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Bump github.com/hashicorp/terraform-plugin-sdk/v2 from 2.26.1 to 2.27.0

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Bumps [github.com/hashicorp/terraform-plugin-sdk/v2](https://github.com/hashicorp/terraform-plugin-sdk) from 2.26.1 to 2.27.0.
- [Release notes](https://github.com/hashicorp/terraform-plugin-sdk/releases)
- [Changelog](https://github.com/hashicorp/terraform-plugin-sdk/blob/main/CHANGELOG.md)
- [Commits](https://github.com/hashicorp/terraform-plugin-sdk/compare/v2.26.1...v2.27.0)

---
updated-dependencies:
- dependency-name: github.com/hashicorp/terraform-plugin-sdk/v2
  dependency-type: direct:production
  update-type: version-update:semver-minor
...

Signed-off-by: dependabot[bot] <support@github.com>
This commit is contained in:
dependabot[bot] 2023-07-03 20:21:30 +00:00 committed by GitHub
parent b2403e2569
commit 910ccdb092
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722 changed files with 31260 additions and 8125 deletions
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48
go.mod
View File

@ -5,39 +5,41 @@ go 1.18
require (
code.gitea.io/sdk/gitea v0.15.1
github.com/hashicorp/terraform-plugin-docs v0.14.1
github.com/hashicorp/terraform-plugin-log v0.8.0
github.com/hashicorp/terraform-plugin-sdk/v2 v2.26.1
github.com/hashicorp/terraform-plugin-log v0.9.0
github.com/hashicorp/terraform-plugin-sdk/v2 v2.27.0
)
require (
github.com/Masterminds/goutils v1.1.1 // indirect
github.com/Masterminds/semver/v3 v3.1.1 // indirect
github.com/Masterminds/sprig/v3 v3.2.2 // indirect
github.com/ProtonMail/go-crypto v0.0.0-20230217124315-7d5c6f04bbb8 // indirect
github.com/agext/levenshtein v1.2.2 // indirect
github.com/apparentlymart/go-textseg/v13 v13.0.0 // indirect
github.com/armon/go-radix v1.0.0 // indirect
github.com/bgentry/speakeasy v0.1.0 // indirect
github.com/cloudflare/circl v1.3.3 // indirect
github.com/fatih/color v1.13.0 // indirect
github.com/golang/protobuf v1.5.2 // indirect
github.com/golang/protobuf v1.5.3 // indirect
github.com/google/go-cmp v0.5.9 // indirect
github.com/google/uuid v1.3.0 // indirect
github.com/hashicorp/errwrap v1.1.0 // indirect
github.com/hashicorp/go-checkpoint v0.5.0 // indirect
github.com/hashicorp/go-cleanhttp v0.5.2 // indirect
github.com/hashicorp/go-cty v1.4.1-0.20200414143053-d3edf31b6320 // indirect
github.com/hashicorp/go-hclog v1.4.0 // indirect
github.com/hashicorp/go-hclog v1.5.0 // indirect
