||
}
|
||||
|
|
@ -0,0 +1,52 @@
|
|||
package goldilocks
|
||||
|
||||
import fp "github.com/cloudflare/circl/math/fp448"
|
||||
|
||||
func (Curve) pull(P *twistPoint) *Point { return twistCurve{}.push(P) }
|
||||
func (twistCurve) pull(P *Point) *twistPoint { return Curve{}.push(P) }
|
||||
|
||||
// push sends a point on the Goldilocks curve to a point on the twist curve.
|
||||
func (Curve) push(P *Point) *twistPoint {
|
||||
Q := &twistPoint{}
|
||||
Px, Py, Pz := &P.x, &P.y, &P.z
|
||||
a, b, c, d, e, f, g, h := &Q.x, &Q.y, &Q.z, &fp.Elt{}, &Q.ta, &Q.x, &Q.y, &Q.tb
|
||||
fp.Add(e, Px, Py) // x+y
|
||||
fp.Sqr(a, Px) // A = x^2
|
||||
fp.Sqr(b, Py) // B = y^2
|
||||
fp.Sqr(c, Pz) // z^2
|
||||
fp.Add(c, c, c) // C = 2*z^2
|
||||
*d = *a // D = A
|
||||
fp.Sqr(e, e) // (x+y)^2
|
||||
fp.Sub(e, e, a) // (x+y)^2-A
|
||||
fp.Sub(e, e, b) // E = (x+y)^2-A-B
|
||||
fp.Add(h, b, d) // H = B+D
|
||||
fp.Sub(g, b, d) // G = B-D
|
||||
fp.Sub(f, c, h) // F = C-H
|
||||
fp.Mul(&Q.z, f, g) // Z = F * G
|
||||
fp.Mul(&Q.x, e, f) // X = E * F
|
||||
fp.Mul(&Q.y, g, h) // Y = G * H, // T = E * H
|
||||
return Q
|
||||
}
|
||||
|
||||
// push sends a point on the twist curve to a point on the Goldilocks curve.
|
||||
func (twistCurve) push(P *twistPoint) *Point {
|
||||
Q := &Point{}
|
||||
Px, Py, Pz := &P.x, &P.y, &P.z
|
||||
a, b, c, d, e, f, g, h := &Q.x, &Q.y, &Q.z, &fp.Elt{}, &Q.ta, &Q.x, &Q.y, &Q.tb
|
||||
fp.Add(e, Px, Py) // x+y
|
||||
fp.Sqr(a, Px) // A = x^2
|
||||
fp.Sqr(b, Py) // B = y^2
|
||||
fp.Sqr(c, Pz) // z^2
|
||||
fp.Add(c, c, c) // C = 2*z^2
|
||||
fp.Neg(d, a) // D = -A
|
||||
fp.Sqr(e, e) // (x+y)^2
|
||||
fp.Sub(e, e, a) // (x+y)^2-A
|
||||
fp.Sub(e, e, b) // E = (x+y)^2-A-B
|
||||
fp.Add(h, b, d) // H = B+D
|
||||
fp.Sub(g, b, d) // G = B-D
|
||||
fp.Sub(f, c, h) // F = C-H
|
||||
fp.Mul(&Q.z, f, g) // Z = F * G
|
||||
fp.Mul(&Q.x, e, f) // X = E * F
|
||||
fp.Mul(&Q.y, g, h) // Y = G * H, // T = E * H
|
||||
return Q
|
||||
}
|
||||
|
|
@ -0,0 +1,171 @@
|
|||
package goldilocks
|
||||
|
||||
import (
|
||||
"errors"
|
||||
"fmt"
|
||||
|
||||
fp "github.com/cloudflare/circl/math/fp448"
|
||||
)
|
||||
|
||||
// Point is a point on the Goldilocks Curve.
|
||||
type Point struct{ x, y, z, ta, tb fp.Elt }
|
||||
|
||||
func (P Point) String() string {
|
||||
return fmt.Sprintf("x: %v\ny: %v\nz: %v\nta: %v\ntb: %v", P.x, P.y, P.z, P.ta, P.tb)
|
||||
}
|
||||
|
||||
// FromAffine creates a point from affine coordinates.
|
||||
func FromAffine(x, y *fp.Elt) (*Point, error) {
|
||||
P := &Point{
|
||||
x: *x,
|
||||
y: *y,
|
||||
z: fp.One(),
|
||||
ta: *x,
|
||||
tb: *y,
|
||||
}
|
||||
if !(Curve{}).IsOnCurve(P) {
|
||||
return P, errors.New("point not on curve")
|
||||
}
|
||||
return P, nil
|
||||
}
|
||||
|
||||
// isLessThan returns true if 0 <= x < y, and assumes that slices are of the
|
||||
// same length and are interpreted in little-endian order.
|
||||
func isLessThan(x, y []byte) bool {
|
||||
i := len(x) - 1
|
||||
for i > 0 && x[i] == y[i] {
|
||||
i--
|
||||
}
|
||||
return x[i] < y[i]
|
||||
}
|
||||
|
||||
// FromBytes returns a point from the input buffer.
|
||||
func FromBytes(in []byte) (*Point, error) {
|
||||
if len(in) < fp.Size+1 {
|
||||
return nil, errors.New("wrong input length")
|
||||
}
|
||||
err := errors.New("invalid decoding")
|
||||
P := &Point{}
|
||||
signX := in[fp.Size] >> 7
|
||||
copy(P.y[:], in[:fp.Size])
|
||||
p := fp.P()
|
||||
if !isLessThan(P.y[:], p[:]) {
|
||||
return nil, err
|
||||
}
|
||||
|
||||
u, v := &fp.Elt{}, &fp.Elt{}
|
||||
one := fp.One()
|
||||
fp.Sqr(u, &P.y) // u = y^2
|
||||
fp.Mul(v, u, ¶mD) // v = dy^2
|
||||
fp.Sub(u, u, &one) // u = y^2-1
|
||||
fp.Sub(v, v, &one) // v = dy^2-1
|
||||
isQR := fp.InvSqrt(&P.x, u, v) // x = sqrt(u/v)
|
||||
if !isQR {
|
||||
return nil, err
|
||||
}
|
||||
fp.Modp(&P.x) // x = x mod p
|
||||
if fp.IsZero(&P.x) && signX == 1 {
|
||||
return nil, err
|
||||
}
|
||||
if signX != (P.x[0] & 1) {
|
||||
fp.Neg(&P.x, &P.x)
|
||||
}
|
||||
P.ta = P.x
|
||||
P.tb = P.y
|
||||
P.z = fp.One()
|
||||
return P, nil
|
||||
}
|
||||
|
||||
// IsIdentity returns true is P is the identity Point.
|
||||
func (P *Point) IsIdentity() bool {
|
||||
return fp.IsZero(&P.x) && !fp.IsZero(&P.y) && !fp.IsZero(&P.z) && P.y == P.z
|
||||
}
|
||||
|
||||
// IsEqual returns true if P is equivalent to Q.
|
||||
func (P *Point) IsEqual(Q *Point) bool {
|
||||
l, r := &fp.Elt{}, &fp.Elt{}
|
||||
fp.Mul(l, &P.x, &Q.z)
|
||||
fp.Mul(r, &Q.x, &P.z)
|
||||
fp.Sub(l, l, r)
|
||||
b := fp.IsZero(l)
|
||||
fp.Mul(l, &P.y, &Q.z)
|
||||
fp.Mul(r, &Q.y, &P.z)
|
||||
fp.Sub(l, l, r)
|
||||
b = b && fp.IsZero(l)
|
||||
fp.Mul(l, &P.ta, &P.tb)
|
||||
fp.Mul(l, l, &Q.z)
|
||||
fp.Mul(r, &Q.ta, &Q.tb)
|
||||
fp.Mul(r, r, &P.z)
|
||||
fp.Sub(l, l, r)
|
||||
b = b && fp.IsZero(l)
|
||||
return b
|
||||
}
|
||||
|
||||
// Neg obtains the inverse of the Point.
|
||||
func (P *Point) Neg() { fp.Neg(&P.x, &P.x); fp.Neg(&P.ta, &P.ta) }
|
||||
|
||||
// ToAffine returns the x,y affine coordinates of P.
|
||||
func (P *Point) ToAffine() (x, y fp.Elt) {
|
||||
fp.Inv(&P.z, &P.z) // 1/z
|
||||
fp.Mul(&P.x, &P.x, &P.z) // x/z
|
||||
fp.Mul(&P.y, &P.y, &P.z) // y/z
|
||||
fp.Modp(&P.x)
|
||||
fp.Modp(&P.y)
|
||||
fp.SetOne(&P.z)
|
||||
P.ta = P.x
|
||||
P.tb = P.y
|
||||
return P.x, P.y
|
||||
}
|
||||
|
||||
// ToBytes stores P into a slice of bytes.
|
||||
func (P *Point) ToBytes(out []byte) error {
|
||||
if len(out) < fp.Size+1 {
|
||||
return errors.New("invalid decoding")
|
||||
}
|
||||
x, y := P.ToAffine()
|
||||
out[fp.Size] = (x[0] & 1) << 7
|
||||
return fp.ToBytes(out[:fp.Size], &y)
|
||||
}
|
||||
|
||||
// MarshalBinary encodes the receiver into a binary form and returns the result.
|
||||
func (P *Point) MarshalBinary() (data []byte, err error) {
|
||||
data = make([]byte, fp.Size+1)
|
||||
err = P.ToBytes(data[:fp.Size+1])
|
||||
return data, err
|
||||
}
|
||||
|
||||
// UnmarshalBinary must be able to decode the form generated by MarshalBinary.
|
||||
func (P *Point) UnmarshalBinary(data []byte) error { Q, err := FromBytes(data); *P = *Q; return err }
|
||||
|
||||
// Double sets P = 2Q.
|
||||
func (P *Point) Double() { P.Add(P) }
|
||||
|
||||
// Add sets P =P+Q..
|
||||
func (P *Point) Add(Q *Point) {
|
||||
// This is formula (5) from "Twisted Edwards Curves Revisited" by
|
||||
// Hisil H., Wong K.KH., Carter G., Dawson E. (2008)
|
||||
// https://doi.org/10.1007/978-3-540-89255-7_20
|
||||
x1, y1, z1, ta1, tb1 := &P.x, &P.y, &P.z, &P.ta, &P.tb
|
||||
x2, y2, z2, ta2, tb2 := &Q.x, &Q.y, &Q.z, &Q.ta, &Q.tb
|
||||
x3, y3, z3, E, H := &P.x, &P.y, &P.z, &P.ta, &P.tb
|
||||
A, B, C, D := &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{}
|
||||
t1, t2, F, G := C, D, &fp.Elt{}, &fp.Elt{}
|
||||
fp.Mul(t1, ta1, tb1) // t1 = ta1*tb1
|
||||
fp.Mul(t2, ta2, tb2) // t2 = ta2*tb2
|
||||
fp.Mul(A, x1, x2) // A = x1*x2
|
||||
fp.Mul(B, y1, y2) // B = y1*y2
|
||||
fp.Mul(C, t1, t2) // t1*t2
|
||||
fp.Mul(C, C, ¶mD) // C = d*t1*t2
|
||||
fp.Mul(D, z1, z2) // D = z1*z2
|
||||
fp.Add(F, x1, y1) // x1+y1
|
||||
fp.Add(E, x2, y2) // x2+y2
|
||||
fp.Mul(E, E, F) // (x1+y1)*(x2+y2)
|
||||
fp.Sub(E, E, A) // (x1+y1)*(x2+y2)-A
|
||||
fp.Sub(E, E, B) // E = (x1+y1)*(x2+y2)-A-B
|
||||
fp.Sub(F, D, C) // F = D-C
|
||||
fp.Add(G, D, C) // G = D+C
|
||||
fp.Sub(H, B, A) // H = B-A
|
||||
fp.Mul(z3, F, G) // Z = F * G
|
||||
fp.Mul(x3, E, F) // X = E * F
|
||||
fp.Mul(y3, G, H) // Y = G * H, T = E * H
|
||||
}
|
||||
|
|
@ -0,0 +1,203 @@
|
|||
package goldilocks
|
||||
|
||||
import (
|
||||
"encoding/binary"
|
||||
"math/bits"
|
||||
)
|
||||
|
||||
// ScalarSize is the size (in bytes) of scalars.
|
||||
const ScalarSize = 56 // 448 / 8
|
||||
|
||||
// _N is the number of 64-bit words to store scalars.
|
||||
const _N = 7 // 448 / 64
|
||||
|
||||
// Scalar represents a positive integer stored in little-endian order.
|
||||
type Scalar [ScalarSize]byte
|
||||
|
||||
type scalar64 [_N]uint64
|
||||
|
||||
func (z *scalar64) fromScalar(x *Scalar) {
|
||||
z[0] = binary.LittleEndian.Uint64(x[0*8 : 1*8])
|
||||
z[1] = binary.LittleEndian.Uint64(x[1*8 : 2*8])
|
||||
z[2] = binary.LittleEndian.Uint64(x[2*8 : 3*8])
|
||||
z[3] = binary.LittleEndian.Uint64(x[3*8 : 4*8])
|
||||
z[4] = binary.LittleEndian.Uint64(x[4*8 : 5*8])
|
||||
z[5] = binary.LittleEndian.Uint64(x[5*8 : 6*8])
|
||||
z[6] = binary.LittleEndian.Uint64(x[6*8 : 7*8])
|
||||
}
|
||||
|
||||
func (z *scalar64) toScalar(x *Scalar) {
|
||||
binary.LittleEndian.PutUint64(x[0*8:1*8], z[0])
|
||||
binary.LittleEndian.PutUint64(x[1*8:2*8], z[1])
|
||||
binary.LittleEndian.PutUint64(x[2*8:3*8], z[2])
|
||||
binary.LittleEndian.PutUint64(x[3*8:4*8], z[3])
|
||||
binary.LittleEndian.PutUint64(x[4*8:5*8], z[4])
|
||||
binary.LittleEndian.PutUint64(x[5*8:6*8], z[5])
|
||||
binary.LittleEndian.PutUint64(x[6*8:7*8], z[6])
|
||||
}
|
||||
|
||||
// add calculates z = x + y. Assumes len(z) > max(len(x),len(y)).
|
||||
func add(z, x, y []uint64) uint64 {
|
||||
l, L, zz := len(x), len(y), y
|
||||
if l > L {
|
||||
l, L, zz = L, l, x
|
||||
}
|
||||
c := uint64(0)
|
||||
for i := 0; i < l; i++ {
|
||||
z[i], c = bits.Add64(x[i], y[i], c)
|
||||
}
|
||||
for i := l; i < L; i++ {
|
||||
z[i], c = bits.Add64(zz[i], 0, c)
|
||||
}
|
||||
return c
|
||||
}
|
||||
|
||||
// sub calculates z = x - y. Assumes len(z) > max(len(x),len(y)).
|
||||
func sub(z, x, y []uint64) uint64 {
|
||||
l, L, zz := len(x), len(y), y
|
||||
if l > L {
|
||||
l, L, zz = L, l, x
|
||||
}
|
||||
c := uint64(0)
|
||||
for i := 0; i < l; i++ {
|
||||
z[i], c = bits.Sub64(x[i], y[i], c)
|
||||
}
|
||||
for i := l; i < L; i++ {
|
||||
z[i], c = bits.Sub64(zz[i], 0, c)
|
||||
}
|
||||
return c
|
||||
}
|
||||
|
||||
// mulWord calculates z = x * y. Assumes len(z) >= len(x)+1.
|
||||
func mulWord(z, x []uint64, y uint64) {
|
||||
for i := range z {
|
||||
z[i] = 0
|
||||
}
|
||||
carry := uint64(0)
|
||||
for i := range x {
|
||||
hi, lo := bits.Mul64(x[i], y)
|
||||
lo, cc := bits.Add64(lo, z[i], 0)
|
||||
hi, _ = bits.Add64(hi, 0, cc)
|
||||
z[i], cc = bits.Add64(lo, carry, 0)
|
||||
carry, _ = bits.Add64(hi, 0, cc)
|
||||
}
|
||||
z[len(x)] = carry
|
||||
}
|
||||
|
||||
// Cmov moves x into z if b=1.
|
||||
func (z *scalar64) Cmov(b uint64, x *scalar64) {
|
||||
m := uint64(0) - b
|
||||
for i := range z {
|
||||
z[i] = (z[i] &^ m) | (x[i] & m)
|
||||
}
|
||||
}
|
||||
|
||||
// leftShift shifts to the left the words of z returning the more significant word.
|
||||
func (z *scalar64) leftShift(low uint64) uint64 {
|
||||
high := z[_N-1]
|
||||
for i := _N - 1; i > 0; i-- {
|
||||
z[i] = z[i-1]
|
||||
}
|
||||
z[0] = low
|
||||
return high
|
||||
}
|
||||
|
||||
// reduceOneWord calculates z = z + 2^448*x such that the result fits in a Scalar.
|
||||
func (z *scalar64) reduceOneWord(x uint64) {
|
||||
prod := (&scalar64{})[:]
|
||||
mulWord(prod, residue448[:], x)
|
||||
cc := add(z[:], z[:], prod)
|
||||
mulWord(prod, residue448[:], cc)
|
||||
add(z[:], z[:], prod)
|
||||
}
|
||||
|
||||
// modOrder reduces z mod order.
|
||||
func (z *scalar64) modOrder() {
|
||||
var o64, x scalar64
|
||||
o64.fromScalar(&order)
|
||||
// Performs: while (z >= order) { z = z-order }
|
||||
// At most 8 (eight) iterations reduce 3 bits by subtracting.
|
||||
for i := 0; i < 8; i++ {
|
||||
c := sub(x[:], z[:], o64[:]) // (c || x) = z-order
|
||||
z.Cmov(1-c, &x) // if c != 0 { z = x }
|
||||
}
|
||||
}
|
||||
|
||||
// FromBytes stores z = x mod order, where x is a number stored in little-endian order.
