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

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>

go.mod

@@ -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-log v0.9.0
-	github.com/hashicorp/terraform-plugin-sdk/v2 v2.26.1
+	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/hc-install v0.5.2 // indirect
-	github.com/hashicorp/hcl/v2 v2.16.2 // 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-json v0.17.0 // indirect
-	github.com/hashicorp/terraform-plugin-go v0.14.3 // indirect
+	github.com/hashicorp/terraform-plugin-go v0.16.0 // indirect
-	github.com/hashicorp/terraform-registry-address v0.1.0 // indirect
+	github.com/hashicorp/terraform-registry-address v0.2.1 // indirect
-	github.com/hashicorp/terraform-svchost v0.0.0-20200729002733-f050f53b9734 // 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/msgpack/v5 v5.3.5 // indirect
-	github.com/vmihailenco/tagparser v0.1.1 // indirect
+	github.com/vmihailenco/tagparser/v2 v2.0.0 // indirect
-	github.com/zclconf/go-cty v1.13.1 // indirect
+	github.com/zclconf/go-cty v1.13.2 // indirect
-	golang.org/x/crypto v0.7.0 // indirect
+	golang.org/x/crypto v0.10.0 // indirect
-	golang.org/x/mod v0.8.0 // indirect
+	golang.org/x/mod v0.10.0 // indirect
-	golang.org/x/net v0.8.0 // indirect
+	golang.org/x/net v0.11.0 // indirect
-	golang.org/x/sys v0.6.0 // indirect
+	golang.org/x/sys v0.9.0 // indirect
-	golang.org/x/text v0.8.0 // indirect
+	golang.org/x/text v0.10.0 // indirect
-	google.golang.org/appengine v1.6.6 // indirect
+	google.golang.org/appengine v1.6.7 // indirect
-	google.golang.org/genproto v0.0.0-20200711021454-869866162049 // indirect
+	google.golang.org/genproto v0.0.0-20230410155749-daa745c078e1 // indirect
-	google.golang.org/grpc v1.51.0 // indirect
+	google.golang.org/grpc v1.56.0 // indirect
-	google.golang.org/protobuf v1.28.1 // indirect
+	google.golang.org/protobuf v1.30.0 // indirect
 )

go.sum

@@ -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 v0.5.2 h1:a9IhgEQBCUEk6QCdml9CiJGhAws+YwffDHEMp1VMrpA=
-github.com/Microsoft/go-winio v0.4.16 h1:FtSW/jqD+l4ba5iPBj9CODVtgfYAD8w2wS923g/cFDk=
+github.com/ProtonMail/go-crypto v0.0.0-20230217124315-7d5c6f04bbb8 h1:wPbRQzjjwFc0ih8puEVAOFGELsn1zoIIYdxvML7mDxA=
-github.com/Microsoft/go-winio v0.4.16/go.mod h1:XB6nPKklQyQ7GC9LdcBEcBl8PF76WugXOPRXwdLnMv0=
+github.com/ProtonMail/go-crypto v0.0.0-20230217124315-7d5c6f04bbb8/go.mod h1:I0gYDMZ6Z5GRU7l58bNFSkPTFN6Yl12dsUlAZ8xy98g=
-github.com/ProtonMail/go-crypto v0.0.0-20210428141323-04723f9f07d7 h1:YoJbenK9C67SkzkDfmQuVln04ygHj3vjZfd9FL+GmQQ=
+github.com/acomagu/bufpipe v1.0.4 h1:e3H4WUzM3npvo5uv95QuJM3cQspFNtFBzvJ2oNjKIDQ=
-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/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/bwesterb/go-ristretto v1.2.0/go.mod h1:fUIoIZaG73pV5biE2Blr2xEzDoMj7NFEuV9ekS419A0=
-github.com/client9/misspell v0.3.4/go.mod h1:qj6jICC3Q7zFZvVWo7KLAzC3yx5G7kyvSDkc90ppPyw=
+github.com/cloudflare/circl v1.1.0/go.mod h1:prBCrKB9DV4poKZY1l9zBXg2QJY7mvgRvtMxxK7fi4I=
-github.com/creack/pty v1.1.9/go.mod h1:oKZEueFk5CKHvIhNR5MUki03XCEU+Q6VDXinZuGJ33E=
+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 v1.18.1 h1:FXtiHYKDGKCW2KzwZKx0iC0PQmdlorYgdFG9jPXJ1Bc=
-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/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 v5.4.1 h1:Uwp5tDRkPr+l/TnbHOQzp+tmJfLceOlbVucgpTz8ix4=
-github.com/go-git/go-billy/v5 v5.2.0/go.mod h1:pmpqyWchKfYfrkb/UVH4otLvyi/5gJlGI4Hb3ZqZ3W0=
+github.com/go-git/go-git/v5 v5.6.1 h1:q4ZRqQl4pR/ZJHc1L5CFjGA1a10u76aV1iC+nh+bHsk=
-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-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 v1.5.3 h1:KhyjKVUg7Usr/dYsdSqoFveMYd5ko72D+zANwlG1mmg=
-github.com/golang/protobuf v1.5.2/go.mod h1:XVQd3VNwM+JqD3oG2Ue2ip4fOMUkwXdXDdiuN0vRsmY=
+github.com/golang/protobuf v1.5.3/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/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=
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vendor/github.com/ProtonMail/go-crypto/AUTHORS

@@ -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.

vendor/github.com/ProtonMail/go-crypto/CONTRIBUTORS

@@ -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.

vendor/github.com/ProtonMail/go-crypto/LICENSE

@@ -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.

vendor/github.com/ProtonMail/go-crypto/PATENTS

@@ -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.

vendor/github.com/ProtonMail/go-crypto/bitcurves/bitcurve.go

@@ -0,0 +1,381 @@
+package bitcurves
+
+// Copyright 2010 The Go Authors. All rights reserved.
+// Copyright 2011 ThePiachu. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package bitelliptic implements several Koblitz elliptic curves over prime
+// fields.
+
+// This package operates, internally, on Jacobian coordinates. For a given
+// (x, y) position on the curve, the Jacobian coordinates are (x1, y1, z1)
+// where x = x1/z1² and y = y1/z1³. The greatest speedups come when the whole
+// calculation can be performed within the transform (as in ScalarMult and
+// ScalarBaseMult). But even for Add and Double, it's faster to apply and
+// reverse the transform than to operate in affine coordinates.
+
+import (
+	"crypto/elliptic"
+	"io"
+	"math/big"
+	"sync"
+)
+
+// A BitCurve represents a Koblitz Curve with a=0.
+// See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html
+type BitCurve struct {
+	Name    string
+	P       *big.Int // the order of the underlying field
+	N       *big.Int // the order of the base point
+	B       *big.Int // the constant of the BitCurve equation
+	Gx, Gy  *big.Int // (x,y) of the base point
+	BitSize int      // the size of the underlying field
+}
+
+// Params returns the parameters of the given BitCurve (see BitCurve struct)
+func (bitCurve *BitCurve) Params() (cp *elliptic.CurveParams) {
+	cp = new(elliptic.CurveParams)
+	cp.Name = bitCurve.Name
+	cp.P = bitCurve.P
+	cp.N = bitCurve.N
+	cp.Gx = bitCurve.Gx
+	cp.Gy = bitCurve.Gy
+	cp.BitSize = bitCurve.BitSize
+	return cp
+}
+
+// IsOnCurve returns true if the given (x,y) lies on the BitCurve.
+func (bitCurve *BitCurve) IsOnCurve(x, y *big.Int) bool {
+	// y² = x³ + b
+	y2 := new(big.Int).Mul(y, y) //y²
+	y2.Mod(y2, bitCurve.P)       //y²%P
+
+	x3 := new(big.Int).Mul(x, x) //x²
+	x3.Mul(x3, x)                //x³
+
+	x3.Add(x3, bitCurve.B) //x³+B
+	x3.Mod(x3, bitCurve.P) //(x³+B)%P
+
+	return x3.Cmp(y2) == 0
+}
+
+// affineFromJacobian reverses the Jacobian transform. See the comment at the
+// top of the file.
+func (bitCurve *BitCurve) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) {
+	if z.Cmp(big.NewInt(0)) == 0 {
+		panic("bitcurve: Can't convert to affine with Jacobian Z = 0")
+	}
+	// x = YZ^2 mod P
+	zinv := new(big.Int).ModInverse(z, bitCurve.P)
+	zinvsq := new(big.Int).Mul(zinv, zinv)
+
+	xOut = new(big.Int).Mul(x, zinvsq)
+	xOut.Mod(xOut, bitCurve.P)
+	// y = YZ^3 mod P
+	zinvsq.Mul(zinvsq, zinv)
+	yOut = new(big.Int).Mul(y, zinvsq)
+	yOut.Mod(yOut, bitCurve.P)
+	return xOut, yOut
+}
+
+// Add returns the sum of (x1,y1) and (x2,y2)
+func (bitCurve *BitCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
+	z := new(big.Int).SetInt64(1)
+	x, y, z := bitCurve.addJacobian(x1, y1, z, x2, y2, z)
+	return bitCurve.affineFromJacobian(x, y, z)
+}
+
+// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and
+// (x2, y2, z2) and returns their sum, also in Jacobian form.
+func (bitCurve *BitCurve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) {
+	// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl
+	z1z1 := new(big.Int).Mul(z1, z1)
+	z1z1.Mod(z1z1, bitCurve.P)
+	z2z2 := new(big.Int).Mul(z2, z2)
+	z2z2.Mod(z2z2, bitCurve.P)
+
+	u1 := new(big.Int).Mul(x1, z2z2)
+	u1.Mod(u1, bitCurve.P)
+	u2 := new(big.Int).Mul(x2, z1z1)
+	u2.Mod(u2, bitCurve.P)
+	h := new(big.Int).Sub(u2, u1)
+	if h.Sign() == -1 {
+		h.Add(h, bitCurve.P)
+	}
+	i := new(big.Int).Lsh(h, 1)
+	i.Mul(i, i)
+	j := new(big.Int).Mul(h, i)
+
+	s1 := new(big.Int).Mul(y1, z2)
+	s1.Mul(s1, z2z2)
+	s1.Mod(s1, bitCurve.P)
+	s2 := new(big.Int).Mul(y2, z1)
+	s2.Mul(s2, z1z1)
+	s2.Mod(s2, bitCurve.P)
+	r := new(big.Int).Sub(s2, s1)
+	if r.Sign() == -1 {
+		r.Add(r, bitCurve.P)
+	}
+	r.Lsh(r, 1)
+	v := new(big.Int).Mul(u1, i)
+
+	x3 := new(big.Int).Set(r)
+	x3.Mul(x3, x3)
+	x3.Sub(x3, j)
+	x3.Sub(x3, v)
+	x3.Sub(x3, v)
+	x3.Mod(x3, bitCurve.P)
+
+	y3 := new(big.Int).Set(r)
+	v.Sub(v, x3)
+	y3.Mul(y3, v)
+	s1.Mul(s1, j)
+	s1.Lsh(s1, 1)
+	y3.Sub(y3, s1)
+	y3.Mod(y3, bitCurve.P)
+
+	z3 := new(big.Int).Add(z1, z2)
+	z3.Mul(z3, z3)
+	z3.Sub(z3, z1z1)
+	if z3.Sign() == -1 {
+		z3.Add(z3, bitCurve.P)
+	}
+	z3.Sub(z3, z2z2)
+	if z3.Sign() == -1 {
+		z3.Add(z3, bitCurve.P)
+	}
+	z3.Mul(z3, h)
+	z3.Mod(z3, bitCurve.P)
+
+	return x3, y3, z3
+}
+
+// Double returns 2*(x,y)
+func (bitCurve *BitCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
+	z1 := new(big.Int).SetInt64(1)
+	return bitCurve.affineFromJacobian(bitCurve.doubleJacobian(x1, y1, z1))
+}
+
+// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
+// returns its double, also in Jacobian form.
+func (bitCurve *BitCurve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
+	// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
+
+	a := new(big.Int).Mul(x, x) //X1²
+	b := new(big.Int).Mul(y, y) //Y1²
+	c := new(big.Int).Mul(b, b) //B²
+
+	d := new(big.Int).Add(x, b) //X1+B
+	d.Mul(d, d)                 //(X1+B)²
+	d.Sub(d, a)                 //(X1+B)²-A
+	d.Sub(d, c)                 //(X1+B)²-A-C
+	d.Mul(d, big.NewInt(2))     //2*((X1+B)²-A-C)
+
+	e := new(big.Int).Mul(big.NewInt(3), a) //3*A
+	f := new(big.Int).Mul(e, e)             //E²
+
+	x3 := new(big.Int).Mul(big.NewInt(2), d) //2*D
+	x3.Sub(f, x3)                            //F-2*D
+	x3.Mod(x3, bitCurve.P)
+
+	y3 := new(big.Int).Sub(d, x3)                  //D-X3
+	y3.Mul(e, y3)                                  //E*(D-X3)
+	y3.Sub(y3, new(big.Int).Mul(big.NewInt(8), c)) //E*(D-X3)-8*C
+	y3.Mod(y3, bitCurve.P)
+
+	z3 := new(big.Int).Mul(y, z) //Y1*Z1
+	z3.Mul(big.NewInt(2), z3)    //3*Y1*Z1
+	z3.Mod(z3, bitCurve.P)
+
+	return x3, y3, z3
+}
+
+//TODO: double check if it is okay
+// ScalarMult returns k*(Bx,By) where k is a number in big-endian form.
+func (bitCurve *BitCurve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
+	// We have a slight problem in that the identity of the group (the
+	// point at infinity) cannot be represented in (x, y) form on a finite
+	// machine. Thus the standard add/double algorithm has to be tweaked
+	// slightly: our initial state is not the identity, but x, and we
+	// ignore the first true bit in |k|.  If we don't find any true bits in
+	// |k|, then we return nil, nil, because we cannot return the identity
+	// element.
+
+	Bz := new(big.Int).SetInt64(1)
+	x := Bx
+	y := By
+	z := Bz
+
+	seenFirstTrue := false
+	for _, byte := range k {
+		for bitNum := 0; bitNum < 8; bitNum++ {
+			if seenFirstTrue {
+				x, y, z = bitCurve.doubleJacobian(x, y, z)
+			}
+			if byte&0x80 == 0x80 {
+				if !seenFirstTrue {
+					seenFirstTrue = true
+				} else {
+					x, y, z = bitCurve.addJacobian(Bx, By, Bz, x, y, z)
+				}
+			}
+			byte <<= 1
+		}
+	}
+
+	if !seenFirstTrue {
+		return nil, nil
+	}
+
+	return bitCurve.affineFromJacobian(x, y, z)
+}
+
+// ScalarBaseMult returns k*G, where G is the base point of the group and k is
+// an integer in big-endian form.
+func (bitCurve *BitCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
+	return bitCurve.ScalarMult(bitCurve.Gx, bitCurve.Gy, k)
+}
+
+var mask = []byte{0xff, 0x1, 0x3, 0x7, 0xf, 0x1f, 0x3f, 0x7f}
+
+//TODO: double check if it is okay
+// GenerateKey returns a public/private key pair. The private key is generated
+// using the given reader, which must return random data.
+func (bitCurve *BitCurve) GenerateKey(rand io.Reader) (priv []byte, x, y *big.Int, err error) {
+	byteLen := (bitCurve.BitSize + 7) >> 3
+	priv = make([]byte, byteLen)
+
+	for x == nil {
+		_, err = io.ReadFull(rand, priv)
+		if err != nil {
+			return
+		}
+		// We have to mask off any excess bits in the case that the size of the
+		// underlying field is not a whole number of bytes.
+		priv[0] &= mask[bitCurve.BitSize%8]
+		// This is because, in tests, rand will return all zeros and we don't
+		// want to get the point at infinity and loop forever.
+		priv[1] ^= 0x42
+		x, y = bitCurve.ScalarBaseMult(priv)
+	}
+	return
+}
+
+// Marshal converts a point into the form specified in section 4.3.6 of ANSI
+// X9.62.
+func (bitCurve *BitCurve) Marshal(x, y *big.Int) []byte {
+	byteLen := (bitCurve.BitSize + 7) >> 3
+
+	ret := make([]byte, 1+2*byteLen)
+	ret[0] = 4 // uncompressed point
+
+	xBytes := x.Bytes()
+	copy(ret[1+byteLen-len(xBytes):], xBytes)
+	yBytes := y.Bytes()
+	copy(ret[1+2*byteLen-len(yBytes):], yBytes)
+	return ret
+}
+
+// Unmarshal converts a point, serialised by Marshal, into an x, y pair. On
+// error, x = nil.
+func (bitCurve *BitCurve) Unmarshal(data []byte) (x, y *big.Int) {
+	byteLen := (bitCurve.BitSize + 7) >> 3
+	if len(data) != 1+2*byteLen {
+		return
+	}
+	if data[0] != 4 { // uncompressed form
+		return
+	}
+	x = new(big.Int).SetBytes(data[1 : 1+byteLen])
+	y = new(big.Int).SetBytes(data[1+byteLen:])
+	return
+}
+
+//curve parameters taken from:
+//http://www.secg.org/collateral/sec2_final.pdf
+
+var initonce sync.Once
+var secp160k1 *BitCurve
+var secp192k1 *BitCurve
+var secp224k1 *BitCurve
+var secp256k1 *BitCurve
+
+func initAll() {
+	initS160()
+	initS192()
+	initS224()
+	initS256()
+}
+
+func initS160() {
+	// See SEC 2 section 2.4.1
+	secp160k1 = new(BitCurve)
+	secp160k1.Name = "secp160k1"
+	secp160k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73", 16)
+	secp160k1.N, _ = new(big.Int).SetString("0100000000000000000001B8FA16DFAB9ACA16B6B3", 16)
+	secp160k1.B, _ = new(big.Int).SetString("0000000000000000000000000000000000000007", 16)
+	secp160k1.Gx, _ = new(big.Int).SetString("3B4C382CE37AA192A4019E763036F4F5DD4D7EBB", 16)
+	secp160k1.Gy, _ = new(big.Int).SetString("938CF935318FDCED6BC28286531733C3F03C4FEE", 16)
+	secp160k1.BitSize = 160
+}
+
+func initS192() {
+	// See SEC 2 section 2.5.1
+	secp192k1 = new(BitCurve)
+	secp192k1.Name = "secp192k1"
+	secp192k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37", 16)
+	secp192k1.N, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D", 16)
+	secp192k1.B, _ = new(big.Int).SetString("000000000000000000000000000000000000000000000003", 16)
+	secp192k1.Gx, _ = new(big.Int).SetString("DB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D", 16)
+	secp192k1.Gy, _ = new(big.Int).SetString("9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D", 16)
+	secp192k1.BitSize = 192
+}
+
+func initS224() {
+	// See SEC 2 section 2.6.1
+	secp224k1 = new(BitCurve)
+	secp224k1.Name = "secp224k1"
+	secp224k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D", 16)
+	secp224k1.N, _ = new(big.Int).SetString("010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7", 16)
+	secp224k1.B, _ = new(big.Int).SetString("00000000000000000000000000000000000000000000000000000005", 16)
+	secp224k1.Gx, _ = new(big.Int).SetString("A1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C", 16)
+	secp224k1.Gy, _ = new(big.Int).SetString("7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5", 16)
+	secp224k1.BitSize = 224
+}
+
+func initS256() {
+	// See SEC 2 section 2.7.1
+	secp256k1 = new(BitCurve)
+	secp256k1.Name = "secp256k1"
+	secp256k1.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", 16)
+	secp256k1.N, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 16)
+	secp256k1.B, _ = new(big.Int).SetString("0000000000000000000000000000000000000000000000000000000000000007", 16)
+	secp256k1.Gx, _ = new(big.Int).SetString("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 16)
+	secp256k1.Gy, _ = new(big.Int).SetString("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 16)
+	secp256k1.BitSize = 256
+}
+
+// S160 returns a BitCurve which implements secp160k1 (see SEC 2 section 2.4.1)
+func S160() *BitCurve {
+	initonce.Do(initAll)
+	return secp160k1
+}
+
+// S192 returns a BitCurve which implements secp192k1 (see SEC 2 section 2.5.1)
+func S192() *BitCurve {
+	initonce.Do(initAll)
+	return secp192k1
+}
+
+// S224 returns a BitCurve which implements secp224k1 (see SEC 2 section 2.6.1)
+func S224() *BitCurve {
+	initonce.Do(initAll)
+	return secp224k1
+}
+
+// S256 returns a BitCurve which implements bitcurves (see SEC 2 section 2.7.1)
+func S256() *BitCurve {
+	initonce.Do(initAll)
+	return secp256k1
+}

vendor/github.com/ProtonMail/go-crypto/brainpool/brainpool.go

@@ -0,0 +1,134 @@
+// Package brainpool implements Brainpool elliptic curves.
+// Implementation of rcurves is from github.com/ebfe/brainpool
+// Note that these curves are implemented with naive, non-constant time operations
+// and are likely not suitable for environments where timing attacks are a concern.
+package brainpool
+
+import (
+	"crypto/elliptic"
+	"math/big"
+	"sync"
+)
+
+var (
+	once                   sync.Once
+	p256t1, p384t1, p512t1 *elliptic.CurveParams
+	p256r1, p384r1, p512r1 *rcurve
+)
+
+func initAll() {
+	initP256t1()
+	initP384t1()
+	initP512t1()
+	initP256r1()
+	initP384r1()
+	initP512r1()
+}
+
+func initP256t1() {
+	p256t1 = &elliptic.CurveParams{Name: "brainpoolP256t1"}
+	p256t1.P, _ = new(big.Int).SetString("A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377", 16)
+	p256t1.N, _ = new(big.Int).SetString("A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7", 16)
+	p256t1.B, _ = new(big.Int).SetString("662C61C430D84EA4FE66A7733D0B76B7BF93EBC4AF2F49256AE58101FEE92B04", 16)
+	p256t1.Gx, _ = new(big.Int).SetString("A3E8EB3CC1CFE7B7732213B23A656149AFA142C47AAFBC2B79A191562E1305F4", 16)
+	p256t1.Gy, _ = new(big.Int).SetString("2D996C823439C56D7F7B22E14644417E69BCB6DE39D027001DABE8F35B25C9BE", 16)
+	p256t1.BitSize = 256
+}
+
+func initP256r1() {
+	twisted := p256t1
+	params := &elliptic.CurveParams{
+		Name:    "brainpoolP256r1",
+		P:       twisted.P,
+		N:       twisted.N,
+		BitSize: twisted.BitSize,
+	}
+	params.Gx, _ = new(big.Int).SetString("8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262", 16)
+	params.Gy, _ = new(big.Int).SetString("547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997", 16)
+	z, _ := new(big.Int).SetString("3E2D4BD9597B58639AE7AA669CAB9837CF5CF20A2C852D10F655668DFC150EF0", 16)
+	p256r1 = newrcurve(twisted, params, z)
+}
+
+func initP384t1() {
+	p384t1 = &elliptic.CurveParams{Name: "brainpoolP384t1"}
+	p384t1.P, _ = new(big.Int).SetString("8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB71123ACD3A729901D1A71874700133107EC53", 16)
+	p384t1.N, _ = new(big.Int).SetString("8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC3103B883202E9046565", 16)
+	p384t1.B, _ = new(big.Int).SetString("7F519EADA7BDA81BD826DBA647910F8C4B9346ED8CCDC64E4B1ABD11756DCE1D2074AA263B88805CED70355A33B471EE", 16)
+	p384t1.Gx, _ = new(big.Int).SetString("18DE98B02DB9A306F2AFCD7235F72A819B80AB12EBD653172476FECD462AABFFC4FF191B946A5F54D8D0AA2F418808CC", 16)
+	p384t1.Gy, _ = new(big.Int).SetString("25AB056962D30651A114AFD2755AD336747F93475B7A1FCA3B88F2B6A208CCFE469408584DC2B2912675BF5B9E582928", 16)
+	p384t1.BitSize = 384
+}
+
+func initP384r1() {
+	twisted := p384t1
+	params := &elliptic.CurveParams{
+		Name:    "brainpoolP384r1",
+		P:       twisted.P,
+		N:       twisted.N,
+		BitSize: twisted.BitSize,
+	}
+	params.Gx, _ = new(big.Int).SetString("1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10E8E826E03436D646AAEF87B2E247D4AF1E", 16)
+	params.Gy, _ = new(big.Int).SetString("8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129280E4646217791811142820341263C5315", 16)
+	z, _ := new(big.Int).SetString("41DFE8DD399331F7166A66076734A89CD0D2BCDB7D068E44E1F378F41ECBAE97D2D63DBC87BCCDDCCC5DA39E8589291C", 16)
+	p384r1 = newrcurve(twisted, params, z)
+}
+
+func initP512t1() {
+	p512t1 = &elliptic.CurveParams{Name: "brainpoolP512t1"}
+	p512t1.P, _ = new(big.Int).SetString("AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3", 16)
+	p512t1.N, _ = new(big.Int).SetString("AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA70330870553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069", 16)
+	p512t1.B, _ = new(big.Int).SetString("7CBBBCF9441CFAB76E1890E46884EAE321F70C0BCB4981527897504BEC3E36A62BCDFA2304976540F6450085F2DAE145C22553B465763689180EA2571867423E", 16)
+	p512t1.Gx, _ = new(big.Int).SetString("640ECE5C12788717B9C1BA06CBC2A6FEBA85842458C56DDE9DB1758D39C0313D82BA51735CDB3EA499AA77A7D6943A64F7A3F25FE26F06B51BAA2696FA9035DA", 16)
+	p512t1.Gy, _ = new(big.Int).SetString("5B534BD595F5AF0FA2C892376C84ACE1BB4E3019B71634C01131159CAE03CEE9D9932184BEEF216BD71DF2DADF86A627306ECFF96DBB8BACE198B61E00F8B332", 16)
+	p512t1.BitSize = 512
+}
+
+func initP512r1() {
+	twisted := p512t1
+	params := &elliptic.CurveParams{
+		Name:    "brainpoolP512r1",
+		P:       twisted.P,
+		N:       twisted.N,
+		BitSize: twisted.BitSize,
+	}
+	params.Gx, _ = new(big.Int).SetString("81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D0098EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822", 16)
+	params.Gy, _ = new(big.Int).SetString("7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F8111B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892", 16)
+	z, _ := new(big.Int).SetString("12EE58E6764838B69782136F0F2D3BA06E27695716054092E60A80BEDB212B64E585D90BCE13761F85C3F1D2A64E3BE8FEA2220F01EBA5EEB0F35DBD29D922AB", 16)
+	p512r1 = newrcurve(twisted, params, z)
+}
+
+// P256t1 returns a Curve which implements Brainpool P256t1 (see RFC 5639, section 3.4)
+func P256t1() elliptic.Curve {
+	once.Do(initAll)
+	return p256t1
+}
+
+// P256r1 returns a Curve which implements Brainpool P256r1 (see RFC 5639, section 3.4)
+func P256r1() elliptic.Curve {
+	once.Do(initAll)
+	return p256r1
+}
+
+// P384t1 returns a Curve which implements Brainpool P384t1 (see RFC 5639, section 3.6)
+func P384t1() elliptic.Curve {
+	once.Do(initAll)
+	return p384t1
+}
+
+// P384r1 returns a Curve which implements Brainpool P384r1 (see RFC 5639, section 3.6)
+func P384r1() elliptic.Curve {
+	once.Do(initAll)
+	return p384r1
+}
+
+// P512t1 returns a Curve which implements Brainpool P512t1 (see RFC 5639, section 3.7)
+func P512t1() elliptic.Curve {
+	once.Do(initAll)
+	return p512t1
+}
+
+// P512r1 returns a Curve which implements Brainpool P512r1 (see RFC 5639, section 3.7)
+func P512r1() elliptic.Curve {
+	once.Do(initAll)
+	return p512r1
+}

vendor/github.com/ProtonMail/go-crypto/brainpool/rcurve.go

@@ -0,0 +1,83 @@
+package brainpool
+
+import (
+	"crypto/elliptic"
+	"math/big"
+)
+
+var _ elliptic.Curve = (*rcurve)(nil)
+
+type rcurve struct {
+	twisted elliptic.Curve
+	params  *elliptic.CurveParams
+	z       *big.Int
+	zinv    *big.Int
+	z2      *big.Int
+	z3      *big.Int
+	zinv2   *big.Int
+	zinv3   *big.Int
+}
+
+var (
+	two   = big.NewInt(2)
+	three = big.NewInt(3)
+)
+
+func newrcurve(twisted elliptic.Curve, params *elliptic.CurveParams, z *big.Int) *rcurve {
+	zinv := new(big.Int).ModInverse(z, params.P)
+	return &rcurve{
+		twisted: twisted,
+		params:  params,
+		z:       z,
+		zinv:    zinv,
+		z2:      new(big.Int).Exp(z, two, params.P),
+		z3:      new(big.Int).Exp(z, three, params.P),
+		zinv2:   new(big.Int).Exp(zinv, two, params.P),
+		zinv3:   new(big.Int).Exp(zinv, three, params.P),
+	}
+}
+
+func (curve *rcurve) toTwisted(x, y *big.Int) (*big.Int, *big.Int) {
+	var tx, ty big.Int
+	tx.Mul(x, curve.z2)
+	tx.Mod(&tx, curve.params.P)
+	ty.Mul(y, curve.z3)
+	ty.Mod(&ty, curve.params.P)
+	return &tx, &ty
+}
+
+func (curve *rcurve) fromTwisted(tx, ty *big.Int) (*big.Int, *big.Int) {
+	var x, y big.Int
+	x.Mul(tx, curve.zinv2)
+	x.Mod(&x, curve.params.P)
+	y.Mul(ty, curve.zinv3)
+	y.Mod(&y, curve.params.P)
+	return &x, &y
+}
+
+func (curve *rcurve) Params() *elliptic.CurveParams {
+	return curve.params
+}
+
+func (curve *rcurve) IsOnCurve(x, y *big.Int) bool {
+	return curve.twisted.IsOnCurve(curve.toTwisted(x, y))
+}
+
+func (curve *rcurve) Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int) {
+	tx1, ty1 := curve.toTwisted(x1, y1)
+	tx2, ty2 := curve.toTwisted(x2, y2)
+	return curve.fromTwisted(curve.twisted.Add(tx1, ty1, tx2, ty2))
+}
+
+func (curve *rcurve) Double(x1, y1 *big.Int) (x, y *big.Int) {
+	return curve.fromTwisted(curve.twisted.Double(curve.toTwisted(x1, y1)))
+}
+
+func (curve *rcurve) ScalarMult(x1, y1 *big.Int, scalar []byte) (x, y *big.Int) {
+	tx1, ty1 := curve.toTwisted(x1, y1)
+	return curve.fromTwisted(curve.twisted.ScalarMult(tx1, ty1, scalar))
+}
+
+func (curve *rcurve) ScalarBaseMult(scalar []byte) (x, y *big.Int) {
+	return curve.fromTwisted(curve.twisted.ScalarBaseMult(scalar))
+}

vendor/github.com/ProtonMail/go-crypto/eax/eax.go

@@ -0,0 +1,162 @@
+// Copyright (C) 2019 ProtonTech AG
+
+// Package eax provides an implementation of the EAX
+// (encrypt-authenticate-translate) mode of operation, as described in
+// Bellare, Rogaway, and Wagner "THE EAX MODE OF OPERATION: A TWO-PASS
+// AUTHENTICATED-ENCRYPTION SCHEME OPTIMIZED FOR SIMPLICITY AND EFFICIENCY."
+// In FSE'04, volume 3017 of LNCS, 2004
+package eax
+
+import (
+	"crypto/cipher"
+	"crypto/subtle"
+	"errors"
+	"github.com/ProtonMail/go-crypto/internal/byteutil"
+)
+
+const (
+	defaultTagSize   = 16
+	defaultNonceSize = 16
+)
+
+type eax struct {
+	block     cipher.Block // Only AES-{128, 192, 256} supported
+	tagSize   int          // At least 12 bytes recommended
+	nonceSize int
+}
+
+func (e *eax) NonceSize() int {
+	return e.nonceSize
+}
+
+func (e *eax) Overhead() int {
+	return e.tagSize
+}
+
+// NewEAX returns an EAX instance with AES-{KEYLENGTH} and default nonce and
+// tag lengths. Supports {128, 192, 256}- bit key length.
+func NewEAX(block cipher.Block) (cipher.AEAD, error) {
+	return NewEAXWithNonceAndTagSize(block, defaultNonceSize, defaultTagSize)
+}
+
+// NewEAXWithNonceAndTagSize returns an EAX instance with AES-{keyLength} and
+// given nonce and tag lengths in bytes. Panics on zero nonceSize and
+// exceedingly long tags.
+//
+// It is recommended to use at least 12 bytes as tag length (see, for instance,
+// NIST SP 800-38D).
+//
+// Only to be used for compatibility with existing cryptosystems with
+// non-standard parameters. For all other cases, prefer NewEAX.
+func NewEAXWithNonceAndTagSize(
+	block cipher.Block, nonceSize, tagSize int) (cipher.AEAD, error) {
+	if nonceSize < 1 {
+		return nil, eaxError("Cannot initialize EAX with nonceSize = 0")
+	}
+	if tagSize > block.BlockSize() {
+		return nil, eaxError("Custom tag length exceeds blocksize")
+	}
+	return &eax{
+		block:     block,
+		tagSize:   tagSize,
+		nonceSize: nonceSize,
+	}, nil
+}
+
+func (e *eax) Seal(dst, nonce, plaintext, adata []byte) []byte {
+	if len(nonce) > e.nonceSize {
+		panic("crypto/eax: Nonce too long for this instance")
+	}
+	ret, out := byteutil.SliceForAppend(dst, len(plaintext) + e.tagSize)
+	omacNonce := e.omacT(0, nonce)
+	omacAdata := e.omacT(1, adata)
+
+	// Encrypt message using CTR mode and omacNonce as IV
+	ctr := cipher.NewCTR(e.block, omacNonce)
+	ciphertextData := out[:len(plaintext)]
+	ctr.XORKeyStream(ciphertextData, plaintext)
+
+	omacCiphertext := e.omacT(2, ciphertextData)
+
+	tag := out[len(plaintext):]
+	for i := 0; i < e.tagSize; i++ {
+		tag[i] = omacCiphertext[i] ^ omacNonce[i] ^ omacAdata[i]
+	}
+	return ret
+}
+
+func (e* eax) Open(dst, nonce, ciphertext, adata []byte) ([]byte, error) {
+	if len(nonce) > e.nonceSize {
+		panic("crypto/eax: Nonce too long for this instance")
+	}
+	if len(ciphertext) < e.tagSize {
+		return nil, eaxError("Ciphertext shorter than tag length")
+	}
+	sep := len(ciphertext) - e.tagSize
+
+	// Compute tag
+	omacNonce := e.omacT(0, nonce)
+	omacAdata := e.omacT(1, adata)
+	omacCiphertext := e.omacT(2, ciphertext[:sep])
+
+	tag := make([]byte, e.tagSize)
+	for i := 0; i < e.tagSize; i++ {
+		tag[i] = omacCiphertext[i] ^ omacNonce[i] ^ omacAdata[i]
+	}
+
+	// Compare tags
+	if subtle.ConstantTimeCompare(ciphertext[sep:], tag) != 1 {
+		return nil, eaxError("Tag authentication failed")
+	}
+
+	// Decrypt ciphertext
+	ret, out := byteutil.SliceForAppend(dst, len(ciphertext))
+	ctr := cipher.NewCTR(e.block, omacNonce)
+	ctr.XORKeyStream(out, ciphertext[:sep])
+
+	return ret[:sep], nil
+}
+
+// Tweakable OMAC - Calls OMAC_K([t]_n || plaintext)
+func (e *eax) omacT(t byte, plaintext []byte) []byte {
+	blockSize := e.block.BlockSize()
+	byteT := make([]byte, blockSize)
+	byteT[blockSize-1] = t
+	concat := append(byteT, plaintext...)
+	return e.omac(concat)
+}
+
+func (e *eax) omac(plaintext []byte) []byte {
+	blockSize := e.block.BlockSize()
+	// L ← E_K(0^n); B ← 2L; P ← 4L
+	L := make([]byte, blockSize)
+	e.block.Encrypt(L, L)
+	B := byteutil.GfnDouble(L)
+	P := byteutil.GfnDouble(B)
+
+	// CBC with IV = 0
+	cbc := cipher.NewCBCEncrypter(e.block, make([]byte, blockSize))
+	padded := e.pad(plaintext, B, P)
+	cbcCiphertext := make([]byte, len(padded))
+	cbc.CryptBlocks(cbcCiphertext, padded)
+
+	return cbcCiphertext[len(cbcCiphertext)-blockSize:]
+}
+
+func (e *eax) pad(plaintext, B, P []byte) []byte {
+	// if |M| in {n, 2n, 3n, ...}
+	blockSize := e.block.BlockSize()
+	if len(plaintext) != 0 && len(plaintext)%blockSize == 0 {
+		return byteutil.RightXor(plaintext, B)
+	}
+
+	// else return (M || 1 || 0^(n−1−(|M| % n))) xor→ P
+	ending := make([]byte, blockSize-len(plaintext)%blockSize)
+	ending[0] = 0x80
+	padded := append(plaintext, ending...)
+	return byteutil.RightXor(padded, P)
+}
+
+func eaxError(err string) error {
+	return errors.New("crypto/eax: " + err)
+}

vendor/github.com/ProtonMail/go-crypto/eax/eax_test_vectors.go

@@ -0,0 +1,58 @@
+package eax
+
+// Test vectors from
+// https://web.cs.ucdavis.edu/~rogaway/papers/eax.pdf
+var testVectors = []struct {
+	msg, key, nonce, header, ciphertext string
+}{
+	{"",
+		"233952DEE4D5ED5F9B9C6D6FF80FF478",
+		"62EC67F9C3A4A407FCB2A8C49031A8B3",
+		"6BFB914FD07EAE6B",
+		"E037830E8389F27B025A2D6527E79D01"},
+	{"F7FB",
+		"91945D3F4DCBEE0BF45EF52255F095A4",
+		"BECAF043B0A23D843194BA972C66DEBD",
+		"FA3BFD4806EB53FA",
+		"19DD5C4C9331049D0BDAB0277408F67967E5"},
+	{"1A47CB4933",
+		"01F74AD64077F2E704C0F60ADA3DD523",
+		"70C3DB4F0D26368400A10ED05D2BFF5E",
+		"234A3463C1264AC6",
+		"D851D5BAE03A59F238A23E39199DC9266626C40F80"},
+	{"481C9E39B1",
+		"D07CF6CBB7F313BDDE66B727AFD3C5E8",
+		"8408DFFF3C1A2B1292DC199E46B7D617",
+		"33CCE2EABFF5A79D",
+		"632A9D131AD4C168A4225D8E1FF755939974A7BEDE"},
+	{"40D0C07DA5E4",
+		"35B6D0580005BBC12B0587124557D2C2",
+		"FDB6B06676EEDC5C61D74276E1F8E816",
+		"AEB96EAEBE2970E9",
+		"071DFE16C675CB0677E536F73AFE6A14B74EE49844DD"},
+	{"4DE3B35C3FC039245BD1FB7D",
+		"BD8E6E11475E60B268784C38C62FEB22",
+		"6EAC5C93072D8E8513F750935E46DA1B",
+		"D4482D1CA78DCE0F",
+		"835BB4F15D743E350E728414ABB8644FD6CCB86947C5E10590210A4F"},
+	{"8B0A79306C9CE7ED99DAE4F87F8DD61636",
+		"7C77D6E813BED5AC98BAA417477A2E7D",
+		"1A8C98DCD73D38393B2BF1569DEEFC19",
+		"65D2017990D62528",
+		"02083E3979DA014812F59F11D52630DA30137327D10649B0AA6E1C181DB617D7F2"},
+	{"1BDA122BCE8A8DBAF1877D962B8592DD2D56",
+		"5FFF20CAFAB119CA2FC73549E20F5B0D",
+		"DDE59B97D722156D4D9AFF2BC7559826",
+		"54B9F04E6A09189A",
+		"2EC47B2C4954A489AFC7BA4897EDCDAE8CC33B60450599BD02C96382902AEF7F832A"},
+	{"6CF36720872B8513F6EAB1A8A44438D5EF11",
+		"A4A4782BCFFD3EC5E7EF6D8C34A56123",
+		"B781FCF2F75FA5A8DE97A9CA48E522EC",
+		"899A175897561D7E",
+		"0DE18FD0FDD91E7AF19F1D8EE8733938B1E8E7F6D2231618102FDB7FE55FF1991700"},
+	{"CA40D7446E545FFAED3BD12A740A659FFBBB3CEAB7",
+		"8395FCF1E95BEBD697BD010BC766AAC3",
+		"22E7ADD93CFC6393C57EC0B3C17D6B44",
+		"126735FCC320D25A",
+		"CB8920F87A6C75CFF39627B56E3ED197C552D295A7CFC46AFC253B4652B1AF3795B124AB6E"},
+}

vendor/github.com/ProtonMail/go-crypto/eax/random_vectors.go

@@ -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"},
+}

vendor/github.com/ProtonMail/go-crypto/internal/byteutil/byteutil.go

@@ -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
+}
+

vendor/github.com/ProtonMail/go-crypto/ocb/ocb.go

@@ -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)
+}

vendor/github.com/ProtonMail/go-crypto/ocb/random_vectors.go

@@ -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"},
+}

vendor/github.com/ProtonMail/go-crypto/ocb/rfc7253_test_vectors_suite_a.go

@@ -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"},
+}

vendor/github.com/ProtonMail/go-crypto/ocb/rfc7253_test_vectors_suite_b.go

@@ -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"},
+	}

vendor/github.com/ProtonMail/go-crypto/openpgp/aes/keywrap/keywrap.go

@@ -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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/armor/armor.go

@@ -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.
-//
+package armor // import "github.com/ProtonMail/go-crypto/openpgp/armor"
-// 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"
 
 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
 	}
 

vendor/github.com/ProtonMail/go-crypto/openpgp/armor/encode.go

@@ -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

vendor/github.com/ProtonMail/go-crypto/openpgp/canonical_text.go

@@ -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])
+				cw.Write(buf[start:i])
-				cth.h.Write(newline)
+				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)
 }

vendor/github.com/ProtonMail/go-crypto/openpgp/ecdh/ecdh.go

@@ -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)
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/ecdsa/ecdsa.go

@@ -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())
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/eddsa/eddsa.go

@@ -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)
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/elgamal/elgamal.go

@@ -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.
-//
+package elgamal // import "github.com/ProtonMail/go-crypto/openpgp/elgamal"
-// 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"
 
 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
+// be used to break the cryptosystem.  See ``Chosen Ciphertext Attacks
-// Against Protocols Based on the RSA Encryption Standard PKCS #1”, Daniel
+// 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)

vendor/github.com/ProtonMail/go-crypto/openpgp/errors/errors.go

@@ -3,13 +3,7 @@
 // license that can be found in the LICENSE file.
 
 // Package errors contains common error types for the OpenPGP packages.
-//
+package errors // import "github.com/ProtonMail/go-crypto/openpgp/errors"
-// 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"
 
 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)
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/aead.go

@@ -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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/cipher.go

@@ -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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/algorithm/hash.go

@@ -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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curve25519.go

@@ -0,0 +1,171 @@
+// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
+package ecc
+
+import (
+	"crypto/subtle"
+	"io"
+
+	"github.com/ProtonMail/go-crypto/openpgp/errors"
+	x25519lib "github.com/cloudflare/circl/dh/x25519"
+)
+
+type curve25519 struct {}
+
+func NewCurve25519() *curve25519 {
+	return &curve25519{}
+}
+
+func (c *curve25519) GetCurveName() string {
+	return "curve25519"
+}
+
+// MarshalBytePoint encodes the public point from native format, adding the prefix.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6
+func (c *curve25519) MarshalBytePoint(point [] byte) []byte {
+	return append([]byte{0x40}, point...)
+}
+
+// UnmarshalBytePoint decodes the public point to native format, removing the prefix.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6
+func (c *curve25519) UnmarshalBytePoint(point []byte) []byte {
+	if len(point) != x25519lib.Size + 1 {
+		return nil
+	}
+
+	// Remove prefix
+	return point[1:]
+}
+
+// MarshalByteSecret encodes the secret scalar from native format.
+// Note that the EC secret scalar differs from the definition of public keys in
+// [Curve25519] in two ways: (1) the byte-ordering is big-endian, which is
+// more uniform with how big integers are represented in OpenPGP, and (2) the
+// leading zeros are truncated.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6.1.1
+// Note that leading zero bytes are stripped later when encoding as an MPI.
+func (c *curve25519) MarshalByteSecret(secret []byte) []byte {
+	d := make([]byte, x25519lib.Size)
+	copyReversed(d, secret)
+
+	// The following ensures that the private key is a number of the form
+	// 2^{254} + 8 * [0, 2^{251}), in order to avoid the small subgroup of
+	// the curve.
+	//
+	// This masking is done internally in the underlying lib and so is unnecessary
+	// for security, but OpenPGP implementations require that private keys be
+	// pre-masked.
+	d[0] &= 127
+	d[0] |= 64
+	d[31] &= 248
+
+	return d
+}
+
+// UnmarshalByteSecret decodes the secret scalar from native format.
+// Note that the EC secret scalar differs from the definition of public keys in
+// [Curve25519] in two ways: (1) the byte-ordering is big-endian, which is
+// more uniform with how big integers are represented in OpenPGP, and (2) the
+// leading zeros are truncated.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.6.1.1
+func (c *curve25519) UnmarshalByteSecret(d []byte) []byte {
+	if len(d) > x25519lib.Size {
+		return nil
+	}
+
+	// Ensure truncated leading bytes are re-added
+	secret := make([]byte, x25519lib.Size)
+	copyReversed(secret, d)
+
+	return secret
+}
+
+// generateKeyPairBytes Generates a private-public key-pair.
+// 'priv' is a private key; a little-endian scalar belonging to the set
+// 2^{254} + 8 * [0, 2^{251}), in order to avoid the small subgroup of the
+// curve. 'pub' is simply 'priv' * G where G is the base point.
+// See https://cr.yp.to/ecdh.html and RFC7748, sec 5.
+func (c *curve25519) generateKeyPairBytes(rand io.Reader) (priv, pub x25519lib.Key, err error) {
+	_, err = io.ReadFull(rand, priv[:])
+	if err != nil {
+		return
+	}
+
+	x25519lib.KeyGen(&pub, &priv)
+	return
+}
+
+func (c *curve25519) GenerateECDH(rand io.Reader) (point []byte, secret []byte, err error) {
+	priv, pub, err := c.generateKeyPairBytes(rand)
+	if err != nil {
+		return
+	}
+
+	return pub[:], priv[:], nil
+}
+
+func (c *genericCurve) MaskSecret(secret []byte) []byte {
+	return secret
+}
+
+func (c *curve25519) Encaps(rand io.Reader, point []byte) (ephemeral, sharedSecret []byte, err error) {
+	// RFC6637 §8: "Generate an ephemeral key pair {v, V=vG}"
+	// ephemeralPrivate corresponds to `v`.
+	// ephemeralPublic corresponds to `V`.
+	ephemeralPrivate, ephemeralPublic, err := c.generateKeyPairBytes(rand)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// RFC6637 §8: "Obtain the authenticated recipient public key R"
+	// pubKey corresponds to `R`.
+	var pubKey x25519lib.Key
+	copy(pubKey[:], point)
+
+	// RFC6637 §8: "Compute the shared point S = vR"
+	//	"VB = convert point V to the octet string"
+	// sharedPoint corresponds to `VB`.
+	var sharedPoint x25519lib.Key
+	x25519lib.Shared(&sharedPoint, &ephemeralPrivate, &pubKey)
+
+	return ephemeralPublic[:], sharedPoint[:], nil
+}
+
+func (c *curve25519) Decaps(vsG, secret []byte) (sharedSecret []byte, err error) {
+	var ephemeralPublic, decodedPrivate, sharedPoint x25519lib.Key
+	// RFC6637 §8: "The decryption is the inverse of the method given."
+	// All quoted descriptions in comments below describe encryption, and
+	// the reverse is performed.
+	// vsG corresponds to `VB` in RFC6637 §8 .
+
+	// RFC6637 §8: "VB = convert point V to the octet string"
+	copy(ephemeralPublic[:], vsG)
+
+	// decodedPrivate corresponds to `r` in RFC6637 §8 .
+	copy(decodedPrivate[:], secret)
+
+	// RFC6637 §8: "Note that the recipient obtains the shared secret by calculating
+	//   S = rV = rvG, where (r,R) is the recipient's key pair."
+	// sharedPoint corresponds to `S`.
+	x25519lib.Shared(&sharedPoint, &decodedPrivate, &ephemeralPublic)
+
+	return sharedPoint[:], nil
+}
+
+func (c *curve25519) ValidateECDH(point []byte, secret []byte) (err error) {
+	var pk, sk x25519lib.Key
+	copy(sk[:], secret)
+	x25519lib.KeyGen(&pk, &sk)
+
+	if subtle.ConstantTimeCompare(point, pk[:]) == 0 {
+		return errors.KeyInvalidError("ecc: invalid curve25519 public point")
+	}
+
+	return nil
+}
+
+func copyReversed(out []byte, in []byte) {
+	l := len(in)
+	for i := 0; i < l; i++ {
+		out[i] = in[l-i-1]
+	}
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curve_info.go

@@ -0,0 +1,140 @@
+// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
+package ecc
+
+import (
+	"bytes"
+	"crypto/elliptic"
+	"github.com/ProtonMail/go-crypto/bitcurves"
+	"github.com/ProtonMail/go-crypto/brainpool"
+	"github.com/ProtonMail/go-crypto/openpgp/internal/encoding"
+)
+
+type CurveInfo struct {
+	GenName string
+	Oid *encoding.OID
+	Curve Curve
+}
+
+var Curves = []CurveInfo{
+	{
+		// NIST P-256
+		GenName: "P256",
+		Oid: encoding.NewOID([]byte{0x2A, 0x86, 0x48, 0xCE, 0x3D, 0x03, 0x01, 0x07}),
+		Curve: NewGenericCurve(elliptic.P256()),
+	},
+	{
+		// NIST P-384
+		GenName: "P384",
+		Oid: encoding.NewOID([]byte{0x2B, 0x81, 0x04, 0x00, 0x22}),
+		Curve: NewGenericCurve(elliptic.P384()),
+	},
+	{
+		// NIST P-521
+		GenName: "P521",
+		Oid: encoding.NewOID([]byte{0x2B, 0x81, 0x04, 0x00, 0x23}),
+		Curve: NewGenericCurve(elliptic.P521()),
+	},
+	{
+		// SecP256k1
+		GenName: "SecP256k1",
+		Oid: encoding.NewOID([]byte{0x2B, 0x81, 0x04, 0x00, 0x0A}),
+		Curve: NewGenericCurve(bitcurves.S256()),
+	},
+	{
+		// Curve25519
+		GenName: "Curve25519",
+		Oid: encoding.NewOID([]byte{0x2B, 0x06, 0x01, 0x04, 0x01, 0x97, 0x55, 0x01, 0x05, 0x01}),
+		Curve: NewCurve25519(),
+	},
+	{
+		// X448
+		GenName: "Curve448",
+		Oid: encoding.NewOID([]byte{0x2B, 0x65, 0x6F}),
+		Curve: NewX448(),
+	},
+	{
+		// Ed25519
+		GenName: "Curve25519",
+		Oid: encoding.NewOID([]byte{0x2B, 0x06, 0x01, 0x04, 0x01, 0xDA, 0x47, 0x0F, 0x01}),
+		Curve: NewEd25519(),
+	},
+	{
+		// Ed448
+		GenName: "Curve448",
+		Oid: encoding.NewOID([]byte{0x2B, 0x65, 0x71}),
+		Curve: NewEd448(),
+	},
+	{
+		// BrainpoolP256r1
+		GenName: "BrainpoolP256",
+		Oid: encoding.NewOID([]byte{0x2B, 0x24, 0x03, 0x03, 0x02, 0x08, 0x01, 0x01, 0x07}),
+		Curve: NewGenericCurve(brainpool.P256r1()),
+	},
+	{
+		// BrainpoolP384r1
+		GenName: "BrainpoolP384",
+		Oid: encoding.NewOID([]byte{0x2B, 0x24, 0x03, 0x03, 0x02, 0x08, 0x01, 0x01, 0x0B}),
+		Curve: NewGenericCurve(brainpool.P384r1()),
+	},
+	{
+		// BrainpoolP512r1
+		GenName: "BrainpoolP512",
+		Oid: encoding.NewOID([]byte{0x2B, 0x24, 0x03, 0x03, 0x02, 0x08, 0x01, 0x01, 0x0D}),
+		Curve: NewGenericCurve(brainpool.P512r1()),
+	},
+}
+
+func FindByCurve(curve Curve) *CurveInfo {
+	for _, curveInfo := range Curves {
+		if curveInfo.Curve.GetCurveName() == curve.GetCurveName() {
+			return &curveInfo
+		}
+	}
+	return nil
+}
+
+func FindByOid(oid encoding.Field) *CurveInfo {
+	var rawBytes = oid.Bytes()
+	for _, curveInfo := range Curves {
+		if bytes.Equal(curveInfo.Oid.Bytes(), rawBytes) {
+			return &curveInfo
+		}
+	}
+	return nil
+}
+
+func FindEdDSAByGenName(curveGenName string) EdDSACurve {
+	for _, curveInfo := range Curves {
+		if curveInfo.GenName == curveGenName {
+			curve, ok := curveInfo.Curve.(EdDSACurve)
+			if ok {
+				return curve
+			}
+		}
+	}
+	return nil
+}
+
+func FindECDSAByGenName(curveGenName string) ECDSACurve {
+	for _, curveInfo := range Curves {
+		if curveInfo.GenName == curveGenName {
+			curve, ok := curveInfo.Curve.(ECDSACurve)
+			if ok {
+				return curve
+			}
+		}
+	}
+	return nil
+}
+
+func FindECDHByGenName(curveGenName string) ECDHCurve {
+	for _, curveInfo := range Curves {
+		if curveInfo.GenName == curveGenName {
+			curve, ok := curveInfo.Curve.(ECDHCurve)
+			if ok {
+				return curve
+			}
+		}
+	}
+	return nil
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/curves.go

@@ -0,0 +1,48 @@
+// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
+package ecc
+
+import (
+	"io"
+	"math/big"
+)
+
+type Curve interface {
+	GetCurveName() string
+}
+
+type ECDSACurve interface {
+	Curve
+	MarshalIntegerPoint(x, y *big.Int) []byte
+	UnmarshalIntegerPoint([]byte) (x, y *big.Int)
+	MarshalIntegerSecret(d *big.Int) []byte
+	UnmarshalIntegerSecret(d []byte) *big.Int
+	GenerateECDSA(rand io.Reader) (x, y, secret *big.Int, err error)
+	Sign(rand io.Reader, x, y, d *big.Int, hash []byte) (r, s *big.Int, err error)
+	Verify(x, y *big.Int, hash []byte, r, s *big.Int) bool
+	ValidateECDSA(x, y *big.Int, secret []byte) error
+}
+
+type EdDSACurve interface {
+	Curve
+	MarshalBytePoint(x []byte) []byte
+	UnmarshalBytePoint([]byte) (x []byte)
+	MarshalByteSecret(d []byte) []byte
+	UnmarshalByteSecret(d []byte) []byte
+	MarshalSignature(sig []byte) (r, s []byte)
+	UnmarshalSignature(r, s []byte) (sig []byte)
+	GenerateEdDSA(rand io.Reader) (pub, priv []byte, err error)
+	Sign(publicKey, privateKey, message []byte) (sig []byte, err error)
+	Verify(publicKey, message, sig []byte) bool
+	ValidateEdDSA(publicKey, privateKey []byte) (err error)
+}
+type ECDHCurve interface {
+	Curve
+	MarshalBytePoint([]byte) (encoded []byte)
+	UnmarshalBytePoint(encoded []byte) ([]byte)
+	MarshalByteSecret(d []byte) []byte
+	UnmarshalByteSecret(d []byte) []byte
+	GenerateECDH(rand io.Reader) (point []byte, secret []byte, err error)
+	Encaps(rand io.Reader, point []byte) (ephemeral, sharedSecret []byte, err error)
+	Decaps(ephemeral, secret []byte) (sharedSecret []byte, err error)
+	ValidateECDH(public []byte, secret []byte) error
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/ed25519.go

@@ -0,0 +1,111 @@
+// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
+package ecc
+
+import (
+	"crypto/subtle"
+	"io"
+
+	"github.com/ProtonMail/go-crypto/openpgp/errors"
+	ed25519lib "github.com/cloudflare/circl/sign/ed25519"
+)
+
+const ed25519Size = 32
+type ed25519 struct {}
+
+func NewEd25519() *ed25519 {
+	return &ed25519{}
+}
+
+func (c *ed25519) GetCurveName() string {
+	return "ed25519"
+}
+
+// MarshalBytePoint encodes the public point from native format, adding the prefix.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
+func (c *ed25519) MarshalBytePoint(x []byte) []byte {
+	return append([]byte{0x40}, x...)
+}
+
+// UnmarshalBytePoint decodes a point from prefixed format to native.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
+func (c *ed25519) UnmarshalBytePoint(point []byte) (x []byte) {
+	if len(point) != ed25519lib.PublicKeySize + 1 {
+		return nil
+	}
+
+	// Return unprefixed
+	return point[1:]
+}
+
+// MarshalByteSecret encodes a scalar in native format.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
+func (c *ed25519) MarshalByteSecret(d []byte) []byte {
+	return d
+}
+
+// UnmarshalByteSecret decodes a scalar in native format and re-adds the stripped leading zeroes
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
+func (c *ed25519) UnmarshalByteSecret(s []byte) (d []byte) {
+	if len(s) > ed25519lib.SeedSize {
+		return nil
+	}
+
+	// Handle stripped leading zeroes
+	d = make([]byte, ed25519lib.SeedSize)
+	copy(d[ed25519lib.SeedSize - len(s):], s)
+	return
+}
+
+// MarshalSignature splits a signature in R and S.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.2.3.3.1
+func (c *ed25519) MarshalSignature(sig []byte) (r, s []byte) {
+	return sig[:ed25519Size], sig[ed25519Size:]
+}
+
+// UnmarshalSignature decodes R and S in the native format, re-adding the stripped leading zeroes
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.2.3.3.1
+func (c *ed25519) UnmarshalSignature(r, s []byte) (sig []byte) {
+	// Check size
+	if len(r) > 32 || len(s) > 32 {
+		return nil
+	}
+
+	sig = make([]byte, ed25519lib.SignatureSize)
+
+	// Handle stripped leading zeroes
+	copy(sig[ed25519Size-len(r):ed25519Size], r)
+	copy(sig[ed25519lib.SignatureSize-len(s):], s)
+	return sig
+}
+
+func (c *ed25519) GenerateEdDSA(rand io.Reader) (pub, priv []byte, err error) {
+	pk, sk, err := ed25519lib.GenerateKey(rand)
+
+	if err != nil {
+		return nil, nil, err
+	}
+
+	return pk, sk[:ed25519lib.SeedSize], nil
+}
+
+func getEd25519Sk(publicKey, privateKey []byte) ed25519lib.PrivateKey {
+	return append(privateKey, publicKey...)
+}
+
+func (c *ed25519) Sign(publicKey, privateKey, message []byte) (sig []byte, err error) {
+	sig = ed25519lib.Sign(getEd25519Sk(publicKey, privateKey), message)
+	return sig, nil
+}
+
+func (c *ed25519) Verify(publicKey, message, sig []byte) bool {
+	return ed25519lib.Verify(publicKey, message, sig)
+}
+
+func (c *ed25519) ValidateEdDSA(publicKey, privateKey []byte) (err error) {
+	priv := getEd25519Sk(publicKey, privateKey)
+	expectedPriv := ed25519lib.NewKeyFromSeed(priv.Seed())
+	if subtle.ConstantTimeCompare(priv, expectedPriv) == 0 {
+		return errors.KeyInvalidError("ecc: invalid ed25519 secret")
+	}
+	return nil
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/ed448.go

@@ -0,0 +1,111 @@
+// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
+package ecc
+
+import (
+	"crypto/subtle"
+	"io"
+
+	"github.com/ProtonMail/go-crypto/openpgp/errors"
+	ed448lib "github.com/cloudflare/circl/sign/ed448"
+)
+
+type ed448 struct {}
+
+func NewEd448() *ed448 {
+	return &ed448{}
+}
+
+func (c *ed448) GetCurveName() string {
+	return "ed448"
+}
+
+// MarshalBytePoint encodes the public point from native format, adding the prefix.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
+func (c *ed448) MarshalBytePoint(x []byte) []byte {
+	// Return prefixed
+	return append([]byte{0x40}, x...)
+}
+
+// UnmarshalBytePoint decodes a point from prefixed format to native.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
+func (c *ed448) UnmarshalBytePoint(point []byte) (x []byte) {
+	if len(point) != ed448lib.PublicKeySize + 1 {
+		return nil
+	}
+
+	// Strip prefix
+	return point[1:]
+}
+
+// MarshalByteSecret encoded a scalar from native format to prefixed.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
+func (c *ed448) MarshalByteSecret(d []byte) []byte {
+	// Return prefixed
+	return append([]byte{0x40}, d...)
+}
+
+// UnmarshalByteSecret decodes a scalar from prefixed format to native.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.5.5.5
+func (c *ed448) UnmarshalByteSecret(s []byte) (d []byte) {
+	// Check prefixed size
+	if len(s) != ed448lib.SeedSize + 1 {
+		return nil
+	}
+
+	// Strip prefix
+	return s[1:]
+}
+
+// MarshalSignature splits a signature in R and S, where R is in prefixed native format and
+// S is an MPI with value zero.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.2.3.3.2
+func (c *ed448) MarshalSignature(sig []byte) (r, s []byte) {
+	return append([]byte{0x40}, sig...), []byte{}
+}
+
+// UnmarshalSignature decodes R and S in the native format. Only R is used, in prefixed native format.
+// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-5.2.3.3.2
+func (c *ed448) UnmarshalSignature(r, s []byte) (sig []byte) {
+	if len(r) != ed448lib.SignatureSize + 1 {
+		return nil
+	}
+
+	return r[1:]
+}
+
+func (c *ed448) GenerateEdDSA(rand io.Reader) (pub, priv []byte, err error) {
+	pk, sk, err := ed448lib.GenerateKey(rand)
+
+	if err != nil {
+		return nil, nil, err
+	}
+
+	return pk, sk[:ed448lib.SeedSize], nil
+}
+
+func getEd448Sk(publicKey, privateKey []byte) ed448lib.PrivateKey {
+	return append(privateKey, publicKey...)
+}
+
+func (c *ed448) Sign(publicKey, privateKey, message []byte) (sig []byte, err error) {
+	// Ed448 is used with the empty string as a context string.
+	// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-13.7
+	sig = ed448lib.Sign(getEd448Sk(publicKey, privateKey), message, "")
+
+	return sig, nil
+}
+
+func (c *ed448) Verify(publicKey, message, sig []byte) bool {
+	// Ed448 is used with the empty string as a context string.
+	// See https://datatracker.ietf.org/doc/html/draft-ietf-openpgp-crypto-refresh-06#section-13.7
+	return ed448lib.Verify(publicKey, message, sig, "")
+}
+
+func (c *ed448) ValidateEdDSA(publicKey, privateKey []byte) (err error) {
+	priv := getEd448Sk(publicKey, privateKey)
+	expectedPriv := ed448lib.NewKeyFromSeed(priv.Seed())
+	if subtle.ConstantTimeCompare(priv, expectedPriv) == 0 {
+		return errors.KeyInvalidError("ecc: invalid ed448 secret")
+	}
+	return nil
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/generic.go

@@ -0,0 +1,149 @@
+// Package ecc implements a generic interface for ECDH, ECDSA, and EdDSA.
+package ecc
+
+import (
+	"crypto/ecdsa"
+	"crypto/elliptic"
+	"fmt"
+	"github.com/ProtonMail/go-crypto/openpgp/errors"
+	"io"
+	"math/big"
+)
+
+type genericCurve struct {
+	Curve elliptic.Curve
+}
+
+func NewGenericCurve(c elliptic.Curve) *genericCurve {
+	return &genericCurve{
+		Curve: c,
+	}
+}
+
+func (c *genericCurve) GetCurveName() string {
+	return c.Curve.Params().Name
+}
+
+func (c *genericCurve) MarshalBytePoint(point []byte) []byte {
+	return point
+}
+
+func (c *genericCurve) UnmarshalBytePoint(point []byte) []byte {
+	return point
+}
+
+func (c *genericCurve) MarshalIntegerPoint(x, y *big.Int) []byte {
+	return elliptic.Marshal(c.Curve, x, y)
+}
+
+func (c *genericCurve) UnmarshalIntegerPoint(point []byte) (x, y *big.Int) {
+	return elliptic.Unmarshal(c.Curve, point)
+}
+
+func (c *genericCurve) MarshalByteSecret(d []byte) []byte {
+	return d
+}
+
+func (c *genericCurve) UnmarshalByteSecret(d []byte) []byte {
+	return d
+}
+
+func (c *genericCurve) MarshalIntegerSecret(d *big.Int) []byte {
+	return d.Bytes()
+}
+
+func (c *genericCurve) UnmarshalIntegerSecret(d []byte) *big.Int {
+	return new(big.Int).SetBytes(d)
+}
+
+func (c *genericCurve) GenerateECDH(rand io.Reader) (point, secret []byte, err error) {
+	secret, x, y, err := elliptic.GenerateKey(c.Curve, rand)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	point = elliptic.Marshal(c.Curve, x, y)
+	return point, secret, nil
+}
+
+func (c *genericCurve) GenerateECDSA(rand io.Reader) (x, y, secret *big.Int, err error) {
+	priv, err := ecdsa.GenerateKey(c.Curve, rand)
+	if err != nil {
+		return
+	}
+
+	return priv.X, priv.Y, priv.D, nil
+}
+
+func (c *genericCurve) Encaps(rand io.Reader, point []byte) (ephemeral, sharedSecret []byte, err error) {
+	xP, yP := elliptic.Unmarshal(c.Curve, point)
+	if xP == nil {
+		panic("invalid point")
+	}
+
+	d, x, y, err := elliptic.GenerateKey(c.Curve, rand)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	vsG := elliptic.Marshal(c.Curve, x, y)
+	zbBig, _ := c.Curve.ScalarMult(xP, yP, d)
+
+	byteLen := (c.Curve.Params().BitSize + 7) >> 3
+	zb := make([]byte, byteLen)
+	zbBytes := zbBig.Bytes()
+	copy(zb[byteLen-len(zbBytes):], zbBytes)
+
+	return vsG, zb, nil
+}
+
+func (c *genericCurve) Decaps(ephemeral, secret []byte) (sharedSecret []byte, err error) {
+	x, y := elliptic.Unmarshal(c.Curve, ephemeral)
+	zbBig, _ := c.Curve.ScalarMult(x, y, secret)
+	byteLen := (c.Curve.Params().BitSize + 7) >> 3
+	zb := make([]byte, byteLen)
+	zbBytes := zbBig.Bytes()
+	copy(zb[byteLen-len(zbBytes):], zbBytes)
+
+	return zb, nil
+}
+
+func (c *genericCurve) Sign(rand io.Reader, x, y, d *big.Int, hash []byte) (r, s *big.Int, err error) {
+	priv := &ecdsa.PrivateKey{D: d, PublicKey: ecdsa.PublicKey{X: x, Y: y, Curve: c.Curve}}
+	return ecdsa.Sign(rand, priv, hash)
+}
+
+func (c *genericCurve) Verify(x, y *big.Int, hash []byte, r, s *big.Int) bool {
+	pub := &ecdsa.PublicKey{X: x, Y: y, Curve: c.Curve}
+	return ecdsa.Verify(pub, hash, r, s)
+}
+
+func (c *genericCurve) validate(xP, yP *big.Int, secret []byte) error {
+	// the public point should not be at infinity (0,0)
+	zero := new(big.Int)
+	if xP.Cmp(zero) == 0 && yP.Cmp(zero) == 0 {
+		return errors.KeyInvalidError(fmt.Sprintf("ecc (%s): infinity point", c.Curve.Params().Name))
+	}
+
+	// re-derive the public point Q' = (X,Y) = dG
+	// to compare to declared Q in public key
+	expectedX, expectedY := c.Curve.ScalarBaseMult(secret)
+	if xP.Cmp(expectedX) != 0 || yP.Cmp(expectedY) != 0 {
+		return errors.KeyInvalidError(fmt.Sprintf("ecc (%s): invalid point", c.Curve.Params().Name))
+	}
+
+	return nil
+}
+
+func (c *genericCurve) ValidateECDSA(xP, yP *big.Int, secret []byte) error {
+	return c.validate(xP, yP, secret)
+}
+
+func (c *genericCurve) ValidateECDH(point []byte, secret []byte) error {
+	xP, yP := elliptic.Unmarshal(c.Curve, point)
+	if xP == nil {
+		return errors.KeyInvalidError(fmt.Sprintf("ecc (%s): invalid point", c.Curve.Params().Name))
+	}
+
+	return c.validate(xP, yP, secret)
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/ecc/x448.go

@@ -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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/encoding.go

@@ -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)
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/mpi.go

@@ -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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/internal/encoding/oid.go

@@ -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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/key_generation.go

@@ -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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/keys.go

@@ -5,13 +5,13 @@
 package openpgp
 
 import (
-	"crypto/rsa"
+	goerrors "errors"
 	"io"
 	"time"
 
-	"golang.org/x/crypto/openpgp/armor"
+	"github.com/ProtonMail/go-crypto/openpgp/armor"
-	"golang.org/x/crypto/openpgp/errors"
+	"github.com/ProtonMail/go-crypto/openpgp/errors"
-	"golang.org/x/crypto/openpgp/packet"
+	"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
+// PrimaryIdentity returns an Identity, preferring non-revoked identities,
-// if none are so marked.
+// identities marked as primary, or the latest-created identity, in that order.
-func (e *Entity) primaryIdentity() *Identity {
+func (e *Entity) PrimaryIdentity() *Identity {
-	var firstIdentity *Identity
+	var primaryIdentity *Identity
 	for _, ident := range e.Identities {
-		if firstIdentity == nil {
+		if shouldPreferIdentity(primaryIdentity, ident) {
-			firstIdentity = ident
+			primaryIdentity = ident
-		}
-		if ident.SelfSignature.IsPrimaryId != nil && *ident.SelfSignature.IsPrimaryId {
-			return ident
 		}
 	}
-	return firstIdentity
+	return primaryIdentity
 }
 