github.com/hashicorp/go-multierror v1.1.1 // indirect
github.com/hashicorp/go-plugin v1.4.8 // indirect
github.com/hashicorp/go-plugin v1.4.10 // indirect
github.com/hashicorp/go-uuid v1.0.3 // indirect
github.com/hashicorp/go-version v1.6.0 // indirect
github.com/hashicorp/hc-install v0.5.0 // indirect
github.com/hashicorp/hcl/v2 v2.16.2 // indirect
github.com/hashicorp/hc-install v0.5.2 // indirect
github.com/hashicorp/hcl/v2 v2.17.0 // indirect
github.com/hashicorp/logutils v1.0.0 // indirect
github.com/hashicorp/terraform-exec v0.18.1 // indirect
github.com/hashicorp/terraform-json v0.16.0 // indirect
github.com/hashicorp/terraform-plugin-go v0.14.3 // indirect
github.com/hashicorp/terraform-registry-address v0.1.0 // indirect
github.com/hashicorp/terraform-svchost v0.0.0-20200729002733-f050f53b9734 // indirect
github.com/hashicorp/terraform-json v0.17.0 // indirect
github.com/hashicorp/terraform-plugin-go v0.16.0 // indirect
github.com/hashicorp/terraform-registry-address v0.2.1 // indirect
github.com/hashicorp/terraform-svchost v0.1.1 // indirect
github.com/hashicorp/yamux v0.0.0-20181012175058-2f1d1f20f75d // indirect
github.com/huandu/xstrings v1.3.2 // indirect
github.com/imdario/mergo v0.3.13 // indirect
@ -55,16 +57,16 @@ require (
github.com/shopspring/decimal v1.3.1 // indirect
github.com/spf13/cast v1.5.0 // indirect
github.com/vmihailenco/msgpack v4.0.4+incompatible // indirect
github.com/vmihailenco/msgpack/v4 v4.3.12 // indirect
github.com/vmihailenco/tagparser v0.1.1 // indirect
github.com/zclconf/go-cty v1.13.1 // indirect
golang.org/x/crypto v0.7.0 // indirect
golang.org/x/mod v0.8.0 // indirect
golang.org/x/net v0.8.0 // indirect
golang.org/x/sys v0.6.0 // indirect
golang.org/x/text v0.8.0 // indirect
google.golang.org/appengine v1.6.6 // indirect
google.golang.org/genproto v0.0.0-20200711021454-869866162049 // indirect
google.golang.org/grpc v1.51.0 // indirect
google.golang.org/protobuf v1.28.1 // indirect
github.com/vmihailenco/msgpack/v5 v5.3.5 // indirect
github.com/vmihailenco/tagparser/v2 v2.0.0 // indirect
github.com/zclconf/go-cty v1.13.2 // indirect
golang.org/x/crypto v0.10.0 // indirect
golang.org/x/mod v0.10.0 // indirect
golang.org/x/net v0.11.0 // indirect
golang.org/x/sys v0.9.0 // indirect
golang.org/x/text v0.10.0 // indirect
google.golang.org/appengine v1.6.7 // indirect
google.golang.org/genproto v0.0.0-20230410155749-daa745c078e1 // indirect
google.golang.org/grpc v1.56.0 // indirect
google.golang.org/protobuf v1.30.0 // indirect
)