|
||||
func (z *Scalar) FromBytes(x []byte) {
|
||||
n := len(x)
|
||||
nCeil := (n + 7) >> 3
|
||||
for i := range z {
|
||||
z[i] = 0
|
||||
}
|
||||
if nCeil < _N {
|
||||
copy(z[:], x)
|
||||
return
|
||||
}
|
||||
copy(z[:], x[8*(nCeil-_N):])
|
||||
var z64 scalar64
|
||||
z64.fromScalar(z)
|
||||
for i := nCeil - _N - 1; i >= 0; i-- {
|
||||
low := binary.LittleEndian.Uint64(x[8*i:])
|
||||
high := z64.leftShift(low)
|
||||
z64.reduceOneWord(high)
|
||||
}
|
||||
z64.modOrder()
|
||||
z64.toScalar(z)
|
||||
}
|
||||
|
||||
// divBy4 calculates z = x/4 mod order.
|
||||
func (z *Scalar) divBy4(x *Scalar) { z.Mul(x, &invFour) }
|
||||
|
||||
// Red reduces z mod order.
|
||||
func (z *Scalar) Red() { var t scalar64; t.fromScalar(z); t.modOrder(); t.toScalar(z) }
|
||||
|
||||
// Neg calculates z = -z mod order.
|
||||
func (z *Scalar) Neg() { z.Sub(&order, z) }
|
||||
|
||||
// Add calculates z = x+y mod order.
|
||||
func (z *Scalar) Add(x, y *Scalar) {
|
||||
var z64, x64, y64, t scalar64
|
||||
x64.fromScalar(x)
|
||||
y64.fromScalar(y)
|
||||
c := add(z64[:], x64[:], y64[:])
|
||||
add(t[:], z64[:], residue448[:])
|
||||
z64.Cmov(c, &t)
|
||||
z64.modOrder()
|
||||
z64.toScalar(z)
|
||||
}
|
||||
|
||||
// Sub calculates z = x-y mod order.
|
||||
func (z *Scalar) Sub(x, y *Scalar) {
|
||||
var z64, x64, y64, t scalar64
|
||||
x64.fromScalar(x)
|
||||
y64.fromScalar(y)
|
||||
c := sub(z64[:], x64[:], y64[:])
|
||||
sub(t[:], z64[:], residue448[:])
|
||||
z64.Cmov(c, &t)
|
||||
z64.modOrder()
|
||||
z64.toScalar(z)
|
||||
}
|
||||
|
||||
// Mul calculates z = x*y mod order.
|
||||
func (z *Scalar) Mul(x, y *Scalar) {
|
||||
var z64, x64, y64 scalar64
|
||||
prod := (&[_N + 1]uint64{})[:]
|
||||
x64.fromScalar(x)
|
||||
y64.fromScalar(y)
|
||||
mulWord(prod, x64[:], y64[_N-1])
|
||||
copy(z64[:], prod[:_N])
|
||||
z64.reduceOneWord(prod[_N])
|
||||
for i := _N - 2; i >= 0; i-- {
|
||||
h := z64.leftShift(0)
|
||||
z64.reduceOneWord(h)
|
||||
mulWord(prod, x64[:], y64[i])
|
||||
c := add(z64[:], z64[:], prod[:_N])
|
||||
z64.reduceOneWord(prod[_N] + c)
|
||||
}
|
||||
z64.modOrder()
|
||||
z64.toScalar(z)
|
||||
}
|
||||
|
||||
// IsZero returns true if z=0.
|
||||
func (z *Scalar) IsZero() bool { z.Red(); return *z == Scalar{} }
|
||||
|
|
@ -0,0 +1,138 @@
|
|||
package goldilocks
|
||||
|
||||
import (
|
||||
"crypto/subtle"
|
||||
"math/bits"
|
||||
|
||||
"github.com/cloudflare/circl/internal/conv"
|
||||
"github.com/cloudflare/circl/math"
|
||||
fp "github.com/cloudflare/circl/math/fp448"
|
||||
)
|
||||
|
||||
// twistCurve is -x^2+y^2=1-39082x^2y^2 and is 4-isogeneous to Goldilocks.
|
||||
type twistCurve struct{}
|
||||
|
||||
// Identity returns the identity point.
|
||||
func (twistCurve) Identity() *twistPoint {
|
||||
return &twistPoint{
|
||||
y: fp.One(),
|
||||
z: fp.One(),
|
||||
}
|
||||
}
|
||||
|
||||
// subYDiv16 update x = (x - y) / 16.
|
||||
func subYDiv16(x *scalar64, y int64) {
|
||||
s := uint64(y >> 63)
|
||||
x0, b0 := bits.Sub64((*x)[0], uint64(y), 0)
|
||||
x1, b1 := bits.Sub64((*x)[1], s, b0)
|
||||
x2, b2 := bits.Sub64((*x)[2], s, b1)
|
||||
x3, b3 := bits.Sub64((*x)[3], s, b2)
|
||||
x4, b4 := bits.Sub64((*x)[4], s, b3)
|
||||
x5, b5 := bits.Sub64((*x)[5], s, b4)
|
||||
x6, _ := bits.Sub64((*x)[6], s, b5)
|
||||
x[0] = (x0 >> 4) | (x1 << 60)
|
||||
x[1] = (x1 >> 4) | (x2 << 60)
|
||||
x[2] = (x2 >> 4) | (x3 << 60)
|
||||
x[3] = (x3 >> 4) | (x4 << 60)
|
||||
x[4] = (x4 >> 4) | (x5 << 60)
|
||||
x[5] = (x5 >> 4) | (x6 << 60)
|
||||
x[6] = (x6 >> 4)
|
||||
}
|
||||
|
||||
func recodeScalar(d *[113]int8, k *Scalar) {
|
||||
var k64 scalar64
|
||||
k64.fromScalar(k)
|
||||
for i := 0; i < 112; i++ {
|
||||
d[i] = int8((k64[0] & 0x1f) - 16)
|
||||
subYDiv16(&k64, int64(d[i]))
|
||||
}
|
||||
d[112] = int8(k64[0])
|
||||
}
|
||||
|
||||
// ScalarMult returns kP.
|
||||
func (e twistCurve) ScalarMult(k *Scalar, P *twistPoint) *twistPoint {
|
||||
var TabP [8]preTwistPointProy
|
||||
var S preTwistPointProy
|
||||
var d [113]int8
|
||||
|
||||
var isZero int
|
||||
if k.IsZero() {
|
||||
isZero = 1
|
||||
}
|
||||
subtle.ConstantTimeCopy(isZero, k[:], order[:])
|
||||
|
||||
minusK := *k
|
||||
isEven := 1 - int(k[0]&0x1)
|
||||
minusK.Neg()
|
||||
subtle.ConstantTimeCopy(isEven, k[:], minusK[:])
|
||||
recodeScalar(&d, k)
|
||||
|
||||
P.oddMultiples(TabP[:])
|
||||
Q := e.Identity()
|
||||
for i := 112; i >= 0; i-- {
|
||||
Q.Double()
|
||||
Q.Double()
|
||||
Q.Double()
|
||||
Q.Double()
|
||||
mask := d[i] >> 7
|
||||
absDi := (d[i] + mask) ^ mask
|
||||
inx := int32((absDi - 1) >> 1)
|
||||
sig := int((d[i] >> 7) & 0x1)
|
||||
for j := range TabP {
|
||||
S.cmov(&TabP[j], uint(subtle.ConstantTimeEq(inx, int32(j))))
|
||||
}
|
||||
S.cneg(sig)
|
||||
Q.mixAdd(&S)
|
||||
}
|
||||
Q.cneg(uint(isEven))
|
||||
return Q
|
||||
}
|
||||
|
||||
const (
|
||||
omegaFix = 7
|
||||
omegaVar = 5
|
||||
)
|
||||
|
||||
// CombinedMult returns mG+nP.
|
||||
func (e twistCurve) CombinedMult(m, n *Scalar, P *twistPoint) *twistPoint {
|
||||
nafFix := math.OmegaNAF(conv.BytesLe2BigInt(m[:]), omegaFix)
|
||||
nafVar := math.OmegaNAF(conv.BytesLe2BigInt(n[:]), omegaVar)
|
||||
|
||||
if len(nafFix) > len(nafVar) {
|
||||
nafVar = append(nafVar, make([]int32, len(nafFix)-len(nafVar))...)
|
||||
} else if len(nafFix) < len(nafVar) {
|
||||
nafFix = append(nafFix, make([]int32, len(nafVar)-len(nafFix))...)
|
||||
}
|
||||
|
||||
var TabQ [1 << (omegaVar - 2)]preTwistPointProy
|
||||
P.oddMultiples(TabQ[:])
|
||||
Q := e.Identity()
|
||||
for i := len(nafFix) - 1; i >= 0; i-- {
|
||||
Q.Double()
|
||||
// Generator point
|
||||
if nafFix[i] != 0 {
|
||||
idxM := absolute(nafFix[i]) >> 1
|
||||
R := tabVerif[idxM]
|
||||
if nafFix[i] < 0 {
|
||||
R.neg()
|
||||
}
|
||||
Q.mixAddZ1(&R)
|
||||
}
|
||||
// Variable input point
|
||||
if nafVar[i] != 0 {
|
||||
idxN := absolute(nafVar[i]) >> 1
|
||||
S := TabQ[idxN]
|
||||
if nafVar[i] < 0 {
|
||||
S.neg()
|
||||
}
|
||||
Q.mixAdd(&S)
|
||||
}
|
||||
}
|
||||
return Q
|
||||
}
|
||||
|
||||
// absolute returns always a positive value.
|
||||
func absolute(x int32) int32 {
|
||||
mask := x >> 31
|
||||
return (x + mask) ^ mask
|
||||
}
|
||||
|
|
@ -0,0 +1,135 @@
|
|||
package goldilocks
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
|
||||
fp "github.com/cloudflare/circl/math/fp448"
|
||||
)
|
||||
|
||||
type twistPoint struct{ x, y, z, ta, tb fp.Elt }
|
||||
|
||||
type preTwistPointAffine struct{ addYX, subYX, dt2 fp.Elt }
|
||||
|
||||
type preTwistPointProy struct {
|
||||
preTwistPointAffine
|
||||
z2 fp.Elt
|
||||
}
|
||||
|
||||
func (P *twistPoint) String() string {
|
||||
return fmt.Sprintf("x: %v\ny: %v\nz: %v\nta: %v\ntb: %v", P.x, P.y, P.z, P.ta, P.tb)
|
||||
}
|
||||
|
||||
// cneg conditionally negates the point if b=1.
|
||||
func (P *twistPoint) cneg(b uint) {
|
||||
t := &fp.Elt{}
|
||||
fp.Neg(t, &P.x)
|
||||
fp.Cmov(&P.x, t, b)
|
||||
fp.Neg(t, &P.ta)
|
||||
fp.Cmov(&P.ta, t, b)
|
||||
}
|
||||
|
||||
// Double updates P with 2P.
|
||||
func (P *twistPoint) Double() {
|
||||
// This is formula (7) from "Twisted Edwards Curves Revisited" by
|
||||
// Hisil H., Wong K.KH., Carter G., Dawson E. (2008)
|
||||
// https://doi.org/10.1007/978-3-540-89255-7_20
|
||||
Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb
|
||||
a, b, c, e, f, g, h := Px, Py, Pz, Pta, Px, Py, Ptb
|
||||
fp.Add(e, Px, Py) // x+y
|
||||
fp.Sqr(a, Px) // A = x^2
|
||||
fp.Sqr(b, Py) // B = y^2
|
||||
fp.Sqr(c, Pz) // z^2
|
||||
fp.Add(c, c, c) // C = 2*z^2
|
||||
fp.Add(h, a, b) // H = A+B
|
||||
fp.Sqr(e, e) // (x+y)^2
|
||||
fp.Sub(e, e, h) // E = (x+y)^2-A-B
|
||||
fp.Sub(g, b, a) // G = B-A
|
||||
fp.Sub(f, c, g) // F = C-G
|
||||
fp.Mul(Pz, f, g) // Z = F * G
|
||||
fp.Mul(Px, e, f) // X = E * F
|
||||
fp.Mul(Py, g, h) // Y = G * H, T = E * H
|
||||
}
|
||||
|
||||
// mixAdd calculates P= P+Q, where Q is a precomputed point with Z_Q = 1.
|
||||
func (P *twistPoint) mixAddZ1(Q *preTwistPointAffine) {
|
||||
fp.Add(&P.z, &P.z, &P.z) // D = 2*z1 (z2=1)
|
||||
P.coreAddition(Q)
|
||||
}
|
||||
|
||||
// coreAddition calculates P=P+Q for curves with A=-1.
|
||||
func (P *twistPoint) coreAddition(Q *preTwistPointAffine) {
|
||||
// This is the formula following (5) from "Twisted Edwards Curves Revisited" by
|
||||
// Hisil H., Wong K.KH., Carter G., Dawson E. (2008)
|
||||
// https://doi.org/10.1007/978-3-540-89255-7_20
|
||||
Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb
|
||||
addYX2, subYX2, dt2 := &Q.addYX, &Q.subYX, &Q.dt2
|
||||
a, b, c, d, e, f, g, h := Px, Py, &fp.Elt{}, Pz, Pta, Px, Py, Ptb
|
||||
fp.Mul(c, Pta, Ptb) // t1 = ta*tb
|
||||
fp.Sub(h, Py, Px) // y1-x1
|
||||
fp.Add(b, Py, Px) // y1+x1
|
||||
fp.Mul(a, h, subYX2) // A = (y1-x1)*(y2-x2)
|
||||
fp.Mul(b, b, addYX2) // B = (y1+x1)*(y2+x2)
|
||||
fp.Mul(c, c, dt2) // C = 2*D*t1*t2
|
||||
fp.Sub(e, b, a) // E = B-A
|
||||
fp.Add(h, b, a) // H = B+A
|
||||
fp.Sub(f, d, c) // F = D-C
|
||||
fp.Add(g, d, c) // G = D+C
|
||||
fp.Mul(Pz, f, g) // Z = F * G
|
||||
fp.Mul(Px, e, f) // X = E * F
|
||||
fp.Mul(Py, g, h) // Y = G * H, T = E * H
|
||||
}
|
||||
|
||||
func (P *preTwistPointAffine) neg() {
|
||||
P.addYX, P.subYX = P.subYX, P.addYX
|
||||
fp.Neg(&P.dt2, &P.dt2)
|
||||
}
|
||||
|
||||
func (P *preTwistPointAffine) cneg(b int) {
|
||||
t := &fp.Elt{}
|
||||
fp.Cswap(&P.addYX, &P.subYX, uint(b))
|
||||
fp.Neg(t, &P.dt2)
|
||||
fp.Cmov(&P.dt2, t, uint(b))
|
||||
}
|
||||
|
||||
func (P *preTwistPointAffine) cmov(Q *preTwistPointAffine, b uint) {
|
||||
fp.Cmov(&P.addYX, &Q.addYX, b)
|
||||
fp.Cmov(&P.subYX, &Q.subYX, b)
|
||||
fp.Cmov(&P.dt2, &Q.dt2, b)
|
||||
}
|
||||
|
||||
// mixAdd calculates P= P+Q, where Q is a precomputed point with Z_Q != 1.
|
||||
func (P *twistPoint) mixAdd(Q *preTwistPointProy) {
|
||||
fp.Mul(&P.z, &P.z, &Q.z2) // D = 2*z1*z2
|
||||
P.coreAddition(&Q.preTwistPointAffine)
|
||||
}
|
||||
|
||||
// oddMultiples calculates T[i] = (2*i-1)P for 0 < i < len(T).
|
||||
func (P *twistPoint) oddMultiples(T []preTwistPointProy) {
|
||||
if n := len(T); n > 0 {
|
||||
T[0].FromTwistPoint(P)
|
||||
_2P := *P
|
||||
_2P.Double()
|
||||
R := &preTwistPointProy{}
|
||||
R.FromTwistPoint(&_2P)
|
||||
for i := 1; i < n; i++ {
|
||||
P.mixAdd(R)
|
||||
T[i].FromTwistPoint(P)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// cmov conditionally moves Q into P if b=1.
|
||||
func (P *preTwistPointProy) cmov(Q *preTwistPointProy, b uint) {
|
||||
P.preTwistPointAffine.cmov(&Q.preTwistPointAffine, b)
|
||||
fp.Cmov(&P.z2, &Q.z2, b)
|
||||
}
|
||||
|
||||
// FromTwistPoint precomputes some coordinates of Q for missed addition.