-// encryptionKey returns the best candidate Key for encrypting a message to the
+func shouldPreferIdentity(existingId, potentialNewId *Identity) bool {
+	if existingId == nil {
+		return true
+	}
+
+	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) {
+func (e *Entity) EncryptionKey(now time.Time) (Key, bool) {
-	candidateSubkey := -1
+	// 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 key
+	// 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.
+	// marked as ok to encrypt with, then we can obviously use it.
-	i := e.primaryIdentity()
 	if !i.SelfSignature.FlagsValid || i.SelfSignature.FlagEncryptCommunications &&
-		e.PrimaryKey.PubKeyAlgo.CanEncrypt() &&
+		e.PrimaryKey.PubKeyAlgo.CanEncrypt() {
-		!i.SelfSignature.KeyExpired(now) {
+		return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature, e.Revocations}, true
-		return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature}, 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) {
+			!subkey.PublicKey.KeyExpired(subkey.Sig, now) &&
-			candidateSubkey = i
+			!subkey.Sig.SigExpired(now) &&
-			break
+			!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.
+	// with the primary key.  Or, if the primary key is marked as ok to
-	i := e.primaryIdentity()
+	// sign with, then we can use it.
-	if !i.SelfSignature.FlagsValid || i.SelfSignature.FlagSign &&
+	if !i.SelfSignature.FlagsValid || (
-		!i.SelfSignature.KeyExpired(now) {
+			(flags & packet.KeyFlagCertify == 0 || i.SelfSignature.FlagCertify) &&
-		return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature}, true
+			(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
+			ident := e.PrimaryIdentity()
-			for _, ident := range e.Identities {
+			selfSig := ident.SelfSignature
-				if selfSig == nil {
+			keys = append(keys, Key{e, e.PrimaryKey, e.PrivateKey, selfSig, e.Revocations})
-					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})
 		}
 
 		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 {
+		if key.SelfSignature != nil && key.SelfSignature.FlagsValid && requiredUsage != 0 {
-			continue
-		}
-
-		if key.SelfSignature.RevocationReason != nil {
-			continue
-		}
-
-		if 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 subKey.Sig == nil || sig.CreationTime.After(subKey.Sig.CreationTime) {
-			if shouldReplaceSubkeySig(subKey.Sig, sig) {
 				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 {
+	for _, revocation := range e.Revocations {
-		err = ident.UserId.Serialize(w)
+		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 {
+	certificationKey, ok := signer.CertificationKey(config.Now())
-		return errors.InvalidArgumentError("signing Entity must have a private key")
+	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{
+	sig := createSignaturePacket(certificationKey.PublicKey, packet.SigTypeGenericCert, config)
-		SigType:      packet.SigTypeGenericCert,
+
-		PubKeyAlgo:   signer.PrivateKey.PubKeyAlgo,
+	signingUserID := config.SigningUserId()
-		Hash:         config.Hash(),
+	if signingUserID != "" {
-		CreationTime: config.Now(),
+		if _, ok := signer.Identities[signingUserID]; !ok {
-		IssuerKeyId:  &signer.PrivateKey.KeyId,
+			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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_config.go

@@ -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)
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_crypter.go

@@ -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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/aead_encrypted.go

@@ -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}
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/compressed.go

@@ -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:

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/config.go

@@ -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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/encrypted_key.go

@@ -12,8 +12,10 @@ import (
 	"math/big"
 	"strconv"
 
-	"golang.org/x/crypto/openpgp/elgamal"
+	"github.com/ProtonMail/go-crypto/openpgp/ecdh"
-	"golang.org/x/crypto/openpgp/errors"
+	"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)
+		e.encryptedMPI1 = new(encoding.MPI)
-		if err != nil {
+		if _, err = e.encryptedMPI1.ReadFrom(r); err != nil {
 			return
 		}
 	case PubKeyAlgoElGamal:
-		e.encryptedMPI1.bytes, e.encryptedMPI1.bitLength, err = readMPI(r)
+		e.encryptedMPI1 = new(encoding.MPI)
-		if err != nil {
+		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)
+		c1 := new(big.Int).SetBytes(e.encryptedMPI1.Bytes())
-		c2 := new(big.Int).SetBytes(e.encryptedMPI2.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
 }

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/literal.go

@@ -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])

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/notation.go

@@ -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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/ocfb.go

@@ -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
+// block size. On successful exit, blockSize+2 bytes of decrypted data are written into
-// 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 {

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/one_pass_signature.go

@@ -7,8 +7,8 @@ package packet
 import (
 	"crypto"
 	"encoding/binary"
-	"golang.org/x/crypto/openpgp/errors"
+	"github.com/ProtonMail/go-crypto/openpgp/errors"
-	"golang.org/x/crypto/openpgp/s2k"
+	"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)))
 	}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/opaque.go

@@ -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

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/packet.go

@@ -4,26 +4,16 @@
 
 // Package packet implements parsing and serialization of OpenPGP packets, as
 // specified in RFC 4880.
-//
+package packet // import "github.com/ProtonMail/go-crypto/openpgp/packet"
-// 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"
 
 import (
-	"bufio"
+	"bytes"
-	"crypto/aes"
 	"crypto/cipher"
-	"crypto/des"
 	"crypto/rsa"
 	"io"
-	"math/big"
-	"math/bits"
 
-	"golang.org/x/crypto/cast5"
+	"github.com/ProtonMail/go-crypto/openpgp/errors"
-	"golang.org/x/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
+	bufLen := w.buf.Len()
-	if !w.sentFirst {
+	if bufLen > 512 {
-		if len(w.buf) > 0 || len(p) < minFirstPartialWrite {
+		for power := uint(30); ; power-- {
-			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 {
 			l := 1 << power
-		if len(p) < l {
+			if bufLen >= l {
-			power = uint8(bits.Len32(uint32(len(p)))) - 1
+				w.lengthByte[0] = 224 + uint8(power)
-			l = 1 << power
-		}
-		w.lengthByte[0] = 224 + power
 				_, err = w.w.Write(w.lengthByte[:])
-		if err == nil {
-			var m int
-			m, err = w.w.Write(p[:l])
-			n += m
-		}
 				if err != nil {
-			if n < off {
+					return
-				return 0, err
 				}
-			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 {
+func (w *partialLengthWriter) Close() (err error) {
-	if len(w.buf) > 0 {
+	len := w.buf.Len()
-		// In this case we can't send a 512 byte packet.
+	err = serializeLength(w.w, len)
-		// Just send what we have.
+	if err != nil {
-		p := w.buf
-		w.sentFirst = true
-		w.buf = nil
-		if _, err := w.Write(p); err != nil {
 		return err
 	}
-	}
+	_, err = w.buf.WriteTo(w.w)
-
-	w.lengthByte[0] = 0
-	_, err := w.w.Write(w.lengthByte[:])
 	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)
+		buf[0] = byte(length)
-		n = 2
+		n = 1
 	} else if length < 8384 {
 		length -= 192
-		buf[1] = 192 + byte(length>>8)
+		buf[0] = 192 + byte(length>>8)
-		buf[2] = byte(length)
+		buf[1] = byte(length)
-		n = 3
+		n = 2
 	} else {
-		buf[1] = 255
+		buf[0] = 255
-		buf[2] = byte(length >> 24)
+		buf[1] = byte(length >> 24)
-		buf[3] = byte(length >> 16)
+		buf[2] = byte(length >> 16)
-		buf[4] = byte(length >> 8)
+		buf[3] = byte(length >> 8)
-		buf[5] = byte(length)
+		buf[4] = byte(length)
-		n = 6
+		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
+	err = serializeType(w, ptype)
-	buf[0] = 0x80 | 0x40 | byte(ptype)
-	_, err = w.Write(buf[:])
 	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
+// EncryptedDataPacket holds encrypted data. It is currently implemented by
-// be read. A bufio.Reader at the original position of the io.Reader
+// SymmetricallyEncrypted and AEADEncrypted.
-// is returned.
+type EncryptedDataPacket interface {
-func peekVersion(r io.Reader) (bufr *bufio.Reader, ver byte, err error) {
+	Decrypt(CipherFunction, []byte) (io.ReadCloser, error)
-	bufr = bufio.NewReader(r)
-	var verBuf []byte
-	if verBuf, err = bufr.Peek(1); err != nil {
-		return
-	}
-	ver = verBuf[0]
-	return
 }
 
 // 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
+	SigTypeBinary            SignatureType = 0x00
-	SigTypeText                            = 1
+	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 {
+	return algorithm.CipherFunction(cipher).KeySize()
-	case Cipher3DES:
-		return 24
-	case CipherCAST5:
-		return cast5.KeySize
-	case CipherAES128:
-		return 16
-	case CipherAES192:
-		return 24
-	case CipherAES256:
-		return 32
 }
-	return 0
+
+// 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 {
+	return algorithm.CipherFunction(cipher).BlockSize()
-	case Cipher3DES:
-		return des.BlockSize
-	case CipherCAST5:
-		return 8
-	case CipherAES128, CipherAES192, CipherAES256:
-		return 16
-	}
-	return 0
 }
 
 // new returns a fresh instance of the given cipher.
 func (cipher CipherFunction) new(key []byte) (block cipher.Block) {
-	switch cipher {
+	return algorithm.CipherFunction(cipher).New(key)
-	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())
 }
 
 // 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

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/private_key.go

@@ -0,0 +1,739 @@
+// Copyright 2011 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package packet
+
+import (
+	"bytes"
+	"crypto"
+	"crypto/cipher"
+	"crypto/dsa"
+	"crypto/rand"
+	"crypto/rsa"
+	"crypto/sha1"
+	"io"
+	"io/ioutil"
+	"math/big"
+	"strconv"
+	"time"
+
+	"github.com/ProtonMail/go-crypto/openpgp/ecdh"
+	"github.com/ProtonMail/go-crypto/openpgp/ecdsa"
+	"github.com/ProtonMail/go-crypto/openpgp/eddsa"
+	"github.com/ProtonMail/go-crypto/openpgp/elgamal"
+	"github.com/ProtonMail/go-crypto/openpgp/errors"
+	"github.com/ProtonMail/go-crypto/openpgp/internal/encoding"
+	"github.com/ProtonMail/go-crypto/openpgp/s2k"
+)
+
+// PrivateKey represents a possibly encrypted private key. See RFC 4880,
+// section 5.5.3.
+type PrivateKey struct {
+	PublicKey
+	Encrypted     bool // if true then the private key is unavailable until Decrypt has been called.
+	encryptedData []byte
+	cipher        CipherFunction
+	s2k           func(out, in []byte)
+	// An *{rsa|dsa|elgamal|ecdh|ecdsa|ed25519}.PrivateKey or
+	// crypto.Signer/crypto.Decrypter (Decryptor RSA only).
+	PrivateKey   interface{}
+	sha1Checksum bool
+	iv           []byte
+
+	// Type of encryption of the S2K packet
+	// Allowed values are 0 (Not encrypted), 254 (SHA1), or
+	// 255 (2-byte checksum)
+	s2kType S2KType
+	// Full parameters of the S2K packet
+	s2kParams *s2k.Params
+}
+
+//S2KType s2k packet type
+type S2KType uint8
+
+const (
+	// S2KNON unencrypt
+	S2KNON S2KType = 0
+	// S2KSHA1 sha1 sum check
+	S2KSHA1 S2KType = 254
+	// S2KCHECKSUM sum check
+	S2KCHECKSUM S2KType = 255
+)
+
+func NewRSAPrivateKey(creationTime time.Time, priv *rsa.PrivateKey) *PrivateKey {
+	pk := new(PrivateKey)
+	pk.PublicKey = *NewRSAPublicKey(creationTime, &priv.PublicKey)
+	pk.PrivateKey = priv
+	return pk
+}
+
+func NewDSAPrivateKey(creationTime time.Time, priv *dsa.PrivateKey) *PrivateKey {
+	pk := new(PrivateKey)
+	pk.PublicKey = *NewDSAPublicKey(creationTime, &priv.PublicKey)
+	pk.PrivateKey = priv
+	return pk
+}
+
+func NewElGamalPrivateKey(creationTime time.Time, priv *elgamal.PrivateKey) *PrivateKey {
+	pk := new(PrivateKey)
+	pk.PublicKey = *NewElGamalPublicKey(creationTime, &priv.PublicKey)
+	pk.PrivateKey = priv
+	return pk
+}
+
+func NewECDSAPrivateKey(creationTime time.Time, priv *ecdsa.PrivateKey) *PrivateKey {
+	pk := new(PrivateKey)
+	pk.PublicKey = *NewECDSAPublicKey(creationTime, &priv.PublicKey)
+	pk.PrivateKey = priv
+	return pk
+}
+
+func NewEdDSAPrivateKey(creationTime time.Time, priv *eddsa.PrivateKey) *PrivateKey {
+	pk := new(PrivateKey)
+	pk.PublicKey = *NewEdDSAPublicKey(creationTime, &priv.PublicKey)
+	pk.PrivateKey = priv
+	return pk
+}
+
+func NewECDHPrivateKey(creationTime time.Time, priv *ecdh.PrivateKey) *PrivateKey {
+	pk := new(PrivateKey)
+	pk.PublicKey = *NewECDHPublicKey(creationTime, &priv.PublicKey)
+	pk.PrivateKey = priv
+	return pk
+}
+
+// NewSignerPrivateKey creates a PrivateKey from a crypto.Signer that
+// implements RSA, ECDSA or EdDSA.
+func NewSignerPrivateKey(creationTime time.Time, signer interface{}) *PrivateKey {
+	pk := new(PrivateKey)
+	// In general, the public Keys should be used as pointers. We still
+	// type-switch on the values, for backwards-compatibility.
+	switch pubkey := signer.(type) {
+	case *rsa.PrivateKey:
+		pk.PublicKey = *NewRSAPublicKey(creationTime, &pubkey.PublicKey)
+	case rsa.PrivateKey:
+		pk.PublicKey = *NewRSAPublicKey(creationTime, &pubkey.PublicKey)
+	case *ecdsa.PrivateKey:
+		pk.PublicKey = *NewECDSAPublicKey(creationTime, &pubkey.PublicKey)
+	case ecdsa.PrivateKey:
+		pk.PublicKey = *NewECDSAPublicKey(creationTime, &pubkey.PublicKey)
+	case *eddsa.PrivateKey:
+		pk.PublicKey = *NewEdDSAPublicKey(creationTime, &pubkey.PublicKey)
+	case eddsa.PrivateKey:
+		pk.PublicKey = *NewEdDSAPublicKey(creationTime, &pubkey.PublicKey)
+	default:
+		panic("openpgp: unknown signer type in NewSignerPrivateKey")
+	}
+	pk.PrivateKey = signer
+	return pk
+}
+
+// NewDecrypterPrivateKey creates a PrivateKey from a *{rsa|elgamal|ecdh}.PrivateKey.
+func NewDecrypterPrivateKey(creationTime time.Time, decrypter interface{}) *PrivateKey {
+	pk := new(PrivateKey)
+	switch priv := decrypter.(type) {
+	case *rsa.PrivateKey:
+		pk.PublicKey = *NewRSAPublicKey(creationTime, &priv.PublicKey)
+	case *elgamal.PrivateKey:
+		pk.PublicKey = *NewElGamalPublicKey(creationTime, &priv.PublicKey)
+	case *ecdh.PrivateKey:
+		pk.PublicKey = *NewECDHPublicKey(creationTime, &priv.PublicKey)
+	default:
+		panic("openpgp: unknown decrypter type in NewDecrypterPrivateKey")
+	}
+	pk.PrivateKey = decrypter
+	return pk
+}
+
+func (pk *PrivateKey) parse(r io.Reader) (err error) {
+	err = (&pk.PublicKey).parse(r)
+	if err != nil {
+		return
+	}
+	v5 := pk.PublicKey.Version == 5
+
+	var buf [1]byte
+	_, err = readFull(r, buf[:])
+	if err != nil {
+		return
+	}
+	pk.s2kType = S2KType(buf[0])
+	var optCount [1]byte
+	if v5 {
+		if _, err = readFull(r, optCount[:]); err != nil {
+			return
+		}
+	}
+
+	switch pk.s2kType {
+	case S2KNON:
+		pk.s2k = nil
+		pk.Encrypted = false
+	case S2KSHA1, S2KCHECKSUM:
+		if v5 && pk.s2kType == S2KCHECKSUM {
+			return errors.StructuralError("wrong s2k identifier for version 5")
+		}
+		_, err = readFull(r, buf[:])
+		if err != nil {
+			return
+		}
+		pk.cipher = CipherFunction(buf[0])
+		if pk.cipher != 0 && !pk.cipher.IsSupported() {
+			return errors.UnsupportedError("unsupported cipher function in private key")
+		}
+		pk.s2kParams, err = s2k.ParseIntoParams(r)
+		if err != nil {
+			return
+		}
+		if pk.s2kParams.Dummy() {
+			return
+		}
+		pk.s2k, err = pk.s2kParams.Function()
+		if err != nil {
+			return
+		}
+		pk.Encrypted = true
+		if pk.s2kType == S2KSHA1 {
+			pk.sha1Checksum = true
+		}
+	default:
+		return errors.UnsupportedError("deprecated s2k function in private key")
+	}
+
+	if pk.Encrypted {
+		blockSize := pk.cipher.blockSize()
+		if blockSize == 0 {
+			return errors.UnsupportedError("unsupported cipher in private key: " + strconv.Itoa(int(pk.cipher)))
+		}
+		pk.iv = make([]byte, blockSize)
+		_, err = readFull(r, pk.iv)
+		if err != nil {
+			return
+		}
+	}
+
+	var privateKeyData []byte
+	if v5 {
+		var n [4]byte /* secret material four octet count */
+		_, err = readFull(r, n[:])
+		if err != nil {
+			return
+		}
+		count := uint32(uint32(n[0])<<24 | uint32(n[1])<<16 | uint32(n[2])<<8 | uint32(n[3]))
+		if !pk.Encrypted {
+			count = count + 2 /* two octet checksum */
+		}
+		privateKeyData = make([]byte, count)
+		_, err = readFull(r, privateKeyData)
+		if err != nil {
+			return
+		}
+	} else {
+		privateKeyData, err = ioutil.ReadAll(r)
+		if err != nil {
+			return
+		}
+	}
+	if !pk.Encrypted {
+		if len(privateKeyData) < 2 {
+			return errors.StructuralError("truncated private key data")
+		}
+		var sum uint16
+		for i := 0; i < len(privateKeyData)-2; i++ {
+			sum += uint16(privateKeyData[i])
+		}
+		if privateKeyData[len(privateKeyData)-2] != uint8(sum>>8) ||
+			privateKeyData[len(privateKeyData)-1] != uint8(sum) {
+			return errors.StructuralError("private key checksum failure")
+		}
+		privateKeyData = privateKeyData[:len(privateKeyData)-2]
+		return pk.parsePrivateKey(privateKeyData)
+	}
+
+	pk.encryptedData = privateKeyData
+	return
+}
+
+// Dummy returns true if the private key is a dummy key. This is a GNU extension.
+func (pk *PrivateKey) Dummy() bool {
+	return pk.s2kParams.Dummy()
+}
+
+func mod64kHash(d []byte) uint16 {
+	var h uint16
+	for _, b := range d {
+		h += uint16(b)
+	}
+	return h
+}
+
+func (pk *PrivateKey) Serialize(w io.Writer) (err error) {
+	contents := bytes.NewBuffer(nil)
+	err = pk.PublicKey.serializeWithoutHeaders(contents)
+	if err != nil {
+		return
+	}
+	if _, err = contents.Write([]byte{uint8(pk.s2kType)}); err != nil {
+		return
+	}
+
+	optional := bytes.NewBuffer(nil)
+	if pk.Encrypted || pk.Dummy() {
+		optional.Write([]byte{uint8(pk.cipher)})
+		if err := pk.s2kParams.Serialize(optional); err != nil {
+			return err
+		}
+		if pk.Encrypted {
+			optional.Write(pk.iv)
+		}
+	}
+	if pk.Version == 5 {
+		contents.Write([]byte{uint8(optional.Len())})
+	}
+	io.Copy(contents, optional)
+
+	if !pk.Dummy() {
+		l := 0
+		var priv []byte
+		if !pk.Encrypted {
+			buf := bytes.NewBuffer(nil)
+			err = pk.serializePrivateKey(buf)
+			if err != nil {
+				return err
+			}
+			l = buf.Len()
+			checksum := mod64kHash(buf.Bytes())
+			buf.Write([]byte{byte(checksum >> 8), byte(checksum)})
+			priv = buf.Bytes()
+		} else {
+			priv, l = pk.encryptedData, len(pk.encryptedData)
+		}
+
+		if pk.Version == 5 {
+			contents.Write([]byte{byte(l >> 24), byte(l >> 16), byte(l >> 8), byte(l)})
+		}
+		contents.Write(priv)
+	}
+
+	ptype := packetTypePrivateKey
+	if pk.IsSubkey {
+		ptype = packetTypePrivateSubkey
+	}
+	err = serializeHeader(w, ptype, contents.Len())
+	if err != nil {
+		return
+	}
+	_, err = io.Copy(w, contents)
+	if err != nil {
+		return
+	}
+	return
+}
+
+func serializeRSAPrivateKey(w io.Writer, priv *rsa.PrivateKey) error {
+	if _, err := w.Write(new(encoding.MPI).SetBig(priv.D).EncodedBytes()); err != nil {
+		return err
+	}
+	if _, err := w.Write(new(encoding.MPI).SetBig(priv.Primes[1]).EncodedBytes()); err != nil {
+		return err
+	}
+	if _, err := w.Write(new(encoding.MPI).SetBig(priv.Primes[0]).EncodedBytes()); err != nil {
+		return err
+	}
+	_, err := w.Write(new(encoding.MPI).SetBig(priv.Precomputed.Qinv).EncodedBytes())
+	return err
+}
+
+func serializeDSAPrivateKey(w io.Writer, priv *dsa.PrivateKey) error {
+	_, err := w.Write(new(encoding.MPI).SetBig(priv.X).EncodedBytes())
+	return err
+}
+
+func serializeElGamalPrivateKey(w io.Writer, priv *elgamal.PrivateKey) error {
+	_, err := w.Write(new(encoding.MPI).SetBig(priv.X).EncodedBytes())
+	return err
+}
+
+func serializeECDSAPrivateKey(w io.Writer, priv *ecdsa.PrivateKey) error {
+	_, err := w.Write(encoding.NewMPI(priv.MarshalIntegerSecret()).EncodedBytes())
+	return err
+}
+
+func serializeEdDSAPrivateKey(w io.Writer, priv *eddsa.PrivateKey) error {
+	_, err := w.Write(encoding.NewMPI(priv.MarshalByteSecret()).EncodedBytes())
+	return err
+}
+
+func serializeECDHPrivateKey(w io.Writer, priv *ecdh.PrivateKey) error {
+	_, err := w.Write(encoding.NewMPI(priv.MarshalByteSecret()).EncodedBytes())
+	return err
+}
+
+// Decrypt decrypts an encrypted private key using a passphrase.
+func (pk *PrivateKey) Decrypt(passphrase []byte) error {
+	if pk.Dummy() {
+		return errors.ErrDummyPrivateKey("dummy key found")
+	}
+	if !pk.Encrypted {
+		return nil
+	}
+
+	key := make([]byte, pk.cipher.KeySize())
+	pk.s2k(key, passphrase)
+	block := pk.cipher.new(key)
+	cfb := cipher.NewCFBDecrypter(block, pk.iv)
+
+	data := make([]byte, len(pk.encryptedData))
+	cfb.XORKeyStream(data, pk.encryptedData)
+
+	if pk.sha1Checksum {
+		if len(data) < sha1.Size {
+			return errors.StructuralError("truncated private key data")
+		}
+		h := sha1.New()
+		h.Write(data[:len(data)-sha1.Size])
+		sum := h.Sum(nil)
+		if !bytes.Equal(sum, data[len(data)-sha1.Size:]) {
+			return errors.StructuralError("private key checksum failure")
+		}
+		data = data[:len(data)-sha1.Size]
+	} else {
+		if len(data) < 2 {
+			return errors.StructuralError("truncated private key data")
+		}
+		var sum uint16
+		for i := 0; i < len(data)-2; i++ {
+			sum += uint16(data[i])
+		}
+		if data[len(data)-2] != uint8(sum>>8) ||
+			data[len(data)-1] != uint8(sum) {
+			return errors.StructuralError("private key checksum failure")
+		}
+		data = data[:len(data)-2]
+	}
+
+	err := pk.parsePrivateKey(data)
+	if _, ok := err.(errors.KeyInvalidError); ok {
+		return errors.KeyInvalidError("invalid key parameters")
+	}
+	if err != nil {
+		return err
+	}
+
+	// Mark key as unencrypted
+	pk.s2kType = S2KNON
+	pk.s2k = nil
+	pk.Encrypted = false
+	pk.encryptedData = nil
+
+	return nil
+}
+
+// Encrypt encrypts an unencrypted private key using a passphrase.
+func (pk *PrivateKey) Encrypt(passphrase []byte) error {
+	priv := bytes.NewBuffer(nil)
+	err := pk.serializePrivateKey(priv)
+	if err != nil {
+		return err
+	}
+
+	//Default config of private key encryption
+	pk.cipher = CipherAES256
+	s2kConfig := &s2k.Config{
+		S2KMode:  3, //Iterated
+		S2KCount: 65536,
+		Hash:     crypto.SHA256,
+	}
+
+	pk.s2kParams, err = s2k.Generate(rand.Reader, s2kConfig)
+	if err != nil {
+		return err
+	}
+	privateKeyBytes := priv.Bytes()
+	key := make([]byte, pk.cipher.KeySize())
+
+	pk.sha1Checksum = true
+	pk.s2k, err = pk.s2kParams.Function()
+	if err != nil {
+		return err
+	}
+	pk.s2k(key, passphrase)
+	block := pk.cipher.new(key)
+	pk.iv = make([]byte, pk.cipher.blockSize())
+	_, err = rand.Read(pk.iv)
+	if err != nil {
+		return err
+	}
+	cfb := cipher.NewCFBEncrypter(block, pk.iv)
+
+	if pk.sha1Checksum {
+		pk.s2kType = S2KSHA1
+		h := sha1.New()
+		h.Write(privateKeyBytes)
+		sum := h.Sum(nil)
+		privateKeyBytes = append(privateKeyBytes, sum...)
+	} else {
+		pk.s2kType = S2KCHECKSUM
+		var sum uint16
+		for _, b := range privateKeyBytes {
+			sum += uint16(b)
+		}
+		priv.Write([]byte{uint8(sum >> 8), uint8(sum)})
+	}
+
+	pk.encryptedData = make([]byte, len(privateKeyBytes))
+	cfb.XORKeyStream(pk.encryptedData, privateKeyBytes)
+	pk.Encrypted = true
+	pk.PrivateKey = nil
+	return err
+}
+
+func (pk *PrivateKey) serializePrivateKey(w io.Writer) (err error) {
+	switch priv := pk.PrivateKey.(type) {
+	case *rsa.PrivateKey:
+		err = serializeRSAPrivateKey(w, priv)
+	case *dsa.PrivateKey:
+		err = serializeDSAPrivateKey(w, priv)
+	case *elgamal.PrivateKey:
+		err = serializeElGamalPrivateKey(w, priv)
+	case *ecdsa.PrivateKey:
+		err = serializeECDSAPrivateKey(w, priv)
+	case *eddsa.PrivateKey:
+		err = serializeEdDSAPrivateKey(w, priv)
+	case *ecdh.PrivateKey:
+		err = serializeECDHPrivateKey(w, priv)
+	default:
+		err = errors.InvalidArgumentError("unknown private key type")
+	}
+	return
+}
+
+func (pk *PrivateKey) parsePrivateKey(data []byte) (err error) {
+	switch pk.PublicKey.PubKeyAlgo {
+	case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoRSAEncryptOnly:
+		return pk.parseRSAPrivateKey(data)
+	case PubKeyAlgoDSA:
+		return pk.parseDSAPrivateKey(data)
+	case PubKeyAlgoElGamal:
+		return pk.parseElGamalPrivateKey(data)
+	case PubKeyAlgoECDSA:
+		return pk.parseECDSAPrivateKey(data)
+	case PubKeyAlgoECDH:
+		return pk.parseECDHPrivateKey(data)
+	case PubKeyAlgoEdDSA:
+		return pk.parseEdDSAPrivateKey(data)
+	}
+	panic("impossible")
+}
+
+func (pk *PrivateKey) parseRSAPrivateKey(data []byte) (err error) {
+	rsaPub := pk.PublicKey.PublicKey.(*rsa.PublicKey)
+	rsaPriv := new(rsa.PrivateKey)
+	rsaPriv.PublicKey = *rsaPub
+
+	buf := bytes.NewBuffer(data)
+	d := new(encoding.MPI)
+	if _, err := d.ReadFrom(buf); err != nil {
+		return err
+	}
+
+	p := new(encoding.MPI)
+	if _, err := p.ReadFrom(buf); err != nil {
+		return err
+	}
+
+	q := new(encoding.MPI)
+	if _, err := q.ReadFrom(buf); err != nil {
+		return err
+	}
+
+	rsaPriv.D = new(big.Int).SetBytes(d.Bytes())
+	rsaPriv.Primes = make([]*big.Int, 2)
+	rsaPriv.Primes[0] = new(big.Int).SetBytes(p.Bytes())
+	rsaPriv.Primes[1] = new(big.Int).SetBytes(q.Bytes())
+	if err := rsaPriv.Validate(); err != nil {
+		return errors.KeyInvalidError(err.Error())
+	}
+	rsaPriv.Precompute()
+	pk.PrivateKey = rsaPriv
+
+	return nil
+}
+
+func (pk *PrivateKey) parseDSAPrivateKey(data []byte) (err error) {
+	dsaPub := pk.PublicKey.PublicKey.(*dsa.PublicKey)
+	dsaPriv := new(dsa.PrivateKey)
+	dsaPriv.PublicKey = *dsaPub
+
+	buf := bytes.NewBuffer(data)
+	x := new(encoding.MPI)
+	if _, err := x.ReadFrom(buf); err != nil {
+		return err
+	}
+
+	dsaPriv.X = new(big.Int).SetBytes(x.Bytes())
+	if err := validateDSAParameters(dsaPriv); err != nil {
+		return err
+	}
+	pk.PrivateKey = dsaPriv
+
+	return nil
+}
+
+func (pk *PrivateKey) parseElGamalPrivateKey(data []byte) (err error) {
+	pub := pk.PublicKey.PublicKey.(*elgamal.PublicKey)
+	priv := new(elgamal.PrivateKey)
+	priv.PublicKey = *pub
+
+	buf := bytes.NewBuffer(data)
+	x := new(encoding.MPI)
+	if _, err := x.ReadFrom(buf); err != nil {
+		return err
+	}
+
+	priv.X = new(big.Int).SetBytes(x.Bytes())
+	if err := validateElGamalParameters(priv); err != nil {
+		return err
+	}
+	pk.PrivateKey = priv
+
+	return nil
+}
+
+func (pk *PrivateKey) parseECDSAPrivateKey(data []byte) (err error) {
+	ecdsaPub := pk.PublicKey.PublicKey.(*ecdsa.PublicKey)
+	ecdsaPriv := ecdsa.NewPrivateKey(*ecdsaPub)
+
+	buf := bytes.NewBuffer(data)
+	d := new(encoding.MPI)
+	if _, err := d.ReadFrom(buf); err != nil {
+		return err
+	}
+
+	if err := ecdsaPriv.UnmarshalIntegerSecret(d.Bytes()); err != nil {
+		return err
+	}
+	if err := ecdsa.Validate(ecdsaPriv); err != nil {
+		return err
+	}
+	pk.PrivateKey = ecdsaPriv
+
+	return nil
+}
+
+func (pk *PrivateKey) parseECDHPrivateKey(data []byte) (err error) {
+	ecdhPub := pk.PublicKey.PublicKey.(*ecdh.PublicKey)
+	ecdhPriv := ecdh.NewPrivateKey(*ecdhPub)
+
+	buf := bytes.NewBuffer(data)
+	d := new(encoding.MPI)
+	if _, err := d.ReadFrom(buf); err != nil {
+		return err
+	}
+
+	if err := ecdhPriv.UnmarshalByteSecret(d.Bytes()); err != nil {
+		return err
+	}
+
+	if err := ecdh.Validate(ecdhPriv); err != nil {
+		return err
+	}
+
+	pk.PrivateKey = ecdhPriv
+
+	return nil
+}
+
+func (pk *PrivateKey) parseEdDSAPrivateKey(data []byte) (err error) {
+	eddsaPub := pk.PublicKey.PublicKey.(*eddsa.PublicKey)
+	eddsaPriv := eddsa.NewPrivateKey(*eddsaPub)
+	eddsaPriv.PublicKey = *eddsaPub
+
+	buf := bytes.NewBuffer(data)
+	d := new(encoding.MPI)
+	if _, err := d.ReadFrom(buf); err != nil {
+		return err
+	}
+
+	if err = eddsaPriv.UnmarshalByteSecret(d.Bytes()); err != nil {
+		return err
+	}
+
+	if err := eddsa.Validate(eddsaPriv); err != nil {
+		return err
+	}
+
+	pk.PrivateKey = eddsaPriv
+
+	return nil
+}
+
+func validateDSAParameters(priv *dsa.PrivateKey) error {
+	p := priv.P // group prime
+	q := priv.Q // subgroup order
+	g := priv.G // g has order q mod p
+	x := priv.X // secret
+	y := priv.Y // y == g**x mod p
+	one := big.NewInt(1)
+	// expect g, y >= 2 and g < p
+	if g.Cmp(one) <= 0 || y.Cmp(one) <= 0 || g.Cmp(p) > 0 {
+		return errors.KeyInvalidError("dsa: invalid group")
+	}
+	// expect p > q
+	if p.Cmp(q) <= 0 {
+		return errors.KeyInvalidError("dsa: invalid group prime")
+	}
+	// q should be large enough and divide p-1
+	pSub1 := new(big.Int).Sub(p, one)
+	if q.BitLen() < 150 || new(big.Int).Mod(pSub1, q).Cmp(big.NewInt(0)) != 0 {
+		return errors.KeyInvalidError("dsa: invalid order")
+	}
+	// confirm that g has order q mod p
+	if !q.ProbablyPrime(32) || new(big.Int).Exp(g, q, p).Cmp(one) != 0 {
+		return errors.KeyInvalidError("dsa: invalid order")
+	}
+	// check y
+	if new(big.Int).Exp(g, x, p).Cmp(y) != 0 {
+		return errors.KeyInvalidError("dsa: mismatching values")
+	}
+
+	return nil
+}
+
+func validateElGamalParameters(priv *elgamal.PrivateKey) error {
+	p := priv.P // group prime
+	g := priv.G // g has order p-1 mod p
+	x := priv.X // secret
+	y := priv.Y // y == g**x mod p
+	one := big.NewInt(1)
+	// Expect g, y >= 2 and g < p
+	if g.Cmp(one) <= 0 || y.Cmp(one) <= 0 || g.Cmp(p) > 0 {
+		return errors.KeyInvalidError("elgamal: invalid group")
+	}
+	if p.BitLen() < 1024 {
+		return errors.KeyInvalidError("elgamal: group order too small")
+	}
+	pSub1 := new(big.Int).Sub(p, one)
+	if new(big.Int).Exp(g, pSub1, p).Cmp(one) != 0 {
+		return errors.KeyInvalidError("elgamal: invalid group")
+	}
+	// Since p-1 is not prime, g might have a smaller order that divides p-1.
+	// We cannot confirm the exact order of g, but we make sure it is not too small.
+	gExpI := new(big.Int).Set(g)
+	i := 1
+	threshold := 2 << 17 // we want order > threshold
+	for i < threshold {
+		i++ // we check every order to make sure key validation is not easily bypassed by guessing y'
+		gExpI.Mod(new(big.Int).Mul(gExpI, g), p)
+		if gExpI.Cmp(one) == 0 {
+			return errors.KeyInvalidError("elgamal: order too small")
+		}
+	}
+	// Check y
+	if new(big.Int).Exp(g, x, p).Cmp(y) != 0 {
+		return errors.KeyInvalidError("elgamal: mismatching values")
+	}
+
+	return nil
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/private_key_test_data.go

@@ -0,0 +1,12 @@
+package packet
+
+// Generated with `gpg --export-secret-keys "Test Key 2"`
+const privKeyRSAHex = "9501fe044cc349a8010400b70ca0010e98c090008d45d1ee8f9113bd5861fd57b88bacb7c68658747663f1e1a3b5a98f32fda6472373c024b97359cd2efc88ff60f77751adfbf6af5e615e6a1408cfad8bf0cea30b0d5f53aa27ad59089ba9b15b7ebc2777a25d7b436144027e3bcd203909f147d0e332b240cf63d3395f5dfe0df0a6c04e8655af7eacdf0011010001fe0303024a252e7d475fd445607de39a265472aa74a9320ba2dac395faa687e9e0336aeb7e9a7397e511b5afd9dc84557c80ac0f3d4d7bfec5ae16f20d41c8c84a04552a33870b930420e230e179564f6d19bb153145e76c33ae993886c388832b0fa042ddda7f133924f3854481533e0ede31d51278c0519b29abc3bf53da673e13e3e1214b52413d179d7f66deee35cac8eacb060f78379d70ef4af8607e68131ff529439668fc39c9ce6dfef8a5ac234d234802cbfb749a26107db26406213ae5c06d4673253a3cbee1fcbae58d6ab77e38d6e2c0e7c6317c48e054edadb5a40d0d48acb44643d998139a8a66bb820be1f3f80185bc777d14b5954b60effe2448a036d565c6bc0b915fcea518acdd20ab07bc1529f561c58cd044f723109b93f6fd99f876ff891d64306b5d08f48bab59f38695e9109c4dec34013ba3153488ce070268381ba923ee1eb77125b36afcb4347ec3478c8f2735b06ef17351d872e577fa95d0c397c88c71b59629a36aec"
+
+// 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 = "3082025d02010002818100e98edfa1c3b35884a54d0b36a6a603b0290fa85e49e30fa23fc94fef9c6790bc4849928607aa48d809da326fb42a969d06ad756b98b9c1a90f5d4a2b6d0ac05953c97f4da3120164a21a679793ce181c906dc01d235cc085ddcdf6ea06c389b6ab8885dfd685959e693138856a68a7e5db263337ff82a088d583a897cf2d59e9020301000102818100b6d5c9eb70b02d5369b3ee5b520a14490b5bde8a317d36f7e4c74b7460141311d1e5067735f8f01d6f5908b2b96fbd881f7a1ab9a84d82753e39e19e2d36856be960d05ac9ef8e8782ea1b6d65aee28fdfe1d61451e8cff0adfe84322f12cf455028b581cf60eb9e0e140ba5d21aeba6c2634d7c65318b9a665fc01c3191ca21024100fa5e818da3705b0fa33278bb28d4b6f6050388af2d4b75ec9375dd91ccf2e7d7068086a8b82a8f6282e4fbbdb8a7f2622eb97295249d87acea7f5f816f54d347024100eecf9406d7dc49cdfb95ab1eff4064de84c7a30f64b2798936a0d2018ba9eb52e4b636f82e96c49cc63b80b675e91e40d1b2e4017d4b9adaf33ab3d9cf1c214f024100c173704ace742c082323066226a4655226819a85304c542b9dacbeacbf5d1881ee863485fcf6f59f3a604f9b42289282067447f2b13dfeed3eab7851fc81e0550240741fc41f3fc002b382eed8730e33c5d8de40256e4accee846667f536832f711ab1d4590e7db91a8a116ac5bff3be13d3f9243ff2e976662aa9b395d907f8e9c9024046a5696c9ef882363e06c9fa4e2f5b580906452befba03f4a99d0f873697ef1f851d2226ca7934b30b7c3e80cb634a67172bbbf4781735fe3e09263e2dd723e7"

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/public_key.go

@@ -0,0 +1,802 @@
+// Copyright 2011 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package packet
+
+import (
+	"crypto"
+	"crypto/dsa"
+	"crypto/rsa"
+	"crypto/sha1"
+	"crypto/sha256"
+	_ "crypto/sha512"
+	"encoding/binary"
+	"fmt"
+	"hash"
+	"io"
+	"math/big"
+	"strconv"
+	"time"
+
+	"github.com/ProtonMail/go-crypto/openpgp/ecdh"
+	"github.com/ProtonMail/go-crypto/openpgp/ecdsa"
+	"github.com/ProtonMail/go-crypto/openpgp/eddsa"
+	"github.com/ProtonMail/go-crypto/openpgp/elgamal"
+	"github.com/ProtonMail/go-crypto/openpgp/errors"
+	"github.com/ProtonMail/go-crypto/openpgp/internal/algorithm"
+	"github.com/ProtonMail/go-crypto/openpgp/internal/ecc"
+	"github.com/ProtonMail/go-crypto/openpgp/internal/encoding"
+)
+
+type kdfHashFunction byte
+type kdfAlgorithm byte
+
+// PublicKey represents an OpenPGP public key. See RFC 4880, section 5.5.2.
+type PublicKey struct {
+	Version      int
+	CreationTime time.Time
+	PubKeyAlgo   PublicKeyAlgorithm
+	PublicKey    interface{} // *rsa.PublicKey, *dsa.PublicKey, *ecdsa.PublicKey or *eddsa.PublicKey
+	Fingerprint  []byte
+	KeyId        uint64
+	IsSubkey     bool
+
+	// RFC 4880 fields
+	n, e, p, q, g, y encoding.Field
+
+	// RFC 6637 fields
+	// oid contains the OID byte sequence identifying the elliptic curve used
+	oid encoding.Field
+
+	// kdf stores key derivation function parameters
+	// used for ECDH encryption. See RFC 6637, Section 9.
+	kdf encoding.Field
+}
+
+// UpgradeToV5 updates the version of the key to v5, and updates all necessary
+// fields.
+func (pk *PublicKey) UpgradeToV5() {
+	pk.Version = 5
+	pk.setFingerprintAndKeyId()
+}
+
+// signingKey provides a convenient abstraction over signature verification
+// for v3 and v4 public keys.
+type signingKey interface {
+	SerializeForHash(io.Writer) error
+	SerializeSignaturePrefix(io.Writer)
+	serializeWithoutHeaders(io.Writer) error
+}
+
+// NewRSAPublicKey returns a PublicKey that wraps the given rsa.PublicKey.
+func NewRSAPublicKey(creationTime time.Time, pub *rsa.PublicKey) *PublicKey {
+	pk := &PublicKey{
+		Version:      4,
+		CreationTime: creationTime,
+		PubKeyAlgo:   PubKeyAlgoRSA,
+		PublicKey:    pub,
+		n:            new(encoding.MPI).SetBig(pub.N),
+		e:            new(encoding.MPI).SetBig(big.NewInt(int64(pub.E))),
+	}
+
+	pk.setFingerprintAndKeyId()
+	return pk
+}
+
+// NewDSAPublicKey returns a PublicKey that wraps the given dsa.PublicKey.
+func NewDSAPublicKey(creationTime time.Time, pub *dsa.PublicKey) *PublicKey {
+	pk := &PublicKey{
+		Version:      4,
+		CreationTime: creationTime,
+		PubKeyAlgo:   PubKeyAlgoDSA,
+		PublicKey:    pub,
+		p:            new(encoding.MPI).SetBig(pub.P),
+		q:            new(encoding.MPI).SetBig(pub.Q),
+		g:            new(encoding.MPI).SetBig(pub.G),
+		y:            new(encoding.MPI).SetBig(pub.Y),
+	}
+
+	pk.setFingerprintAndKeyId()
+	return pk
+}
+
+// NewElGamalPublicKey returns a PublicKey that wraps the given elgamal.PublicKey.
+func NewElGamalPublicKey(creationTime time.Time, pub *elgamal.PublicKey) *PublicKey {
+	pk := &PublicKey{
+		Version:      4,
+		CreationTime: creationTime,
+		PubKeyAlgo:   PubKeyAlgoElGamal,
+		PublicKey:    pub,
+		p:            new(encoding.MPI).SetBig(pub.P),
+		g:            new(encoding.MPI).SetBig(pub.G),
+		y:            new(encoding.MPI).SetBig(pub.Y),
+	}
+
+	pk.setFingerprintAndKeyId()
+	return pk
+}
+
+func NewECDSAPublicKey(creationTime time.Time, pub *ecdsa.PublicKey) *PublicKey {
+	pk := &PublicKey{
+		Version:      4,
+		CreationTime: creationTime,
+		PubKeyAlgo:   PubKeyAlgoECDSA,
+		PublicKey:    pub,
+		p:            encoding.NewMPI(pub.MarshalPoint()),
+	}
+
+	curveInfo := ecc.FindByCurve(pub.GetCurve())
+	if curveInfo == nil {
+		panic("unknown elliptic curve")
+	}
+	pk.oid = curveInfo.Oid
+	pk.setFingerprintAndKeyId()
+	return pk
+}
+
+func NewECDHPublicKey(creationTime time.Time, pub *ecdh.PublicKey) *PublicKey {
+	var pk *PublicKey
+	var kdf = encoding.NewOID([]byte{0x1, pub.Hash.Id(), pub.Cipher.Id()})
+	pk = &PublicKey{
+		Version:      4,
+		CreationTime: creationTime,
+		PubKeyAlgo:   PubKeyAlgoECDH,
+		PublicKey:    pub,
+		p:            encoding.NewMPI(pub.MarshalPoint()),
+		kdf:          kdf,
+	}
+
+	curveInfo := ecc.FindByCurve(pub.GetCurve())
+
+	if curveInfo == nil {
+		panic("unknown elliptic curve")
+	}
+
+	pk.oid = curveInfo.Oid
+	pk.setFingerprintAndKeyId()
+	return pk
+}
+
+func NewEdDSAPublicKey(creationTime time.Time, pub *eddsa.PublicKey) *PublicKey {
+	curveInfo := ecc.FindByCurve(pub.GetCurve())
+	pk := &PublicKey{
+		Version:      4,
+		CreationTime: creationTime,
+		PubKeyAlgo:   PubKeyAlgoEdDSA,
+		PublicKey:    pub,
+		oid:          curveInfo.Oid,
+		// Native point format, see draft-koch-eddsa-for-openpgp-04, Appendix B
+		p: encoding.NewMPI(pub.MarshalPoint()),
+	}
+
+	pk.setFingerprintAndKeyId()
+	return pk
+}
+
+func (pk *PublicKey) parse(r io.Reader) (err error) {
+	// RFC 4880, section 5.5.2
+	var buf [6]byte
+	_, err = readFull(r, buf[:])
+	if err != nil {
+		return
+	}
+	if buf[0] != 4 && buf[0] != 5 {
+		return errors.UnsupportedError("public key version " + strconv.Itoa(int(buf[0])))
+	}
+
+	pk.Version = int(buf[0])
+	if pk.Version == 5 {
+		var n [4]byte
+		_, err = readFull(r, n[:])
+		if err != nil {
+			return
+		}
+	}
+	pk.CreationTime = time.Unix(int64(uint32(buf[1])<<24|uint32(buf[2])<<16|uint32(buf[3])<<8|uint32(buf[4])), 0)
+	pk.PubKeyAlgo = PublicKeyAlgorithm(buf[5])
+	switch pk.PubKeyAlgo {
+	case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly:
+		err = pk.parseRSA(r)
+	case PubKeyAlgoDSA:
+		err = pk.parseDSA(r)
+	case PubKeyAlgoElGamal:
+		err = pk.parseElGamal(r)
+	case PubKeyAlgoECDSA:
+		err = pk.parseECDSA(r)
+	case PubKeyAlgoECDH:
+		err = pk.parseECDH(r)
+	case PubKeyAlgoEdDSA:
+		err = pk.parseEdDSA(r)
+	default:
+		err = errors.UnsupportedError("public key type: " + strconv.Itoa(int(pk.PubKeyAlgo)))
+	}
+	if err != nil {
+		return
+	}
+
+	pk.setFingerprintAndKeyId()
+	return
+}
+
+func (pk *PublicKey) setFingerprintAndKeyId() {
+	// RFC 4880, section 12.2
+	if pk.Version == 5 {
+		fingerprint := sha256.New()
+		pk.SerializeForHash(fingerprint)
+		pk.Fingerprint = make([]byte, 32)
+		copy(pk.Fingerprint, fingerprint.Sum(nil))
+		pk.KeyId = binary.BigEndian.Uint64(pk.Fingerprint[:8])
+	} else {
+		fingerprint := sha1.New()
+		pk.SerializeForHash(fingerprint)
+		pk.Fingerprint = make([]byte, 20)
+		copy(pk.Fingerprint, fingerprint.Sum(nil))
+		pk.KeyId = binary.BigEndian.Uint64(pk.Fingerprint[12:20])
+	}
+}
+
+// parseRSA parses RSA public key material from the given Reader. See RFC 4880,
+// section 5.5.2.
+func (pk *PublicKey) parseRSA(r io.Reader) (err error) {
+	pk.n = new(encoding.MPI)
+	if _, err = pk.n.ReadFrom(r); err != nil {
+		return
+	}
+	pk.e = new(encoding.MPI)
+	if _, err = pk.e.ReadFrom(r); err != nil {
+		return
+	}
+
+	if len(pk.e.Bytes()) > 3 {
+		err = errors.UnsupportedError("large public exponent")
+		return
+	}
+	rsa := &rsa.PublicKey{
+		N: new(big.Int).SetBytes(pk.n.Bytes()),
+		E: 0,
+	}
+	for i := 0; i < len(pk.e.Bytes()); i++ {
+		rsa.E <<= 8
+		rsa.E |= int(pk.e.Bytes()[i])
+	}
+	pk.PublicKey = rsa
+	return
+}
+
+// parseDSA parses DSA public key material from the given Reader. See RFC 4880,
+// section 5.5.2.
+func (pk *PublicKey) parseDSA(r io.Reader) (err error) {
+	pk.p = new(encoding.MPI)
+	if _, err = pk.p.ReadFrom(r); err != nil {
+		return
+	}
+	pk.q = new(encoding.MPI)
+	if _, err = pk.q.ReadFrom(r); err != nil {
+		return
+	}
+	pk.g = new(encoding.MPI)
+	if _, err = pk.g.ReadFrom(r); err != nil {
+		return
+	}
+	pk.y = new(encoding.MPI)
+	if _, err = pk.y.ReadFrom(r); err != nil {
+		return
+	}
+
+	dsa := new(dsa.PublicKey)
+	dsa.P = new(big.Int).SetBytes(pk.p.Bytes())
+	dsa.Q = new(big.Int).SetBytes(pk.q.Bytes())
+	dsa.G = new(big.Int).SetBytes(pk.g.Bytes())
+	dsa.Y = new(big.Int).SetBytes(pk.y.Bytes())
+	pk.PublicKey = dsa
+	return
+}
+
+// parseElGamal parses ElGamal public key material from the given Reader. See
+// RFC 4880, section 5.5.2.
+func (pk *PublicKey) parseElGamal(r io.Reader) (err error) {
+	pk.p = new(encoding.MPI)
+	if _, err = pk.p.ReadFrom(r); err != nil {
+		return
+	}
+	pk.g = new(encoding.MPI)
+	if _, err = pk.g.ReadFrom(r); err != nil {
+		return
+	}
+	pk.y = new(encoding.MPI)
+	if _, err = pk.y.ReadFrom(r); err != nil {
+		return
+	}
+
+	elgamal := new(elgamal.PublicKey)
+	elgamal.P = new(big.Int).SetBytes(pk.p.Bytes())
+	elgamal.G = new(big.Int).SetBytes(pk.g.Bytes())
+	elgamal.Y = new(big.Int).SetBytes(pk.y.Bytes())
+	pk.PublicKey = elgamal
+	return
+}
+
+// parseECDSA parses ECDSA public key material from the given Reader. See
+// RFC 6637, Section 9.
+func (pk *PublicKey) parseECDSA(r io.Reader) (err error) {
+	pk.oid = new(encoding.OID)
+	if _, err = pk.oid.ReadFrom(r); err != nil {
+		return
+	}
+	pk.p = new(encoding.MPI)
+	if _, err = pk.p.ReadFrom(r); err != nil {
+		return
+	}
+
+	curveInfo := ecc.FindByOid(pk.oid)
+	if curveInfo == nil {
+		return errors.UnsupportedError(fmt.Sprintf("unknown oid: %x", pk.oid))
+	}
+
+	c, ok := curveInfo.Curve.(ecc.ECDSACurve)
+	if !ok {
+		return errors.UnsupportedError(fmt.Sprintf("unsupported oid: %x", pk.oid))
+	}
+
+	ecdsaKey := ecdsa.NewPublicKey(c)
+	err = ecdsaKey.UnmarshalPoint(pk.p.Bytes())
+	pk.PublicKey = ecdsaKey
+
+	return
+}
+
+// parseECDH parses ECDH public key material from the given Reader. See
+// RFC 6637, Section 9.
+func (pk *PublicKey) parseECDH(r io.Reader) (err error) {
+	pk.oid = new(encoding.OID)
+	if _, err = pk.oid.ReadFrom(r); err != nil {
+		return
+	}
+	pk.p = new(encoding.MPI)
+	if _, err = pk.p.ReadFrom(r); err != nil {
+		return
+	}
+	pk.kdf = new(encoding.OID)
+	if _, err = pk.kdf.ReadFrom(r); err != nil {
+		return
+	}
+
+	curveInfo := ecc.FindByOid(pk.oid)
+
+	if curveInfo == nil {
+		return errors.UnsupportedError(fmt.Sprintf("unknown oid: %x", pk.oid))
+	}
+
+	c, ok := curveInfo.Curve.(ecc.ECDHCurve)
+	if !ok {
+		return errors.UnsupportedError(fmt.Sprintf("unsupported oid: %x", pk.oid))
+	}
+
+	if kdfLen := len(pk.kdf.Bytes()); kdfLen < 3 {
+		return errors.UnsupportedError("unsupported ECDH KDF length: " + strconv.Itoa(kdfLen))
+	}
+	if reserved := pk.kdf.Bytes()[0]; reserved != 0x01 {
+		return errors.UnsupportedError("unsupported KDF reserved field: " + strconv.Itoa(int(reserved)))
+	}
+	kdfHash, ok := algorithm.HashById[pk.kdf.Bytes()[1]]
+	if !ok {
+		return errors.UnsupportedError("unsupported ECDH KDF hash: " + strconv.Itoa(int(pk.kdf.Bytes()[1])))
+	}
+	kdfCipher, ok := algorithm.CipherById[pk.kdf.Bytes()[2]]
+	if !ok {
+		return errors.UnsupportedError("unsupported ECDH KDF cipher: " + strconv.Itoa(int(pk.kdf.Bytes()[2])))
+	}
+
+	ecdhKey := ecdh.NewPublicKey(c, kdfHash, kdfCipher)
+	err = ecdhKey.UnmarshalPoint(pk.p.Bytes())
+	pk.PublicKey = ecdhKey
+
+	return
+}
+
+func (pk *PublicKey) parseEdDSA(r io.Reader) (err error) {
+	pk.oid = new(encoding.OID)
+	if _, err = pk.oid.ReadFrom(r); err != nil {
+		return
+	}
+	curveInfo := ecc.FindByOid(pk.oid)
+	if curveInfo == nil {
+		return errors.UnsupportedError(fmt.Sprintf("unknown oid: %x", pk.oid))
+	}
+
+	c, ok := curveInfo.Curve.(ecc.EdDSACurve)
+	if !ok {
+		return errors.UnsupportedError(fmt.Sprintf("unsupported oid: %x", pk.oid))
+	}
+
+	pk.p = new(encoding.MPI)
+	if _, err = pk.p.ReadFrom(r); err != nil {
+		return
+	}
+
+	pub := eddsa.NewPublicKey(c)
+
+	switch flag := pk.p.Bytes()[0]; flag {
+	case 0x04:
+		// TODO: see _grcy_ecc_eddsa_ensure_compact in grcypt
+		return errors.UnsupportedError("unsupported EdDSA compression: " + strconv.Itoa(int(flag)))
+	case 0x40:
+		err = pub.UnmarshalPoint(pk.p.Bytes())
+	default:
+		return errors.UnsupportedError("unsupported EdDSA compression: " + strconv.Itoa(int(flag)))
+	}
+
+	pk.PublicKey = pub
+	return
+}
+
+// SerializeForHash serializes the PublicKey to w with the special packet
+// header format needed for hashing.
+func (pk *PublicKey) SerializeForHash(w io.Writer) error {
+	pk.SerializeSignaturePrefix(w)
+	return pk.serializeWithoutHeaders(w)
+}
+
+// SerializeSignaturePrefix writes the prefix for this public key to the given Writer.
+// The prefix is used when calculating a signature over this public key. See
+// RFC 4880, section 5.2.4.
+func (pk *PublicKey) SerializeSignaturePrefix(w io.Writer) {
+	var pLength = pk.algorithmSpecificByteCount()
+	if pk.Version == 5 {
+		pLength += 10 // version, timestamp (4), algorithm, key octet count (4).
+		w.Write([]byte{
+			0x9A,
+			byte(pLength >> 24),
+			byte(pLength >> 16),
+			byte(pLength >> 8),
+			byte(pLength),
+		})
+		return
+	}
+	pLength += 6
+	w.Write([]byte{0x99, byte(pLength >> 8), byte(pLength)})
+}
+
+func (pk *PublicKey) Serialize(w io.Writer) (err error) {
+	length := 6 // 6 byte header
+	length += pk.algorithmSpecificByteCount()
+	if pk.Version == 5 {
+		length += 4 // octet key count
+	}
+	packetType := packetTypePublicKey
+	if pk.IsSubkey {
+		packetType = packetTypePublicSubkey
+	}
+	err = serializeHeader(w, packetType, length)
+	if err != nil {
+		return
+	}
+	return pk.serializeWithoutHeaders(w)
+}
+
+func (pk *PublicKey) algorithmSpecificByteCount() int {
+	length := 0
+	switch pk.PubKeyAlgo {
+	case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly:
+		length += int(pk.n.EncodedLength())
+		length += int(pk.e.EncodedLength())
+	case PubKeyAlgoDSA:
+		length += int(pk.p.EncodedLength())
+		length += int(pk.q.EncodedLength())
+		length += int(pk.g.EncodedLength())
+		length += int(pk.y.EncodedLength())
+	case PubKeyAlgoElGamal:
+		length += int(pk.p.EncodedLength())
+		length += int(pk.g.EncodedLength())
+		length += int(pk.y.EncodedLength())
+	case PubKeyAlgoECDSA:
+		length += int(pk.oid.EncodedLength())
+		length += int(pk.p.EncodedLength())
+	case PubKeyAlgoECDH:
+		length += int(pk.oid.EncodedLength())
+		length += int(pk.p.EncodedLength())
+		length += int(pk.kdf.EncodedLength())
+	case PubKeyAlgoEdDSA:
+		length += int(pk.oid.EncodedLength())
+		length += int(pk.p.EncodedLength())
+	default:
+		panic("unknown public key algorithm")
+	}
+	return length
+}
+
+// serializeWithoutHeaders marshals the PublicKey to w in the form of an
+// OpenPGP public key packet, not including the packet header.
+func (pk *PublicKey) serializeWithoutHeaders(w io.Writer) (err error) {
+	t := uint32(pk.CreationTime.Unix())
+	if _, err = w.Write([]byte{
+		byte(pk.Version),
+		byte(t >> 24), byte(t >> 16), byte(t >> 8), byte(t),
+		byte(pk.PubKeyAlgo),
+	}); err != nil {
+		return
+	}
+
+	if pk.Version == 5 {
+		n := pk.algorithmSpecificByteCount()
+		if _, err = w.Write([]byte{
+			byte(n >> 24), byte(n >> 16), byte(n >> 8), byte(n),
+		}); err != nil {
+			return
+		}
+	}
+
+	switch pk.PubKeyAlgo {
+	case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly:
+		if _, err = w.Write(pk.n.EncodedBytes()); err != nil {
+			return
+		}
+		_, err = w.Write(pk.e.EncodedBytes())
+		return
+	case PubKeyAlgoDSA:
+		if _, err = w.Write(pk.p.EncodedBytes()); err != nil {
+			return
+		}
+		if _, err = w.Write(pk.q.EncodedBytes()); err != nil {
+			return
+		}
+		if _, err = w.Write(pk.g.EncodedBytes()); err != nil {
+			return
+		}
+		_, err = w.Write(pk.y.EncodedBytes())
+		return
+	case PubKeyAlgoElGamal:
+		if _, err = w.Write(pk.p.EncodedBytes()); err != nil {
+			return
+		}
+		if _, err = w.Write(pk.g.EncodedBytes()); err != nil {
+			return
+		}
+		_, err = w.Write(pk.y.EncodedBytes())
+		return
+	case PubKeyAlgoECDSA:
+		if _, err = w.Write(pk.oid.EncodedBytes()); err != nil {
+			return
+		}
+		_, err = w.Write(pk.p.EncodedBytes())
+		return
+	case PubKeyAlgoECDH:
+		if _, err = w.Write(pk.oid.EncodedBytes()); err != nil {
+			return
+		}
+		if _, err = w.Write(pk.p.EncodedBytes()); err != nil {
+			return
+		}
+		_, err = w.Write(pk.kdf.EncodedBytes())
+		return
+	case PubKeyAlgoEdDSA:
+		if _, err = w.Write(pk.oid.EncodedBytes()); err != nil {
+			return
+		}
+		_, err = w.Write(pk.p.EncodedBytes())
+		return
+	}
+	return errors.InvalidArgumentError("bad public-key algorithm")
+}
+
+// CanSign returns true iff this public key can generate signatures
+func (pk *PublicKey) CanSign() bool {
+	return pk.PubKeyAlgo != PubKeyAlgoRSAEncryptOnly && pk.PubKeyAlgo != PubKeyAlgoElGamal && pk.PubKeyAlgo != PubKeyAlgoECDH
+}
+
+// VerifySignature returns nil iff sig is a valid signature, made by this
+// public key, of the data hashed into signed. signed is mutated by this call.
+func (pk *PublicKey) VerifySignature(signed hash.Hash, sig *Signature) (err error) {
+	if !pk.CanSign() {
+		return errors.InvalidArgumentError("public key cannot generate signatures")
+	}
+	if sig.Version == 5 && (sig.SigType == 0x00 || sig.SigType == 0x01) {
+		sig.AddMetadataToHashSuffix()
+	}
+	signed.Write(sig.HashSuffix)
+	hashBytes := signed.Sum(nil)
+	if hashBytes[0] != sig.HashTag[0] || hashBytes[1] != sig.HashTag[1] {
+		return errors.SignatureError("hash tag doesn't match")
+	}
+
+	if pk.PubKeyAlgo != sig.PubKeyAlgo {
+		return errors.InvalidArgumentError("public key and signature use different algorithms")
+	}
+
+	switch pk.PubKeyAlgo {
+	case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly:
+		rsaPublicKey, _ := pk.PublicKey.(*rsa.PublicKey)
+		err = rsa.VerifyPKCS1v15(rsaPublicKey, sig.Hash, hashBytes, padToKeySize(rsaPublicKey, sig.RSASignature.Bytes()))
+		if err != nil {
+			return errors.SignatureError("RSA verification failure")
+		}
+		return nil
+	case PubKeyAlgoDSA:
+		dsaPublicKey, _ := pk.PublicKey.(*dsa.PublicKey)
+		// Need to truncate hashBytes to match FIPS 186-3 section 4.6.
+		subgroupSize := (dsaPublicKey.Q.BitLen() + 7) / 8
+		if len(hashBytes) > subgroupSize {
+			hashBytes = hashBytes[:subgroupSize]
+		}
+		if !dsa.Verify(dsaPublicKey, hashBytes, new(big.Int).SetBytes(sig.DSASigR.Bytes()), new(big.Int).SetBytes(sig.DSASigS.Bytes())) {
+			return errors.SignatureError("DSA verification failure")
+		}
+		return nil
+	case PubKeyAlgoECDSA:
+		ecdsaPublicKey := pk.PublicKey.(*ecdsa.PublicKey)
+		if !ecdsa.Verify(ecdsaPublicKey, hashBytes, new(big.Int).SetBytes(sig.ECDSASigR.Bytes()), new(big.Int).SetBytes(sig.ECDSASigS.Bytes())) {
+			return errors.SignatureError("ECDSA verification failure")
+		}
+		return nil
+	case PubKeyAlgoEdDSA:
+		eddsaPublicKey := pk.PublicKey.(*eddsa.PublicKey)
+		if !eddsa.Verify(eddsaPublicKey, hashBytes, sig.EdDSASigR.Bytes(), sig.EdDSASigS.Bytes()) {
+			return errors.SignatureError("EdDSA verification failure")
+		}
+		return nil
+	default:
+		return errors.SignatureError("Unsupported public key algorithm used in signature")
+	}
+}
+
+// keySignatureHash returns a Hash of the message that needs to be signed for
+// pk to assert a subkey relationship to signed.
+func keySignatureHash(pk, signed signingKey, hashFunc crypto.Hash) (h hash.Hash, err error) {
+	if !hashFunc.Available() {
+		return nil, errors.UnsupportedError("hash function")
+	}
+	h = hashFunc.New()
+
+	// RFC 4880, section 5.2.4
+	err = pk.SerializeForHash(h)
+	if err != nil {
+		return nil, err
+	}
+
+	err = signed.SerializeForHash(h)
+	return
+}
+
+// VerifyKeySignature returns nil iff sig is a valid signature, made by this
+// public key, of signed.
+func (pk *PublicKey) VerifyKeySignature(signed *PublicKey, sig *Signature) error {
+	h, err := keySignatureHash(pk, signed, sig.Hash)
+	if err != nil {
+		return err
+	}
+	if err = pk.VerifySignature(h, sig); err != nil {
+		return err
+	}
+
+	if sig.FlagSign {
+		// Signing subkeys must be cross-signed. See
+		// https://www.gnupg.org/faq/subkey-cross-certify.html.
+		if sig.EmbeddedSignature == nil {
+			return errors.StructuralError("signing subkey is missing cross-signature")
+		}
+		// Verify the cross-signature. This is calculated over the same
+		// data as the main signature, so we cannot just recursively
+		// call signed.VerifyKeySignature(...)
+		if h, err = keySignatureHash(pk, signed, sig.EmbeddedSignature.Hash); err != nil {
+			return errors.StructuralError("error while hashing for cross-signature: " + err.Error())
+		}
+		if err := signed.VerifySignature(h, sig.EmbeddedSignature); err != nil {
+			return errors.StructuralError("error while verifying cross-signature: " + err.Error())
+		}
+	}
+
+	return nil
+}
+
+func keyRevocationHash(pk signingKey, hashFunc crypto.Hash) (h hash.Hash, err error) {
+	if !hashFunc.Available() {
+		return nil, errors.UnsupportedError("hash function")
+	}
+	h = hashFunc.New()
+
+	// RFC 4880, section 5.2.4
+	err = pk.SerializeForHash(h)
+
+	return
+}
+
+// VerifyRevocationSignature returns nil iff sig is a valid signature, made by this
+// public key.
+func (pk *PublicKey) VerifyRevocationSignature(sig *Signature) (err error) {
+	h, err := keyRevocationHash(pk, sig.Hash)
+	if err != nil {
+		return err
+	}
+	return pk.VerifySignature(h, sig)
+}
+
+// VerifySubkeyRevocationSignature returns nil iff sig is a valid subkey revocation signature,
+// made by this public key, of signed.
+func (pk *PublicKey) VerifySubkeyRevocationSignature(sig *Signature, signed *PublicKey) (err error) {
+	h, err := keySignatureHash(pk, signed, sig.Hash)
+	if err != nil {
+		return err
+	}
+	return pk.VerifySignature(h, sig)
+}
+
+// userIdSignatureHash returns a Hash of the message that needs to be signed
+// to assert that pk is a valid key for id.
+func userIdSignatureHash(id string, pk *PublicKey, hashFunc crypto.Hash) (h hash.Hash, err error) {
+	if !hashFunc.Available() {
+		return nil, errors.UnsupportedError("hash function")
+	}
+	h = hashFunc.New()
+
+	// RFC 4880, section 5.2.4
+	pk.SerializeSignaturePrefix(h)
+	pk.serializeWithoutHeaders(h)
+
+	var buf [5]byte
+	buf[0] = 0xb4
+	buf[1] = byte(len(id) >> 24)
+	buf[2] = byte(len(id) >> 16)
+	buf[3] = byte(len(id) >> 8)
+	buf[4] = byte(len(id))
+	h.Write(buf[:])
+	h.Write([]byte(id))
+
+	return
+}
+
+// VerifyUserIdSignature returns nil iff sig is a valid signature, made by this
+// public key, that id is the identity of pub.
+func (pk *PublicKey) VerifyUserIdSignature(id string, pub *PublicKey, sig *Signature) (err error) {
+	h, err := userIdSignatureHash(id, pub, sig.Hash)
+	if err != nil {
+		return err
+	}
+	return pk.VerifySignature(h, sig)
+}
+
+// KeyIdString returns the public key's fingerprint in capital hex
+// (e.g. "6C7EE1B8621CC013").
+func (pk *PublicKey) KeyIdString() string {
+	return fmt.Sprintf("%X", pk.Fingerprint[12:20])
+}
+
+// KeyIdShortString returns the short form of public key's fingerprint
+// in capital hex, as shown by gpg --list-keys (e.g. "621CC013").
+func (pk *PublicKey) KeyIdShortString() string {
+	return fmt.Sprintf("%X", pk.Fingerprint[16:20])
+}
+
+// BitLength returns the bit length for the given public key.
+func (pk *PublicKey) BitLength() (bitLength uint16, err error) {
+	switch pk.PubKeyAlgo {
+	case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly:
+		bitLength = pk.n.BitLength()
+	case PubKeyAlgoDSA:
+		bitLength = pk.p.BitLength()
+	case PubKeyAlgoElGamal:
+		bitLength = pk.p.BitLength()
+	case PubKeyAlgoECDSA:
+		bitLength = pk.p.BitLength()
+	case PubKeyAlgoECDH:
+		bitLength = pk.p.BitLength()
+	case PubKeyAlgoEdDSA:
+		bitLength = pk.p.BitLength()
+	default:
+		err = errors.InvalidArgumentError("bad public-key algorithm")
+	}
+	return
+}
+
+// KeyExpired returns whether sig is a self-signature of a key that has
+// expired or is created in the future.
+func (pk *PublicKey) KeyExpired(sig *Signature, currentTime time.Time) bool {
+	if pk.CreationTime.After(currentTime) {
+		return true
+	}
+	if sig.KeyLifetimeSecs == nil || *sig.KeyLifetimeSecs == 0 {
+		return false
+	}
+	expiry := pk.CreationTime.Add(time.Duration(*sig.KeyLifetimeSecs) * time.Second)
+	return currentTime.After(expiry)
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/public_key_test_data.go