250
go.sum
View File

@ -1,9 +1,6 @@
cloud.google.com/go v0.26.0/go.mod h1:aQUYkXzVsufM+DwF1aE+0xfcU+56JwCaLick0ClmMTw=
cloud.google.com/go v0.34.0/go.mod h1:aQUYkXzVsufM+DwF1aE+0xfcU+56JwCaLick0ClmMTw=
code.gitea.io/gitea-vet v0.2.1/go.mod h1:zcNbT/aJEmivCAhfmkHOlT645KNOf9W2KnkLgFjGGfE=
code.gitea.io/sdk/gitea v0.15.1 h1:WJreC7YYuxbn0UDaPuWIe/mtiNKTvLN8MLkaw71yx/M=
code.gitea.io/sdk/gitea v0.15.1/go.mod h1:klY2LVI3s3NChzIk/MzMn7G1FHrfU7qd63iSMVoHRBA=
github.com/BurntSushi/toml v0.3.1/go.mod h1:xHWCNGjB5oqiDr8zfno3MHue2Ht5sIBksp03qcyfWMU=
github.com/Masterminds/goutils v1.1.1 h1:5nUrii3FMTL5diU80unEVvNevw1nH4+ZV4DSLVJLSYI=
github.com/Masterminds/goutils v1.1.1/go.mod h1:8cTjp+g8YejhMuvIA5y2vz3BpJxksy863GQaJW2MFNU=
github.com/Masterminds/semver/v3 v3.1.1 h1:hLg3sBzpNErnxhQtUy/mmLR2I9foDujNK030IGemrRc=
@ -11,71 +8,42 @@ github.com/Masterminds/semver/v3 v3.1.1/go.mod h1:VPu/7SZ7ePZ3QOrcuXROw5FAcLl4a0
github.com/Masterminds/sprig/v3 v3.2.1/go.mod h1:UoaO7Yp8KlPnJIYWTFkMaqPUYKTfGFPhxNuwnnxkKlk=
github.com/Masterminds/sprig/v3 v3.2.2 h1:17jRggJu518dr3QaafizSXOjKYp94wKfABxUmyxvxX8=
github.com/Masterminds/sprig/v3 v3.2.2/go.mod h1:UoaO7Yp8KlPnJIYWTFkMaqPUYKTfGFPhxNuwnnxkKlk=
github.com/Microsoft/go-winio v0.4.14/go.mod h1:qXqCSQ3Xa7+6tgxaGTIe4Kpcdsi+P8jBhyzoq1bpyYA=
github.com/Microsoft/go-winio v0.4.16 h1:FtSW/jqD+l4ba5iPBj9CODVtgfYAD8w2wS923g/cFDk=
github.com/Microsoft/go-winio v0.4.16/go.mod h1:XB6nPKklQyQ7GC9LdcBEcBl8PF76WugXOPRXwdLnMv0=
github.com/ProtonMail/go-crypto v0.0.0-20210428141323-04723f9f07d7 h1:YoJbenK9C67SkzkDfmQuVln04ygHj3vjZfd9FL+GmQQ=
github.com/ProtonMail/go-crypto v0.0.0-20210428141323-04723f9f07d7/go.mod h1:z4/9nQmJSSwwds7ejkxaJwO37dru3geImFUdJlaLzQo=
github.com/acomagu/bufpipe v1.0.3 h1:fxAGrHZTgQ9w5QqVItgzwj235/uYZYgbXitB+dLupOk=
github.com/acomagu/bufpipe v1.0.3/go.mod h1:mxdxdup/WdsKVreO5GpW4+M/1CE2sMG4jeGJ2sYmHc4=
github.com/Microsoft/go-winio v0.5.2 h1:a9IhgEQBCUEk6QCdml9CiJGhAws+YwffDHEMp1VMrpA=
github.com/ProtonMail/go-crypto v0.0.0-20230217124315-7d5c6f04bbb8 h1:wPbRQzjjwFc0ih8puEVAOFGELsn1zoIIYdxvML7mDxA=
github.com/ProtonMail/go-crypto v0.0.0-20230217124315-7d5c6f04bbb8/go.mod h1:I0gYDMZ6Z5GRU7l58bNFSkPTFN6Yl12dsUlAZ8xy98g=
github.com/acomagu/bufpipe v1.0.4 h1:e3H4WUzM3npvo5uv95QuJM3cQspFNtFBzvJ2oNjKIDQ=
github.com/agext/levenshtein v1.2.2 h1:0S/Yg6LYmFJ5stwQeRp6EeOcCbj7xiqQSdNelsXvaqE=
github.com/agext/levenshtein v1.2.2/go.mod h1:JEDfjyjHDjOF/1e4FlBE/PkbqA9OfWu2ki2W0IB5558=
github.com/anmitsu/go-shlex v0.0.0-20161002113705-648efa622239/go.mod h1:2FmKhYUyUczH0OGQWaF5ceTx0UBShxjsH6f8oGKYe2c=
github.com/apparentlymart/go-textseg v1.0.0/go.mod h1:z96Txxhf3xSFMPmb5X/1W05FF/Nj9VFpLOpjS5yuumk=
github.com/apparentlymart/go-textseg/v12 v12.0.0/go.mod h1:S/4uRK2UtaQttw1GenVJEynmyUenKwP++x/+DdGV/Ec=
github.com/apparentlymart/go-textseg/v13 v13.0.0 h1:Y+KvPE1NYz0xl601PVImeQfFyEy6iT90AvPUL1NNfNw=