|
||||
func (P *preTwistPointProy) FromTwistPoint(Q *twistPoint) {
|
||||
fp.Add(&P.addYX, &Q.y, &Q.x) // addYX = X + Y
|
||||
fp.Sub(&P.subYX, &Q.y, &Q.x) // subYX = Y - X
|
||||
fp.Mul(&P.dt2, &Q.ta, &Q.tb) // T = ta*tb
|
||||
fp.Mul(&P.dt2, &P.dt2, ¶mDTwist) // D*T
|
||||
fp.Add(&P.dt2, &P.dt2, &P.dt2) // dt2 = 2*D*T
|
||||
fp.Add(&P.z2, &Q.z, &Q.z) // z2 = 2*Z
|
||||
}
|
||||
|
|
@ -0,0 +1,216 @@
|
|||
package goldilocks
|
||||
|
||||
import fp "github.com/cloudflare/circl/math/fp448"
|
||||
|
||||
var tabFixMult = [fxV][fx2w1]preTwistPointAffine{
|
||||
{
|
||||
{
|
||||
addYX: fp.Elt{0x65, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2b, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05},
|
||||
subYX: fp.Elt{0x64, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2d, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05},
|
||||
dt2: fp.Elt{0x1a, 0x33, 0xea, 0x64, 0x45, 0x1c, 0xdf, 0x17, 0x1d, 0x16, 0x34, 0x28, 0xd6, 0x61, 0x19, 0x67, 0x79, 0xb4, 0x13, 0xcf, 0x3e, 0x7c, 0x0e, 0x72, 0xda, 0xf1, 0x5f, 0xda, 0xe6, 0xcf, 0x42, 0xd3, 0xb6, 0x17, 0xc2, 0x68, 0x13, 0x2d, 0xd9, 0x60, 0x3e, 0xae, 0xf0, 0x5b, 0x96, 0xf0, 0xcd, 0xaf, 0xea, 0xb7, 0x0d, 0x59, 0x16, 0xa7, 0xff, 0x55},
|
||||
},
|
||||
{
|
||||
addYX: fp.Elt{0xca, 0xd8, 0x7d, 0x86, 0x1a, 0xef, 0xad, 0x11, 0xe3, 0x27, 0x41, 0x7e, 0x7f, 0x3e, 0xa9, 0xd2, 0xb5, 0x4e, 0x50, 0xe0, 0x77, 0x91, 0xc2, 0x13, 0x52, 0x73, 0x41, 0x09, 0xa6, 0x57, 0x9a, 0xc8, 0xa8, 0x90, 0x9d, 0x26, 0x14, 0xbb, 0xa1, 0x2a, 0xf7, 0x45, 0x43, 0x4e, 0xea, 0x35, 0x62, 0xe1, 0x08, 0x85, 0x46, 0xb8, 0x24, 0x05, 0x2d, 0xab},
|
||||
subYX: fp.Elt{0x9b, 0xe6, 0xd3, 0xe5, 0xfe, 0x50, 0x36, 0x3c, 0x3c, 0x6d, 0x74, 0x1d, 0x74, 0xc0, 0xde, 0x5b, 0x45, 0x27, 0xe5, 0x12, 0xee, 0x63, 0x35, 0x6b, 0x13, 0xe2, 0x41, 0x6b, 0x3a, 0x05, 0x2b, 0xb1, 0x89, 0x26, 0xb6, 0xc6, 0xd1, 0x84, 0xff, 0x0e, 0x9b, 0xa3, 0xfb, 0x21, 0x36, 0x6b, 0x01, 0xf7, 0x9f, 0x7c, 0xeb, 0xf5, 0x18, 0x7a, 0x2a, 0x70},
|
||||
dt2: fp.Elt{0x09, 0xad, 0x99, 0x1a, 0x38, 0xd3, 0xdf, 0x22, 0x37, 0x32, 0x61, 0x8b, 0xf3, 0x19, 0x48, 0x08, 0xe8, 0x49, 0xb6, 0x4a, 0xa7, 0xed, 0xa4, 0xa2, 0xee, 0x86, 0xd7, 0x31, 0x5e, 0xce, 0x95, 0x76, 0x86, 0x42, 0x1c, 0x9d, 0x07, 0x14, 0x8c, 0x34, 0x18, 0x9c, 0x6d, 0x3a, 0xdf, 0xa9, 0xe8, 0x36, 0x7e, 0xe4, 0x95, 0xbe, 0xb5, 0x09, 0xf8, 0x9c},
|
||||
},
|
||||
{
|
||||
addYX: fp.Elt{0x51, 0xdb, 0x49, 0xa8, 0x9f, 0xe3, 0xd7, 0xec, 0x0d, 0x0f, 0x49, 0xe8, 0xb6, 0xc5, 0x0f, 0x5a, 0x1c, 0xce, 0x54, 0x0d, 0xb1, 0x8d, 0x5b, 0xbf, 0xf4, 0xaa, 0x34, 0x77, 0xc4, 0x5d, 0x59, 0xb6, 0xc5, 0x0e, 0x5a, 0xd8, 0x5b, 0x30, 0xc2, 0x1d, 0xec, 0x85, 0x1c, 0x42, 0xbe, 0x24, 0x2e, 0x50, 0x55, 0x44, 0xb2, 0x3a, 0x01, 0xaa, 0x98, 0xfb},
|
||||
subYX: fp.Elt{0xe7, 0x29, 0xb7, 0xd0, 0xaa, 0x4f, 0x32, 0x53, 0x56, 0xde, 0xbc, 0xd1, 0x92, 0x5d, 0x19, 0xbe, 0xa3, 0xe3, 0x75, 0x48, 0xe0, 0x7a, 0x1b, 0x54, 0x7a, 0xb7, 0x41, 0x77, 0x84, 0x38, 0xdd, 0x14, 0x9f, 0xca, 0x3f, 0xa3, 0xc8, 0xa7, 0x04, 0x70, 0xf1, 0x4d, 0x3d, 0xb3, 0x84, 0x79, 0xcb, 0xdb, 0xe4, 0xc5, 0x42, 0x9b, 0x57, 0x19, 0xf1, 0x2d},
|
||||
dt2: fp.Elt{0x20, 0xb4, 0x94, 0x9e, 0xdf, 0x31, 0x44, 0x0b, 0xc9, 0x7b, 0x75, 0x40, 0x9d, 0xd1, 0x96, 0x39, 0x70, 0x71, 0x15, 0xc8, 0x93, 0xd5, 0xc5, 0xe5, 0xba, 0xfe, 0xee, 0x08, 0x6a, 0x98, 0x0a, 0x1b, 0xb2, 0xaa, 0x3a, 0xf4, 0xa4, 0x79, 0xf9, 0x8e, 0x4d, 0x65, 0x10, 0x9b, 0x3a, 0x6e, 0x7c, 0x87, 0x94, 0x92, 0x11, 0x65, 0xbf, 0x1a, 0x09, 0xde},
|
||||
},
|
||||
{
|
||||
addYX: fp.Elt{0xf3, 0x84, 0x76, 0x77, 0xa5, 0x6b, 0x27, 0x3b, 0x83, 0x3d, 0xdf, 0xa0, 0xeb, 0x32, 0x6d, 0x58, 0x81, 0x57, 0x64, 0xc2, 0x21, 0x7c, 0x9b, 0xea, 0xe6, 0xb0, 0x93, 0xf9, 0xe7, 0xc3, 0xed, 0x5a, 0x8e, 0xe2, 0xb4, 0x72, 0x76, 0x66, 0x0f, 0x22, 0x29, 0x94, 0x3e, 0x63, 0x48, 0x5e, 0x80, 0xcb, 0xac, 0xfa, 0x95, 0xb6, 0x4b, 0xc4, 0x95, 0x33},
|
||||
subYX: fp.Elt{0x0c, 0x55, 0xd1, 0x5e, 0x5f, 0xbf, 0xbf, 0xe2, 0x4c, 0xfc, 0x37, 0x4a, 0xc4, 0xb1, 0xf4, 0x83, 0x61, 0x93, 0x60, 0x8e, 0x9f, 0x31, 0xf0, 0xa0, 0x41, 0xff, 0x1d, 0xe2, 0x7f, 0xca, 0x40, 0xd6, 0x88, 0xe8, 0x91, 0x61, 0xe2, 0x11, 0x18, 0x83, 0xf3, 0x25, 0x2f, 0x3f, 0x49, 0x40, 0xd4, 0x83, 0xe2, 0xd7, 0x74, 0x6a, 0x16, 0x86, 0x4e, 0xab},
|
||||
dt2: fp.Elt{0xdd, 0x58, 0x65, 0xd8, 0x9f, 0xdd, 0x70, 0x7f, 0x0f, 0xec, 0xbd, 0x5c, 0x5c, 0x9b, 0x7e, 0x1b, 0x9f, 0x79, 0x36, 0x1f, 0xfd, 0x79, 0x10, 0x1c, 0x52, 0xf3, 0x22, 0xa4, 0x1f, 0x71, 0x6e, 0x63, 0x14, 0xf4, 0xa7, 0x3e, 0xbe, 0xad, 0x43, 0x30, 0x38, 0x8c, 0x29, 0xc6, 0xcf, 0x50, 0x75, 0x21, 0xe5, 0x78, 0xfd, 0xb0, 0x9a, 0xc4, 0x6d, 0xd4},
|
||||
},
|
||||
},
|
||||
{
|
||||
{
|
||||
addYX: fp.Elt{0x7a, 0xa1, 0x38, 0xa6, 0xfd, 0x0e, 0x96, 0xd5, 0x26, 0x76, 0x86, 0x70, 0x80, 0x30, 0xa6, 0x67, 0xeb, 0xf4, 0x39, 0xdb, 0x22, 0xf5, 0x9f, 0x98, 0xe4, 0xb5, 0x3a, 0x0c, 0x59, 0xbf, 0x85, 0xc6, 0xf0, 0x0b, 0x1c, 0x41, 0x38, 0x09, 0x01, 0xdb, 0xd6, 0x3c, 0xb7, 0xf1, 0x08, 0x6b, 0x4b, 0x9e, 0x63, 0x53, 0x83, 0xd3, 0xab, 0xa3, 0x72, 0x0d},
|
||||
subYX: fp.Elt{0x84, 0x68, 0x25, 0xe8, 0xe9, 0x8f, 0x91, 0xbf, 0xf7, 0xa4, 0x30, 0xae, 0xea, 0x9f, 0xdd, 0x56, 0x64, 0x09, 0xc9, 0x54, 0x68, 0x4e, 0x33, 0xc5, 0x6f, 0x7b, 0x2d, 0x52, 0x2e, 0x42, 0xbe, 0xbe, 0xf5, 0x64, 0xbf, 0x77, 0x54, 0xdf, 0xb0, 0x10, 0xd2, 0x16, 0x5d, 0xce, 0xaf, 0x9f, 0xfb, 0xa3, 0x63, 0x50, 0xcb, 0xc0, 0xd0, 0x88, 0x44, 0xa3},
|
||||
dt2: fp.Elt{0xc3, 0x8b, 0xa5, 0xf1, 0x44, 0xe4, 0x41, 0xcd, 0x75, 0xe3, 0x17, 0x69, 0x5b, 0xb9, 0xbb, 0xee, 0x82, 0xbb, 0xce, 0x57, 0xdf, 0x2a, 0x9c, 0x12, 0xab, 0x66, 0x08, 0x68, 0x05, 0x1b, 0x87, 0xee, 0x5d, 0x1e, 0x18, 0x14, 0x22, 0x4b, 0x99, 0x61, 0x75, 0x28, 0xe7, 0x65, 0x1c, 0x36, 0xb6, 0x18, 0x09, 0xa8, 0xdf, 0xef, 0x30, 0x35, 0xbc, 0x58},
|
||||
},
|
||||
{
|
||||
addYX: fp.Elt{0xc5, 0xd3, 0x0e, 0x6f, 0xaf, 0x06, 0x69, 0xc4, 0x07, 0x9e, 0x58, 0x6e, 0x3f, 0x49, 0xd9, 0x0a, 0x3c, 0x2c, 0x37, 0xcd, 0x27, 0x4d, 0x87, 0x91, 0x7a, 0xb0, 0x28, 0xad, 0x2f, 0x68, 0x92, 0x05, 0x97, 0xf1, 0x30, 0x5f, 0x4c, 0x10, 0x20, 0x30, 0xd3, 0x08, 0x3f, 0xc1, 0xc6, 0xb7, 0xb5, 0xd1, 0x71, 0x7b, 0xa8, 0x0a, 0xd8, 0xf5, 0x17, 0xcf},
|
||||
subYX: fp.Elt{0x64, 0xd4, 0x8f, 0x91, 0x40, 0xab, 0x6e, 0x1a, 0x62, 0x83, 0xdc, 0xd7, 0x30, 0x1a, 0x4a, 0x2a, 0x4c, 0x54, 0x86, 0x19, 0x81, 0x5d, 0x04, 0x52, 0xa3, 0xca, 0x82, 0x38, 0xdc, 0x1e, 0xf0, 0x7a, 0x78, 0x76, 0x49, 0x4f, 0x71, 0xc4, 0x74, 0x2f, 0xf0, 0x5b, 0x2e, 0x5e, 0xac, 0xef, 0x17, 0xe4, 0x8e, 0x6e, 0xed, 0x43, 0x23, 0x61, 0x99, 0x49},
|
||||
dt2: fp.Elt{0x64, 0x90, 0x72, 0x76, 0xf8, 0x2c, 0x7d, 0x57, 0xf9, 0x30, 0x5e, 0x7a, 0x10, 0x74, 0x19, 0x39, 0xd9, 0xaf, 0x0a, 0xf1, 0x43, 0xed, 0x88, 0x9c, 0x8b, 0xdc, 0x9b, 0x1c, 0x90, 0xe7, 0xf7, 0xa3, 0xa5, 0x0d, 0xc6, 0xbc, 0x30, 0xfb, 0x91, 0x1a, 0x51, 0xba, 0x2d, 0xbe, 0x89, 0xdf, 0x1d, 0xdc, 0x53, 0xa8, 0x82, 0x8a, 0xd3, 0x8d, 0x16, 0x68},
|
||||
},
|
||||
{
|
||||
addYX: fp.Elt{0xef, 0x5c, 0xe3, 0x74, 0xbf, 0x13, 0x4a, 0xbf, 0x66, 0x73, 0x64, 0xb7, 0xd4, 0xce, 0x98, 0x82, 0x05, 0xfa, 0x98, 0x0c, 0x0a, 0xae, 0xe5, 0x6b, 0x9f, 0xac, 0xbb, 0x6e, 0x1f, 0xcf, 0xff, 0xa6, 0x71, 0x9a, 0xa8, 0x7a, 0x9e, 0x64, 0x1f, 0x20, 0x4a, 0x61, 0xa2, 0xd6, 0x50, 0xe3, 0xba, 0x81, 0x0c, 0x50, 0x59, 0x69, 0x59, 0x15, 0x55, 0xdb},
|
||||
subYX: fp.Elt{0xe8, 0x77, 0x4d, 0xe8, 0x66, 0x3d, 0xc1, 0x00, 0x3c, 0xf2, 0x25, 0x00, 0xdc, 0xb2, 0xe5, 0x9b, 0x12, 0x89, 0xf3, 0xd6, 0xea, 0x85, 0x60, 0xfe, 0x67, 0x91, 0xfd, 0x04, 0x7c, 0xe0, 0xf1, 0x86, 0x06, 0x11, 0x66, 0xee, 0xd4, 0xd5, 0xbe, 0x3b, 0x0f, 0xe3, 0x59, 0xb3, 0x4f, 0x00, 0xb6, 0xce, 0x80, 0xc1, 0x61, 0xf7, 0xaf, 0x04, 0x6a, 0x3c},
|
||||
dt2: fp.Elt{0x00, 0xd7, 0x32, 0x93, 0x67, 0x70, 0x6f, 0xd7, 0x69, 0xab, 0xb1, 0xd3, 0xdc, 0xd6, 0xa8, 0xdd, 0x35, 0x25, 0xca, 0xd3, 0x8a, 0x6d, 0xce, 0xfb, 0xfd, 0x2b, 0x83, 0xf0, 0xd4, 0xac, 0x66, 0xfb, 0x72, 0x87, 0x7e, 0x55, 0xb7, 0x91, 0x58, 0x10, 0xc3, 0x11, 0x7e, 0x15, 0xfe, 0x7c, 0x55, 0x90, 0xa3, 0x9e, 0xed, 0x9a, 0x7f, 0xa7, 0xb7, 0xeb},
|
||||
},
|
||||
{
|
||||
addYX: fp.Elt{0x25, 0x0f, 0xc2, 0x09, 0x9c, 0x10, 0xc8, 0x7c, 0x93, 0xa7, 0xbe, 0xe9, 0x26, 0x25, 0x7c, 0x21, 0xfe, 0xe7, 0x5f, 0x3c, 0x02, 0x83, 0xa7, 0x9e, 0xdf, 0xc0, 0x94, 0x2b, 0x7d, 0x1a, 0xd0, 0x1d, 0xcc, 0x2e, 0x7d, 0xd4, 0x85, 0xe7, 0xc1, 0x15, 0x66, 0xd6, 0xd6, 0x32, 0xb8, 0xf7, 0x63, 0xaa, 0x3b, 0xa5, 0xea, 0x49, 0xad, 0x88, 0x9b, 0x66},
|
||||
subYX: fp.Elt{0x09, 0x97, 0x79, 0x36, 0x41, 0x56, 0x9b, 0xdf, 0x15, 0xd8, 0x43, 0x28, 0x17, 0x5b, 0x96, 0xc9, 0xcf, 0x39, 0x1f, 0x13, 0xf7, 0x4d, 0x1d, 0x1f, 0xda, 0x51, 0x56, 0xe7, 0x0a, 0x5a, 0x65, 0xb6, 0x2a, 0x87, 0x49, 0x86, 0xc2, 0x2b, 0xcd, 0xfe, 0x07, 0xf6, 0x4c, 0xe2, 0x1d, 0x9b, 0xd8, 0x82, 0x09, 0x5b, 0x11, 0x10, 0x62, 0x56, 0x89, 0xbd},
|
||||
dt2: fp.Elt{0xd9, 0x15, 0x73, 0xf2, 0x96, 0x35, 0x53, 0xb0, 0xe7, 0xa8, 0x0b, 0x93, 0x35, 0x0b, 0x3a, 0x00, 0xf5, 0x18, 0xb1, 0xc3, 0x12, 0x3f, 0x91, 0x17, 0xc1, 0x4c, 0x15, 0x5a, 0x86, 0x92, 0x11, 0xbd, 0x44, 0x40, 0x5a, 0x7b, 0x15, 0x89, 0xba, 0xc1, 0xc1, 0xbc, 0x43, 0x45, 0xe6, 0x52, 0x02, 0x73, 0x0a, 0xd0, 0x2a, 0x19, 0xda, 0x47, 0xa8, 0xff},
|
||||
},
|
||||
},
|
||||
}
|
||||
|
||||
// tabVerif contains the odd multiples of P. The entry T[i] = (2i+1)P, where
|
||||
// P = phi(G) and G is the generator of the Goldilocks curve, and phi is a
|
||||
// 4-degree isogeny.