@@ -0,0 +1,24 @@
+package packet
+
+const rsaFingerprintHex = "5fb74b1d03b1e3cb31bc2f8aa34d7e18c20c31bb"
+
+const rsaPkDataHex = "988d044d3c5c10010400b1d13382944bd5aba23a4312968b5095d14f947f600eb478e14a6fcb16b0e0cac764884909c020bc495cfcc39a935387c661507bdb236a0612fb582cac3af9b29cc2c8c70090616c41b662f4da4c1201e195472eb7f4ae1ccbcbf9940fe21d985e379a5563dde5b9a23d35f1cfaa5790da3b79db26f23695107bfaca8e7b5bcd0011010001"
+
+const dsaFingerprintHex = "eece4c094db002103714c63c8e8fbe54062f19ed"
+
+const dsaPkDataHex = "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"
+
+const ecdsaFingerprintHex = "9892270b38b8980b05c8d56d43fe956c542ca00b"
+
+const ecdsaPkDataHex = "9893045071c29413052b8104002304230401f4867769cedfa52c325018896245443968e52e51d0c2df8d939949cb5b330f2921711fbee1c9b9dddb95d15cb0255e99badeddda7cc23d9ddcaacbc290969b9f24019375d61c2e4e3b36953a28d8b2bc95f78c3f1d592fb24499be348656a7b17e3963187b4361afe497bc5f9f81213f04069f8e1fb9e6a6290ae295ca1a92b894396cb4"
+
+const ecdhFingerprintHex = "722354df2475a42164d1d49faa8b938f9a201946"
+
+const ecdhPkDataHex = "b90073044d53059212052b810400220303042faa84024a20b6735c4897efa5bfb41bf85b7eefeab5ca0cb9ffc8ea04a46acb25534a577694f9e25340a4ab5223a9dd1eda530c8aa2e6718db10d7e672558c7736fe09369ea5739a2a3554bf16d41faa50562f11c6d39bbd5dffb6b9a9ec91803010909"
+
+const eddsaFingerprintHex = "b2d5e5ec0e6deca6bc8eeeb00907e75e1dd99ad8"
+
+const eddsaPkDataHex = "98330456e2132b16092b06010401da470f01010740bbda39266affa511a8c2d02edf690fb784b0499c4406185811a163539ef11dc1b41d74657374696e67203c74657374696e674074657374696e672e636f6d3e8879041316080021050256e2132b021b03050b09080702061508090a0b020416020301021e01021780000a09100907e75e1dd99ad86d0c00fe39d2008359352782bc9b61ac382584cd8eff3f57a18c2287e3afeeb05d1f04ba00fe2d0bc1ddf3ff8adb9afa3e7d9287244b4ec567f3db4d60b74a9b5465ed528203"
+
+// Source: https://sites.google.com/site/brainhub/pgpecckeys#TOC-ECC-NIST-P-384-key
+const ecc384PubHex = `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`

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/reader.go

@@ -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

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/signature.go

@@ -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"
+	"github.com/ProtonMail/go-crypto/openpgp/ecdsa"
-	"golang.org/x/crypto/openpgp/s2k"
+	"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
+	RSASignature         encoding.Field
-	DSASigR, DSASigS     parsedMPI
+	DSASigR, DSASigS     encoding.Field
-	ECDSASigR, ECDSASigS parsedMPI
+	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
+	// In a self-signature, these flags are set there is a features subpacket
-	// support for MDC subpackets.
+	// indicating that the issuer implementation supports these features
-	MDC bool
+	// 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
+	hashedSubpackets := make([]byte, hashedSubpacketsLength)
-	sig.HashSuffix = make([]byte, l+6)
-	sig.HashSuffix[0] = 4
-	copy(sig.HashSuffix[1:], buf[:5])
-	hashedSubpackets := sig.HashSuffix[6:l]
 	_, err = readFull(r, hashedSubpackets)
 	if err != nil {
 		return
 	}
-	// See RFC 4880, section 5.2.4
+	err = sig.buildHashSuffix(hashedSubpackets)
-	trailer := sig.HashSuffix[l:]
+	if err != nil {
-	trailer[0] = 4
+		return
-	trailer[1] = 0xff
+	}
-	trailer[2] = uint8(l >> 24)
-	trailer[3] = uint8(l >> 16)
-	trailer[4] = uint8(l >> 8)
-	trailer[5] = uint8(l)
 
 	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)
+		sig.DSASigR = new(encoding.MPI)
-		if err == nil {
+		if _, err = sig.DSASigR.ReadFrom(r); err != nil {
-			sig.DSASigS.bytes, sig.DSASigS.bitLength, err = readMPI(r)
+			return
 		}
+
+		sig.DSASigS = new(encoding.MPI)
+		_, err = sig.DSASigS.ReadFrom(r)
 	case PubKeyAlgoECDSA:
-		sig.ECDSASigR.bytes, sig.ECDSASigR.bitLength, err = readMPI(r)
+		sig.ECDSASigR = new(encoding.MPI)
-		if err == nil {
+		if _, err = sig.ECDSASigR.ReadFrom(r); err != nil {
-			sig.ECDSASigS.bytes, sig.ECDSASigS.bitLength, err = readMPI(r)
+			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 {
+	if !isHashed &&
-	case creationTimeSubpacket:
+		packetType != issuerSubpacket &&
-		if !isHashed {
+		packetType != issuerFingerprintSubpacket &&
-			err = errors.StructuralError("signature creation time in non-hashed area")
+		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:
+	case trustSubpacket:
-		// Key expiration time, section 5.2.3.6
+		// Trust level and amount, section 5.2.3.13
-		if !isHashed {
+		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:
+	case notationDataSubpacket:
-		// Preferred hash algorithms, section 5.2.3.8
+		// Notation data, section 5.2.3.16
-		if !isHashed {
+		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 = new(ReasonForRevocation)
-		*sig.RevocationReason = subpacket[0]
+		*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
+		// features.
-		// indicate support for MDC-protected encryption.
+		if len(subpacket) > 0 {
-		sig.MDC = len(subpacket) >= 1 && subpacket[0]&1 == 1
+			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
+// SigExpired returns whether sig is a signature that has expired or is created
-// expired.
+// in the future.
-func (sig *Signature) KeyExpired(currentTime time.Time) bool {
+func (sig *Signature) SigExpired(currentTime time.Time) bool {
-	if sig.KeyLifetimeSecs == nil {
+	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) {
+func (sig *Signature) buildHashSuffix(hashedSubpackets []byte) (err error) {
-	hashedSubpacketsLen := subpacketsLength(sig.outSubpackets, true)
+	var hashId byte
-
 	var ok bool
-	l := 6 + hashedSubpacketsLen
+
-	sig.HashSuffix = make([]byte, l+6)
+	if sig.Version < 5 {
-	sig.HashSuffix[0] = 4
+		hashId, ok = algorithm.HashToHashIdWithSha1(sig.Hash)
-	sig.HashSuffix[1] = uint8(sig.SigType)
+	} else {
-	sig.HashSuffix[2] = uint8(sig.PubKeyAlgo)
+		hashId, ok = algorithm.HashToHashId(sig.Hash)
-	sig.HashSuffix[3], ok = s2k.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)
+	hashedFields := bytes.NewBuffer([]byte{
-	serializeSubpackets(sig.HashSuffix[6:l], sig.outSubpackets, true)
+		uint8(sig.Version),
-	trailer := sig.HashSuffix[l:]
+		uint8(sig.SigType),
-	trailer[0] = 4
+		uint8(sig.PubKeyAlgo),
-	trailer[1] = 0xff
+		uint8(hashId),
-	trailer[2] = byte(l >> 24)
+		uint8(len(hashedSubpackets) >> 8),
-	trailer[3] = byte(l >> 16)
+		uint8(len(hashedSubpackets)),
-	trailer[4] = byte(l >> 8)
+	})
-	trailer[5] = byte(l)
+	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)
+		sigdata, err := priv.PrivateKey.(crypto.Signer).Sign(config.Random(), digest, sig.Hash)
-		sig.RSASignature.bitLength = uint16(8 * len(sig.RSASignature.bytes))
+		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 = new(encoding.MPI).SetBig(r)
-			sig.DSASigR.bitLength = uint16(8 * len(sig.DSASigR.bytes))
+			sig.DSASigS = new(encoding.MPI).SetBig(s)
-			sig.DSASigS.bytes = s.Bytes()
-			sig.DSASigS.bitLength = uint16(8 * len(sig.DSASigS.bytes))
 		}
 	case PubKeyAlgoECDSA:
-		var r, s *big.Int
+		sk := priv.PrivateKey.(*ecdsa.PrivateKey)
-		if pk, ok := priv.PrivateKey.(*ecdsa.PrivateKey); ok {
+		r, s, err := ecdsa.Sign(config.Random(), sk, digest)
-			// direct support, avoid asn1 wrapping/unwrapping
+
-			r, s, err = ecdsa.Sign(config.Random(), pk, digest)
-		} else {
-			var b []byte
-			b, err = priv.PrivateKey.(crypto.Signer).Sign(config.Random(), digest, sig.Hash)
 		if err == nil {
-				r, s, err = unwrapECDSASig(b)
+			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.EdDSASigR = encoding.NewMPI(r)
-			sig.ECDSASigS = fromBig(s)
+			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 = int(sig.DSASigR.EncodedLength())
-		sigLength += 2 + len(sig.DSASigS.bytes)
+		sigLength += int(sig.DSASigS.EncodedLength())
 	case PubKeyAlgoECDSA:
-		sigLength = 2 + len(sig.ECDSASigR.bytes)
+		sigLength = int(sig.ECDSASigR.EncodedLength())
-		sigLength += 2 + len(sig.ECDSASigS.bytes)
+		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()
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetric_key_encrypted.go

@@ -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)
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted.go

@@ -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)
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted_aead.go

@@ -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
+}

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/symmetrically_encrypted_mdc.go

@@ -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
+// seMdcReader wraps an io.Reader with a no-op Close method.
-// encrypted contents will consist of more OpenPGP packets. See RFC 4880,
+type seMdcReader struct {
-// sections 5.7 and 5.13.
+	in io.Reader
-type SymmetricallyEncrypted struct {
-	MDC      bool // true iff this is a type 18 packet and thus has an embedded MAC.
-	contents io.Reader
-	prefix   []byte
 }
 
-const symmetricallyEncryptedVersion = 1
+func (ser seMdcReader) Read(buf []byte) (int, error) {
+	return ser.in.Read(buf)
+}
 
-func (se *SymmetricallyEncrypted) parse(r io.Reader) error {
+func (ser seMdcReader) Close() 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
 	return nil
 }
 
-// Decrypt returns a ReadCloser, from which the decrypted contents of the
+func (se *SymmetricallyEncrypted) decryptMdc(c CipherFunction, key []byte) (io.ReadCloser, error) {
-// packet can be read. An incorrect key can, with high probability, be detected
+	if !c.IsSupported() {
-// immediately and this will result in a KeyIncorrect error being returned.
+		return nil, errors.UnsupportedError("unsupported cipher: " + strconv.Itoa(int(c)))
-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)))
 	}
-	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 {
+	if se.IntegrityProtected {
-		// MDC packets have an embedded hash that we need to check.
+		// 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
+	return seMdcReader{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
 }
 
 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
+func serializeSymmetricallyEncryptedMdc(ciphertext io.WriteCloser, c CipherFunction, key []byte, config *Config) (Contents io.WriteCloser, err error) {
-// to w and returns a WriteCloser to which the to-be-encrypted packets can be
+	// Disallow old cipher suites
-// written.
+	if !c.IsSupported() ||  c < CipherAES128 {
-// If config is nil, sensible defaults will be used.
+		return nil, errors.InvalidArgumentError("invalid mdc cipher function")
-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
 	}
 
-	_, 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
 }

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/userattribute.go

@@ -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

vendor/github.com/ProtonMail/go-crypto/openpgp/packet/userid.go

@@ -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
 }

vendor/github.com/ProtonMail/go-crypto/openpgp/read.go

@@ -3,24 +3,21 @@
 // license that can be found in the LICENSE file.
 
 // Package openpgp implements high level operations on OpenPGP messages.
-//
+package openpgp // import "github.com/ProtonMail/go-crypto/openpgp"
-// 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"
 
 import (
 	"crypto"
 	_ "crypto/sha256"
+	_ "crypto/sha512"
 	"hash"
 	"io"
 	"strconv"
 
-	"golang.org/x/crypto/openpgp/armor"
+	"github.com/ProtonMail/go-crypto/openpgp/armor"
-	"golang.org/x/crypto/openpgp/errors"
+	"github.com/ProtonMail/go-crypto/openpgp/errors"
-	"golang.org/x/crypto/openpgp/packet"
+	"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)
+	UnverifiedSignatures []*packet.Signature // all other unverified signature packets.
-	SignatureV3    *packet.SignatureV3 // the signature packet if it is a v2 or v3 signature
 
 	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)
+					errDec := pk.encryptedKey.Decrypt(pk.key.PrivateKey, config)
-				}
+					if errDec != nil {
-				if len(pk.encryptedKey.Key) == 0 {
 						continue
 					}
-				decrypted, err = se.Decrypt(pk.encryptedKey.CipherFunc, pk.encryptedKey.Key)
+				}
+				// Try to decrypt symmetrically encrypted
+				decrypted, err = edp.Decrypt(pk.encryptedKey.CipherFunc, pk.encryptedKey.Key)
 				if err != nil && err != errors.ErrKeyIncorrect {
 					return nil, err
 				}
@@ -204,16 +211,17 @@ FindKey:
 		if len(symKeys) != 0 && passphrase != nil {
 			for _, s := range symKeys {
 				key, cipherFunc, err := s.Decrypt(passphrase)
+				// In v4, on wrong passphrase, session key decryption is very likely to result in an invalid cipherFunc:
+				// only for < 5% of cases we will proceed to decrypt the data
 				if err == nil {
-					decrypted, err = se.Decrypt(cipherFunc, key)
+					decrypted, err = edp.Decrypt(cipherFunc, key)
-					if err != nil && err != errors.ErrKeyIncorrect {
+					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 {
+			if prevLast {
-				return nil, errors.UnsupportedError("nested signatures")
+				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
+				md.SignatureError = err
-				return
 			}
 
 			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 {
+	if md.IsSigned && md.SignatureError == nil {
-		md.UnverifiedBody = &signatureCheckReader{packets, h, wrappedHash, md}
+		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) {
+func hashForSignature(hashFunc crypto.Hash, sigType packet.SignatureType) (hash.Hash, hash.Hash, error) {
-	if !hashId.Available() {
+	if _, ok := algorithm.HashToHashIdWithSha1(hashFunc); !ok {
-		return nil, nil, errors.UnsupportedError("hash not available: " + strconv.Itoa(int(hashId)))
+		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) {
+func (cr checkReader) Read(buf []byte) (int, error) {
-	n, err = cr.md.LiteralData.Body.Read(buf)
+	n, sensitiveParsingError := cr.md.LiteralData.Body.Read(buf)
-	if err == io.EOF {
+	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) {
+func (scr *signatureCheckReader) Read(buf []byte) (int, error) {
-	n, err = scr.md.LiteralData.Body.Read(buf)
+	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 {
+			if sig, ok = p.(*packet.Signature); ok {
-			scr.md.SignatureError = scr.md.SignedBy.PublicKey.VerifySignature(scr.h, scr.md.Signature)
+				if sig.Version == 5 && (sig.SigType == 0x00 || sig.SigType == 0x01) {
-		} else if scr.md.SignatureV3, ok = p.(*packet.SignatureV3); ok {
+					sig.Metadata = scr.md.LiteralData
-			scr.md.SignatureError = scr.md.SignedBy.PublicKey.VerifySignatureV3(scr.h, scr.md.SignatureV3)
+				}
+
+				// 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")
+					scr.md.UnverifiedSignatures = append(scr.md.UnverifiedSignatures, sig)
-			return
+				}
+			}
+
+			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) {
+		var ok bool
-		case *packet.Signature:
+		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
+		for i, expectedHash := range expectedHashes {
-			hashFunc = sig.Hash
+			if hashFunc == expectedHash {
-			sigType = sig.SigType
+				break
-		default:
+			}
-			return nil, errors.StructuralError("non signature packet found")
+			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
 }

vendor/github.com/ProtonMail/go-crypto/openpgp/s2k/s2k.go

@@ -4,13 +4,7 @@
 
 // Package s2k implements the various OpenPGP string-to-key transforms as
 // specified in RFC 4800 section 3.7.1.
-//
+package s2k // import "github.com/ProtonMail/go-crypto/openpgp/s2k"
-// 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"
 
 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
+	// should be between 65536 and 65011712, inclusive. If Config
-	// is nil or S2KCount is 0, the value 65536 used. Not all
+	// 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
+	// be encoded exactly. See RFC 4880 Section 3.7.1.3.
-	// use a value that is at least 65536. 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.SHA256
-		return crypto.SHA1
 	}
 
 	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 < 65536:
-	case i < 1024:
+		i = 65536
-		i = 1024
 	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])
+	params = &Params{
-	if !ok {
+		mode:   buf[0],
-		return nil, errors.UnsupportedError("hash for S2K function: " + strconv.Itoa(int(buf[1])))
+		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) {
+		return params, nil
-			Simple(out, h, in)
-		}
-		return f, 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])
+		params.salt = buf[:8]
-		}
+		return params, nil
-		return f, 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
+	params, err := Generate(rand, c)
-	buf[0] = 3 /* iterated and salted */
+	if err != nil {
-	buf[1], _ = HashToHashId(c.hash())
-	salt := buf[2:10]
-	if _, err := io.ReadFull(rand, salt); err != nil {
 		return err
 	}
-	encodedCount := c.encodedCount()
+	err = params.Serialize(w)
-	count := decodeCount(encodedCount)
+	if err != nil {
-	buf[10] = encodedCount
-	if _, err := w.Write(buf[:]); 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
-}

vendor/github.com/ProtonMail/go-crypto/openpgp/write.go

@@ -11,10 +11,10 @@ import (
 	"strconv"
 	"time"
 
-	"golang.org/x/crypto/openpgp/armor"
+	"github.com/ProtonMail/go-crypto/openpgp/armor"
-	"golang.org/x/crypto/openpgp/errors"
+	"github.com/ProtonMail/go-crypto/openpgp/errors"
-	"golang.org/x/crypto/openpgp/packet"
+	"github.com/ProtonMail/go-crypto/openpgp/internal/algorithm"
-	"golang.org/x/crypto/openpgp/s2k"
+	"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 := createSignaturePacket(signingKey.PublicKey, sigType, config)
-	sig.SigType = sigType
-	sig.PubKeyAlgo = signer.PrivateKey.PubKeyAlgo
-	sig.Hash = config.Hash()
-	sig.CreationTime = config.Now()
-	sig.IssuerKeyId = &signer.PrivateKey.KeyId
 
 	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.SHA3_256),
-		hashToHashId(crypto.RIPEMD160),
+		hashToHashId(crypto.SHA3_512),
+	}
+
+	// Prefer GCM if everyone supports it
+	candidateCipherSuites := [][2]uint8{
+		{uint8(packet.CipherAES256), uint8(packet.AEADModeGCM)},
+		{uint8(packet.CipherAES256), uint8(packet.AEADModeEAX)},
+		{uint8(packet.CipherAES256), uint8(packet.AEADModeOCB)},
+		{uint8(packet.CipherAES128), uint8(packet.AEADModeGCM)},
+		{uint8(packet.CipherAES128), uint8(packet.AEADModeEAX)},
+		{uint8(packet.CipherAES128), uint8(packet.AEADModeOCB)},
+	}
+
+	candidateCompression := []uint8{
+		uint8(packet.CompressionNone),
+		uint8(packet.CompressionZIP),
+		uint8(packet.CompressionZLIB),
 	}
-	// In the event that a recipient doesn't specify any supported ciphers
-	// or hash functions, these are the ones that we assume that every
-	// implementation supports.
-	defaultCiphers := candidateCiphers[len(candidateCiphers)-1:]
-	defaultHashes := candidateHashes[len(candidateHashes)-1:]
 
 	encryptKeys := make([]Key, len(to))
+
+	// AEAD is used only if config enables it and every key supports it
+	aeadSupported := config.AEAD() != nil
+
 	for i := range to {
 		var ok bool
-		encryptKeys[i], ok = to[i].encryptionKey(config.Now())
+		encryptKeys[i], ok = to[i].EncryptionKey(config.Now())
 		if !ok {
-			return nil, errors.InvalidArgumentError("cannot encrypt a message to key id " + strconv.FormatUint(to[i].PrimaryKey.KeyId, 16) + " because it has no encryption keys")
+			return nil, errors.InvalidArgumentError("cannot encrypt a message to key id " + strconv.FormatUint(to[i].PrimaryKey.KeyId, 16) + " because it has no valid encryption keys")
 		}
 
-		sig := to[i].primaryIdentity().SelfSignature
+		sig := to[i].PrimaryIdentity().SelfSignature
-
+		if sig.SEIPDv2 == false {
-		preferredSymmetric := sig.PreferredSymmetric
+			aeadSupported = false
-		if len(preferredSymmetric) == 0 {
-			preferredSymmetric = defaultCiphers
-		}
-		preferredHashes := sig.PreferredHash
-		if len(preferredHashes) == 0 {
-			preferredHashes = defaultHashes
-		}
-		candidateCiphers = intersectPreferences(candidateCiphers, preferredSymmetric)
-		candidateHashes = intersectPreferences(candidateHashes, preferredHashes)
 		}
 
-	if len(candidateCiphers) == 0 || len(candidateHashes) == 0 {
+		candidateCiphers = intersectPreferences(candidateCiphers, sig.PreferredSymmetric)
-		return nil, errors.InvalidArgumentError("cannot encrypt because recipient set shares no common algorithms")
+		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.SHA3_256),
-		hashToHashId(crypto.RIPEMD160),
+		hashToHashId(crypto.SHA3_512),
 	}
-	defaultHashes := candidateHashes[len(candidateHashes)-1:]
+	defaultHashes := candidateHashes[0:1]
-	preferredHashes := signed.primaryIdentity().SelfSignature.PreferredHash
+	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{
+	sig := createSignaturePacket(&s.signer.PublicKey, s.sigType, s.config)
-		SigType:      packet.SigTypeBinary,
+	sig.Hash = s.hashType
-		PubKeyAlgo:   s.signer.PubKeyAlgo,
+	sig.Metadata = s.metadata
-		Hash:         s.hashType,
-		CreationTime: s.config.Now(),
-		IssuerKeyId:  &s.signer.KeyId,
-	}
 
 	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
+}

vendor/github.com/cloudflare/circl/LICENSE

@@ -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.

vendor/github.com/cloudflare/circl/dh/x25519/curve.go

@@ -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,
+	},
+}

vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.go

@@ -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)

vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.h

@@ -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)

vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.s

@@ -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

vendor/github.com/cloudflare/circl/dh/x25519/curve_generic.go

@@ -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])
+	}
+}

vendor/github.com/cloudflare/circl/dh/x25519/curve_noasm.go

@@ -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) }

vendor/github.com/cloudflare/circl/dh/x25519/doc.go

@@ -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

vendor/github.com/cloudflare/circl/dh/x25519/key.go

@@ -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
+}

vendor/github.com/cloudflare/circl/dh/x25519/table.go

@@ -0,0 +1,268 @@
+package x25519
+
+import "github.com/cloudflare/circl/math/fp25519"
+
+// tableGenerator contains the set of points:
+//
+//	t[i] = (xi+1)/(xi-1),
+//
+// where (xi,yi) = 2^iG and G is the generator point
+// Size = (256)*(256/8) = 8192 bytes.
+var tableGenerator = [256 * fp25519.Size]byte{
+	/* (2^  0)P */ 0xf3, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x5f,
+	/* (2^  1)P */ 0x96, 0xfe, 0xaa, 0x16, 0xf4, 0x20, 0x82, 0x6b, 0x34, 0x6a, 0x56, 0x4f, 0x2b, 0xeb, 0xeb, 0x82, 0x0f, 0x95, 0xa5, 0x75, 0xb0, 0xa5, 0xa9, 0xd5, 0xf4, 0x88, 0x24, 0x4b, 0xcf, 0xb2, 0x42, 0x51,
+	/* (2^  2)P */ 0x0c, 0x68, 0x69, 0x00, 0x75, 0xbc, 0xae, 0x6a, 0x41, 0x9c, 0xf9, 0xa0, 0x20, 0x78, 0xcf, 0x89, 0xf4, 0xd0, 0x56, 0x3b, 0x18, 0xd9, 0x58, 0x2a, 0xa4, 0x11, 0x60, 0xe3, 0x80, 0xca, 0x5a, 0x4b,
+	/* (2^  3)P */ 0x5d, 0x74, 0x29, 0x8c, 0x34, 0x32, 0x91, 0x32, 0xd7, 0x2f, 0x64, 0xe1, 0x16, 0xe6, 0xa2, 0xf4, 0x34, 0xbc, 0x67, 0xff, 0x03, 0xbb, 0x45, 0x1e, 0x4a, 0x9b, 0x2a, 0xf4, 0xd0, 0x12, 0x69, 0x30,
+	/* (2^  4)P */ 0x54, 0x71, 0xaf, 0xe6, 0x07, 0x65, 0x88, 0xff, 0x2f, 0xc8, 0xee, 0xdf, 0x13, 0x0e, 0xf5, 0x04, 0xce, 0xb5, 0xba, 0x2a, 0xe8, 0x2f, 0x51, 0xaa, 0x22, 0xf2, 0xd5, 0x68, 0x1a, 0x25, 0x4e, 0x17,
+	/* (2^  5)P */ 0x98, 0x88, 0x02, 0x82, 0x0d, 0x70, 0x96, 0xcf, 0xc5, 0x02, 0x2c, 0x0a, 0x37, 0xe3, 0x43, 0x17, 0xaa, 0x6e, 0xe8, 0xb4, 0x98, 0xec, 0x9e, 0x37, 0x2e, 0x48, 0xe0, 0x51, 0x8a, 0x88, 0x59, 0x0c,
+	/* (2^  6)P */ 0x89, 0xd1, 0xb5, 0x99, 0xd6, 0xf1, 0xcb, 0xfb, 0x84, 0xdc, 0x9f, 0x8e, 0xd5, 0xf0, 0xae, 0xac, 0x14, 0x76, 0x1f, 0x23, 0x06, 0x0d, 0xc2, 0xc1, 0x72, 0xf9, 0x74, 0xa2, 0x8d, 0x21, 0x38, 0x29,
+	/* (2^  7)P */ 0x18, 0x7f, 0x1d, 0xff, 0xbe, 0x49, 0xaf, 0xf6, 0xc2, 0xc9, 0x7a, 0x38, 0x22, 0x1c, 0x54, 0xcc, 0x6b, 0xc5, 0x15, 0x40, 0xef, 0xc9, 0xfc, 0x96, 0xa9, 0x13, 0x09, 0x69, 0x7c, 0x62, 0xc1, 0x69,
+	/* (2^  8)P */ 0x0e, 0xdb, 0x33, 0x47, 0x2f, 0xfd, 0x86, 0x7a, 0xe9, 0x7d, 0x08, 0x9e, 0xf2, 0xc4, 0xb8, 0xfd, 0x29, 0xa2, 0xa2, 0x8e, 0x1a, 0x4b, 0x5e, 0x09, 0x79, 0x7a, 0xb3, 0x29, 0xc8, 0xa7, 0xd7, 0x1a,
+	/* (2^  9)P */ 0xc0, 0xa0, 0x7e, 0xd1, 0xca, 0x89, 0x2d, 0x34, 0x51, 0x20, 0xed, 0xcc, 0xa6, 0xdd, 0xbe, 0x67, 0x74, 0x2f, 0xb4, 0x2b, 0xbf, 0x31, 0xca, 0x19, 0xbb, 0xac, 0x80, 0x49, 0xc8, 0xb4, 0xf7, 0x3d,
+	/* (2^ 10)P */ 0x83, 0xd8, 0x0a, 0xc8, 0x4d, 0x44, 0xc6, 0xa8, 0x85, 0xab, 0xe3, 0x66, 0x03, 0x44, 0x1e, 0xb9, 0xd8, 0xf6, 0x64, 0x01, 0xa0, 0xcd, 0x15, 0xc2, 0x68, 0xe6, 0x47, 0xf2, 0x6e, 0x7c, 0x86, 0x3d,
+	/* (2^ 11)P */ 0x8c, 0x65, 0x3e, 0xcc, 0x2b, 0x58, 0xdd, 0xc7, 0x28, 0x55, 0x0e, 0xee, 0x48, 0x47, 0x2c, 0xfd, 0x71, 0x4f, 0x9f, 0xcc, 0x95, 0x9b, 0xfd, 0xa0, 0xdf, 0x5d, 0x67, 0xb0, 0x71, 0xd8, 0x29, 0x75,
+	/* (2^ 12)P */ 0x78, 0xbd, 0x3c, 0x2d, 0xb4, 0x68, 0xf5, 0xb8, 0x82, 0xda, 0xf3, 0x91, 0x1b, 0x01, 0x33, 0x12, 0x62, 0x3b, 0x7c, 0x4a, 0xcd, 0x6c, 0xce, 0x2d, 0x03, 0x86, 0x49, 0x9e, 0x8e, 0xfc, 0xe7, 0x75,
+	/* (2^ 13)P */ 0xec, 0xb6, 0xd0, 0xfc, 0xf1, 0x13, 0x4f, 0x2f, 0x45, 0x7a, 0xff, 0x29, 0x1f, 0xca, 0xa8, 0xf1, 0x9b, 0xe2, 0x81, 0x29, 0xa7, 0xc1, 0x49, 0xc2, 0x6a, 0xb5, 0x83, 0x8c, 0xbb, 0x0d, 0xbe, 0x6e,
+	/* (2^ 14)P */ 0x22, 0xb2, 0x0b, 0x17, 0x8d, 0xfa, 0x14, 0x71, 0x5f, 0x93, 0x93, 0xbf, 0xd5, 0xdc, 0xa2, 0x65, 0x9a, 0x97, 0x9c, 0xb5, 0x68, 0x1f, 0xc4, 0xbd, 0x89, 0x92, 0xce, 0xa2, 0x79, 0xef, 0x0e, 0x2f,
+	/* (2^ 15)P */ 0xce, 0x37, 0x3c, 0x08, 0x0c, 0xbf, 0xec, 0x42, 0x22, 0x63, 0x49, 0xec, 0x09, 0xbc, 0x30, 0x29, 0x0d, 0xac, 0xfe, 0x9c, 0xc1, 0xb0, 0x94, 0xf2, 0x80, 0xbb, 0xfa, 0xed, 0x4b, 0xaa, 0x80, 0x37,
+	/* (2^ 16)P */ 0x29, 0xd9, 0xea, 0x7c, 0x3e, 0x7d, 0xc1, 0x56, 0xc5, 0x22, 0x57, 0x2e, 0xeb, 0x4b, 0xcb, 0xe7, 0x5a, 0xe1, 0xbf, 0x2d, 0x73, 0x31, 0xe9, 0x0c, 0xf8, 0x52, 0x10, 0x62, 0xc7, 0x83, 0xb8, 0x41,
+	/* (2^ 17)P */ 0x50, 0x53, 0xd2, 0xc3, 0xa0, 0x5c, 0xf7, 0xdb, 0x51, 0xe3, 0xb1, 0x6e, 0x08, 0xbe, 0x36, 0x29, 0x12, 0xb2, 0xa9, 0xb4, 0x3c, 0xe0, 0x36, 0xc9, 0xaa, 0x25, 0x22, 0x32, 0x82, 0xbf, 0x45, 0x1d,
+	/* (2^ 18)P */ 0xc5, 0x4c, 0x02, 0x6a, 0x03, 0xb1, 0x1a, 0xe8, 0x72, 0x9a, 0x4c, 0x30, 0x1c, 0x20, 0x12, 0xe2, 0xfc, 0xb1, 0x32, 0x68, 0xba, 0x3f, 0xd7, 0xc5, 0x81, 0x95, 0x83, 0x4d, 0x5a, 0xdb, 0xff, 0x20,
+	/* (2^ 19)P */ 0xad, 0x0f, 0x5d, 0xbe, 0x67, 0xd3, 0x83, 0xa2, 0x75, 0x44, 0x16, 0x8b, 0xca, 0x25, 0x2b, 0x6c, 0x2e, 0xf2, 0xaa, 0x7c, 0x46, 0x35, 0x49, 0x9d, 0x49, 0xff, 0x85, 0xee, 0x8e, 0x40, 0x66, 0x51,
+	/* (2^ 20)P */ 0x61, 0xe3, 0xb4, 0xfa, 0xa2, 0xba, 0x67, 0x3c, 0xef, 0x5c, 0xf3, 0x7e, 0xc6, 0x33, 0xe4, 0xb3, 0x1c, 0x9b, 0x15, 0x41, 0x92, 0x72, 0x59, 0x52, 0x33, 0xab, 0xb0, 0xd5, 0x92, 0x18, 0x62, 0x6a,
+	/* (2^ 21)P */ 0xcb, 0xcd, 0x55, 0x75, 0x38, 0x4a, 0xb7, 0x20, 0x3f, 0x92, 0x08, 0x12, 0x0e, 0xa1, 0x2a, 0x53, 0xd1, 0x1d, 0x28, 0x62, 0x77, 0x7b, 0xa1, 0xea, 0xbf, 0x44, 0x5c, 0xf0, 0x43, 0x34, 0xab, 0x61,
+	/* (2^ 22)P */ 0xf8, 0xde, 0x24, 0x23, 0x42, 0x6c, 0x7a, 0x25, 0x7f, 0xcf, 0xe3, 0x17, 0x10, 0x6c, 0x1c, 0x13, 0x57, 0xa2, 0x30, 0xf6, 0x39, 0x87, 0x75, 0x23, 0x80, 0x85, 0xa7, 0x01, 0x7a, 0x40, 0x5a, 0x29,
+	/* (2^ 23)P */ 0xd9, 0xa8, 0x5d, 0x6d, 0x24, 0x43, 0xc4, 0xf8, 0x5d, 0xfa, 0x52, 0x0c, 0x45, 0x75, 0xd7, 0x19, 0x3d, 0xf8, 0x1b, 0x73, 0x92, 0xfc, 0xfc, 0x2a, 0x00, 0x47, 0x2b, 0x1b, 0xe8, 0xc8, 0x10, 0x7d,
+	/* (2^ 24)P */ 0x0b, 0xa2, 0xba, 0x70, 0x1f, 0x27, 0xe0, 0xc8, 0x57, 0x39, 0xa6, 0x7c, 0x86, 0x48, 0x37, 0x99, 0xbb, 0xd4, 0x7e, 0xcb, 0xb3, 0xef, 0x12, 0x54, 0x75, 0x29, 0xe6, 0x73, 0x61, 0xd3, 0x96, 0x31,
+	/* (2^ 25)P */ 0xfc, 0xdf, 0xc7, 0x41, 0xd1, 0xca, 0x5b, 0xde, 0x48, 0xc8, 0x95, 0xb3, 0xd2, 0x8c, 0xcc, 0x47, 0xcb, 0xf3, 0x1a, 0xe1, 0x42, 0xd9, 0x4c, 0xa3, 0xc2, 0xce, 0x4e, 0xd0, 0xf2, 0xdb, 0x56, 0x02,
+	/* (2^ 26)P */ 0x7f, 0x66, 0x0e, 0x4b, 0xe9, 0xb7, 0x5a, 0x87, 0x10, 0x0d, 0x85, 0xc0, 0x83, 0xdd, 0xd4, 0xca, 0x9f, 0xc7, 0x72, 0x4e, 0x8f, 0x2e, 0xf1, 0x47, 0x9b, 0xb1, 0x85, 0x8c, 0xbb, 0x87, 0x1a, 0x5f,
+	/* (2^ 27)P */ 0xb8, 0x51, 0x7f, 0x43, 0xb6, 0xd0, 0xe9, 0x7a, 0x65, 0x90, 0x87, 0x18, 0x55, 0xce, 0xc7, 0x12, 0xee, 0x7a, 0xf7, 0x5c, 0xfe, 0x09, 0xde, 0x2a, 0x27, 0x56, 0x2c, 0x7d, 0x2f, 0x5a, 0xa0, 0x23,
+	/* (2^ 28)P */ 0x9a, 0x16, 0x7c, 0xf1, 0x28, 0xe1, 0x08, 0x59, 0x2d, 0x85, 0xd0, 0x8a, 0xdd, 0x98, 0x74, 0xf7, 0x64, 0x2f, 0x10, 0xab, 0xce, 0xc4, 0xb4, 0x74, 0x45, 0x98, 0x13, 0x10, 0xdd, 0xba, 0x3a, 0x18,
+	/* (2^ 29)P */ 0xac, 0xaa, 0x92, 0xaa, 0x8d, 0xba, 0x65, 0xb1, 0x05, 0x67, 0x38, 0x99, 0x95, 0xef, 0xc5, 0xd5, 0xd1, 0x40, 0xfc, 0xf8, 0x0c, 0x8f, 0x2f, 0xbe, 0x14, 0x45, 0x20, 0xee, 0x35, 0xe6, 0x01, 0x27,
+	/* (2^ 30)P */ 0x14, 0x65, 0x15, 0x20, 0x00, 0xa8, 0x9f, 0x62, 0xce, 0xc1, 0xa8, 0x64, 0x87, 0x86, 0x23, 0xf2, 0x0e, 0x06, 0x3f, 0x0b, 0xff, 0x4f, 0x89, 0x5b, 0xfa, 0xa3, 0x08, 0xf7, 0x4c, 0x94, 0xd9, 0x60,
+	/* (2^ 31)P */ 0x1f, 0x20, 0x7a, 0x1c, 0x1a, 0x00, 0xea, 0xae, 0x63, 0xce, 0xe2, 0x3e, 0x63, 0x6a, 0xf1, 0xeb, 0xe1, 0x07, 0x7a, 0x4c, 0x59, 0x09, 0x77, 0x6f, 0xcb, 0x08, 0x02, 0x0d, 0x15, 0x58, 0xb9, 0x79,
+	/* (2^ 32)P */ 0xe7, 0x10, 0xd4, 0x01, 0x53, 0x5e, 0xb5, 0x24, 0x4d, 0xc8, 0xfd, 0xf3, 0xdf, 0x4e, 0xa3, 0xe3, 0xd8, 0x32, 0x40, 0x90, 0xe4, 0x68, 0x87, 0xd8, 0xec, 0xae, 0x3a, 0x7b, 0x42, 0x84, 0x13, 0x13,
+	/* (2^ 33)P */ 0x14, 0x4f, 0x23, 0x86, 0x12, 0xe5, 0x05, 0x84, 0x29, 0xc5, 0xb4, 0xad, 0x39, 0x47, 0xdc, 0x14, 0xfd, 0x4f, 0x63, 0x50, 0xb2, 0xb5, 0xa2, 0xb8, 0x93, 0xff, 0xa7, 0xd8, 0x4a, 0xa9, 0xe2, 0x2f,
+	/* (2^ 34)P */ 0xdd, 0xfa, 0x43, 0xe8, 0xef, 0x57, 0x5c, 0xec, 0x18, 0x99, 0xbb, 0xf0, 0x40, 0xce, 0x43, 0x28, 0x05, 0x63, 0x3d, 0xcf, 0xd6, 0x61, 0xb5, 0xa4, 0x7e, 0x77, 0xfb, 0xe8, 0xbd, 0x29, 0x36, 0x74,
+	/* (2^ 35)P */ 0x8f, 0x73, 0xaf, 0xbb, 0x46, 0xdd, 0x3e, 0x34, 0x51, 0xa6, 0x01, 0xb1, 0x28, 0x18, 0x98, 0xed, 0x7a, 0x79, 0x2c, 0x88, 0x0b, 0x76, 0x01, 0xa4, 0x30, 0x87, 0xc8, 0x8d, 0xe2, 0x23, 0xc2, 0x1f,
+	/* (2^ 36)P */ 0x0e, 0xba, 0x0f, 0xfc, 0x91, 0x4e, 0x60, 0x48, 0xa4, 0x6f, 0x2c, 0x05, 0x8f, 0xf7, 0x37, 0xb6, 0x9c, 0x23, 0xe9, 0x09, 0x3d, 0xac, 0xcc, 0x91, 0x7c, 0x68, 0x7a, 0x43, 0xd4, 0xee, 0xf7, 0x23,
+	/* (2^ 37)P */ 0x00, 0xd8, 0x9b, 0x8d, 0x11, 0xb1, 0x73, 0x51, 0xa7, 0xd4, 0x89, 0x31, 0xb6, 0x41, 0xd6, 0x29, 0x86, 0xc5, 0xbb, 0x88, 0x79, 0x17, 0xbf, 0xfd, 0xf5, 0x1d, 0xd8, 0xca, 0x4f, 0x89, 0x59, 0x29,
+	/* (2^ 38)P */ 0x99, 0xc8, 0xbb, 0xb4, 0xf3, 0x8e, 0xbc, 0xae, 0xb9, 0x92, 0x69, 0xb2, 0x5a, 0x99, 0x48, 0x41, 0xfb, 0x2c, 0xf9, 0x34, 0x01, 0x0b, 0xe2, 0x24, 0xe8, 0xde, 0x05, 0x4a, 0x89, 0x58, 0xd1, 0x40,
+	/* (2^ 39)P */ 0xf6, 0x76, 0xaf, 0x85, 0x11, 0x0b, 0xb0, 0x46, 0x79, 0x7a, 0x18, 0x73, 0x78, 0xc7, 0xba, 0x26, 0x5f, 0xff, 0x8f, 0xab, 0x95, 0xbf, 0xc0, 0x3d, 0xd7, 0x24, 0x55, 0x94, 0xd8, 0x8b, 0x60, 0x2a,
+	/* (2^ 40)P */ 0x02, 0x63, 0x44, 0xbd, 0x88, 0x95, 0x44, 0x26, 0x9c, 0x43, 0x88, 0x03, 0x1c, 0xc2, 0x4b, 0x7c, 0xb2, 0x11, 0xbd, 0x83, 0xf3, 0xa4, 0x98, 0x8e, 0xb9, 0x76, 0xd8, 0xc9, 0x7b, 0x8d, 0x21, 0x26,
+	/* (2^ 41)P */ 0x8a, 0x17, 0x7c, 0x99, 0x42, 0x15, 0x08, 0xe3, 0x6f, 0x60, 0xb6, 0x6f, 0xa8, 0x29, 0x2d, 0x3c, 0x74, 0x93, 0x27, 0xfa, 0x36, 0x77, 0x21, 0x5c, 0xfa, 0xb1, 0xfe, 0x4a, 0x73, 0x05, 0xde, 0x7d,
+	/* (2^ 42)P */ 0xab, 0x2b, 0xd4, 0x06, 0x39, 0x0e, 0xf1, 0x3b, 0x9c, 0x64, 0x80, 0x19, 0x3e, 0x80, 0xf7, 0xe4, 0x7a, 0xbf, 0x95, 0x95, 0xf8, 0x3b, 0x05, 0xe6, 0x30, 0x55, 0x24, 0xda, 0x38, 0xaf, 0x4f, 0x39,
+	/* (2^ 43)P */ 0xf4, 0x28, 0x69, 0x89, 0x58, 0xfb, 0x8e, 0x7a, 0x3c, 0x11, 0x6a, 0xcc, 0xe9, 0x78, 0xc7, 0xfb, 0x6f, 0x59, 0xaf, 0x30, 0xe3, 0x0c, 0x67, 0x72, 0xf7, 0x6c, 0x3d, 0x1d, 0xa8, 0x22, 0xf2, 0x48,
+	/* (2^ 44)P */ 0xa7, 0xca, 0x72, 0x0d, 0x41, 0xce, 0x1f, 0xf0, 0x95, 0x55, 0x3b, 0x21, 0xc7, 0xec, 0x20, 0x5a, 0x83, 0x14, 0xfa, 0xc1, 0x65, 0x11, 0xc2, 0x7b, 0x41, 0xa7, 0xa8, 0x1d, 0xe3, 0x9a, 0xf8, 0x07,
+	/* (2^ 45)P */ 0xf9, 0x0f, 0x83, 0xc6, 0xb4, 0xc2, 0xd2, 0x05, 0x93, 0x62, 0x31, 0xc6, 0x0f, 0x33, 0x3e, 0xd4, 0x04, 0xa9, 0xd3, 0x96, 0x0a, 0x59, 0xa5, 0xa5, 0xb6, 0x33, 0x53, 0xa6, 0x91, 0xdb, 0x5e, 0x70,
+	/* (2^ 46)P */ 0xf7, 0xa5, 0xb9, 0x0b, 0x5e, 0xe1, 0x8e, 0x04, 0x5d, 0xaf, 0x0a, 0x9e, 0xca, 0xcf, 0x40, 0x32, 0x0b, 0xa4, 0xc4, 0xed, 0xce, 0x71, 0x4b, 0x8f, 0x6d, 0x4a, 0x54, 0xde, 0xa3, 0x0d, 0x1c, 0x62,
+	/* (2^ 47)P */ 0x91, 0x40, 0x8c, 0xa0, 0x36, 0x28, 0x87, 0x92, 0x45, 0x14, 0xc9, 0x10, 0xb0, 0x75, 0x83, 0xce, 0x94, 0x63, 0x27, 0x4f, 0x52, 0xeb, 0x72, 0x8a, 0x35, 0x36, 0xc8, 0x7e, 0xfa, 0xfc, 0x67, 0x26,
+	/* (2^ 48)P */ 0x2a, 0x75, 0xe8, 0x45, 0x33, 0x17, 0x4c, 0x7f, 0xa5, 0x79, 0x70, 0xee, 0xfe, 0x47, 0x1b, 0x06, 0x34, 0xff, 0x86, 0x9f, 0xfa, 0x9a, 0xdd, 0x25, 0x9c, 0xc8, 0x5d, 0x42, 0xf5, 0xce, 0x80, 0x37,
+	/* (2^ 49)P */ 0xe9, 0xb4, 0x3b, 0x51, 0x5a, 0x03, 0x46, 0x1a, 0xda, 0x5a, 0x57, 0xac, 0x79, 0xf3, 0x1e, 0x3e, 0x50, 0x4b, 0xa2, 0x5f, 0x1c, 0x5f, 0x8c, 0xc7, 0x22, 0x9f, 0xfd, 0x34, 0x76, 0x96, 0x1a, 0x32,
+	/* (2^ 50)P */ 0xfa, 0x27, 0x6e, 0x82, 0xb8, 0x07, 0x67, 0x94, 0xd0, 0x6f, 0x50, 0x4c, 0xd6, 0x84, 0xca, 0x3d, 0x36, 0x14, 0xe9, 0x75, 0x80, 0x21, 0x89, 0xc1, 0x84, 0x84, 0x3b, 0x9b, 0x16, 0x84, 0x92, 0x6d,
+	/* (2^ 51)P */ 0xdf, 0x2d, 0x3f, 0x38, 0x40, 0xe8, 0x67, 0x3a, 0x75, 0x9b, 0x4f, 0x0c, 0xa3, 0xc9, 0xee, 0x33, 0x47, 0xef, 0x83, 0xa7, 0x6f, 0xc8, 0xc7, 0x3e, 0xc4, 0xfb, 0xc9, 0xba, 0x9f, 0x44, 0xec, 0x26,
+	/* (2^ 52)P */ 0x7d, 0x9e, 0x9b, 0xa0, 0xcb, 0x38, 0x0f, 0x5c, 0x8c, 0x47, 0xa3, 0x62, 0xc7, 0x8c, 0x16, 0x81, 0x1c, 0x12, 0xfc, 0x06, 0xd3, 0xb0, 0x23, 0x3e, 0xdd, 0xdc, 0xef, 0xa5, 0xa0, 0x8a, 0x23, 0x5a,
+	/* (2^ 53)P */ 0xff, 0x43, 0xea, 0xc4, 0x21, 0x61, 0xa2, 0x1b, 0xb5, 0x32, 0x88, 0x7c, 0x7f, 0xc7, 0xf8, 0x36, 0x9a, 0xf9, 0xdc, 0x0a, 0x0b, 0xea, 0xfb, 0x88, 0xf9, 0xeb, 0x5b, 0xc2, 0x8e, 0x93, 0xa9, 0x5c,
+	/* (2^ 54)P */ 0xa0, 0xcd, 0xfc, 0x51, 0x5e, 0x6a, 0x43, 0xd5, 0x3b, 0x89, 0xcd, 0xc2, 0x97, 0x47, 0xbc, 0x1d, 0x08, 0x4a, 0x22, 0xd3, 0x65, 0x6a, 0x34, 0x19, 0x66, 0xf4, 0x9a, 0x9b, 0xe4, 0x34, 0x50, 0x0f,
+	/* (2^ 55)P */ 0x6e, 0xb9, 0xe0, 0xa1, 0x67, 0x39, 0x3c, 0xf2, 0x88, 0x4d, 0x7a, 0x86, 0xfa, 0x08, 0x8b, 0xe5, 0x79, 0x16, 0x34, 0xa7, 0xc6, 0xab, 0x2f, 0xfb, 0x46, 0x69, 0x02, 0xb6, 0x1e, 0x38, 0x75, 0x2a,
+	/* (2^ 56)P */ 0xac, 0x20, 0x94, 0xc1, 0xe4, 0x3b, 0x0a, 0xc8, 0xdc, 0xb6, 0xf2, 0x81, 0xc6, 0xf6, 0xb1, 0x66, 0x88, 0x33, 0xe9, 0x61, 0x67, 0x03, 0xf7, 0x7c, 0xc4, 0xa4, 0x60, 0xa6, 0xd8, 0xbb, 0xab, 0x25,
+	/* (2^ 57)P */ 0x98, 0x51, 0xfd, 0x14, 0xba, 0x12, 0xea, 0x91, 0xa9, 0xff, 0x3c, 0x4a, 0xfc, 0x50, 0x49, 0x68, 0x28, 0xad, 0xf5, 0x30, 0x21, 0x84, 0x26, 0xf8, 0x41, 0xa4, 0x01, 0x53, 0xf7, 0x88, 0xa9, 0x3e,
+	/* (2^ 58)P */ 0x6f, 0x8c, 0x5f, 0x69, 0x9a, 0x10, 0x78, 0xc9, 0xf3, 0xc3, 0x30, 0x05, 0x4a, 0xeb, 0x46, 0x17, 0x95, 0x99, 0x45, 0xb4, 0x77, 0x6d, 0x4d, 0x44, 0xc7, 0x5c, 0x4e, 0x05, 0x8c, 0x2b, 0x95, 0x75,
+	/* (2^ 59)P */ 0xaa, 0xd6, 0xf4, 0x15, 0x79, 0x3f, 0x70, 0xa3, 0xd8, 0x47, 0x26, 0x2f, 0x20, 0x46, 0xc3, 0x66, 0x4b, 0x64, 0x1d, 0x81, 0xdf, 0x69, 0x14, 0xd0, 0x1f, 0xd7, 0xa5, 0x81, 0x7d, 0xa4, 0xfe, 0x77,
+	/* (2^ 60)P */ 0x81, 0xa3, 0x7c, 0xf5, 0x9e, 0x52, 0xe9, 0xc5, 0x1a, 0x88, 0x2f, 0xce, 0xb9, 0xb4, 0xee, 0x6e, 0xd6, 0x9b, 0x00, 0xe8, 0x28, 0x1a, 0xe9, 0xb6, 0xec, 0x3f, 0xfc, 0x9a, 0x3e, 0xbe, 0x80, 0x4b,
+	/* (2^ 61)P */ 0xc5, 0xd2, 0xae, 0x26, 0xc5, 0x73, 0x37, 0x7e, 0x9d, 0xa4, 0xc9, 0x53, 0xb4, 0xfc, 0x4a, 0x1b, 0x4d, 0xb2, 0xff, 0xba, 0xd7, 0xbd, 0x20, 0xa9, 0x0e, 0x40, 0x2d, 0x12, 0x9f, 0x69, 0x54, 0x7c,
+	/* (2^ 62)P */ 0xc8, 0x4b, 0xa9, 0x4f, 0xe1, 0xc8, 0x46, 0xef, 0x5e, 0xed, 0x52, 0x29, 0xce, 0x74, 0xb0, 0xe0, 0xd5, 0x85, 0xd8, 0xdb, 0xe1, 0x50, 0xa4, 0xbe, 0x2c, 0x71, 0x0f, 0x32, 0x49, 0x86, 0xb6, 0x61,
+	/* (2^ 63)P */ 0xd1, 0xbd, 0xcc, 0x09, 0x73, 0x5f, 0x48, 0x8a, 0x2d, 0x1a, 0x4d, 0x7d, 0x0d, 0x32, 0x06, 0xbd, 0xf4, 0xbe, 0x2d, 0x32, 0x73, 0x29, 0x23, 0x25, 0x70, 0xf7, 0x17, 0x8c, 0x75, 0xc4, 0x5d, 0x44,
+	/* (2^ 64)P */ 0x3c, 0x93, 0xc8, 0x7c, 0x17, 0x34, 0x04, 0xdb, 0x9f, 0x05, 0xea, 0x75, 0x21, 0xe8, 0x6f, 0xed, 0x34, 0xdb, 0x53, 0xc0, 0xfd, 0xbe, 0xfe, 0x1e, 0x99, 0xaf, 0x5d, 0xc6, 0x67, 0xe8, 0xdb, 0x4a,
+	/* (2^ 65)P */ 0xdf, 0x09, 0x06, 0xa9, 0xa2, 0x71, 0xcd, 0x3a, 0x50, 0x40, 0xd0, 0x6d, 0x85, 0x91, 0xe9, 0xe5, 0x3c, 0xc2, 0x57, 0x81, 0x68, 0x9b, 0xc6, 0x1e, 0x4d, 0xfe, 0x5c, 0x88, 0xf6, 0x27, 0x74, 0x69,
+	/* (2^ 66)P */ 0x51, 0xa8, 0xe1, 0x65, 0x9b, 0x7b, 0xbe, 0xd7, 0xdd, 0x36, 0xc5, 0x22, 0xd5, 0x28, 0x3d, 0xa0, 0x45, 0xb6, 0xd2, 0x8f, 0x65, 0x9d, 0x39, 0x28, 0xe1, 0x41, 0x26, 0x7c, 0xe1, 0xb7, 0xe5, 0x49,
+	/* (2^ 67)P */ 0xa4, 0x57, 0x04, 0x70, 0x98, 0x3a, 0x8c, 0x6f, 0x78, 0x67, 0xbb, 0x5e, 0xa2, 0xf0, 0x78, 0x50, 0x0f, 0x96, 0x82, 0xc3, 0xcb, 0x3c, 0x3c, 0xd1, 0xb1, 0x84, 0xdf, 0xa7, 0x58, 0x32, 0x00, 0x2e,
+	/* (2^ 68)P */ 0x1c, 0x6a, 0x29, 0xe6, 0x9b, 0xf3, 0xd1, 0x8a, 0xb2, 0xbf, 0x5f, 0x2a, 0x65, 0xaa, 0xee, 0xc1, 0xcb, 0xf3, 0x26, 0xfd, 0x73, 0x06, 0xee, 0x33, 0xcc, 0x2c, 0x9d, 0xa6, 0x73, 0x61, 0x25, 0x59,
+	/* (2^ 69)P */ 0x41, 0xfc, 0x18, 0x4e, 0xaa, 0x07, 0xea, 0x41, 0x1e, 0xa5, 0x87, 0x7c, 0x52, 0x19, 0xfc, 0xd9, 0x6f, 0xca, 0x31, 0x58, 0x80, 0xcb, 0xaa, 0xbd, 0x4f, 0x69, 0x16, 0xc9, 0x2d, 0x65, 0x5b, 0x44,
+	/* (2^ 70)P */ 0x15, 0x23, 0x17, 0xf2, 0xa7, 0xa3, 0x92, 0xce, 0x64, 0x99, 0x1b, 0xe1, 0x2d, 0x28, 0xdc, 0x1e, 0x4a, 0x31, 0x4c, 0xe0, 0xaf, 0x3a, 0x82, 0xa1, 0x86, 0xf5, 0x7c, 0x43, 0x94, 0x2d, 0x0a, 0x79,
+	/* (2^ 71)P */ 0x09, 0xe0, 0xf6, 0x93, 0xfb, 0x47, 0xc4, 0x71, 0x76, 0x52, 0x84, 0x22, 0x67, 0xa5, 0x22, 0x89, 0x69, 0x51, 0x4f, 0x20, 0x3b, 0x90, 0x70, 0xbf, 0xfe, 0x19, 0xa3, 0x1b, 0x89, 0x89, 0x7a, 0x2f,
+	/* (2^ 72)P */ 0x0c, 0x14, 0xe2, 0x77, 0xb5, 0x8e, 0xa0, 0x02, 0xf4, 0xdc, 0x7b, 0x42, 0xd4, 0x4e, 0x9a, 0xed, 0xd1, 0x3c, 0x32, 0xe4, 0x44, 0xec, 0x53, 0x52, 0x5b, 0x35, 0xe9, 0x14, 0x3c, 0x36, 0x88, 0x3e,
+	/* (2^ 73)P */ 0x8c, 0x0b, 0x11, 0x77, 0x42, 0xc1, 0x66, 0xaa, 0x90, 0x33, 0xa2, 0x10, 0x16, 0x39, 0xe0, 0x1a, 0xa2, 0xc2, 0x3f, 0xc9, 0x12, 0xbd, 0x30, 0x20, 0xab, 0xc7, 0x55, 0x95, 0x57, 0x41, 0xe1, 0x3e,
+	/* (2^ 74)P */ 0x41, 0x7d, 0x6e, 0x6d, 0x3a, 0xde, 0x14, 0x92, 0xfe, 0x7e, 0xf1, 0x07, 0x86, 0xd8, 0xcd, 0x3c, 0x17, 0x12, 0xe1, 0xf8, 0x88, 0x12, 0x4f, 0x67, 0xd0, 0x93, 0x9f, 0x32, 0x0f, 0x25, 0x82, 0x56,
+	/* (2^ 75)P */ 0x6e, 0x39, 0x2e, 0x6d, 0x13, 0x0b, 0xf0, 0x6c, 0xbf, 0xde, 0x14, 0x10, 0x6f, 0xf8, 0x4c, 0x6e, 0x83, 0x4e, 0xcc, 0xbf, 0xb5, 0xb1, 0x30, 0x59, 0xb6, 0x16, 0xba, 0x8a, 0xb4, 0x69, 0x70, 0x04,
+	/* (2^ 76)P */ 0x93, 0x07, 0xb2, 0x69, 0xab, 0xe4, 0x4c, 0x0d, 0x9e, 0xfb, 0xd0, 0x97, 0x1a, 0xb9, 0x4d, 0xb2, 0x1d, 0xd0, 0x00, 0x4e, 0xf5, 0x50, 0xfa, 0xcd, 0xb5, 0xdd, 0x8b, 0x36, 0x85, 0x10, 0x1b, 0x22,
+	/* (2^ 77)P */ 0xd2, 0xd8, 0xe3, 0xb1, 0x68, 0x94, 0xe5, 0xe7, 0x93, 0x2f, 0x12, 0xbd, 0x63, 0x65, 0xc5, 0x53, 0x09, 0x3f, 0x66, 0xe0, 0x03, 0xa9, 0xe8, 0xee, 0x42, 0x3d, 0xbe, 0xcb, 0x62, 0xa6, 0xef, 0x61,
+	/* (2^ 78)P */ 0x2a, 0xab, 0x6e, 0xde, 0xdd, 0xdd, 0xf8, 0x2c, 0x31, 0xf2, 0x35, 0x14, 0xd5, 0x0a, 0xf8, 0x9b, 0x73, 0x49, 0xf0, 0xc9, 0xce, 0xda, 0xea, 0x5d, 0x27, 0x9b, 0xd2, 0x41, 0x5d, 0x5b, 0x27, 0x29,
+	/* (2^ 79)P */ 0x4f, 0xf1, 0xeb, 0x95, 0x08, 0x0f, 0xde, 0xcf, 0xa7, 0x05, 0x49, 0x05, 0x6b, 0xb9, 0xaa, 0xb9, 0xfd, 0x20, 0xc4, 0xa1, 0xd9, 0x0d, 0xe8, 0xca, 0xc7, 0xbb, 0x73, 0x16, 0x2f, 0xbf, 0x63, 0x0a,
+	/* (2^ 80)P */ 0x8c, 0xbc, 0x8f, 0x95, 0x11, 0x6e, 0x2f, 0x09, 0xad, 0x2f, 0x82, 0x04, 0xe8, 0x81, 0x2a, 0x67, 0x17, 0x25, 0xd5, 0x60, 0x15, 0x35, 0xc8, 0xca, 0xf8, 0x92, 0xf1, 0xc8, 0x22, 0x77, 0x3f, 0x6f,
+	/* (2^ 81)P */ 0xb7, 0x94, 0xe8, 0xc2, 0xcc, 0x90, 0xba, 0xf8, 0x0d, 0x9f, 0xff, 0x38, 0xa4, 0x57, 0x75, 0x2c, 0x59, 0x23, 0xe5, 0x5a, 0x85, 0x1d, 0x4d, 0x89, 0x69, 0x3d, 0x74, 0x7b, 0x15, 0x22, 0xe1, 0x68,
+	/* (2^ 82)P */ 0xf3, 0x19, 0xb9, 0xcf, 0x70, 0x55, 0x7e, 0xd8, 0xb9, 0x8d, 0x79, 0x95, 0xcd, 0xde, 0x2c, 0x3f, 0xce, 0xa2, 0xc0, 0x10, 0x47, 0x15, 0x21, 0x21, 0xb2, 0xc5, 0x6d, 0x24, 0x15, 0xa1, 0x66, 0x3c,
+	/* (2^ 83)P */ 0x72, 0xcb, 0x4e, 0x29, 0x62, 0xc5, 0xed, 0xcb, 0x16, 0x0b, 0x28, 0x6a, 0xc3, 0x43, 0x71, 0xba, 0x67, 0x8b, 0x07, 0xd4, 0xef, 0xc2, 0x10, 0x96, 0x1e, 0x4b, 0x6a, 0x94, 0x5d, 0x73, 0x44, 0x61,
+	/* (2^ 84)P */ 0x50, 0x33, 0x5b, 0xd7, 0x1e, 0x11, 0x6f, 0x53, 0x1b, 0xd8, 0x41, 0x20, 0x8c, 0xdb, 0x11, 0x02, 0x3c, 0x41, 0x10, 0x0e, 0x00, 0xb1, 0x3c, 0xf9, 0x76, 0x88, 0x9e, 0x03, 0x3c, 0xfd, 0x9d, 0x14,
+	/* (2^ 85)P */ 0x5b, 0x15, 0x63, 0x6b, 0xe4, 0xdd, 0x79, 0xd4, 0x76, 0x79, 0x83, 0x3c, 0xe9, 0x15, 0x6e, 0xb6, 0x38, 0xe0, 0x13, 0x1f, 0x3b, 0xe4, 0xfd, 0xda, 0x35, 0x0b, 0x4b, 0x2e, 0x1a, 0xda, 0xaf, 0x5f,
+	/* (2^ 86)P */ 0x81, 0x75, 0x19, 0x17, 0xdf, 0xbb, 0x00, 0x36, 0xc2, 0xd2, 0x3c, 0xbe, 0x0b, 0x05, 0x72, 0x39, 0x86, 0xbe, 0xd5, 0xbd, 0x6d, 0x90, 0x38, 0x59, 0x0f, 0x86, 0x9b, 0x3f, 0xe4, 0xe5, 0xfc, 0x34,
+	/* (2^ 87)P */ 0x02, 0x4d, 0xd1, 0x42, 0xcd, 0xa4, 0xa8, 0x75, 0x65, 0xdf, 0x41, 0x34, 0xc5, 0xab, 0x8d, 0x82, 0xd3, 0x31, 0xe1, 0xd2, 0xed, 0xab, 0xdc, 0x33, 0x5f, 0xd2, 0x14, 0xb8, 0x6f, 0xd7, 0xba, 0x3e,
+	/* (2^ 88)P */ 0x0f, 0xe1, 0x70, 0x6f, 0x56, 0x6f, 0x90, 0xd4, 0x5a, 0x0f, 0x69, 0x51, 0xaa, 0xf7, 0x12, 0x5d, 0xf2, 0xfc, 0xce, 0x76, 0x6e, 0xb1, 0xad, 0x45, 0x99, 0x29, 0x23, 0xad, 0xae, 0x68, 0xf7, 0x01,
+	/* (2^ 89)P */ 0xbd, 0xfe, 0x48, 0x62, 0x7b, 0xc7, 0x6c, 0x2b, 0xfd, 0xaf, 0x3a, 0xec, 0x28, 0x06, 0xd3, 0x3c, 0x6a, 0x48, 0xef, 0xd4, 0x80, 0x0b, 0x1c, 0xce, 0x23, 0x6c, 0xf6, 0xa6, 0x2e, 0xff, 0x3b, 0x4c,
+	/* (2^ 90)P */ 0x5f, 0xeb, 0xea, 0x4a, 0x09, 0xc4, 0x2e, 0x3f, 0xa7, 0x2c, 0x37, 0x6e, 0x28, 0x9b, 0xb1, 0x61, 0x1d, 0x70, 0x2a, 0xde, 0x66, 0xa9, 0xef, 0x5e, 0xef, 0xe3, 0x55, 0xde, 0x65, 0x05, 0xb2, 0x23,
+	/* (2^ 91)P */ 0x57, 0x85, 0xd5, 0x79, 0x52, 0xca, 0x01, 0xe3, 0x4f, 0x87, 0xc2, 0x27, 0xce, 0xd4, 0xb2, 0x07, 0x67, 0x1d, 0xcf, 0x9d, 0x8a, 0xcd, 0x32, 0xa5, 0x56, 0xff, 0x2b, 0x3f, 0xe2, 0xfe, 0x52, 0x2a,
+	/* (2^ 92)P */ 0x3d, 0x66, 0xd8, 0x7c, 0xb3, 0xef, 0x24, 0x86, 0x94, 0x75, 0xbd, 0xff, 0x20, 0xac, 0xc7, 0xbb, 0x45, 0x74, 0xd3, 0x82, 0x9c, 0x5e, 0xb8, 0x57, 0x66, 0xec, 0xa6, 0x86, 0xcb, 0x52, 0x30, 0x7b,
+	/* (2^ 93)P */ 0x1e, 0xe9, 0x25, 0x25, 0xad, 0xf0, 0x82, 0x34, 0xa0, 0xdc, 0x8e, 0xd2, 0x43, 0x80, 0xb6, 0x2c, 0x3a, 0x00, 0x1b, 0x2e, 0x05, 0x6d, 0x4f, 0xaf, 0x0a, 0x1b, 0x78, 0x29, 0x25, 0x8c, 0x5f, 0x18,
+	/* (2^ 94)P */ 0xd6, 0xe0, 0x0c, 0xd8, 0x5b, 0xde, 0x41, 0xaa, 0xd6, 0xe9, 0x53, 0x68, 0x41, 0xb2, 0x07, 0x94, 0x3a, 0x4c, 0x7f, 0x35, 0x6e, 0xc3, 0x3e, 0x56, 0xce, 0x7b, 0x29, 0x0e, 0xdd, 0xb8, 0xc4, 0x4c,
+	/* (2^ 95)P */ 0x0e, 0x73, 0xb8, 0xff, 0x52, 0x1a, 0xfc, 0xa2, 0x37, 0x8e, 0x05, 0x67, 0x6e, 0xf1, 0x11, 0x18, 0xe1, 0x4e, 0xdf, 0xcd, 0x66, 0xa3, 0xf9, 0x10, 0x99, 0xf0, 0xb9, 0xa0, 0xc4, 0xa0, 0xf4, 0x72,
+	/* (2^ 96)P */ 0xa7, 0x4e, 0x3f, 0x66, 0x6f, 0xc0, 0x16, 0x8c, 0xba, 0x0f, 0x97, 0x4e, 0xf7, 0x3a, 0x3b, 0x69, 0x45, 0xc3, 0x9e, 0xd6, 0xf1, 0xe7, 0x02, 0x21, 0x89, 0x80, 0x8a, 0x96, 0xbc, 0x3c, 0xa5, 0x0b,
+	/* (2^ 97)P */ 0x37, 0x55, 0xa1, 0xfe, 0xc7, 0x9d, 0x3d, 0xca, 0x93, 0x64, 0x53, 0x51, 0xbb, 0x24, 0x68, 0x4c, 0xb1, 0x06, 0x40, 0x84, 0x14, 0x63, 0x88, 0xb9, 0x60, 0xcc, 0x54, 0xb4, 0x2a, 0xa7, 0xd2, 0x40,
+	/* (2^ 98)P */ 0x75, 0x09, 0x57, 0x12, 0xb7, 0xa1, 0x36, 0x59, 0x57, 0xa6, 0xbd, 0xde, 0x48, 0xd6, 0xb9, 0x91, 0xea, 0x30, 0x43, 0xb6, 0x4b, 0x09, 0x44, 0x33, 0xd0, 0x51, 0xee, 0x12, 0x0d, 0xa1, 0x6b, 0x00,
+	/* (2^ 99)P */ 0x58, 0x5d, 0xde, 0xf5, 0x68, 0x84, 0x22, 0x19, 0xb0, 0x05, 0xcc, 0x38, 0x4c, 0x2f, 0xb1, 0x0e, 0x90, 0x19, 0x60, 0xd5, 0x9d, 0x9f, 0x03, 0xa1, 0x0b, 0x0e, 0xff, 0x4f, 0xce, 0xd4, 0x02, 0x45,
+	/* (2^100)P */ 0x89, 0xc1, 0x37, 0x68, 0x10, 0x54, 0x20, 0xeb, 0x3c, 0xb9, 0xd3, 0x6d, 0x4c, 0x54, 0xf6, 0xd0, 0x4f, 0xd7, 0x16, 0xc4, 0x64, 0x70, 0x72, 0x40, 0xf0, 0x2e, 0x50, 0x4b, 0x11, 0xc6, 0x15, 0x6e,
+	/* (2^101)P */ 0x6b, 0xa7, 0xb1, 0xcf, 0x98, 0xa3, 0xf2, 0x4d, 0xb1, 0xf6, 0xf2, 0x19, 0x74, 0x6c, 0x25, 0x11, 0x43, 0x60, 0x6e, 0x06, 0x62, 0x79, 0x49, 0x4a, 0x44, 0x5b, 0x35, 0x41, 0xab, 0x3a, 0x5b, 0x70,
+	/* (2^102)P */ 0xd8, 0xb1, 0x97, 0xd7, 0x36, 0xf5, 0x5e, 0x36, 0xdb, 0xf0, 0xdd, 0x22, 0xd6, 0x6b, 0x07, 0x00, 0x88, 0x5a, 0x57, 0xe0, 0xb0, 0x33, 0xbf, 0x3b, 0x4d, 0xca, 0xe4, 0xc8, 0x05, 0xaa, 0x77, 0x37,
+	/* (2^103)P */ 0x5f, 0xdb, 0x78, 0x55, 0xc8, 0x45, 0x27, 0x39, 0xe2, 0x5a, 0xae, 0xdb, 0x49, 0x41, 0xda, 0x6f, 0x67, 0x98, 0xdc, 0x8a, 0x0b, 0xb0, 0xf0, 0xb1, 0xa3, 0x1d, 0x6f, 0xd3, 0x37, 0x34, 0x96, 0x09,
+	/* (2^104)P */ 0x53, 0x38, 0xdc, 0xa5, 0x90, 0x4e, 0x82, 0x7e, 0xbd, 0x5c, 0x13, 0x1f, 0x64, 0xf6, 0xb5, 0xcc, 0xcc, 0x8f, 0xce, 0x87, 0x6c, 0xd8, 0x36, 0x67, 0x9f, 0x24, 0x04, 0x66, 0xe2, 0x3c, 0x5f, 0x62,
+	/* (2^105)P */ 0x3f, 0xf6, 0x02, 0x95, 0x05, 0xc8, 0x8a, 0xaf, 0x69, 0x14, 0x35, 0x2e, 0x0a, 0xe7, 0x05, 0x0c, 0x05, 0x63, 0x4b, 0x76, 0x9c, 0x2e, 0x29, 0x35, 0xc3, 0x3a, 0xe2, 0xc7, 0x60, 0x43, 0x39, 0x1a,
+	/* (2^106)P */ 0x64, 0x32, 0x18, 0x51, 0x32, 0xd5, 0xc6, 0xd5, 0x4f, 0xb7, 0xc2, 0x43, 0xbd, 0x5a, 0x06, 0x62, 0x9b, 0x3f, 0x97, 0x3b, 0xd0, 0xf5, 0xfb, 0xb5, 0x5e, 0x6e, 0x20, 0x61, 0x36, 0xda, 0xa3, 0x13,
+	/* (2^107)P */ 0xe5, 0x94, 0x5d, 0x72, 0x37, 0x58, 0xbd, 0xc6, 0xc5, 0x16, 0x50, 0x20, 0x12, 0x09, 0xe3, 0x18, 0x68, 0x3c, 0x03, 0x70, 0x15, 0xce, 0x88, 0x20, 0x87, 0x79, 0x83, 0x5c, 0x49, 0x1f, 0xba, 0x7f,
+	/* (2^108)P */ 0x9d, 0x07, 0xf9, 0xf2, 0x23, 0x74, 0x8c, 0x5a, 0xc5, 0x3f, 0x02, 0x34, 0x7b, 0x15, 0x35, 0x17, 0x51, 0xb3, 0xfa, 0xd2, 0x9a, 0xb4, 0xf9, 0xe4, 0x3c, 0xe3, 0x78, 0xc8, 0x72, 0xff, 0x91, 0x66,
+	/* (2^109)P */ 0x3e, 0xff, 0x5e, 0xdc, 0xde, 0x2a, 0x2c, 0x12, 0xf4, 0x6c, 0x95, 0xd8, 0xf1, 0x4b, 0xdd, 0xf8, 0xda, 0x5b, 0x9e, 0x9e, 0x5d, 0x20, 0x86, 0xeb, 0x43, 0xc7, 0x75, 0xd9, 0xb9, 0x92, 0x9b, 0x04,
+	/* (2^110)P */ 0x5a, 0xc0, 0xf6, 0xb0, 0x30, 0x97, 0x37, 0xa5, 0x53, 0xa5, 0xf3, 0xc6, 0xac, 0xff, 0xa0, 0x72, 0x6d, 0xcd, 0x0d, 0xb2, 0x34, 0x2c, 0x03, 0xb0, 0x4a, 0x16, 0xd5, 0x88, 0xbc, 0x9d, 0x0e, 0x47,
+	/* (2^111)P */ 0x47, 0xc0, 0x37, 0xa2, 0x0c, 0xf1, 0x9c, 0xb1, 0xa2, 0x81, 0x6c, 0x1f, 0x71, 0x66, 0x54, 0xb6, 0x43, 0x0b, 0xd8, 0x6d, 0xd1, 0x1b, 0x32, 0xb3, 0x8e, 0xbe, 0x5f, 0x0c, 0x60, 0x4f, 0xc1, 0x48,
+	/* (2^112)P */ 0x03, 0xc8, 0xa6, 0x4a, 0x26, 0x1c, 0x45, 0x66, 0xa6, 0x7d, 0xfa, 0xa4, 0x04, 0x39, 0x6e, 0xb6, 0x95, 0x83, 0x12, 0xb3, 0xb0, 0x19, 0x5f, 0xd4, 0x10, 0xbc, 0xc9, 0xc3, 0x27, 0x26, 0x60, 0x31,
+	/* (2^113)P */ 0x0d, 0xe1, 0xe4, 0x32, 0x48, 0xdc, 0x20, 0x31, 0xf7, 0x17, 0xc7, 0x56, 0x67, 0xc4, 0x20, 0xeb, 0x94, 0x02, 0x28, 0x67, 0x3f, 0x2e, 0xf5, 0x00, 0x09, 0xc5, 0x30, 0x47, 0xc1, 0x4f, 0x6d, 0x56,
+	/* (2^114)P */ 0x06, 0x72, 0x83, 0xfd, 0x40, 0x5d, 0x3a, 0x7e, 0x7a, 0x54, 0x59, 0x71, 0xdc, 0x26, 0xe9, 0xc1, 0x95, 0x60, 0x8d, 0xa6, 0xfb, 0x30, 0x67, 0x21, 0xa7, 0xce, 0x69, 0x3f, 0x84, 0xc3, 0xe8, 0x22,
+	/* (2^115)P */ 0x2b, 0x4b, 0x0e, 0x93, 0xe8, 0x74, 0xd0, 0x33, 0x16, 0x58, 0xd1, 0x84, 0x0e, 0x35, 0xe4, 0xb6, 0x65, 0x23, 0xba, 0xd6, 0x6a, 0xc2, 0x34, 0x55, 0xf3, 0xf3, 0xf1, 0x89, 0x2f, 0xc1, 0x73, 0x77,
+	/* (2^116)P */ 0xaa, 0x62, 0x79, 0xa5, 0x4d, 0x40, 0xba, 0x8c, 0x56, 0xce, 0x99, 0x19, 0xa8, 0x97, 0x98, 0x5b, 0xfc, 0x92, 0x16, 0x12, 0x2f, 0x86, 0x8e, 0x50, 0x91, 0xc2, 0x93, 0xa0, 0x7f, 0x90, 0x81, 0x3a,
+	/* (2^117)P */ 0x10, 0xa5, 0x25, 0x47, 0xff, 0xd0, 0xde, 0x0d, 0x03, 0xc5, 0x3f, 0x67, 0x10, 0xcc, 0xd8, 0x10, 0x89, 0x4e, 0x1f, 0x9f, 0x1c, 0x15, 0x9d, 0x5b, 0x4c, 0xa4, 0x09, 0xcb, 0xd5, 0xc1, 0xa5, 0x32,
+	/* (2^118)P */ 0xfb, 0x41, 0x05, 0xb9, 0x42, 0xa4, 0x0a, 0x1e, 0xdb, 0x85, 0xb4, 0xc1, 0x7c, 0xeb, 0x85, 0x5f, 0xe5, 0xf2, 0x9d, 0x8a, 0xce, 0x95, 0xe5, 0xbe, 0x36, 0x22, 0x42, 0x22, 0xc7, 0x96, 0xe4, 0x25,
+	/* (2^119)P */ 0xb9, 0xe5, 0x0f, 0xcd, 0x46, 0x3c, 0xdf, 0x5e, 0x88, 0x33, 0xa4, 0xd2, 0x7e, 0x5a, 0xe7, 0x34, 0x52, 0xe3, 0x61, 0xd7, 0x11, 0xde, 0x88, 0xe4, 0x5c, 0x54, 0x85, 0xa0, 0x01, 0x8a, 0x87, 0x0e,
+	/* (2^120)P */ 0x04, 0xbb, 0x21, 0xe0, 0x77, 0x3c, 0x49, 0xba, 0x9a, 0x89, 0xdf, 0xc7, 0x43, 0x18, 0x4d, 0x2b, 0x67, 0x0d, 0xe8, 0x7a, 0x48, 0x7a, 0xa3, 0x9e, 0x94, 0x17, 0xe4, 0x11, 0x80, 0x95, 0xa9, 0x67,
+	/* (2^121)P */ 0x65, 0xb0, 0x97, 0x66, 0x1a, 0x05, 0x58, 0x4b, 0xd4, 0xa6, 0x6b, 0x8d, 0x7d, 0x3f, 0xe3, 0x47, 0xc1, 0x46, 0xca, 0x83, 0xd4, 0xa8, 0x4d, 0xbb, 0x0d, 0xdb, 0xc2, 0x81, 0xa1, 0xca, 0xbe, 0x68,
+	/* (2^122)P */ 0xa5, 0x9a, 0x98, 0x0b, 0xe9, 0x80, 0x89, 0x8d, 0x9b, 0xc9, 0x93, 0x2c, 0x4a, 0xb1, 0x5e, 0xf9, 0xa2, 0x73, 0x6e, 0x79, 0xc4, 0xc7, 0xc6, 0x51, 0x69, 0xb5, 0xef, 0xb5, 0x63, 0x83, 0x22, 0x6e,
+	/* (2^123)P */ 0xc8, 0x24, 0xd6, 0x2d, 0xb0, 0xc0, 0xbb, 0xc6, 0xee, 0x70, 0x81, 0xec, 0x7d, 0xb4, 0x7e, 0x77, 0xa9, 0xaf, 0xcf, 0x04, 0xa0, 0x15, 0xde, 0x3c, 0x9b, 0xbf, 0x60, 0x71, 0x08, 0xbc, 0xc6, 0x1d,
+	/* (2^124)P */ 0x02, 0x40, 0xc3, 0xee, 0x43, 0xe0, 0x07, 0x2e, 0x7f, 0xdc, 0x68, 0x7a, 0x67, 0xfc, 0xe9, 0x18, 0x9a, 0x5b, 0xd1, 0x8b, 0x18, 0x03, 0xda, 0xd8, 0x53, 0x82, 0x56, 0x00, 0xbb, 0xc3, 0xfb, 0x48,
+	/* (2^125)P */ 0xe1, 0x4c, 0x65, 0xfb, 0x4c, 0x7d, 0x54, 0x57, 0xad, 0xe2, 0x58, 0xa0, 0x82, 0x5b, 0x56, 0xd3, 0x78, 0x44, 0x15, 0xbf, 0x0b, 0xaf, 0x3e, 0xf6, 0x18, 0xbb, 0xdf, 0x14, 0xf1, 0x1e, 0x53, 0x47,
+	/* (2^126)P */ 0x87, 0xc5, 0x78, 0x42, 0x0a, 0x63, 0xec, 0xe1, 0xf3, 0x83, 0x8e, 0xca, 0x46, 0xd5, 0x07, 0x55, 0x2b, 0x0c, 0xdc, 0x3a, 0xc6, 0x35, 0xe1, 0x85, 0x4e, 0x84, 0x82, 0x56, 0xa8, 0xef, 0xa7, 0x0a,
+	/* (2^127)P */ 0x15, 0xf6, 0xe1, 0xb3, 0xa8, 0x1b, 0x69, 0x72, 0xfa, 0x3f, 0xbe, 0x1f, 0x70, 0xe9, 0xb4, 0x32, 0x68, 0x78, 0xbb, 0x39, 0x2e, 0xd9, 0xb6, 0x97, 0xe8, 0x39, 0x2e, 0xa0, 0xde, 0x53, 0xfe, 0x2c,
+	/* (2^128)P */ 0xb0, 0x52, 0xcd, 0x85, 0xcd, 0x92, 0x73, 0x68, 0x31, 0x98, 0xe2, 0x10, 0xc9, 0x66, 0xff, 0x27, 0x06, 0x2d, 0x83, 0xa9, 0x56, 0x45, 0x13, 0x97, 0xa0, 0xf8, 0x84, 0x0a, 0x36, 0xb0, 0x9b, 0x26,
+	/* (2^129)P */ 0x5c, 0xf8, 0x43, 0x76, 0x45, 0x55, 0x6e, 0x70, 0x1b, 0x7d, 0x59, 0x9b, 0x8c, 0xa4, 0x34, 0x37, 0x72, 0xa4, 0xef, 0xc6, 0xe8, 0x91, 0xee, 0x7a, 0xe0, 0xd9, 0xa9, 0x98, 0xc1, 0xab, 0xd6, 0x5c,
+	/* (2^130)P */ 0x1a, 0xe4, 0x3c, 0xcb, 0x06, 0xde, 0x04, 0x0e, 0x38, 0xe1, 0x02, 0x34, 0x89, 0xeb, 0xc6, 0xd8, 0x72, 0x37, 0x6e, 0x68, 0xbb, 0x59, 0x46, 0x90, 0xc8, 0xa8, 0x6b, 0x74, 0x71, 0xc3, 0x15, 0x72,
+	/* (2^131)P */ 0xd9, 0xa2, 0xe4, 0xea, 0x7e, 0xa9, 0x12, 0xfd, 0xc5, 0xf2, 0x94, 0x63, 0x51, 0xb7, 0x14, 0x95, 0x94, 0xf2, 0x08, 0x92, 0x80, 0xd5, 0x6f, 0x26, 0xb9, 0x26, 0x9a, 0x61, 0x85, 0x70, 0x84, 0x5c,
+	/* (2^132)P */ 0xea, 0x94, 0xd6, 0xfe, 0x10, 0x54, 0x98, 0x52, 0x54, 0xd2, 0x2e, 0x4a, 0x93, 0x5b, 0x90, 0x3c, 0x67, 0xe4, 0x3b, 0x2d, 0x69, 0x47, 0xbb, 0x10, 0xe1, 0xe9, 0xe5, 0x69, 0x2d, 0x3d, 0x3b, 0x06,
+	/* (2^133)P */ 0xeb, 0x7d, 0xa5, 0xdd, 0xee, 0x26, 0x27, 0x47, 0x91, 0x18, 0xf4, 0x10, 0xae, 0xc4, 0xb6, 0xef, 0x14, 0x76, 0x30, 0x7b, 0x91, 0x41, 0x16, 0x2b, 0x7c, 0x5b, 0xf4, 0xc4, 0x4f, 0x55, 0x7c, 0x11,
+	/* (2^134)P */ 0x12, 0x88, 0x9d, 0x8f, 0x11, 0xf3, 0x7c, 0xc0, 0x39, 0x79, 0x01, 0x50, 0x20, 0xd8, 0xdb, 0x01, 0x27, 0x28, 0x1b, 0x17, 0xf4, 0x03, 0xe8, 0xd7, 0xea, 0x25, 0xd2, 0x87, 0x74, 0xe8, 0x15, 0x10,
+	/* (2^135)P */ 0x4d, 0xcc, 0x3a, 0xd2, 0xfe, 0xe3, 0x8d, 0xc5, 0x2d, 0xbe, 0xa7, 0x94, 0xc2, 0x91, 0xdb, 0x50, 0x57, 0xf4, 0x9c, 0x1c, 0x3d, 0xd4, 0x94, 0x0b, 0x4a, 0x52, 0x37, 0x6e, 0xfa, 0x40, 0x16, 0x6b,
+	/* (2^136)P */ 0x09, 0x0d, 0xda, 0x5f, 0x6c, 0x34, 0x2f, 0x69, 0x51, 0x31, 0x4d, 0xfa, 0x59, 0x1c, 0x0b, 0x20, 0x96, 0xa2, 0x77, 0x07, 0x76, 0x6f, 0xc4, 0xb8, 0xcf, 0xfb, 0xfd, 0x3f, 0x5f, 0x39, 0x38, 0x4b,
+	/* (2^137)P */ 0x71, 0xd6, 0x54, 0xbe, 0x00, 0x5e, 0xd2, 0x18, 0xa6, 0xab, 0xc8, 0xbe, 0x82, 0x05, 0xd5, 0x60, 0x82, 0xb9, 0x78, 0x3b, 0x26, 0x8f, 0xad, 0x87, 0x32, 0x04, 0xda, 0x9c, 0x4e, 0xf6, 0xfd, 0x50,
+	/* (2^138)P */ 0xf0, 0xdc, 0x78, 0xc5, 0xaa, 0x67, 0xf5, 0x90, 0x3b, 0x13, 0xa3, 0xf2, 0x0e, 0x9b, 0x1e, 0xef, 0x71, 0xde, 0xd9, 0x42, 0x92, 0xba, 0xeb, 0x0e, 0xc7, 0x01, 0x31, 0xf0, 0x9b, 0x3c, 0x47, 0x15,
+	/* (2^139)P */ 0x95, 0x80, 0xb7, 0x56, 0xae, 0xe8, 0x77, 0x7c, 0x8e, 0x07, 0x6f, 0x6e, 0x66, 0xe7, 0x78, 0xb6, 0x1f, 0xba, 0x48, 0x53, 0x61, 0xb9, 0xa0, 0x2d, 0x0b, 0x3f, 0x73, 0xff, 0xc1, 0x31, 0xf9, 0x7c,
+	/* (2^140)P */ 0x6c, 0x36, 0x0a, 0x0a, 0xf5, 0x57, 0xb3, 0x26, 0x32, 0xd7, 0x87, 0x2b, 0xf4, 0x8c, 0x70, 0xe9, 0xc0, 0xb2, 0x1c, 0xf9, 0xa5, 0xee, 0x3a, 0xc1, 0x4c, 0xbb, 0x43, 0x11, 0x99, 0x0c, 0xd9, 0x35,
+	/* (2^141)P */ 0xdc, 0xd9, 0xa0, 0xa9, 0x04, 0xc4, 0xc1, 0x47, 0x51, 0xd2, 0x72, 0x19, 0x45, 0x58, 0x9e, 0x65, 0x31, 0x8c, 0xb3, 0x73, 0xc4, 0xa8, 0x75, 0x38, 0x24, 0x1f, 0x56, 0x79, 0xd3, 0x9e, 0xbd, 0x1f,
+	/* (2^142)P */ 0x8d, 0xc2, 0x1e, 0xd4, 0x6f, 0xbc, 0xfa, 0x11, 0xca, 0x2d, 0x2a, 0xcd, 0xe3, 0xdf, 0xf8, 0x7e, 0x95, 0x45, 0x40, 0x8c, 0x5d, 0x3b, 0xe7, 0x72, 0x27, 0x2f, 0xb7, 0x54, 0x49, 0xfa, 0x35, 0x61,
+	/* (2^143)P */ 0x9c, 0xb6, 0x24, 0xde, 0xa2, 0x32, 0xfc, 0xcc, 0x88, 0x5d, 0x09, 0x1f, 0x8c, 0x69, 0x55, 0x3f, 0x29, 0xf9, 0xc3, 0x5a, 0xed, 0x50, 0x33, 0xbe, 0xeb, 0x7e, 0x47, 0xca, 0x06, 0xf8, 0x9b, 0x5e,
+	/* (2^144)P */ 0x68, 0x9f, 0x30, 0x3c, 0xb6, 0x8f, 0xce, 0xe9, 0xf4, 0xf9, 0xe1, 0x65, 0x35, 0xf6, 0x76, 0x53, 0xf1, 0x93, 0x63, 0x5a, 0xb3, 0xcf, 0xaf, 0xd1, 0x06, 0x35, 0x62, 0xe5, 0xed, 0xa1, 0x32, 0x66,
+	/* (2^145)P */ 0x4c, 0xed, 0x2d, 0x0c, 0x39, 0x6c, 0x7d, 0x0b, 0x1f, 0xcb, 0x04, 0xdf, 0x81, 0x32, 0xcb, 0x56, 0xc7, 0xc3, 0xec, 0x49, 0x12, 0x5a, 0x30, 0x66, 0x2a, 0xa7, 0x8c, 0xa3, 0x60, 0x8b, 0x58, 0x5d,
+	/* (2^146)P */ 0x2d, 0xf4, 0xe5, 0xe8, 0x78, 0xbf, 0xec, 0xa6, 0xec, 0x3e, 0x8a, 0x3c, 0x4b, 0xb4, 0xee, 0x86, 0x04, 0x16, 0xd2, 0xfb, 0x48, 0x9c, 0x21, 0xec, 0x31, 0x67, 0xc3, 0x17, 0xf5, 0x1a, 0xaf, 0x1a,
+	/* (2^147)P */ 0xe7, 0xbd, 0x69, 0x67, 0x83, 0xa2, 0x06, 0xc3, 0xdb, 0x2a, 0x1e, 0x2b, 0x62, 0x80, 0x82, 0x20, 0xa6, 0x94, 0xff, 0xfb, 0x1f, 0xf5, 0x27, 0x80, 0x6b, 0xf2, 0x24, 0x11, 0xce, 0xa1, 0xcf, 0x76,
+	/* (2^148)P */ 0xb6, 0xab, 0x22, 0x24, 0x56, 0x00, 0xeb, 0x18, 0xc3, 0x29, 0x8c, 0x8f, 0xd5, 0xc4, 0x77, 0xf3, 0x1a, 0x56, 0x31, 0xf5, 0x07, 0xc2, 0xbb, 0x4d, 0x27, 0x8a, 0x12, 0x82, 0xf0, 0xb7, 0x53, 0x02,
+	/* (2^149)P */ 0xe0, 0x17, 0x2c, 0xb6, 0x1c, 0x09, 0x1f, 0x3d, 0xa9, 0x28, 0x46, 0xd6, 0xab, 0xe1, 0x60, 0x48, 0x53, 0x42, 0x9d, 0x30, 0x36, 0x74, 0xd1, 0x52, 0x76, 0xe5, 0xfa, 0x3e, 0xe1, 0x97, 0x6f, 0x35,
+	/* (2^150)P */ 0x5b, 0x53, 0x50, 0xa1, 0x1a, 0xe1, 0x51, 0xd3, 0xcc, 0x78, 0xd8, 0x1d, 0xbb, 0x45, 0x6b, 0x3e, 0x98, 0x2c, 0xd9, 0xbe, 0x28, 0x61, 0x77, 0x0c, 0xb8, 0x85, 0x28, 0x03, 0x93, 0xae, 0x34, 0x1d,
+	/* (2^151)P */ 0xc3, 0xa4, 0x5b, 0xa8, 0x8c, 0x48, 0xa0, 0x4b, 0xce, 0xe6, 0x9c, 0x3c, 0xc3, 0x48, 0x53, 0x98, 0x70, 0xa7, 0xbd, 0x97, 0x6f, 0x4c, 0x12, 0x66, 0x4a, 0x12, 0x54, 0x06, 0x29, 0xa0, 0x81, 0x0f,
+	/* (2^152)P */ 0xfd, 0x86, 0x9b, 0x56, 0xa6, 0x9c, 0xd0, 0x9e, 0x2d, 0x9a, 0xaf, 0x18, 0xfd, 0x09, 0x10, 0x81, 0x0a, 0xc2, 0xd8, 0x93, 0x3f, 0xd0, 0x08, 0xff, 0x6b, 0xf2, 0xae, 0x9f, 0x19, 0x48, 0xa1, 0x52,
+	/* (2^153)P */ 0x73, 0x1b, 0x8d, 0x2d, 0xdc, 0xf9, 0x03, 0x3e, 0x70, 0x1a, 0x96, 0x73, 0x18, 0x80, 0x05, 0x42, 0x70, 0x59, 0xa3, 0x41, 0xf0, 0x87, 0xd9, 0xc0, 0x49, 0xd5, 0xc0, 0xa1, 0x15, 0x1f, 0xaa, 0x07,
+	/* (2^154)P */ 0x24, 0x72, 0xd2, 0x8c, 0xe0, 0x6c, 0xd4, 0xdf, 0x39, 0x42, 0x4e, 0x93, 0x4f, 0x02, 0x0a, 0x6d, 0x59, 0x7b, 0x89, 0x99, 0x63, 0x7a, 0x8a, 0x80, 0xa2, 0x95, 0x3d, 0xe1, 0xe9, 0x56, 0x45, 0x0a,
+	/* (2^155)P */ 0x45, 0x30, 0xc1, 0xe9, 0x1f, 0x99, 0x1a, 0xd2, 0xb8, 0x51, 0x77, 0xfe, 0x48, 0x85, 0x0e, 0x9b, 0x35, 0x00, 0xf3, 0x4b, 0xcb, 0x43, 0xa6, 0x5d, 0x21, 0xf7, 0x40, 0x39, 0xd6, 0x28, 0xdb, 0x77,
+	/* (2^156)P */ 0x11, 0x90, 0xdc, 0x4a, 0x61, 0xeb, 0x5e, 0xfc, 0xeb, 0x11, 0xc4, 0xe8, 0x9a, 0x41, 0x29, 0x52, 0x74, 0xcf, 0x1d, 0x7d, 0x78, 0xe7, 0xc3, 0x9e, 0xb5, 0x4c, 0x6e, 0x21, 0x3e, 0x05, 0x0d, 0x34,
+	/* (2^157)P */ 0xb4, 0xf2, 0x8d, 0xb4, 0x39, 0xaf, 0xc7, 0xca, 0x94, 0x0a, 0xa1, 0x71, 0x28, 0xec, 0xfa, 0xc0, 0xed, 0x75, 0xa5, 0x5c, 0x24, 0x69, 0x0a, 0x14, 0x4c, 0x3a, 0x27, 0x34, 0x71, 0xc3, 0xf1, 0x0c,
+	/* (2^158)P */ 0xa5, 0xb8, 0x24, 0xc2, 0x6a, 0x30, 0xee, 0xc8, 0xb0, 0x30, 0x49, 0xcb, 0x7c, 0xee, 0xea, 0x57, 0x4f, 0xe7, 0xcb, 0xaa, 0xbd, 0x06, 0xe8, 0xa1, 0x7d, 0x65, 0xeb, 0x2e, 0x74, 0x62, 0x9a, 0x7d,
+	/* (2^159)P */ 0x30, 0x48, 0x6c, 0x54, 0xef, 0xb6, 0xb6, 0x9e, 0x2e, 0x6e, 0xb3, 0xdd, 0x1f, 0xca, 0x5c, 0x88, 0x05, 0x71, 0x0d, 0xef, 0x83, 0xf3, 0xb9, 0xe6, 0x12, 0x04, 0x2e, 0x9d, 0xef, 0x4f, 0x65, 0x58,
+	/* (2^160)P */ 0x26, 0x8e, 0x0e, 0xbe, 0xff, 0xc4, 0x05, 0xa9, 0x6e, 0x81, 0x31, 0x9b, 0xdf, 0xe5, 0x2d, 0x94, 0xe1, 0x88, 0x2e, 0x80, 0x3f, 0x72, 0x7d, 0x49, 0x8d, 0x40, 0x2f, 0x60, 0xea, 0x4d, 0x68, 0x30,
+	/* (2^161)P */ 0x34, 0xcb, 0xe6, 0xa3, 0x78, 0xa2, 0xe5, 0x21, 0xc4, 0x1d, 0x15, 0x5b, 0x6f, 0x6e, 0xfb, 0xae, 0x15, 0xca, 0x77, 0x9d, 0x04, 0x8e, 0x0b, 0xb3, 0x81, 0x89, 0xb9, 0x53, 0xcf, 0xc9, 0xc3, 0x28,
+	/* (2^162)P */ 0x2a, 0xdd, 0x6c, 0x55, 0x21, 0xb7, 0x7f, 0x28, 0x74, 0x22, 0x02, 0x97, 0xa8, 0x7c, 0x31, 0x0d, 0x58, 0x32, 0x54, 0x3a, 0x42, 0xc7, 0x68, 0x74, 0x2f, 0x64, 0xb5, 0x4e, 0x46, 0x11, 0x7f, 0x4a,
+	/* (2^163)P */ 0xa6, 0x3a, 0x19, 0x4d, 0x77, 0xa4, 0x37, 0xa2, 0xa1, 0x29, 0x21, 0xa9, 0x6e, 0x98, 0x65, 0xd8, 0x88, 0x1a, 0x7c, 0xf8, 0xec, 0x15, 0xc5, 0x24, 0xeb, 0xf5, 0x39, 0x5f, 0x57, 0x03, 0x40, 0x60,
+	/* (2^164)P */ 0x27, 0x9b, 0x0a, 0x57, 0x89, 0xf1, 0xb9, 0x47, 0x78, 0x4b, 0x5e, 0x46, 0xde, 0xce, 0x98, 0x2b, 0x20, 0x5c, 0xb8, 0xdb, 0x51, 0xf5, 0x6d, 0x02, 0x01, 0x19, 0xe2, 0x47, 0x10, 0xd9, 0xfc, 0x74,
+	/* (2^165)P */ 0xa3, 0xbf, 0xc1, 0x23, 0x0a, 0xa9, 0xe2, 0x13, 0xf6, 0x19, 0x85, 0x47, 0x4e, 0x07, 0xb0, 0x0c, 0x44, 0xcf, 0xf6, 0x3a, 0xbe, 0xcb, 0xf1, 0x5f, 0xbe, 0x2d, 0x81, 0xbe, 0x38, 0x54, 0xfe, 0x67,
+	/* (2^166)P */ 0xb0, 0x05, 0x0f, 0xa4, 0x4f, 0xf6, 0x3c, 0xd1, 0x87, 0x37, 0x28, 0x32, 0x2f, 0xfb, 0x4d, 0x05, 0xea, 0x2a, 0x0d, 0x7f, 0x5b, 0x91, 0x73, 0x41, 0x4e, 0x0d, 0x61, 0x1f, 0x4f, 0x14, 0x2f, 0x48,
+	/* (2^167)P */ 0x34, 0x82, 0x7f, 0xb4, 0x01, 0x02, 0x21, 0xf6, 0x90, 0xb9, 0x70, 0x9e, 0x92, 0xe1, 0x0a, 0x5d, 0x7c, 0x56, 0x49, 0xb0, 0x55, 0xf4, 0xd7, 0xdc, 0x01, 0x6f, 0x91, 0xf0, 0xf1, 0xd0, 0x93, 0x7e,
+	/* (2^168)P */ 0xfa, 0xb4, 0x7d, 0x8a, 0xf1, 0xcb, 0x79, 0xdd, 0x2f, 0xc6, 0x74, 0x6f, 0xbf, 0x91, 0x83, 0xbe, 0xbd, 0x91, 0x82, 0x4b, 0xd1, 0x45, 0x71, 0x02, 0x05, 0x17, 0xbf, 0x2c, 0xea, 0x73, 0x5a, 0x58,
+	/* (2^169)P */ 0xb2, 0x0d, 0x8a, 0x92, 0x3e, 0xa0, 0x5c, 0x48, 0xe7, 0x57, 0x28, 0x74, 0xa5, 0x01, 0xfc, 0x10, 0xa7, 0x51, 0xd5, 0xd6, 0xdb, 0x2e, 0x48, 0x2f, 0x8a, 0xdb, 0x8f, 0x04, 0xb5, 0x33, 0x04, 0x0f,
+	/* (2^170)P */ 0x47, 0x62, 0xdc, 0xd7, 0x8d, 0x2e, 0xda, 0x60, 0x9a, 0x81, 0xd4, 0x8c, 0xd3, 0xc9, 0xb4, 0x88, 0x97, 0x66, 0xf6, 0x01, 0xc0, 0x3a, 0x03, 0x13, 0x75, 0x7d, 0x36, 0x3b, 0xfe, 0x24, 0x3b, 0x27,
+	/* (2^171)P */ 0xd4, 0xb9, 0xb3, 0x31, 0x6a, 0xf6, 0xe8, 0xc6, 0xd5, 0x49, 0xdf, 0x94, 0xa4, 0x14, 0x15, 0x28, 0xa7, 0x3d, 0xb2, 0xc8, 0xdf, 0x6f, 0x72, 0xd1, 0x48, 0xe5, 0xde, 0x03, 0xd1, 0xe7, 0x3a, 0x4b,
+	/* (2^172)P */ 0x7e, 0x9d, 0x4b, 0xce, 0x19, 0x6e, 0x25, 0xc6, 0x1c, 0xc6, 0xe3, 0x86, 0xf1, 0x5c, 0x5c, 0xff, 0x45, 0xc1, 0x8e, 0x4b, 0xa3, 0x3c, 0xc6, 0xac, 0x74, 0x65, 0xe6, 0xfe, 0x88, 0x18, 0x62, 0x74,
+	/* (2^173)P */ 0x1e, 0x0a, 0x29, 0x45, 0x96, 0x40, 0x6f, 0x95, 0x2e, 0x96, 0x3a, 0x26, 0xe3, 0xf8, 0x0b, 0xef, 0x7b, 0x64, 0xc2, 0x5e, 0xeb, 0x50, 0x6a, 0xed, 0x02, 0x75, 0xca, 0x9d, 0x3a, 0x28, 0x94, 0x06,
+	/* (2^174)P */ 0xd1, 0xdc, 0xa2, 0x43, 0x36, 0x96, 0x9b, 0x76, 0x53, 0x53, 0xfc, 0x09, 0xea, 0xc8, 0xb7, 0x42, 0xab, 0x7e, 0x39, 0x13, 0xee, 0x2a, 0x00, 0x4f, 0x3a, 0xd6, 0xb7, 0x19, 0x2c, 0x5e, 0x00, 0x63,
+	/* (2^175)P */ 0xea, 0x3b, 0x02, 0x63, 0xda, 0x36, 0x67, 0xca, 0xb7, 0x99, 0x2a, 0xb1, 0x6d, 0x7f, 0x6c, 0x96, 0xe1, 0xc5, 0x37, 0xc5, 0x90, 0x93, 0xe0, 0xac, 0xee, 0x89, 0xaa, 0xa1, 0x63, 0x60, 0x69, 0x0b,
+	/* (2^176)P */ 0xe5, 0x56, 0x8c, 0x28, 0x97, 0x3e, 0xb0, 0xeb, 0xe8, 0x8b, 0x8c, 0x93, 0x9f, 0x9f, 0x2a, 0x43, 0x71, 0x7f, 0x71, 0x5b, 0x3d, 0xa9, 0xa5, 0xa6, 0x97, 0x9d, 0x8f, 0xe1, 0xc3, 0xb4, 0x5f, 0x1a,
+	/* (2^177)P */ 0xce, 0xcd, 0x60, 0x1c, 0xad, 0xe7, 0x94, 0x1c, 0xa0, 0xc4, 0x02, 0xfc, 0x43, 0x2a, 0x20, 0xee, 0x20, 0x6a, 0xc4, 0x67, 0xd8, 0xe4, 0xaf, 0x8d, 0x58, 0x7b, 0xc2, 0x8a, 0x3c, 0x26, 0x10, 0x0a,
+	/* (2^178)P */ 0x4a, 0x2a, 0x43, 0xe4, 0xdf, 0xa9, 0xde, 0xd0, 0xc5, 0x77, 0x92, 0xbe, 0x7b, 0xf8, 0x6a, 0x85, 0x1a, 0xc7, 0x12, 0xc2, 0xac, 0x72, 0x84, 0xce, 0x91, 0x1e, 0xbb, 0x9b, 0x6d, 0x1b, 0x15, 0x6f,
+	/* (2^179)P */ 0x6a, 0xd5, 0xee, 0x7c, 0x52, 0x6c, 0x77, 0x26, 0xec, 0xfa, 0xf8, 0xfb, 0xb7, 0x1c, 0x21, 0x7d, 0xcc, 0x09, 0x46, 0xfd, 0xa6, 0x66, 0xae, 0x37, 0x42, 0x0c, 0x77, 0xd2, 0x02, 0xb7, 0x81, 0x1f,
+	/* (2^180)P */ 0x92, 0x83, 0xc5, 0xea, 0x57, 0xb0, 0xb0, 0x2f, 0x9d, 0x4e, 0x74, 0x29, 0xfe, 0x89, 0xdd, 0xe1, 0xf8, 0xb4, 0xbe, 0x17, 0xeb, 0xf8, 0x64, 0xc9, 0x1e, 0xd4, 0xa2, 0xc9, 0x73, 0x10, 0x57, 0x29,
+	/* (2^181)P */ 0x54, 0xe2, 0xc0, 0x81, 0x89, 0xa1, 0x48, 0xa9, 0x30, 0x28, 0xb2, 0x65, 0x9b, 0x36, 0xf6, 0x2d, 0xc6, 0xd3, 0xcf, 0x5f, 0xd7, 0xb2, 0x3e, 0xa3, 0x1f, 0xa0, 0x99, 0x41, 0xec, 0xd6, 0x8c, 0x07,
+	/* (2^182)P */ 0x2f, 0x0d, 0x90, 0xad, 0x41, 0x4a, 0x58, 0x4a, 0x52, 0x4c, 0xc7, 0xe2, 0x78, 0x2b, 0x14, 0x32, 0x78, 0xc9, 0x31, 0x84, 0x33, 0xe8, 0xc4, 0x68, 0xc2, 0x9f, 0x68, 0x08, 0x90, 0xea, 0x69, 0x7f,
+	/* (2^183)P */ 0x65, 0x82, 0xa3, 0x46, 0x1e, 0xc8, 0xf2, 0x52, 0xfd, 0x32, 0xa8, 0x04, 0x2d, 0x07, 0x78, 0xfd, 0x94, 0x9e, 0x35, 0x25, 0xfa, 0xd5, 0xd7, 0x8c, 0xd2, 0x29, 0xcc, 0x54, 0x74, 0x1b, 0xe7, 0x4d,
+	/* (2^184)P */ 0xc9, 0x6a, 0xda, 0x1e, 0xad, 0x60, 0xeb, 0x42, 0x3a, 0x9c, 0xc0, 0xdb, 0xdf, 0x37, 0xad, 0x0a, 0x91, 0xc1, 0x3c, 0xe3, 0x71, 0x4b, 0x00, 0x81, 0x3c, 0x80, 0x22, 0x51, 0x34, 0xbe, 0xe6, 0x44,
+	/* (2^185)P */ 0xdb, 0x20, 0x19, 0xba, 0x88, 0x83, 0xfe, 0x03, 0x08, 0xb0, 0x0d, 0x15, 0x32, 0x7c, 0xd5, 0xf5, 0x29, 0x0c, 0xf6, 0x1a, 0x28, 0xc4, 0xc8, 0x49, 0xee, 0x1a, 0x70, 0xde, 0x18, 0xb5, 0xed, 0x21,
+	/* (2^186)P */ 0x99, 0xdc, 0x06, 0x8f, 0x41, 0x3e, 0xb6, 0x7f, 0xb8, 0xd7, 0x66, 0xc1, 0x99, 0x0d, 0x46, 0xa4, 0x83, 0x0a, 0x52, 0xce, 0x48, 0x52, 0xdd, 0x24, 0x58, 0x83, 0x92, 0x2b, 0x71, 0xad, 0xc3, 0x5e,
+	/* (2^187)P */ 0x0f, 0x93, 0x17, 0xbd, 0x5f, 0x2a, 0x02, 0x15, 0xe3, 0x70, 0x25, 0xd8, 0x77, 0x4a, 0xf6, 0xa4, 0x12, 0x37, 0x78, 0x15, 0x69, 0x8d, 0xbc, 0x12, 0xbb, 0x0a, 0x62, 0xfc, 0xc0, 0x94, 0x81, 0x49,
+	/* (2^188)P */ 0x82, 0x6c, 0x68, 0x55, 0xd2, 0xd9, 0xa2, 0x38, 0xf0, 0x21, 0x3e, 0x19, 0xd9, 0x6b, 0x5c, 0x78, 0x84, 0x54, 0x4a, 0xb2, 0x1a, 0xc8, 0xd5, 0xe4, 0x89, 0x09, 0xe2, 0xb2, 0x60, 0x78, 0x30, 0x56,
+	/* (2^189)P */ 0xc4, 0x74, 0x4d, 0x8b, 0xf7, 0x55, 0x9d, 0x42, 0x31, 0x01, 0x35, 0x43, 0x46, 0x83, 0xf1, 0x22, 0xff, 0x1f, 0xc7, 0x98, 0x45, 0xc2, 0x60, 0x1e, 0xef, 0x83, 0x99, 0x97, 0x14, 0xf0, 0xf2, 0x59,
+	/* (2^190)P */ 0x44, 0x4a, 0x49, 0xeb, 0x56, 0x7d, 0xa4, 0x46, 0x8e, 0xa1, 0x36, 0xd6, 0x54, 0xa8, 0x22, 0x3e, 0x3b, 0x1c, 0x49, 0x74, 0x52, 0xe1, 0x46, 0xb3, 0xe7, 0xcd, 0x90, 0x53, 0x4e, 0xfd, 0xea, 0x2c,
+	/* (2^191)P */ 0x75, 0x66, 0x0d, 0xbe, 0x38, 0x85, 0x8a, 0xba, 0x23, 0x8e, 0x81, 0x50, 0xbb, 0x74, 0x90, 0x4b, 0xc3, 0x04, 0xd3, 0x85, 0x90, 0xb8, 0xda, 0xcb, 0xc4, 0x92, 0x61, 0xe5, 0xe0, 0x4f, 0xa2, 0x61,
+	/* (2^192)P */ 0xcb, 0x5b, 0x52, 0xdb, 0xe6, 0x15, 0x76, 0xcb, 0xca, 0xe4, 0x67, 0xa5, 0x35, 0x8c, 0x7d, 0xdd, 0x69, 0xdd, 0xfc, 0xca, 0x3a, 0x15, 0xb4, 0xe6, 0x66, 0x97, 0x3c, 0x7f, 0x09, 0x8e, 0x66, 0x2d,
+	/* (2^193)P */ 0xf0, 0x5e, 0xe5, 0x5c, 0x26, 0x7e, 0x7e, 0xa5, 0x67, 0xb9, 0xd4, 0x7c, 0x52, 0x4e, 0x9f, 0x5d, 0xe5, 0xd1, 0x2f, 0x49, 0x06, 0x36, 0xc8, 0xfb, 0xae, 0xf7, 0xc3, 0xb7, 0xbe, 0x52, 0x0d, 0x09,
+	/* (2^194)P */ 0x7c, 0x4d, 0x7b, 0x1e, 0x5a, 0x51, 0xb9, 0x09, 0xc0, 0x44, 0xda, 0x99, 0x25, 0x6a, 0x26, 0x1f, 0x04, 0x55, 0xc5, 0xe2, 0x48, 0x95, 0xc4, 0xa1, 0xcc, 0x15, 0x6f, 0x12, 0x87, 0x42, 0xf0, 0x7e,
+	/* (2^195)P */ 0x15, 0xef, 0x30, 0xbd, 0x9d, 0x65, 0xd1, 0xfe, 0x7b, 0x27, 0xe0, 0xc4, 0xee, 0xb9, 0x4a, 0x8b, 0x91, 0x32, 0xdf, 0xa5, 0x36, 0x62, 0x4d, 0x88, 0x88, 0xf7, 0x5c, 0xbf, 0xa6, 0x6e, 0xd9, 0x1f,
+	/* (2^196)P */ 0x9a, 0x0d, 0x19, 0x1f, 0x98, 0x61, 0xa1, 0x42, 0xc1, 0x52, 0x60, 0x7e, 0x50, 0x49, 0xd8, 0x61, 0xd5, 0x2c, 0x5a, 0x28, 0xbf, 0x13, 0xe1, 0x9f, 0xd8, 0x85, 0xad, 0xdb, 0x76, 0xd6, 0x22, 0x7c,
+	/* (2^197)P */ 0x7d, 0xd2, 0xfb, 0x2b, 0xed, 0x70, 0xe7, 0x82, 0xa5, 0xf5, 0x96, 0xe9, 0xec, 0xb2, 0x05, 0x4c, 0x50, 0x01, 0x90, 0xb0, 0xc2, 0xa9, 0x40, 0xcd, 0x64, 0xbf, 0xd9, 0x13, 0x92, 0x31, 0x95, 0x58,
+	/* (2^198)P */ 0x08, 0x2e, 0xea, 0x3f, 0x70, 0x5d, 0xcc, 0xe7, 0x8c, 0x18, 0xe2, 0x58, 0x12, 0x49, 0x0c, 0xb5, 0xf0, 0x5b, 0x20, 0x48, 0xaa, 0x0b, 0xe3, 0xcc, 0x62, 0x2d, 0xa3, 0xcf, 0x9c, 0x65, 0x7c, 0x53,
+	/* (2^199)P */ 0x88, 0xc0, 0xcf, 0x98, 0x3a, 0x62, 0xb6, 0x37, 0xa4, 0xac, 0xd6, 0xa4, 0x1f, 0xed, 0x9b, 0xfe, 0xb0, 0xd1, 0xa8, 0x56, 0x8e, 0x9b, 0xd2, 0x04, 0x75, 0x95, 0x51, 0x0b, 0xc4, 0x71, 0x5f, 0x72,
+	/* (2^200)P */ 0xe6, 0x9c, 0x33, 0xd0, 0x9c, 0xf8, 0xc7, 0x28, 0x8b, 0xc1, 0xdd, 0x69, 0x44, 0xb1, 0x67, 0x83, 0x2c, 0x65, 0xa1, 0xa6, 0x83, 0xda, 0x3a, 0x88, 0x17, 0x6c, 0x4d, 0x03, 0x74, 0x19, 0x5f, 0x58,
+	/* (2^201)P */ 0x88, 0x91, 0xb1, 0xf1, 0x66, 0xb2, 0xcf, 0x89, 0x17, 0x52, 0xc3, 0xe7, 0x63, 0x48, 0x3b, 0xe6, 0x6a, 0x52, 0xc0, 0xb4, 0xa6, 0x9d, 0x8c, 0xd8, 0x35, 0x46, 0x95, 0xf0, 0x9d, 0x5c, 0x03, 0x3e,
+	/* (2^202)P */ 0x9d, 0xde, 0x45, 0xfb, 0x12, 0x54, 0x9d, 0xdd, 0x0d, 0xf4, 0xcf, 0xe4, 0x32, 0x45, 0x68, 0xdd, 0x1c, 0x67, 0x1d, 0x15, 0x9b, 0x99, 0x5c, 0x4b, 0x90, 0xf6, 0xe7, 0x11, 0xc8, 0x2c, 0x8c, 0x2d,
+	/* (2^203)P */ 0x40, 0x5d, 0x05, 0x90, 0x1d, 0xbe, 0x54, 0x7f, 0x40, 0xaf, 0x4a, 0x46, 0xdf, 0xc5, 0x64, 0xa4, 0xbe, 0x17, 0xe9, 0xf0, 0x24, 0x96, 0x97, 0x33, 0x30, 0x6b, 0x35, 0x27, 0xc5, 0x8d, 0x01, 0x2c,
+	/* (2^204)P */ 0xd4, 0xb3, 0x30, 0xe3, 0x24, 0x50, 0x41, 0xa5, 0xd3, 0x52, 0x16, 0x69, 0x96, 0x3d, 0xff, 0x73, 0xf1, 0x59, 0x9b, 0xef, 0xc4, 0x42, 0xec, 0x94, 0x5a, 0x8e, 0xd0, 0x18, 0x16, 0x20, 0x47, 0x07,
+	/* (2^205)P */ 0x53, 0x1c, 0x41, 0xca, 0x8a, 0xa4, 0x6c, 0x4d, 0x19, 0x61, 0xa6, 0xcf, 0x2f, 0x5f, 0x41, 0x66, 0xff, 0x27, 0xe2, 0x51, 0x00, 0xd4, 0x4d, 0x9c, 0xeb, 0xf7, 0x02, 0x9a, 0xc0, 0x0b, 0x81, 0x59,
+	/* (2^206)P */ 0x1d, 0x10, 0xdc, 0xb3, 0x71, 0xb1, 0x7e, 0x2a, 0x8e, 0xf6, 0xfe, 0x9f, 0xb9, 0x5a, 0x1c, 0x44, 0xea, 0x59, 0xb3, 0x93, 0x9b, 0x5c, 0x02, 0x32, 0x2f, 0x11, 0x9d, 0x1e, 0xa7, 0xe0, 0x8c, 0x5e,
+	/* (2^207)P */ 0xfd, 0x03, 0x95, 0x42, 0x92, 0xcb, 0xcc, 0xbf, 0x55, 0x5d, 0x09, 0x2f, 0x75, 0xba, 0x71, 0xd2, 0x1e, 0x09, 0x2d, 0x97, 0x5e, 0xad, 0x5e, 0x34, 0xba, 0x03, 0x31, 0xa8, 0x11, 0xdf, 0xc8, 0x18,
+	/* (2^208)P */ 0x4c, 0x0f, 0xed, 0x9a, 0x9a, 0x94, 0xcd, 0x90, 0x7e, 0xe3, 0x60, 0x66, 0xcb, 0xf4, 0xd1, 0xc5, 0x0b, 0x2e, 0xc5, 0x56, 0x2d, 0xc5, 0xca, 0xb8, 0x0d, 0x8e, 0x80, 0xc5, 0x00, 0xe4, 0x42, 0x6e,
+	/* (2^209)P */ 0x23, 0xfd, 0xae, 0xee, 0x66, 0x69, 0xb4, 0xa3, 0xca, 0xcd, 0x9e, 0xe3, 0x0b, 0x1f, 0x4f, 0x0c, 0x1d, 0xa5, 0x83, 0xd6, 0xc9, 0xc8, 0x9d, 0x18, 0x1b, 0x35, 0x09, 0x4c, 0x05, 0x7f, 0xf2, 0x51,
+	/* (2^210)P */ 0x82, 0x06, 0x32, 0x2a, 0xcd, 0x7c, 0x48, 0x4c, 0x96, 0x1c, 0xdf, 0xb3, 0x5b, 0xa9, 0x7e, 0x58, 0xe8, 0xb8, 0x5c, 0x55, 0x9e, 0xf7, 0xcc, 0xc8, 0x3d, 0xd7, 0x06, 0xa2, 0x29, 0xc8, 0x7d, 0x54,
+	/* (2^211)P */ 0x06, 0x9b, 0xc3, 0x80, 0xcd, 0xa6, 0x22, 0xb8, 0xc6, 0xd4, 0x00, 0x20, 0x73, 0x54, 0x6d, 0xe9, 0x4d, 0x3b, 0x46, 0x91, 0x6f, 0x5b, 0x53, 0x28, 0x1d, 0x6e, 0x48, 0xe2, 0x60, 0x46, 0x8f, 0x22,
+	/* (2^212)P */ 0xbf, 0x3a, 0x8d, 0xde, 0x38, 0x95, 0x79, 0x98, 0x6e, 0xca, 0xeb, 0x45, 0x00, 0x33, 0xd8, 0x8c, 0x38, 0xe7, 0x21, 0x82, 0x00, 0x2a, 0x95, 0x79, 0xbb, 0xd2, 0x5c, 0x53, 0xa7, 0xe1, 0x22, 0x43,
+	/* (2^213)P */ 0x1c, 0x80, 0xd1, 0x19, 0x18, 0xc1, 0x14, 0xb1, 0xc7, 0x5e, 0x3f, 0x4f, 0xd8, 0xe4, 0x16, 0x20, 0x4c, 0x0f, 0x26, 0x09, 0xf4, 0x2d, 0x0e, 0xdd, 0x66, 0x72, 0x5f, 0xae, 0xc0, 0x62, 0xc3, 0x5e,
+	/* (2^214)P */ 0xee, 0xb4, 0xb2, 0xb8, 0x18, 0x2b, 0x46, 0xc0, 0xfb, 0x1a, 0x4d, 0x27, 0x50, 0xd9, 0xc8, 0x7c, 0xd2, 0x02, 0x6b, 0x43, 0x05, 0x71, 0x5f, 0xf2, 0xd3, 0xcc, 0xf9, 0xbf, 0xdc, 0xf8, 0xbb, 0x43,
+	/* (2^215)P */ 0xdf, 0xe9, 0x39, 0xa0, 0x67, 0x17, 0xad, 0xb6, 0x83, 0x35, 0x9d, 0xf6, 0xa8, 0x4d, 0x71, 0xb0, 0xf5, 0x31, 0x29, 0xb4, 0x18, 0xfa, 0x55, 0x5e, 0x61, 0x09, 0xc6, 0x33, 0x8f, 0x55, 0xd5, 0x4e,
+	/* (2^216)P */ 0xdd, 0xa5, 0x47, 0xc6, 0x01, 0x79, 0xe3, 0x1f, 0x57, 0xd3, 0x81, 0x80, 0x1f, 0xdf, 0x3d, 0x59, 0xa6, 0xd7, 0x3f, 0x81, 0xfd, 0xa4, 0x49, 0x02, 0x61, 0xaf, 0x9c, 0x4e, 0x27, 0xca, 0xac, 0x69,
+	/* (2^217)P */ 0xc9, 0x21, 0x07, 0x33, 0xea, 0xa3, 0x7b, 0x04, 0xa0, 0x1e, 0x7e, 0x0e, 0xc2, 0x3f, 0x42, 0x83, 0x60, 0x4a, 0x31, 0x01, 0xaf, 0xc0, 0xf4, 0x1d, 0x27, 0x95, 0x28, 0x89, 0xab, 0x2d, 0xa6, 0x09,
+	/* (2^218)P */ 0x00, 0xcb, 0xc6, 0x9c, 0xa4, 0x25, 0xb3, 0xa5, 0xb6, 0x6c, 0xb5, 0x54, 0xc6, 0x5d, 0x4b, 0xe9, 0xa0, 0x94, 0xc9, 0xad, 0x79, 0x87, 0xe2, 0x3b, 0xad, 0x4a, 0x3a, 0xba, 0xf8, 0xe8, 0x96, 0x42,
+	/* (2^219)P */ 0xab, 0x1e, 0x45, 0x1e, 0x76, 0x89, 0x86, 0x32, 0x4a, 0x59, 0x59, 0xff, 0x8b, 0x59, 0x4d, 0x2e, 0x4a, 0x08, 0xa7, 0xd7, 0x53, 0x68, 0xb9, 0x49, 0xa8, 0x20, 0x14, 0x60, 0x19, 0xa3, 0x80, 0x49,
+	/* (2^220)P */ 0x42, 0x2c, 0x55, 0x2f, 0xe1, 0xb9, 0x65, 0x95, 0x96, 0xfe, 0x00, 0x71, 0xdb, 0x18, 0x53, 0x8a, 0xd7, 0xd0, 0xad, 0x43, 0x4d, 0x0b, 0xc9, 0x05, 0xda, 0x4e, 0x5d, 0x6a, 0xd6, 0x4c, 0x8b, 0x53,
+	/* (2^221)P */ 0x9f, 0x03, 0x9f, 0xe8, 0xc3, 0x4f, 0xe9, 0xf4, 0x45, 0x80, 0x61, 0x6f, 0xf2, 0x9a, 0x2c, 0x59, 0x50, 0x95, 0x4b, 0xfd, 0xb5, 0x6e, 0xa3, 0x08, 0x19, 0x14, 0xed, 0xc2, 0xf6, 0xfa, 0xff, 0x25,
+	/* (2^222)P */ 0x54, 0xd3, 0x79, 0xcc, 0x59, 0x44, 0x43, 0x34, 0x6b, 0x47, 0xd5, 0xb1, 0xb4, 0xbf, 0xec, 0xee, 0x99, 0x5d, 0x61, 0x61, 0xa0, 0x34, 0xeb, 0xdd, 0x73, 0xb7, 0x64, 0xeb, 0xcc, 0xce, 0x29, 0x51,
+	/* (2^223)P */ 0x20, 0x35, 0x99, 0x94, 0x58, 0x21, 0x43, 0xee, 0x3b, 0x0b, 0x4c, 0xf1, 0x7c, 0x9c, 0x2f, 0x77, 0xd5, 0xda, 0xbe, 0x06, 0xe3, 0xfc, 0xe2, 0xd2, 0x97, 0x6a, 0xf0, 0x46, 0xb5, 0x42, 0x5f, 0x71,
+	/* (2^224)P */ 0x1a, 0x5f, 0x5b, 0xda, 0xce, 0xcd, 0x4e, 0x43, 0xa9, 0x41, 0x97, 0xa4, 0x15, 0x71, 0xa1, 0x0d, 0x2e, 0xad, 0xed, 0x73, 0x7c, 0xd7, 0x0b, 0x68, 0x41, 0x90, 0xdd, 0x4e, 0x35, 0x02, 0x7c, 0x48,
+	/* (2^225)P */ 0xc4, 0xd9, 0x0e, 0xa7, 0xf3, 0xef, 0xef, 0xb8, 0x02, 0xe3, 0x57, 0xe8, 0xa3, 0x2a, 0xa3, 0x56, 0xa0, 0xa5, 0xa2, 0x48, 0xbd, 0x68, 0x3a, 0xdf, 0x44, 0xc4, 0x76, 0x31, 0xb7, 0x50, 0xf6, 0x07,
+	/* (2^226)P */ 0xb1, 0xcc, 0xe0, 0x26, 0x16, 0x9b, 0x8b, 0xe3, 0x36, 0xfb, 0x09, 0x8b, 0xc1, 0x53, 0xe0, 0x79, 0x64, 0x49, 0xf9, 0xc9, 0x19, 0x03, 0xd9, 0x56, 0xc4, 0xf5, 0x9f, 0xac, 0xe7, 0x41, 0xa9, 0x1c,
+	/* (2^227)P */ 0xbb, 0xa0, 0x2f, 0x16, 0x29, 0xdf, 0xc4, 0x49, 0x05, 0x33, 0xb3, 0x82, 0x32, 0xcf, 0x88, 0x84, 0x7d, 0x43, 0xbb, 0xca, 0x14, 0xda, 0xdf, 0x95, 0x86, 0xad, 0xd5, 0x64, 0x82, 0xf7, 0x91, 0x33,
+	/* (2^228)P */ 0x5d, 0x09, 0xb5, 0xe2, 0x6a, 0xe0, 0x9a, 0x72, 0x46, 0xa9, 0x59, 0x32, 0xd7, 0x58, 0x8a, 0xd5, 0xed, 0x21, 0x39, 0xd1, 0x62, 0x42, 0x83, 0xe9, 0x92, 0xb5, 0x4b, 0xa5, 0xfa, 0xda, 0xfe, 0x27,
+	/* (2^229)P */ 0xbb, 0x48, 0xad, 0x29, 0xb8, 0xc5, 0x9d, 0xa9, 0x60, 0xe2, 0x9e, 0x49, 0x42, 0x57, 0x02, 0x5f, 0xfd, 0x13, 0x75, 0x5d, 0xcd, 0x8e, 0x2c, 0x80, 0x38, 0xd9, 0x6d, 0x3f, 0xef, 0xb3, 0xce, 0x78,
+	/* (2^230)P */ 0x94, 0x5d, 0x13, 0x8a, 0x4f, 0xf4, 0x42, 0xc3, 0xa3, 0xdd, 0x8c, 0x82, 0x44, 0xdb, 0x9e, 0x7b, 0xe7, 0xcf, 0x37, 0x05, 0x1a, 0xd1, 0x36, 0x94, 0xc8, 0xb4, 0x1a, 0xec, 0x64, 0xb1, 0x64, 0x50,
+	/* (2^231)P */ 0xfc, 0xb2, 0x7e, 0xd3, 0xcf, 0xec, 0x20, 0x70, 0xfc, 0x25, 0x0d, 0xd9, 0x3e, 0xea, 0x31, 0x1f, 0x34, 0xbb, 0xa1, 0xdf, 0x7b, 0x0d, 0x93, 0x1b, 0x44, 0x30, 0x11, 0x48, 0x7a, 0x46, 0x44, 0x53,
+	/* (2^232)P */ 0xfb, 0x6d, 0x5e, 0xf2, 0x70, 0x31, 0x07, 0x70, 0xc8, 0x4c, 0x11, 0x50, 0x1a, 0xdc, 0x85, 0xe3, 0x00, 0x4f, 0xfc, 0xc8, 0x8a, 0x69, 0x48, 0x23, 0xd8, 0x40, 0xdd, 0x84, 0x52, 0xa5, 0x77, 0x2a,
+	/* (2^233)P */ 0xe4, 0x6c, 0x8c, 0xc9, 0xe0, 0xaf, 0x06, 0xfe, 0xe4, 0xd6, 0xdf, 0xdd, 0x96, 0xdf, 0x35, 0xc2, 0xd3, 0x1e, 0xbf, 0x33, 0x1e, 0xd0, 0x28, 0x14, 0xaf, 0xbd, 0x00, 0x93, 0xec, 0x68, 0x57, 0x78,
+	/* (2^234)P */ 0x3b, 0xb6, 0xde, 0x91, 0x7a, 0xe5, 0x02, 0x97, 0x80, 0x8b, 0xce, 0xe5, 0xbf, 0xb8, 0xbd, 0x61, 0xac, 0x58, 0x1d, 0x3d, 0x6f, 0x42, 0x5b, 0x64, 0xbc, 0x57, 0xa5, 0x27, 0x22, 0xa8, 0x04, 0x48,
+	/* (2^235)P */ 0x01, 0x26, 0x4d, 0xb4, 0x8a, 0x04, 0x57, 0x8e, 0x35, 0x69, 0x3a, 0x4b, 0x1a, 0x50, 0xd6, 0x68, 0x93, 0xc2, 0xe1, 0xf9, 0xc3, 0x9e, 0x9c, 0xc3, 0xe2, 0x63, 0xde, 0xd4, 0x57, 0xf2, 0x72, 0x41,
+	/* (2^236)P */ 0x01, 0x64, 0x0c, 0x33, 0x50, 0xb4, 0x68, 0xd3, 0x91, 0x23, 0x8f, 0x41, 0x17, 0x30, 0x0d, 0x04, 0x0d, 0xd9, 0xb7, 0x90, 0x60, 0xbb, 0x34, 0x2c, 0x1f, 0xd5, 0xdf, 0x8f, 0x22, 0x49, 0xf6, 0x16,
+	/* (2^237)P */ 0xf5, 0x8e, 0x92, 0x2b, 0x8e, 0x81, 0xa6, 0xbe, 0x72, 0x1e, 0xc1, 0xcd, 0x91, 0xcf, 0x8c, 0xe2, 0xcd, 0x36, 0x7a, 0xe7, 0x68, 0xaa, 0x4a, 0x59, 0x0f, 0xfd, 0x7f, 0x6c, 0x80, 0x34, 0x30, 0x31,
+	/* (2^238)P */ 0x65, 0xbd, 0x49, 0x22, 0xac, 0x27, 0x9d, 0x8a, 0x12, 0x95, 0x8e, 0x01, 0x64, 0xb4, 0xa3, 0x19, 0xc7, 0x7e, 0xb3, 0x52, 0xf3, 0xcf, 0x6c, 0xc2, 0x21, 0x7b, 0x79, 0x1d, 0x34, 0x68, 0x6f, 0x05,
+	/* (2^239)P */ 0x27, 0x23, 0xfd, 0x7e, 0x75, 0xd6, 0x79, 0x5e, 0x15, 0xfe, 0x3a, 0x55, 0xb6, 0xbc, 0xbd, 0xfa, 0x60, 0x5a, 0xaf, 0x6e, 0x2c, 0x22, 0xe7, 0xd3, 0x3b, 0x74, 0xae, 0x4d, 0x6d, 0xc7, 0x46, 0x70,
+	/* (2^240)P */ 0x55, 0x4a, 0x8d, 0xb1, 0x72, 0xe8, 0x0b, 0x66, 0x96, 0x14, 0x4e, 0x57, 0x18, 0x25, 0x99, 0x19, 0xbb, 0xdc, 0x2b, 0x30, 0x3a, 0x05, 0x03, 0xc1, 0x8e, 0x8e, 0x21, 0x0b, 0x80, 0xe9, 0xd8, 0x3e,
+	/* (2^241)P */ 0x3e, 0xe0, 0x75, 0xfa, 0x39, 0x92, 0x0b, 0x7b, 0x83, 0xc0, 0x33, 0x46, 0x68, 0xfb, 0xe9, 0xef, 0x93, 0x77, 0x1a, 0x39, 0xbe, 0x5f, 0xa3, 0x98, 0x34, 0xfe, 0xd0, 0xe2, 0x0f, 0x51, 0x65, 0x60,
+	/* (2^242)P */ 0x0c, 0xad, 0xab, 0x48, 0x85, 0x66, 0xcb, 0x55, 0x27, 0xe5, 0x87, 0xda, 0x48, 0x45, 0x58, 0xb4, 0xdd, 0xc1, 0x07, 0x01, 0xea, 0xec, 0x43, 0x2c, 0x35, 0xde, 0x72, 0x93, 0x80, 0x28, 0x60, 0x52,
+	/* (2^243)P */ 0x1f, 0x3b, 0x21, 0xf9, 0x6a, 0xc5, 0x15, 0x34, 0xdb, 0x98, 0x7e, 0x01, 0x4d, 0x1a, 0xee, 0x5b, 0x9b, 0x70, 0xcf, 0xb5, 0x05, 0xb1, 0xf6, 0x13, 0xb6, 0x9a, 0xb2, 0x82, 0x34, 0x0e, 0xf2, 0x5f,
+	/* (2^244)P */ 0x90, 0x6c, 0x2e, 0xcc, 0x75, 0x9c, 0xa2, 0x0a, 0x06, 0xe2, 0x70, 0x3a, 0xca, 0x73, 0x7d, 0xfc, 0x15, 0xc5, 0xb5, 0xc4, 0x8f, 0xc3, 0x9f, 0x89, 0x07, 0xc2, 0xff, 0x24, 0xb1, 0x86, 0x03, 0x25,
+	/* (2^245)P */ 0x56, 0x2b, 0x3d, 0xae, 0xd5, 0x28, 0xea, 0x54, 0xce, 0x60, 0xde, 0xd6, 0x9d, 0x14, 0x13, 0x99, 0xc1, 0xd6, 0x06, 0x8f, 0xc5, 0x4f, 0x69, 0x16, 0xc7, 0x8f, 0x01, 0xeb, 0x75, 0x39, 0xb2, 0x46,
+	/* (2^246)P */ 0xe2, 0xb4, 0xb7, 0xb4, 0x0f, 0x6a, 0x0a, 0x47, 0xde, 0x53, 0x72, 0x8f, 0x5a, 0x47, 0x92, 0x5d, 0xdb, 0x3a, 0xbd, 0x2f, 0xb5, 0xe5, 0xee, 0xab, 0x68, 0x69, 0x80, 0xa0, 0x01, 0x08, 0xa2, 0x7f,
+	/* (2^247)P */ 0xd2, 0x14, 0x77, 0x9f, 0xf1, 0xfa, 0xf3, 0x76, 0xc3, 0x60, 0x46, 0x2f, 0xc1, 0x40, 0xe8, 0xb3, 0x4e, 0x74, 0x12, 0xf2, 0x8d, 0xcd, 0xb4, 0x0f, 0xd2, 0x2d, 0x3a, 0x1d, 0x25, 0x5a, 0x06, 0x4b,
+	/* (2^248)P */ 0x4a, 0xcd, 0x77, 0x3d, 0x38, 0xde, 0xeb, 0x5c, 0xb1, 0x9c, 0x2c, 0x88, 0xdf, 0x39, 0xdf, 0x6a, 0x59, 0xf7, 0x9a, 0xb0, 0x2e, 0x24, 0xdd, 0xa2, 0x22, 0x64, 0x5f, 0x0e, 0xe5, 0xc0, 0x47, 0x31,
+	/* (2^249)P */ 0xdb, 0x50, 0x13, 0x1d, 0x10, 0xa5, 0x4c, 0x16, 0x62, 0xc9, 0x3f, 0xc3, 0x79, 0x34, 0xd1, 0xf8, 0x08, 0xda, 0xe5, 0x13, 0x4d, 0xce, 0x40, 0xe6, 0xba, 0xf8, 0x61, 0x50, 0xc4, 0xe0, 0xde, 0x4b,
+	/* (2^250)P */ 0xc9, 0xb1, 0xed, 0xa4, 0xc1, 0x6d, 0xc4, 0xd7, 0x8a, 0xd9, 0x7f, 0x43, 0xb6, 0xd7, 0x14, 0x55, 0x0b, 0xc0, 0xa1, 0xb2, 0x6b, 0x2f, 0x94, 0x58, 0x0e, 0x71, 0x70, 0x1d, 0xab, 0xb2, 0xff, 0x2d,
+	/* (2^251)P */ 0x68, 0x6d, 0x8b, 0xc1, 0x2f, 0xcf, 0xdf, 0xcc, 0x67, 0x61, 0x80, 0xb7, 0xa8, 0xcb, 0xeb, 0xa8, 0xe3, 0x37, 0x29, 0x5e, 0xf9, 0x97, 0x06, 0x98, 0x8c, 0x6e, 0x12, 0xd0, 0x1c, 0xba, 0xfb, 0x02,
+	/* (2^252)P */ 0x65, 0x45, 0xff, 0xad, 0x60, 0xc3, 0x98, 0xcb, 0x19, 0x15, 0xdb, 0x4b, 0xd2, 0x01, 0x71, 0x44, 0xd5, 0x15, 0xfb, 0x75, 0x74, 0xc8, 0xc4, 0x98, 0x7d, 0xa2, 0x22, 0x6e, 0x6d, 0xc7, 0xf8, 0x05,
+	/* (2^253)P */ 0x94, 0xf4, 0xb9, 0xfe, 0xdf, 0xe5, 0x69, 0xab, 0x75, 0x6b, 0x40, 0x18, 0x9d, 0xc7, 0x09, 0xae, 0x1d, 0x2d, 0xa4, 0x94, 0xfb, 0x45, 0x9b, 0x19, 0x84, 0xfa, 0x2a, 0xae, 0xeb, 0x0a, 0x71, 0x79,
+	/* (2^254)P */ 0xdf, 0xd2, 0x34, 0xf3, 0xa7, 0xed, 0xad, 0xa6, 0xb4, 0x57, 0x2a, 0xaf, 0x51, 0x9c, 0xde, 0x7b, 0xa8, 0xea, 0xdc, 0x86, 0x4f, 0xc6, 0x8f, 0xa9, 0x7b, 0xd0, 0x0e, 0xc2, 0x35, 0x03, 0xbe, 0x6b,
+	/* (2^255)P */ 0x44, 0x43, 0x98, 0x53, 0xbe, 0xdc, 0x7f, 0x66, 0xa8, 0x49, 0x59, 0x00, 0x1c, 0xbc, 0x72, 0x07, 0x8e, 0xd6, 0xbe, 0x4e, 0x9f, 0xa4, 0x07, 0xba, 0xbf, 0x30, 0xdf, 0xba, 0x85, 0xb0, 0xa7, 0x1f,
+}