github.com/apparentlymart/go-textseg/v13 v13.0.0/go.mod h1:ZK2fH7c4NqDTLtiYLvIkEghdlcqw7yxLeM89kiTRPUo=
github.com/armon/go-radix v0.0.0-20180808171621-7fddfc383310/go.mod h1:ufUuZ+zHj4x4TnLV4JWEpy2hxWSpsRywHrMgIH9cCH8=
github.com/armon/go-radix v1.0.0 h1:F4z6KzEeeQIMeLFa97iZU6vupzoecKdU5TX24SNppXI=
github.com/armon/go-radix v1.0.0/go.mod h1:ufUuZ+zHj4x4TnLV4JWEpy2hxWSpsRywHrMgIH9cCH8=
github.com/armon/go-socks5 v0.0.0-20160902184237-e75332964ef5/go.mod h1:wHh0iHkYZB8zMSxRWpUBQtwG5a7fFgvEO+odwuTv2gs=
github.com/bgentry/speakeasy v0.1.0 h1:ByYyxL9InA1OWqxJqqp2A5pYHUrCiAL6K3J+LKSsQkY=
github.com/bgentry/speakeasy v0.1.0/go.mod h1:+zsyZBPWlz7T6j88CTgSN5bM796AkVf0kBD4zp0CCIs=
github.com/census-instrumentation/opencensus-proto v0.2.1/go.mod h1:f6KPmirojxKA12rnyqOA5BBL4O983OfeGPqjHWSTneU=
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=
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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=
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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=
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github.com/xanzy/ssh-agent v0.3.0/go.mod h1:3s9xbODqPuuhK9JV1R321M/FlMZSBvE5aY6eAcqrDh0=
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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=
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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=
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golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
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golang.org/x/crypto v0.0.0-20200414173820-0848c9571904/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto=
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golang.org/x/crypto v0.7.0/go.mod h1:pYwdfH91IfpZVANVyUOhSIPZaFoJGxTFbZhFTx+dXZU=
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golang.org/x/crypto v0.10.0/go.mod h1:o4eNf7Ede1fv+hwOwZsTHl9EsPFO6q6ZvYR8vYfY45I=
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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=
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golang.org/x/sys v0.9.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
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golang.org/x/text v0.8.0/go.mod h1:e1OnstbJyHTd6l/uOt8jFFHp6TRDWZR/bV3emEE/zU8=
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golang.org/x/text v0.10.0/go.mod h1:TvPlkZtksWOMsz7fbANvkp4WM8x/WCo/om8BMLbz+aE=
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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=
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vendor/github.com/ProtonMail/go-crypto/AUTHORS generated vendored Normal file
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@ -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.