|
||||
var tabVerif = [1 << (omegaFix - 2)]preTwistPointAffine{
|
||||
{ /* 1P*/
|
||||
addYX: fp.Elt{0x65, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2b, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05},
|
||||
subYX: fp.Elt{0x64, 0x4a, 0xdd, 0xdf, 0xb4, 0x79, 0x60, 0xc8, 0xa1, 0x70, 0xb4, 0x3a, 0x1e, 0x0c, 0x9b, 0x19, 0xe5, 0x48, 0x3f, 0xd7, 0x44, 0x18, 0x18, 0x14, 0x14, 0x27, 0x45, 0xd0, 0x2d, 0x24, 0xd5, 0x93, 0xc3, 0x74, 0x4c, 0x50, 0x70, 0x43, 0x26, 0x05, 0x08, 0x24, 0xca, 0x78, 0x30, 0xc1, 0x06, 0x8d, 0xd4, 0x86, 0x42, 0xf0, 0x14, 0xde, 0x08, 0x05},
|
||||
dt2: fp.Elt{0x1a, 0x33, 0xea, 0x64, 0x45, 0x1c, 0xdf, 0x17, 0x1d, 0x16, 0x34, 0x28, 0xd6, 0x61, 0x19, 0x67, 0x79, 0xb4, 0x13, 0xcf, 0x3e, 0x7c, 0x0e, 0x72, 0xda, 0xf1, 0x5f, 0xda, 0xe6, 0xcf, 0x42, 0xd3, 0xb6, 0x17, 0xc2, 0x68, 0x13, 0x2d, 0xd9, 0x60, 0x3e, 0xae, 0xf0, 0x5b, 0x96, 0xf0, 0xcd, 0xaf, 0xea, 0xb7, 0x0d, 0x59, 0x16, 0xa7, 0xff, 0x55},
|
||||
},
|
||||
{ /* 3P*/
|
||||
addYX: fp.Elt{0xd1, 0xe9, 0xa8, 0x33, 0x20, 0x76, 0x18, 0x08, 0x45, 0x2a, 0xc9, 0x67, 0x2a, 0xc3, 0x15, 0x24, 0xf9, 0x74, 0x21, 0x30, 0x99, 0x59, 0x8b, 0xb2, 0xf0, 0xa4, 0x07, 0xe2, 0x6a, 0x36, 0x8d, 0xd9, 0xd2, 0x4a, 0x7f, 0x73, 0x50, 0x39, 0x3d, 0xaa, 0xa7, 0x51, 0x73, 0x0d, 0x2b, 0x8b, 0x96, 0x47, 0xac, 0x3c, 0x5d, 0xaa, 0x39, 0x9c, 0xcf, 0xd5},
|
||||
subYX: fp.Elt{0x6b, 0x11, 0x5d, 0x1a, 0xf9, 0x41, 0x9d, 0xc5, 0x30, 0x3e, 0xad, 0x25, 0x2c, 0x04, 0x45, 0xea, 0xcc, 0x67, 0x07, 0x85, 0xe9, 0xda, 0x0e, 0xb5, 0x40, 0xb7, 0x32, 0xb4, 0x49, 0xdd, 0xff, 0xaa, 0xfc, 0xbb, 0x19, 0xca, 0x8b, 0x79, 0x2b, 0x8f, 0x8d, 0x00, 0x33, 0xc2, 0xad, 0xe9, 0xd3, 0x12, 0xa8, 0xaa, 0x87, 0x62, 0xad, 0x2d, 0xff, 0xa4},
|
||||
dt2: fp.Elt{0xb0, 0xaf, 0x3b, 0xea, 0xf0, 0x42, 0x0b, 0x5e, 0x88, 0xd3, 0x98, 0x08, 0x87, 0x59, 0x72, 0x0a, 0xc2, 0xdf, 0xcb, 0x7f, 0x59, 0xb5, 0x4c, 0x63, 0x68, 0xe8, 0x41, 0x38, 0x67, 0x4f, 0xe9, 0xc6, 0xb2, 0x6b, 0x08, 0xa7, 0xf7, 0x0e, 0xcd, 0xea, 0xca, 0x3d, 0xaf, 0x8e, 0xda, 0x4b, 0x2e, 0xd2, 0x88, 0x64, 0x8d, 0xc5, 0x5f, 0x76, 0x0f, 0x3d},
|
||||
},
|
||||
{ /* 5P*/
|
||||
addYX: fp.Elt{0xe5, 0x65, 0xc9, 0xe2, 0x75, 0xf0, 0x7d, 0x1a, 0xba, 0xa4, 0x40, 0x4b, 0x93, 0x12, 0xa2, 0x80, 0x95, 0x0d, 0x03, 0x93, 0xe8, 0xa5, 0x4d, 0xe2, 0x3d, 0x81, 0xf5, 0xce, 0xd4, 0x2d, 0x25, 0x59, 0x16, 0x5c, 0xe7, 0xda, 0xc7, 0x45, 0xd2, 0x7e, 0x2c, 0x38, 0xd4, 0x37, 0x64, 0xb2, 0xc2, 0x28, 0xc5, 0x72, 0x16, 0x32, 0x45, 0x36, 0x6f, 0x9f},
|
||||
subYX: fp.Elt{0x09, 0xf4, 0x7e, 0xbd, 0x89, 0xdb, 0x19, 0x58, 0xe1, 0x08, 0x00, 0x8a, 0xf4, 0x5f, 0x2a, 0x32, 0x40, 0xf0, 0x2c, 0x3f, 0x5d, 0xe4, 0xfc, 0x89, 0x11, 0x24, 0xb4, 0x2f, 0x97, 0xad, 0xac, 0x8f, 0x19, 0xab, 0xfa, 0x12, 0xe5, 0xf9, 0x50, 0x4e, 0x50, 0x6f, 0x32, 0x30, 0x88, 0xa6, 0xe5, 0x48, 0x28, 0xa2, 0x1b, 0x9f, 0xcd, 0xe2, 0x43, 0x38},
|
||||
dt2: fp.Elt{0xa9, 0xcc, 0x53, 0x39, 0x86, 0x02, 0x60, 0x75, 0x34, 0x99, 0x57, 0xbd, 0xfc, 0x5a, 0x8e, 0xce, 0x5e, 0x98, 0x22, 0xd0, 0xa5, 0x24, 0xff, 0x90, 0x28, 0x9f, 0x58, 0xf3, 0x39, 0xe9, 0xba, 0x36, 0x23, 0xfb, 0x7f, 0x41, 0xcc, 0x2b, 0x5a, 0x25, 0x3f, 0x4c, 0x2a, 0xf1, 0x52, 0x6f, 0x2f, 0x07, 0xe3, 0x88, 0x81, 0x77, 0xdd, 0x7c, 0x88, 0x82},
|
||||
},
|
||||
{ /* 7P*/
|
||||
addYX: fp.Elt{0xf7, 0xee, 0x88, 0xfd, 0x3a, 0xbf, 0x7e, 0x28, 0x39, 0x23, 0x79, 0xe6, 0x5c, 0x56, 0xcb, 0xb5, 0x48, 0x6a, 0x80, 0x6d, 0x37, 0x60, 0x6c, 0x10, 0x35, 0x49, 0x4b, 0x46, 0x60, 0xd4, 0x79, 0xd4, 0x53, 0xd3, 0x67, 0x88, 0xd0, 0x41, 0xd5, 0x43, 0x85, 0xc8, 0x71, 0xe3, 0x1c, 0xb6, 0xda, 0x22, 0x64, 0x8f, 0x80, 0xac, 0xad, 0x7d, 0xd5, 0x82},
|
||||
subYX: fp.Elt{0x92, 0x40, 0xc1, 0x83, 0x21, 0x9b, 0xd5, 0x7d, 0x3f, 0x29, 0xb6, 0x26, 0xef, 0x12, 0xb9, 0x27, 0x39, 0x42, 0x37, 0x97, 0x09, 0x9a, 0x08, 0xe1, 0x68, 0xb6, 0x7a, 0x3f, 0x9f, 0x45, 0xf8, 0x37, 0x19, 0x83, 0x97, 0xe6, 0x73, 0x30, 0x32, 0x35, 0xcf, 0xae, 0x5c, 0x12, 0x68, 0xdf, 0x6e, 0x2b, 0xde, 0x83, 0xa0, 0x44, 0x74, 0x2e, 0x4a, 0xe9},
|
||||
dt2: fp.Elt{0xcb, 0x22, 0x0a, 0xda, 0x6b, 0xc1, 0x8a, 0x29, 0xa1, 0xac, 0x8b, 0x5b, 0x8b, 0x32, 0x20, 0xf2, 0x21, 0xae, 0x0c, 0x43, 0xc4, 0xd7, 0x19, 0x37, 0x3d, 0x79, 0x25, 0x98, 0x6c, 0x9c, 0x22, 0x31, 0x2a, 0x55, 0x9f, 0xda, 0x5e, 0xa8, 0x13, 0xdb, 0x8e, 0x2e, 0x16, 0x39, 0xf4, 0x91, 0x6f, 0xec, 0x71, 0x71, 0xc9, 0x10, 0xf2, 0xa4, 0x8f, 0x11},
|
||||
},
|
||||
{ /* 9P*/
|
||||
addYX: fp.Elt{0x85, 0xdd, 0x37, 0x62, 0x74, 0x8e, 0x33, 0x5b, 0x25, 0x12, 0x1b, 0xe7, 0xdf, 0x47, 0xe5, 0x12, 0xfd, 0x3a, 0x3a, 0xf5, 0x5d, 0x4c, 0xa2, 0x29, 0x3c, 0x5c, 0x2f, 0xee, 0x18, 0x19, 0x0a, 0x2b, 0xef, 0x67, 0x50, 0x7a, 0x0d, 0x29, 0xae, 0x55, 0x82, 0xcd, 0xd6, 0x41, 0x90, 0xb4, 0x13, 0x31, 0x5d, 0x11, 0xb8, 0xaa, 0x12, 0x86, 0x08, 0xac},
|
||||
subYX: fp.Elt{0xcc, 0x37, 0x8d, 0x83, 0x5f, 0xfd, 0xde, 0xd5, 0xf7, 0xf1, 0xae, 0x0a, 0xa7, 0x0b, 0xeb, 0x6d, 0x19, 0x8a, 0xb6, 0x1a, 0x59, 0xd8, 0xff, 0x3c, 0xbc, 0xbc, 0xef, 0x9c, 0xda, 0x7b, 0x75, 0x12, 0xaf, 0x80, 0x8f, 0x2c, 0x3c, 0xaa, 0x0b, 0x17, 0x86, 0x36, 0x78, 0x18, 0xc8, 0x8a, 0xf6, 0xb8, 0x2c, 0x2f, 0x57, 0x2c, 0x62, 0x57, 0xf6, 0x90},
|
||||
dt2: fp.Elt{0x83, 0xbc, 0xa2, 0x07, 0xa5, 0x38, 0x96, 0xea, 0xfe, 0x11, 0x46, 0x1d, 0x3b, 0xcd, 0x42, 0xc5, 0xee, 0x67, 0x04, 0x72, 0x08, 0xd8, 0xd9, 0x96, 0x07, 0xf7, 0xac, 0xc3, 0x64, 0xf1, 0x98, 0x2c, 0x55, 0xd7, 0x7d, 0xc8, 0x6c, 0xbd, 0x2c, 0xff, 0x15, 0xd6, 0x6e, 0xb8, 0x17, 0x8e, 0xa8, 0x27, 0x66, 0xb1, 0x73, 0x79, 0x96, 0xff, 0x29, 0x10},
|
||||
},
|
||||
{ /* 11P*/
|
||||
addYX: fp.Elt{0x76, 0xcb, 0x9b, 0x0c, 0x5b, 0xfe, 0xe1, 0x2a, 0xdd, 0x6f, 0x6c, 0xdd, 0x6f, 0xb4, 0xc0, 0xc2, 0x1b, 0x4b, 0x38, 0xe8, 0x66, 0x8c, 0x1e, 0x31, 0x63, 0xb9, 0x94, 0xcd, 0xc3, 0x8c, 0x44, 0x25, 0x7b, 0xd5, 0x39, 0x80, 0xfc, 0x01, 0xaa, 0xf7, 0x2a, 0x61, 0x8a, 0x25, 0xd2, 0x5f, 0xc5, 0x66, 0x38, 0xa4, 0x17, 0xcf, 0x3e, 0x11, 0x0f, 0xa3},
|
||||
subYX: fp.Elt{0xe0, 0xb6, 0xd1, 0x9c, 0x71, 0x49, 0x2e, 0x7b, 0xde, 0x00, 0xda, 0x6b, 0xf1, 0xec, 0xe6, 0x7a, 0x15, 0x38, 0x71, 0xe9, 0x7b, 0xdb, 0xf8, 0x98, 0xc0, 0x91, 0x2e, 0x53, 0xee, 0x92, 0x87, 0x25, 0xc9, 0xb0, 0xbb, 0x33, 0x15, 0x46, 0x7f, 0xfd, 0x4f, 0x8b, 0x77, 0x05, 0x96, 0xb6, 0xe2, 0x08, 0xdb, 0x0d, 0x09, 0xee, 0x5b, 0xd1, 0x2a, 0x63},
|
||||
dt2: fp.Elt{0x8f, 0x7b, 0x57, 0x8c, 0xbf, 0x06, 0x0d, 0x43, 0x21, 0x92, 0x94, 0x2d, 0x6a, 0x38, 0x07, 0x0f, 0xa0, 0xf1, 0xe3, 0xd8, 0x2a, 0xbf, 0x46, 0xc6, 0x9e, 0x1f, 0x8f, 0x2b, 0x46, 0x84, 0x0b, 0x74, 0xed, 0xff, 0xf8, 0xa5, 0x94, 0xae, 0xf1, 0x67, 0xb1, 0x9b, 0xdd, 0x4a, 0xd0, 0xdb, 0xc2, 0xb5, 0x58, 0x49, 0x0c, 0xa9, 0x1d, 0x7d, 0xa9, 0xd3},
|
||||
},
|
||||
{ /* 13P*/
|
||||
addYX: fp.Elt{0x73, 0x84, 0x2e, 0x31, 0x1f, 0xdc, 0xed, 0x9f, 0x74, 0xfa, 0xe0, 0x35, 0xb1, 0x85, 0x6a, 0x8d, 0x86, 0xd0, 0xff, 0xd6, 0x08, 0x43, 0x73, 0x1a, 0xd5, 0xf8, 0x43, 0xd4, 0xb3, 0xe5, 0x3f, 0xa8, 0x84, 0x17, 0x59, 0x65, 0x4e, 0xe6, 0xee, 0x54, 0x9c, 0xda, 0x5e, 0x7e, 0x98, 0x29, 0x6d, 0x73, 0x34, 0x1f, 0x99, 0x80, 0x54, 0x54, 0x81, 0x0b},
|
||||
subYX: fp.Elt{0xb1, 0xe5, 0xbb, 0x80, 0x22, 0x9c, 0x81, 0x6d, 0xaf, 0x27, 0x65, 0x6f, 0x7e, 0x9c, 0xb6, 0x8d, 0x35, 0x5c, 0x2e, 0x20, 0x48, 0x7a, 0x28, 0xf0, 0x97, 0xfe, 0xb7, 0x71, 0xce, 0xd6, 0xad, 0x3a, 0x81, 0xf6, 0x74, 0x5e, 0xf3, 0xfd, 0x1b, 0xd4, 0x1e, 0x7c, 0xc2, 0xb7, 0xc8, 0xa6, 0xc9, 0x89, 0x03, 0x47, 0xec, 0x24, 0xd6, 0x0e, 0xec, 0x9c},
|
||||
dt2: fp.Elt{0x91, 0x0a, 0x43, 0x34, 0x20, 0xc2, 0x64, 0xf7, 0x4e, 0x48, 0xc8, 0xd2, 0x95, 0x83, 0xd1, 0xa4, 0xfb, 0x4e, 0x41, 0x3b, 0x0d, 0xd5, 0x07, 0xd9, 0xf1, 0x13, 0x16, 0x78, 0x54, 0x57, 0xd0, 0xf1, 0x4f, 0x20, 0xac, 0xcf, 0x9c, 0x3b, 0x33, 0x0b, 0x99, 0x54, 0xc3, 0x7f, 0x3e, 0x57, 0x26, 0x86, 0xd5, 0xa5, 0x2b, 0x8d, 0xe3, 0x19, 0x36, 0xf7},
|
||||
},
|
||||
{ /* 15P*/
|
||||
addYX: fp.Elt{0x23, 0x69, 0x47, 0x14, 0xf9, 0x9a, 0x50, 0xff, 0x64, 0xd1, 0x50, 0x35, 0xc3, 0x11, 0xd3, 0x19, 0xcf, 0x87, 0xda, 0x30, 0x0b, 0x50, 0xda, 0xc0, 0xe0, 0x25, 0x00, 0xe5, 0x68, 0x93, 0x04, 0xc2, 0xaf, 0xbd, 0x2f, 0x36, 0x5f, 0x47, 0x96, 0x10, 0xa8, 0xbd, 0xe4, 0x88, 0xac, 0x80, 0x52, 0x61, 0x73, 0xe9, 0x63, 0xdd, 0x99, 0xad, 0x20, 0x5b},
|
||||
subYX: fp.Elt{0x1b, 0x5e, 0xa2, 0x2a, 0x25, 0x0f, 0x86, 0xc0, 0xb1, 0x2e, 0x0c, 0x13, 0x40, 0x8d, 0xf0, 0xe6, 0x00, 0x55, 0x08, 0xc5, 0x7d, 0xf4, 0xc9, 0x31, 0x25, 0x3a, 0x99, 0x69, 0xdd, 0x67, 0x63, 0x9a, 0xd6, 0x89, 0x2e, 0xa1, 0x19, 0xca, 0x2c, 0xd9, 0x59, 0x5f, 0x5d, 0xc3, 0x6e, 0x62, 0x36, 0x12, 0x59, 0x15, 0xe1, 0xdc, 0xa4, 0xad, 0xc9, 0xd0},
|
||||
dt2: fp.Elt{0xbc, 0xea, 0xfc, 0xaf, 0x66, 0x23, 0xb7, 0x39, 0x6b, 0x2a, 0x96, 0xa8, 0x54, 0x43, 0xe9, 0xaa, 0x32, 0x40, 0x63, 0x92, 0x5e, 0xdf, 0x35, 0xc2, 0x9f, 0x24, 0x0c, 0xed, 0xfc, 0xde, 0x73, 0x8f, 0xa7, 0xd5, 0xa3, 0x2b, 0x18, 0x1f, 0xb0, 0xf8, 0xeb, 0x55, 0xd9, 0xc3, 0xfd, 0x28, 0x7c, 0x4f, 0xce, 0x0d, 0xf7, 0xae, 0xc2, 0x83, 0xc3, 0x78},
|
||||
},
|
||||
{ /* 17P*/
|
||||
addYX: fp.Elt{0x71, 0xe6, 0x60, 0x93, 0x37, 0xdb, 0x01, 0xa5, 0x4c, 0xba, 0xe8, 0x8e, 0xd5, 0xf9, 0xd3, 0x98, 0xe5, 0xeb, 0xab, 0x3a, 0x15, 0x8b, 0x35, 0x60, 0xbe, 0xe5, 0x9c, 0x2d, 0x10, 0x9b, 0x2e, 0xcf, 0x65, 0x64, 0xea, 0x8f, 0x72, 0xce, 0xf5, 0x18, 0xe5, 0xe2, 0xf0, 0x0e, 0xae, 0x04, 0xec, 0xa0, 0x20, 0x65, 0x63, 0x07, 0xb1, 0x9f, 0x03, 0x97},