vendor/github.com/cloudflare/circl/dh/x448/curve.go

@@ -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,
+	},
+}

vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.go

@@ -0,0 +1,30 @@
+//go:build amd64 && !purego
+// +build amd64,!purego
+
+package x448
+
+import (
+	fp "github.com/cloudflare/circl/math/fp448"
+	"golang.org/x/sys/cpu"
+)
+
+var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX
+
+var _ = hasBmi2Adx
+
+func double(x, z *fp.Elt)             { doubleAmd64(x, z) }
+func diffAdd(w *[5]fp.Elt, b uint)    { diffAddAmd64(w, b) }
+func ladderStep(w *[5]fp.Elt, b uint) { ladderStepAmd64(w, b) }
+func mulA24(z, x *fp.Elt)             { mulA24Amd64(z, x) }
+
+//go:noescape
+func doubleAmd64(x, z *fp.Elt)
+
+//go:noescape
+func diffAddAmd64(w *[5]fp.Elt, b uint)
+
+//go:noescape
+func ladderStepAmd64(w *[5]fp.Elt, b uint)
+
+//go:noescape
+func mulA24Amd64(z, x *fp.Elt)

vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.h

@@ -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)

vendor/github.com/cloudflare/circl/dh/x448/curve_amd64.s

@@ -0,0 +1,193 @@
+// +build amd64
+
+#include "textflag.h"
+
+// Depends on circl/math/fp448 package
+#include "../../math/fp448/fp_amd64.h"
+#include "curve_amd64.h"
+
+// CTE_A24 is (A+2)/4 from Curve448
+#define CTE_A24 39082
+
+#define Size 56
+
+// multiplyA24Leg multiplies x times CTE_A24 and stores in z
+// Uses: AX, DX, R8-R15, FLAGS
+// Instr: x86_64, cmov, adx
+#define multiplyA24Leg(z,x) \
+    MOVQ $CTE_A24, R15; \
+    MOVQ  0+x, AX; MULQ R15; MOVQ AX,  R8; ;;;;;;;;;;;;  MOVQ DX,  R9; \
+    MOVQ  8+x, AX; MULQ R15; ADDQ AX,  R9; ADCQ $0, DX;  MOVQ DX, R10; \
+    MOVQ 16+x, AX; MULQ R15; ADDQ AX, R10; ADCQ $0, DX;  MOVQ DX, R11; \
+    MOVQ 24+x, AX; MULQ R15; ADDQ AX, R11; ADCQ $0, DX;  MOVQ DX, R12; \
+    MOVQ 32+x, AX; MULQ R15; ADDQ AX, R12; ADCQ $0, DX;  MOVQ DX, R13; \
+    MOVQ 40+x, AX; MULQ R15; ADDQ AX, R13; ADCQ $0, DX;  MOVQ DX, R14; \
+    MOVQ 48+x, AX; MULQ R15; ADDQ AX, R14; ADCQ $0, DX; \
+    MOVQ DX,  AX; \
+    SHLQ $32, AX; \
+    ADDQ DX,  R8; MOVQ $0, DX; \
+    ADCQ $0,  R9; \
+    ADCQ $0, R10; \
+    ADCQ AX, R11; \
+    ADCQ $0, R12; \
+    ADCQ $0, R13; \
+    ADCQ $0, R14; \
+    ADCQ $0,  DX; \
+    MOVQ DX,  AX; \
+    SHLQ $32, AX; \
+    ADDQ DX,  R8; \
+    ADCQ $0,  R9; \
+    ADCQ $0, R10; \
+    ADCQ AX, R11; \
+    ADCQ $0, R12; \
+    ADCQ $0, R13; \
+    ADCQ $0, R14; \
+    MOVQ  R8,  0+z; \
+    MOVQ  R9,  8+z; \
+    MOVQ R10, 16+z; \
+    MOVQ R11, 24+z; \
+    MOVQ R12, 32+z; \
+    MOVQ R13, 40+z; \
+    MOVQ R14, 48+z;
+
+// multiplyA24Adx multiplies x times CTE_A24 and stores in z
+// Uses: AX, DX, R8-R14, FLAGS
+// Instr: x86_64, bmi2
+#define multiplyA24Adx(z,x) \
+    MOVQ $CTE_A24, DX; \
+    MULXQ  0+x, R8,  R9; \
+    MULXQ  8+x, AX, R10;  ADDQ AX,  R9; \
+    MULXQ 16+x, AX, R11;  ADCQ AX, R10; \
+    MULXQ 24+x, AX, R12;  ADCQ AX, R11; \
+    MULXQ 32+x, AX, R13;  ADCQ AX, R12; \
+    MULXQ 40+x, AX, R14;  ADCQ AX, R13; \
+    MULXQ 48+x, AX,  DX;  ADCQ AX, R14; \
+    ;;;;;;;;;;;;;;;;;;;;  ADCQ $0,  DX; \
+    MOVQ DX,  AX; \
+    SHLQ $32, AX; \
+    ADDQ DX,  R8; MOVQ $0, DX; \
+    ADCQ $0,  R9; \
+    ADCQ $0, R10; \
+    ADCQ AX, R11; \
+    ADCQ $0, R12; \
+    ADCQ $0, R13; \
+    ADCQ $0, R14; \
+    ADCQ $0,  DX; \
+    MOVQ DX,  AX; \
+    SHLQ $32, AX; \
+    ADDQ DX,  R8; \
+    ADCQ $0,  R9; \
+    ADCQ $0, R10; \
+    ADCQ AX, R11; \
+    ADCQ $0, R12; \
+    ADCQ $0, R13; \
+    ADCQ $0, R14; \
+    MOVQ  R8,  0+z; \
+    MOVQ  R9,  8+z; \
+    MOVQ R10, 16+z; \
+    MOVQ R11, 24+z; \
+    MOVQ R12, 32+z; \
+    MOVQ R13, 40+z; \
+    MOVQ R14, 48+z;
+
+#define mulA24Legacy \
+    multiplyA24Leg(0(DI),0(SI))
+#define mulA24Bmi2Adx \
+    multiplyA24Adx(0(DI),0(SI))
+
+// func mulA24Amd64(z, x *fp448.Elt)
+TEXT ·mulA24Amd64(SB),NOSPLIT,$0-16
+    MOVQ z+0(FP), DI
+    MOVQ x+8(FP), SI
+    CHECK_BMI2ADX(LMA24, mulA24Legacy, mulA24Bmi2Adx)
+
+// func ladderStepAmd64(w *[5]fp448.Elt, b uint)
+// ladderStepAmd64 calculates a point addition and doubling as follows:
+// (x2,z2) = 2*(x2,z2) and (x3,z3) = (x2,z2)+(x3,z3) using as a difference (x1,-).
+//    w    = {x1,x2,z2,x3,z4} are five fp255.Elt of 56 bytes.
+//  stack  = (t0,t1) are two fp.Elt of fp.Size bytes, and
+//           (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes.
+TEXT ·ladderStepAmd64(SB),NOSPLIT,$336-16
+    // Parameters
+    #define regWork DI
+    #define regMove SI
+    #define x1 0*Size(regWork)
+    #define x2 1*Size(regWork)
+    #define z2 2*Size(regWork)
+    #define x3 3*Size(regWork)
+    #define z3 4*Size(regWork)
+    // Local variables
+    #define t0 0*Size(SP)
+    #define t1 1*Size(SP)
+    #define b0 2*Size(SP)
+    #define b1 4*Size(SP)
+    MOVQ w+0(FP), regWork
+    MOVQ b+8(FP), regMove
+    CHECK_BMI2ADX(LLADSTEP, ladderStepLeg, ladderStepBmi2Adx)
+    #undef regWork
+    #undef regMove
+    #undef x1
+    #undef x2
+    #undef z2
+    #undef x3
+    #undef z3
+    #undef t0
+    #undef t1
+    #undef b0
+    #undef b1
+
+// func diffAddAmd64(work *[5]fp.Elt, swap uint)
+// diffAddAmd64 calculates a differential point addition using a precomputed point.
+// (x1,z1) = (x1,z1)+(mu) using a difference point (x2,z2)
+//    work = {mu,x1,z1,x2,z2} are five fp448.Elt of 56 bytes, and
+//   stack = (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes.
+// This is Equation 7 at https://eprint.iacr.org/2017/264.
+TEXT ·diffAddAmd64(SB),NOSPLIT,$224-16
+    // Parameters
+    #define regWork DI
+    #define regSwap SI
+    #define ui 0*Size(regWork)
+    #define x1 1*Size(regWork)
+    #define z1 2*Size(regWork)
+    #define x2 3*Size(regWork)
+    #define z2 4*Size(regWork)
+    // Local variables
+    #define b0 0*Size(SP)
+    #define b1 2*Size(SP)
+    MOVQ w+0(FP), regWork
+    MOVQ b+8(FP), regSwap
+    cswap(x1,x2,regSwap)
+    cswap(z1,z2,regSwap)
+    CHECK_BMI2ADX(LDIFADD, difAddLeg, difAddBmi2Adx)
+    #undef regWork
+    #undef regSwap
+    #undef ui
+    #undef x1
+    #undef z1
+    #undef x2
+    #undef z2
+    #undef b0
+    #undef b1
+
+// func doubleAmd64(x, z *fp448.Elt)
+// doubleAmd64 calculates a point doubling (x1,z1) = 2*(x1,z1).
+//  stack = (t0,t1) are two fp.Elt of fp.Size bytes, and
+//          (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes.
+TEXT ·doubleAmd64(SB),NOSPLIT,$336-16
+    // Parameters
+    #define x1 0(DI)
+    #define z1 0(SI)
+    // Local variables
+    #define t0 0*Size(SP)
+    #define t1 1*Size(SP)
+    #define b0 2*Size(SP)
+    #define b1 4*Size(SP)
+    MOVQ x+0(FP), DI
+    MOVQ z+8(FP), SI
+    CHECK_BMI2ADX(LDOUB,doubleLeg,doubleBmi2Adx)
+    #undef x1
+    #undef z1
+    #undef t0
+    #undef t1
+    #undef b0
+    #undef b1

vendor/github.com/cloudflare/circl/dh/x448/curve_generic.go

@@ -0,0 +1,100 @@
+package x448
+
+import (
+	"encoding/binary"
+	"math/bits"
+
+	"github.com/cloudflare/circl/math/fp448"
+)
+
+func doubleGeneric(x, z *fp448.Elt) {
+	t0, t1 := &fp448.Elt{}, &fp448.Elt{}
+	fp448.AddSub(x, z)
+	fp448.Sqr(x, x)
+	fp448.Sqr(z, z)
+	fp448.Sub(t0, x, z)
+	mulA24Generic(t1, t0)
+	fp448.Add(t1, t1, z)
+	fp448.Mul(x, x, z)
+	fp448.Mul(z, t0, t1)
+}
+
+func diffAddGeneric(w *[5]fp448.Elt, b uint) {
+	mu, x1, z1, x2, z2 := &w[0], &w[1], &w[2], &w[3], &w[4]
+	fp448.Cswap(x1, x2, b)
+	fp448.Cswap(z1, z2, b)
+	fp448.AddSub(x1, z1)
+	fp448.Mul(z1, z1, mu)
+	fp448.AddSub(x1, z1)
+	fp448.Sqr(x1, x1)
+	fp448.Sqr(z1, z1)
+	fp448.Mul(x1, x1, z2)
+	fp448.Mul(z1, z1, x2)
+}
+
+func ladderStepGeneric(w *[5]fp448.Elt, b uint) {
+	x1, x2, z2, x3, z3 := &w[0], &w[1], &w[2], &w[3], &w[4]
+	t0 := &fp448.Elt{}
+	t1 := &fp448.Elt{}
+	fp448.AddSub(x2, z2)
+	fp448.AddSub(x3, z3)
+	fp448.Mul(t0, x2, z3)
+	fp448.Mul(t1, x3, z2)
+	fp448.AddSub(t0, t1)
+	fp448.Cmov(x2, x3, b)
+	fp448.Cmov(z2, z3, b)
+	fp448.Sqr(x3, t0)
+	fp448.Sqr(z3, t1)
+	fp448.Mul(z3, x1, z3)
+	fp448.Sqr(x2, x2)
+	fp448.Sqr(z2, z2)
+	fp448.Sub(t0, x2, z2)
+	mulA24Generic(t1, t0)
+	fp448.Add(t1, t1, z2)
+	fp448.Mul(x2, x2, z2)
+	fp448.Mul(z2, t0, t1)
+}
+
+func mulA24Generic(z, x *fp448.Elt) {
+	const A24 = 39082
+	const n = 8
+	var xx [7]uint64
+	for i := range xx {
+		xx[i] = binary.LittleEndian.Uint64(x[i*n : (i+1)*n])
+	}
+	h0, l0 := bits.Mul64(xx[0], A24)
+	h1, l1 := bits.Mul64(xx[1], A24)
+	h2, l2 := bits.Mul64(xx[2], A24)
+	h3, l3 := bits.Mul64(xx[3], A24)
+	h4, l4 := bits.Mul64(xx[4], A24)
+	h5, l5 := bits.Mul64(xx[5], A24)
+	h6, l6 := bits.Mul64(xx[6], A24)
+
+	l1, c0 := bits.Add64(h0, l1, 0)
+	l2, c1 := bits.Add64(h1, l2, c0)
+	l3, c2 := bits.Add64(h2, l3, c1)
+	l4, c3 := bits.Add64(h3, l4, c2)
+	l5, c4 := bits.Add64(h4, l5, c3)
+	l6, c5 := bits.Add64(h5, l6, c4)
+	l7, _ := bits.Add64(h6, 0, c5)
+
+	l0, c0 = bits.Add64(l0, l7, 0)
+	l1, c1 = bits.Add64(l1, 0, c0)
+	l2, c2 = bits.Add64(l2, 0, c1)
+	l3, c3 = bits.Add64(l3, l7<<32, c2)
+	l4, c4 = bits.Add64(l4, 0, c3)
+	l5, c5 = bits.Add64(l5, 0, c4)
+	l6, l7 = bits.Add64(l6, 0, c5)
+
+	xx[0], c0 = bits.Add64(l0, l7, 0)
+	xx[1], c1 = bits.Add64(l1, 0, c0)
+	xx[2], c2 = bits.Add64(l2, 0, c1)
+	xx[3], c3 = bits.Add64(l3, l7<<32, c2)
+	xx[4], c4 = bits.Add64(l4, 0, c3)
+	xx[5], c5 = bits.Add64(l5, 0, c4)
+	xx[6], _ = bits.Add64(l6, 0, c5)
+
+	for i := range xx {
+		binary.LittleEndian.PutUint64(z[i*n:(i+1)*n], xx[i])
+	}
+}

vendor/github.com/cloudflare/circl/dh/x448/curve_noasm.go

@@ -0,0 +1,11 @@
+//go:build !amd64 || purego
+// +build !amd64 purego
+
+package x448
+
+import fp "github.com/cloudflare/circl/math/fp448"
+
+func double(x, z *fp.Elt)             { doubleGeneric(x, z) }
+func diffAdd(w *[5]fp.Elt, b uint)    { diffAddGeneric(w, b) }
+func ladderStep(w *[5]fp.Elt, b uint) { ladderStepGeneric(w, b) }
+func mulA24(z, x *fp.Elt)             { mulA24Generic(z, x) }

vendor/github.com/cloudflare/circl/dh/x448/doc.go

@@ -0,0 +1,19 @@
+/*
+Package x448 provides Diffie-Hellman functions as specified in RFC-7748.
+
+Validation of public keys.
+
+The Diffie-Hellman function, as described in RFC-7748 [1], works for any
+public key. However, if a different protocol requires contributory
+behaviour [2,3], then the public keys must be validated against low-order
+points [3,4]. To do that, the Shared function performs this validation
+internally and returns false when the public key is invalid (i.e., it
+is a low-order point).
+
+References:
+  - [1] RFC7748 by Langley, Hamburg, Turner (https://rfc-editor.org/rfc/rfc7748.txt)
+  - [2] Curve25519 by Bernstein (https://cr.yp.to/ecdh.html)
+  - [3] Bernstein (https://cr.yp.to/ecdh.html#validate)
+  - [4] Cremers&Jackson (https://eprint.iacr.org/2019/526)
+*/
+package x448

vendor/github.com/cloudflare/circl/dh/x448/key.go

@@ -0,0 +1,46 @@
+package x448
+
+import (
+	"crypto/subtle"
+
+	fp "github.com/cloudflare/circl/math/fp448"
+)
+
+// Size is the length in bytes of a X448 key.
+const Size = 56
+
+// Key represents a X448 key.
+type Key [Size]byte
+
+func (k *Key) clamp(in *Key) *Key {
+	*k = *in
+	k[0] &= 252
+	k[55] |= 128
+	return k
+}
+
+// isValidPubKey verifies if the public key is not a low-order point.
+func (k *Key) isValidPubKey() bool {
+	fp.Modp((*fp.Elt)(k))
+	var isLowOrder int
+	for _, P := range lowOrderPoints {
+		isLowOrder |= subtle.ConstantTimeCompare(P[:], k[:])
+	}
+	return isLowOrder == 0
+}
+
+// KeyGen obtains a public key given a secret key.
+func KeyGen(public, secret *Key) {
+	ladderJoye(public.clamp(secret))
+}
+
+// Shared calculates Alice's shared key from Alice's secret key and Bob's
+// public key returning true on success. A failure case happens when the public
+// key is a low-order point, thus the shared key is all-zeros and the function
+// returns false.
+func Shared(shared, secret, public *Key) bool {
+	validPk := *public
+	ok := validPk.isValidPubKey()
+	ladderMontgomery(shared.clamp(secret), &validPk)
+	return ok
+}