3
vendor/github.com/ProtonMail/go-crypto/CONTRIBUTORS generated vendored Normal file
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@ -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.

27
vendor/github.com/ProtonMail/go-crypto/LICENSE generated vendored Normal file
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@ -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.

22
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@ -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.

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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
}

134
vendor/github.com/ProtonMail/go-crypto/brainpool/brainpool.go generated vendored Normal file
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// 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
}

83
vendor/github.com/ProtonMail/go-crypto/brainpool/rcurve.go generated vendored Normal file
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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))
}

162
vendor/github.com/ProtonMail/go-crypto/eax/eax.go generated vendored Normal file
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// 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)
}

58
vendor/github.com/ProtonMail/go-crypto/eax/eax_test_vectors.go generated vendored Normal file
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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"},
}

131
vendor/github.com/ProtonMail/go-crypto/eax/random_vectors.go generated vendored Normal file
View File

@ -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
View 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
}

317
vendor/github.com/ProtonMail/go-crypto/ocb/ocb.go generated vendored Normal file
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@ -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)
}

136
vendor/github.com/ProtonMail/go-crypto/ocb/random_vectors.go generated vendored Normal file
View File

@ -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
View 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
View 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
View 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
}

14
vendor/golang.org/x/crypto/openpgp/armor/armor.go → vendor/github.com/ProtonMail/go-crypto/openpgp/armor/armor.go generated vendored
View File

@ -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
//
// 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
}

1
vendor/golang.org/x/crypto/openpgp/armor/encode.go → vendor/github.com/ProtonMail/go-crypto/openpgp/armor/encode.go generated vendored
View File

@ -96,7 +96,6 @@ func (l *lineBreaker) Close() (err error) {
// trailer.
//
// It's built into a stack of io.Writers:
//
// encoding -> base64 encoder -> lineBreaker -> out
type encoding struct {
out io.Writer

24
vendor/golang.org/x/crypto/openpgp/canonical_text.go → vendor/github.com/ProtonMail/go-crypto/openpgp/canonical_text.go generated vendored
View File

@ -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)
}

206
vendor/github.com/ProtonMail/go-crypto/openpgp/ecdh/ecdh.go generated vendored Normal file
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@ -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)
}

80
vendor/github.com/ProtonMail/go-crypto/openpgp/ecdsa/ecdsa.go generated vendored Normal file
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@ -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())
}

91
vendor/github.com/ProtonMail/go-crypto/openpgp/eddsa/eddsa.go generated vendored Normal file
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@ -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)
}

12
vendor/golang.org/x/crypto/openpgp/elgamal/elgamal.go → vendor/github.com/ProtonMail/go-crypto/openpgp/elgamal/elgamal.go generated vendored
View File

@ -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)

52
vendor/golang.org/x/crypto/openpgp/errors/errors.go → vendor/github.com/ProtonMail/go-crypto/openpgp/errors/errors.go generated vendored
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@ -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
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@ -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
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@ -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
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@ -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
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// 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
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// 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
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// 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
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// 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
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// 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
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// 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
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@ -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
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@ -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
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@ -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
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@ -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
}

389
vendor/github.com/ProtonMail/go-crypto/openpgp/key_generation.go generated vendored Normal file
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@ -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
}

489
vendor/golang.org/x/crypto/openpgp/keys.go → vendor/github.com/ProtonMail/go-crypto/openpgp/keys.go generated vendored
View File

@ -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.
@ -37,7 +37,8 @@ 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
@ -46,6 +47,7 @@ type Subkey struct {
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())
}
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
}
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)
}
for _, sig := range ident.Signatures {
err = sig.Serialize(w)
if err != nil {
return
return err
}
}
}
for _, subkey := range e.Subkeys {
@ -613,10 +660,25 @@ func (e *Entity) SerializePrivate(w io.Writer, config *packet.Config) (err error
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 {
return
@ -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")
}
if err := sig.SignUserId(identity, e.PrimaryKey, signer.PrivateKey, config); err != nil {
sig.SignerUserId = &signingUserID
}
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
}

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@ -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)
}

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@ -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
View 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}
}

4
vendor/golang.org/x/crypto/openpgp/packet/compressed.go → vendor/github.com/ProtonMail/go-crypto/openpgp/packet/compressed.go generated vendored
View File

@ -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:

224
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/config.go generated vendored Normal file
View File

@ -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
}

128
vendor/golang.org/x/crypto/openpgp/packet/encrypted_key.go → vendor/github.com/ProtonMail/go-crypto/openpgp/packet/encrypted_key.go generated vendored
View File

@ -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
}

4
vendor/golang.org/x/crypto/openpgp/packet/literal.go → vendor/github.com/ProtonMail/go-crypto/openpgp/packet/literal.go generated vendored
View File

@ -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])

29
vendor/github.com/ProtonMail/go-crypto/openpgp/packet/notation.go generated vendored Normal file
View File

@ -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
}

8
vendor/golang.org/x/crypto/openpgp/packet/ocfb.go → vendor/github.com/ProtonMail/go-crypto/openpgp/packet/ocfb.go generated vendored
View File