|
||||
subYX: fp.Elt{0x9e, 0x41, 0x64, 0x30, 0x95, 0x7f, 0x3a, 0x89, 0x7b, 0x0a, 0x79, 0x59, 0x23, 0x9a, 0x3b, 0xfe, 0xa4, 0x13, 0x08, 0xb2, 0x2e, 0x04, 0x50, 0x10, 0x30, 0xcd, 0x2e, 0xa4, 0x91, 0x71, 0x50, 0x36, 0x4a, 0x02, 0xf4, 0x8d, 0xa3, 0x36, 0x1b, 0xf4, 0x52, 0xba, 0x15, 0x04, 0x8b, 0x80, 0x25, 0xd9, 0xae, 0x67, 0x20, 0xd9, 0x88, 0x8f, 0x97, 0xa6},
|
||||
dt2: fp.Elt{0xb5, 0xe7, 0x46, 0xbd, 0x55, 0x23, 0xa0, 0x68, 0xc0, 0x12, 0xd9, 0xf1, 0x0a, 0x75, 0xe2, 0xda, 0xf4, 0x6b, 0xca, 0x14, 0xe4, 0x9f, 0x0f, 0xb5, 0x3c, 0xa6, 0xa5, 0xa2, 0x63, 0x94, 0xd1, 0x1c, 0x39, 0x58, 0x57, 0x02, 0x27, 0x98, 0xb6, 0x47, 0xc6, 0x61, 0x4b, 0x5c, 0xab, 0x6f, 0x2d, 0xab, 0xe3, 0xc1, 0x69, 0xf9, 0x12, 0xb0, 0xc8, 0xd5},
|
||||
},
|
||||
{ /* 19P*/
|
||||
addYX: fp.Elt{0x19, 0x7d, 0xd5, 0xac, 0x79, 0xa2, 0x82, 0x9b, 0x28, 0x31, 0x22, 0xc0, 0x73, 0x02, 0x76, 0x17, 0x10, 0x70, 0x79, 0x57, 0xc9, 0x84, 0x62, 0x8e, 0x04, 0x04, 0x61, 0x67, 0x08, 0x48, 0xb4, 0x4b, 0xde, 0x53, 0x8c, 0xff, 0x36, 0x1b, 0x62, 0x86, 0x5d, 0xe1, 0x9b, 0xb1, 0xe5, 0xe8, 0x44, 0x64, 0xa1, 0x68, 0x3f, 0xa8, 0x45, 0x52, 0x91, 0xed},
|
||||
subYX: fp.Elt{0x42, 0x1a, 0x36, 0x1f, 0x90, 0x15, 0x24, 0x8d, 0x24, 0x80, 0xe6, 0xfe, 0x1e, 0xf0, 0xad, 0xaf, 0x6a, 0x93, 0xf0, 0xa6, 0x0d, 0x5d, 0xea, 0xf6, 0x62, 0x96, 0x7a, 0x05, 0x76, 0x85, 0x74, 0x32, 0xc7, 0xc8, 0x64, 0x53, 0x62, 0xe7, 0x54, 0x84, 0xe0, 0x40, 0x66, 0x19, 0x70, 0x40, 0x95, 0x35, 0x68, 0x64, 0x43, 0xcd, 0xba, 0x29, 0x32, 0xa8},
|
||||
dt2: fp.Elt{0x3e, 0xf6, 0xd6, 0xe4, 0x99, 0xeb, 0x20, 0x66, 0x08, 0x2e, 0x26, 0x64, 0xd7, 0x76, 0xf3, 0xb4, 0xc5, 0xa4, 0x35, 0x92, 0xd2, 0x99, 0x70, 0x5a, 0x1a, 0xe9, 0xe9, 0x3d, 0x3b, 0xe1, 0xcd, 0x0e, 0xee, 0x24, 0x13, 0x03, 0x22, 0xd6, 0xd6, 0x72, 0x08, 0x2b, 0xde, 0xfd, 0x93, 0xed, 0x0c, 0x7f, 0x5e, 0x31, 0x22, 0x4d, 0x80, 0x78, 0xc0, 0x48},
|
||||
},
|
||||
{ /* 21P*/
|
||||
addYX: fp.Elt{0x8f, 0x72, 0xd2, 0x9e, 0xc4, 0xcd, 0x2c, 0xbf, 0xa8, 0xd3, 0x24, 0x62, 0x28, 0xee, 0x39, 0x0a, 0x19, 0x3a, 0x58, 0xff, 0x21, 0x2e, 0x69, 0x6c, 0x6e, 0x18, 0xd0, 0xcd, 0x61, 0xc1, 0x18, 0x02, 0x5a, 0xe9, 0xe3, 0xef, 0x1f, 0x8e, 0x10, 0xe8, 0x90, 0x2b, 0x48, 0xcd, 0xee, 0x38, 0xbd, 0x3a, 0xca, 0xbc, 0x2d, 0xe2, 0x3a, 0x03, 0x71, 0x02},
|
||||
subYX: fp.Elt{0xf8, 0xa4, 0x32, 0x26, 0x66, 0xaf, 0x3b, 0x53, 0xe7, 0xb0, 0x91, 0x92, 0xf5, 0x3c, 0x74, 0xce, 0xf2, 0xdd, 0x68, 0xa9, 0xf4, 0xcd, 0x5f, 0x60, 0xab, 0x71, 0xdf, 0xcd, 0x5c, 0x5d, 0x51, 0x72, 0x3a, 0x96, 0xea, 0xd6, 0xde, 0x54, 0x8e, 0x55, 0x4c, 0x08, 0x4c, 0x60, 0xdd, 0x34, 0xa9, 0x6f, 0xf3, 0x04, 0x02, 0xa8, 0xa6, 0x4e, 0x4d, 0x62},
|
||||
dt2: fp.Elt{0x76, 0x4a, 0xae, 0x38, 0x62, 0x69, 0x72, 0xdc, 0xe8, 0x43, 0xbe, 0x1d, 0x61, 0xde, 0x31, 0xc3, 0x42, 0x8f, 0x33, 0x9d, 0xca, 0xc7, 0x9c, 0xec, 0x6a, 0xe2, 0xaa, 0x01, 0x49, 0x78, 0x8d, 0x72, 0x4f, 0x38, 0xea, 0x52, 0xc2, 0xd3, 0xc9, 0x39, 0x71, 0xba, 0xb9, 0x09, 0x9b, 0xa3, 0x7f, 0x45, 0x43, 0x65, 0x36, 0x29, 0xca, 0xe7, 0x5c, 0x5f},
|
||||
},
|
||||
{ /* 23P*/
|
||||
addYX: fp.Elt{0x89, 0x42, 0x35, 0x48, 0x6d, 0x74, 0xe5, 0x1f, 0xc3, 0xdd, 0x28, 0x5b, 0x84, 0x41, 0x33, 0x9f, 0x42, 0xf3, 0x1d, 0x5d, 0x15, 0x6d, 0x76, 0x33, 0x36, 0xaf, 0xe9, 0xdd, 0xfa, 0x63, 0x4f, 0x7a, 0x9c, 0xeb, 0x1c, 0x4f, 0x34, 0x65, 0x07, 0x54, 0xbb, 0x4c, 0x8b, 0x62, 0x9d, 0xd0, 0x06, 0x99, 0xb3, 0xe9, 0xda, 0x85, 0x19, 0xb0, 0x3d, 0x3c},
|
||||
subYX: fp.Elt{0xbb, 0x99, 0xf6, 0xbf, 0xaf, 0x2c, 0x22, 0x0d, 0x7a, 0xaa, 0x98, 0x6f, 0x01, 0x82, 0x99, 0xcf, 0x88, 0xbd, 0x0e, 0x3a, 0x89, 0xe0, 0x9c, 0x8c, 0x17, 0x20, 0xc4, 0xe0, 0xcf, 0x43, 0x7a, 0xef, 0x0d, 0x9f, 0x87, 0xd4, 0xfb, 0xf2, 0x96, 0xb8, 0x03, 0xe8, 0xcb, 0x5c, 0xec, 0x65, 0x5f, 0x49, 0xa4, 0x7c, 0x85, 0xb4, 0xf6, 0xc7, 0xdb, 0xa3},
|
||||
dt2: fp.Elt{0x11, 0xf3, 0x32, 0xa3, 0xa7, 0xb2, 0x7d, 0x51, 0x82, 0x44, 0xeb, 0xa2, 0x7d, 0x72, 0xcb, 0xc6, 0xf6, 0xc7, 0xb2, 0x38, 0x0e, 0x0f, 0x4f, 0x29, 0x00, 0xe4, 0x5b, 0x94, 0x46, 0x86, 0x66, 0xa1, 0x83, 0xb3, 0xeb, 0x15, 0xb6, 0x31, 0x50, 0x28, 0xeb, 0xed, 0x0d, 0x32, 0x39, 0xe9, 0x23, 0x81, 0x99, 0x3e, 0xff, 0x17, 0x4c, 0x11, 0x43, 0xd1},
|
||||
},
|
||||
{ /* 25P*/
|
||||
addYX: fp.Elt{0xce, 0xe7, 0xf8, 0x94, 0x8f, 0x96, 0xf8, 0x96, 0xe6, 0x72, 0x20, 0x44, 0x2c, 0xa7, 0xfc, 0xba, 0xc8, 0xe1, 0xbb, 0xc9, 0x16, 0x85, 0xcd, 0x0b, 0xe5, 0xb5, 0x5a, 0x7f, 0x51, 0x43, 0x63, 0x8b, 0x23, 0x8e, 0x1d, 0x31, 0xff, 0x46, 0x02, 0x66, 0xcc, 0x9e, 0x4d, 0xa2, 0xca, 0xe2, 0xc7, 0xfd, 0x22, 0xb1, 0xdb, 0xdf, 0x6f, 0xe6, 0xa5, 0x82},
|
||||
subYX: fp.Elt{0xd0, 0xf5, 0x65, 0x40, 0xec, 0x8e, 0x65, 0x42, 0x78, 0xc1, 0x65, 0xe4, 0x10, 0xc8, 0x0b, 0x1b, 0xdd, 0x96, 0x68, 0xce, 0xee, 0x45, 0x55, 0xd8, 0x6e, 0xd3, 0xe6, 0x77, 0x19, 0xae, 0xc2, 0x8d, 0x8d, 0x3e, 0x14, 0x3f, 0x6d, 0x00, 0x2f, 0x9b, 0xd1, 0x26, 0x60, 0x28, 0x0f, 0x3a, 0x47, 0xb3, 0xe6, 0x68, 0x28, 0x24, 0x25, 0xca, 0xc8, 0x06},
|
||||
dt2: fp.Elt{0x54, 0xbb, 0x60, 0x92, 0xdb, 0x8f, 0x0f, 0x38, 0xe0, 0xe6, 0xe4, 0xc9, 0xcc, 0x14, 0x62, 0x01, 0xc4, 0x2b, 0x0f, 0xcf, 0xed, 0x7d, 0x8e, 0xa4, 0xd9, 0x73, 0x0b, 0xba, 0x0c, 0xaf, 0x0c, 0xf9, 0xe2, 0xeb, 0x29, 0x2a, 0x53, 0xdf, 0x2c, 0x5a, 0xfa, 0x8f, 0xc1, 0x01, 0xd7, 0xb1, 0x45, 0x73, 0x92, 0x32, 0x83, 0x85, 0x12, 0x74, 0x89, 0x44},
|
||||
},
|
||||
{ /* 27P*/
|
||||
addYX: fp.Elt{0x0b, 0x73, 0x3c, 0xc2, 0xb1, 0x2e, 0xe1, 0xa7, 0xf5, 0xc9, 0x7a, 0xfb, 0x3d, 0x2d, 0xac, 0x59, 0xdb, 0xfa, 0x36, 0x11, 0xd1, 0x13, 0x04, 0x51, 0x1d, 0xab, 0x9b, 0x6b, 0x93, 0xfe, 0xda, 0xb0, 0x8e, 0xb4, 0x79, 0x11, 0x21, 0x0f, 0x65, 0xb9, 0xbb, 0x79, 0x96, 0x2a, 0xfd, 0x30, 0xe0, 0xb4, 0x2d, 0x9a, 0x55, 0x25, 0x5d, 0xd4, 0xad, 0x2a},
|
||||
subYX: fp.Elt{0x9e, 0xc5, 0x04, 0xfe, 0xec, 0x3c, 0x64, 0x1c, 0xed, 0x95, 0xed, 0xae, 0xaf, 0x5c, 0x6e, 0x08, 0x9e, 0x02, 0x29, 0x59, 0x7e, 0x5f, 0xc4, 0x9a, 0xd5, 0x32, 0x72, 0x86, 0xe1, 0x4e, 0x3c, 0xce, 0x99, 0x69, 0x3b, 0xc4, 0xdd, 0x4d, 0xb7, 0xbb, 0xda, 0x3b, 0x1a, 0x99, 0xaa, 0x62, 0x15, 0xc1, 0xf0, 0xb6, 0x6c, 0xec, 0x56, 0xc1, 0xff, 0x0c},
|
||||
dt2: fp.Elt{0x2f, 0xf1, 0x3f, 0x7a, 0x2d, 0x56, 0x19, 0x7f, 0xea, 0xbe, 0x59, 0x2e, 0x13, 0x67, 0x81, 0xfb, 0xdb, 0xc8, 0xa3, 0x1d, 0xd5, 0xe9, 0x13, 0x8b, 0x29, 0xdf, 0xcf, 0x9f, 0xe7, 0xd9, 0x0b, 0x70, 0xd3, 0x15, 0x57, 0x4a, 0xe9, 0x50, 0x12, 0x1b, 0x81, 0x4b, 0x98, 0x98, 0xa8, 0x31, 0x1d, 0x27, 0x47, 0x38, 0xed, 0x57, 0x99, 0x26, 0xb2, 0xee},
|
||||
},
|
||||
{ /* 29P*/
|
||||
addYX: fp.Elt{0x1c, 0xb2, 0xb2, 0x67, 0x3b, 0x8b, 0x3d, 0x5a, 0x30, 0x7e, 0x38, 0x7e, 0x3c, 0x3d, 0x28, 0x56, 0x59, 0xd8, 0x87, 0x53, 0x8b, 0xe6, 0x6c, 0x5d, 0xe5, 0x0a, 0x33, 0x10, 0xce, 0xa2, 0x17, 0x0d, 0xe8, 0x76, 0xee, 0x68, 0xa8, 0x72, 0x54, 0xbd, 0xa6, 0x24, 0x94, 0x6e, 0x77, 0xc7, 0x53, 0xb7, 0x89, 0x1c, 0x7a, 0xe9, 0x78, 0x9a, 0x74, 0x5f},
|
||||
subYX: fp.Elt{0x76, 0x96, 0x1c, 0xcf, 0x08, 0x55, 0xd8, 0x1e, 0x0d, 0xa3, 0x59, 0x95, 0x32, 0xf4, 0xc2, 0x8e, 0x84, 0x5e, 0x4b, 0x04, 0xda, 0x71, 0xc9, 0x78, 0x52, 0xde, 0x14, 0xb4, 0x31, 0xf4, 0xd4, 0xb8, 0x58, 0xc5, 0x20, 0xe8, 0xdd, 0x15, 0xb5, 0xee, 0xea, 0x61, 0xe0, 0xf5, 0xd6, 0xae, 0x55, 0x59, 0x05, 0x3e, 0xaf, 0x74, 0xac, 0x1f, 0x17, 0x82},
|
||||
dt2: fp.Elt{0x59, 0x24, 0xcd, 0xfc, 0x11, 0x7e, 0x85, 0x18, 0x3d, 0x69, 0xf7, 0x71, 0x31, 0x66, 0x98, 0x42, 0x95, 0x00, 0x8c, 0xb2, 0xae, 0x39, 0x7e, 0x85, 0xd6, 0xb0, 0x02, 0xec, 0xce, 0xfc, 0x25, 0xb2, 0xe3, 0x99, 0x8e, 0x5b, 0x61, 0x96, 0x2e, 0x6d, 0x96, 0x57, 0x71, 0xa5, 0x93, 0x41, 0x0e, 0x6f, 0xfd, 0x0a, 0xbf, 0xa9, 0xf7, 0x56, 0xa9, 0x3e},
|
||||
},
|
||||
{ /* 31P*/
|
||||
addYX: fp.Elt{0xa2, 0x2e, 0x0c, 0x17, 0x4d, 0xcc, 0x85, 0x2c, 0x18, 0xa0, 0xd2, 0x08, 0xba, 0x11, 0xfa, 0x47, 0x71, 0x86, 0xaf, 0x36, 0x6a, 0xd7, 0xfe, 0xb9, 0xb0, 0x2f, 0x89, 0x98, 0x49, 0x69, 0xf8, 0x6a, 0xad, 0x27, 0x5e, 0x0a, 0x22, 0x60, 0x5e, 0x5d, 0xca, 0x06, 0x51, 0x27, 0x99, 0x29, 0x85, 0x68, 0x98, 0xe1, 0xc4, 0x21, 0x50, 0xa0, 0xe9, 0xc1},
|
||||
subYX: fp.Elt{0x4d, 0x70, 0xee, 0x91, 0x92, 0x3f, 0xb7, 0xd3, 0x1d, 0xdb, 0x8d, 0x6e, 0x16, 0xf5, 0x65, 0x7d, 0x5f, 0xb5, 0x6c, 0x59, 0x26, 0x70, 0x4b, 0xf2, 0xfc, 0xe7, 0xdf, 0x86, 0xfe, 0xa5, 0xa7, 0xa6, 0x5d, 0xfb, 0x06, 0xe9, 0xf9, 0xcc, 0xc0, 0x37, 0xcc, 0xd8, 0x09, 0x04, 0xd2, 0xa5, 0x1d, 0xd7, 0xb7, 0xce, 0x92, 0xac, 0x3c, 0xad, 0xfb, 0xae},
|
||||
dt2: fp.Elt{0x17, 0xa3, 0x9a, 0xc7, 0x86, 0x2a, 0x51, 0xf7, 0x96, 0x79, 0x49, 0x22, 0x2e, 0x5a, 0x01, 0x5c, 0xb5, 0x95, 0xd4, 0xe8, 0xcb, 0x00, 0xca, 0x2d, 0x55, 0xb6, 0x34, 0x36, 0x0b, 0x65, 0x46, 0xf0, 0x49, 0xfc, 0x87, 0x86, 0xe5, 0xc3, 0x15, 0xdb, 0x32, 0xcd, 0xf2, 0xd3, 0x82, 0x4c, 0xe6, 0x61, 0x8a, 0xaf, 0xd4, 0x9e, 0x0f, 0x5a, 0xf2, 0x81},
|
||||
},
|
||||
{ /* 33P*/
|
||||
addYX: fp.Elt{0x88, 0x10, 0xc0, 0xcb, 0xf5, 0x77, 0xae, 0xa5, 0xbe, 0xf6, 0xcd, 0x2e, 0x8b, 0x7e, 0xbd, 0x79, 0x62, 0x4a, 0xeb, 0x69, 0xc3, 0x28, 0xaa, 0x72, 0x87, 0xa9, 0x25, 0x87, 0x46, 0xea, 0x0e, 0x62, 0xa3, 0x6a, 0x1a, 0xe2, 0xba, 0xdc, 0x81, 0x10, 0x33, 0x01, 0xf6, 0x16, 0x89, 0x80, 0xc6, 0xcd, 0xdb, 0xdc, 0xba, 0x0e, 0x09, 0x4a, 0x35, 0x4a},
|
||||