vendor/github.com/cloudflare/circl/dh/x448/table.go

@@ -0,0 +1,460 @@
+package x448
+
+import fp "github.com/cloudflare/circl/math/fp448"
+
+// tableGenerator contains the set of points:
+//
+//	t[i] = (xi+1)/(xi-1),
+//
+// where (xi,yi) = 2^iG and G is the generator point
+// Size = (448)*(448/8) = 25088 bytes.
+var tableGenerator = [448 * fp.Size]byte{
+	/* (2^  0)P */ 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f,
+	/* (2^  1)P */ 0x37, 0xfa, 0xaa, 0x0d, 0x86, 0xa6, 0x24, 0xe9, 0x6c, 0x95, 0x08, 0x34, 0xba, 0x1a, 0x81, 0x3a, 0xae, 0x01, 0xa5, 0xa7, 0x05, 0x85, 0x96, 0x00, 0x06, 0x5a, 0xd7, 0xff, 0xee, 0x8e, 0x8f, 0x94, 0xd2, 0xdc, 0xd7, 0xfc, 0xe7, 0xe5, 0x99, 0x1d, 0x05, 0x46, 0x43, 0xe8, 0xbc, 0x12, 0xb7, 0xeb, 0x30, 0x5e, 0x7a, 0x85, 0x68, 0xed, 0x9d, 0x28,
+	/* (2^  2)P */ 0xf1, 0x7d, 0x08, 0x2b, 0x32, 0x4a, 0x62, 0x80, 0x36, 0xe7, 0xa4, 0x76, 0x5a, 0x2a, 0x1e, 0xf7, 0x9e, 0x3c, 0x40, 0x46, 0x9a, 0x1b, 0x61, 0xc1, 0xbf, 0x1a, 0x1b, 0xae, 0x91, 0x80, 0xa3, 0x76, 0x6c, 0xd4, 0x8f, 0xa4, 0xee, 0x26, 0x39, 0x23, 0xa4, 0x80, 0xf4, 0x66, 0x92, 0xe4, 0xe1, 0x18, 0x76, 0xc5, 0xe2, 0x19, 0x87, 0xd5, 0xc3, 0xe8,
+	/* (2^  3)P */ 0xfb, 0xc9, 0xf0, 0x07, 0xf2, 0x93, 0xd8, 0x50, 0x36, 0xed, 0xfb, 0xbd, 0xb2, 0xd3, 0xfc, 0xdf, 0xd5, 0x2a, 0x6e, 0x26, 0x09, 0xce, 0xd4, 0x07, 0x64, 0x9f, 0x40, 0x74, 0xad, 0x98, 0x2f, 0x1c, 0xb6, 0xdc, 0x2d, 0x42, 0xff, 0xbf, 0x97, 0xd8, 0xdb, 0xef, 0x99, 0xca, 0x73, 0x99, 0x1a, 0x04, 0x3b, 0x56, 0x2c, 0x1f, 0x87, 0x9d, 0x9f, 0x03,
+	/* (2^  4)P */ 0x4c, 0x35, 0x97, 0xf7, 0x81, 0x2c, 0x84, 0xa6, 0xe0, 0xcb, 0xce, 0x37, 0x4c, 0x21, 0x1c, 0x67, 0xfa, 0xab, 0x18, 0x4d, 0xef, 0xd0, 0xf0, 0x44, 0xa9, 0xfb, 0xc0, 0x8e, 0xda, 0x57, 0xa1, 0xd8, 0xeb, 0x87, 0xf4, 0x17, 0xea, 0x66, 0x0f, 0x16, 0xea, 0xcd, 0x5f, 0x3e, 0x88, 0xea, 0x09, 0x68, 0x40, 0xdf, 0x43, 0xcc, 0x54, 0x61, 0x58, 0xaa,
+	/* (2^  5)P */ 0x8d, 0xe7, 0x59, 0xd7, 0x5e, 0x63, 0x37, 0xa7, 0x3f, 0xd1, 0x49, 0x85, 0x01, 0xdd, 0x5e, 0xb3, 0xe6, 0x29, 0xcb, 0x25, 0x93, 0xdd, 0x08, 0x96, 0x83, 0x52, 0x76, 0x85, 0xf5, 0x5d, 0x02, 0xbf, 0xe9, 0x6d, 0x15, 0x27, 0xc1, 0x09, 0xd1, 0x14, 0x4d, 0x6e, 0xe8, 0xaf, 0x59, 0x58, 0x34, 0x9d, 0x2a, 0x99, 0x85, 0x26, 0xbe, 0x4b, 0x1e, 0xb9,
+	/* (2^  6)P */ 0x8d, 0xce, 0x94, 0xe2, 0x18, 0x56, 0x0d, 0x82, 0x8e, 0xdf, 0x85, 0x01, 0x8f, 0x93, 0x3c, 0xc6, 0xbd, 0x61, 0xfb, 0xf4, 0x22, 0xc5, 0x16, 0x87, 0xd1, 0xb1, 0x9e, 0x09, 0xc5, 0x83, 0x2e, 0x4a, 0x07, 0x88, 0xee, 0xe0, 0x29, 0x8d, 0x2e, 0x1f, 0x88, 0xad, 0xfd, 0x18, 0x93, 0xb7, 0xed, 0x42, 0x86, 0x78, 0xf0, 0xb8, 0x70, 0xbe, 0x01, 0x67,
+	/* (2^  7)P */ 0xdf, 0x62, 0x2d, 0x94, 0xc7, 0x35, 0x23, 0xda, 0x27, 0xbb, 0x2b, 0xdb, 0x30, 0x80, 0x68, 0x16, 0xa3, 0xae, 0xd7, 0xd2, 0xa7, 0x7c, 0xbf, 0x6a, 0x1d, 0x83, 0xde, 0x96, 0x0a, 0x43, 0xb6, 0x30, 0x37, 0xd6, 0xee, 0x63, 0x59, 0x9a, 0xbf, 0xa3, 0x30, 0x6c, 0xaf, 0x0c, 0xee, 0x3d, 0xcb, 0x35, 0x4b, 0x55, 0x5f, 0x84, 0x85, 0xcb, 0x4f, 0x1e,
+	/* (2^  8)P */ 0x9d, 0x04, 0x68, 0x89, 0xa4, 0xa9, 0x0d, 0x87, 0xc1, 0x70, 0xf1, 0xeb, 0xfb, 0x47, 0x0a, 0xf0, 0xde, 0x67, 0xb7, 0x94, 0xcd, 0x36, 0x43, 0xa5, 0x49, 0x43, 0x67, 0xc3, 0xee, 0x3c, 0x6b, 0xec, 0xd0, 0x1a, 0xf4, 0xad, 0xef, 0x06, 0x4a, 0xe8, 0x46, 0x24, 0xd7, 0x93, 0xbf, 0xf0, 0xe3, 0x81, 0x61, 0xec, 0xea, 0x64, 0xfe, 0x67, 0xeb, 0xc7,
+	/* (2^  9)P */ 0x95, 0x45, 0x79, 0xcf, 0x2c, 0xfd, 0x9b, 0xfe, 0x84, 0x46, 0x4b, 0x8f, 0xa1, 0xcf, 0xc3, 0x04, 0x94, 0x78, 0xdb, 0xc9, 0xa6, 0x01, 0x75, 0xa4, 0xb4, 0x93, 0x72, 0x43, 0xa7, 0x7d, 0xda, 0x31, 0x38, 0x54, 0xab, 0x4e, 0x3f, 0x89, 0xa6, 0xab, 0x57, 0xc0, 0x16, 0x65, 0xdb, 0x92, 0x96, 0xe4, 0xc8, 0xae, 0xe7, 0x4c, 0x7a, 0xeb, 0xbb, 0x5a,
+	/* (2^ 10)P */ 0xbe, 0xfe, 0x86, 0xc3, 0x97, 0xe0, 0x6a, 0x18, 0x20, 0x21, 0xca, 0x22, 0x55, 0xa1, 0xeb, 0xf5, 0x74, 0xe5, 0xc9, 0x59, 0xa7, 0x92, 0x65, 0x15, 0x08, 0x71, 0xd1, 0x09, 0x7e, 0x83, 0xfc, 0xbc, 0x5a, 0x93, 0x38, 0x0d, 0x43, 0x42, 0xfd, 0x76, 0x30, 0xe8, 0x63, 0x60, 0x09, 0x8d, 0x6c, 0xd3, 0xf8, 0x56, 0x3d, 0x68, 0x47, 0xab, 0xa0, 0x1d,
+	/* (2^ 11)P */ 0x38, 0x50, 0x1c, 0xb1, 0xac, 0x88, 0x8f, 0x38, 0xe3, 0x69, 0xe6, 0xfc, 0x4f, 0x8f, 0xe1, 0x9b, 0xb1, 0x1a, 0x09, 0x39, 0x19, 0xdf, 0xcd, 0x98, 0x7b, 0x64, 0x42, 0xf6, 0x11, 0xea, 0xc7, 0xe8, 0x92, 0x65, 0x00, 0x2c, 0x75, 0xb5, 0x94, 0x1e, 0x5b, 0xa6, 0x66, 0x81, 0x77, 0xf3, 0x39, 0x94, 0xac, 0xbd, 0xe4, 0x2a, 0x66, 0x84, 0x9c, 0x60,
+	/* (2^ 12)P */ 0xb5, 0xb6, 0xd9, 0x03, 0x67, 0xa4, 0xa8, 0x0a, 0x4a, 0x2b, 0x9d, 0xfa, 0x13, 0xe1, 0x99, 0x25, 0x4a, 0x5c, 0x67, 0xb9, 0xb2, 0xb7, 0xdd, 0x1e, 0xaf, 0xeb, 0x63, 0x41, 0xb6, 0xb9, 0xa0, 0x87, 0x0a, 0xe0, 0x06, 0x07, 0xaa, 0x97, 0xf8, 0xf9, 0x38, 0x4f, 0xdf, 0x0c, 0x40, 0x7c, 0xc3, 0x98, 0xa9, 0x74, 0xf1, 0x5d, 0xda, 0xd1, 0xc0, 0x0a,
+	/* (2^ 13)P */ 0xf2, 0x0a, 0xab, 0xab, 0x94, 0x50, 0xf0, 0xa3, 0x6f, 0xc6, 0x66, 0xba, 0xa6, 0xdc, 0x44, 0xdd, 0xd6, 0x08, 0xf4, 0xd3, 0xed, 0xb1, 0x40, 0x93, 0xee, 0xf6, 0xb8, 0x8e, 0xb4, 0x7c, 0xb9, 0x82, 0xc9, 0x9d, 0x45, 0x3b, 0x8e, 0x10, 0xcb, 0x70, 0x1e, 0xba, 0x3c, 0x62, 0x50, 0xda, 0xa9, 0x93, 0xb5, 0xd7, 0xd0, 0x6f, 0x29, 0x52, 0x95, 0xae,
+	/* (2^ 14)P */ 0x14, 0x68, 0x69, 0x23, 0xa8, 0x44, 0x87, 0x9e, 0x22, 0x91, 0xe8, 0x92, 0xdf, 0xf7, 0xae, 0xba, 0x1c, 0x96, 0xe1, 0xc3, 0x94, 0xed, 0x6c, 0x95, 0xae, 0x96, 0xa7, 0x15, 0x9f, 0xf1, 0x17, 0x11, 0x92, 0x42, 0xd5, 0xcd, 0x18, 0xe7, 0xa9, 0xb5, 0x2f, 0xcd, 0xde, 0x6c, 0xc9, 0x7d, 0xfc, 0x7e, 0xbd, 0x7f, 0x10, 0x3d, 0x01, 0x00, 0x8d, 0x95,
+	/* (2^ 15)P */ 0x3b, 0x76, 0x72, 0xae, 0xaf, 0x84, 0xf2, 0xf7, 0xd1, 0x6d, 0x13, 0x9c, 0x47, 0xe1, 0xb7, 0xa3, 0x19, 0x16, 0xee, 0x75, 0x45, 0xf6, 0x1a, 0x7b, 0x78, 0x49, 0x79, 0x05, 0x86, 0xf0, 0x7f, 0x9f, 0xfc, 0xc4, 0xbd, 0x86, 0xf3, 0x41, 0xa7, 0xfe, 0x01, 0xd5, 0x67, 0x16, 0x10, 0x5b, 0xa5, 0x16, 0xf3, 0x7f, 0x60, 0xce, 0xd2, 0x0c, 0x8e, 0x4b,
+	/* (2^ 16)P */ 0x4a, 0x07, 0x99, 0x4a, 0x0f, 0x74, 0x91, 0x14, 0x68, 0xb9, 0x48, 0xb7, 0x44, 0x77, 0x9b, 0x4a, 0xe0, 0x68, 0x0e, 0x43, 0x4d, 0x98, 0x98, 0xbf, 0xa8, 0x3a, 0xb7, 0x6d, 0x2a, 0x9a, 0x77, 0x5f, 0x62, 0xf5, 0x6b, 0x4a, 0xb7, 0x7d, 0xe5, 0x09, 0x6b, 0xc0, 0x8b, 0x9c, 0x88, 0x37, 0x33, 0xf2, 0x41, 0xac, 0x22, 0x1f, 0xcf, 0x3b, 0x82, 0x34,
+	/* (2^ 17)P */ 0x00, 0xc3, 0x78, 0x42, 0x32, 0x2e, 0xdc, 0xda, 0xb1, 0x96, 0x21, 0xa4, 0xe4, 0xbb, 0xe9, 0x9d, 0xbb, 0x0f, 0x93, 0xed, 0x26, 0x3d, 0xb5, 0xdb, 0x94, 0x31, 0x37, 0x07, 0xa2, 0xb2, 0xd5, 0x99, 0x0d, 0x93, 0xe1, 0xce, 0x3f, 0x0b, 0x96, 0x82, 0x47, 0xfe, 0x60, 0x6f, 0x8f, 0x61, 0x88, 0xd7, 0x05, 0x95, 0x0b, 0x46, 0x06, 0xb7, 0x32, 0x06,
+	/* (2^ 18)P */ 0x44, 0xf5, 0x34, 0xdf, 0x2f, 0x9c, 0x5d, 0x9f, 0x53, 0x5c, 0x42, 0x8f, 0xc9, 0xdc, 0xd8, 0x40, 0xa2, 0xe7, 0x6a, 0x4a, 0x05, 0xf7, 0x86, 0x77, 0x2b, 0xae, 0x37, 0xed, 0x48, 0xfb, 0xf7, 0x62, 0x7c, 0x17, 0x59, 0x92, 0x41, 0x61, 0x93, 0x38, 0x30, 0xd1, 0xef, 0x54, 0x54, 0x03, 0x17, 0x57, 0x91, 0x15, 0x11, 0x33, 0xb5, 0xfa, 0xfb, 0x17,
+	/* (2^ 19)P */ 0x29, 0xbb, 0xd4, 0xb4, 0x9c, 0xf1, 0x72, 0x94, 0xce, 0x6a, 0x29, 0xa8, 0x89, 0x18, 0x19, 0xf7, 0xb7, 0xcc, 0xee, 0x9a, 0x02, 0xe3, 0xc0, 0xb1, 0xe0, 0xee, 0x83, 0x78, 0xb4, 0x9e, 0x07, 0x87, 0xdf, 0xb0, 0x82, 0x26, 0x4e, 0xa4, 0x0c, 0x33, 0xaf, 0x40, 0x59, 0xb6, 0xdd, 0x52, 0x45, 0xf0, 0xb4, 0xf6, 0xe8, 0x4e, 0x4e, 0x79, 0x1a, 0x5d,
+	/* (2^ 20)P */ 0x27, 0x33, 0x4d, 0x4c, 0x6b, 0x4f, 0x75, 0xb1, 0xbc, 0x1f, 0xab, 0x5b, 0x2b, 0xf0, 0x1c, 0x57, 0x86, 0xdd, 0xfd, 0x60, 0xb0, 0x8c, 0xe7, 0x9a, 0xe5, 0x5c, 0xeb, 0x11, 0x3a, 0xda, 0x22, 0x25, 0x99, 0x06, 0x8d, 0xf4, 0xaf, 0x29, 0x7a, 0xc9, 0xe5, 0xd2, 0x16, 0x9e, 0xd4, 0x63, 0x1d, 0x64, 0xa6, 0x47, 0x96, 0x37, 0x6f, 0x93, 0x2c, 0xcc,
+	/* (2^ 21)P */ 0xc1, 0x94, 0x74, 0x86, 0x75, 0xf2, 0x91, 0x58, 0x23, 0x85, 0x63, 0x76, 0x54, 0xc7, 0xb4, 0x8c, 0xbc, 0x4e, 0xc4, 0xa7, 0xba, 0xa0, 0x55, 0x26, 0x71, 0xd5, 0x33, 0x72, 0xc9, 0xad, 0x1e, 0xf9, 0x5d, 0x78, 0x70, 0x93, 0x4e, 0x85, 0xfc, 0x39, 0x06, 0x73, 0x76, 0xff, 0xe8, 0x64, 0x69, 0x42, 0x45, 0xb2, 0x69, 0xb5, 0x32, 0xe7, 0x2c, 0xde,
+	/* (2^ 22)P */ 0xde, 0x16, 0xd8, 0x33, 0x49, 0x32, 0xe9, 0x0e, 0x3a, 0x60, 0xee, 0x2e, 0x24, 0x75, 0xe3, 0x9c, 0x92, 0x07, 0xdb, 0xad, 0x92, 0xf5, 0x11, 0xdf, 0xdb, 0xb0, 0x17, 0x5c, 0xd6, 0x1a, 0x70, 0x00, 0xb7, 0xe2, 0x18, 0xec, 0xdc, 0xc2, 0x02, 0x93, 0xb3, 0xc8, 0x3f, 0x4f, 0x1b, 0x96, 0xe6, 0x33, 0x8c, 0xfb, 0xcc, 0xa5, 0x4e, 0xe8, 0xe7, 0x11,
+	/* (2^ 23)P */ 0x05, 0x7a, 0x74, 0x52, 0xf8, 0xdf, 0x0d, 0x7c, 0x6a, 0x1a, 0x4e, 0x9a, 0x02, 0x1d, 0xae, 0x77, 0xf8, 0x8e, 0xf9, 0xa2, 0x38, 0x54, 0x50, 0xb2, 0x2c, 0x08, 0x9d, 0x9b, 0x9f, 0xfb, 0x2b, 0x06, 0xde, 0x9d, 0xc2, 0x03, 0x0b, 0x22, 0x2b, 0x10, 0x5b, 0x3a, 0x73, 0x29, 0x8e, 0x3e, 0x37, 0x08, 0x2c, 0x3b, 0xf8, 0x80, 0xc1, 0x66, 0x1e, 0x98,
+	/* (2^ 24)P */ 0xd8, 0xd6, 0x3e, 0xcd, 0x63, 0x8c, 0x2b, 0x41, 0x81, 0xc0, 0x0c, 0x06, 0x87, 0xd6, 0xe7, 0x92, 0xfe, 0xf1, 0x0c, 0x4a, 0x84, 0x5b, 0xaf, 0x40, 0x53, 0x6f, 0x60, 0xd6, 0x6b, 0x76, 0x4b, 0xc2, 0xad, 0xc9, 0xb6, 0xb6, 0x6a, 0xa2, 0xb3, 0xf5, 0xf5, 0xc2, 0x55, 0x83, 0xb2, 0xd3, 0xe9, 0x41, 0x6c, 0x63, 0x51, 0xb8, 0x81, 0x74, 0xc8, 0x2c,
+	/* (2^ 25)P */ 0xb2, 0xaf, 0x1c, 0xee, 0x07, 0xb0, 0x58, 0xa8, 0x2c, 0x6a, 0xc9, 0x2d, 0x62, 0x28, 0x75, 0x0c, 0x40, 0xb6, 0x11, 0x33, 0x96, 0x80, 0x28, 0x6d, 0xd5, 0x9e, 0x87, 0x90, 0x01, 0x66, 0x1d, 0x1c, 0xf8, 0xb4, 0x92, 0xac, 0x38, 0x18, 0x05, 0xc2, 0x4c, 0x4b, 0x54, 0x7d, 0x80, 0x46, 0x87, 0x2d, 0x99, 0x8e, 0x70, 0x80, 0x69, 0x71, 0x8b, 0xed,
+	/* (2^ 26)P */ 0x37, 0xa7, 0x6b, 0x71, 0x36, 0x75, 0x8e, 0xff, 0x0f, 0x42, 0xda, 0x5a, 0x46, 0xa6, 0x97, 0x79, 0x7e, 0x30, 0xb3, 0x8f, 0xc7, 0x3a, 0xa0, 0xcb, 0x1d, 0x9c, 0x78, 0x77, 0x36, 0xc2, 0xe7, 0xf4, 0x2f, 0x29, 0x07, 0xb1, 0x07, 0xfd, 0xed, 0x1b, 0x39, 0x77, 0x06, 0x38, 0x77, 0x0f, 0x50, 0x31, 0x12, 0xbf, 0x92, 0xbf, 0x72, 0x79, 0x54, 0xa9,
+	/* (2^ 27)P */ 0xbd, 0x4d, 0x46, 0x6b, 0x1a, 0x80, 0x46, 0x2d, 0xed, 0xfd, 0x64, 0x6d, 0x94, 0xbc, 0x4a, 0x6e, 0x0c, 0x12, 0xf6, 0x12, 0xab, 0x54, 0x88, 0xd3, 0x85, 0xac, 0x51, 0xae, 0x6f, 0xca, 0xc4, 0xb7, 0xec, 0x22, 0x54, 0x6d, 0x80, 0xb2, 0x1c, 0x63, 0x33, 0x76, 0x6b, 0x8e, 0x6d, 0x59, 0xcd, 0x73, 0x92, 0x5f, 0xff, 0xad, 0x10, 0x35, 0x70, 0x5f,
+	/* (2^ 28)P */ 0xb3, 0x84, 0xde, 0xc8, 0x04, 0x43, 0x63, 0xfa, 0x29, 0xd9, 0xf0, 0x69, 0x65, 0x5a, 0x0c, 0xe8, 0x2e, 0x0b, 0xfe, 0xb0, 0x7a, 0x42, 0xb3, 0xc3, 0xfc, 0xe6, 0xb8, 0x92, 0x29, 0xae, 0xed, 0xec, 0xd5, 0xe8, 0x4a, 0xa1, 0xbd, 0x3b, 0xd3, 0xc0, 0x07, 0xab, 0x65, 0x65, 0x35, 0x9a, 0xa6, 0x5e, 0x78, 0x18, 0x76, 0x1c, 0x15, 0x49, 0xe6, 0x75,
+	/* (2^ 29)P */ 0x45, 0xb3, 0x92, 0xa9, 0xc3, 0xb8, 0x11, 0x68, 0x64, 0x3a, 0x83, 0x5d, 0xa8, 0x94, 0x6a, 0x9d, 0xaa, 0x27, 0x9f, 0x98, 0x5d, 0xc0, 0x29, 0xf0, 0xc0, 0x4b, 0x14, 0x3c, 0x05, 0xe7, 0xf8, 0xbd, 0x38, 0x22, 0x96, 0x75, 0x65, 0x5e, 0x0d, 0x3f, 0xbb, 0x6f, 0xe8, 0x3f, 0x96, 0x76, 0x9f, 0xba, 0xd9, 0x44, 0x92, 0x96, 0x22, 0xe7, 0x52, 0xe7,
+	/* (2^ 30)P */ 0xf4, 0xa3, 0x95, 0x90, 0x47, 0xdf, 0x7d, 0xdc, 0xf4, 0x13, 0x87, 0x67, 0x7d, 0x4f, 0x9d, 0xa0, 0x00, 0x46, 0x72, 0x08, 0xc3, 0xa2, 0x7a, 0x3e, 0xe7, 0x6d, 0x52, 0x7c, 0x11, 0x36, 0x50, 0x83, 0x89, 0x64, 0xcb, 0x1f, 0x08, 0x83, 0x46, 0xcb, 0xac, 0xa6, 0xd8, 0x9c, 0x1b, 0xe8, 0x05, 0x47, 0xc7, 0x26, 0x06, 0x83, 0x39, 0xe9, 0xb1, 0x1c,
+	/* (2^ 31)P */ 0x11, 0xe8, 0xc8, 0x42, 0xbf, 0x30, 0x9c, 0xa3, 0xf1, 0x85, 0x96, 0x95, 0x4f, 0x4f, 0x52, 0xa2, 0xf5, 0x8b, 0x68, 0x24, 0x16, 0xac, 0x9b, 0xa9, 0x27, 0x28, 0x0e, 0x84, 0x03, 0x46, 0x22, 0x5f, 0xf7, 0x0d, 0xa6, 0x85, 0x88, 0xc1, 0x45, 0x4b, 0x85, 0x1a, 0x10, 0x7f, 0xc9, 0x94, 0x20, 0xb0, 0x04, 0x28, 0x12, 0x30, 0xb9, 0xe6, 0x40, 0x6b,
+	/* (2^ 32)P */ 0xac, 0x1b, 0x57, 0xb6, 0x42, 0xdb, 0x81, 0x8d, 0x76, 0xfd, 0x9b, 0x1c, 0x29, 0x30, 0xd5, 0x3a, 0xcc, 0x53, 0xd9, 0x26, 0x7a, 0x0f, 0x9c, 0x2e, 0x79, 0xf5, 0x62, 0xeb, 0x61, 0x9d, 0x9b, 0x80, 0x39, 0xcd, 0x60, 0x2e, 0x1f, 0x08, 0x22, 0xbc, 0x19, 0xb3, 0x2a, 0x43, 0x44, 0xf2, 0x4e, 0x66, 0xf4, 0x36, 0xa6, 0xa7, 0xbc, 0xa4, 0x15, 0x7e,
+	/* (2^ 33)P */ 0xc1, 0x90, 0x8a, 0xde, 0xff, 0x78, 0xc3, 0x73, 0x16, 0xee, 0x76, 0xa0, 0x84, 0x60, 0x8d, 0xe6, 0x82, 0x0f, 0xde, 0x4e, 0xc5, 0x99, 0x34, 0x06, 0x90, 0x44, 0x55, 0xf8, 0x91, 0xd8, 0xe1, 0xe4, 0x2c, 0x8a, 0xde, 0x94, 0x1e, 0x78, 0x25, 0x3d, 0xfd, 0xd8, 0x59, 0x7d, 0xaf, 0x6e, 0xbe, 0x96, 0xbe, 0x3c, 0x16, 0x23, 0x0f, 0x4c, 0xa4, 0x28,
+	/* (2^ 34)P */ 0xba, 0x11, 0x35, 0x57, 0x03, 0xb6, 0xf4, 0x24, 0x89, 0xb8, 0x5a, 0x0d, 0x50, 0x9c, 0xaa, 0x51, 0x7f, 0xa4, 0x0e, 0xfc, 0x71, 0xb3, 0x3b, 0xf1, 0x96, 0x50, 0x23, 0x15, 0xf5, 0xf5, 0xd4, 0x23, 0xdc, 0x8b, 0x26, 0x9e, 0xae, 0xb7, 0x50, 0xcd, 0xc4, 0x25, 0xf6, 0x75, 0x40, 0x9c, 0x37, 0x79, 0x33, 0x60, 0xd4, 0x4b, 0x13, 0x32, 0xee, 0xe2,
+	/* (2^ 35)P */ 0x43, 0xb8, 0x56, 0x59, 0xf0, 0x68, 0x23, 0xb3, 0xea, 0x70, 0x58, 0x4c, 0x1e, 0x5a, 0x16, 0x54, 0x03, 0xb2, 0xf4, 0x73, 0xb6, 0xd9, 0x5c, 0x9c, 0x6f, 0xcf, 0x82, 0x2e, 0x54, 0x15, 0x46, 0x2c, 0xa3, 0xda, 0x4e, 0x87, 0xf5, 0x2b, 0xba, 0x91, 0xa3, 0xa0, 0x89, 0xba, 0x48, 0x2b, 0xfa, 0x64, 0x02, 0x7f, 0x78, 0x03, 0xd1, 0xe8, 0x3b, 0xe9,
+	/* (2^ 36)P */ 0x15, 0xa4, 0x71, 0xd4, 0x0c, 0x24, 0xe9, 0x07, 0xa1, 0x43, 0xf4, 0x7f, 0xbb, 0xa2, 0xa6, 0x6b, 0xfa, 0xb7, 0xea, 0x58, 0xd1, 0x96, 0xb0, 0x24, 0x5c, 0xc7, 0x37, 0x4e, 0x60, 0x0f, 0x40, 0xf2, 0x2f, 0x44, 0x70, 0xea, 0x80, 0x63, 0xfe, 0xfc, 0x46, 0x59, 0x12, 0x27, 0xb5, 0x27, 0xfd, 0xb7, 0x73, 0x0b, 0xca, 0x8b, 0xc2, 0xd3, 0x71, 0x08,
+	/* (2^ 37)P */ 0x26, 0x0e, 0xd7, 0x52, 0x6f, 0xf1, 0xf2, 0x9d, 0xb8, 0x3d, 0xbd, 0xd4, 0x75, 0x97, 0xd8, 0xbf, 0xa8, 0x86, 0x96, 0xa5, 0x80, 0xa0, 0x45, 0x75, 0xf6, 0x77, 0x71, 0xdb, 0x77, 0x96, 0x55, 0x99, 0x31, 0xd0, 0x4f, 0x34, 0xf4, 0x35, 0x39, 0x41, 0xd3, 0x7d, 0xf7, 0xe2, 0x74, 0xde, 0xbe, 0x5b, 0x1f, 0x39, 0x10, 0x21, 0xa3, 0x4d, 0x3b, 0xc8,
+	/* (2^ 38)P */ 0x04, 0x00, 0x2a, 0x45, 0xb2, 0xaf, 0x9b, 0x18, 0x6a, 0xeb, 0x96, 0x28, 0xa4, 0x77, 0xd0, 0x13, 0xcf, 0x17, 0x65, 0xe8, 0xc5, 0x81, 0x28, 0xad, 0x39, 0x7a, 0x0b, 0xaa, 0x55, 0x2b, 0xf3, 0xfc, 0x86, 0x40, 0xad, 0x0d, 0x1e, 0x28, 0xa2, 0x2d, 0xc5, 0xd6, 0x04, 0x15, 0xa2, 0x30, 0x3d, 0x12, 0x8e, 0xd6, 0xb5, 0xf7, 0x69, 0xbb, 0x84, 0x20,
+	/* (2^ 39)P */ 0xd7, 0x7a, 0x77, 0x2c, 0xfb, 0x81, 0x80, 0xe9, 0x1e, 0xc6, 0x36, 0x31, 0x79, 0xc3, 0x7c, 0xa9, 0x57, 0x6b, 0xb5, 0x70, 0xfb, 0xe4, 0xa1, 0xff, 0xfd, 0x21, 0xa5, 0x7c, 0xfa, 0x44, 0xba, 0x0d, 0x96, 0x3d, 0xc4, 0x5c, 0x39, 0x52, 0x87, 0xd7, 0x22, 0x0f, 0x52, 0x88, 0x91, 0x87, 0x96, 0xac, 0xfa, 0x3b, 0xdf, 0xdc, 0x83, 0x8c, 0x99, 0x29,
+	/* (2^ 40)P */ 0x98, 0x6b, 0x3a, 0x8d, 0x83, 0x17, 0xe1, 0x62, 0xd8, 0x80, 0x4c, 0x97, 0xce, 0x6b, 0xaa, 0x10, 0xa7, 0xc4, 0xe9, 0xeb, 0xa5, 0xfb, 0xc9, 0xdd, 0x2d, 0xeb, 0xfc, 0x9a, 0x71, 0xcd, 0x68, 0x6e, 0xc0, 0x35, 0x64, 0x62, 0x1b, 0x95, 0x12, 0xe8, 0x53, 0xec, 0xf0, 0xf4, 0x86, 0x86, 0x78, 0x18, 0xc4, 0xc6, 0xbc, 0x5a, 0x59, 0x8f, 0x7c, 0x7e,
+	/* (2^ 41)P */ 0x7f, 0xd7, 0x1e, 0xc5, 0x83, 0xdc, 0x1f, 0xbe, 0x0b, 0xcf, 0x2e, 0x01, 0x01, 0xed, 0xac, 0x17, 0x3b, 0xed, 0xa4, 0x30, 0x96, 0x0e, 0x14, 0x7e, 0x19, 0x2b, 0xa5, 0x67, 0x1e, 0xb3, 0x34, 0x03, 0xa8, 0xbb, 0x0a, 0x7d, 0x08, 0x2d, 0xd5, 0x53, 0x19, 0x6f, 0x13, 0xd5, 0xc0, 0x90, 0x8a, 0xcc, 0xc9, 0x5c, 0xab, 0x24, 0xd7, 0x03, 0xf6, 0x57,
+	/* (2^ 42)P */ 0x49, 0xcb, 0xb4, 0x96, 0x5f, 0xa6, 0xf8, 0x71, 0x6f, 0x59, 0xad, 0x05, 0x24, 0x2d, 0xaf, 0x67, 0xa8, 0xbe, 0x95, 0xdf, 0x0d, 0x28, 0x5a, 0x7f, 0x6e, 0x87, 0x8c, 0x6e, 0x67, 0x0c, 0xf4, 0xe0, 0x1c, 0x30, 0xc2, 0x66, 0xae, 0x20, 0xa1, 0x34, 0xec, 0x9c, 0xbc, 0xae, 0x3d, 0xa1, 0x28, 0x28, 0x95, 0x1d, 0xc9, 0x3a, 0xa8, 0xfd, 0xfc, 0xa1,
+	/* (2^ 43)P */ 0xe2, 0x2b, 0x9d, 0xed, 0x02, 0x99, 0x67, 0xbb, 0x2e, 0x16, 0x62, 0x05, 0x70, 0xc7, 0x27, 0xb9, 0x1c, 0x3f, 0xf2, 0x11, 0x01, 0xd8, 0x51, 0xa4, 0x18, 0x92, 0xa9, 0x5d, 0xfb, 0xa9, 0xe4, 0x42, 0xba, 0x38, 0x34, 0x1a, 0x4a, 0xc5, 0x6a, 0x37, 0xde, 0xa7, 0x0c, 0xb4, 0x7e, 0x7f, 0xde, 0xa6, 0xee, 0xcd, 0x55, 0x57, 0x05, 0x06, 0xfd, 0x5d,
+	/* (2^ 44)P */ 0x2f, 0x32, 0xcf, 0x2e, 0x2c, 0x7b, 0xbe, 0x9a, 0x0c, 0x57, 0x35, 0xf8, 0x87, 0xda, 0x9c, 0xec, 0x48, 0xf2, 0xbb, 0xe2, 0xda, 0x10, 0x58, 0x20, 0xc6, 0xd3, 0x87, 0xe9, 0xc7, 0x26, 0xd1, 0x9a, 0x46, 0x87, 0x90, 0xda, 0xdc, 0xde, 0xc3, 0xb3, 0xf2, 0xe8, 0x6f, 0x4a, 0xe6, 0xe8, 0x9d, 0x98, 0x36, 0x20, 0x03, 0x47, 0x15, 0x3f, 0x64, 0x59,
+	/* (2^ 45)P */ 0xd4, 0x71, 0x49, 0x0a, 0x67, 0x97, 0xaa, 0x3f, 0xf4, 0x1b, 0x3a, 0x6e, 0x5e, 0x17, 0xcc, 0x0a, 0x8f, 0x81, 0x6a, 0x41, 0x38, 0x77, 0x40, 0x8a, 0x11, 0x42, 0x62, 0xd2, 0x50, 0x32, 0x79, 0x78, 0x28, 0xc2, 0x2e, 0x10, 0x01, 0x94, 0x30, 0x4f, 0x7f, 0x18, 0x17, 0x56, 0x85, 0x4e, 0xad, 0xf7, 0xcb, 0x87, 0x3c, 0x3f, 0x50, 0x2c, 0xc0, 0xba,
+	/* (2^ 46)P */ 0xbc, 0x30, 0x8e, 0x65, 0x8e, 0x57, 0x5b, 0x38, 0x7a, 0xd4, 0x95, 0x52, 0x7a, 0x32, 0x59, 0x69, 0xcd, 0x9d, 0x47, 0x34, 0x5b, 0x55, 0xa5, 0x24, 0x60, 0xdd, 0xc0, 0xc1, 0x62, 0x73, 0x44, 0xae, 0x4c, 0x9c, 0x65, 0x55, 0x1b, 0x9d, 0x8a, 0x29, 0xb0, 0x1a, 0x52, 0xa8, 0xf1, 0xe6, 0x9a, 0xb3, 0xf6, 0xa3, 0xc9, 0x0a, 0x70, 0x7d, 0x0f, 0xee,
+	/* (2^ 47)P */ 0x77, 0xd3, 0xe5, 0x8e, 0xfa, 0x00, 0xeb, 0x1b, 0x7f, 0xdc, 0x68, 0x3f, 0x92, 0xbd, 0xb7, 0x0b, 0xb7, 0xb5, 0x24, 0xdf, 0xc5, 0x67, 0x53, 0xd4, 0x36, 0x79, 0xc4, 0x7b, 0x57, 0xbc, 0x99, 0x97, 0x60, 0xef, 0xe4, 0x01, 0xa1, 0xa7, 0xaa, 0x12, 0x36, 0x29, 0xb1, 0x03, 0xc2, 0x83, 0x1c, 0x2b, 0x83, 0xef, 0x2e, 0x2c, 0x23, 0x92, 0xfd, 0xd1,
+	/* (2^ 48)P */ 0x94, 0xef, 0x03, 0x59, 0xfa, 0x8a, 0x18, 0x76, 0xee, 0x58, 0x08, 0x4d, 0x44, 0xce, 0xf1, 0x52, 0x33, 0x49, 0xf6, 0x69, 0x71, 0xe3, 0xa9, 0xbc, 0x86, 0xe3, 0x43, 0xde, 0x33, 0x7b, 0x90, 0x8b, 0x3e, 0x7d, 0xd5, 0x4a, 0xf0, 0x23, 0x99, 0xa6, 0xea, 0x5f, 0x08, 0xe5, 0xb9, 0x49, 0x8b, 0x0d, 0x6a, 0x21, 0xab, 0x07, 0x62, 0xcd, 0xc4, 0xbe,
+	/* (2^ 49)P */ 0x61, 0xbf, 0x70, 0x14, 0xfa, 0x4e, 0x9e, 0x7c, 0x0c, 0xf8, 0xb2, 0x48, 0x71, 0x62, 0x83, 0xd6, 0xd1, 0xdc, 0x9c, 0x29, 0x66, 0xb1, 0x34, 0x9c, 0x8d, 0xe6, 0x88, 0xaf, 0xbe, 0xdc, 0x4d, 0xeb, 0xb0, 0xe7, 0x28, 0xae, 0xb2, 0x05, 0x56, 0xc6, 0x0e, 0x10, 0x26, 0xab, 0x2c, 0x59, 0x72, 0x03, 0x66, 0xfe, 0x8f, 0x2c, 0x51, 0x2d, 0xdc, 0xae,
+	/* (2^ 50)P */ 0xdc, 0x63, 0xf1, 0x8b, 0x5c, 0x65, 0x0b, 0xf1, 0xa6, 0x22, 0xe2, 0xd9, 0xdb, 0x49, 0xb1, 0x3c, 0x47, 0xc2, 0xfe, 0xac, 0x86, 0x07, 0x52, 0xec, 0xb0, 0x08, 0x69, 0xfb, 0xd1, 0x06, 0xdc, 0x48, 0x5c, 0x3d, 0xb2, 0x4d, 0xb8, 0x1a, 0x4e, 0xda, 0xb9, 0xc1, 0x2b, 0xab, 0x4b, 0x62, 0x81, 0x21, 0x9a, 0xfc, 0x3d, 0x39, 0x83, 0x11, 0x36, 0xeb,
+	/* (2^ 51)P */ 0x94, 0xf3, 0x17, 0xef, 0xf9, 0x60, 0x54, 0xc3, 0xd7, 0x27, 0x35, 0xc5, 0x98, 0x5e, 0xf6, 0x63, 0x6c, 0xa0, 0x4a, 0xd3, 0xa3, 0x98, 0xd9, 0x42, 0xe3, 0xf1, 0xf8, 0x81, 0x96, 0xa9, 0xea, 0x6d, 0x4b, 0x8e, 0x33, 0xca, 0x94, 0x0d, 0xa0, 0xf7, 0xbb, 0x64, 0xa3, 0x36, 0x6f, 0xdc, 0x5a, 0x94, 0x42, 0xca, 0x06, 0xb2, 0x2b, 0x9a, 0x9f, 0x71,
+	/* (2^ 52)P */ 0xec, 0xdb, 0xa6, 0x1f, 0xdf, 0x15, 0x36, 0xa3, 0xda, 0x8a, 0x7a, 0xb6, 0xa7, 0xe3, 0xaf, 0x52, 0xe0, 0x8d, 0xe8, 0xf2, 0x44, 0x20, 0xeb, 0xa1, 0x20, 0xc4, 0x65, 0x3c, 0x7c, 0x6c, 0x49, 0xed, 0x2f, 0x66, 0x23, 0x68, 0x61, 0x91, 0x40, 0x9f, 0x50, 0x19, 0xd1, 0x84, 0xa7, 0xe2, 0xed, 0x34, 0x37, 0xe3, 0xe4, 0x11, 0x7f, 0x87, 0x55, 0x0f,
+	/* (2^ 53)P */ 0xb3, 0xa1, 0x0f, 0xb0, 0x48, 0xc0, 0x4d, 0x96, 0xa7, 0xcf, 0x5a, 0x81, 0xb8, 0x4a, 0x46, 0xef, 0x0a, 0xd3, 0x40, 0x7e, 0x02, 0xe3, 0x63, 0xaa, 0x50, 0xd1, 0x2a, 0x37, 0x22, 0x4a, 0x7f, 0x4f, 0xb6, 0xf9, 0x01, 0x82, 0x78, 0x3d, 0x93, 0x14, 0x11, 0x8a, 0x90, 0x60, 0xcd, 0x45, 0x4e, 0x7b, 0x42, 0xb9, 0x3e, 0x6e, 0x68, 0x1f, 0x36, 0x41,
+	/* (2^ 54)P */ 0x13, 0x73, 0x0e, 0x4f, 0x79, 0x93, 0x9e, 0x29, 0x70, 0x7b, 0x4a, 0x59, 0x1a, 0x9a, 0xf4, 0x55, 0x08, 0xf0, 0xdb, 0x17, 0x58, 0xec, 0x64, 0xad, 0x7f, 0x29, 0xeb, 0x3f, 0x85, 0x4e, 0x60, 0x28, 0x98, 0x1f, 0x73, 0x4e, 0xe6, 0xa8, 0xab, 0xd5, 0xd6, 0xfc, 0xa1, 0x36, 0x6d, 0x15, 0xc6, 0x13, 0x83, 0xa0, 0xc2, 0x6e, 0xd9, 0xdb, 0xc9, 0xcc,
+	/* (2^ 55)P */ 0xff, 0xd8, 0x52, 0xa3, 0xdc, 0x99, 0xcf, 0x3e, 0x19, 0xb3, 0x68, 0xd0, 0xb5, 0x0d, 0xb8, 0xee, 0x3f, 0xef, 0x6e, 0xc0, 0x38, 0x28, 0x44, 0x92, 0x78, 0x91, 0x1a, 0x08, 0x78, 0x6c, 0x65, 0x24, 0xf3, 0xa2, 0x3d, 0xf2, 0xe5, 0x79, 0x62, 0x69, 0x29, 0xf4, 0x22, 0xc5, 0xdb, 0x6a, 0xae, 0xf4, 0x44, 0xa3, 0x6f, 0xc7, 0x86, 0xab, 0xef, 0xef,
+	/* (2^ 56)P */ 0xbf, 0x54, 0x9a, 0x09, 0x5d, 0x17, 0xd0, 0xde, 0xfb, 0xf5, 0xca, 0xff, 0x13, 0x20, 0x88, 0x82, 0x3a, 0xe2, 0xd0, 0x3b, 0xfb, 0x05, 0x76, 0xd1, 0xc0, 0x02, 0x71, 0x3b, 0x94, 0xe8, 0xc9, 0x84, 0xcf, 0xa4, 0xe9, 0x28, 0x7b, 0xf5, 0x09, 0xc3, 0x2b, 0x22, 0x40, 0xf1, 0x68, 0x24, 0x24, 0x7d, 0x9f, 0x6e, 0xcd, 0xfe, 0xb0, 0x19, 0x61, 0xf5,
+	/* (2^ 57)P */ 0xe8, 0x63, 0x51, 0xb3, 0x95, 0x6b, 0x7b, 0x74, 0x92, 0x52, 0x45, 0xa4, 0xed, 0xea, 0x0e, 0x0d, 0x2b, 0x01, 0x1e, 0x2c, 0xbc, 0x91, 0x06, 0x69, 0xdb, 0x1f, 0xb5, 0x77, 0x1d, 0x56, 0xf5, 0xb4, 0x02, 0x80, 0x49, 0x56, 0x12, 0xce, 0x86, 0x05, 0xc9, 0xd9, 0xae, 0xf3, 0x6d, 0xe6, 0x3f, 0x40, 0x52, 0xe9, 0x49, 0x2b, 0x31, 0x06, 0x86, 0x14,
+	/* (2^ 58)P */ 0xf5, 0x09, 0x3b, 0xd2, 0xff, 0xdf, 0x11, 0xa5, 0x1c, 0x99, 0xe8, 0x1b, 0xa4, 0x2c, 0x7d, 0x8e, 0xc8, 0xf7, 0x03, 0x46, 0xfa, 0xb6, 0xde, 0x73, 0x91, 0x7e, 0x5a, 0x7a, 0xd7, 0x9a, 0x5b, 0x80, 0x24, 0x62, 0x5e, 0x92, 0xf1, 0xa3, 0x45, 0xa3, 0x43, 0x92, 0x8a, 0x2a, 0x5b, 0x0c, 0xb4, 0xc8, 0xad, 0x1c, 0xb6, 0x6c, 0x5e, 0x81, 0x18, 0x91,
+	/* (2^ 59)P */ 0x96, 0xb3, 0xca, 0x2b, 0xe3, 0x7a, 0x59, 0x72, 0x17, 0x74, 0x29, 0x21, 0xe7, 0x78, 0x07, 0xad, 0xda, 0xb6, 0xcd, 0xf9, 0x27, 0x4d, 0xc8, 0xf2, 0x98, 0x22, 0xca, 0xf2, 0x33, 0x74, 0x7a, 0xdd, 0x1e, 0x71, 0xec, 0xe3, 0x3f, 0xe2, 0xa2, 0xd2, 0x38, 0x75, 0xb0, 0xd0, 0x0a, 0xcf, 0x7d, 0x36, 0xdc, 0x49, 0x38, 0x25, 0x34, 0x4f, 0x20, 0x9a,
+	/* (2^ 60)P */ 0x2b, 0x6e, 0x04, 0x0d, 0x4f, 0x3d, 0x3b, 0x24, 0xf6, 0x4e, 0x5e, 0x0a, 0xbd, 0x48, 0x96, 0xba, 0x81, 0x8f, 0x39, 0x82, 0x13, 0xe6, 0x72, 0xf3, 0x0f, 0xb6, 0x94, 0xf4, 0xc5, 0x90, 0x74, 0x91, 0xa8, 0xf2, 0xc9, 0xca, 0x9a, 0x4d, 0x98, 0xf2, 0xdf, 0x52, 0x4e, 0x97, 0x2f, 0xeb, 0x84, 0xd3, 0xaf, 0xc2, 0xcc, 0xfb, 0x4c, 0x26, 0x4b, 0xe4,
+	/* (2^ 61)P */ 0x12, 0x9e, 0xfb, 0x9d, 0x78, 0x79, 0x99, 0xdd, 0xb3, 0x0b, 0x2e, 0x56, 0x41, 0x8e, 0x3f, 0x39, 0xb8, 0x97, 0x89, 0x53, 0x9b, 0x8a, 0x3c, 0x40, 0x9d, 0xa4, 0x6c, 0x2e, 0x31, 0x71, 0xc6, 0x0a, 0x41, 0xd4, 0x95, 0x06, 0x5e, 0xc1, 0xab, 0xc2, 0x14, 0xc4, 0xc7, 0x15, 0x08, 0x3a, 0xad, 0x7a, 0xb4, 0x62, 0xa3, 0x0c, 0x90, 0xf4, 0x47, 0x08,
+	/* (2^ 62)P */ 0x7f, 0xec, 0x09, 0x82, 0xf5, 0x94, 0x09, 0x93, 0x32, 0xd3, 0xdc, 0x56, 0x80, 0x7b, 0x5b, 0x22, 0x80, 0x6a, 0x96, 0x72, 0xb1, 0xc2, 0xd9, 0xa1, 0x8b, 0x66, 0x42, 0x16, 0xe2, 0x07, 0xb3, 0x2d, 0xf1, 0x75, 0x35, 0x72, 0xc7, 0x98, 0xbe, 0x63, 0x3b, 0x20, 0x75, 0x05, 0xc1, 0x3e, 0x31, 0x5a, 0xf7, 0xaa, 0xae, 0x4b, 0xdb, 0x1d, 0xd0, 0x74,
+	/* (2^ 63)P */ 0x36, 0x5c, 0x74, 0xe6, 0x5d, 0x59, 0x3f, 0x15, 0x4b, 0x4d, 0x4e, 0x67, 0x41, 0xfe, 0x98, 0x1f, 0x49, 0x76, 0x91, 0x0f, 0x9b, 0xf4, 0xaf, 0x86, 0xaf, 0x66, 0x19, 0xed, 0x46, 0xf1, 0x05, 0x9a, 0xcc, 0xd1, 0x14, 0x1f, 0x82, 0x12, 0x8e, 0xe6, 0xf4, 0xc3, 0x42, 0x5c, 0x4e, 0x33, 0x93, 0xbe, 0x30, 0xe7, 0x64, 0xa9, 0x35, 0x00, 0x4d, 0xf9,
+	/* (2^ 64)P */ 0x1f, 0xc1, 0x1e, 0xb7, 0xe3, 0x7c, 0xfa, 0xa3, 0x6b, 0x76, 0xaf, 0x9c, 0x05, 0x85, 0x4a, 0xa9, 0xfb, 0xe3, 0x7e, 0xf2, 0x49, 0x56, 0xdc, 0x2f, 0x57, 0x10, 0xba, 0x37, 0xb2, 0x62, 0xf5, 0x6b, 0xe5, 0x8f, 0x0a, 0x87, 0xd1, 0x6a, 0xcb, 0x9d, 0x07, 0xd0, 0xf6, 0x38, 0x99, 0x2c, 0x61, 0x4a, 0x4e, 0xd8, 0xd2, 0x88, 0x29, 0x99, 0x11, 0x95,
+	/* (2^ 65)P */ 0x6f, 0xdc, 0xd5, 0xd6, 0xd6, 0xa7, 0x4c, 0x46, 0x93, 0x65, 0x62, 0x23, 0x95, 0x32, 0x9c, 0xde, 0x40, 0x41, 0x68, 0x2c, 0x18, 0x4e, 0x5a, 0x8c, 0xc0, 0xc5, 0xc5, 0xea, 0x5c, 0x45, 0x0f, 0x60, 0x78, 0x39, 0xb6, 0x36, 0x23, 0x12, 0xbc, 0x21, 0x9a, 0xf8, 0x91, 0xac, 0xc4, 0x70, 0xdf, 0x85, 0x8e, 0x3c, 0xec, 0x22, 0x04, 0x98, 0xa8, 0xaa,
+	/* (2^ 66)P */ 0xcc, 0x52, 0x10, 0x5b, 0x4b, 0x6c, 0xc5, 0xfa, 0x3e, 0xd4, 0xf8, 0x1c, 0x04, 0x14, 0x48, 0x33, 0xd9, 0xfc, 0x5f, 0xb0, 0xa5, 0x48, 0x8c, 0x45, 0x8a, 0xee, 0x3e, 0xa7, 0xc1, 0x2e, 0x34, 0xca, 0xf6, 0xc9, 0xeb, 0x10, 0xbb, 0xe1, 0x59, 0x84, 0x25, 0xe8, 0x81, 0x70, 0xc0, 0x09, 0x42, 0xa7, 0x3b, 0x0d, 0x33, 0x00, 0xb5, 0x77, 0xbe, 0x25,
+	/* (2^ 67)P */ 0xcd, 0x1f, 0xbc, 0x7d, 0xef, 0xe5, 0xca, 0x91, 0xaf, 0xa9, 0x59, 0x6a, 0x09, 0xca, 0xd6, 0x1b, 0x3d, 0x55, 0xde, 0xa2, 0x6a, 0x80, 0xd6, 0x95, 0x47, 0xe4, 0x5f, 0x68, 0x54, 0x08, 0xdf, 0x29, 0xba, 0x2a, 0x02, 0x84, 0xe8, 0xe9, 0x00, 0x77, 0x99, 0x36, 0x03, 0xf6, 0x4a, 0x3e, 0x21, 0x81, 0x7d, 0xb8, 0xa4, 0x8a, 0xa2, 0x05, 0xef, 0xbc,
+	/* (2^ 68)P */ 0x7c, 0x59, 0x5f, 0x66, 0xd9, 0xb7, 0x83, 0x43, 0x8a, 0xa1, 0x8d, 0x51, 0x70, 0xba, 0xf2, 0x9b, 0x95, 0xc0, 0x4b, 0x4c, 0xa0, 0x14, 0xd3, 0xa4, 0x5d, 0x4a, 0x37, 0x36, 0x97, 0x31, 0x1e, 0x12, 0xe7, 0xbb, 0x08, 0x67, 0xa5, 0x23, 0xd7, 0xfb, 0x97, 0xd8, 0x6a, 0x03, 0xb1, 0xf8, 0x7f, 0xda, 0x58, 0xd9, 0x3f, 0x73, 0x4a, 0x53, 0xe1, 0x7b,
+	/* (2^ 69)P */ 0x55, 0x83, 0x98, 0x78, 0x6c, 0x56, 0x5e, 0xed, 0xf7, 0x23, 0x3e, 0x4c, 0x7d, 0x09, 0x2d, 0x09, 0x9c, 0x58, 0x8b, 0x32, 0xca, 0xfe, 0xbf, 0x47, 0x03, 0xeb, 0x4d, 0xe7, 0xeb, 0x9c, 0x83, 0x05, 0x68, 0xaa, 0x80, 0x89, 0x44, 0xf9, 0xd4, 0xdc, 0xdb, 0xb1, 0xdb, 0x77, 0xac, 0xf9, 0x2a, 0xae, 0x35, 0xac, 0x74, 0xb5, 0x95, 0x62, 0x18, 0x85,
+	/* (2^ 70)P */ 0xab, 0x82, 0x7e, 0x10, 0xd7, 0xe6, 0x57, 0xd1, 0x66, 0x12, 0x31, 0x9c, 0x9c, 0xa6, 0x27, 0x59, 0x71, 0x2e, 0xeb, 0xa0, 0x68, 0xc5, 0x87, 0x51, 0xf4, 0xca, 0x3f, 0x98, 0x56, 0xb0, 0x89, 0xb1, 0xc7, 0x7b, 0x46, 0xb3, 0xae, 0x36, 0xf2, 0xee, 0x15, 0x1a, 0x60, 0xf4, 0x50, 0x76, 0x4f, 0xc4, 0x53, 0x0d, 0x36, 0x4d, 0x31, 0xb1, 0x20, 0x51,
+	/* (2^ 71)P */ 0xf7, 0x1d, 0x8c, 0x1b, 0x5e, 0xe5, 0x02, 0x6f, 0xc5, 0xa5, 0xe0, 0x5f, 0xc6, 0xb6, 0x63, 0x43, 0xaf, 0x3c, 0x19, 0x6c, 0xf4, 0xaf, 0xa4, 0x33, 0xb1, 0x0a, 0x37, 0x3d, 0xd9, 0x4d, 0xe2, 0x29, 0x24, 0x26, 0x94, 0x7c, 0x02, 0xe4, 0xe2, 0xf2, 0xbe, 0xbd, 0xac, 0x1b, 0x48, 0xb8, 0xdd, 0xe9, 0x0d, 0x9a, 0x50, 0x1a, 0x98, 0x71, 0x6e, 0xdc,
+	/* (2^ 72)P */ 0x9f, 0x40, 0xb1, 0xb3, 0x66, 0x28, 0x6c, 0xfe, 0xa6, 0x7d, 0xf8, 0x3e, 0xb8, 0xf3, 0xde, 0x52, 0x76, 0x52, 0xa3, 0x92, 0x98, 0x23, 0xab, 0x4f, 0x88, 0x97, 0xfc, 0x22, 0xe1, 0x6b, 0x67, 0xcd, 0x13, 0x95, 0xda, 0x65, 0xdd, 0x3b, 0x67, 0x3f, 0x5f, 0x4c, 0xf2, 0x8a, 0xad, 0x98, 0xa7, 0x94, 0x24, 0x45, 0x87, 0x11, 0x7c, 0x75, 0x79, 0x85,
+	/* (2^ 73)P */ 0x70, 0xbf, 0xf9, 0x3b, 0xa9, 0x44, 0x57, 0x72, 0x96, 0xc9, 0xa4, 0x98, 0x65, 0xbf, 0x87, 0xb3, 0x3a, 0x39, 0x12, 0xde, 0xe5, 0x39, 0x01, 0x4f, 0xf7, 0xc0, 0x71, 0x52, 0x36, 0x85, 0xb3, 0x18, 0xf8, 0x14, 0xc0, 0x6d, 0xae, 0x9e, 0x4f, 0xb0, 0x72, 0x87, 0xac, 0x5c, 0xd1, 0x6c, 0x41, 0x6c, 0x90, 0x9d, 0x22, 0x81, 0xe4, 0x2b, 0xea, 0xe5,
+	/* (2^ 74)P */ 0xfc, 0xea, 0x1a, 0x65, 0xd9, 0x49, 0x6a, 0x39, 0xb5, 0x96, 0x72, 0x7b, 0x32, 0xf1, 0xd0, 0xe9, 0x45, 0xd9, 0x31, 0x55, 0xc7, 0x34, 0xe9, 0x5a, 0xec, 0x73, 0x0b, 0x03, 0xc4, 0xb3, 0xe6, 0xc9, 0x5e, 0x0a, 0x17, 0xfe, 0x53, 0x66, 0x7f, 0x21, 0x18, 0x74, 0x54, 0x1b, 0xc9, 0x49, 0x16, 0xd2, 0x48, 0xaf, 0x5b, 0x47, 0x7b, 0xeb, 0xaa, 0xc9,
+	/* (2^ 75)P */ 0x47, 0x04, 0xf5, 0x5a, 0x87, 0x77, 0x9e, 0x21, 0x34, 0x4e, 0x83, 0x88, 0xaf, 0x02, 0x1d, 0xb0, 0x5a, 0x1d, 0x1d, 0x7d, 0x8d, 0x2c, 0xd3, 0x8d, 0x63, 0xa9, 0x45, 0xfb, 0x15, 0x6d, 0x86, 0x45, 0xcd, 0x38, 0x0e, 0xf7, 0x37, 0x79, 0xed, 0x6d, 0x5a, 0xbc, 0x32, 0xcc, 0x66, 0xf1, 0x3a, 0xb2, 0x87, 0x6f, 0x70, 0x71, 0xd9, 0xf2, 0xfa, 0x7b,
+	/* (2^ 76)P */ 0x68, 0x07, 0xdc, 0x61, 0x40, 0xe4, 0xec, 0x32, 0xc8, 0xbe, 0x66, 0x30, 0x54, 0x80, 0xfd, 0x13, 0x7a, 0xef, 0xae, 0xed, 0x2e, 0x00, 0x6d, 0x3f, 0xbd, 0xfc, 0x91, 0x24, 0x53, 0x7f, 0x63, 0x9d, 0x2e, 0xe3, 0x76, 0xe0, 0xf3, 0xe1, 0x8f, 0x7a, 0xc4, 0x77, 0x0c, 0x91, 0xc0, 0xc2, 0x18, 0x6b, 0x04, 0xad, 0xb6, 0x70, 0x9a, 0x64, 0xc5, 0x82,
+	/* (2^ 77)P */ 0x7f, 0xea, 0x13, 0xd8, 0x9e, 0xfc, 0x5b, 0x06, 0xb5, 0x4f, 0xda, 0x38, 0xe0, 0x9c, 0xd2, 0x3a, 0xc1, 0x1c, 0x62, 0x70, 0x7f, 0xc6, 0x24, 0x0a, 0x47, 0x04, 0x01, 0xc4, 0x55, 0x09, 0xd1, 0x7a, 0x07, 0xba, 0xa3, 0x80, 0x4f, 0xc1, 0x65, 0x36, 0x6d, 0xc0, 0x10, 0xcf, 0x94, 0xa9, 0xa2, 0x01, 0x44, 0xd1, 0xf9, 0x1c, 0x4c, 0xfb, 0xf8, 0x99,
+	/* (2^ 78)P */ 0x6c, 0xb9, 0x6b, 0xee, 0x43, 0x5b, 0xb9, 0xbb, 0xee, 0x2e, 0x52, 0xc1, 0xc6, 0xb9, 0x61, 0xd2, 0x93, 0xa5, 0xaf, 0x52, 0xf4, 0xa4, 0x1a, 0x51, 0x61, 0xa7, 0xcb, 0x9e, 0xbb, 0x56, 0x65, 0xe2, 0xbf, 0x75, 0xb9, 0x9c, 0x50, 0x96, 0x60, 0x81, 0x74, 0x47, 0xc0, 0x04, 0x88, 0x71, 0x76, 0x39, 0x9a, 0xa7, 0xb1, 0x4e, 0x43, 0x15, 0xe0, 0xbb,
+	/* (2^ 79)P */ 0xbb, 0xce, 0xe2, 0xbb, 0xf9, 0x17, 0x0f, 0x82, 0x40, 0xad, 0x73, 0xe3, 0xeb, 0x3b, 0x06, 0x1a, 0xcf, 0x8e, 0x6e, 0x28, 0xb8, 0x26, 0xd9, 0x5b, 0xb7, 0xb3, 0xcf, 0xb4, 0x6a, 0x1c, 0xbf, 0x7f, 0xb8, 0xb5, 0x79, 0xcf, 0x45, 0x68, 0x7d, 0xc5, 0xeb, 0xf3, 0xbe, 0x39, 0x40, 0xfc, 0x07, 0x90, 0x7a, 0x62, 0xad, 0x86, 0x08, 0x71, 0x25, 0xe1,
+	/* (2^ 80)P */ 0x9b, 0x46, 0xac, 0xef, 0xc1, 0x4e, 0xa1, 0x97, 0x95, 0x76, 0xf9, 0x1b, 0xc2, 0xb2, 0x6a, 0x41, 0xea, 0x80, 0x3d, 0xe9, 0x08, 0x52, 0x5a, 0xe3, 0xf2, 0x08, 0xc5, 0xea, 0x39, 0x3f, 0x44, 0x71, 0x4d, 0xea, 0x0d, 0x05, 0x23, 0xe4, 0x2e, 0x3c, 0x89, 0xfe, 0x12, 0x8a, 0x95, 0x42, 0x0a, 0x68, 0xea, 0x5a, 0x28, 0x06, 0x9e, 0xe3, 0x5f, 0xe0,
+	/* (2^ 81)P */ 0x00, 0x61, 0x6c, 0x98, 0x9b, 0xe7, 0xb9, 0x06, 0x1c, 0xc5, 0x1b, 0xed, 0xbe, 0xc8, 0xb3, 0xea, 0x87, 0xf0, 0xc4, 0x24, 0x7d, 0xbb, 0x5d, 0xa4, 0x1d, 0x7a, 0x16, 0x00, 0x55, 0x94, 0x67, 0x78, 0xbd, 0x58, 0x02, 0x82, 0x90, 0x53, 0x76, 0xd4, 0x72, 0x99, 0x51, 0x6f, 0x7b, 0xcf, 0x80, 0x30, 0x31, 0x3b, 0x01, 0xc7, 0xc1, 0xef, 0xe6, 0x42,
+	/* (2^ 82)P */ 0xe2, 0x35, 0xaf, 0x4b, 0x79, 0xc6, 0x12, 0x24, 0x99, 0xc0, 0x68, 0xb0, 0x43, 0x3e, 0xe5, 0xef, 0xe2, 0x29, 0xea, 0xb8, 0xb3, 0xbc, 0x6a, 0x53, 0x2c, 0x69, 0x18, 0x5a, 0xf9, 0x15, 0xae, 0x66, 0x58, 0x18, 0xd3, 0x2d, 0x4b, 0x00, 0xfd, 0x84, 0xab, 0x4f, 0xae, 0x70, 0x6b, 0x9e, 0x9a, 0xdf, 0x83, 0xfd, 0x2e, 0x3c, 0xcf, 0xf8, 0x88, 0x5b,
+	/* (2^ 83)P */ 0xa4, 0x90, 0x31, 0x85, 0x13, 0xcd, 0xdf, 0x64, 0xc9, 0xa1, 0x0b, 0xe7, 0xb6, 0x73, 0x8a, 0x1b, 0x22, 0x78, 0x4c, 0xd4, 0xae, 0x48, 0x18, 0x00, 0x00, 0xa8, 0x9f, 0x06, 0xf9, 0xfb, 0x2d, 0xc3, 0xb1, 0x2a, 0xbc, 0x13, 0x99, 0x57, 0xaf, 0xf0, 0x8d, 0x61, 0x54, 0x29, 0xd5, 0xf2, 0x72, 0x00, 0x96, 0xd1, 0x85, 0x12, 0x8a, 0xf0, 0x23, 0xfb,
+	/* (2^ 84)P */ 0x69, 0xc7, 0xdb, 0xd9, 0x92, 0x75, 0x08, 0x9b, 0xeb, 0xa5, 0x93, 0xd1, 0x1a, 0xf4, 0xf5, 0xaf, 0xe6, 0xc4, 0x4a, 0x0d, 0x35, 0x26, 0x39, 0x9d, 0xd3, 0x17, 0x3e, 0xae, 0x2d, 0xbf, 0x73, 0x9f, 0xb7, 0x74, 0x91, 0xd1, 0xd8, 0x5c, 0x14, 0xf9, 0x75, 0xdf, 0xeb, 0xc2, 0x22, 0xd8, 0x14, 0x8d, 0x86, 0x23, 0x4d, 0xd1, 0x2d, 0xdb, 0x6b, 0x42,
+	/* (2^ 85)P */ 0x8c, 0xda, 0xc6, 0xf8, 0x71, 0xba, 0x2b, 0x06, 0x78, 0xae, 0xcc, 0x3a, 0xe3, 0xe3, 0xa1, 0x8b, 0xe2, 0x34, 0x6d, 0x28, 0x9e, 0x46, 0x13, 0x4d, 0x9e, 0xa6, 0x73, 0x49, 0x65, 0x79, 0x88, 0xb9, 0x3a, 0xd1, 0x6d, 0x2f, 0x48, 0x2b, 0x0a, 0x7f, 0x58, 0x20, 0x37, 0xf4, 0x0e, 0xbb, 0x4a, 0x95, 0x58, 0x0c, 0x88, 0x30, 0xc4, 0x74, 0xdd, 0xfd,
+	/* (2^ 86)P */ 0x6d, 0x13, 0x4e, 0x89, 0x2d, 0xa9, 0xa3, 0xed, 0x09, 0xe3, 0x0e, 0x71, 0x3e, 0x4a, 0xab, 0x90, 0xde, 0x03, 0xeb, 0x56, 0x46, 0x60, 0x06, 0xf5, 0x71, 0xe5, 0xee, 0x9b, 0xef, 0xff, 0xc4, 0x2c, 0x9f, 0x37, 0x48, 0x45, 0x94, 0x12, 0x41, 0x81, 0x15, 0x70, 0x91, 0x99, 0x5e, 0x56, 0x6b, 0xf4, 0xa6, 0xc9, 0xf5, 0x69, 0x9d, 0x78, 0x37, 0x57,
+	/* (2^ 87)P */ 0xf3, 0x51, 0x57, 0x7e, 0x43, 0x6f, 0xc6, 0x67, 0x59, 0x0c, 0xcf, 0x94, 0xe6, 0x3d, 0xb5, 0x07, 0xc9, 0x77, 0x48, 0xc9, 0x68, 0x0d, 0x98, 0x36, 0x62, 0x35, 0x38, 0x1c, 0xf5, 0xc5, 0xec, 0x66, 0x78, 0xfe, 0x47, 0xab, 0x26, 0xd6, 0x44, 0xb6, 0x06, 0x0f, 0x89, 0xe3, 0x19, 0x40, 0x1a, 0xe7, 0xd8, 0x65, 0x55, 0xf7, 0x1a, 0xfc, 0xa3, 0x0e,
+	/* (2^ 88)P */ 0x0e, 0x30, 0xa6, 0xb7, 0x58, 0x60, 0x62, 0x2a, 0x6c, 0x13, 0xa8, 0x14, 0x9b, 0xb8, 0xf2, 0x70, 0xd8, 0xb1, 0x71, 0x88, 0x8c, 0x18, 0x31, 0x25, 0x93, 0x90, 0xb4, 0xc7, 0x49, 0xd8, 0xd4, 0xdb, 0x1e, 0x1e, 0x7f, 0xaa, 0xba, 0xc9, 0xf2, 0x5d, 0xa9, 0x3a, 0x43, 0xb4, 0x5c, 0xee, 0x7b, 0xc7, 0x97, 0xb7, 0x66, 0xd7, 0x23, 0xd9, 0x22, 0x59,
+	/* (2^ 89)P */ 0x28, 0x19, 0xa6, 0xf9, 0x89, 0x20, 0x78, 0xd4, 0x6d, 0xcb, 0x79, 0x8f, 0x61, 0x6f, 0xb2, 0x5c, 0x4f, 0xa6, 0x54, 0x84, 0x95, 0x24, 0x36, 0x64, 0xcb, 0x39, 0xe7, 0x8f, 0x97, 0x9c, 0x5c, 0x3c, 0xfb, 0x51, 0x11, 0x01, 0x17, 0xdb, 0xc9, 0x9b, 0x51, 0x03, 0x9a, 0xe9, 0xe5, 0x24, 0x1e, 0xf5, 0xda, 0xe0, 0x48, 0x02, 0x23, 0xd0, 0x2c, 0x81,
+	/* (2^ 90)P */ 0x42, 0x1b, 0xe4, 0x91, 0x85, 0x2a, 0x0c, 0xd2, 0x28, 0x66, 0x57, 0x9e, 0x33, 0x8d, 0x25, 0x71, 0x10, 0x65, 0x76, 0xa2, 0x8c, 0x21, 0x86, 0x81, 0x15, 0xc2, 0x27, 0xeb, 0x54, 0x2d, 0x4f, 0x6c, 0xe6, 0xd6, 0x24, 0x9c, 0x1a, 0x12, 0xb8, 0x81, 0xe2, 0x0a, 0xf3, 0xd3, 0xf0, 0xd3, 0xe1, 0x74, 0x1f, 0x9b, 0x11, 0x47, 0xd0, 0xcf, 0xb6, 0x54,
+	/* (2^ 91)P */ 0x26, 0x45, 0xa2, 0x10, 0xd4, 0x2d, 0xae, 0xc0, 0xb0, 0xe8, 0x86, 0xb3, 0xc7, 0xea, 0x70, 0x87, 0x61, 0xb5, 0xa5, 0x55, 0xbe, 0x88, 0x1d, 0x7a, 0xd9, 0x6f, 0xeb, 0x83, 0xe2, 0x44, 0x7f, 0x98, 0x04, 0xd6, 0x50, 0x9d, 0xa7, 0x86, 0x66, 0x09, 0x63, 0xe1, 0xed, 0x72, 0xb1, 0xe4, 0x1d, 0x3a, 0xfd, 0x47, 0xce, 0x1c, 0xaa, 0x3b, 0x8f, 0x1b,
+	/* (2^ 92)P */ 0xf4, 0x3c, 0x4a, 0xb6, 0xc2, 0x9c, 0xe0, 0x2e, 0xb7, 0x38, 0xea, 0x61, 0x35, 0x97, 0x10, 0x90, 0xae, 0x22, 0x48, 0xb3, 0xa9, 0xc6, 0x7a, 0xbb, 0x23, 0xf2, 0xf8, 0x1b, 0xa7, 0xa1, 0x79, 0xcc, 0xc4, 0xf8, 0x08, 0x76, 0x8a, 0x5a, 0x1c, 0x1b, 0xc5, 0x33, 0x91, 0xa9, 0xb8, 0xb9, 0xd3, 0xf8, 0x49, 0xcd, 0xe5, 0x82, 0x43, 0xf7, 0xca, 0x68,
+	/* (2^ 93)P */ 0x38, 0xba, 0xae, 0x44, 0xfe, 0x57, 0x64, 0x56, 0x7c, 0x0e, 0x9c, 0xca, 0xff, 0xa9, 0x82, 0xbb, 0x38, 0x4a, 0xa7, 0xf7, 0x47, 0xab, 0xbe, 0x6d, 0x23, 0x0b, 0x8a, 0xed, 0xc2, 0xb9, 0x8f, 0xf1, 0xec, 0x91, 0x44, 0x73, 0x64, 0xba, 0xd5, 0x8f, 0x37, 0x38, 0x0d, 0xd5, 0xf8, 0x73, 0x57, 0xb6, 0xc2, 0x45, 0xdc, 0x25, 0xb2, 0xb6, 0xea, 0xd9,
+	/* (2^ 94)P */ 0xbf, 0xe9, 0x1a, 0x40, 0x4d, 0xcc, 0xe6, 0x1d, 0x70, 0x1a, 0x65, 0xcc, 0x34, 0x2c, 0x37, 0x2c, 0x2d, 0x6b, 0x6d, 0xe5, 0x2f, 0x19, 0x9e, 0xe4, 0xe1, 0xaa, 0xd4, 0xab, 0x54, 0xf4, 0xa8, 0xe4, 0x69, 0x2d, 0x8e, 0x4d, 0xd7, 0xac, 0xb0, 0x5b, 0xfe, 0xe3, 0x26, 0x07, 0xc3, 0xf8, 0x1b, 0x43, 0xa8, 0x1d, 0x64, 0xa5, 0x25, 0x88, 0xbb, 0x77,
+	/* (2^ 95)P */ 0x92, 0xcd, 0x6e, 0xa0, 0x79, 0x04, 0x18, 0xf4, 0x11, 0x58, 0x48, 0xb5, 0x3c, 0x7b, 0xd1, 0xcc, 0xd3, 0x14, 0x2c, 0xa0, 0xdd, 0x04, 0x44, 0x11, 0xb3, 0x6d, 0x2f, 0x0d, 0xf5, 0x2a, 0x75, 0x5d, 0x1d, 0xda, 0x86, 0x8d, 0x7d, 0x6b, 0x32, 0x68, 0xb6, 0x6c, 0x64, 0x9e, 0xde, 0x80, 0x88, 0xce, 0x08, 0xbf, 0x0b, 0xe5, 0x8e, 0x4f, 0x1d, 0xfb,
+	/* (2^ 96)P */ 0xaf, 0xe8, 0x85, 0xbf, 0x7f, 0x37, 0x8d, 0x66, 0x7c, 0xd5, 0xd3, 0x96, 0xa5, 0x81, 0x67, 0x95, 0xff, 0x48, 0xde, 0xde, 0xd7, 0x7a, 0x46, 0x34, 0xb1, 0x13, 0x70, 0x29, 0xed, 0x87, 0x90, 0xb0, 0x40, 0x2c, 0xa6, 0x43, 0x6e, 0xb6, 0xbc, 0x48, 0x8a, 0xc1, 0xae, 0xb8, 0xd4, 0xe2, 0xc0, 0x32, 0xb2, 0xa6, 0x2a, 0x8f, 0xb5, 0x16, 0x9e, 0xc3,
+	/* (2^ 97)P */ 0xff, 0x4d, 0xd2, 0xd6, 0x74, 0xef, 0x2c, 0x96, 0xc1, 0x11, 0xa8, 0xb8, 0xfe, 0x94, 0x87, 0x3e, 0xa0, 0xfb, 0x57, 0xa3, 0xfc, 0x7a, 0x7e, 0x6a, 0x59, 0x6c, 0x54, 0xbb, 0xbb, 0xa2, 0x25, 0x38, 0x1b, 0xdf, 0x5d, 0x7b, 0x94, 0x14, 0xde, 0x07, 0x6e, 0xd3, 0xab, 0x02, 0x26, 0x74, 0x16, 0x12, 0xdf, 0x2e, 0x2a, 0xa7, 0xb0, 0xe8, 0x29, 0xc0,
+	/* (2^ 98)P */ 0x6a, 0x38, 0x0b, 0xd3, 0xba, 0x45, 0x23, 0xe0, 0x04, 0x3b, 0x83, 0x39, 0xc5, 0x11, 0xe6, 0xcf, 0x39, 0x0a, 0xb3, 0xb0, 0x3b, 0x27, 0x29, 0x63, 0x1c, 0xf3, 0x00, 0xe6, 0xd2, 0x55, 0x21, 0x1f, 0x84, 0x97, 0x9f, 0x01, 0x49, 0x43, 0x30, 0x5f, 0xe0, 0x1d, 0x24, 0xc4, 0x4e, 0xa0, 0x2b, 0x0b, 0x12, 0x55, 0xc3, 0x27, 0xae, 0x08, 0x83, 0x7c,
+	/* (2^ 99)P */ 0x5d, 0x1a, 0xb7, 0xa9, 0xf5, 0xfd, 0xec, 0xad, 0xb7, 0x87, 0x02, 0x5f, 0x0d, 0x30, 0x4d, 0xe2, 0x65, 0x87, 0xa4, 0x41, 0x45, 0x1d, 0x67, 0xe0, 0x30, 0x5c, 0x13, 0x87, 0xf6, 0x2e, 0x08, 0xc1, 0xc7, 0x12, 0x45, 0xc8, 0x9b, 0xad, 0xb8, 0xd5, 0x57, 0xbb, 0x5c, 0x48, 0x3a, 0xe1, 0x91, 0x5e, 0xf6, 0x4d, 0x8a, 0x63, 0x75, 0x69, 0x0c, 0x01,
+	/* (2^100)P */ 0x8f, 0x53, 0x2d, 0xa0, 0x71, 0x3d, 0xfc, 0x45, 0x10, 0x96, 0xcf, 0x56, 0xf9, 0xbb, 0x40, 0x3c, 0x86, 0x52, 0x76, 0xbe, 0x84, 0xf9, 0xa6, 0x9d, 0x3d, 0x27, 0xbe, 0xb4, 0x00, 0x49, 0x94, 0xf5, 0x5d, 0xe1, 0x62, 0x85, 0x66, 0xe5, 0xb8, 0x20, 0x2c, 0x09, 0x7d, 0x9d, 0x3d, 0x6e, 0x74, 0x39, 0xab, 0xad, 0xa0, 0x90, 0x97, 0x5f, 0xbb, 0xa7,
+	/* (2^101)P */ 0xdb, 0x2d, 0x99, 0x08, 0x16, 0x46, 0x83, 0x7a, 0xa8, 0xea, 0x3d, 0x28, 0x5b, 0x49, 0xfc, 0xb9, 0x6d, 0x00, 0x9e, 0x54, 0x4f, 0x47, 0x64, 0x9b, 0x58, 0x4d, 0x07, 0x0c, 0x6f, 0x29, 0x56, 0x0b, 0x00, 0x14, 0x85, 0x96, 0x41, 0x04, 0xb9, 0x5c, 0xa4, 0xf6, 0x16, 0x73, 0x6a, 0xc7, 0x62, 0x0c, 0x65, 0x2f, 0x93, 0xbf, 0xf7, 0xb9, 0xb7, 0xf1,
+	/* (2^102)P */ 0xeb, 0x6d, 0xb3, 0x46, 0x32, 0xd2, 0xcb, 0x08, 0x94, 0x14, 0xbf, 0x3f, 0xc5, 0xcb, 0x5f, 0x9f, 0x8a, 0x89, 0x0c, 0x1b, 0x45, 0xad, 0x4c, 0x50, 0xb4, 0xe1, 0xa0, 0x6b, 0x11, 0x92, 0xaf, 0x1f, 0x00, 0xcc, 0xe5, 0x13, 0x7e, 0xe4, 0x2e, 0xa0, 0x57, 0xf3, 0xa7, 0x84, 0x79, 0x7a, 0xc2, 0xb7, 0xb7, 0xfc, 0x5d, 0xa5, 0xa9, 0x64, 0xcc, 0xd8,
+	/* (2^103)P */ 0xa9, 0xc4, 0x12, 0x8b, 0x34, 0x78, 0x3e, 0x38, 0xfd, 0x3f, 0x87, 0xfa, 0x88, 0x94, 0xd5, 0xd9, 0x7f, 0xeb, 0x58, 0xff, 0xb9, 0x45, 0xdb, 0xa1, 0xed, 0x22, 0x28, 0x1d, 0x00, 0x6d, 0x79, 0x85, 0x7a, 0x75, 0x5d, 0xf0, 0xb1, 0x9e, 0x47, 0x28, 0x8c, 0x62, 0xdf, 0xfb, 0x4c, 0x7b, 0xc5, 0x1a, 0x42, 0x95, 0xef, 0x9a, 0xb7, 0x27, 0x7e, 0xda,
+	/* (2^104)P */ 0xca, 0xd5, 0xc0, 0x17, 0xa1, 0x66, 0x79, 0x9c, 0x2a, 0xb7, 0x0a, 0xfe, 0x62, 0xe4, 0x26, 0x78, 0x90, 0xa7, 0xcb, 0xb0, 0x4f, 0x6d, 0xf9, 0x8f, 0xf7, 0x7d, 0xac, 0xb8, 0x78, 0x1f, 0x41, 0xea, 0x97, 0x1e, 0x62, 0x97, 0x43, 0x80, 0x58, 0x80, 0xb6, 0x69, 0x7d, 0xee, 0x16, 0xd2, 0xa1, 0x81, 0xd7, 0xb1, 0x27, 0x03, 0x48, 0xda, 0xab, 0xec,
+	/* (2^105)P */ 0x5b, 0xed, 0x40, 0x8e, 0x8c, 0xc1, 0x66, 0x90, 0x7f, 0x0c, 0xb2, 0xfc, 0xbd, 0x16, 0xac, 0x7d, 0x4c, 0x6a, 0xf9, 0xae, 0xe7, 0x4e, 0x11, 0x12, 0xe9, 0xbe, 0x17, 0x09, 0xc6, 0xc1, 0x5e, 0xb5, 0x7b, 0x50, 0x5c, 0x27, 0xfb, 0x80, 0xab, 0x01, 0xfa, 0x5b, 0x9b, 0x75, 0x16, 0x6e, 0xb2, 0x5c, 0x8c, 0x2f, 0xa5, 0x6a, 0x1a, 0x68, 0xa6, 0x90,
+	/* (2^106)P */ 0x75, 0xfe, 0xb6, 0x96, 0x96, 0x87, 0x4c, 0x12, 0xa9, 0xd1, 0xd8, 0x03, 0xa3, 0xc1, 0x15, 0x96, 0xe8, 0xa0, 0x75, 0x82, 0xa0, 0x6d, 0xea, 0x54, 0xdc, 0x5f, 0x0d, 0x7e, 0xf6, 0x70, 0xb5, 0xdc, 0x7a, 0xf6, 0xc4, 0xd4, 0x21, 0x49, 0xf5, 0xd4, 0x14, 0x6d, 0x48, 0x1d, 0x7c, 0x99, 0x42, 0xdf, 0x78, 0x6b, 0x9d, 0xb9, 0x30, 0x3c, 0xd0, 0x29,
+	/* (2^107)P */ 0x85, 0xd6, 0xd8, 0xf3, 0x91, 0x74, 0xdd, 0xbd, 0x72, 0x96, 0x10, 0xe4, 0x76, 0x02, 0x5a, 0x72, 0x67, 0xd3, 0x17, 0x72, 0x14, 0x9a, 0x20, 0x5b, 0x0f, 0x8d, 0xed, 0x6d, 0x4e, 0xe3, 0xd9, 0x82, 0xc2, 0x99, 0xee, 0x39, 0x61, 0x69, 0x8a, 0x24, 0x01, 0x92, 0x15, 0xe7, 0xfc, 0xf9, 0x4d, 0xac, 0xf1, 0x30, 0x49, 0x01, 0x0b, 0x6e, 0x0f, 0x20,
+	/* (2^108)P */ 0xd8, 0x25, 0x94, 0x5e, 0x43, 0x29, 0xf5, 0xcc, 0xe8, 0xe3, 0x55, 0x41, 0x3c, 0x9f, 0x58, 0x5b, 0x00, 0xeb, 0xc5, 0xdf, 0xcf, 0xfb, 0xfd, 0x6e, 0x92, 0xec, 0x99, 0x30, 0xd6, 0x05, 0xdd, 0x80, 0x7a, 0x5d, 0x6d, 0x16, 0x85, 0xd8, 0x9d, 0x43, 0x65, 0xd8, 0x2c, 0x33, 0x2f, 0x5c, 0x41, 0xea, 0xb7, 0x95, 0x77, 0xf2, 0x9e, 0x59, 0x09, 0xe8,
+	/* (2^109)P */ 0x00, 0xa0, 0x03, 0x80, 0xcd, 0x60, 0xe5, 0x17, 0xd4, 0x15, 0x99, 0xdd, 0x4f, 0xbf, 0x66, 0xb8, 0xc0, 0xf5, 0xf9, 0xfc, 0x6d, 0x42, 0x18, 0x34, 0x1c, 0x7d, 0x5b, 0xb5, 0x09, 0xd0, 0x99, 0x57, 0x81, 0x0b, 0x62, 0xb3, 0xa2, 0xf9, 0x0b, 0xae, 0x95, 0xb8, 0xc2, 0x3b, 0x0d, 0x5b, 0x00, 0xf1, 0xed, 0xbc, 0x05, 0x9d, 0x61, 0xbc, 0x73, 0x9d,
+	/* (2^110)P */ 0xd4, 0xdb, 0x29, 0xe5, 0x85, 0xe9, 0xc6, 0x89, 0x2a, 0xa8, 0x54, 0xab, 0xb3, 0x7f, 0x88, 0xc0, 0x4d, 0xe0, 0xd1, 0x74, 0x6e, 0xa3, 0xa7, 0x39, 0xd5, 0xcc, 0xa1, 0x8a, 0xcb, 0x5b, 0x34, 0xad, 0x92, 0xb4, 0xd8, 0xd5, 0x17, 0xf6, 0x77, 0x18, 0x9e, 0xaf, 0x45, 0x3b, 0x03, 0xe2, 0xf8, 0x52, 0x60, 0xdc, 0x15, 0x20, 0x9e, 0xdf, 0xd8, 0x5d,
+	/* (2^111)P */ 0x02, 0xc1, 0xac, 0x1a, 0x15, 0x8e, 0x6c, 0xf5, 0x1e, 0x1e, 0xba, 0x7e, 0xc2, 0xda, 0x7d, 0x02, 0xda, 0x43, 0xae, 0x04, 0x70, 0x28, 0x54, 0x78, 0x94, 0xf5, 0x4f, 0x07, 0x84, 0x8f, 0xed, 0xaa, 0xc0, 0xb8, 0xcd, 0x7f, 0x7e, 0x33, 0xa3, 0xbe, 0x21, 0x29, 0xc8, 0x56, 0x34, 0xc0, 0x76, 0x87, 0x8f, 0xc7, 0x73, 0x58, 0x90, 0x16, 0xfc, 0xd6,