@ -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 {

8
vendor/golang.org/x/crypto/openpgp/packet/one_pass_signature.go → vendor/github.com/ProtonMail/go-crypto/openpgp/packet/one_pass_signature.go generated vendored
View File

@ -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)))
}

16
vendor/golang.org/x/crypto/openpgp/packet/opaque.go → vendor/github.com/ProtonMail/go-crypto/openpgp/packet/opaque.go generated vendored
View File

@ -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
}
@ -84,6 +85,7 @@ func (or *OpaqueReader) Next() (op *OpaquePacket, err error) {
// as found in signature and user attribute packets.
type OpaqueSubpacket struct {
SubType uint8
EncodedLength []byte // Store the original encoded length for signature verifications.
Contents []byte
}
@ -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

323
vendor/golang.org/x/crypto/openpgp/packet/packet.go → vendor/github.com/ProtonMail/go-crypto/openpgp/packet/packet.go generated vendored
View File

@ -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
}
p = w.buf
w.buf = nil
}
w.sentFirst = true
}
power := uint8(30)
for len(p) > 0 {
bufLen := w.buf.Len()
if bufLen > 512 {
for power := uint(30); ; power-- {
l := 1 << power
if len(p) < l {
power = uint8(bits.Len32(uint32(len(p)))) - 1
l = 1 << power
}
w.lengthByte[0] = 224 + power
if bufLen >= l {
w.lengthByte[0] = 224 + uint8(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
}
return n - off, err
var m int
m, err = w.w.Write(w.buf.Next(l))
if err != nil {
return
}
p = p[l:]
if m != l {
return 0, io.ErrShortWrite
}
return n - off, nil
break
}
}
}
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 {
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
}
@ -334,20 +315,14 @@ const (
packetTypeUserId packetType = 13
packetTypePublicSubkey packetType = 14
packetTypeUserAttribute packetType = 17
packetTypeSymmetricallyEncryptedMDC packetType = 18
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)
}
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}
}
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
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// 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
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@ -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
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// 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
View 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 = `99006f044d53059213052b81040022030304f6b8c5aced5b84ef9f4a209db2e4a9dfb70d28cb8c10ecd57674a9fa5a67389942b62d5e51367df4c7bfd3f8e500feecf07ed265a621a8ebbbe53e947ec78c677eba143bd1533c2b350e1c29f82313e1e1108eba063be1e64b10e6950e799c2db42465635f6473615f64685f333834203c6f70656e70677040627261696e6875622e6f72673e8900cb04101309005305024d530592301480000000002000077072656665727265642d656d61696c2d656e636f64696e67407067702e636f6d7067706d696d65040b090807021901051b03000000021602051e010000000415090a08000a0910098033880f54719fca2b0180aa37350968bd5f115afd8ce7bc7b103822152dbff06d0afcda835329510905b98cb469ba208faab87c7412b799e7b633017f58364ea480e8a1a3f253a0c5f22c446e8be9a9fce6210136ee30811abbd49139de28b5bdf8dc36d06ae748579e9ff503b90073044d53059212052b810400220303042faa84024a20b6735c4897efa5bfb41bf85b7eefeab5ca0cb9ffc8ea04a46acb25534a577694f9e25340a4ab5223a9dd1eda530c8aa2e6718db10d7e672558c7736fe09369ea5739a2a3554bf16d41faa50562f11c6d39bbd5dffb6b9a9ec9180301090989008404181309000c05024d530592051b0c000000000a0910098033880f54719f80970180eee7a6d8fcee41ee4f9289df17f9bcf9d955dca25c583b94336f3a2b2d4986dc5cf417b8d2dc86f741a9e1a6d236c0e3017d1c76575458a0cfb93ae8a2b274fcc65ceecd7a91eec83656ba13219969f06945b48c56bd04152c3a0553c5f2f4bd1267`

14
vendor/golang.org/x/crypto/openpgp/packet/reader.go → vendor/github.com/ProtonMail/go-crypto/openpgp/packet/reader.go generated vendored
View File