subYX: fp.Elt{0x86, 0xb2, 0x2b, 0xd0, 0xb8, 0x4a, 0x6d, 0x66, 0x7b, 0x32, 0xdf, 0x3b, 0x1a, 0x19, 0x1f, 0x63, 0xee, 0x1f, 0x3d, 0x1c, 0x5c, 0x14, 0x60, 0x5b, 0x72, 0x49, 0x07, 0xb1, 0x0d, 0x72, 0xc6, 0x35, 0xf0, 0xbc, 0x5e, 0xda, 0x80, 0x6b, 0x64, 0x5b, 0xe5, 0x34, 0x54, 0x39, 0xdd, 0xe6, 0x3c, 0xcb, 0xe5, 0x29, 0x32, 0x06, 0xc6, 0xb1, 0x96, 0x34},
|
||||
dt2: fp.Elt{0x85, 0x86, 0xf5, 0x84, 0x86, 0xe6, 0x77, 0x8a, 0x71, 0x85, 0x0c, 0x4f, 0x81, 0x5b, 0x29, 0x06, 0xb5, 0x2e, 0x26, 0x71, 0x07, 0x78, 0x07, 0xae, 0xbc, 0x95, 0x46, 0xc3, 0x65, 0xac, 0xe3, 0x76, 0x51, 0x7d, 0xd4, 0x85, 0x31, 0xe3, 0x43, 0xf3, 0x1b, 0x7c, 0xf7, 0x6b, 0x2c, 0xf8, 0x1c, 0xbb, 0x8d, 0xca, 0xab, 0x4b, 0xba, 0x7f, 0xa4, 0xe2},
|
||||
},
|
||||
{ /* 35P*/
|
||||
addYX: fp.Elt{0x1a, 0xee, 0xe7, 0xa4, 0x8a, 0x9d, 0x53, 0x80, 0xc6, 0xb8, 0x4e, 0xdc, 0x89, 0xe0, 0xc4, 0x2b, 0x60, 0x52, 0x6f, 0xec, 0x81, 0xd2, 0x55, 0x6b, 0x1b, 0x6f, 0x17, 0x67, 0x8e, 0x42, 0x26, 0x4c, 0x65, 0x23, 0x29, 0xc6, 0x7b, 0xcd, 0x9f, 0xad, 0x4b, 0x42, 0xd3, 0x0c, 0x75, 0xc3, 0x8a, 0xf5, 0xbe, 0x9e, 0x55, 0xf7, 0x47, 0x5d, 0xbd, 0x3a},
|
||||
subYX: fp.Elt{0x0d, 0xa8, 0x3b, 0xf9, 0xc7, 0x7e, 0xc6, 0x86, 0x94, 0xc0, 0x01, 0xff, 0x27, 0xce, 0x43, 0xac, 0xe5, 0xe1, 0xd2, 0x8d, 0xc1, 0x22, 0x31, 0xbe, 0xe1, 0xaf, 0xf9, 0x4a, 0x78, 0xa1, 0x0c, 0xaa, 0xd4, 0x80, 0xe4, 0x09, 0x8d, 0xfb, 0x1d, 0x52, 0xc8, 0x60, 0x2d, 0xf2, 0xa2, 0x89, 0x02, 0x56, 0x3d, 0x56, 0x27, 0x85, 0xc7, 0xf0, 0x2b, 0x9a},
|
||||
dt2: fp.Elt{0x62, 0x7c, 0xc7, 0x6b, 0x2c, 0x9d, 0x0a, 0x7c, 0xe5, 0x50, 0x3c, 0xe6, 0x87, 0x1c, 0x82, 0x30, 0x67, 0x3c, 0x39, 0xb6, 0xa0, 0x31, 0xfb, 0x03, 0x7b, 0xa1, 0x58, 0xdf, 0x12, 0x76, 0x5d, 0x5d, 0x0a, 0x8f, 0x9b, 0x37, 0x32, 0xc3, 0x60, 0x33, 0xea, 0x9f, 0x0a, 0x99, 0xfa, 0x20, 0xd0, 0x33, 0x21, 0xc3, 0x94, 0xd4, 0x86, 0x49, 0x7c, 0x4e},
|
||||
},
|
||||
{ /* 37P*/
|
||||
addYX: fp.Elt{0xc7, 0x0c, 0x71, 0xfe, 0x55, 0xd1, 0x95, 0x8f, 0x43, 0xbb, 0x6b, 0x74, 0x30, 0xbd, 0xe8, 0x6f, 0x1c, 0x1b, 0x06, 0x62, 0xf5, 0xfc, 0x65, 0xa0, 0xeb, 0x81, 0x12, 0xc9, 0x64, 0x66, 0x61, 0xde, 0xf3, 0x6d, 0xd4, 0xae, 0x8e, 0xb1, 0x72, 0xe0, 0xcd, 0x37, 0x01, 0x28, 0x52, 0xd7, 0x39, 0x46, 0x0c, 0x55, 0xcf, 0x47, 0x70, 0xef, 0xa1, 0x17},
|
||||
subYX: fp.Elt{0x8d, 0x58, 0xde, 0x83, 0x88, 0x16, 0x0e, 0x12, 0x42, 0x03, 0x50, 0x60, 0x4b, 0xdf, 0xbf, 0x95, 0xcc, 0x7d, 0x18, 0x17, 0x7e, 0x31, 0x5d, 0x8a, 0x66, 0xc1, 0xcf, 0x14, 0xea, 0xf4, 0xf4, 0xe5, 0x63, 0x2d, 0x32, 0x86, 0x9b, 0xed, 0x1f, 0x4f, 0x03, 0xaf, 0x33, 0x92, 0xcb, 0xaf, 0x9c, 0x05, 0x0d, 0x47, 0x1b, 0x42, 0xba, 0x13, 0x22, 0x98},
|
||||
dt2: fp.Elt{0xb5, 0x48, 0xeb, 0x7d, 0x3d, 0x10, 0x9f, 0x59, 0xde, 0xf8, 0x1c, 0x4f, 0x7d, 0x9d, 0x40, 0x4d, 0x9e, 0x13, 0x24, 0xb5, 0x21, 0x09, 0xb7, 0xee, 0x98, 0x5c, 0x56, 0xbc, 0x5e, 0x2b, 0x78, 0x38, 0x06, 0xac, 0xe3, 0xe0, 0xfa, 0x2e, 0xde, 0x4f, 0xd2, 0xb3, 0xfb, 0x2d, 0x71, 0x84, 0xd1, 0x9d, 0x12, 0x5b, 0x35, 0xc8, 0x03, 0x68, 0x67, 0xc7},
|
||||
},
|
||||
{ /* 39P*/
|
||||
addYX: fp.Elt{0xb6, 0x65, 0xfb, 0xa7, 0x06, 0x35, 0xbb, 0xe0, 0x31, 0x8d, 0x91, 0x40, 0x98, 0xab, 0x30, 0xe4, 0xca, 0x12, 0x59, 0x89, 0xed, 0x65, 0x5d, 0x7f, 0xae, 0x69, 0xa0, 0xa4, 0xfa, 0x78, 0xb4, 0xf7, 0xed, 0xae, 0x86, 0x78, 0x79, 0x64, 0x24, 0xa6, 0xd4, 0xe1, 0xf6, 0xd3, 0xa0, 0x89, 0xba, 0x20, 0xf4, 0x54, 0x0d, 0x8f, 0xdb, 0x1a, 0x79, 0xdb},
|
||||
subYX: fp.Elt{0xe1, 0x82, 0x0c, 0x4d, 0xde, 0x9f, 0x40, 0xf0, 0xc1, 0xbd, 0x8b, 0xd3, 0x24, 0x03, 0xcd, 0xf2, 0x92, 0x7d, 0xe2, 0x68, 0x7f, 0xf1, 0xbe, 0x69, 0xde, 0x34, 0x67, 0x4c, 0x85, 0x3b, 0xec, 0x98, 0xcc, 0x4d, 0x3e, 0xc0, 0x96, 0x27, 0xe6, 0x75, 0xfc, 0xdf, 0x37, 0xc0, 0x1e, 0x27, 0xe0, 0xf6, 0xc2, 0xbd, 0xbc, 0x3d, 0x9b, 0x39, 0xdc, 0xe2},
|
||||
dt2: fp.Elt{0xd8, 0x29, 0xa7, 0x39, 0xe3, 0x9f, 0x2f, 0x0e, 0x4b, 0x24, 0x21, 0x70, 0xef, 0xfd, 0x91, 0xea, 0xbf, 0xe1, 0x72, 0x90, 0xcc, 0xc9, 0x84, 0x0e, 0xad, 0xd5, 0xe6, 0xbb, 0xc5, 0x99, 0x7f, 0xa4, 0xf0, 0x2e, 0xcc, 0x95, 0x64, 0x27, 0x19, 0xd8, 0x4c, 0x27, 0x0d, 0xff, 0xb6, 0x29, 0xe2, 0x6c, 0xfa, 0xbb, 0x4d, 0x9c, 0xbb, 0xaf, 0xa5, 0xec},
|
||||
},
|
||||
{ /* 41P*/
|
||||
addYX: fp.Elt{0xd6, 0x33, 0x3f, 0x9f, 0xcf, 0xfd, 0x4c, 0xd1, 0xfe, 0xe5, 0xeb, 0x64, 0x27, 0xae, 0x7a, 0xa2, 0x82, 0x50, 0x6d, 0xaa, 0xe3, 0x5d, 0xe2, 0x48, 0x60, 0xb3, 0x76, 0x04, 0xd9, 0x19, 0xa7, 0xa1, 0x73, 0x8d, 0x38, 0xa9, 0xaf, 0x45, 0xb5, 0xb2, 0x62, 0x9b, 0xf1, 0x35, 0x7b, 0x84, 0x66, 0xeb, 0x06, 0xef, 0xf1, 0xb2, 0x2d, 0x6a, 0x61, 0x15},
|
||||
subYX: fp.Elt{0x86, 0x50, 0x42, 0xf7, 0xda, 0x59, 0xb2, 0xcf, 0x0d, 0x3d, 0xee, 0x8e, 0x53, 0x5d, 0xf7, 0x9e, 0x6a, 0x26, 0x2d, 0xc7, 0x8c, 0x8e, 0x18, 0x50, 0x6d, 0xb7, 0x51, 0x4c, 0xa7, 0x52, 0x6e, 0x0e, 0x0a, 0x16, 0x74, 0xb2, 0x81, 0x8b, 0x56, 0x27, 0x22, 0x84, 0xf4, 0x56, 0xc5, 0x06, 0xe1, 0x8b, 0xca, 0x2d, 0xdb, 0x9a, 0xf6, 0x10, 0x9c, 0x51},
|
||||
dt2: fp.Elt{0x1f, 0x16, 0xa2, 0x78, 0x96, 0x1b, 0x85, 0x9c, 0x76, 0x49, 0xd4, 0x0f, 0xac, 0xb0, 0xf4, 0xd0, 0x06, 0x2c, 0x7e, 0x6d, 0x6e, 0x8e, 0xc7, 0x9f, 0x18, 0xad, 0xfc, 0x88, 0x0c, 0x0c, 0x09, 0x05, 0x05, 0xa0, 0x79, 0x72, 0x32, 0x72, 0x87, 0x0f, 0x49, 0x87, 0x0c, 0xb4, 0x12, 0xc2, 0x09, 0xf8, 0x9f, 0x30, 0x72, 0xa9, 0x47, 0x13, 0x93, 0x49},
|
||||
},
|
||||
{ /* 43P*/
|
||||
addYX: fp.Elt{0xcc, 0xb1, 0x4c, 0xd3, 0xc0, 0x9e, 0x9e, 0x4d, 0x6d, 0x28, 0x0b, 0xa5, 0x94, 0xa7, 0x2e, 0xc2, 0xc7, 0xaf, 0x29, 0x73, 0xc9, 0x68, 0xea, 0x0f, 0x34, 0x37, 0x8d, 0x96, 0x8f, 0x3a, 0x3d, 0x73, 0x1e, 0x6d, 0x9f, 0xcf, 0x8d, 0x83, 0xb5, 0x71, 0xb9, 0xe1, 0x4b, 0x67, 0x71, 0xea, 0xcf, 0x56, 0xe5, 0xeb, 0x72, 0x15, 0x2f, 0x9e, 0xa8, 0xaa},
|
||||
subYX: fp.Elt{0xf4, 0x3e, 0x85, 0x1c, 0x1a, 0xef, 0x50, 0xd1, 0xb4, 0x20, 0xb2, 0x60, 0x05, 0x98, 0xfe, 0x47, 0x3b, 0xc1, 0x76, 0xca, 0x2c, 0x4e, 0x5a, 0x42, 0xa3, 0xf7, 0x20, 0xaa, 0x57, 0x39, 0xee, 0x34, 0x1f, 0xe1, 0x68, 0xd3, 0x7e, 0x06, 0xc4, 0x6c, 0xc7, 0x76, 0x2b, 0xe4, 0x1c, 0x48, 0x44, 0xe6, 0xe5, 0x44, 0x24, 0x8d, 0xb3, 0xb6, 0x88, 0x32},
|
||||
dt2: fp.Elt{0x18, 0xa7, 0xba, 0xd0, 0x44, 0x6f, 0x33, 0x31, 0x00, 0xf8, 0xf6, 0x12, 0xe3, 0xc5, 0xc7, 0xb5, 0x91, 0x9c, 0x91, 0xb5, 0x75, 0x18, 0x18, 0x8a, 0xab, 0xed, 0x24, 0x11, 0x2e, 0xce, 0x5a, 0x0f, 0x94, 0x5f, 0x2e, 0xca, 0xd3, 0x80, 0xea, 0xe5, 0x34, 0x96, 0x67, 0x8b, 0x6a, 0x26, 0x5e, 0xc8, 0x9d, 0x2c, 0x5e, 0x6c, 0xa2, 0x0c, 0xbf, 0xf0},
|
||||
},
|
||||
{ /* 45P*/
|
||||
addYX: fp.Elt{0xb3, 0xbf, 0xa3, 0x85, 0xee, 0xf6, 0x58, 0x02, 0x78, 0xc4, 0x30, 0xd6, 0x57, 0x59, 0x8c, 0x88, 0x08, 0x7c, 0xbc, 0xbe, 0x0a, 0x74, 0xa9, 0xde, 0x69, 0xe7, 0x41, 0xd8, 0xbf, 0x66, 0x8d, 0x3d, 0x28, 0x00, 0x8c, 0x47, 0x65, 0x34, 0xfe, 0x86, 0x9e, 0x6a, 0xf2, 0x41, 0x6a, 0x94, 0xc4, 0x88, 0x75, 0x23, 0x0d, 0x52, 0x69, 0xee, 0x07, 0x89},
|
||||
subYX: fp.Elt{0x22, 0x3c, 0xa1, 0x70, 0x58, 0x97, 0x93, 0xbe, 0x59, 0xa8, 0x0b, 0x8a, 0x46, 0x2a, 0x38, 0x1e, 0x08, 0x6b, 0x61, 0x9f, 0xf2, 0x4a, 0x8b, 0x80, 0x68, 0x6e, 0xc8, 0x92, 0x60, 0xf3, 0xc9, 0x89, 0xb2, 0x6d, 0x63, 0xb0, 0xeb, 0x83, 0x15, 0x63, 0x0e, 0x64, 0xbb, 0xb8, 0xfe, 0xb4, 0x81, 0x90, 0x01, 0x28, 0x10, 0xb9, 0x74, 0x6e, 0xde, 0xa4},
|
||||
dt2: fp.Elt{0x1a, 0x23, 0x45, 0xa8, 0x6f, 0x4e, 0xa7, 0x4a, 0x0c, 0xeb, 0xb0, 0x43, 0xf9, 0xef, 0x99, 0x60, 0x5b, 0xdb, 0x66, 0xc0, 0x86, 0x71, 0x43, 0xb1, 0x22, 0x7b, 0x1c, 0xe7, 0x8d, 0x09, 0x1d, 0x83, 0x76, 0x9c, 0xd3, 0x5a, 0xdd, 0x42, 0xd9, 0x2f, 0x2d, 0xba, 0x7a, 0xc2, 0xd9, 0x6b, 0xd4, 0x7a, 0xf1, 0xd5, 0x5f, 0x6b, 0x85, 0xbf, 0x0b, 0xf1},
|
||||
},
|
||||
{ /* 47P*/
|
||||
addYX: fp.Elt{0xb2, 0x83, 0xfa, 0x1f, 0xd2, 0xce, 0xb6, 0xf2, 0x2d, 0xea, 0x1b, 0xe5, 0x29, 0xa5, 0x72, 0xf9, 0x25, 0x48, 0x4e, 0xf2, 0x50, 0x1b, 0x39, 0xda, 0x34, 0xc5, 0x16, 0x13, 0xb4, 0x0c, 0xa1, 0x00, 0x79, 0x7a, 0xf5, 0x8b, 0xf3, 0x70, 0x14, 0xb6, 0xfc, 0x9a, 0x47, 0x68, 0x1e, 0x42, 0x70, 0x64, 0x2a, 0x84, 0x3e, 0x3d, 0x20, 0x58, 0xf9, 0x6a},
|
||||
subYX: fp.Elt{0xd9, 0xee, 0xc0, 0xc4, 0xf5, 0xc2, 0x86, 0xaf, 0x45, 0xd2, 0xd2, 0x87, 0x1b, 0x64, 0xd5, 0xe0, 0x8c, 0x44, 0x00, 0x4f, 0x43, 0x89, 0x04, 0x48, 0x4a, 0x0b, 0xca, 0x94, 0x06, 0x2f, 0x23, 0x5b, 0x6c, 0x8d, 0x44, 0x66, 0x53, 0xf5, 0x5a, 0x20, 0x72, 0x28, 0x58, 0x84, 0xcc, 0x73, 0x22, 0x5e, 0xd1, 0x0b, 0x56, 0x5e, 0x6a, 0xa3, 0x11, 0x91},
|
||||
dt2: fp.Elt{0x6e, 0x9f, 0x88, 0xa8, 0x68, 0x2f, 0x12, 0x37, 0x88, 0xfc, 0x92, 0x8f, 0x24, 0xeb, 0x5b, 0x2a, 0x2a, 0xd0, 0x14, 0x40, 0x4c, 0xa9, 0xa4, 0x03, 0x0c, 0x45, 0x48, 0x13, 0xe8, 0xa6, 0x37, 0xab, 0xc0, 0x06, 0x38, 0x6c, 0x96, 0x73, 0x40, 0x6c, 0xc6, 0xea, 0x56, 0xc6, 0xe9, 0x1a, 0x69, 0xeb, 0x7a, 0xd1, 0x33, 0x69, 0x58, 0x2b, 0xea, 0x2f},
|
||||
},
|
||||
{ /* 49P*/
|
||||
addYX: fp.Elt{0x58, 0xa8, 0x05, 0x41, 0x00, 0x9d, 0xaa, 0xd9, 0x98, 0xcf, 0xb9, 0x41, 0xb5, 0x4a, 0x8d, 0xe2, 0xe7, 0xc0, 0x72, 0xef, 0xc8, 0x28, 0x6b, 0x68, 0x9d, 0xc9, 0xdf, 0x05, 0x8b, 0xd0, 0x04, 0x74, 0x79, 0x45, 0x52, 0x05, 0xa3, 0x6e, 0x35, 0x3a, 0xe3, 0xef, 0xb2, 0xdc, 0x08, 0x6f, 0x4e, 0x76, 0x85, 0x67, 0xba, 0x23, 0x8f, 0xdd, 0xaf, 0x09},
|
||||
subYX: fp.Elt{0xb4, 0x38, 0xc8, 0xff, 0x4f, 0x65, 0x2a, 0x7e, 0xad, 0xb1, 0xc6, 0xb9, 0x3d, 0xd6, 0xf7, 0x14, 0xcf, 0xf6, 0x98, 0x75, 0xbb, 0x47, 0x83, 0x90, 0xe7, 0xe1, 0xf6, 0x14, 0x99, 0x7e, 0xfa, 0xe4, 0x77, 0x24, 0xe3, 0xe7, 0xf0, 0x1e, 0xdb, 0x27, 0x4e, 0x16, 0x04, 0xf2, 0x08, 0x52, 0xfc, 0xec, 0x55, 0xdb, 0x2e, 0x67, 0xe1, 0x94, 0x32, 0x89},