+	/* (2^112)P */ 0xb8, 0x3f, 0xe1, 0xdf, 0x3a, 0x91, 0x25, 0x0c, 0xf6, 0x47, 0xa8, 0x89, 0xc4, 0xc6, 0x61, 0xec, 0x86, 0x2c, 0xfd, 0xbe, 0xa4, 0x6f, 0xc2, 0xd4, 0x46, 0x19, 0x70, 0x5d, 0x09, 0x02, 0x86, 0xd3, 0x4b, 0xe9, 0x16, 0x7b, 0xf0, 0x0d, 0x6c, 0xff, 0x91, 0x05, 0xbf, 0x55, 0xb4, 0x00, 0x8d, 0xe5, 0x6d, 0x68, 0x20, 0x90, 0x12, 0xb5, 0x5c, 0x32,
+	/* (2^113)P */ 0x80, 0x45, 0xc8, 0x51, 0x87, 0xba, 0x1c, 0x5c, 0xcf, 0x5f, 0x4b, 0x3c, 0x9e, 0x3b, 0x36, 0xd2, 0x26, 0xa2, 0x7f, 0xab, 0xb7, 0xbf, 0xda, 0x68, 0x23, 0x8f, 0xc3, 0xa0, 0xfd, 0xad, 0xf1, 0x56, 0x3b, 0xd0, 0x75, 0x2b, 0x44, 0x61, 0xd8, 0xf4, 0xf1, 0x05, 0x49, 0x53, 0x07, 0xee, 0x47, 0xef, 0xc0, 0x7c, 0x9d, 0xe4, 0x15, 0x88, 0xc5, 0x47,
+	/* (2^114)P */ 0x2d, 0xb5, 0x09, 0x80, 0xb9, 0xd3, 0xd8, 0xfe, 0x4c, 0xd2, 0xa6, 0x6e, 0xd3, 0x75, 0xcf, 0xb0, 0x99, 0xcb, 0x50, 0x8d, 0xe9, 0x67, 0x9b, 0x20, 0xe8, 0x57, 0xd8, 0x14, 0x85, 0x73, 0x6a, 0x74, 0xe0, 0x99, 0xf0, 0x6b, 0x6e, 0x59, 0x30, 0x31, 0x33, 0x96, 0x5f, 0xa1, 0x0c, 0x1b, 0xf4, 0xca, 0x09, 0xe1, 0x9b, 0xb5, 0xcf, 0x6d, 0x0b, 0xeb,
+	/* (2^115)P */ 0x1a, 0xde, 0x50, 0xa9, 0xac, 0x3e, 0x10, 0x43, 0x4f, 0x82, 0x4f, 0xc0, 0xfe, 0x3f, 0x33, 0xd2, 0x64, 0x86, 0x50, 0xa9, 0x51, 0x76, 0x5e, 0x50, 0x97, 0x6c, 0x73, 0x8d, 0x77, 0xa3, 0x75, 0x03, 0xbc, 0xc9, 0xfb, 0x50, 0xd9, 0x6d, 0x16, 0xad, 0x5d, 0x32, 0x3d, 0xac, 0x44, 0xdf, 0x51, 0xf7, 0x19, 0xd4, 0x0b, 0x57, 0x78, 0x0b, 0x81, 0x4e,
+	/* (2^116)P */ 0x32, 0x24, 0xf1, 0x6c, 0x55, 0x62, 0x1d, 0xb3, 0x1f, 0xda, 0xfa, 0x6a, 0x8f, 0x98, 0x01, 0x16, 0xde, 0x44, 0x50, 0x0d, 0x2e, 0x6c, 0x0b, 0xa2, 0xd3, 0x74, 0x0e, 0xa9, 0xbf, 0x8d, 0xa9, 0xc8, 0xc8, 0x2f, 0x62, 0xc1, 0x35, 0x5e, 0xfd, 0x3a, 0xb3, 0x83, 0x2d, 0xee, 0x4e, 0xfd, 0x5c, 0x5e, 0xad, 0x85, 0xa5, 0x10, 0xb5, 0x4f, 0x34, 0xa7,
+	/* (2^117)P */ 0xd1, 0x58, 0x6f, 0xe6, 0x54, 0x2c, 0xc2, 0xcd, 0xcf, 0x83, 0xdc, 0x88, 0x0c, 0xb9, 0xb4, 0x62, 0x18, 0x89, 0x65, 0x28, 0xe9, 0x72, 0x4b, 0x65, 0xcf, 0xd6, 0x90, 0x88, 0xd7, 0x76, 0x17, 0x4f, 0x74, 0x64, 0x1e, 0xcb, 0xd3, 0xf5, 0x4b, 0xaa, 0x2e, 0x4d, 0x2d, 0x7c, 0x13, 0x1f, 0xfd, 0xd9, 0x60, 0x83, 0x7e, 0xda, 0x64, 0x1c, 0xdc, 0x9f,
+	/* (2^118)P */ 0xad, 0xef, 0xac, 0x1b, 0xc1, 0x30, 0x5a, 0x15, 0xc9, 0x1f, 0xac, 0xf1, 0xca, 0x44, 0x95, 0x95, 0xea, 0xf2, 0x22, 0xe7, 0x8d, 0x25, 0xf0, 0xff, 0xd8, 0x71, 0xf7, 0xf8, 0x8f, 0x8f, 0xcd, 0xf4, 0x1e, 0xfe, 0x6c, 0x68, 0x04, 0xb8, 0x78, 0xa1, 0x5f, 0xa6, 0x5d, 0x5e, 0xf9, 0x8d, 0xea, 0x80, 0xcb, 0xf3, 0x17, 0xa6, 0x03, 0xc9, 0x38, 0xd5,
+	/* (2^119)P */ 0x79, 0x14, 0x31, 0xc3, 0x38, 0xe5, 0xaa, 0xbf, 0x17, 0xa3, 0x04, 0x4e, 0x80, 0x59, 0x9c, 0x9f, 0x19, 0x39, 0xe4, 0x2d, 0x23, 0x54, 0x4a, 0x7f, 0x3e, 0xf3, 0xd9, 0xc7, 0xba, 0x6c, 0x8f, 0x6b, 0xfa, 0x34, 0xb5, 0x23, 0x17, 0x1d, 0xff, 0x1d, 0xea, 0x1f, 0xd7, 0xba, 0x61, 0xb2, 0xe0, 0x38, 0x6a, 0xe9, 0xcf, 0x48, 0x5d, 0x6a, 0x10, 0x9c,
+	/* (2^120)P */ 0xc8, 0xbb, 0x13, 0x1c, 0x3f, 0x3c, 0x34, 0xfd, 0xac, 0x37, 0x52, 0x44, 0x25, 0xa8, 0xde, 0x1d, 0x63, 0xf4, 0x81, 0x9a, 0xbe, 0x0b, 0x74, 0x2e, 0xc8, 0x51, 0x16, 0xd3, 0xac, 0x4a, 0xaf, 0xe2, 0x5f, 0x3a, 0x89, 0x32, 0xd1, 0x9b, 0x7c, 0x90, 0x0d, 0xac, 0xdc, 0x8b, 0x73, 0x45, 0x45, 0x97, 0xb1, 0x90, 0x2c, 0x1b, 0x31, 0xca, 0xb1, 0x94,
+	/* (2^121)P */ 0x07, 0x28, 0xdd, 0x10, 0x14, 0xa5, 0x95, 0x7e, 0xf3, 0xe4, 0xd4, 0x14, 0xb4, 0x7e, 0x76, 0xdb, 0x42, 0xd6, 0x94, 0x3e, 0xeb, 0x44, 0x64, 0x88, 0x0d, 0xec, 0xc1, 0x21, 0xf0, 0x79, 0xe0, 0x83, 0x67, 0x55, 0x53, 0xc2, 0xf6, 0xc5, 0xc5, 0x89, 0x39, 0xe8, 0x42, 0xd0, 0x17, 0xbd, 0xff, 0x35, 0x59, 0x0e, 0xc3, 0x06, 0x86, 0xd4, 0x64, 0xcf,
+	/* (2^122)P */ 0x91, 0xa8, 0xdb, 0x57, 0x9b, 0xe2, 0x96, 0x31, 0x10, 0x6e, 0xd7, 0x9a, 0x97, 0xb3, 0xab, 0xb5, 0x15, 0x66, 0xbe, 0xcc, 0x6d, 0x9a, 0xac, 0x06, 0xb3, 0x0d, 0xaa, 0x4b, 0x9c, 0x96, 0x79, 0x6c, 0x34, 0xee, 0x9e, 0x53, 0x4d, 0x6e, 0xbd, 0x88, 0x02, 0xbf, 0x50, 0x54, 0x12, 0x5d, 0x01, 0x02, 0x46, 0xc6, 0x74, 0x02, 0x8c, 0x24, 0xae, 0xb1,
+	/* (2^123)P */ 0xf5, 0x22, 0xea, 0xac, 0x7d, 0x9c, 0x33, 0x8a, 0xa5, 0x36, 0x79, 0x6a, 0x4f, 0xa4, 0xdc, 0xa5, 0x73, 0x64, 0xc4, 0x6f, 0x43, 0x02, 0x3b, 0x94, 0x66, 0xd2, 0x4b, 0x4f, 0xf6, 0x45, 0x33, 0x5d, 0x10, 0x33, 0x18, 0x1e, 0xa3, 0xfc, 0xf7, 0xd2, 0xb8, 0xc8, 0xa7, 0xe0, 0x76, 0x8a, 0xcd, 0xff, 0x4f, 0x99, 0x34, 0x47, 0x84, 0x91, 0x96, 0x9f,
+	/* (2^124)P */ 0x8a, 0x48, 0x3b, 0x48, 0x4a, 0xbc, 0xac, 0xe2, 0x80, 0xd6, 0xd2, 0x35, 0xde, 0xd0, 0x56, 0x42, 0x33, 0xb3, 0x56, 0x5a, 0xcd, 0xb8, 0x3d, 0xb5, 0x25, 0xc1, 0xed, 0xff, 0x87, 0x0b, 0x79, 0xff, 0xf2, 0x62, 0xe1, 0x76, 0xc6, 0xa2, 0x0f, 0xa8, 0x9b, 0x0d, 0xcc, 0x3f, 0x3d, 0x35, 0x27, 0x8d, 0x0b, 0x74, 0xb0, 0xc3, 0x78, 0x8c, 0xcc, 0xc8,
+	/* (2^125)P */ 0xfc, 0x9a, 0x0c, 0xa8, 0x49, 0x42, 0xb8, 0xdf, 0xcf, 0xb3, 0x19, 0xa6, 0x64, 0x57, 0xfe, 0xe8, 0xf8, 0xa6, 0x4b, 0x86, 0xa1, 0xd5, 0x83, 0x7f, 0x14, 0x99, 0x18, 0x0c, 0x7d, 0x5b, 0xf7, 0x3d, 0xf9, 0x4b, 0x79, 0xb1, 0x86, 0x30, 0xb4, 0x5e, 0x6a, 0xe8, 0x9d, 0xfa, 0x8a, 0x41, 0xc4, 0x30, 0xfc, 0x56, 0x74, 0x14, 0x42, 0xc8, 0x96, 0x0e,
+	/* (2^126)P */ 0xdf, 0x66, 0xec, 0xbc, 0x44, 0xdb, 0x19, 0xce, 0xd4, 0xb5, 0x49, 0x40, 0x07, 0x49, 0xe0, 0x3a, 0x61, 0x10, 0xfb, 0x7d, 0xba, 0xb1, 0xe0, 0x28, 0x5b, 0x99, 0x59, 0x96, 0xa2, 0xee, 0xe0, 0x23, 0x37, 0x39, 0x1f, 0xe6, 0x57, 0x9f, 0xf8, 0xf8, 0xdc, 0x74, 0xf6, 0x8f, 0x4f, 0x5e, 0x51, 0xa4, 0x12, 0xac, 0xbe, 0xe4, 0xf3, 0xd1, 0xf0, 0x24,
+	/* (2^127)P */ 0x1e, 0x3e, 0x9a, 0x5f, 0xdf, 0x9f, 0xd6, 0x4e, 0x8a, 0x28, 0xc3, 0xcd, 0x96, 0x9d, 0x57, 0xc7, 0x61, 0x81, 0x90, 0xff, 0xae, 0xb1, 0x4f, 0xc2, 0x96, 0x8b, 0x1a, 0x18, 0xf4, 0x50, 0xcb, 0x31, 0xe1, 0x57, 0xf4, 0x90, 0xa8, 0xea, 0xac, 0xe7, 0x61, 0x98, 0xb6, 0x15, 0xc1, 0x7b, 0x29, 0xa4, 0xc3, 0x18, 0xef, 0xb9, 0xd8, 0xdf, 0xf6, 0xac,
+	/* (2^128)P */ 0xca, 0xa8, 0x6c, 0xf1, 0xb4, 0xca, 0xfe, 0x31, 0xee, 0x48, 0x38, 0x8b, 0x0e, 0xbb, 0x7a, 0x30, 0xaa, 0xf9, 0xee, 0x27, 0x53, 0x24, 0xdc, 0x2e, 0x15, 0xa6, 0x48, 0x8f, 0xa0, 0x7e, 0xf1, 0xdc, 0x93, 0x87, 0x39, 0xeb, 0x7f, 0x38, 0x92, 0x92, 0x4c, 0x29, 0xe9, 0x57, 0xd8, 0x59, 0xfc, 0xe9, 0x9c, 0x44, 0xc0, 0x65, 0xcf, 0xac, 0x4b, 0xdc,
+	/* (2^129)P */ 0xa3, 0xd0, 0x37, 0x8f, 0x86, 0x2f, 0xc6, 0x47, 0x55, 0x46, 0x65, 0x26, 0x4b, 0x91, 0xe2, 0x18, 0x5c, 0x4f, 0x23, 0xc1, 0x37, 0x29, 0xb9, 0xc1, 0x27, 0xc5, 0x3c, 0xbf, 0x7e, 0x23, 0xdb, 0x73, 0x99, 0xbd, 0x1b, 0xb2, 0x31, 0x68, 0x3a, 0xad, 0xb7, 0xb0, 0x10, 0xc5, 0xe5, 0x11, 0x51, 0xba, 0xa7, 0x60, 0x66, 0x54, 0xf0, 0x08, 0xd7, 0x69,
+	/* (2^130)P */ 0x89, 0x41, 0x79, 0xcc, 0xeb, 0x0a, 0xf5, 0x4b, 0xa3, 0x4c, 0xce, 0x52, 0xb0, 0xa7, 0xe4, 0x41, 0x75, 0x7d, 0x04, 0xbb, 0x09, 0x4c, 0x50, 0x9f, 0xdf, 0xea, 0x74, 0x61, 0x02, 0xad, 0xb4, 0x9d, 0xb7, 0x05, 0xb9, 0xea, 0xeb, 0x91, 0x35, 0xe7, 0x49, 0xea, 0xd3, 0x4f, 0x3c, 0x60, 0x21, 0x7a, 0xde, 0xc7, 0xe2, 0x5a, 0xee, 0x8e, 0x93, 0xc7,
+	/* (2^131)P */ 0x00, 0xe8, 0xed, 0xd0, 0xb3, 0x0d, 0xaf, 0xb2, 0xde, 0x2c, 0xf6, 0x00, 0xe2, 0xea, 0x6d, 0xf8, 0x0e, 0xd9, 0x67, 0x59, 0xa9, 0x50, 0xbb, 0x17, 0x8f, 0xff, 0xb1, 0x9f, 0x17, 0xb6, 0xf2, 0xb5, 0xba, 0x80, 0xf7, 0x0f, 0xba, 0xd5, 0x09, 0x43, 0xaa, 0x4e, 0x3a, 0x67, 0x6a, 0x89, 0x9b, 0x18, 0x65, 0x35, 0xf8, 0x3a, 0x49, 0x91, 0x30, 0x51,
+	/* (2^132)P */ 0x8d, 0x25, 0xe9, 0x0e, 0x7d, 0x50, 0x76, 0xe4, 0x58, 0x7e, 0xb9, 0x33, 0xe6, 0x65, 0x90, 0xc2, 0x50, 0x9d, 0x50, 0x2e, 0x11, 0xad, 0xd5, 0x43, 0x52, 0x32, 0x41, 0x4f, 0x7b, 0xb6, 0xa0, 0xec, 0x81, 0x75, 0x36, 0x7c, 0x77, 0x85, 0x59, 0x70, 0xe4, 0xf9, 0xef, 0x66, 0x8d, 0x35, 0xc8, 0x2a, 0x6e, 0x5b, 0xc6, 0x0d, 0x0b, 0x29, 0x60, 0x68,
+	/* (2^133)P */ 0xf8, 0xce, 0xb0, 0x3a, 0x56, 0x7d, 0x51, 0x9a, 0x25, 0x73, 0xea, 0xdd, 0xe4, 0xe0, 0x0e, 0xf0, 0x07, 0xc0, 0x31, 0x00, 0x73, 0x35, 0xd0, 0x39, 0xc4, 0x9b, 0xb7, 0x95, 0xe0, 0x62, 0x70, 0x36, 0x0b, 0xcb, 0xa0, 0x42, 0xde, 0x51, 0xcf, 0x41, 0xe0, 0xb8, 0xb4, 0xc0, 0xe5, 0x46, 0x99, 0x9f, 0x02, 0x7f, 0x14, 0x8c, 0xc1, 0x4e, 0xef, 0xe8,
+	/* (2^134)P */ 0x10, 0x01, 0x57, 0x0a, 0xbe, 0x8b, 0x18, 0xc8, 0xca, 0x00, 0x28, 0x77, 0x4a, 0x9a, 0xc7, 0x55, 0x2a, 0xcc, 0x0c, 0x7b, 0xb9, 0xe9, 0xc8, 0x97, 0x7c, 0x02, 0xe3, 0x09, 0x2f, 0x62, 0x30, 0xb8, 0x40, 0x09, 0x65, 0xe9, 0x55, 0x63, 0xb5, 0x07, 0xca, 0x9f, 0x00, 0xdf, 0x9d, 0x5c, 0xc7, 0xee, 0x57, 0xa5, 0x90, 0x15, 0x1e, 0x22, 0xa0, 0x12,
+	/* (2^135)P */ 0x71, 0x2d, 0xc9, 0xef, 0x27, 0xb9, 0xd8, 0x12, 0x43, 0x6b, 0xa8, 0xce, 0x3b, 0x6d, 0x6e, 0x91, 0x43, 0x23, 0xbc, 0x32, 0xb3, 0xbf, 0xe1, 0xc7, 0x39, 0xcf, 0x7c, 0x42, 0x4c, 0xb1, 0x30, 0xe2, 0xdd, 0x69, 0x06, 0xe5, 0xea, 0xf0, 0x2a, 0x16, 0x50, 0x71, 0xca, 0x92, 0xdf, 0xc1, 0xcc, 0xec, 0xe6, 0x54, 0x07, 0xf3, 0x18, 0x8d, 0xd8, 0x29,
+	/* (2^136)P */ 0x98, 0x51, 0x48, 0x8f, 0xfa, 0x2e, 0x5e, 0x67, 0xb0, 0xc6, 0x17, 0x12, 0xb6, 0x7d, 0xc9, 0xad, 0x81, 0x11, 0xad, 0x0c, 0x1c, 0x2d, 0x45, 0xdf, 0xac, 0x66, 0xbd, 0x08, 0x6f, 0x7c, 0xc7, 0x06, 0x6e, 0x19, 0x08, 0x39, 0x64, 0xd7, 0xe4, 0xd1, 0x11, 0x5f, 0x1c, 0xf4, 0x67, 0xc3, 0x88, 0x6a, 0xe6, 0x07, 0xa3, 0x83, 0xd7, 0xfd, 0x2a, 0xf9,
+	/* (2^137)P */ 0x87, 0xed, 0xeb, 0xd9, 0xdf, 0xff, 0x43, 0x8b, 0xaa, 0x20, 0x58, 0xb0, 0xb4, 0x6b, 0x14, 0xb8, 0x02, 0xc5, 0x40, 0x20, 0x22, 0xbb, 0xf7, 0xb4, 0xf3, 0x05, 0x1e, 0x4d, 0x94, 0xff, 0xe3, 0xc5, 0x22, 0x82, 0xfe, 0xaf, 0x90, 0x42, 0x98, 0x6b, 0x76, 0x8b, 0x3e, 0x89, 0x3f, 0x42, 0x2a, 0xa7, 0x26, 0x00, 0xda, 0x5c, 0xa2, 0x2b, 0xec, 0xdd,
+	/* (2^138)P */ 0x5c, 0x21, 0x16, 0x0d, 0x46, 0xb8, 0xd0, 0xa7, 0x88, 0xe7, 0x25, 0xcb, 0x3e, 0x50, 0x73, 0x61, 0xe7, 0xaf, 0x5a, 0x3f, 0x47, 0x8b, 0x3d, 0x97, 0x79, 0x2c, 0xe6, 0x6d, 0x95, 0x74, 0x65, 0x70, 0x36, 0xfd, 0xd1, 0x9e, 0x13, 0x18, 0x63, 0xb1, 0x2d, 0x0b, 0xb5, 0x36, 0x3e, 0xe7, 0x35, 0x42, 0x3b, 0xe6, 0x1f, 0x4d, 0x9d, 0x59, 0xa2, 0x43,
+	/* (2^139)P */ 0x8c, 0x0c, 0x7c, 0x24, 0x9e, 0xe0, 0xf8, 0x05, 0x1c, 0x9e, 0x1f, 0x31, 0xc0, 0x70, 0xb3, 0xfb, 0x4e, 0xf8, 0x0a, 0x57, 0xb7, 0x49, 0xb5, 0x73, 0xa1, 0x5f, 0x9b, 0x6a, 0x07, 0x6c, 0x87, 0x71, 0x87, 0xd4, 0xbe, 0x98, 0x1e, 0x98, 0xee, 0x52, 0xc1, 0x7b, 0x95, 0x0f, 0x28, 0x32, 0x36, 0x28, 0xd0, 0x3a, 0x0f, 0x7d, 0x2a, 0xa9, 0x62, 0xb9,
+	/* (2^140)P */ 0x97, 0xe6, 0x18, 0x77, 0xf9, 0x34, 0xac, 0xbc, 0xe0, 0x62, 0x9f, 0x42, 0xde, 0xbd, 0x2f, 0xf7, 0x1f, 0xb7, 0x14, 0x52, 0x8a, 0x79, 0xb2, 0x3f, 0xd2, 0x95, 0x71, 0x01, 0xe8, 0xaf, 0x8c, 0xa4, 0xa4, 0xa7, 0x27, 0xf3, 0x5c, 0xdf, 0x3e, 0x57, 0x7a, 0xf1, 0x76, 0x49, 0xe6, 0x42, 0x3f, 0x8f, 0x1e, 0x63, 0x4a, 0x65, 0xb5, 0x41, 0xf5, 0x02,
+	/* (2^141)P */ 0x72, 0x85, 0xc5, 0x0b, 0xe1, 0x47, 0x64, 0x02, 0xc5, 0x4d, 0x81, 0x69, 0xb2, 0xcf, 0x0f, 0x6c, 0xd4, 0x6d, 0xd0, 0xc7, 0xb4, 0x1c, 0xd0, 0x32, 0x59, 0x89, 0xe2, 0xe0, 0x96, 0x8b, 0x12, 0x98, 0xbf, 0x63, 0x7a, 0x4c, 0x76, 0x7e, 0x58, 0x17, 0x8f, 0x5b, 0x0a, 0x59, 0x65, 0x75, 0xbc, 0x61, 0x1f, 0xbe, 0xc5, 0x6e, 0x0a, 0x57, 0x52, 0x70,
+	/* (2^142)P */ 0x92, 0x1c, 0x77, 0xbb, 0x62, 0x02, 0x6c, 0x25, 0x9c, 0x66, 0x07, 0x83, 0xab, 0xcc, 0x80, 0x5d, 0xd2, 0x76, 0x0c, 0xa4, 0xc5, 0xb4, 0x8a, 0x68, 0x23, 0x31, 0x32, 0x29, 0x8a, 0x47, 0x92, 0x12, 0x80, 0xb3, 0xfa, 0x18, 0xe4, 0x8d, 0xc0, 0x4d, 0xfe, 0x97, 0x5f, 0x72, 0x41, 0xb5, 0x5c, 0x7a, 0xbd, 0xf0, 0xcf, 0x5e, 0x97, 0xaa, 0x64, 0x32,
+	/* (2^143)P */ 0x35, 0x3f, 0x75, 0xc1, 0x7a, 0x75, 0x7e, 0xa9, 0xc6, 0x0b, 0x4e, 0x32, 0x62, 0xec, 0xe3, 0x5c, 0xfb, 0x01, 0x43, 0xb6, 0xd4, 0x5b, 0x75, 0xd2, 0xee, 0x7f, 0x5d, 0x23, 0x2b, 0xb3, 0x54, 0x34, 0x4c, 0xd3, 0xb4, 0x32, 0x84, 0x81, 0xb5, 0x09, 0x76, 0x19, 0xda, 0x58, 0xda, 0x7c, 0xdb, 0x2e, 0xdd, 0x4c, 0x8e, 0xdd, 0x5d, 0x89, 0x10, 0x10,
+	/* (2^144)P */ 0x57, 0x25, 0x6a, 0x08, 0x37, 0x92, 0xa8, 0xdf, 0x24, 0xef, 0x8f, 0x33, 0x34, 0x52, 0xa4, 0x4c, 0xf0, 0x77, 0x9f, 0x69, 0x77, 0xd5, 0x8f, 0xd2, 0x9a, 0xb3, 0xb6, 0x1d, 0x2d, 0xa6, 0xf7, 0x1f, 0xda, 0xd7, 0xcb, 0x75, 0x11, 0xc3, 0x6b, 0xc0, 0x38, 0xb1, 0xd5, 0x2d, 0x96, 0x84, 0x16, 0xfa, 0x26, 0xb9, 0xcc, 0x3f, 0x16, 0x47, 0x23, 0x74,
+	/* (2^145)P */ 0x9b, 0x61, 0x2a, 0x1c, 0xdd, 0x39, 0xa5, 0xfa, 0x1c, 0x7d, 0x63, 0x50, 0xca, 0xe6, 0x9d, 0xfa, 0xb7, 0xc4, 0x4c, 0x6a, 0x97, 0x5f, 0x36, 0x4e, 0x47, 0xdd, 0x17, 0xf7, 0xf9, 0x19, 0xce, 0x75, 0x17, 0xad, 0xce, 0x2a, 0xf3, 0xfe, 0x27, 0x8f, 0x3e, 0x48, 0xc0, 0x60, 0x87, 0x24, 0x19, 0xae, 0x59, 0xe4, 0x5a, 0x00, 0x2a, 0xba, 0xa2, 0x1f,
+	/* (2^146)P */ 0x26, 0x88, 0x42, 0x60, 0x9f, 0x6e, 0x2c, 0x7c, 0x39, 0x0f, 0x47, 0x6a, 0x0e, 0x02, 0xbb, 0x4b, 0x34, 0x29, 0x55, 0x18, 0x36, 0xcf, 0x3b, 0x47, 0xf1, 0x2e, 0xfc, 0x6e, 0x94, 0xff, 0xe8, 0x6b, 0x06, 0xd2, 0xba, 0x77, 0x5e, 0x60, 0xd7, 0x19, 0xef, 0x02, 0x9d, 0x3a, 0xc2, 0xb7, 0xa9, 0xd8, 0x57, 0xee, 0x7e, 0x2b, 0xf2, 0x6d, 0x28, 0xda,
+	/* (2^147)P */ 0xdf, 0xd9, 0x92, 0x11, 0x98, 0x23, 0xe2, 0x45, 0x2f, 0x74, 0x70, 0xee, 0x0e, 0x55, 0x65, 0x79, 0x86, 0x38, 0x17, 0x92, 0x85, 0x87, 0x99, 0x50, 0xd9, 0x7c, 0xdb, 0xa1, 0x10, 0xec, 0x30, 0xb7, 0x40, 0xa3, 0x23, 0x9b, 0x0e, 0x27, 0x49, 0x29, 0x03, 0x94, 0xff, 0x53, 0xdc, 0xd7, 0xed, 0x49, 0xa9, 0x5a, 0x3b, 0xee, 0xd7, 0xc7, 0x65, 0xaf,
+	/* (2^148)P */ 0xa0, 0xbd, 0xbe, 0x03, 0xee, 0x0c, 0xbe, 0x32, 0x00, 0x7b, 0x52, 0xcb, 0x92, 0x29, 0xbf, 0xa0, 0xc6, 0xd9, 0xd2, 0xd6, 0x15, 0xe8, 0x3a, 0x75, 0x61, 0x65, 0x56, 0xae, 0xad, 0x3c, 0x2a, 0x64, 0x14, 0x3f, 0x8e, 0xc1, 0x2d, 0x0c, 0x8d, 0x20, 0xdb, 0x58, 0x4b, 0xe5, 0x40, 0x15, 0x4b, 0xdc, 0xa8, 0xbd, 0xef, 0x08, 0xa7, 0xd1, 0xf4, 0xb0,
+	/* (2^149)P */ 0xa9, 0x0f, 0x05, 0x94, 0x66, 0xac, 0x1f, 0x65, 0x3f, 0xe1, 0xb8, 0xe1, 0x34, 0x5e, 0x1d, 0x8f, 0xe3, 0x93, 0x03, 0x15, 0xff, 0xb6, 0x65, 0xb6, 0x6e, 0xc0, 0x2f, 0xd4, 0x2e, 0xb9, 0x2c, 0x13, 0x3c, 0x99, 0x1c, 0xb5, 0x87, 0xba, 0x79, 0xcb, 0xf0, 0x18, 0x06, 0x86, 0x04, 0x14, 0x25, 0x09, 0xcd, 0x1c, 0x14, 0xda, 0x35, 0xd0, 0x38, 0x3b,
+	/* (2^150)P */ 0x1b, 0x04, 0xa3, 0x27, 0xb4, 0xd3, 0x37, 0x48, 0x1e, 0x8f, 0x69, 0xd3, 0x5a, 0x2f, 0x20, 0x02, 0x36, 0xbe, 0x06, 0x7b, 0x6b, 0x6c, 0x12, 0x5b, 0x80, 0x74, 0x44, 0xe6, 0xf8, 0xf5, 0x95, 0x59, 0x29, 0xab, 0x51, 0x47, 0x83, 0x28, 0xe0, 0xad, 0xde, 0xaa, 0xd3, 0xb1, 0x1a, 0xcb, 0xa3, 0xcd, 0x8b, 0x6a, 0xb1, 0xa7, 0x0a, 0xd1, 0xf9, 0xbe,
+	/* (2^151)P */ 0xce, 0x2f, 0x85, 0xca, 0x74, 0x6d, 0x49, 0xb8, 0xce, 0x80, 0x44, 0xe0, 0xda, 0x5b, 0xcf, 0x2f, 0x79, 0x74, 0xfe, 0xb4, 0x2c, 0x99, 0x20, 0x6e, 0x09, 0x04, 0xfb, 0x6d, 0x57, 0x5b, 0x95, 0x0c, 0x45, 0xda, 0x4f, 0x7f, 0x63, 0xcc, 0x85, 0x5a, 0x67, 0x50, 0x68, 0x71, 0xb4, 0x67, 0xb1, 0x2e, 0xc1, 0x1c, 0xdc, 0xff, 0x2a, 0x7c, 0x10, 0x5e,
+	/* (2^152)P */ 0xa6, 0xde, 0xf3, 0xd4, 0x22, 0x30, 0x24, 0x9e, 0x0b, 0x30, 0x54, 0x59, 0x7e, 0xa2, 0xeb, 0x89, 0x54, 0x65, 0x3e, 0x40, 0xd1, 0xde, 0xe6, 0xee, 0x4d, 0xbf, 0x5e, 0x40, 0x1d, 0xee, 0x4f, 0x68, 0xd9, 0xa7, 0x2f, 0xb3, 0x64, 0xb3, 0xf5, 0xc8, 0xd3, 0xaa, 0x70, 0x70, 0x3d, 0xef, 0xd3, 0x95, 0x54, 0xdb, 0x3e, 0x94, 0x95, 0x92, 0x1f, 0x45,
+	/* (2^153)P */ 0x22, 0x80, 0x1d, 0x9d, 0x96, 0xa5, 0x78, 0x6f, 0xe0, 0x1e, 0x1b, 0x66, 0x42, 0xc8, 0xae, 0x9e, 0x46, 0x45, 0x08, 0x41, 0xdf, 0x80, 0xae, 0x6f, 0xdb, 0x15, 0x5a, 0x21, 0x31, 0x7a, 0xd0, 0xf2, 0x54, 0x15, 0x88, 0xd3, 0x0f, 0x7f, 0x14, 0x5a, 0x14, 0x97, 0xab, 0xf4, 0x58, 0x6a, 0x9f, 0xea, 0x74, 0xe5, 0x6b, 0x90, 0x59, 0x2b, 0x48, 0xd9,
+	/* (2^154)P */ 0x12, 0x24, 0x04, 0xf5, 0x50, 0xc2, 0x8c, 0xb0, 0x7c, 0x46, 0x98, 0xd5, 0x24, 0xad, 0xf6, 0x72, 0xdc, 0x82, 0x1a, 0x60, 0xc1, 0xeb, 0x48, 0xef, 0x7f, 0x6e, 0xe6, 0xcc, 0xdb, 0x7b, 0xae, 0xbe, 0x5e, 0x1e, 0x5c, 0xe6, 0x0a, 0x70, 0xdf, 0xa4, 0xa3, 0x85, 0x1b, 0x1b, 0x7f, 0x72, 0xb9, 0x96, 0x6f, 0xdc, 0x03, 0x76, 0x66, 0xfb, 0xa0, 0x33,
+	/* (2^155)P */ 0x37, 0x40, 0xbb, 0xbc, 0x68, 0x58, 0x86, 0xca, 0xbb, 0xa5, 0x24, 0x76, 0x3d, 0x48, 0xd1, 0xad, 0xb4, 0xa8, 0xcf, 0xc3, 0xb6, 0xa8, 0xba, 0x1a, 0x3a, 0xbe, 0x33, 0x75, 0x04, 0x5c, 0x13, 0x8c, 0x0d, 0x70, 0x8d, 0xa6, 0x4e, 0x2a, 0xeb, 0x17, 0x3c, 0x22, 0xdd, 0x3e, 0x96, 0x40, 0x11, 0x9e, 0x4e, 0xae, 0x3d, 0xf8, 0x91, 0xd7, 0x50, 0xc8,
+	/* (2^156)P */ 0xd8, 0xca, 0xde, 0x19, 0xcf, 0x00, 0xe4, 0x73, 0x18, 0x7f, 0x9b, 0x9f, 0xf4, 0x5b, 0x49, 0x49, 0x99, 0xdc, 0xa4, 0x46, 0x21, 0xb5, 0xd7, 0x3e, 0xb7, 0x47, 0x1b, 0xa9, 0x9f, 0x4c, 0x69, 0x7d, 0xec, 0x33, 0xd6, 0x1c, 0x51, 0x7f, 0x47, 0x74, 0x7a, 0x6c, 0xf3, 0xd2, 0x2e, 0xbf, 0xdf, 0x6c, 0x9e, 0x77, 0x3b, 0x34, 0xf6, 0x73, 0x80, 0xed,
+	/* (2^157)P */ 0x16, 0xfb, 0x16, 0xc3, 0xc2, 0x83, 0xe4, 0xf4, 0x03, 0x7f, 0x52, 0xb0, 0x67, 0x51, 0x7b, 0x24, 0x5a, 0x51, 0xd3, 0xb6, 0x4e, 0x59, 0x76, 0xcd, 0x08, 0x7b, 0x1d, 0x7a, 0x9c, 0x65, 0xae, 0xce, 0xaa, 0xd2, 0x1c, 0x85, 0x66, 0x68, 0x06, 0x15, 0xa8, 0x06, 0xe6, 0x16, 0x37, 0xf4, 0x49, 0x9e, 0x0f, 0x50, 0x37, 0xb1, 0xb2, 0x93, 0x70, 0x43,
+	/* (2^158)P */ 0x18, 0x3a, 0x16, 0xe5, 0x8d, 0xc8, 0x35, 0xd6, 0x7b, 0x09, 0xec, 0x61, 0x5f, 0x5c, 0x2a, 0x19, 0x96, 0x2e, 0xc3, 0xfd, 0xab, 0xe6, 0x23, 0xae, 0xab, 0xc5, 0xcb, 0xb9, 0x7b, 0x2d, 0x34, 0x51, 0xb9, 0x41, 0x9e, 0x7d, 0xca, 0xda, 0x25, 0x45, 0x14, 0xb0, 0xc7, 0x4d, 0x26, 0x2b, 0xfe, 0x43, 0xb0, 0x21, 0x5e, 0xfa, 0xdc, 0x7c, 0xf9, 0x5a,
+	/* (2^159)P */ 0x94, 0xad, 0x42, 0x17, 0xf5, 0xcd, 0x1c, 0x0d, 0xf6, 0x41, 0xd2, 0x55, 0xbb, 0x50, 0xf1, 0xc6, 0xbc, 0xa6, 0xc5, 0x3a, 0xfd, 0x9b, 0x75, 0x3e, 0xf6, 0x1a, 0xa7, 0xb2, 0x6e, 0x64, 0x12, 0xdc, 0x3c, 0xe5, 0xf6, 0xfc, 0x3b, 0xfa, 0x43, 0x81, 0xd4, 0xa5, 0xee, 0xf5, 0x9c, 0x47, 0x2f, 0xd0, 0x9c, 0xde, 0xa1, 0x48, 0x91, 0x9a, 0x34, 0xc1,
+	/* (2^160)P */ 0x37, 0x1b, 0xb3, 0x88, 0xc9, 0x98, 0x4e, 0xfb, 0x84, 0x4f, 0x2b, 0x0a, 0xb6, 0x8f, 0x35, 0x15, 0xcd, 0x61, 0x7a, 0x5f, 0x5c, 0xa0, 0xca, 0x23, 0xa0, 0x93, 0x1f, 0xcc, 0x3c, 0x39, 0x3a, 0x24, 0xa7, 0x49, 0xad, 0x8d, 0x59, 0xcc, 0x94, 0x5a, 0x16, 0xf5, 0x70, 0xe8, 0x52, 0x1e, 0xee, 0x20, 0x30, 0x17, 0x7e, 0xf0, 0x4c, 0x93, 0x06, 0x5a,
+	/* (2^161)P */ 0x81, 0xba, 0x3b, 0xd7, 0x3e, 0xb4, 0x32, 0x3a, 0x22, 0x39, 0x2a, 0xfc, 0x19, 0xd9, 0xd2, 0xf6, 0xc5, 0x79, 0x6c, 0x0e, 0xde, 0xda, 0x01, 0xff, 0x52, 0xfb, 0xb6, 0x95, 0x4e, 0x7a, 0x10, 0xb8, 0x06, 0x86, 0x3c, 0xcd, 0x56, 0xd6, 0x15, 0xbf, 0x6e, 0x3e, 0x4f, 0x35, 0x5e, 0xca, 0xbc, 0xa5, 0x95, 0xa2, 0xdf, 0x2d, 0x1d, 0xaf, 0x59, 0xf9,
+	/* (2^162)P */ 0x69, 0xe5, 0xe2, 0xfa, 0xc9, 0x7f, 0xdd, 0x09, 0xf5, 0x6b, 0x4e, 0x2e, 0xbe, 0xb4, 0xbf, 0x3e, 0xb2, 0xf2, 0x81, 0x30, 0xe1, 0x07, 0xa8, 0x0d, 0x2b, 0xd2, 0x5a, 0x55, 0xbe, 0x4b, 0x86, 0x5d, 0xb0, 0x5e, 0x7c, 0x8f, 0xc1, 0x3c, 0x81, 0x4c, 0xf7, 0x6d, 0x7d, 0xe6, 0x4f, 0x8a, 0x85, 0xc2, 0x2f, 0x28, 0xef, 0x8c, 0x69, 0xc2, 0xc2, 0x1a,
+	/* (2^163)P */ 0xd9, 0xe4, 0x0e, 0x1e, 0xc2, 0xf7, 0x2f, 0x9f, 0xa1, 0x40, 0xfe, 0x46, 0x16, 0xaf, 0x2e, 0xd1, 0xec, 0x15, 0x9b, 0x61, 0x92, 0xce, 0xfc, 0x10, 0x43, 0x1d, 0x00, 0xf6, 0xbe, 0x20, 0x80, 0x80, 0x6f, 0x3c, 0x16, 0x94, 0x59, 0xba, 0x03, 0x53, 0x6e, 0xb6, 0xdd, 0x25, 0x7b, 0x86, 0xbf, 0x96, 0xf4, 0x2f, 0xa1, 0x96, 0x8d, 0xf9, 0xb3, 0x29,
+	/* (2^164)P */ 0x3b, 0x04, 0x60, 0x6e, 0xce, 0xab, 0xd2, 0x63, 0x18, 0x53, 0x88, 0x16, 0x4a, 0x6a, 0xab, 0x72, 0x03, 0x68, 0xa5, 0xd4, 0x0d, 0xb2, 0x82, 0x81, 0x1f, 0x2b, 0x5c, 0x75, 0xe8, 0xd2, 0x1d, 0x7f, 0xe7, 0x1b, 0x35, 0x02, 0xde, 0xec, 0xbd, 0xcb, 0xc7, 0x01, 0xd3, 0x95, 0x61, 0xfe, 0xb2, 0x7a, 0x66, 0x09, 0x4c, 0x6d, 0xfd, 0x39, 0xf7, 0x52,
+	/* (2^165)P */ 0x42, 0xc1, 0x5f, 0xf8, 0x35, 0x52, 0xc1, 0xfe, 0xc5, 0x11, 0x80, 0x1c, 0x11, 0x46, 0x31, 0x11, 0xbe, 0xd0, 0xc4, 0xb6, 0x07, 0x13, 0x38, 0xa0, 0x8d, 0x65, 0xf0, 0x56, 0x9e, 0x16, 0xbf, 0x9d, 0xcd, 0x51, 0x34, 0xf9, 0x08, 0x48, 0x7b, 0x76, 0x0c, 0x7b, 0x30, 0x07, 0xa8, 0x76, 0xaf, 0xa3, 0x29, 0x38, 0xb0, 0x58, 0xde, 0x72, 0x4b, 0x45,
+	/* (2^166)P */ 0xd4, 0x16, 0xa7, 0xc0, 0xb4, 0x9f, 0xdf, 0x1a, 0x37, 0xc8, 0x35, 0xed, 0xc5, 0x85, 0x74, 0x64, 0x09, 0x22, 0xef, 0xe9, 0x0c, 0xaf, 0x12, 0x4c, 0x9e, 0xf8, 0x47, 0x56, 0xe0, 0x7f, 0x4e, 0x24, 0x6b, 0x0c, 0xe7, 0xad, 0xc6, 0x47, 0x1d, 0xa4, 0x0d, 0x86, 0x89, 0x65, 0xe8, 0x5f, 0x71, 0xc7, 0xe9, 0xcd, 0xec, 0x6c, 0x62, 0xc7, 0xe3, 0xb3,
+	/* (2^167)P */ 0xb5, 0xea, 0x86, 0xe3, 0x15, 0x18, 0x3f, 0x6d, 0x7b, 0x05, 0x95, 0x15, 0x53, 0x26, 0x1c, 0xeb, 0xbe, 0x7e, 0x16, 0x42, 0x4b, 0xa2, 0x3d, 0xdd, 0x0e, 0xff, 0xba, 0x67, 0xb5, 0xae, 0x7a, 0x17, 0xde, 0x23, 0xad, 0x14, 0xcc, 0xd7, 0xaf, 0x57, 0x01, 0xe0, 0xdd, 0x48, 0xdd, 0xd7, 0xe3, 0xdf, 0xe9, 0x2d, 0xda, 0x67, 0xa4, 0x9f, 0x29, 0x04,
+	/* (2^168)P */ 0x16, 0x53, 0xe6, 0x9c, 0x4e, 0xe5, 0x1e, 0x70, 0x81, 0x25, 0x02, 0x9b, 0x47, 0x6d, 0xd2, 0x08, 0x73, 0xbe, 0x0a, 0xf1, 0x7b, 0xeb, 0x24, 0xeb, 0x38, 0x23, 0x5c, 0xb6, 0x3e, 0xce, 0x1e, 0xe3, 0xbc, 0x82, 0x35, 0x1f, 0xaf, 0x3a, 0x3a, 0xe5, 0x4e, 0xc1, 0xca, 0xbf, 0x47, 0xb4, 0xbb, 0xbc, 0x5f, 0xea, 0xc6, 0xca, 0xf3, 0xa0, 0xa2, 0x73,
+	/* (2^169)P */ 0xef, 0xa4, 0x7a, 0x4e, 0xe4, 0xc7, 0xb6, 0x43, 0x2e, 0xa5, 0xe4, 0xa5, 0xba, 0x1e, 0xa5, 0xfe, 0x9e, 0xce, 0xa9, 0x80, 0x04, 0xcb, 0x4f, 0xd8, 0x74, 0x05, 0x48, 0xfa, 0x99, 0x11, 0x5d, 0x97, 0x3b, 0x07, 0x0d, 0xdd, 0xe6, 0xb1, 0x74, 0x87, 0x1a, 0xd3, 0x26, 0xb7, 0x8f, 0xe1, 0x63, 0x3d, 0xec, 0x53, 0x93, 0xb0, 0x81, 0x78, 0x34, 0xa4,
+	/* (2^170)P */ 0xe1, 0xe7, 0xd4, 0x58, 0x9d, 0x0e, 0x8b, 0x65, 0x66, 0x37, 0x16, 0x48, 0x6f, 0xaa, 0x42, 0x37, 0x77, 0xad, 0xb1, 0x56, 0x48, 0xdf, 0x65, 0x36, 0x30, 0xb8, 0x00, 0x12, 0xd8, 0x32, 0x28, 0x7f, 0xc1, 0x71, 0xeb, 0x93, 0x0f, 0x48, 0x04, 0xe1, 0x5a, 0x6a, 0x96, 0xc1, 0xca, 0x89, 0x6d, 0x1b, 0x82, 0x4c, 0x18, 0x6d, 0x55, 0x4b, 0xea, 0xfd,
+	/* (2^171)P */ 0x62, 0x1a, 0x53, 0xb4, 0xb1, 0xbe, 0x6f, 0x15, 0x18, 0x88, 0xd4, 0x66, 0x61, 0xc7, 0x12, 0x69, 0x02, 0xbd, 0x03, 0x23, 0x2b, 0xef, 0xf9, 0x54, 0xa4, 0x85, 0xa8, 0xe3, 0xb7, 0xbd, 0xa9, 0xa3, 0xf3, 0x2a, 0xdd, 0xf1, 0xd4, 0x03, 0x0f, 0xa9, 0xa1, 0xd8, 0xa3, 0xcd, 0xb2, 0x71, 0x90, 0x4b, 0x35, 0x62, 0xf2, 0x2f, 0xce, 0x67, 0x1f, 0xaa,
+	/* (2^172)P */ 0x9e, 0x1e, 0xcd, 0x43, 0x7e, 0x87, 0x37, 0x94, 0x3a, 0x97, 0x4c, 0x7e, 0xee, 0xc9, 0x37, 0x85, 0xf1, 0xd9, 0x4f, 0xbf, 0xf9, 0x6f, 0x39, 0x9a, 0x39, 0x87, 0x2e, 0x25, 0x84, 0x42, 0xc3, 0x80, 0xcb, 0x07, 0x22, 0xae, 0x30, 0xd5, 0x50, 0xa1, 0x23, 0xcc, 0x31, 0x81, 0x9d, 0xf1, 0x30, 0xd9, 0x2b, 0x73, 0x41, 0x16, 0x50, 0xab, 0x2d, 0xa2,
+	/* (2^173)P */ 0xa4, 0x69, 0x4f, 0xa1, 0x4e, 0xb9, 0xbf, 0x14, 0xe8, 0x2b, 0x04, 0x93, 0xb7, 0x6e, 0x9f, 0x7d, 0x73, 0x0a, 0xc5, 0x14, 0xb8, 0xde, 0x8c, 0xc1, 0xfe, 0xc0, 0xa7, 0xa4, 0xcc, 0x42, 0x42, 0x81, 0x15, 0x65, 0x8a, 0x80, 0xb9, 0xde, 0x1f, 0x60, 0x33, 0x0e, 0xcb, 0xfc, 0xe0, 0xdb, 0x83, 0xa1, 0xe5, 0xd0, 0x16, 0x86, 0x2c, 0xe2, 0x87, 0xed,
+	/* (2^174)P */ 0x7a, 0xc0, 0xeb, 0x6b, 0xf6, 0x0d, 0x4c, 0x6d, 0x1e, 0xdb, 0xab, 0xe7, 0x19, 0x45, 0xc6, 0xe3, 0xb2, 0x06, 0xbb, 0xbc, 0x70, 0x99, 0x83, 0x33, 0xeb, 0x28, 0xc8, 0x77, 0xf6, 0x4d, 0x01, 0xb7, 0x59, 0xa0, 0xd2, 0xb3, 0x2a, 0x72, 0x30, 0xe7, 0x11, 0x39, 0xb6, 0x41, 0x29, 0x65, 0x5a, 0x14, 0xb9, 0x86, 0x08, 0xe0, 0x7d, 0x32, 0x8c, 0xf0,
+	/* (2^175)P */ 0x5c, 0x11, 0x30, 0x9e, 0x05, 0x27, 0xf5, 0x45, 0x0f, 0xb3, 0xc9, 0x75, 0xc3, 0xd7, 0xe1, 0x82, 0x3b, 0x8e, 0x87, 0x23, 0x00, 0x15, 0x19, 0x07, 0xd9, 0x21, 0x53, 0xc7, 0xf1, 0xa3, 0xbf, 0x70, 0x64, 0x15, 0x18, 0xca, 0x23, 0x9e, 0xd3, 0x08, 0xc3, 0x2a, 0x8b, 0xe5, 0x83, 0x04, 0x89, 0x14, 0xfd, 0x28, 0x25, 0x1c, 0xe3, 0x26, 0xa7, 0x22,
+	/* (2^176)P */ 0xdc, 0xd4, 0x75, 0x60, 0x99, 0x94, 0xea, 0x09, 0x8e, 0x8a, 0x3c, 0x1b, 0xf9, 0xbd, 0x33, 0x0d, 0x51, 0x3d, 0x12, 0x6f, 0x4e, 0x72, 0xe0, 0x17, 0x20, 0xe9, 0x75, 0xe6, 0x3a, 0xb2, 0x13, 0x83, 0x4e, 0x7a, 0x08, 0x9e, 0xd1, 0x04, 0x5f, 0x6b, 0x42, 0x0b, 0x76, 0x2a, 0x2d, 0x77, 0x53, 0x6c, 0x65, 0x6d, 0x8e, 0x25, 0x3c, 0xb6, 0x8b, 0x69,
+	/* (2^177)P */ 0xb9, 0x49, 0x28, 0xd0, 0xdc, 0x6c, 0x8f, 0x4c, 0xc9, 0x14, 0x8a, 0x38, 0xa3, 0xcb, 0xc4, 0x9d, 0x53, 0xcf, 0xe9, 0xe3, 0xcf, 0xe0, 0xb1, 0xf2, 0x1b, 0x4c, 0x7f, 0x83, 0x2a, 0x7a, 0xe9, 0x8b, 0x3b, 0x86, 0x61, 0x30, 0xe9, 0x99, 0xbd, 0xba, 0x19, 0x6e, 0x65, 0x2a, 0x12, 0x3e, 0x9c, 0xa8, 0xaf, 0xc3, 0xcf, 0xf8, 0x1f, 0x77, 0x86, 0xea,
+	/* (2^178)P */ 0x30, 0xde, 0xe7, 0xff, 0x54, 0xf7, 0xa2, 0x59, 0xf6, 0x0b, 0xfb, 0x7a, 0xf2, 0x39, 0xf0, 0xdb, 0x39, 0xbc, 0xf0, 0xfa, 0x60, 0xeb, 0x6b, 0x4f, 0x47, 0x17, 0xc8, 0x00, 0x65, 0x6d, 0x25, 0x1c, 0xd0, 0x48, 0x56, 0x53, 0x45, 0x11, 0x30, 0x02, 0x49, 0x20, 0x27, 0xac, 0xf2, 0x4c, 0xac, 0x64, 0x3d, 0x52, 0xb8, 0x89, 0xe0, 0x93, 0x16, 0x0f,
+	/* (2^179)P */ 0x84, 0x09, 0xba, 0x40, 0xb2, 0x2f, 0xa3, 0xa8, 0xc2, 0xba, 0x46, 0x33, 0x05, 0x9d, 0x62, 0xad, 0xa1, 0x3c, 0x33, 0xef, 0x0d, 0xeb, 0xf0, 0x77, 0x11, 0x5a, 0xb0, 0x21, 0x9c, 0xdf, 0x55, 0x24, 0x25, 0x35, 0x51, 0x61, 0x92, 0xf0, 0xb1, 0xce, 0xf5, 0xd4, 0x7b, 0x6c, 0x21, 0x9d, 0x56, 0x52, 0xf8, 0xa1, 0x4c, 0xe9, 0x27, 0x55, 0xac, 0x91,
+	/* (2^180)P */ 0x03, 0x3e, 0x30, 0xd2, 0x0a, 0xfa, 0x7d, 0x82, 0x3d, 0x1f, 0x8b, 0xcb, 0xb6, 0x04, 0x5c, 0xcc, 0x8b, 0xda, 0xe2, 0x68, 0x74, 0x08, 0x8c, 0x44, 0x83, 0x57, 0x6d, 0x6f, 0x80, 0xb0, 0x7e, 0xa9, 0x82, 0x91, 0x7b, 0x4c, 0x37, 0x97, 0xd1, 0x63, 0xd1, 0xbd, 0x45, 0xe6, 0x8a, 0x86, 0xd6, 0x89, 0x54, 0xfd, 0xd2, 0xb1, 0xd7, 0x54, 0xad, 0xaf,
+	/* (2^181)P */ 0x8b, 0x33, 0x62, 0x49, 0x9f, 0x63, 0xf9, 0x87, 0x42, 0x58, 0xbf, 0xb3, 0xe6, 0x68, 0x02, 0x60, 0x5c, 0x76, 0x62, 0xf7, 0x61, 0xd7, 0x36, 0x31, 0xf7, 0x9c, 0xb5, 0xe5, 0x13, 0x6c, 0xea, 0x78, 0xae, 0xcf, 0xde, 0xbf, 0xb6, 0xeb, 0x4f, 0xc8, 0x2a, 0xb4, 0x9a, 0x9f, 0xf3, 0xd1, 0x6a, 0xec, 0x0c, 0xbd, 0x85, 0x98, 0x40, 0x06, 0x1c, 0x2a,
+	/* (2^182)P */ 0x74, 0x3b, 0xe7, 0x81, 0xd5, 0xae, 0x54, 0x56, 0x03, 0xe8, 0x97, 0x16, 0x76, 0xcf, 0x24, 0x96, 0x96, 0x5b, 0xcc, 0x09, 0xab, 0x23, 0x6f, 0x54, 0xae, 0x8f, 0xe4, 0x12, 0xcb, 0xfd, 0xbc, 0xac, 0x93, 0x45, 0x3d, 0x68, 0x08, 0x22, 0x59, 0xc6, 0xf0, 0x47, 0x19, 0x8c, 0x79, 0x93, 0x1e, 0x0e, 0x30, 0xb0, 0x94, 0xfb, 0x17, 0x1d, 0x5a, 0x12,
+	/* (2^183)P */ 0x85, 0xff, 0x40, 0x18, 0x85, 0xff, 0x44, 0x37, 0x69, 0x23, 0x4d, 0x34, 0xe1, 0xeb, 0xa3, 0x1b, 0x55, 0x40, 0xc1, 0x64, 0xf4, 0xd4, 0x13, 0x0a, 0x9f, 0xb9, 0x19, 0xfc, 0x88, 0x7d, 0xc0, 0x72, 0xcf, 0x69, 0x2f, 0xd2, 0x0c, 0x82, 0x0f, 0xda, 0x08, 0xba, 0x0f, 0xaa, 0x3b, 0xe9, 0xe5, 0x83, 0x7a, 0x06, 0xe8, 0x1b, 0x38, 0x43, 0xc3, 0x54,
+	/* (2^184)P */ 0x14, 0xaa, 0xb3, 0x6e, 0xe6, 0x28, 0xee, 0xc5, 0x22, 0x6c, 0x7c, 0xf9, 0xa8, 0x71, 0xcc, 0xfe, 0x68, 0x7e, 0xd3, 0xb8, 0x37, 0x96, 0xca, 0x0b, 0xd9, 0xb6, 0x06, 0xa9, 0xf6, 0x71, 0xe8, 0x31, 0xf7, 0xd8, 0xf1, 0x5d, 0xab, 0xb9, 0xf0, 0x5c, 0x98, 0xcf, 0x22, 0xa2, 0x2a, 0xf6, 0xd0, 0x59, 0xf0, 0x9d, 0xd9, 0x6a, 0x4f, 0x59, 0x57, 0xad,
+	/* (2^185)P */ 0xd7, 0x2b, 0x3d, 0x38, 0x4c, 0x2e, 0x23, 0x4d, 0x49, 0xa2, 0x62, 0x62, 0xf9, 0x0f, 0xde, 0x08, 0xf3, 0x86, 0x71, 0xb6, 0xc7, 0xf9, 0x85, 0x9c, 0x33, 0xa1, 0xcf, 0x16, 0xaa, 0x60, 0xb9, 0xb7, 0xea, 0xed, 0x01, 0x1c, 0x59, 0xdb, 0x3f, 0x3f, 0x97, 0x2e, 0xf0, 0x09, 0x9f, 0x10, 0x85, 0x5f, 0x53, 0x39, 0xf3, 0x13, 0x40, 0x56, 0x95, 0xf9,
+	/* (2^186)P */ 0xb4, 0xe3, 0xda, 0xc6, 0x1f, 0x78, 0x8e, 0xac, 0xd4, 0x20, 0x1d, 0xa0, 0xbf, 0x4c, 0x09, 0x16, 0xa7, 0x30, 0xb5, 0x8d, 0x9e, 0xa1, 0x5f, 0x6d, 0x52, 0xf4, 0x71, 0xb6, 0x32, 0x2d, 0x21, 0x51, 0xc6, 0xfc, 0x2f, 0x08, 0xf4, 0x13, 0x6c, 0x55, 0xba, 0x72, 0x81, 0x24, 0x49, 0x0e, 0x4f, 0x06, 0x36, 0x39, 0x6a, 0xc5, 0x81, 0xfc, 0xeb, 0xb2,
+	/* (2^187)P */ 0x7d, 0x8d, 0xc8, 0x6c, 0xea, 0xb4, 0xb9, 0xe8, 0x40, 0xc9, 0x69, 0xc9, 0x30, 0x05, 0xfd, 0x34, 0x46, 0xfd, 0x94, 0x05, 0x16, 0xf5, 0x4b, 0x13, 0x3d, 0x24, 0x1a, 0xd6, 0x64, 0x2b, 0x9c, 0xe2, 0xa5, 0xd9, 0x98, 0xe0, 0xe8, 0xf4, 0xbc, 0x2c, 0xbd, 0xa2, 0x56, 0xe3, 0x9e, 0x14, 0xdb, 0xbf, 0x05, 0xbf, 0x9a, 0x13, 0x5d, 0xf7, 0x91, 0xa3,
+	/* (2^188)P */ 0x8b, 0xcb, 0x27, 0xf3, 0x15, 0x26, 0x05, 0x40, 0x0f, 0xa6, 0x15, 0x13, 0x71, 0x95, 0xa2, 0xc6, 0x38, 0x04, 0x67, 0xf8, 0x9a, 0x83, 0x06, 0xaa, 0x25, 0x36, 0x72, 0x01, 0x6f, 0x74, 0x5f, 0xe5, 0x6e, 0x44, 0x99, 0xce, 0x13, 0xbc, 0x82, 0xc2, 0x0d, 0xa4, 0x98, 0x50, 0x38, 0xf3, 0xa2, 0xc5, 0xe5, 0x24, 0x1f, 0x6f, 0x56, 0x3e, 0x07, 0xb2,
+	/* (2^189)P */ 0xbd, 0x0f, 0x32, 0x60, 0x07, 0xb1, 0xd7, 0x0b, 0x11, 0x07, 0x57, 0x02, 0x89, 0xe8, 0x8b, 0xe8, 0x5a, 0x1f, 0xee, 0x54, 0x6b, 0xff, 0xb3, 0x04, 0x07, 0x57, 0x13, 0x0b, 0x94, 0xa8, 0x4d, 0x81, 0xe2, 0x17, 0x16, 0x45, 0xd4, 0x4b, 0xf7, 0x7e, 0x64, 0x66, 0x20, 0xe8, 0x0b, 0x26, 0xfd, 0xa9, 0x8a, 0x47, 0x52, 0x89, 0x14, 0xd0, 0xd1, 0xa1,
+	/* (2^190)P */ 0xdc, 0x03, 0xe6, 0x20, 0x44, 0x47, 0x8f, 0x04, 0x16, 0x24, 0x22, 0xc1, 0x55, 0x5c, 0xbe, 0x43, 0xc3, 0x92, 0xc5, 0x54, 0x3d, 0x5d, 0xd1, 0x05, 0x9c, 0xc6, 0x7c, 0xbf, 0x23, 0x84, 0x1a, 0xba, 0x4f, 0x1f, 0xfc, 0xa1, 0xae, 0x1a, 0x64, 0x02, 0x51, 0xf1, 0xcb, 0x7a, 0x20, 0xce, 0xb2, 0x34, 0x3c, 0xca, 0xe0, 0xe4, 0xba, 0x22, 0xd4, 0x7b,
+	/* (2^191)P */ 0xca, 0xfd, 0xca, 0xd7, 0xde, 0x61, 0xae, 0xf0, 0x79, 0x0c, 0x20, 0xab, 0xbc, 0x6f, 0x4d, 0x61, 0xf0, 0xc7, 0x9c, 0x8d, 0x4b, 0x52, 0xf3, 0xb9, 0x48, 0x63, 0x0b, 0xb6, 0xd2, 0x25, 0x9a, 0x96, 0x72, 0xc1, 0x6b, 0x0c, 0xb5, 0xfb, 0x71, 0xaa, 0xad, 0x47, 0x5b, 0xe7, 0xc0, 0x0a, 0x55, 0xb2, 0xd4, 0x16, 0x2f, 0xb1, 0x01, 0xfd, 0xce, 0x27,
+	/* (2^192)P */ 0x64, 0x11, 0x4b, 0xab, 0x57, 0x09, 0xc6, 0x49, 0x4a, 0x37, 0xc3, 0x36, 0xc4, 0x7b, 0x81, 0x1f, 0x42, 0xed, 0xbb, 0xe0, 0xa0, 0x8d, 0x51, 0xe6, 0xca, 0x8b, 0xb9, 0xcd, 0x99, 0x2d, 0x91, 0x53, 0xa9, 0x47, 0xcb, 0x32, 0xc7, 0xa4, 0x92, 0xec, 0x46, 0x74, 0x44, 0x6d, 0x71, 0x9f, 0x6d, 0x0c, 0x69, 0xa4, 0xf8, 0xbe, 0x9f, 0x7f, 0xa0, 0xd7,
+	/* (2^193)P */ 0x5f, 0x33, 0xb6, 0x91, 0xc8, 0xa5, 0x3f, 0x5d, 0x7f, 0x38, 0x6e, 0x74, 0x20, 0x4a, 0xd6, 0x2b, 0x98, 0x2a, 0x41, 0x4b, 0x83, 0x64, 0x0b, 0x92, 0x7a, 0x06, 0x1e, 0xc6, 0x2c, 0xf6, 0xe4, 0x91, 0xe5, 0xb1, 0x2e, 0x6e, 0x4e, 0xa8, 0xc8, 0x14, 0x32, 0x57, 0x44, 0x1c, 0xe4, 0xb9, 0x7f, 0x54, 0x51, 0x08, 0x81, 0xaa, 0x4e, 0xce, 0xa1, 0x5d,
+	/* (2^194)P */ 0x5c, 0xd5, 0x9b, 0x5e, 0x7c, 0xb5, 0xb1, 0x52, 0x73, 0x00, 0x41, 0x56, 0x79, 0x08, 0x7e, 0x07, 0x28, 0x06, 0xa6, 0xfb, 0x7f, 0x69, 0xbd, 0x7a, 0x3c, 0xae, 0x9f, 0x39, 0xbb, 0x54, 0xa2, 0x79, 0xb9, 0x0e, 0x7f, 0xbb, 0xe0, 0xe6, 0xb7, 0x27, 0x64, 0x38, 0x45, 0xdb, 0x84, 0xe4, 0x61, 0x72, 0x3f, 0xe2, 0x24, 0xfe, 0x7a, 0x31, 0x9a, 0xc9,
+	/* (2^195)P */ 0xa1, 0xd2, 0xa4, 0xee, 0x24, 0x96, 0xe5, 0x5b, 0x79, 0x78, 0x3c, 0x7b, 0x82, 0x3b, 0x8b, 0x58, 0x0b, 0xa3, 0x63, 0x2d, 0xbc, 0x75, 0x46, 0xe8, 0x83, 0x1a, 0xc0, 0x2a, 0x92, 0x61, 0xa8, 0x75, 0x37, 0x3c, 0xbf, 0x0f, 0xef, 0x8f, 0x6c, 0x97, 0x75, 0x10, 0x05, 0x7a, 0xde, 0x23, 0xe8, 0x2a, 0x35, 0xeb, 0x41, 0x64, 0x7d, 0xcf, 0xe0, 0x52,
+	/* (2^196)P */ 0x4a, 0xd0, 0x49, 0x93, 0xae, 0xf3, 0x24, 0x8c, 0xe1, 0x09, 0x98, 0x45, 0xd8, 0xb9, 0xfe, 0x8e, 0x8c, 0xa8, 0x2c, 0xc9, 0x9f, 0xce, 0x01, 0xdc, 0x38, 0x11, 0xab, 0x85, 0xb9, 0xe8, 0x00, 0x51, 0xfd, 0x82, 0xe1, 0x9b, 0x4e, 0xfc, 0xb5, 0x2a, 0x0f, 0x8b, 0xda, 0x4e, 0x02, 0xca, 0xcc, 0xe3, 0x91, 0xc4, 0xe0, 0xcf, 0x7b, 0xd6, 0xe6, 0x6a,
+	/* (2^197)P */ 0xfe, 0x11, 0xd7, 0xaa, 0xe3, 0x0c, 0x52, 0x2e, 0x04, 0xe0, 0xe0, 0x61, 0xc8, 0x05, 0xd7, 0x31, 0x4c, 0xc3, 0x9b, 0x2d, 0xce, 0x59, 0xbe, 0x12, 0xb7, 0x30, 0x21, 0xfc, 0x81, 0xb8, 0x5e, 0x57, 0x73, 0xd0, 0xad, 0x8e, 0x9e, 0xe4, 0xeb, 0xcd, 0xcf, 0xd2, 0x0f, 0x01, 0x35, 0x16, 0xed, 0x7a, 0x43, 0x8e, 0x42, 0xdc, 0xea, 0x4c, 0xa8, 0x7c,
+	/* (2^198)P */ 0x37, 0x26, 0xcc, 0x76, 0x0b, 0xe5, 0x76, 0xdd, 0x3e, 0x19, 0x3c, 0xc4, 0x6c, 0x7f, 0xd0, 0x03, 0xc1, 0xb8, 0x59, 0x82, 0xca, 0x36, 0xc1, 0xe4, 0xc8, 0xb2, 0x83, 0x69, 0x9c, 0xc5, 0x9d, 0x12, 0x82, 0x1c, 0xea, 0xb2, 0x84, 0x9f, 0xf3, 0x52, 0x6b, 0xbb, 0xd8, 0x81, 0x56, 0x83, 0x04, 0x66, 0x05, 0x22, 0x49, 0x37, 0x93, 0xb1, 0xfd, 0xd5,
+	/* (2^199)P */ 0xaf, 0x96, 0xbf, 0x03, 0xbe, 0xe6, 0x5d, 0x78, 0x19, 0xba, 0x37, 0x46, 0x0a, 0x2b, 0x52, 0x7c, 0xd8, 0x51, 0x9e, 0x3d, 0x29, 0x42, 0xdb, 0x0e, 0x31, 0x20, 0x94, 0xf8, 0x43, 0x9a, 0x2d, 0x22, 0xd3, 0xe3, 0xa1, 0x79, 0x68, 0xfb, 0x2d, 0x7e, 0xd6, 0x79, 0xda, 0x0b, 0xc6, 0x5b, 0x76, 0x68, 0xf0, 0xfe, 0x72, 0x59, 0xbb, 0xa1, 0x9c, 0x74,
+	/* (2^200)P */ 0x0a, 0xd9, 0xec, 0xc5, 0xbd, 0xf0, 0xda, 0xcf, 0x82, 0xab, 0x46, 0xc5, 0x32, 0x13, 0xdc, 0x5b, 0xac, 0xc3, 0x53, 0x9a, 0x7f, 0xef, 0xa5, 0x40, 0x5a, 0x1f, 0xc1, 0x12, 0x91, 0x54, 0x83, 0x6a, 0xb0, 0x9a, 0x85, 0x4d, 0xbf, 0x36, 0x8e, 0xd3, 0xa2, 0x2b, 0xe5, 0xd6, 0xc6, 0xe1, 0x58, 0x5b, 0x82, 0x9b, 0xc8, 0xf2, 0x03, 0xba, 0xf5, 0x92,
+	/* (2^201)P */ 0xfb, 0x21, 0x7e, 0xde, 0xe7, 0xb4, 0xc0, 0x56, 0x86, 0x3a, 0x5b, 0x78, 0xf8, 0xf0, 0xf4, 0xe7, 0x5c, 0x00, 0xd2, 0xd7, 0xd6, 0xf8, 0x75, 0x5e, 0x0f, 0x3e, 0xd1, 0x4b, 0x77, 0xd8, 0xad, 0xb0, 0xc9, 0x8b, 0x59, 0x7d, 0x30, 0x76, 0x64, 0x7a, 0x76, 0xd9, 0x51, 0x69, 0xfc, 0xbd, 0x8e, 0xb5, 0x55, 0xe0, 0xd2, 0x07, 0x15, 0xa9, 0xf7, 0xa4,
+	/* (2^202)P */ 0xaa, 0x2d, 0x2f, 0x2b, 0x3c, 0x15, 0xdd, 0xcd, 0xe9, 0x28, 0x82, 0x4f, 0xa2, 0xaa, 0x31, 0x48, 0xcc, 0xfa, 0x07, 0x73, 0x8a, 0x34, 0x74, 0x0d, 0xab, 0x1a, 0xca, 0xd2, 0xbf, 0x3a, 0xdb, 0x1a, 0x5f, 0x50, 0x62, 0xf4, 0x6b, 0x83, 0x38, 0x43, 0x96, 0xee, 0x6b, 0x39, 0x1e, 0xf0, 0x17, 0x80, 0x1e, 0x9b, 0xed, 0x2b, 0x2f, 0xcc, 0x65, 0xf7,
+	/* (2^203)P */ 0x03, 0xb3, 0x23, 0x9c, 0x0d, 0xd1, 0xeb, 0x7e, 0x34, 0x17, 0x8a, 0x4c, 0xde, 0x54, 0x39, 0xc4, 0x11, 0x82, 0xd3, 0xa4, 0x00, 0x32, 0x95, 0x9c, 0xa6, 0x64, 0x76, 0x6e, 0xd6, 0x53, 0x27, 0xb4, 0x6a, 0x14, 0x8c, 0x54, 0xf6, 0x58, 0x9e, 0x22, 0x4a, 0x55, 0x18, 0x77, 0xd0, 0x08, 0x6b, 0x19, 0x8a, 0xb5, 0xe7, 0x19, 0xb8, 0x60, 0x92, 0xb1,
+	/* (2^204)P */ 0x66, 0xec, 0xf3, 0x12, 0xde, 0x67, 0x7f, 0xd4, 0x5b, 0xf6, 0x70, 0x64, 0x0a, 0xb5, 0xc2, 0xf9, 0xb3, 0x64, 0xab, 0x56, 0x46, 0xc7, 0x93, 0xc2, 0x8b, 0x2d, 0xd0, 0xd6, 0x39, 0x3b, 0x1f, 0xcd, 0xb3, 0xac, 0xcc, 0x2c, 0x27, 0x6a, 0xbc, 0xb3, 0x4b, 0xa8, 0x3c, 0x69, 0x20, 0xe2, 0x18, 0x35, 0x17, 0xe1, 0x8a, 0xd3, 0x11, 0x74, 0xaa, 0x4d,
+	/* (2^205)P */ 0x96, 0xc4, 0x16, 0x7e, 0xfd, 0xf5, 0xd0, 0x7d, 0x1f, 0x32, 0x1b, 0xdb, 0xa6, 0xfd, 0x51, 0x75, 0x4d, 0xd7, 0x00, 0xe5, 0x7f, 0x58, 0x5b, 0xeb, 0x4b, 0x6a, 0x78, 0xfe, 0xe5, 0xd6, 0x8f, 0x99, 0x17, 0xca, 0x96, 0x45, 0xf7, 0x52, 0xdf, 0x84, 0x06, 0x77, 0xb9, 0x05, 0x63, 0x5d, 0xe9, 0x91, 0xb1, 0x4b, 0x82, 0x5a, 0xdb, 0xd7, 0xca, 0x69,
+	/* (2^206)P */ 0x02, 0xd3, 0x38, 0x38, 0x87, 0xea, 0xbd, 0x9f, 0x11, 0xca, 0xf3, 0x21, 0xf1, 0x9b, 0x35, 0x97, 0x98, 0xff, 0x8e, 0x6d, 0x3d, 0xd6, 0xb2, 0xfa, 0x68, 0xcb, 0x7e, 0x62, 0x85, 0xbb, 0xc7, 0x5d, 0xee, 0x32, 0x30, 0x2e, 0x71, 0x96, 0x63, 0x43, 0x98, 0xc4, 0xa7, 0xde, 0x60, 0xb2, 0xd9, 0x43, 0x4a, 0xfa, 0x97, 0x2d, 0x5f, 0x21, 0xd4, 0xfe,
+	/* (2^207)P */ 0x3b, 0x20, 0x29, 0x07, 0x07, 0xb5, 0x78, 0xc3, 0xc7, 0xab, 0x56, 0xba, 0x40, 0xde, 0x1d, 0xcf, 0xc3, 0x00, 0x56, 0x21, 0x0c, 0xc8, 0x42, 0xd9, 0x0e, 0xcd, 0x02, 0x7c, 0x07, 0xb9, 0x11, 0xd7, 0x96, 0xaf, 0xff, 0xad, 0xc5, 0xba, 0x30, 0x6d, 0x82, 0x3a, 0xbf, 0xef, 0x7b, 0xf7, 0x0a, 0x74, 0xbd, 0x31, 0x0c, 0xe4, 0xec, 0x1a, 0xe5, 0xc5,
+	/* (2^208)P */ 0xcc, 0xf2, 0x28, 0x16, 0x12, 0xbf, 0xef, 0x85, 0xbc, 0xf7, 0xcb, 0x9f, 0xdb, 0xa8, 0xb2, 0x49, 0x53, 0x48, 0xa8, 0x24, 0xa8, 0x68, 0x8d, 0xbb, 0x21, 0x0a, 0x5a, 0xbd, 0xb2, 0x91, 0x61, 0x47, 0xc4, 0x43, 0x08, 0xa6, 0x19, 0xef, 0x8e, 0x88, 0x39, 0xc6, 0x33, 0x30, 0xf3, 0x0e, 0xc5, 0x92, 0x66, 0xd6, 0xfe, 0xc5, 0x12, 0xd9, 0x4c, 0x2d,
+	/* (2^209)P */ 0x30, 0x34, 0x07, 0xbf, 0x9c, 0x5a, 0x4e, 0x65, 0xf1, 0x39, 0x35, 0x38, 0xae, 0x7b, 0x55, 0xac, 0x6a, 0x92, 0x24, 0x7e, 0x50, 0xd3, 0xba, 0x78, 0x51, 0xfe, 0x4d, 0x32, 0x05, 0x11, 0xf5, 0x52, 0xf1, 0x31, 0x45, 0x39, 0x98, 0x7b, 0x28, 0x56, 0xc3, 0x5d, 0x4f, 0x07, 0x6f, 0x84, 0xb8, 0x1a, 0x58, 0x0b, 0xc4, 0x7c, 0xc4, 0x8d, 0x32, 0x8e,
+	/* (2^210)P */ 0x7e, 0xaf, 0x98, 0xce, 0xc5, 0x2b, 0x9d, 0xf6, 0xfa, 0x2c, 0xb6, 0x2a, 0x5a, 0x1d, 0xc0, 0x24, 0x8d, 0xa4, 0xce, 0xb1, 0x12, 0x01, 0xf9, 0x79, 0xc6, 0x79, 0x38, 0x0c, 0xd4, 0x07, 0xc9, 0xf7, 0x37, 0xa1, 0x0b, 0xfe, 0x72, 0xec, 0x5d, 0xd6, 0xb0, 0x1c, 0x70, 0xbe, 0x70, 0x01, 0x13, 0xe0, 0x86, 0x95, 0xc7, 0x2e, 0x12, 0x3b, 0xe6, 0xa6,
+	/* (2^211)P */ 0x24, 0x82, 0x67, 0xe0, 0x14, 0x7b, 0x56, 0x08, 0x38, 0x44, 0xdb, 0xa0, 0x3a, 0x05, 0x47, 0xb2, 0xc0, 0xac, 0xd1, 0xcc, 0x3f, 0x82, 0xb8, 0x8a, 0x88, 0xbc, 0xf5, 0x33, 0xa1, 0x35, 0x0f, 0xf6, 0xe2, 0xef, 0x6c, 0xf7, 0x37, 0x9e, 0xe8, 0x10, 0xca, 0xb0, 0x8e, 0x80, 0x86, 0x00, 0x23, 0xd0, 0x4a, 0x76, 0x9f, 0xf7, 0x2c, 0x52, 0x15, 0x0e,
+	/* (2^212)P */ 0x5e, 0x49, 0xe1, 0x2c, 0x9a, 0x01, 0x76, 0xa6, 0xb3, 0x07, 0x5b, 0xa4, 0x07, 0xef, 0x1d, 0xc3, 0x6a, 0xbb, 0x64, 0xbe, 0x71, 0x15, 0x6e, 0x32, 0x31, 0x46, 0x9a, 0x9e, 0x8f, 0x45, 0x73, 0xce, 0x0b, 0x94, 0x1a, 0x52, 0x07, 0xf4, 0x50, 0x30, 0x49, 0x53, 0x50, 0xfb, 0x71, 0x1f, 0x5a, 0x03, 0xa9, 0x76, 0xf2, 0x8f, 0x42, 0xff, 0xed, 0xed,
+	/* (2^213)P */ 0xed, 0x08, 0xdb, 0x91, 0x1c, 0xee, 0xa2, 0xb4, 0x47, 0xa2, 0xfa, 0xcb, 0x03, 0xd1, 0xff, 0x8c, 0xad, 0x64, 0x50, 0x61, 0xcd, 0xfc, 0x88, 0xa0, 0x31, 0x95, 0x30, 0xb9, 0x58, 0xdd, 0xd7, 0x43, 0xe4, 0x46, 0xc2, 0x16, 0xd9, 0x72, 0x4a, 0x56, 0x51, 0x70, 0x85, 0xf1, 0xa1, 0x80, 0x40, 0xd5, 0xba, 0x67, 0x81, 0xda, 0xcd, 0x03, 0xea, 0x51,
+	/* (2^214)P */ 0x42, 0x50, 0xf0, 0xef, 0x37, 0x61, 0x72, 0x85, 0xe1, 0xf1, 0xff, 0x6f, 0x3d, 0xe8, 0x7b, 0x21, 0x5c, 0xe5, 0x50, 0x03, 0xde, 0x00, 0xc1, 0xf7, 0x3a, 0x55, 0x12, 0x1c, 0x9e, 0x1e, 0xce, 0xd1, 0x2f, 0xaf, 0x05, 0x70, 0x5b, 0x47, 0xf2, 0x04, 0x7a, 0x89, 0xbc, 0x78, 0xa6, 0x65, 0x6c, 0xaa, 0x3c, 0xa2, 0x3c, 0x8b, 0x5c, 0xa9, 0x22, 0x48,
+	/* (2^215)P */ 0x7e, 0x8c, 0x8f, 0x2f, 0x60, 0xe3, 0x5a, 0x94, 0xd4, 0xce, 0xdd, 0x9d, 0x83, 0x3b, 0x77, 0x78, 0x43, 0x1d, 0xfd, 0x8f, 0xc8, 0xe8, 0x02, 0x90, 0xab, 0xf6, 0xc9, 0xfc, 0xf1, 0x63, 0xaa, 0x5f, 0x42, 0xf1, 0x78, 0x34, 0x64, 0x16, 0x75, 0x9c, 0x7d, 0xd0, 0xe4, 0x74, 0x5a, 0xa8, 0xfb, 0xcb, 0xac, 0x20, 0xa3, 0xc2, 0xa6, 0x20, 0xf8, 0x1b,
+	/* (2^216)P */ 0x00, 0x4f, 0x1e, 0x56, 0xb5, 0x34, 0xb2, 0x87, 0x31, 0xe5, 0xee, 0x8d, 0xf1, 0x41, 0x67, 0xb7, 0x67, 0x3a, 0x54, 0x86, 0x5c, 0xf0, 0x0b, 0x37, 0x2f, 0x1b, 0x92, 0x5d, 0x58, 0x93, 0xdc, 0xd8, 0x58, 0xcc, 0x9e, 0x67, 0xd0, 0x97, 0x3a, 0xaf, 0x49, 0x39, 0x2d, 0x3b, 0xd8, 0x98, 0xfb, 0x76, 0x6b, 0xe7, 0xaf, 0xc3, 0x45, 0x44, 0x53, 0x94,
+	/* (2^217)P */ 0x30, 0xbd, 0x90, 0x75, 0xd3, 0xbd, 0x3b, 0x58, 0x27, 0x14, 0x9f, 0x6b, 0xd4, 0x31, 0x99, 0xcd, 0xde, 0x3a, 0x21, 0x1e, 0xb4, 0x02, 0xe4, 0x33, 0x04, 0x02, 0xb0, 0x50, 0x66, 0x68, 0x90, 0xdd, 0x7b, 0x69, 0x31, 0xd9, 0xcf, 0x68, 0x73, 0xf1, 0x60, 0xdd, 0xc8, 0x1d, 0x5d, 0xe3, 0xd6, 0x5b, 0x2a, 0xa4, 0xea, 0xc4, 0x3f, 0x08, 0xcd, 0x9c,
+	/* (2^218)P */ 0x6b, 0x1a, 0xbf, 0x55, 0xc1, 0x1b, 0x0c, 0x05, 0x09, 0xdf, 0xf5, 0x5e, 0xa3, 0x77, 0x95, 0xe9, 0xdf, 0x19, 0xdd, 0xc7, 0x94, 0xcb, 0x06, 0x73, 0xd0, 0x88, 0x02, 0x33, 0x94, 0xca, 0x7a, 0x2f, 0x8e, 0x3d, 0x72, 0x61, 0x2d, 0x4d, 0xa6, 0x61, 0x1f, 0x32, 0x5e, 0x87, 0x53, 0x36, 0x11, 0x15, 0x20, 0xb3, 0x5a, 0x57, 0x51, 0x93, 0x20, 0xd8,
+	/* (2^219)P */ 0xb7, 0x56, 0xf4, 0xab, 0x7d, 0x0c, 0xfb, 0x99, 0x1a, 0x30, 0x29, 0xb0, 0x75, 0x2a, 0xf8, 0x53, 0x71, 0x23, 0xbd, 0xa7, 0xd8, 0x0a, 0xe2, 0x27, 0x65, 0xe9, 0x74, 0x26, 0x98, 0x4a, 0x69, 0x19, 0xb2, 0x4d, 0x0a, 0x17, 0x98, 0xb2, 0xa9, 0x57, 0x4e, 0xf6, 0x86, 0xc8, 0x01, 0xa4, 0xc6, 0x98, 0xad, 0x5a, 0x90, 0x2c, 0x05, 0x46, 0x64, 0xb7,
+	/* (2^220)P */ 0x7b, 0x91, 0xdf, 0xfc, 0xf8, 0x1c, 0x8c, 0x15, 0x9e, 0xf7, 0xd5, 0xa8, 0xe8, 0xe7, 0xe3, 0xa3, 0xb0, 0x04, 0x74, 0xfa, 0x78, 0xfb, 0x26, 0xbf, 0x67, 0x42, 0xf9, 0x8c, 0x9b, 0xb4, 0x69, 0x5b, 0x02, 0x13, 0x6d, 0x09, 0x6c, 0xd6, 0x99, 0x61, 0x7b, 0x89, 0x4a, 0x67, 0x75, 0xa3, 0x98, 0x13, 0x23, 0x1d, 0x18, 0x24, 0x0e, 0xef, 0x41, 0x79,
+	/* (2^221)P */ 0x86, 0x33, 0xab, 0x08, 0xcb, 0xbf, 0x1e, 0x76, 0x3c, 0x0b, 0xbd, 0x30, 0xdb, 0xe9, 0xa3, 0x35, 0x87, 0x1b, 0xe9, 0x07, 0x00, 0x66, 0x7f, 0x3b, 0x35, 0x0c, 0x8a, 0x3f, 0x61, 0xbc, 0xe0, 0xae, 0xf6, 0xcc, 0x54, 0xe1, 0x72, 0x36, 0x2d, 0xee, 0x93, 0x24, 0xf8, 0xd7, 0xc5, 0xf9, 0xcb, 0xb0, 0xe5, 0x88, 0x0d, 0x23, 0x4b, 0x76, 0x15, 0xa2,
+	/* (2^222)P */ 0x37, 0xdb, 0x83, 0xd5, 0x6d, 0x06, 0x24, 0x37, 0x1b, 0x15, 0x85, 0x15, 0xe2, 0xc0, 0x4e, 0x02, 0xa9, 0x6d, 0x0a, 0x3a, 0x94, 0x4a, 0x6f, 0x49, 0x00, 0x01, 0x72, 0xbb, 0x60, 0x14, 0x35, 0xae, 0xb4, 0xc6, 0x01, 0x0a, 0x00, 0x9e, 0xc3, 0x58, 0xc5, 0xd1, 0x5e, 0x30, 0x73, 0x96, 0x24, 0x85, 0x9d, 0xf0, 0xf9, 0xec, 0x09, 0xd3, 0xe7, 0x70,
+	/* (2^223)P */ 0xf3, 0xbd, 0x96, 0x87, 0xe9, 0x71, 0xbd, 0xd6, 0xa2, 0x45, 0xeb, 0x0a, 0xcd, 0x2c, 0xf1, 0x72, 0xa6, 0x31, 0xa9, 0x6f, 0x09, 0xa1, 0x5e, 0xdd, 0xc8, 0x8d, 0x0d, 0xbc, 0x5a, 0x8d, 0xb1, 0x2c, 0x9a, 0xcc, 0x37, 0x74, 0xc2, 0xa9, 0x4e, 0xd6, 0xc0, 0x3c, 0xa0, 0x23, 0xb0, 0xa0, 0x77, 0x14, 0x80, 0x45, 0x71, 0x6a, 0x2d, 0x41, 0xc3, 0x82,