@ -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 {
// 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

621
vendor/golang.org/x/crypto/openpgp/packet/signature.go → vendor/github.com/ProtonMail/go-crypto/openpgp/packet/signature.go generated vendored
View File

@ -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
@ -40,11 +45,18 @@ type Signature struct {
// HashTag contains the first two bytes of the hash for fast rejection
// of bad signed data.
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
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})
switch packetType {
case creationTimeSubpacket:
if !isHashed {
err = errors.StructuralError("signature creation time in non-hashed area")
if !isHashed &&
packetType != issuerSubpacket &&
packetType != issuerFingerprintSubpacket &&
packetType != embeddedSignatureSubpacket {
return
}
switch packetType {
case creationTimeSubpacket:
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, &notation)
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)
sk := priv.PrivateKey.(*ecdsa.PrivateKey)
r, s, err := ecdsa.Sign(config.Random(), sk, digest)
if err == nil {
r, s, err = unwrapECDSASig(b)
}
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.ECDSASigR = fromBig(r)
sig.ECDSASigS = fromBig(s)
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
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@ -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
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@ -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
View 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
}

116
vendor/golang.org/x/crypto/openpgp/packet/symmetrically_encrypted.go → vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted_mdc.go generated vendored
View File

@ -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
}

17
vendor/golang.org/x/crypto/openpgp/packet/userattribute.go → vendor/github.com/ProtonMail/go-crypto/openpgp/packet/userattribute.go generated vendored
View File

@ -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()})
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

10
vendor/golang.org/x/crypto/openpgp/packet/userid.go → vendor/github.com/ProtonMail/go-crypto/openpgp/packet/userid.go generated vendored
View File

@ -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
}

306
vendor/golang.org/x/crypto/openpgp/read.go → vendor/github.com/ProtonMail/go-crypto/openpgp/read.go generated vendored
View File

@ -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.)
Signature *packet.Signature // the signature packet itself.
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
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)
@ -119,11 +117,12 @@ 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
}
if keyring != nil {
var keys []Key
if p.KeyId == 0 {
keys = keyring.DecryptionKeys()
@ -133,8 +132,15 @@ ParsePackets:
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)
}
if len(pk.encryptedKey.Key) == 0 {
errDec := pk.encryptedKey.Decrypt(pk.key.PrivateKey, config)
if errDec != nil {
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()
@ -249,30 +262,35 @@ 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
if keyring != nil {
keys := keyring.KeysByIdUsage(p.KeyId, packet.KeyFlagSign)
if len(keys) > 0 {
md.SignedBy = &keys[0]
}
}
case *packet.LiteralData:
md.LiteralData = p
break 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)
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 err == io.EOF {
var p packet.Packet
p, scr.md.SignatureError = scr.packets.Next()
if scr.md.SignatureError != nil {
return
}
if sensitiveParsingError == io.EOF {
var p packet.Packet
var readError error
var sig *packet.Signature
p, readError = scr.packets.Next()
for readError == nil {
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)
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.SignatureError = errors.StructuralError("LiteralData not followed by Signature")
return
scr.md.UnverifiedSignatures = append(scr.md.UnverifiedSignatures, sig)
}
}
p, readError = scr.packets.Next()
}
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:
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, errors.StructuralError("signature doesn't have an issuer")
return nil, nil, errors.StructuralError("signature doesn't have an issuer")
}
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")
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")
}
}
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")
}
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
View File

File diff suppressed because one or more lines are too long

268
vendor/golang.org/x/crypto/openpgp/s2k/s2k.go → vendor/github.com/ProtonMail/go-crypto/openpgp/s2k/s2k.go generated vendored
View File

@ -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
}

305
vendor/golang.org/x/crypto/openpgp/write.go → vendor/github.com/ProtonMail/go-crypto/openpgp/write.go generated vendored
View File