|
||||
dt2: fp.Elt{0x00, 0xad, 0x03, 0x35, 0x1a, 0xb1, 0x88, 0xf0, 0xc9, 0x11, 0xe4, 0x12, 0x52, 0x61, 0xfd, 0x8a, 0x1b, 0x6a, 0x0a, 0x4c, 0x42, 0x46, 0x22, 0x0e, 0xa5, 0xf9, 0xe2, 0x50, 0xf2, 0xb2, 0x1f, 0x20, 0x78, 0x10, 0xf6, 0xbf, 0x7f, 0x0c, 0x9c, 0xad, 0x40, 0x8b, 0x82, 0xd4, 0xba, 0x69, 0x09, 0xac, 0x4b, 0x6d, 0xc4, 0x49, 0x17, 0x81, 0x57, 0x3b},
|
||||
},
|
||||
{ /* 51P*/
|
||||
addYX: fp.Elt{0x0d, 0xfe, 0xb4, 0x35, 0x11, 0xbd, 0x1d, 0x6b, 0xc2, 0xc5, 0x3b, 0xd2, 0x23, 0x2c, 0x72, 0xe3, 0x48, 0xb1, 0x48, 0x73, 0xfb, 0xa3, 0x21, 0x6e, 0xc0, 0x09, 0x69, 0xac, 0xe1, 0x60, 0xbc, 0x24, 0x03, 0x99, 0x63, 0x0a, 0x00, 0xf0, 0x75, 0xf6, 0x92, 0xc5, 0xd6, 0xdb, 0x51, 0xd4, 0x7d, 0xe6, 0xf4, 0x11, 0x79, 0xd7, 0xc3, 0xaf, 0x48, 0xd0},
|
||||
subYX: fp.Elt{0xf4, 0x4f, 0xaf, 0x31, 0xe3, 0x10, 0x89, 0x95, 0xf0, 0x8a, 0xf6, 0x31, 0x9f, 0x48, 0x02, 0xba, 0x42, 0x2b, 0x3c, 0x22, 0x8b, 0xcc, 0x12, 0x98, 0x6e, 0x7a, 0x64, 0x3a, 0xc4, 0xca, 0x32, 0x2a, 0x72, 0xf8, 0x2c, 0xcf, 0x78, 0x5e, 0x7a, 0x75, 0x6e, 0x72, 0x46, 0x48, 0x62, 0x28, 0xac, 0x58, 0x1a, 0xc6, 0x59, 0x88, 0x2a, 0x44, 0x9e, 0x83},
|
||||
dt2: fp.Elt{0xb3, 0xde, 0x36, 0xfd, 0xeb, 0x1b, 0xd4, 0x24, 0x1b, 0x08, 0x8c, 0xfe, 0xa9, 0x41, 0xa1, 0x64, 0xf2, 0x6d, 0xdb, 0xf9, 0x94, 0xae, 0x86, 0x71, 0xab, 0x10, 0xbf, 0xa3, 0xb2, 0xa0, 0xdf, 0x10, 0x8c, 0x74, 0xce, 0xb3, 0xfc, 0xdb, 0xba, 0x15, 0xf6, 0x91, 0x7a, 0x9c, 0x36, 0x1e, 0x45, 0x07, 0x3c, 0xec, 0x1a, 0x61, 0x26, 0x93, 0xe3, 0x50},
|
||||
},
|
||||
{ /* 53P*/
|
||||
addYX: fp.Elt{0xc5, 0x50, 0xc5, 0x83, 0xb0, 0xbd, 0xd9, 0xf6, 0x6d, 0x15, 0x5e, 0xc1, 0x1a, 0x33, 0xa0, 0xce, 0x13, 0x70, 0x3b, 0xe1, 0x31, 0xc6, 0xc4, 0x02, 0xec, 0x8c, 0xd5, 0x9c, 0x97, 0xd3, 0x12, 0xc4, 0xa2, 0xf9, 0xd5, 0xfb, 0x22, 0x69, 0x94, 0x09, 0x2f, 0x59, 0xce, 0xdb, 0xf2, 0xf2, 0x00, 0xe0, 0xa9, 0x08, 0x44, 0x2e, 0x8b, 0x6b, 0xf5, 0xb3},
|
||||
subYX: fp.Elt{0x90, 0xdd, 0xec, 0xa2, 0x65, 0xb7, 0x61, 0xbc, 0xaa, 0x70, 0xa2, 0x15, 0xd8, 0xb0, 0xf8, 0x8e, 0x23, 0x3d, 0x9f, 0x46, 0xa3, 0x29, 0x20, 0xd1, 0xa1, 0x15, 0x81, 0xc6, 0xb6, 0xde, 0xbe, 0x60, 0x63, 0x24, 0xac, 0x15, 0xfb, 0xeb, 0xd3, 0xea, 0x57, 0x13, 0x86, 0x38, 0x1e, 0x22, 0xf4, 0x8c, 0x5d, 0xaf, 0x1b, 0x27, 0x21, 0x4f, 0xa3, 0x63},
|
||||
dt2: fp.Elt{0x07, 0x15, 0x87, 0xc4, 0xfd, 0xa1, 0x97, 0x7a, 0x07, 0x1f, 0x56, 0xcc, 0xe3, 0x6a, 0x01, 0x90, 0xce, 0xf9, 0xfa, 0x50, 0xb2, 0xe0, 0x87, 0x8b, 0x6c, 0x63, 0x6c, 0xf6, 0x2a, 0x09, 0xef, 0xef, 0xd2, 0x31, 0x40, 0x25, 0xf6, 0x84, 0xcb, 0xe0, 0xc4, 0x23, 0xc1, 0xcb, 0xe2, 0x02, 0x83, 0x2d, 0xed, 0x74, 0x74, 0x8b, 0xf8, 0x7c, 0x81, 0x18},
|
||||
},
|
||||
{ /* 55P*/
|
||||
addYX: fp.Elt{0x9e, 0xe5, 0x59, 0x95, 0x63, 0x2e, 0xac, 0x8b, 0x03, 0x3c, 0xc1, 0x8e, 0xe1, 0x5b, 0x56, 0x3c, 0x16, 0x41, 0xe4, 0xc2, 0x60, 0x0c, 0x6d, 0x65, 0x9f, 0xfc, 0x27, 0x68, 0x43, 0x44, 0x05, 0x12, 0x6c, 0xda, 0x04, 0xef, 0xcf, 0xcf, 0xdc, 0x0a, 0x1a, 0x7f, 0x12, 0xd3, 0xeb, 0x02, 0xb6, 0x04, 0xca, 0xd6, 0xcb, 0xf0, 0x22, 0xba, 0x35, 0x6d},
|
||||
subYX: fp.Elt{0x09, 0x6d, 0xf9, 0x64, 0x4c, 0xe6, 0x41, 0xff, 0x01, 0x4d, 0xce, 0x1e, 0xfa, 0x38, 0xa2, 0x25, 0x62, 0xff, 0x03, 0x39, 0x18, 0x91, 0xbb, 0x9d, 0xce, 0x02, 0xf0, 0xf1, 0x3c, 0x55, 0x18, 0xa9, 0xab, 0x4d, 0xd2, 0x35, 0xfd, 0x8d, 0xa9, 0xb2, 0xad, 0xb7, 0x06, 0x6e, 0xc6, 0x69, 0x49, 0xd6, 0x98, 0x98, 0x0b, 0x22, 0x81, 0x6b, 0xbd, 0xa0},
|
||||
dt2: fp.Elt{0x22, 0xf4, 0x85, 0x5d, 0x2b, 0xf1, 0x55, 0xa5, 0xd6, 0x27, 0x86, 0x57, 0x12, 0x1f, 0x16, 0x0a, 0x5a, 0x9b, 0xf2, 0x38, 0xb6, 0x28, 0xd8, 0x99, 0x0c, 0x89, 0x1d, 0x7f, 0xca, 0x21, 0x17, 0x1a, 0x0b, 0x02, 0x5f, 0x77, 0x2f, 0x73, 0x30, 0x7c, 0xc8, 0xd7, 0x2b, 0xcc, 0xe7, 0xf3, 0x21, 0xac, 0x53, 0xa7, 0x11, 0x5d, 0xd8, 0x1d, 0x9b, 0xf5},
|
||||
},
|
||||
{ /* 57P*/
|
||||
addYX: fp.Elt{0x94, 0x63, 0x5d, 0xef, 0xfd, 0x6d, 0x25, 0x4e, 0x6d, 0x29, 0x03, 0xed, 0x24, 0x28, 0x27, 0x57, 0x47, 0x3e, 0x6a, 0x1a, 0xfe, 0x37, 0xee, 0x5f, 0x83, 0x29, 0x14, 0xfd, 0x78, 0x25, 0x8a, 0xe1, 0x02, 0x38, 0xd8, 0xca, 0x65, 0x55, 0x40, 0x7d, 0x48, 0x2c, 0x7c, 0x7e, 0x60, 0xb6, 0x0c, 0x6d, 0xf7, 0xe8, 0xb3, 0x62, 0x53, 0xd6, 0x9c, 0x2b},
|
||||
subYX: fp.Elt{0x47, 0x25, 0x70, 0x62, 0xf5, 0x65, 0x93, 0x62, 0x08, 0xac, 0x59, 0x66, 0xdb, 0x08, 0xd9, 0x1a, 0x19, 0xaf, 0xf4, 0xef, 0x02, 0xa2, 0x78, 0xa9, 0x55, 0x1c, 0xfa, 0x08, 0x11, 0xcb, 0xa3, 0x71, 0x74, 0xb1, 0x62, 0xe7, 0xc7, 0xf3, 0x5a, 0xb5, 0x8b, 0xd4, 0xf6, 0x10, 0x57, 0x79, 0x72, 0x2f, 0x13, 0x86, 0x7b, 0x44, 0x5f, 0x48, 0xfd, 0x88},
|
||||
dt2: fp.Elt{0x10, 0x02, 0xcd, 0x05, 0x9a, 0xc3, 0x32, 0x6d, 0x10, 0x3a, 0x74, 0xba, 0x06, 0xc4, 0x3b, 0x34, 0xbc, 0x36, 0xed, 0xa3, 0xba, 0x9a, 0xdb, 0x6d, 0xd4, 0x69, 0x99, 0x97, 0xd0, 0xe4, 0xdd, 0xf5, 0xd4, 0x7c, 0xd3, 0x4e, 0xab, 0xd1, 0x3b, 0xbb, 0xe9, 0xc7, 0x6a, 0x94, 0x25, 0x61, 0xf0, 0x06, 0xc5, 0x12, 0xa8, 0x86, 0xe5, 0x35, 0x46, 0xeb},
|
||||
},
|
||||
{ /* 59P*/
|
||||
addYX: fp.Elt{0x9e, 0x95, 0x11, 0xc6, 0xc7, 0xe8, 0xee, 0x5a, 0x26, 0xa0, 0x72, 0x72, 0x59, 0x91, 0x59, 0x16, 0x49, 0x99, 0x7e, 0xbb, 0xd7, 0x15, 0xb4, 0xf2, 0x40, 0xf9, 0x5a, 0x4d, 0xc8, 0xa0, 0xe2, 0x34, 0x7b, 0x34, 0xf3, 0x99, 0xbf, 0xa9, 0xf3, 0x79, 0xc1, 0x1a, 0x0c, 0xf4, 0x86, 0x74, 0x4e, 0xcb, 0xbc, 0x90, 0xad, 0xb6, 0x51, 0x6d, 0xaa, 0x33},
|
||||
subYX: fp.Elt{0x9f, 0xd1, 0xc5, 0xa2, 0x6c, 0x24, 0x88, 0x15, 0x71, 0x68, 0xf6, 0x07, 0x45, 0x02, 0xc4, 0x73, 0x7e, 0x75, 0x87, 0xca, 0x7c, 0xf0, 0x92, 0x00, 0x75, 0xd6, 0x5a, 0xdd, 0xe0, 0x64, 0x16, 0x9d, 0x62, 0x80, 0x33, 0x9f, 0xf4, 0x8e, 0x1a, 0x15, 0x1c, 0xd3, 0x0f, 0x4d, 0x4f, 0x62, 0x2d, 0xd7, 0xa5, 0x77, 0xe3, 0xea, 0xf0, 0xfb, 0x1a, 0xdb},
|
||||
dt2: fp.Elt{0x6a, 0xa2, 0xb1, 0xaa, 0xfb, 0x5a, 0x32, 0x4e, 0xff, 0x47, 0x06, 0xd5, 0x9a, 0x4f, 0xce, 0x83, 0x5b, 0x82, 0x34, 0x3e, 0x47, 0xb8, 0xf8, 0xe9, 0x7c, 0x67, 0x69, 0x8d, 0x9c, 0xb7, 0xde, 0x57, 0xf4, 0x88, 0x41, 0x56, 0x0c, 0x87, 0x1e, 0xc9, 0x2f, 0x54, 0xbf, 0x5c, 0x68, 0x2c, 0xd9, 0xc4, 0xef, 0x53, 0x73, 0x1e, 0xa6, 0x38, 0x02, 0x10},
|
||||
},
|
||||
{ /* 61P*/
|
||||
addYX: fp.Elt{0x08, 0x80, 0x4a, 0xc9, 0xb7, 0xa8, 0x88, 0xd9, 0xfc, 0x6a, 0xc0, 0x3e, 0xc2, 0x33, 0x4d, 0x2b, 0x2a, 0xa3, 0x6d, 0x72, 0x3e, 0xdc, 0x34, 0x68, 0x08, 0xbf, 0x27, 0xef, 0xf4, 0xff, 0xe2, 0x0c, 0x31, 0x0c, 0xa2, 0x0a, 0x1f, 0x65, 0xc1, 0x4c, 0x61, 0xd3, 0x1b, 0xbc, 0x25, 0xb1, 0xd0, 0xd4, 0x89, 0xb2, 0x53, 0xfb, 0x43, 0xa5, 0xaf, 0x04},
|
||||
subYX: fp.Elt{0xe3, 0xe1, 0x37, 0xad, 0x58, 0xa9, 0x55, 0x81, 0xee, 0x64, 0x21, 0xb9, 0xf5, 0x4c, 0x35, 0xea, 0x4a, 0xd3, 0x26, 0xaa, 0x90, 0xd4, 0x60, 0x46, 0x09, 0x4b, 0x4a, 0x62, 0xf9, 0xcd, 0xe1, 0xee, 0xbb, 0xc2, 0x09, 0x0b, 0xb0, 0x96, 0x8e, 0x43, 0x77, 0xaf, 0x25, 0x20, 0x5e, 0x47, 0xe4, 0x1d, 0x50, 0x69, 0x74, 0x08, 0xd7, 0xb9, 0x90, 0x13},
|
||||
dt2: fp.Elt{0x51, 0x91, 0x95, 0x64, 0x03, 0x16, 0xfd, 0x6e, 0x26, 0x94, 0x6b, 0x61, 0xe7, 0xd9, 0xe0, 0x4a, 0x6d, 0x7c, 0xfa, 0xc0, 0xe2, 0x43, 0x23, 0x53, 0x70, 0xf5, 0x6f, 0x73, 0x8b, 0x81, 0xb0, 0x0c, 0xee, 0x2e, 0x46, 0xf2, 0x8d, 0xa6, 0xfb, 0xb5, 0x1c, 0x33, 0xbf, 0x90, 0x59, 0xc9, 0x7c, 0xb8, 0x6f, 0xad, 0x75, 0x02, 0x90, 0x8e, 0x59, 0x75},
|
||||
},
|
||||
{ /* 63P*/
|
||||
addYX: fp.Elt{0x36, 0x4d, 0x77, 0x04, 0xb8, 0x7d, 0x4a, 0xd1, 0xc5, 0xbb, 0x7b, 0x50, 0x5f, 0x8d, 0x9d, 0x62, 0x0f, 0x66, 0x71, 0xec, 0x87, 0xc5, 0x80, 0x82, 0xc8, 0xf4, 0x6a, 0x94, 0x92, 0x5b, 0xb0, 0x16, 0x9b, 0xb2, 0xc9, 0x6f, 0x2b, 0x2d, 0xee, 0x95, 0x73, 0x2e, 0xc2, 0x1b, 0xc5, 0x55, 0x36, 0x86, 0x24, 0xf8, 0x20, 0x05, 0x0d, 0x93, 0xd7, 0x76},
|
||||
subYX: fp.Elt{0x7f, 0x01, 0xeb, 0x2e, 0x48, 0x4d, 0x1d, 0xf1, 0x06, 0x7e, 0x7c, 0x2a, 0x43, 0xbf, 0x28, 0xac, 0xe9, 0x58, 0x13, 0xc8, 0xbf, 0x8e, 0xc0, 0xef, 0xe8, 0x4f, 0x46, 0x8a, 0xe7, 0xc0, 0xf6, 0x0f, 0x0a, 0x03, 0x48, 0x91, 0x55, 0x39, 0x2a, 0xe3, 0xdc, 0xf6, 0x22, 0x9d, 0x4d, 0x71, 0x55, 0x68, 0x25, 0x6e, 0x95, 0x52, 0xee, 0x4c, 0xd9, 0x01},
|
||||
dt2: fp.Elt{0xac, 0x33, 0x3f, 0x7c, 0x27, 0x35, 0x15, 0x91, 0x33, 0x8d, 0xf9, 0xc4, 0xf4, 0xf3, 0x90, 0x09, 0x75, 0x69, 0x62, 0x9f, 0x61, 0x35, 0x83, 0x92, 0x04, 0xef, 0x96, 0x38, 0x80, 0x9e, 0x88, 0xb3, 0x67, 0x95, 0xbe, 0x79, 0x3c, 0x35, 0xd8, 0xdc, 0xb2, 0x3e, 0x2d, 0xe6, 0x46, 0xbe, 0x81, 0xf3, 0x32, 0x0e, 0x37, 0x23, 0x75, 0x2a, 0x3d, 0xa0},
|
||||
},
|
||||
}
|
||||
62
vendor/github.com/cloudflare/circl/ecc/goldilocks/twist_basemult.go
generated
vendored
Normal file
62
vendor/github.com/cloudflare/circl/ecc/goldilocks/twist_basemult.go
generated
vendored
Normal file
|
|
@ -0,0 +1,62 @@
|
|||
package goldilocks
|
||||
|
||||
import (
|
||||
"crypto/subtle"
|
||||
|
||||
mlsb "github.com/cloudflare/circl/math/mlsbset"
|
||||
)
|
||||
|
||||
const (
|
||||
// MLSBRecoding parameters
|
||||
fxT = 448
|
||||
fxV = 2
|
||||
fxW = 3
|
||||
fx2w1 = 1 << (uint(fxW) - 1)
|
||||
)
|
||||
|
||||
// ScalarBaseMult returns kG where G is the generator point.
|
||||
func (e twistCurve) ScalarBaseMult(k *Scalar) *twistPoint {
|
||||
m, err := mlsb.New(fxT, fxV, fxW)
|
||||
if err != nil {
|
||||
panic(err)
|
||||
}
|
||||
if m.IsExtended() {
|
||||
panic("not extended")
|
||||
}