@ -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
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)
sig := to[i].PrimaryIdentity().SelfSignature
if sig.SEIPDv2 == false {
aeadSupported = false
}
if len(candidateCiphers) == 0 || len(candidateHashes) == 0 {
return nil, errors.InvalidArgumentError("cannot encrypt because recipient set shares no common algorithms")
candidateCiphers = intersectPreferences(candidateCiphers, sig.PreferredSymmetric)
candidateHashes = intersectPreferences(candidateHashes, sig.PreferredHash)
candidateCipherSuites = intersectCipherSuites(candidateCipherSuites, sig.PreferredCipherSuites)
candidateCompression = intersectPreferences(candidateCompression, sig.PreferredCompression)
}
// 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 writeAndSign(payload, candidateHashes, signed, hints, config)
payload, err = handleCompression(payload, candidateCompression, config)
if err != nil {
return nil, err
}
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)
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
}

57
vendor/github.com/cloudflare/circl/LICENSE generated vendored Normal file
View File

@ -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.

96
vendor/github.com/cloudflare/circl/dh/x25519/curve.go generated vendored Normal file
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@ -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,
},
}

30
vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.go generated vendored Normal file
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@ -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)

111
vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.h generated vendored Normal file
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@ -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)

156
vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.s generated vendored Normal file
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@ -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

85
vendor/github.com/cloudflare/circl/dh/x25519/curve_generic.go generated vendored Normal file
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@ -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])
}
}

11
vendor/github.com/cloudflare/circl/dh/x25519/curve_noasm.go generated vendored Normal file
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@ -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) }

19
vendor/github.com/cloudflare/circl/dh/x25519/doc.go generated vendored Normal file
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@ -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

47
vendor/github.com/cloudflare/circl/dh/x25519/key.go generated vendored Normal file
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@ -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
}

268
vendor/github.com/cloudflare/circl/dh/x25519/table.go generated vendored Normal file
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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,
}

104
vendor/github.com/cloudflare/circl/dh/x448/curve.go generated vendored Normal file
View File

@ -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,
},
}

30
vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.go generated vendored Normal file
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//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)

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vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.h generated vendored Normal file
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#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)

193
vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.s generated vendored Normal file
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// +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

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vendor/github.com/cloudflare/circl/dh/x448/curve_generic.go generated vendored Normal file
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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])
}
}

11
vendor/github.com/cloudflare/circl/dh/x448/curve_noasm.go generated vendored Normal file
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//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) }

19
vendor/github.com/cloudflare/circl/dh/x448/doc.go generated vendored Normal file
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/*
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

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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
}

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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,
}

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vendor/github.com/cloudflare/circl/ecc/goldilocks/constants.go generated vendored Normal file
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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,
}
)

80
vendor/github.com/cloudflare/circl/ecc/goldilocks/curve.go generated vendored Normal file
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// 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, &paramD) // 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)))
}

52
vendor/github.com/cloudflare/circl/ecc/goldilocks/isogeny.go generated vendored Normal file
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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
}

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vendor/github.com/cloudflare/circl/ecc/goldilocks/point.go generated vendored Normal file
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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, &paramD) // 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, &paramD) // 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
}

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vendor/github.com/cloudflare/circl/ecc/goldilocks/scalar.go generated vendored Normal file
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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{} }

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vendor/github.com/cloudflare/circl/ecc/goldilocks/twist.go generated vendored Normal file
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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
}

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vendor/github.com/cloudflare/circl/ecc/goldilocks/twistPoint.go generated vendored Normal file
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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, &paramDTwist) // 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
}

216
vendor/github.com/cloudflare/circl/ecc/goldilocks/twistTables.go generated vendored Normal file
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@ -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
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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))
}

140
vendor/github.com/cloudflare/circl/internal/conv/conv.go generated vendored Normal file
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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
}
}

62
vendor/github.com/cloudflare/circl/internal/sha3/doc.go generated vendored Normal file
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// 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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