|
||||
|
||||
var isZero int
|
||||
if k.IsZero() {
|
||||
isZero = 1
|
||||
}
|
||||
subtle.ConstantTimeCopy(isZero, k[:], order[:])
|
||||
|
||||
minusK := *k
|
||||
isEven := 1 - int(k[0]&0x1)
|
||||
minusK.Neg()
|
||||
subtle.ConstantTimeCopy(isEven, k[:], minusK[:])
|
||||
c, err := m.Encode(k[:])
|
||||
if err != nil {
|
||||
panic(err)
|
||||
}
|
||||
|
||||
gP := c.Exp(groupMLSB{})
|
||||
P := gP.(*twistPoint)
|
||||
P.cneg(uint(isEven))
|
||||
return P
|
||||
}
|
||||
|
||||
type groupMLSB struct{}
|
||||
|
||||
func (e groupMLSB) ExtendedEltP() mlsb.EltP { return nil }
|
||||
func (e groupMLSB) Sqr(x mlsb.EltG) { x.(*twistPoint).Double() }
|
||||
func (e groupMLSB) Mul(x mlsb.EltG, y mlsb.EltP) { x.(*twistPoint).mixAddZ1(y.(*preTwistPointAffine)) }
|
||||
func (e groupMLSB) Identity() mlsb.EltG { return twistCurve{}.Identity() }
|
||||
func (e groupMLSB) NewEltP() mlsb.EltP { return &preTwistPointAffine{} }
|
||||
func (e groupMLSB) Lookup(a mlsb.EltP, v uint, s, u int32) {
|
||||
Tabj := &tabFixMult[v]
|
||||
P := a.(*preTwistPointAffine)
|
||||
for k := range Tabj {
|
||||
P.cmov(&Tabj[k], uint(subtle.ConstantTimeEq(int32(k), u)))
|
||||
}
|
||||
P.cneg(int(s >> 31))
|
||||
}
|
||||
|
|
@ -0,0 +1,140 @@
|
|||
package conv
|
||||
|
||||
import (
|
||||
"encoding/binary"
|
||||
"fmt"
|
||||
"math/big"
|
||||
"strings"
|
||||
)
|
||||
|
||||
// BytesLe2Hex returns an hexadecimal string of a number stored in a
|
||||
// little-endian order slice x.
|
||||
func BytesLe2Hex(x []byte) string {
|
||||
b := &strings.Builder{}
|
||||
b.Grow(2*len(x) + 2)
|
||||
fmt.Fprint(b, "0x")
|
||||
if len(x) == 0 {
|
||||
fmt.Fprint(b, "00")
|
||||
}
|
||||
for i := len(x) - 1; i >= 0; i-- {
|
||||
fmt.Fprintf(b, "%02x", x[i])
|
||||
}
|
||||
return b.String()
|
||||
}
|
||||
|
||||
// BytesLe2BigInt converts a little-endian slice x into a big-endian
|
||||
// math/big.Int.
|
||||
func BytesLe2BigInt(x []byte) *big.Int {
|
||||
n := len(x)
|
||||
b := new(big.Int)
|
||||
if len(x) > 0 {
|
||||
y := make([]byte, n)
|
||||
for i := 0; i < n; i++ {
|
||||
y[n-1-i] = x[i]
|
||||
}
|
||||
b.SetBytes(y)
|
||||
}
|
||||
return b
|
||||
}
|
||||
|
||||
// BytesBe2Uint64Le converts a big-endian slice x to a little-endian slice of uint64.
|
||||
func BytesBe2Uint64Le(x []byte) []uint64 {
|
||||
l := len(x)
|
||||
z := make([]uint64, (l+7)/8)
|
||||
blocks := l / 8
|
||||
for i := 0; i < blocks; i++ {
|
||||
z[i] = binary.BigEndian.Uint64(x[l-8*(i+1):])
|
||||
}
|
||||
remBytes := l % 8
|
||||
for i := 0; i < remBytes; i++ {
|
||||
z[blocks] |= uint64(x[l-1-8*blocks-i]) << uint(8*i)
|
||||
}
|
||||
return z
|
||||
}
|
||||
|
||||
// BigInt2BytesLe stores a positive big.Int number x into a little-endian slice z.
|
||||
// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros).
|
||||
// If x does not fit in the slice or is negative, z is not modified.
|
||||
func BigInt2BytesLe(z []byte, x *big.Int) {
|
||||
xLen := (x.BitLen() + 7) >> 3
|
||||
zLen := len(z)
|
||||
if zLen >= xLen && x.Sign() >= 0 {
|
||||
y := x.Bytes()
|
||||
for i := 0; i < xLen; i++ {
|
||||
z[i] = y[xLen-1-i]
|
||||
}
|
||||
for i := xLen; i < zLen; i++ {
|
||||
z[i] = 0
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Uint64Le2BigInt converts a little-endian slice x into a big number.
|
||||
func Uint64Le2BigInt(x []uint64) *big.Int {
|
||||
n := len(x)
|
||||
b := new(big.Int)
|
||||
var bi big.Int
|
||||
for i := n - 1; i >= 0; i-- {
|
||||
bi.SetUint64(x[i])
|
||||
b.Lsh(b, 64)
|
||||
b.Add(b, &bi)
|
||||
}
|
||||
return b
|
||||
}
|
||||
|
||||
// Uint64Le2BytesLe converts a little-endian slice x to a little-endian slice of bytes.
|
||||
func Uint64Le2BytesLe(x []uint64) []byte {
|
||||
b := make([]byte, 8*len(x))
|
||||
n := len(x)
|
||||
for i := 0; i < n; i++ {
|
||||
binary.LittleEndian.PutUint64(b[i*8:], x[i])
|
||||
}
|
||||
return b
|
||||
}
|
||||
|
||||
// Uint64Le2BytesBe converts a little-endian slice x to a big-endian slice of bytes.
|
||||
func Uint64Le2BytesBe(x []uint64) []byte {
|
||||
b := make([]byte, 8*len(x))
|
||||
n := len(x)
|
||||
for i := 0; i < n; i++ {
|
||||
binary.BigEndian.PutUint64(b[i*8:], x[n-1-i])
|
||||
}
|
||||
return b
|
||||
}
|
||||
|
||||
// Uint64Le2Hex returns an hexadecimal string of a number stored in a
|
||||
// little-endian order slice x.
|
||||
func Uint64Le2Hex(x []uint64) string {
|
||||
b := new(strings.Builder)
|
||||
b.Grow(16*len(x) + 2)
|
||||
fmt.Fprint(b, "0x")
|
||||
if len(x) == 0 {
|
||||
fmt.Fprint(b, "00")
|
||||
}
|
||||
for i := len(x) - 1; i >= 0; i-- {
|
||||
fmt.Fprintf(b, "%016x", x[i])
|
||||
}
|
||||
return b.String()
|
||||
}
|
||||
|
||||
// BigInt2Uint64Le stores a positive big.Int number x into a little-endian slice z.
|
||||
// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros).
|
||||
// If x does not fit in the slice or is negative, z is not modified.
|
||||
func BigInt2Uint64Le(z []uint64, x *big.Int) {
|
||||
xLen := (x.BitLen() + 63) >> 6 // number of 64-bit words
|
||||
zLen := len(z)
|
||||
if zLen >= xLen && x.Sign() > 0 {
|
||||
var y, yi big.Int
|
||||
y.Set(x)
|
||||
two64 := big.NewInt(1)
|
||||
two64.Lsh(two64, 64).Sub(two64, big.NewInt(1))
|
||||
for i := 0; i < xLen; i++ {
|
||||
yi.And(&y, two64)
|
||||
z[i] = yi.Uint64()
|
||||
y.Rsh(&y, 64)
|
||||
}
|
||||
}
|
||||
for i := xLen; i < zLen; i++ {
|
||||
z[i] = 0
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,62 @@
|
|||
// Copyright 2014 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package sha3 implements the SHA-3 fixed-output-length hash functions and
|
||||
// the SHAKE variable-output-length hash functions defined by FIPS-202.
|
||||
//
|
||||
// Both types of hash function use the "sponge" construction and the Keccak
|
||||
// permutation. For a detailed specification see http://keccak.noekeon.org/
|
||||
//
|
||||
// # Guidance
|
||||
//
|
||||
// If you aren't sure what function you need, use SHAKE256 with at least 64
|
||||
// bytes of output. The SHAKE instances are faster than the SHA3 instances;
|
||||
// the latter have to allocate memory to conform to the hash.Hash interface.
|
||||
//
|
||||
// If you need a secret-key MAC (message authentication code), prepend the
|
||||
// secret key to the input, hash with SHAKE256 and read at least 32 bytes of
|
||||
// output.
|
||||
//
|
||||
// # Security strengths
|
||||
//
|
||||
// The SHA3-x (x equals 224, 256, 384, or 512) functions have a security
|
||||
// strength against preimage attacks of x bits. Since they only produce "x"
|
||||
// bits of output, their collision-resistance is only "x/2" bits.
|
||||
//
|
||||
// The SHAKE-256 and -128 functions have a generic security strength of 256 and
|
||||
// 128 bits against all attacks, provided that at least 2x bits of their output
|
||||
// is used. Requesting more than 64 or 32 bytes of output, respectively, does
|
||||
// not increase the collision-resistance of the SHAKE functions.
|
||||
//
|
||||
// # The sponge construction
|
||||
//
|
||||
// A sponge builds a pseudo-random function from a public pseudo-random
|
||||
// permutation, by applying the permutation to a state of "rate + capacity"
|
||||
// bytes, but hiding "capacity" of the bytes.
|
||||
//
|
||||
// A sponge starts out with a zero state. To hash an input using a sponge, up
|
||||
// to "rate" bytes of the input are XORed into the sponge's state. The sponge
|
||||
// is then "full" and the permutation is applied to "empty" it. This process is
|
||||
// repeated until all the input has been "absorbed". The input is then padded.
|
||||
// The digest is "squeezed" from the sponge in the same way, except that output
|
||||
// is copied out instead of input being XORed in.
|
||||
//
|
||||
// A sponge is parameterized by its generic security strength, which is equal
|
||||
// to half its capacity; capacity + rate is equal to the permutation's width.
|
||||
// Since the KeccakF-1600 permutation is 1600 bits (200 bytes) wide, this means
|
||||
// that the security strength of a sponge instance is equal to (1600 - bitrate) / 2.
|
||||
//
|
||||
// # Recommendations
|
||||
//
|
||||
// The SHAKE functions are recommended for most new uses. They can produce
|
||||
// output of arbitrary length. SHAKE256, with an output length of at least
|
||||
// 64 bytes, provides 256-bit security against all attacks. The Keccak team
|
||||
// recommends it for most applications upgrading from SHA2-512. (NIST chose a
|
||||
// much stronger, but much slower, sponge instance for SHA3-512.)
|
||||
//
|
||||
// The SHA-3 functions are "drop-in" replacements for the SHA-2 functions.
|
||||
// They produce output of the same length, with the same security strengths
|
||||
// against all attacks. This means, in particular, that SHA3-256 only has
|
||||
// 128-bit collision resistance, because its output length is 32 bytes.
|
||||
package sha3
|
||||
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Reference in New Issue