+	/* (2^224)P */ 0x37, 0x44, 0xec, 0x8a, 0x3e, 0xc1, 0x0c, 0xa9, 0x12, 0x9c, 0x08, 0x88, 0xcb, 0xd9, 0xf8, 0xba, 0x00, 0xd6, 0xc3, 0xdf, 0xef, 0x7a, 0x44, 0x7e, 0x25, 0x69, 0xc9, 0xc1, 0x46, 0xe5, 0x20, 0x9e, 0xcc, 0x0b, 0x05, 0x3e, 0xf4, 0x78, 0x43, 0x0c, 0xa6, 0x2f, 0xc1, 0xfa, 0x70, 0xb2, 0x3c, 0x31, 0x7a, 0x63, 0x58, 0xab, 0x17, 0xcf, 0x4c, 0x4f,
+	/* (2^225)P */ 0x2b, 0x08, 0x31, 0x59, 0x75, 0x8b, 0xec, 0x0a, 0xa9, 0x79, 0x70, 0xdd, 0xf1, 0x11, 0xc3, 0x11, 0x1f, 0xab, 0x37, 0xaa, 0x26, 0xea, 0x53, 0xc4, 0x79, 0xa7, 0x91, 0x00, 0xaa, 0x08, 0x42, 0xeb, 0x8b, 0x8b, 0xe8, 0xc3, 0x2f, 0xb8, 0x78, 0x90, 0x38, 0x0e, 0x8a, 0x42, 0x0c, 0x0f, 0xbf, 0x3e, 0xf8, 0xd8, 0x07, 0xcf, 0x6a, 0x34, 0xc9, 0xfa,
+	/* (2^226)P */ 0x11, 0xe0, 0x76, 0x4d, 0x23, 0xc5, 0xa6, 0xcc, 0x9f, 0x9a, 0x2a, 0xde, 0x3a, 0xb5, 0x92, 0x39, 0x19, 0x8a, 0xf1, 0x8d, 0xf9, 0x4d, 0xc9, 0xb4, 0x39, 0x9f, 0x57, 0xd8, 0x72, 0xab, 0x1d, 0x61, 0x6a, 0xb2, 0xff, 0x52, 0xba, 0x54, 0x0e, 0xfb, 0x83, 0x30, 0x8a, 0xf7, 0x3b, 0xf4, 0xd8, 0xae, 0x1a, 0x94, 0x3a, 0xec, 0x63, 0xfe, 0x6e, 0x7c,
+	/* (2^227)P */ 0xdc, 0x70, 0x8e, 0x55, 0x44, 0xbf, 0xd2, 0x6a, 0xa0, 0x14, 0x61, 0x89, 0xd5, 0x55, 0x45, 0x3c, 0xf6, 0x40, 0x0d, 0x83, 0x85, 0x44, 0xb4, 0x62, 0x56, 0xfe, 0x60, 0xd7, 0x07, 0x1d, 0x47, 0x30, 0x3b, 0x73, 0xa4, 0xb5, 0xb7, 0xea, 0xac, 0xda, 0xf1, 0x17, 0xaa, 0x60, 0xdf, 0xe9, 0x84, 0xda, 0x31, 0x32, 0x61, 0xbf, 0xd0, 0x7e, 0x8a, 0x02,
+	/* (2^228)P */ 0xb9, 0x51, 0xb3, 0x89, 0x21, 0x5d, 0xa2, 0xfe, 0x79, 0x2a, 0xb3, 0x2a, 0x3b, 0xe6, 0x6f, 0x2b, 0x22, 0x03, 0xea, 0x7b, 0x1f, 0xaf, 0x85, 0xc3, 0x38, 0x55, 0x5b, 0x8e, 0xb4, 0xaa, 0x77, 0xfe, 0x03, 0x6e, 0xda, 0x91, 0x24, 0x0c, 0x48, 0x39, 0x27, 0x43, 0x16, 0xd2, 0x0a, 0x0d, 0x43, 0xa3, 0x0e, 0xca, 0x45, 0xd1, 0x7f, 0xf5, 0xd3, 0x16,
+	/* (2^229)P */ 0x3d, 0x32, 0x9b, 0x38, 0xf8, 0x06, 0x93, 0x78, 0x5b, 0x50, 0x2b, 0x06, 0xd8, 0x66, 0xfe, 0xab, 0x9b, 0x58, 0xc7, 0xd1, 0x4d, 0xd5, 0xf8, 0x3b, 0x10, 0x7e, 0x85, 0xde, 0x58, 0x4e, 0xdf, 0x53, 0xd9, 0x58, 0xe0, 0x15, 0x81, 0x9f, 0x1a, 0x78, 0xfc, 0x9f, 0x10, 0xc2, 0x23, 0xd6, 0x78, 0xd1, 0x9d, 0xd2, 0xd5, 0x1c, 0x53, 0xe2, 0xc9, 0x76,
+	/* (2^230)P */ 0x98, 0x1e, 0x38, 0x7b, 0x71, 0x18, 0x4b, 0x15, 0xaf, 0xa1, 0xa6, 0x98, 0xcb, 0x26, 0xa3, 0xc8, 0x07, 0x46, 0xda, 0x3b, 0x70, 0x65, 0xec, 0x7a, 0x2b, 0x34, 0x94, 0xa8, 0xb6, 0x14, 0xf8, 0x1a, 0xce, 0xf7, 0xc8, 0x60, 0xf3, 0x88, 0xf4, 0x33, 0x60, 0x7b, 0xd1, 0x02, 0xe7, 0xda, 0x00, 0x4a, 0xea, 0xd2, 0xfd, 0x88, 0xd2, 0x99, 0x28, 0xf3,
+	/* (2^231)P */ 0x28, 0x24, 0x1d, 0x26, 0xc2, 0xeb, 0x8b, 0x3b, 0xb4, 0x6b, 0xbe, 0x6b, 0x77, 0xff, 0xf3, 0x21, 0x3b, 0x26, 0x6a, 0x8c, 0x8e, 0x2a, 0x44, 0xa8, 0x01, 0x2b, 0x71, 0xea, 0x64, 0x30, 0xfd, 0xfd, 0x95, 0xcb, 0x39, 0x38, 0x48, 0xfa, 0x96, 0x97, 0x8c, 0x2f, 0x33, 0xca, 0x03, 0xe6, 0xd7, 0x94, 0x55, 0x6c, 0xc3, 0xb3, 0xa8, 0xf7, 0xae, 0x8c,
+	/* (2^232)P */ 0xea, 0x62, 0x8a, 0xb4, 0xeb, 0x74, 0xf7, 0xb8, 0xae, 0xc5, 0x20, 0x71, 0x06, 0xd6, 0x7c, 0x62, 0x9b, 0x69, 0x74, 0xef, 0xa7, 0x6d, 0xd6, 0x8c, 0x37, 0xb9, 0xbf, 0xcf, 0xeb, 0xe4, 0x2f, 0x04, 0x02, 0x21, 0x7d, 0x75, 0x6b, 0x92, 0x48, 0xf8, 0x70, 0xad, 0x69, 0xe2, 0xea, 0x0e, 0x88, 0x67, 0x72, 0xcc, 0x2d, 0x10, 0xce, 0x2d, 0xcf, 0x65,
+	/* (2^233)P */ 0x49, 0xf3, 0x57, 0x64, 0xe5, 0x5c, 0xc5, 0x65, 0x49, 0x97, 0xc4, 0x8a, 0xcc, 0xa9, 0xca, 0x94, 0x7b, 0x86, 0x88, 0xb6, 0x51, 0x27, 0x69, 0xa5, 0x0f, 0x8b, 0x06, 0x59, 0xa0, 0x94, 0xef, 0x63, 0x1a, 0x01, 0x9e, 0x4f, 0xd2, 0x5a, 0x93, 0xc0, 0x7c, 0xe6, 0x61, 0x77, 0xb6, 0xf5, 0x40, 0xd9, 0x98, 0x43, 0x5b, 0x56, 0x68, 0xe9, 0x37, 0x8f,
+	/* (2^234)P */ 0xee, 0x87, 0xd2, 0x05, 0x1b, 0x39, 0x89, 0x10, 0x07, 0x6d, 0xe8, 0xfd, 0x8b, 0x4d, 0xb2, 0xa7, 0x7b, 0x1e, 0xa0, 0x6c, 0x0d, 0x3d, 0x3d, 0x49, 0xba, 0x61, 0x36, 0x1f, 0xc2, 0x84, 0x4a, 0xcc, 0x87, 0xa9, 0x1b, 0x23, 0x04, 0xe2, 0x3e, 0x97, 0xe1, 0xdb, 0xd5, 0x5a, 0xe8, 0x41, 0x6b, 0xe5, 0x5a, 0xa1, 0x99, 0xe5, 0x7b, 0xa7, 0xe0, 0x3b,
+	/* (2^235)P */ 0xea, 0xa3, 0x6a, 0xdd, 0x77, 0x7f, 0x77, 0x41, 0xc5, 0x6a, 0xe4, 0xaf, 0x11, 0x5f, 0x88, 0xa5, 0x10, 0xee, 0xd0, 0x8c, 0x0c, 0xb4, 0xa5, 0x2a, 0xd0, 0xd8, 0x1d, 0x47, 0x06, 0xc0, 0xd5, 0xce, 0x51, 0x54, 0x9b, 0x2b, 0xe6, 0x2f, 0xe7, 0xe7, 0x31, 0x5f, 0x5c, 0x23, 0x81, 0x3e, 0x03, 0x93, 0xaa, 0x2d, 0x71, 0x84, 0xa0, 0x89, 0x32, 0xa6,
+	/* (2^236)P */ 0x55, 0xa3, 0x13, 0x92, 0x4e, 0x93, 0x7d, 0xec, 0xca, 0x57, 0xfb, 0x37, 0xae, 0xd2, 0x18, 0x2e, 0x54, 0x05, 0x6c, 0xd1, 0x28, 0xca, 0x90, 0x40, 0x82, 0x2e, 0x79, 0xc6, 0x5a, 0xc7, 0xdd, 0x84, 0x93, 0xdf, 0x15, 0xb8, 0x1f, 0xb1, 0xf9, 0xaf, 0x2c, 0xe5, 0x32, 0xcd, 0xc2, 0x99, 0x6d, 0xac, 0x85, 0x5c, 0x63, 0xd3, 0xe2, 0xff, 0x24, 0xda,
+	/* (2^237)P */ 0x2d, 0x8d, 0xfd, 0x65, 0xcc, 0xe5, 0x02, 0xa0, 0xe5, 0xb9, 0xec, 0x59, 0x09, 0x50, 0x27, 0xb7, 0x3d, 0x2a, 0x79, 0xb2, 0x76, 0x5d, 0x64, 0x95, 0xf8, 0xc5, 0xaf, 0x8a, 0x62, 0x11, 0x5c, 0x56, 0x1c, 0x05, 0x64, 0x9e, 0x5e, 0xbd, 0x54, 0x04, 0xe6, 0x9e, 0xab, 0xe6, 0x22, 0x7e, 0x42, 0x54, 0xb5, 0xa5, 0xd0, 0x8d, 0x28, 0x6b, 0x0f, 0x0b,
+	/* (2^238)P */ 0x2d, 0xb2, 0x8c, 0x59, 0x10, 0x37, 0x84, 0x3b, 0x9b, 0x65, 0x1b, 0x0f, 0x10, 0xf9, 0xea, 0x60, 0x1b, 0x02, 0xf5, 0xee, 0x8b, 0xe6, 0x32, 0x7d, 0x10, 0x7f, 0x5f, 0x8c, 0x72, 0x09, 0x4e, 0x1f, 0x29, 0xff, 0x65, 0xcb, 0x3e, 0x3a, 0xd2, 0x96, 0x50, 0x1e, 0xea, 0x64, 0x99, 0xb5, 0x4c, 0x7a, 0x69, 0xb8, 0x95, 0xae, 0x48, 0xc0, 0x7c, 0xb1,
+	/* (2^239)P */ 0xcd, 0x7c, 0x4f, 0x3e, 0xea, 0xf3, 0x90, 0xcb, 0x12, 0x76, 0xd1, 0x17, 0xdc, 0x0d, 0x13, 0x0f, 0xfd, 0x4d, 0xb5, 0x1f, 0xe4, 0xdd, 0xf2, 0x4d, 0x58, 0xea, 0xa5, 0x66, 0x92, 0xcf, 0xe5, 0x54, 0xea, 0x9b, 0x35, 0x83, 0x1a, 0x44, 0x8e, 0x62, 0x73, 0x45, 0x98, 0xa3, 0x89, 0x95, 0x52, 0x93, 0x1a, 0x8d, 0x63, 0x0f, 0xc2, 0x57, 0x3c, 0xb1,
+	/* (2^240)P */ 0x72, 0xb4, 0xdf, 0x51, 0xb7, 0xf6, 0x52, 0xa2, 0x14, 0x56, 0xe5, 0x0a, 0x2e, 0x75, 0x81, 0x02, 0xee, 0x93, 0x48, 0x0a, 0x92, 0x4e, 0x0c, 0x0f, 0xdf, 0x09, 0x89, 0x99, 0xf6, 0xf9, 0x22, 0xa2, 0x32, 0xf8, 0xb0, 0x76, 0x0c, 0xb2, 0x4d, 0x6e, 0xbe, 0x83, 0x35, 0x61, 0x44, 0xd2, 0x58, 0xc7, 0xdd, 0x14, 0xcf, 0xc3, 0x4b, 0x7c, 0x07, 0xee,
+	/* (2^241)P */ 0x8b, 0x03, 0xee, 0xcb, 0xa7, 0x2e, 0x28, 0xbd, 0x97, 0xd1, 0x4c, 0x2b, 0xd1, 0x92, 0x67, 0x5b, 0x5a, 0x12, 0xbf, 0x29, 0x17, 0xfc, 0x50, 0x09, 0x74, 0x76, 0xa2, 0xd4, 0x82, 0xfd, 0x2c, 0x0c, 0x90, 0xf7, 0xe7, 0xe5, 0x9a, 0x2c, 0x16, 0x40, 0xb9, 0x6c, 0xd9, 0xe0, 0x22, 0x9e, 0xf8, 0xdd, 0x73, 0xe4, 0x7b, 0x9e, 0xbe, 0x4f, 0x66, 0x22,
+	/* (2^242)P */ 0xa4, 0x10, 0xbe, 0xb8, 0x83, 0x3a, 0x77, 0x8e, 0xea, 0x0a, 0xc4, 0x97, 0x3e, 0xb6, 0x6c, 0x81, 0xd7, 0x65, 0xd9, 0xf7, 0xae, 0xe6, 0xbe, 0xab, 0x59, 0x81, 0x29, 0x4b, 0xff, 0xe1, 0x0f, 0xc3, 0x2b, 0xad, 0x4b, 0xef, 0xc4, 0x50, 0x9f, 0x88, 0x31, 0xf2, 0xde, 0x80, 0xd6, 0xf4, 0x20, 0x9c, 0x77, 0x9b, 0xbe, 0xbe, 0x08, 0xf5, 0xf0, 0x95,
+	/* (2^243)P */ 0x0e, 0x7c, 0x7b, 0x7c, 0xb3, 0xd8, 0x83, 0xfc, 0x8c, 0x75, 0x51, 0x74, 0x1b, 0xe1, 0x6d, 0x11, 0x05, 0x46, 0x24, 0x0d, 0xa4, 0x2b, 0x32, 0xfd, 0x2c, 0x4e, 0x21, 0xdf, 0x39, 0x6b, 0x96, 0xfc, 0xff, 0x92, 0xfc, 0x35, 0x0d, 0x9a, 0x4b, 0xc0, 0x70, 0x46, 0x32, 0x7d, 0xc0, 0xc4, 0x04, 0xe0, 0x2d, 0x83, 0xa7, 0x00, 0xc7, 0xcb, 0xb4, 0x8f,
+	/* (2^244)P */ 0xa9, 0x5a, 0x7f, 0x0e, 0xdd, 0x2c, 0x85, 0xaa, 0x4d, 0xac, 0xde, 0xb3, 0xb6, 0xaf, 0xe6, 0xd1, 0x06, 0x7b, 0x2c, 0xa4, 0x01, 0x19, 0x22, 0x7d, 0x78, 0xf0, 0x3a, 0xea, 0x89, 0xfe, 0x21, 0x61, 0x6d, 0xb8, 0xfe, 0xa5, 0x2a, 0xab, 0x0d, 0x7b, 0x51, 0x39, 0xb6, 0xde, 0xbc, 0xf0, 0xc5, 0x48, 0xd7, 0x09, 0x82, 0x6e, 0x66, 0x75, 0xc5, 0xcd,
+	/* (2^245)P */ 0xee, 0xdf, 0x2b, 0x6c, 0xa8, 0xde, 0x61, 0xe1, 0x27, 0xfa, 0x2a, 0x0f, 0x68, 0xe7, 0x7a, 0x9b, 0x13, 0xe9, 0x56, 0xd2, 0x1c, 0x3d, 0x2f, 0x3c, 0x7a, 0xf6, 0x6f, 0x45, 0xee, 0xe8, 0xf4, 0xa0, 0xa6, 0xe8, 0xa5, 0x27, 0xee, 0xf2, 0x85, 0xa9, 0xd5, 0x0e, 0xa9, 0x26, 0x60, 0xfe, 0xee, 0xc7, 0x59, 0x99, 0x5e, 0xa3, 0xdf, 0x23, 0x36, 0xd5,
+	/* (2^246)P */ 0x15, 0x66, 0x6f, 0xd5, 0x78, 0xa4, 0x0a, 0xf7, 0xb1, 0xe8, 0x75, 0x6b, 0x48, 0x7d, 0xa6, 0x4d, 0x3d, 0x36, 0x9b, 0xc7, 0xcc, 0x68, 0x9a, 0xfe, 0x2f, 0x39, 0x2a, 0x51, 0x31, 0x39, 0x7d, 0x73, 0x6f, 0xc8, 0x74, 0x72, 0x6f, 0x6e, 0xda, 0x5f, 0xad, 0x48, 0xc8, 0x40, 0xe1, 0x06, 0x01, 0x36, 0xa1, 0x88, 0xc8, 0x99, 0x9c, 0xd1, 0x11, 0x8f,
+	/* (2^247)P */ 0xab, 0xc5, 0xcb, 0xcf, 0xbd, 0x73, 0x21, 0xd0, 0x82, 0xb1, 0x2e, 0x2d, 0xd4, 0x36, 0x1b, 0xed, 0xa9, 0x8a, 0x26, 0x79, 0xc4, 0x17, 0xae, 0xe5, 0x09, 0x0a, 0x0c, 0xa4, 0x21, 0xa0, 0x6e, 0xdd, 0x62, 0x8e, 0x44, 0x62, 0xcc, 0x50, 0xff, 0x93, 0xb3, 0x9a, 0x72, 0x8c, 0x3f, 0xa1, 0xa6, 0x4d, 0x87, 0xd5, 0x1c, 0x5a, 0xc0, 0x0b, 0x1a, 0xd6,
+	/* (2^248)P */ 0x67, 0x36, 0x6a, 0x1f, 0x96, 0xe5, 0x80, 0x20, 0xa9, 0xe8, 0x0b, 0x0e, 0x21, 0x29, 0x3f, 0xc8, 0x0a, 0x6d, 0x27, 0x47, 0xca, 0xd9, 0x05, 0x55, 0xbf, 0x11, 0xcf, 0x31, 0x7a, 0x37, 0xc7, 0x90, 0xa9, 0xf4, 0x07, 0x5e, 0xd5, 0xc3, 0x92, 0xaa, 0x95, 0xc8, 0x23, 0x2a, 0x53, 0x45, 0xe3, 0x3a, 0x24, 0xe9, 0x67, 0x97, 0x3a, 0x82, 0xf9, 0xa6,
+	/* (2^249)P */ 0x92, 0x9e, 0x6d, 0x82, 0x67, 0xe9, 0xf9, 0x17, 0x96, 0x2c, 0xa7, 0xd3, 0x89, 0xf9, 0xdb, 0xd8, 0x20, 0xc6, 0x2e, 0xec, 0x4a, 0x76, 0x64, 0xbf, 0x27, 0x40, 0xe2, 0xb4, 0xdf, 0x1f, 0xa0, 0xef, 0x07, 0x80, 0xfb, 0x8e, 0x12, 0xf8, 0xb8, 0xe1, 0xc6, 0xdf, 0x7c, 0x69, 0x35, 0x5a, 0xe1, 0x8e, 0x5d, 0x69, 0x84, 0x56, 0xb6, 0x31, 0x1c, 0x0b,
+	/* (2^250)P */ 0xd6, 0x94, 0x5c, 0xef, 0xbb, 0x46, 0x45, 0x44, 0x5b, 0xa1, 0xae, 0x03, 0x65, 0xdd, 0xb5, 0x66, 0x88, 0x35, 0x29, 0x95, 0x16, 0x54, 0xa6, 0xf5, 0xc9, 0x78, 0x34, 0xe6, 0x0f, 0xc4, 0x2b, 0x5b, 0x79, 0x51, 0x68, 0x48, 0x3a, 0x26, 0x87, 0x05, 0x70, 0xaf, 0x8b, 0xa6, 0xc7, 0x2e, 0xb3, 0xa9, 0x10, 0x01, 0xb0, 0xb9, 0x31, 0xfd, 0xdc, 0x80,
+	/* (2^251)P */ 0x25, 0xf2, 0xad, 0xd6, 0x75, 0xa3, 0x04, 0x05, 0x64, 0x8a, 0x97, 0x60, 0x27, 0x2a, 0xe5, 0x6d, 0xb0, 0x73, 0xf4, 0x07, 0x2a, 0x9d, 0xe9, 0x46, 0xb4, 0x1c, 0x51, 0xf8, 0x63, 0x98, 0x7e, 0xe5, 0x13, 0x51, 0xed, 0x98, 0x65, 0x98, 0x4f, 0x8f, 0xe7, 0x7e, 0x72, 0xd7, 0x64, 0x11, 0x2f, 0xcd, 0x12, 0xf8, 0xc4, 0x63, 0x52, 0x0f, 0x7f, 0xc4,
+	/* (2^252)P */ 0x5c, 0xd9, 0x85, 0x63, 0xc7, 0x8a, 0x65, 0x9a, 0x25, 0x83, 0x31, 0x73, 0x49, 0xf0, 0x93, 0x96, 0x70, 0x67, 0x6d, 0xb1, 0xff, 0x95, 0x54, 0xe4, 0xf8, 0x15, 0x6c, 0x5f, 0xbd, 0xf6, 0x0f, 0x38, 0x7b, 0x68, 0x7d, 0xd9, 0x3d, 0xf0, 0xa9, 0xa0, 0xe4, 0xd1, 0xb6, 0x34, 0x6d, 0x14, 0x16, 0xc2, 0x4c, 0x30, 0x0e, 0x67, 0xd3, 0xbe, 0x2e, 0xc0,
+	/* (2^253)P */ 0x06, 0x6b, 0x52, 0xc8, 0x14, 0xcd, 0xae, 0x03, 0x93, 0xea, 0xc1, 0xf2, 0xf6, 0x8b, 0xc5, 0xb6, 0xdc, 0x82, 0x42, 0x29, 0x94, 0xe0, 0x25, 0x6c, 0x3f, 0x9f, 0x5d, 0xe4, 0x96, 0xf6, 0x8e, 0x3f, 0xf9, 0x72, 0xc4, 0x77, 0x60, 0x8b, 0xa4, 0xf9, 0xa8, 0xc3, 0x0a, 0x81, 0xb1, 0x97, 0x70, 0x18, 0xab, 0xea, 0x37, 0x8a, 0x08, 0xc7, 0xe2, 0x95,
+	/* (2^254)P */ 0x94, 0x49, 0xd9, 0x5f, 0x76, 0x72, 0x82, 0xad, 0x2d, 0x50, 0x1a, 0x7a, 0x5b, 0xe6, 0x95, 0x1e, 0x95, 0x65, 0x87, 0x1c, 0x52, 0xd7, 0x44, 0xe6, 0x9b, 0x56, 0xcd, 0x6f, 0x05, 0xff, 0x67, 0xc5, 0xdb, 0xa2, 0xac, 0xe4, 0xa2, 0x28, 0x63, 0x5f, 0xfb, 0x0c, 0x3b, 0xf1, 0x87, 0xc3, 0x36, 0x78, 0x3f, 0x77, 0xfa, 0x50, 0x85, 0xf9, 0xd7, 0x82,
+	/* (2^255)P */ 0x64, 0xc0, 0xe0, 0xd8, 0x2d, 0xed, 0xcb, 0x6a, 0xfd, 0xcd, 0xbc, 0x7e, 0x9f, 0xc8, 0x85, 0xe9, 0xc1, 0x7c, 0x0f, 0xe5, 0x18, 0xea, 0xd4, 0x51, 0xad, 0x59, 0x13, 0x75, 0xd9, 0x3d, 0xd4, 0x8a, 0xb2, 0xbe, 0x78, 0x52, 0x2b, 0x52, 0x94, 0x37, 0x41, 0xd6, 0xb4, 0xb6, 0x45, 0x20, 0x76, 0xe0, 0x1f, 0x31, 0xdb, 0xb1, 0xa1, 0x43, 0xf0, 0x18,
+	/* (2^256)P */ 0x74, 0xa9, 0xa4, 0xa9, 0xdd, 0x6e, 0x3e, 0x68, 0xe5, 0xc3, 0x2e, 0x92, 0x17, 0xa4, 0xcb, 0x80, 0xb1, 0xf0, 0x06, 0x93, 0xef, 0xe6, 0x00, 0xe6, 0x3b, 0xb1, 0x32, 0x65, 0x7b, 0x83, 0xb6, 0x8a, 0x49, 0x1b, 0x14, 0x89, 0xee, 0xba, 0xf5, 0x6a, 0x8d, 0x36, 0xef, 0xb0, 0xd8, 0xb2, 0x16, 0x99, 0x17, 0x35, 0x02, 0x16, 0x55, 0x58, 0xdd, 0x82,
+	/* (2^257)P */ 0x36, 0x95, 0xe8, 0xf4, 0x36, 0x42, 0xbb, 0xc5, 0x3e, 0xfa, 0x30, 0x84, 0x9e, 0x59, 0xfd, 0xd2, 0x95, 0x42, 0xf8, 0x64, 0xd9, 0xb9, 0x0e, 0x9f, 0xfa, 0xd0, 0x7b, 0x20, 0x31, 0x77, 0x48, 0x29, 0x4d, 0xd0, 0x32, 0x57, 0x56, 0x30, 0xa6, 0x17, 0x53, 0x04, 0xbf, 0x08, 0x28, 0xec, 0xb8, 0x46, 0xc1, 0x03, 0x89, 0xdc, 0xed, 0xa0, 0x35, 0x53,
+	/* (2^258)P */ 0xc5, 0x7f, 0x9e, 0xd8, 0xc5, 0xba, 0x5f, 0x68, 0xc8, 0x23, 0x75, 0xea, 0x0d, 0xd9, 0x5a, 0xfd, 0x61, 0x1a, 0xa3, 0x2e, 0x45, 0x63, 0x14, 0x55, 0x86, 0x21, 0x29, 0xbe, 0xef, 0x5e, 0x50, 0xe5, 0x18, 0x59, 0xe7, 0xe3, 0xce, 0x4d, 0x8c, 0x15, 0x8f, 0x89, 0x66, 0x44, 0x52, 0x3d, 0xfa, 0xc7, 0x9a, 0x59, 0x90, 0x8e, 0xc0, 0x06, 0x3f, 0xc9,
+	/* (2^259)P */ 0x8e, 0x04, 0xd9, 0x16, 0x50, 0x1d, 0x8c, 0x9f, 0xd5, 0xe3, 0xce, 0xfd, 0x47, 0x04, 0x27, 0x4d, 0xc2, 0xfa, 0x71, 0xd9, 0x0b, 0xb8, 0x65, 0xf4, 0x11, 0xf3, 0x08, 0xee, 0x81, 0xc8, 0x67, 0x99, 0x0b, 0x8d, 0x77, 0xa3, 0x4f, 0xb5, 0x9b, 0xdb, 0x26, 0xf1, 0x97, 0xeb, 0x04, 0x54, 0xeb, 0x80, 0x08, 0x1d, 0x1d, 0xf6, 0x3d, 0x1f, 0x5a, 0xb8,
+	/* (2^260)P */ 0xb7, 0x9c, 0x9d, 0xee, 0xb9, 0x5c, 0xad, 0x0d, 0x9e, 0xfd, 0x60, 0x3c, 0x27, 0x4e, 0xa2, 0x95, 0xfb, 0x64, 0x7e, 0x79, 0x64, 0x87, 0x10, 0xb4, 0x73, 0xe0, 0x9d, 0x46, 0x4d, 0x3d, 0xee, 0x83, 0xe4, 0x16, 0x88, 0x97, 0xe6, 0x4d, 0xba, 0x70, 0xb6, 0x96, 0x7b, 0xff, 0x4b, 0xc8, 0xcf, 0x72, 0x83, 0x3e, 0x5b, 0x24, 0x2e, 0x57, 0xf1, 0x82,
+	/* (2^261)P */ 0x30, 0x71, 0x40, 0x51, 0x4f, 0x44, 0xbb, 0xc7, 0xf0, 0x54, 0x6e, 0x9d, 0xeb, 0x15, 0xad, 0xf8, 0x61, 0x43, 0x5a, 0xef, 0xc0, 0xb1, 0x57, 0xae, 0x03, 0x40, 0xe8, 0x68, 0x6f, 0x03, 0x20, 0x4f, 0x8a, 0x51, 0x2a, 0x9e, 0xd2, 0x45, 0xaf, 0xb4, 0xf5, 0xd4, 0x95, 0x7f, 0x3d, 0x3d, 0xb7, 0xb6, 0x28, 0xc5, 0x08, 0x8b, 0x44, 0xd6, 0x3f, 0xe7,
+	/* (2^262)P */ 0xa9, 0x52, 0x04, 0x67, 0xcb, 0x20, 0x63, 0xf8, 0x18, 0x01, 0x44, 0x21, 0x6a, 0x8a, 0x83, 0x48, 0xd4, 0xaf, 0x23, 0x0f, 0x35, 0x8d, 0xe5, 0x5a, 0xc4, 0x7c, 0x55, 0x46, 0x19, 0x5f, 0x35, 0xe0, 0x5d, 0x97, 0x4c, 0x2d, 0x04, 0xed, 0x59, 0xd4, 0xb0, 0xb2, 0xc6, 0xe3, 0x51, 0xe1, 0x38, 0xc6, 0x30, 0x49, 0x8f, 0xae, 0x61, 0x64, 0xce, 0xa8,
+	/* (2^263)P */ 0x9b, 0x64, 0x83, 0x3c, 0xd3, 0xdf, 0xb9, 0x27, 0xe7, 0x5b, 0x7f, 0xeb, 0xf3, 0x26, 0xcf, 0xb1, 0x8f, 0xaf, 0x26, 0xc8, 0x48, 0xce, 0xa1, 0xac, 0x7d, 0x10, 0x34, 0x28, 0xe1, 0x1f, 0x69, 0x03, 0x64, 0x77, 0x61, 0xdd, 0x4a, 0x9b, 0x18, 0x47, 0xf8, 0xca, 0x63, 0xc9, 0x03, 0x2d, 0x20, 0x2a, 0x69, 0x6e, 0x42, 0xd0, 0xe7, 0xaa, 0xb5, 0xf3,
+	/* (2^264)P */ 0xea, 0x31, 0x0c, 0x57, 0x0f, 0x3e, 0xe3, 0x35, 0xd8, 0x30, 0xa5, 0x6f, 0xdd, 0x95, 0x43, 0xc6, 0x66, 0x07, 0x4f, 0x34, 0xc3, 0x7e, 0x04, 0x10, 0x2d, 0xc4, 0x1c, 0x94, 0x52, 0x2e, 0x5b, 0x9a, 0x65, 0x2f, 0x91, 0xaa, 0x4f, 0x3c, 0xdc, 0x23, 0x18, 0xe1, 0x4f, 0x85, 0xcd, 0xf4, 0x8c, 0x51, 0xf7, 0xab, 0x4f, 0xdc, 0x15, 0x5c, 0x9e, 0xc5,
+	/* (2^265)P */ 0x54, 0x57, 0x23, 0x17, 0xe7, 0x82, 0x2f, 0x04, 0x7d, 0xfe, 0xe7, 0x1f, 0xa2, 0x57, 0x79, 0xe9, 0x58, 0x9b, 0xbe, 0xc6, 0x16, 0x4a, 0x17, 0x50, 0x90, 0x4a, 0x34, 0x70, 0x87, 0x37, 0x01, 0x26, 0xd8, 0xa3, 0x5f, 0x07, 0x7c, 0xd0, 0x7d, 0x05, 0x8a, 0x93, 0x51, 0x2f, 0x99, 0xea, 0xcf, 0x00, 0xd8, 0xc7, 0xe6, 0x9b, 0x8c, 0x62, 0x45, 0x87,
+	/* (2^266)P */ 0xc3, 0xfd, 0x29, 0x66, 0xe7, 0x30, 0x29, 0x77, 0xe0, 0x0d, 0x63, 0x5b, 0xe6, 0x90, 0x1a, 0x1e, 0x99, 0xc2, 0xa7, 0xab, 0xff, 0xa7, 0xbd, 0x79, 0x01, 0x97, 0xfd, 0x27, 0x1b, 0x43, 0x2b, 0xe6, 0xfe, 0x5e, 0xf1, 0xb9, 0x35, 0x38, 0x08, 0x25, 0x55, 0x90, 0x68, 0x2e, 0xc3, 0x67, 0x39, 0x9f, 0x2b, 0x2c, 0x70, 0x48, 0x8c, 0x47, 0xee, 0x56,
+	/* (2^267)P */ 0xf7, 0x32, 0x70, 0xb5, 0xe6, 0x42, 0xfd, 0x0a, 0x39, 0x9b, 0x07, 0xfe, 0x0e, 0xf4, 0x47, 0xba, 0x6a, 0x3f, 0xf5, 0x2c, 0x15, 0xf3, 0x60, 0x3f, 0xb1, 0x83, 0x7b, 0x2e, 0x34, 0x58, 0x1a, 0x6e, 0x4a, 0x49, 0x05, 0x45, 0xca, 0xdb, 0x00, 0x01, 0x0c, 0x42, 0x5e, 0x60, 0x40, 0x5f, 0xd9, 0xc7, 0x3a, 0x9e, 0x1c, 0x8d, 0xab, 0x11, 0x55, 0x65,
+	/* (2^268)P */ 0x87, 0x40, 0xb7, 0x0d, 0xaa, 0x34, 0x89, 0x90, 0x75, 0x6d, 0xa2, 0xfe, 0x3b, 0x6d, 0x5c, 0x39, 0x98, 0x10, 0x9e, 0x15, 0xc5, 0x35, 0xa2, 0x27, 0x23, 0x0a, 0x2d, 0x60, 0xe2, 0xa8, 0x7f, 0x3e, 0x77, 0x8f, 0xcc, 0x44, 0xcc, 0x30, 0x28, 0xe2, 0xf0, 0x04, 0x8c, 0xee, 0xe4, 0x5f, 0x68, 0x8c, 0xdf, 0x70, 0xbf, 0x31, 0xee, 0x2a, 0xfc, 0xce,
+	/* (2^269)P */ 0x92, 0xf2, 0xa0, 0xd9, 0x58, 0x3b, 0x7c, 0x1a, 0x99, 0x46, 0x59, 0x54, 0x60, 0x06, 0x8d, 0x5e, 0xf0, 0x22, 0xa1, 0xed, 0x92, 0x8a, 0x4d, 0x76, 0x95, 0x05, 0x0b, 0xff, 0xfc, 0x9a, 0xd1, 0xcc, 0x05, 0xb9, 0x5e, 0x99, 0xe8, 0x2a, 0x76, 0x7b, 0xfd, 0xa6, 0xe2, 0xd1, 0x1a, 0xd6, 0x76, 0x9f, 0x2f, 0x0e, 0xd1, 0xa8, 0x77, 0x5a, 0x40, 0x5a,
+	/* (2^270)P */ 0xff, 0xf9, 0x3f, 0xa9, 0xa6, 0x6c, 0x6d, 0x03, 0x8b, 0xa7, 0x10, 0x5d, 0x3f, 0xec, 0x3e, 0x1c, 0x0b, 0x6b, 0xa2, 0x6a, 0x22, 0xa9, 0x28, 0xd0, 0x66, 0xc9, 0xc2, 0x3d, 0x47, 0x20, 0x7d, 0xa6, 0x1d, 0xd8, 0x25, 0xb5, 0xf2, 0xf9, 0x70, 0x19, 0x6b, 0xf8, 0x43, 0x36, 0xc5, 0x1f, 0xe4, 0x5a, 0x4c, 0x13, 0xe4, 0x6d, 0x08, 0x0b, 0x1d, 0xb1,
+	/* (2^271)P */ 0x3f, 0x20, 0x9b, 0xfb, 0xec, 0x7d, 0x31, 0xc5, 0xfc, 0x88, 0x0b, 0x30, 0xed, 0x36, 0xc0, 0x63, 0xb1, 0x7d, 0x10, 0xda, 0xb6, 0x2e, 0xad, 0xf3, 0xec, 0x94, 0xe7, 0xec, 0xb5, 0x9c, 0xfe, 0xf5, 0x35, 0xf0, 0xa2, 0x2d, 0x7f, 0xca, 0x6b, 0x67, 0x1a, 0xf6, 0xb3, 0xda, 0x09, 0x2a, 0xaa, 0xdf, 0xb1, 0xca, 0x9b, 0xfb, 0xeb, 0xb3, 0xcd, 0xc0,
+	/* (2^272)P */ 0xcd, 0x4d, 0x89, 0x00, 0xa4, 0x3b, 0x48, 0xf0, 0x76, 0x91, 0x35, 0xa5, 0xf8, 0xc9, 0xb6, 0x46, 0xbc, 0xf6, 0x9a, 0x45, 0x47, 0x17, 0x96, 0x80, 0x5b, 0x3a, 0x28, 0x33, 0xf9, 0x5a, 0xef, 0x43, 0x07, 0xfe, 0x3b, 0xf4, 0x8e, 0x19, 0xce, 0xd2, 0x94, 0x4b, 0x6d, 0x8e, 0x67, 0x20, 0xc7, 0x4f, 0x2f, 0x59, 0x8e, 0xe1, 0xa1, 0xa9, 0xf9, 0x0e,
+	/* (2^273)P */ 0xdc, 0x7b, 0xb5, 0x50, 0x2e, 0xe9, 0x7e, 0x8b, 0x78, 0xa1, 0x38, 0x96, 0x22, 0xc3, 0x61, 0x67, 0x6d, 0xc8, 0x58, 0xed, 0x41, 0x1d, 0x5d, 0x86, 0x98, 0x7f, 0x2f, 0x1b, 0x8d, 0x3e, 0xaa, 0xc1, 0xd2, 0x0a, 0xf3, 0xbf, 0x95, 0x04, 0xf3, 0x10, 0x3c, 0x2b, 0x7f, 0x90, 0x46, 0x04, 0xaa, 0x6a, 0xa9, 0x35, 0x76, 0xac, 0x49, 0xb5, 0x00, 0x45,
+	/* (2^274)P */ 0xb1, 0x93, 0x79, 0x84, 0x4a, 0x2a, 0x30, 0x78, 0x16, 0xaa, 0xc5, 0x74, 0x06, 0xce, 0xa5, 0xa7, 0x32, 0x86, 0xe0, 0xf9, 0x10, 0xd2, 0x58, 0x76, 0xfb, 0x66, 0x49, 0x76, 0x3a, 0x90, 0xba, 0xb5, 0xcc, 0x99, 0xcd, 0x09, 0xc1, 0x9a, 0x74, 0x23, 0xdf, 0x0c, 0xfe, 0x99, 0x52, 0x80, 0xa3, 0x7c, 0x1c, 0x71, 0x5f, 0x2c, 0x49, 0x57, 0xf4, 0xf9,
+	/* (2^275)P */ 0x6d, 0xbf, 0x52, 0xe6, 0x25, 0x98, 0xed, 0xcf, 0xe3, 0xbc, 0x08, 0xa2, 0x1a, 0x90, 0xae, 0xa0, 0xbf, 0x07, 0x15, 0xad, 0x0a, 0x9f, 0x3e, 0x47, 0x44, 0xc2, 0x10, 0x46, 0xa6, 0x7a, 0x9e, 0x2f, 0x57, 0xbc, 0xe2, 0xf0, 0x1d, 0xd6, 0x9a, 0x06, 0xed, 0xfc, 0x54, 0x95, 0x92, 0x15, 0xa2, 0xf7, 0x8d, 0x6b, 0xef, 0xb2, 0x05, 0xed, 0x5c, 0x63,
+	/* (2^276)P */ 0xbc, 0x0b, 0x27, 0x3a, 0x3a, 0xf8, 0xe1, 0x48, 0x02, 0x7e, 0x27, 0xe6, 0x81, 0x62, 0x07, 0x73, 0x74, 0xe5, 0x52, 0xd7, 0xf8, 0x26, 0xca, 0x93, 0x4d, 0x3e, 0x9b, 0x55, 0x09, 0x8e, 0xe3, 0xd7, 0xa6, 0xe3, 0xb6, 0x2a, 0xa9, 0xb3, 0xb0, 0xa0, 0x8c, 0x01, 0xbb, 0x07, 0x90, 0x78, 0x6d, 0x6d, 0xe9, 0xf0, 0x7a, 0x90, 0xbd, 0xdc, 0x0c, 0x36,
+	/* (2^277)P */ 0x7f, 0x20, 0x12, 0x0f, 0x40, 0x00, 0x53, 0xd8, 0x0c, 0x27, 0x47, 0x47, 0x22, 0x80, 0xfb, 0x62, 0xe4, 0xa7, 0xf7, 0xbd, 0x42, 0xa5, 0xc3, 0x2b, 0xb2, 0x7f, 0x50, 0xcc, 0xe2, 0xfb, 0xd5, 0xc0, 0x63, 0xdd, 0x24, 0x5f, 0x7c, 0x08, 0x91, 0xbf, 0x6e, 0x47, 0x44, 0xd4, 0x6a, 0xc0, 0xc3, 0x09, 0x39, 0x27, 0xdd, 0xc7, 0xca, 0x06, 0x29, 0x55,
+	/* (2^278)P */ 0x76, 0x28, 0x58, 0xb0, 0xd2, 0xf3, 0x0f, 0x04, 0xe9, 0xc9, 0xab, 0x66, 0x5b, 0x75, 0x51, 0xdc, 0xe5, 0x8f, 0xe8, 0x1f, 0xdb, 0x03, 0x0f, 0xb0, 0x7d, 0xf9, 0x20, 0x64, 0x89, 0xe9, 0xdc, 0xe6, 0x24, 0xc3, 0xd5, 0xd2, 0x41, 0xa6, 0xe4, 0xe3, 0xc4, 0x79, 0x7c, 0x0f, 0xa1, 0x61, 0x2f, 0xda, 0xa4, 0xc9, 0xfd, 0xad, 0x5c, 0x65, 0x6a, 0xf3,
+	/* (2^279)P */ 0xd5, 0xab, 0x72, 0x7a, 0x3b, 0x59, 0xea, 0xcf, 0xd5, 0x17, 0xd2, 0xb2, 0x5f, 0x2d, 0xab, 0xad, 0x9e, 0x88, 0x64, 0x55, 0x96, 0x6e, 0xf3, 0x44, 0xa9, 0x11, 0xf5, 0xf8, 0x3a, 0xf1, 0xcd, 0x79, 0x4c, 0x99, 0x6d, 0x23, 0x6a, 0xa0, 0xc2, 0x1a, 0x19, 0x45, 0xb5, 0xd8, 0x95, 0x2f, 0x49, 0xe9, 0x46, 0x39, 0x26, 0x60, 0x04, 0x15, 0x8b, 0xcc,
+	/* (2^280)P */ 0x66, 0x0c, 0xf0, 0x54, 0x41, 0x02, 0x91, 0xab, 0xe5, 0x85, 0x8a, 0x44, 0xa6, 0x34, 0x96, 0x32, 0xc0, 0xdf, 0x6c, 0x41, 0x39, 0xd4, 0xc6, 0xe1, 0xe3, 0x81, 0xb0, 0x4c, 0x34, 0x4f, 0xe5, 0xf4, 0x35, 0x46, 0x1f, 0xeb, 0x75, 0xfd, 0x43, 0x37, 0x50, 0x99, 0xab, 0xad, 0xb7, 0x8c, 0xa1, 0x57, 0xcb, 0xe6, 0xce, 0x16, 0x2e, 0x85, 0xcc, 0xf9,
+	/* (2^281)P */ 0x63, 0xd1, 0x3f, 0x9e, 0xa2, 0x17, 0x2e, 0x1d, 0x3e, 0xce, 0x48, 0x2d, 0xbb, 0x8f, 0x69, 0xc9, 0xa6, 0x3d, 0x4e, 0xfe, 0x09, 0x56, 0xb3, 0x02, 0x5f, 0x99, 0x97, 0x0c, 0x54, 0xda, 0x32, 0x97, 0x9b, 0xf4, 0x95, 0xf1, 0xad, 0xe3, 0x2b, 0x04, 0xa7, 0x9b, 0x3f, 0xbb, 0xe7, 0x87, 0x2e, 0x1f, 0x8b, 0x4b, 0x7a, 0xa4, 0x43, 0x0c, 0x0f, 0x35,
+	/* (2^282)P */ 0x05, 0xdc, 0xe0, 0x2c, 0xa1, 0xc1, 0xd0, 0xf1, 0x1f, 0x4e, 0xc0, 0x6c, 0x35, 0x7b, 0xca, 0x8f, 0x8b, 0x02, 0xb1, 0xf7, 0xd6, 0x2e, 0xe7, 0x93, 0x80, 0x85, 0x18, 0x88, 0x19, 0xb9, 0xb4, 0x4a, 0xbc, 0xeb, 0x5a, 0x78, 0x38, 0xed, 0xc6, 0x27, 0x2a, 0x74, 0x76, 0xf0, 0x1b, 0x79, 0x92, 0x2f, 0xd2, 0x81, 0x98, 0xdf, 0xa9, 0x50, 0x19, 0xeb,
+	/* (2^283)P */ 0xb5, 0xe7, 0xb4, 0x11, 0x3a, 0x81, 0xb6, 0xb4, 0xf8, 0xa2, 0xb3, 0x6c, 0xfc, 0x9d, 0xe0, 0xc0, 0xe0, 0x59, 0x7f, 0x05, 0x37, 0xef, 0x2c, 0xa9, 0x3a, 0x24, 0xac, 0x7b, 0x25, 0xa0, 0x55, 0xd2, 0x44, 0x82, 0x82, 0x6e, 0x64, 0xa3, 0x58, 0xc8, 0x67, 0xae, 0x26, 0xa7, 0x0f, 0x42, 0x63, 0xe1, 0x93, 0x01, 0x52, 0x19, 0xaf, 0x49, 0x3e, 0x33,
+	/* (2^284)P */ 0x05, 0x85, 0xe6, 0x66, 0xaf, 0x5f, 0xdf, 0xbf, 0x9d, 0x24, 0x62, 0x60, 0x90, 0xe2, 0x4c, 0x7d, 0x4e, 0xc3, 0x74, 0x5d, 0x4f, 0x53, 0xf3, 0x63, 0x13, 0xf4, 0x74, 0x28, 0x6b, 0x7d, 0x57, 0x0c, 0x9d, 0x84, 0xa7, 0x1a, 0xff, 0xa0, 0x79, 0xdf, 0xfc, 0x65, 0x98, 0x8e, 0x22, 0x0d, 0x62, 0x7e, 0xf2, 0x34, 0x60, 0x83, 0x05, 0x14, 0xb1, 0xc1,
+	/* (2^285)P */ 0x64, 0x22, 0xcc, 0xdf, 0x5c, 0xbc, 0x88, 0x68, 0x4c, 0xd9, 0xbc, 0x0e, 0xc9, 0x8b, 0xb4, 0x23, 0x52, 0xad, 0xb0, 0xb3, 0xf1, 0x17, 0xd8, 0x15, 0x04, 0x6b, 0x99, 0xf0, 0xc4, 0x7d, 0x48, 0x22, 0x4a, 0xf8, 0x6f, 0xaa, 0x88, 0x0d, 0xc5, 0x5e, 0xa9, 0x1c, 0x61, 0x3d, 0x95, 0xa9, 0x7b, 0x6a, 0x79, 0x33, 0x0a, 0x2b, 0x99, 0xe3, 0x4e, 0x48,
+	/* (2^286)P */ 0x6b, 0x9b, 0x6a, 0x2a, 0xf1, 0x60, 0x31, 0xb4, 0x73, 0xd1, 0x87, 0x45, 0x9c, 0x15, 0x58, 0x4b, 0x91, 0x6d, 0x94, 0x1c, 0x41, 0x11, 0x4a, 0x83, 0xec, 0xaf, 0x65, 0xbc, 0x34, 0xaa, 0x26, 0xe2, 0xaf, 0xed, 0x46, 0x05, 0x4e, 0xdb, 0xc6, 0x4e, 0x10, 0x28, 0x4e, 0x72, 0xe5, 0x31, 0xa3, 0x20, 0xd7, 0xb1, 0x96, 0x64, 0xf6, 0xce, 0x08, 0x08,
+	/* (2^287)P */ 0x16, 0xa9, 0x5c, 0x9f, 0x9a, 0xb4, 0xb8, 0xc8, 0x32, 0x78, 0xc0, 0x3a, 0xd9, 0x5f, 0x94, 0xac, 0x3a, 0x42, 0x1f, 0x43, 0xd6, 0x80, 0x47, 0x2c, 0xdc, 0x76, 0x27, 0xfa, 0x50, 0xe5, 0xa1, 0xe4, 0xc3, 0xcb, 0x61, 0x31, 0xe1, 0x2e, 0xde, 0x81, 0x3b, 0x77, 0x1c, 0x39, 0x3c, 0xdb, 0xda, 0x87, 0x4b, 0x84, 0x12, 0xeb, 0xdd, 0x54, 0xbf, 0xe7,
+	/* (2^288)P */ 0xbf, 0xcb, 0x73, 0x21, 0x3d, 0x7e, 0x13, 0x8c, 0xa6, 0x34, 0x21, 0x2b, 0xa5, 0xe4, 0x9f, 0x8e, 0x9c, 0x01, 0x9c, 0x43, 0xd9, 0xc7, 0xb9, 0xf1, 0xbe, 0x7f, 0x45, 0x51, 0x97, 0xa1, 0x8e, 0x01, 0xf8, 0xbd, 0xd2, 0xbf, 0x81, 0x3a, 0x8b, 0xab, 0xe4, 0x89, 0xb7, 0xbd, 0xf2, 0xcd, 0xa9, 0x8a, 0x8a, 0xde, 0xfb, 0x8a, 0x55, 0x12, 0x7b, 0x17,
+	/* (2^289)P */ 0x1b, 0x95, 0x58, 0x4d, 0xe6, 0x51, 0x31, 0x52, 0x1c, 0xd8, 0x15, 0x84, 0xb1, 0x0d, 0x36, 0x25, 0x88, 0x91, 0x46, 0x71, 0x42, 0x56, 0xe2, 0x90, 0x08, 0x9e, 0x77, 0x1b, 0xee, 0x22, 0x3f, 0xec, 0xee, 0x8c, 0x7b, 0x2e, 0x79, 0xc4, 0x6c, 0x07, 0xa1, 0x7e, 0x52, 0xf5, 0x26, 0x5c, 0x84, 0x2a, 0x50, 0x6e, 0x82, 0xb3, 0x76, 0xda, 0x35, 0x16,
+	/* (2^290)P */ 0x0a, 0x6f, 0x99, 0x87, 0xc0, 0x7d, 0x8a, 0xb2, 0xca, 0xae, 0xe8, 0x65, 0x98, 0x0f, 0xb3, 0x44, 0xe1, 0xdc, 0x52, 0x79, 0x75, 0xec, 0x8f, 0x95, 0x87, 0x45, 0xd1, 0x32, 0x18, 0x55, 0x15, 0xce, 0x64, 0x9b, 0x08, 0x4f, 0x2c, 0xea, 0xba, 0x1c, 0x57, 0x06, 0x63, 0xc8, 0xb1, 0xfd, 0xc5, 0x67, 0xe7, 0x1f, 0x87, 0x9e, 0xde, 0x72, 0x7d, 0xec,
+	/* (2^291)P */ 0x36, 0x8b, 0x4d, 0x2c, 0xc2, 0x46, 0xe8, 0x96, 0xac, 0x0b, 0x8c, 0xc5, 0x09, 0x10, 0xfc, 0xf2, 0xda, 0xea, 0x22, 0xb2, 0xd3, 0x89, 0xeb, 0xb2, 0x85, 0x0f, 0xff, 0x59, 0x50, 0x2c, 0x99, 0x5a, 0x1f, 0xec, 0x2a, 0x6f, 0xec, 0xcf, 0xe9, 0xce, 0x12, 0x6b, 0x19, 0xd8, 0xde, 0x9b, 0xce, 0x0e, 0x6a, 0xaa, 0xe1, 0x32, 0xea, 0x4c, 0xfe, 0x92,
+	/* (2^292)P */ 0x5f, 0x17, 0x70, 0x53, 0x26, 0x03, 0x0b, 0xab, 0xd1, 0xc1, 0x42, 0x0b, 0xab, 0x2b, 0x3d, 0x31, 0xa4, 0xd5, 0x2b, 0x5e, 0x00, 0xd5, 0x9a, 0x22, 0x34, 0xe0, 0x53, 0x3f, 0x59, 0x7f, 0x2c, 0x6d, 0x72, 0x9a, 0xa4, 0xbe, 0x3d, 0x42, 0x05, 0x1b, 0xf2, 0x7f, 0x88, 0x56, 0xd1, 0x7c, 0x7d, 0x6b, 0x9f, 0x43, 0xfe, 0x65, 0x19, 0xae, 0x9c, 0x4c,
+	/* (2^293)P */ 0xf3, 0x7c, 0x20, 0xa9, 0xfc, 0xf2, 0xf2, 0x3b, 0x3c, 0x57, 0x41, 0x94, 0xe5, 0xcc, 0x6a, 0x37, 0x5d, 0x09, 0xf2, 0xab, 0xc2, 0xca, 0x60, 0x38, 0x6b, 0x7a, 0xe1, 0x78, 0x2b, 0xc1, 0x1d, 0xe8, 0xfd, 0xbc, 0x3d, 0x5c, 0xa2, 0xdb, 0x49, 0x20, 0x79, 0xe6, 0x1b, 0x9b, 0x65, 0xd9, 0x6d, 0xec, 0x57, 0x1d, 0xd2, 0xe9, 0x90, 0xeb, 0x43, 0x7b,
+	/* (2^294)P */ 0x2a, 0x8b, 0x2e, 0x19, 0x18, 0x10, 0xb8, 0x83, 0xe7, 0x7d, 0x2d, 0x9a, 0x3a, 0xe5, 0xd1, 0xe4, 0x7c, 0x38, 0xe5, 0x59, 0x2a, 0x6e, 0xd9, 0x01, 0x29, 0x3d, 0x23, 0xf7, 0x52, 0xba, 0x61, 0x04, 0x9a, 0xde, 0xc4, 0x31, 0x50, 0xeb, 0x1b, 0xaa, 0xde, 0x39, 0x58, 0xd8, 0x1b, 0x1e, 0xfc, 0x57, 0x9a, 0x28, 0x43, 0x9e, 0x97, 0x5e, 0xaa, 0xa3,
+	/* (2^295)P */ 0x97, 0x0a, 0x74, 0xc4, 0x39, 0x99, 0x6b, 0x40, 0xc7, 0x3e, 0x8c, 0xa7, 0xb1, 0x4e, 0x9a, 0x59, 0x6e, 0x1c, 0xfe, 0xfc, 0x2a, 0x5e, 0x73, 0x2b, 0x8c, 0xa9, 0x71, 0xf5, 0xda, 0x6b, 0x15, 0xab, 0xf7, 0xbe, 0x2a, 0x44, 0x5f, 0xba, 0xae, 0x67, 0x93, 0xc5, 0x86, 0xc1, 0xb8, 0xdf, 0xdc, 0xcb, 0xd7, 0xff, 0xb1, 0x71, 0x7c, 0x6f, 0x88, 0xf8,
+	/* (2^296)P */ 0x3f, 0x89, 0xb1, 0xbf, 0x24, 0x16, 0xac, 0x56, 0xfe, 0xdf, 0x94, 0x71, 0xbf, 0xd6, 0x57, 0x0c, 0xb4, 0x77, 0x37, 0xaa, 0x2a, 0x70, 0x76, 0x49, 0xaf, 0x0c, 0x97, 0x8e, 0x78, 0x2a, 0x67, 0xc9, 0x3b, 0x3d, 0x5b, 0x01, 0x2f, 0xda, 0xd5, 0xa8, 0xde, 0x02, 0xa9, 0xac, 0x76, 0x00, 0x0b, 0x46, 0xc6, 0x2d, 0xdc, 0x08, 0xf4, 0x10, 0x2c, 0xbe,
+	/* (2^297)P */ 0xcb, 0x07, 0xf9, 0x91, 0xc6, 0xd5, 0x3e, 0x54, 0x63, 0xae, 0xfc, 0x10, 0xbe, 0x3a, 0x20, 0x73, 0x4e, 0x65, 0x0e, 0x2d, 0x86, 0x77, 0x83, 0x9d, 0xe2, 0x0a, 0xe9, 0xac, 0x22, 0x52, 0x76, 0xd4, 0x6e, 0xfa, 0xe0, 0x09, 0xef, 0x78, 0x82, 0x9f, 0x26, 0xf9, 0x06, 0xb5, 0xe7, 0x05, 0x0e, 0xf2, 0x46, 0x72, 0x93, 0xd3, 0x24, 0xbd, 0x87, 0x60,
+	/* (2^298)P */ 0x14, 0x55, 0x84, 0x7b, 0x6c, 0x60, 0x80, 0x73, 0x8c, 0xbe, 0x2d, 0xd6, 0x69, 0xd6, 0x17, 0x26, 0x44, 0x9f, 0x88, 0xa2, 0x39, 0x7c, 0x89, 0xbc, 0x6d, 0x9e, 0x46, 0xb6, 0x68, 0x66, 0xea, 0xdc, 0x31, 0xd6, 0x21, 0x51, 0x9f, 0x28, 0x28, 0xaf, 0x9e, 0x47, 0x2c, 0x4c, 0x8f, 0xf3, 0xaf, 0x1f, 0xe4, 0xab, 0xac, 0xe9, 0x0c, 0x91, 0x3a, 0x61,
+	/* (2^299)P */ 0xb0, 0x37, 0x55, 0x4b, 0xe9, 0xc3, 0xb1, 0xce, 0x42, 0xe6, 0xc5, 0x11, 0x7f, 0x2c, 0x11, 0xfc, 0x4e, 0x71, 0x17, 0x00, 0x74, 0x7f, 0xbf, 0x07, 0x4d, 0xfd, 0x40, 0xb2, 0x87, 0xb0, 0xef, 0x1f, 0x35, 0x2c, 0x2d, 0xd7, 0xe1, 0xe4, 0xad, 0x0e, 0x7f, 0x63, 0x66, 0x62, 0x23, 0x41, 0xf6, 0xc1, 0x14, 0xa6, 0xd7, 0xa9, 0x11, 0x56, 0x9d, 0x1b,
+	/* (2^300)P */ 0x02, 0x82, 0x42, 0x18, 0x4f, 0x1b, 0xc9, 0x5d, 0x78, 0x5f, 0xee, 0xed, 0x01, 0x49, 0x8f, 0xf2, 0xa0, 0xe2, 0x6e, 0xbb, 0x6b, 0x04, 0x8d, 0xb2, 0x41, 0xae, 0xc8, 0x1b, 0x59, 0x34, 0xb8, 0x2a, 0xdb, 0x1f, 0xd2, 0x52, 0xdf, 0x3f, 0x35, 0x00, 0x8b, 0x61, 0xbc, 0x97, 0xa0, 0xc4, 0x77, 0xd1, 0xe4, 0x2c, 0x59, 0x68, 0xff, 0x30, 0xf2, 0xe2,
+	/* (2^301)P */ 0x79, 0x08, 0xb1, 0xdb, 0x55, 0xae, 0xd0, 0xed, 0xda, 0xa0, 0xec, 0x6c, 0xae, 0x68, 0xf2, 0x0b, 0x61, 0xb3, 0xf5, 0x21, 0x69, 0x87, 0x0b, 0x03, 0xea, 0x8a, 0x15, 0xd9, 0x7e, 0xca, 0xf7, 0xcd, 0xf3, 0x33, 0xb3, 0x4c, 0x5b, 0x23, 0x4e, 0x6f, 0x90, 0xad, 0x91, 0x4b, 0x4f, 0x46, 0x37, 0xe5, 0xe8, 0xb7, 0xeb, 0xd5, 0xca, 0x34, 0x4e, 0x23,
+	/* (2^302)P */ 0x09, 0x02, 0xdd, 0xfd, 0x70, 0xac, 0x56, 0x80, 0x36, 0x5e, 0x49, 0xd0, 0x3f, 0xc2, 0xe0, 0xba, 0x46, 0x7f, 0x5c, 0xf7, 0xc5, 0xbd, 0xd5, 0x55, 0x7d, 0x3f, 0xd5, 0x7d, 0x06, 0xdf, 0x27, 0x20, 0x4f, 0xe9, 0x30, 0xec, 0x1b, 0xa0, 0x0c, 0xd4, 0x2c, 0xe1, 0x2b, 0x65, 0x73, 0xea, 0x75, 0x35, 0xe8, 0xe6, 0x56, 0xd6, 0x07, 0x15, 0x99, 0xdf,
+	/* (2^303)P */ 0x4e, 0x10, 0xb7, 0xd0, 0x63, 0x8c, 0xcf, 0x16, 0x00, 0x7c, 0x58, 0xdf, 0x86, 0xdc, 0x4e, 0xca, 0x9c, 0x40, 0x5a, 0x42, 0xfd, 0xec, 0x98, 0xa4, 0x42, 0x53, 0xae, 0x16, 0x9d, 0xfd, 0x75, 0x5a, 0x12, 0x56, 0x1e, 0xc6, 0x57, 0xcc, 0x79, 0x27, 0x96, 0x00, 0xcf, 0x80, 0x4f, 0x8a, 0x36, 0x5c, 0xbb, 0xe9, 0x12, 0xdb, 0xb6, 0x2b, 0xad, 0x96,
+	/* (2^304)P */ 0x92, 0x32, 0x1f, 0xfd, 0xc6, 0x02, 0x94, 0x08, 0x1b, 0x60, 0x6a, 0x9f, 0x8b, 0xd6, 0xc8, 0xad, 0xd5, 0x1b, 0x27, 0x4e, 0xa4, 0x4d, 0x4a, 0x00, 0x10, 0x5f, 0x86, 0x11, 0xf5, 0xe3, 0x14, 0x32, 0x43, 0xee, 0xb9, 0xc7, 0xab, 0xf4, 0x6f, 0xe5, 0x66, 0x0c, 0x06, 0x0d, 0x96, 0x79, 0x28, 0xaf, 0x45, 0x2b, 0x56, 0xbe, 0xe4, 0x4a, 0x52, 0xd6,
+	/* (2^305)P */ 0x15, 0x16, 0x69, 0xef, 0x60, 0xca, 0x82, 0x25, 0x0f, 0xc6, 0x30, 0xa0, 0x0a, 0xd1, 0x83, 0x29, 0xcd, 0xb6, 0x89, 0x6c, 0xf5, 0xb2, 0x08, 0x38, 0xe6, 0xca, 0x6b, 0x19, 0x93, 0xc6, 0x5f, 0x75, 0x8e, 0x60, 0x34, 0x23, 0xc4, 0x13, 0x17, 0x69, 0x55, 0xcc, 0x72, 0x9c, 0x2b, 0x6c, 0x80, 0xf4, 0x4b, 0x8b, 0xb6, 0x97, 0x65, 0x07, 0xb6, 0xfb,
+	/* (2^306)P */ 0x01, 0x99, 0x74, 0x28, 0xa6, 0x67, 0xa3, 0xe5, 0x25, 0xfb, 0xdf, 0x82, 0x93, 0xe7, 0x35, 0x74, 0xce, 0xe3, 0x15, 0x1c, 0x1d, 0x79, 0x52, 0x84, 0x08, 0x04, 0x2f, 0x5c, 0xb8, 0xcd, 0x7f, 0x89, 0xb0, 0x39, 0x93, 0x63, 0xc9, 0x5d, 0x06, 0x01, 0x59, 0xf7, 0x7e, 0xf1, 0x4c, 0x3d, 0x12, 0x8d, 0x69, 0x1d, 0xb7, 0x21, 0x5e, 0x88, 0x82, 0xa2,
+	/* (2^307)P */ 0x8e, 0x69, 0xaf, 0x9a, 0x41, 0x0d, 0x9d, 0xcf, 0x8e, 0x8d, 0x5c, 0x51, 0x6e, 0xde, 0x0e, 0x48, 0x23, 0x89, 0xe5, 0x37, 0x80, 0xd6, 0x9d, 0x72, 0x32, 0x26, 0x38, 0x2d, 0x63, 0xa0, 0xfa, 0xd3, 0x40, 0xc0, 0x8c, 0x68, 0x6f, 0x2b, 0x1e, 0x9a, 0x39, 0x51, 0x78, 0x74, 0x9a, 0x7b, 0x4a, 0x8f, 0x0c, 0xa0, 0x88, 0x60, 0xa5, 0x21, 0xcd, 0xc7,
+	/* (2^308)P */ 0x3a, 0x7f, 0x73, 0x14, 0xbf, 0x89, 0x6a, 0x4c, 0x09, 0x5d, 0xf2, 0x93, 0x20, 0x2d, 0xc4, 0x29, 0x86, 0x06, 0x95, 0xab, 0x22, 0x76, 0x4c, 0x54, 0xe1, 0x7e, 0x80, 0x6d, 0xab, 0x29, 0x61, 0x87, 0x77, 0xf6, 0xc0, 0x3e, 0xda, 0xab, 0x65, 0x7e, 0x39, 0x12, 0xa1, 0x6b, 0x42, 0xf7, 0xc5, 0x97, 0x77, 0xec, 0x6f, 0x22, 0xbe, 0x44, 0xc7, 0x03,
+	/* (2^309)P */ 0xa5, 0x23, 0x90, 0x41, 0xa3, 0xc5, 0x3e, 0xe0, 0xa5, 0x32, 0x49, 0x1f, 0x39, 0x78, 0xb1, 0xd8, 0x24, 0xea, 0xd4, 0x87, 0x53, 0x42, 0x51, 0xf4, 0xd9, 0x46, 0x25, 0x2f, 0x62, 0xa9, 0x90, 0x9a, 0x4a, 0x25, 0x8a, 0xd2, 0x10, 0xe7, 0x3c, 0xbc, 0x58, 0x8d, 0x16, 0x14, 0x96, 0xa4, 0x6f, 0xf8, 0x12, 0x69, 0x91, 0x73, 0xe2, 0xfa, 0xf4, 0x57,
+	/* (2^310)P */ 0x51, 0x45, 0x3f, 0x96, 0xdc, 0x97, 0x38, 0xa6, 0x01, 0x63, 0x09, 0xea, 0xc2, 0x13, 0x30, 0xb0, 0x00, 0xb8, 0x0a, 0xce, 0xd1, 0x8f, 0x3e, 0x69, 0x62, 0x46, 0x33, 0x9c, 0xbf, 0x4b, 0xcb, 0x0c, 0x90, 0x1c, 0x45, 0xcf, 0x37, 0x5b, 0xf7, 0x4b, 0x5e, 0x95, 0xc3, 0x28, 0x9f, 0x08, 0x83, 0x53, 0x74, 0xab, 0x0c, 0xb4, 0xc0, 0xa1, 0xbc, 0x89,
+	/* (2^311)P */ 0x06, 0xb1, 0x51, 0x15, 0x65, 0x60, 0x21, 0x17, 0x7a, 0x20, 0x65, 0xee, 0x12, 0x35, 0x4d, 0x46, 0xf4, 0xf8, 0xd0, 0xb1, 0xca, 0x09, 0x30, 0x08, 0x89, 0x23, 0x3b, 0xe7, 0xab, 0x8b, 0x77, 0xa6, 0xad, 0x25, 0xdd, 0xea, 0x3c, 0x7d, 0xa5, 0x24, 0xb3, 0xe8, 0xfa, 0xfb, 0xc9, 0xf2, 0x71, 0xe9, 0xfa, 0xf2, 0xdc, 0x54, 0xdd, 0x55, 0x2e, 0x2f,
+	/* (2^312)P */ 0x7f, 0x96, 0x96, 0xfb, 0x52, 0x86, 0xcf, 0xea, 0x62, 0x18, 0xf1, 0x53, 0x1f, 0x61, 0x2a, 0x9f, 0x8c, 0x51, 0xca, 0x2c, 0xde, 0x6d, 0xce, 0xab, 0x58, 0x32, 0x0b, 0x33, 0x9b, 0x99, 0xb4, 0x5c, 0x88, 0x2a, 0x76, 0xcc, 0x3e, 0x54, 0x1e, 0x9d, 0xa2, 0x89, 0xe4, 0x19, 0xba, 0x80, 0xc8, 0x39, 0x32, 0x7f, 0x0f, 0xc7, 0x84, 0xbb, 0x43, 0x56,
+	/* (2^313)P */ 0x9b, 0x07, 0xb4, 0x42, 0xa9, 0xa0, 0x78, 0x4f, 0x28, 0x70, 0x2b, 0x7e, 0x61, 0xe0, 0xdd, 0x02, 0x98, 0xfc, 0xed, 0x31, 0x80, 0xf1, 0x15, 0x52, 0x89, 0x23, 0xcd, 0x5d, 0x2b, 0xc5, 0x19, 0x32, 0xfb, 0x70, 0x50, 0x7a, 0x97, 0x6b, 0x42, 0xdb, 0xca, 0xdb, 0xc4, 0x59, 0x99, 0xe0, 0x12, 0x1f, 0x17, 0xba, 0x8b, 0xf0, 0xc4, 0x38, 0x5d, 0x27,
+	/* (2^314)P */ 0x29, 0x1d, 0xdc, 0x2b, 0xf6, 0x5b, 0x04, 0x61, 0x36, 0x76, 0xa0, 0x56, 0x36, 0x6e, 0xd7, 0x24, 0x4d, 0xe7, 0xef, 0x44, 0xd2, 0xd5, 0x07, 0xcd, 0xc4, 0x9d, 0x80, 0x48, 0xc3, 0x38, 0xcf, 0xd8, 0xa3, 0xdd, 0xb2, 0x5e, 0xb5, 0x70, 0x15, 0xbb, 0x36, 0x85, 0x8a, 0xd7, 0xfb, 0x56, 0x94, 0x73, 0x9c, 0x81, 0xbe, 0xb1, 0x44, 0x28, 0xf1, 0x37,
+	/* (2^315)P */ 0xbf, 0xcf, 0x5c, 0xd2, 0xe2, 0xea, 0xc2, 0xcd, 0x70, 0x7a, 0x9d, 0xcb, 0x81, 0xc1, 0xe9, 0xf1, 0x56, 0x71, 0x52, 0xf7, 0x1b, 0x87, 0xc6, 0xd8, 0xcc, 0xb2, 0x69, 0xf3, 0xb0, 0xbd, 0xba, 0x83, 0x12, 0x26, 0xc4, 0xce, 0x72, 0xde, 0x3b, 0x21, 0x28, 0x9e, 0x5a, 0x94, 0xf5, 0x04, 0xa3, 0xc8, 0x0f, 0x5e, 0xbc, 0x71, 0xf9, 0x0d, 0xce, 0xf5,
+	/* (2^316)P */ 0x93, 0x97, 0x00, 0x85, 0xf4, 0xb4, 0x40, 0xec, 0xd9, 0x2b, 0x6c, 0xd6, 0x63, 0x9e, 0x93, 0x0a, 0x5a, 0xf4, 0xa7, 0x9a, 0xe3, 0x3c, 0xf0, 0x55, 0xd1, 0x96, 0x6c, 0xf5, 0x2a, 0xce, 0xd7, 0x95, 0x72, 0xbf, 0xc5, 0x0c, 0xce, 0x79, 0xa2, 0x0a, 0x78, 0xe0, 0x72, 0xd0, 0x66, 0x28, 0x05, 0x75, 0xd3, 0x23, 0x09, 0x91, 0xed, 0x7e, 0xc4, 0xbc,
+	/* (2^317)P */ 0x77, 0xc2, 0x9a, 0xf7, 0xa6, 0xe6, 0x18, 0xb4, 0xe7, 0xf6, 0xda, 0xec, 0x44, 0x6d, 0xfb, 0x08, 0xee, 0x65, 0xa8, 0x92, 0x85, 0x1f, 0xba, 0x38, 0x93, 0x20, 0x5c, 0x4d, 0xd2, 0x18, 0x0f, 0x24, 0xbe, 0x1a, 0x96, 0x44, 0x7d, 0xeb, 0xb3, 0xda, 0x95, 0xf4, 0xaf, 0x6c, 0x06, 0x0f, 0x47, 0x37, 0xc8, 0x77, 0x63, 0xe1, 0x29, 0xef, 0xff, 0xa5,
+	/* (2^318)P */ 0x16, 0x12, 0xd9, 0x47, 0x90, 0x22, 0x9b, 0x05, 0xf2, 0xa5, 0x9a, 0xae, 0x83, 0x98, 0xb5, 0xac, 0xab, 0x29, 0xaa, 0xdc, 0x5f, 0xde, 0xcd, 0xf7, 0x42, 0xad, 0x3b, 0x96, 0xd6, 0x3e, 0x6e, 0x52, 0x47, 0xb1, 0xab, 0x51, 0xde, 0x49, 0x7c, 0x87, 0x8d, 0x86, 0xe2, 0x70, 0x13, 0x21, 0x51, 0x1c, 0x0c, 0x25, 0xc1, 0xb0, 0xe6, 0x19, 0xcf, 0x12,
+	/* (2^319)P */ 0xf0, 0xbc, 0x97, 0x8f, 0x4b, 0x2f, 0xd1, 0x1f, 0x8c, 0x57, 0xed, 0x3c, 0xf4, 0x26, 0x19, 0xbb, 0x60, 0xca, 0x24, 0xc5, 0xd9, 0x97, 0xe2, 0x5f, 0x76, 0x49, 0x39, 0x7e, 0x2d, 0x12, 0x21, 0x98, 0xda, 0xe6, 0xdb, 0xd2, 0xd8, 0x9f, 0x18, 0xd8, 0x83, 0x6c, 0xba, 0x89, 0x8d, 0x29, 0xfa, 0x46, 0x33, 0x8c, 0x28, 0xdf, 0x6a, 0xb3, 0x69, 0x28,
+	/* (2^320)P */ 0x86, 0x17, 0xbc, 0xd6, 0x7c, 0xba, 0x1e, 0x83, 0xbb, 0x84, 0xb5, 0x8c, 0xad, 0xdf, 0xa1, 0x24, 0x81, 0x70, 0x40, 0x0f, 0xad, 0xad, 0x3b, 0x23, 0xd0, 0x93, 0xa0, 0x49, 0x5c, 0x4b, 0x51, 0xbe, 0x20, 0x49, 0x4e, 0xda, 0x2d, 0xd3, 0xad, 0x1b, 0x74, 0x08, 0x41, 0xf0, 0xef, 0x19, 0xe9, 0x45, 0x5d, 0x02, 0xae, 0x26, 0x25, 0xd9, 0xd1, 0xc2,
+	/* (2^321)P */ 0x48, 0x81, 0x3e, 0xb2, 0x83, 0xf8, 0x4d, 0xb3, 0xd0, 0x4c, 0x75, 0xb3, 0xa0, 0x52, 0x26, 0xf2, 0xaf, 0x5d, 0x36, 0x70, 0x72, 0xd6, 0xb7, 0x88, 0x08, 0x69, 0xbd, 0x15, 0x25, 0xb1, 0x45, 0x1b, 0xb7, 0x0b, 0x5f, 0x71, 0x5d, 0x83, 0x49, 0xb9, 0x84, 0x3b, 0x7c, 0xc1, 0x50, 0x93, 0x05, 0x53, 0xe0, 0x61, 0xea, 0xc1, 0xef, 0xdb, 0x82, 0x97,
+	/* (2^322)P */ 0x00, 0xd5, 0xc3, 0x3a, 0x4d, 0x8a, 0x23, 0x7a, 0xef, 0xff, 0x37, 0xef, 0xf3, 0xbc, 0xa9, 0xb6, 0xae, 0xd7, 0x3a, 0x7b, 0xfd, 0x3e, 0x8e, 0x9b, 0xab, 0x44, 0x54, 0x60, 0x28, 0x6c, 0xbf, 0x15, 0x24, 0x4a, 0x56, 0x60, 0x7f, 0xa9, 0x7a, 0x28, 0x59, 0x2c, 0x8a, 0xd1, 0x7d, 0x6b, 0x00, 0xfd, 0xa5, 0xad, 0xbc, 0x19, 0x3f, 0xcb, 0x73, 0xe0,
+	/* (2^323)P */ 0xcf, 0x9e, 0x66, 0x06, 0x4d, 0x2b, 0xf5, 0x9c, 0xc2, 0x9d, 0x9e, 0xed, 0x5a, 0x5c, 0x2d, 0x00, 0xbf, 0x29, 0x90, 0x88, 0xe4, 0x5d, 0xfd, 0xe2, 0xf0, 0x38, 0xec, 0x4d, 0x26, 0xea, 0x54, 0xf0, 0x3c, 0x84, 0x10, 0x6a, 0xf9, 0x66, 0x9c, 0xe7, 0x21, 0xfd, 0x0f, 0xc7, 0x13, 0x50, 0x81, 0xb6, 0x50, 0xf9, 0x04, 0x7f, 0xa4, 0x37, 0x85, 0x14,
+	/* (2^324)P */ 0xdb, 0x87, 0x49, 0xc7, 0xa8, 0x39, 0x0c, 0x32, 0x98, 0x0c, 0xb9, 0x1a, 0x1b, 0x4d, 0xe0, 0x8a, 0x9a, 0x8e, 0x8f, 0xab, 0x5a, 0x17, 0x3d, 0x04, 0x21, 0xce, 0x3e, 0x2c, 0xf9, 0xa3, 0x97, 0xe4, 0x77, 0x95, 0x0e, 0xb6, 0xa5, 0x15, 0xad, 0x3a, 0x1e, 0x46, 0x53, 0x17, 0x09, 0x83, 0x71, 0x4e, 0x86, 0x38, 0xd5, 0x23, 0x44, 0x16, 0x8d, 0xc8,
+	/* (2^325)P */ 0x05, 0x5e, 0x99, 0x08, 0xbb, 0xc3, 0xc0, 0xb7, 0x6c, 0x12, 0xf2, 0xf3, 0xf4, 0x7c, 0x6a, 0x4d, 0x9e, 0xeb, 0x3d, 0xb9, 0x63, 0x94, 0xce, 0x81, 0xd8, 0x11, 0xcb, 0x55, 0x69, 0x4a, 0x20, 0x0b, 0x4c, 0x2e, 0x14, 0xb8, 0xd4, 0x6a, 0x7c, 0xf0, 0xed, 0xfc, 0x8f, 0xef, 0xa0, 0xeb, 0x6c, 0x01, 0xe2, 0xdc, 0x10, 0x22, 0xa2, 0x01, 0x85, 0x64,
+	/* (2^326)P */ 0x58, 0xe1, 0x9c, 0x27, 0x55, 0xc6, 0x25, 0xa6, 0x7d, 0x67, 0x88, 0x65, 0x99, 0x6c, 0xcb, 0xdb, 0x27, 0x4f, 0x44, 0x29, 0xf5, 0x4a, 0x23, 0x10, 0xbc, 0x03, 0x3f, 0x36, 0x1e, 0xef, 0xb0, 0xba, 0x75, 0xe8, 0x74, 0x5f, 0x69, 0x3e, 0x26, 0x40, 0xb4, 0x2f, 0xdc, 0x43, 0xbf, 0xa1, 0x8b, 0xbd, 0xca, 0x6e, 0xc1, 0x6e, 0x21, 0x79, 0xa0, 0xd0,
+	/* (2^327)P */ 0x78, 0x93, 0x4a, 0x2d, 0x22, 0x6e, 0x6e, 0x7d, 0x74, 0xd2, 0x66, 0x58, 0xce, 0x7b, 0x1d, 0x97, 0xb1, 0xf2, 0xda, 0x1c, 0x79, 0xfb, 0xba, 0xd1, 0xc0, 0xc5, 0x6e, 0xc9, 0x11, 0x89, 0xd2, 0x41, 0x8d, 0x70, 0xb9, 0xcc, 0xea, 0x6a, 0xb3, 0x45, 0xb6, 0x05, 0x2e, 0xf2, 0x17, 0xf1, 0x27, 0xb8, 0xed, 0x06, 0x1f, 0xdb, 0x9d, 0x1f, 0x69, 0x28,
+	/* (2^328)P */ 0x93, 0x12, 0xa8, 0x11, 0xe1, 0x92, 0x30, 0x8d, 0xac, 0xe1, 0x1c, 0x60, 0x7c, 0xed, 0x2d, 0x2e, 0xd3, 0x03, 0x5c, 0x9c, 0xc5, 0xbd, 0x64, 0x4a, 0x8c, 0xba, 0x76, 0xfe, 0xc6, 0xc1, 0xea, 0xc2, 0x4f, 0xbe, 0x70, 0x3d, 0x64, 0xcf, 0x8e, 0x18, 0xcb, 0xcd, 0x57, 0xa7, 0xf7, 0x36, 0xa9, 0x6b, 0x3e, 0xb8, 0x69, 0xee, 0x47, 0xa2, 0x7e, 0xb2,
+	/* (2^329)P */ 0x96, 0xaf, 0x3a, 0xf5, 0xed, 0xcd, 0xaf, 0xf7, 0x82, 0xaf, 0x59, 0x62, 0x0b, 0x36, 0x85, 0xf9, 0xaf, 0xd6, 0x38, 0xff, 0x87, 0x2e, 0x1d, 0x6c, 0x8b, 0xaf, 0x3b, 0xdf, 0x28, 0xa2, 0xd6, 0x4d, 0x80, 0x92, 0xc3, 0x0f, 0x34, 0xa8, 0xae, 0x69, 0x5d, 0x7b, 0x9d, 0xbc, 0xf5, 0xfd, 0x1d, 0xb1, 0x96, 0x55, 0x86, 0xe1, 0x5c, 0xb6, 0xac, 0xb9,
+	/* (2^330)P */ 0x50, 0x9e, 0x37, 0x28, 0x7d, 0xa8, 0x33, 0x63, 0xda, 0x3f, 0x20, 0x98, 0x0e, 0x09, 0xa8, 0x77, 0x3b, 0x7a, 0xfc, 0x16, 0x85, 0x44, 0x64, 0x77, 0x65, 0x68, 0x92, 0x41, 0xc6, 0x1f, 0xdf, 0x27, 0xf9, 0xec, 0xa0, 0x61, 0x22, 0xea, 0x19, 0xe7, 0x75, 0x8b, 0x4e, 0xe5, 0x0f, 0xb7, 0xf7, 0xd2, 0x53, 0xf4, 0xdd, 0x4a, 0xaa, 0x78, 0x40, 0xb7,
+	/* (2^331)P */ 0xd4, 0x89, 0xe3, 0x79, 0xba, 0xb6, 0xc3, 0xda, 0xe6, 0x78, 0x65, 0x7d, 0x6e, 0x22, 0x62, 0xb1, 0x3d, 0xea, 0x90, 0x84, 0x30, 0x5e, 0xd4, 0x39, 0x84, 0x78, 0xd9, 0x75, 0xd6, 0xce, 0x2a, 0x11, 0x29, 0x69, 0xa4, 0x5e, 0xaa, 0x2a, 0x98, 0x5a, 0xe5, 0x91, 0x8f, 0xb2, 0xfb, 0xda, 0x97, 0xe8, 0x83, 0x6f, 0x04, 0xb9, 0x5d, 0xaf, 0xe1, 0x9b,
+	/* (2^332)P */ 0x8b, 0xe4, 0xe1, 0x48, 0x9c, 0xc4, 0x83, 0x89, 0xdf, 0x65, 0xd3, 0x35, 0x55, 0x13, 0xf4, 0x1f, 0x36, 0x92, 0x33, 0x38, 0xcb, 0xed, 0x15, 0xe6, 0x60, 0x2d, 0x25, 0xf5, 0x36, 0x60, 0x3a, 0x37, 0x9b, 0x71, 0x9d, 0x42, 0xb0, 0x14, 0xc8, 0xba, 0x62, 0xa3, 0x49, 0xb0, 0x88, 0xc1, 0x72, 0x73, 0xdd, 0x62, 0x40, 0xa9, 0x62, 0x88, 0x99, 0xca,
+	/* (2^333)P */ 0x47, 0x7b, 0xea, 0xda, 0x46, 0x2f, 0x45, 0xc6, 0xe3, 0xb4, 0x4d, 0x8d, 0xac, 0x0b, 0x54, 0x22, 0x06, 0x31, 0x16, 0x66, 0x3e, 0xe4, 0x38, 0x12, 0xcd, 0xf3, 0xe7, 0x99, 0x37, 0xd9, 0x62, 0x24, 0x4b, 0x05, 0xf2, 0x58, 0xe6, 0x29, 0x4b, 0x0d, 0xf6, 0xc1, 0xba, 0xa0, 0x1e, 0x0f, 0xcb, 0x1f, 0xc6, 0x2b, 0x19, 0xfc, 0x82, 0x01, 0xd0, 0x86,
+	/* (2^334)P */ 0xa2, 0xae, 0x77, 0x20, 0xfb, 0xa8, 0x18, 0xb4, 0x61, 0xef, 0xe8, 0x52, 0x79, 0xbb, 0x86, 0x90, 0x5d, 0x2e, 0x76, 0xed, 0x66, 0x60, 0x5d, 0x00, 0xb5, 0xa4, 0x00, 0x40, 0x89, 0xec, 0xd1, 0xd2, 0x0d, 0x26, 0xb9, 0x30, 0xb2, 0xd2, 0xb8, 0xe8, 0x0e, 0x56, 0xf9, 0x67, 0x94, 0x2e, 0x62, 0xe1, 0x79, 0x48, 0x2b, 0xa9, 0xfa, 0xea, 0xdb, 0x28,
+	/* (2^335)P */ 0x35, 0xf1, 0xb0, 0x43, 0xbd, 0x27, 0xef, 0x18, 0x44, 0xa2, 0x04, 0xb4, 0x69, 0xa1, 0x97, 0x1f, 0x8c, 0x04, 0x82, 0x9b, 0x00, 0x6d, 0xf8, 0xbf, 0x7d, 0xc1, 0x5b, 0xab, 0xe8, 0xb2, 0x34, 0xbd, 0xaf, 0x7f, 0xb2, 0x0d, 0xf3, 0xed, 0xfc, 0x5b, 0x50, 0xee, 0xe7, 0x4a, 0x20, 0xd9, 0xf5, 0xc6, 0x9a, 0x97, 0x6d, 0x07, 0x2f, 0xb9, 0x31, 0x02,
+	/* (2^336)P */ 0xf9, 0x54, 0x4a, 0xc5, 0x61, 0x7e, 0x1d, 0xa6, 0x0e, 0x1a, 0xa8, 0xd3, 0x8c, 0x36, 0x7d, 0xf1, 0x06, 0xb1, 0xac, 0x93, 0xcd, 0xe9, 0x8f, 0x61, 0x6c, 0x5d, 0x03, 0x23, 0xdf, 0x85, 0x53, 0x39, 0x63, 0x5e, 0xeb, 0xf3, 0xd3, 0xd3, 0x75, 0x97, 0x9b, 0x62, 0x9b, 0x01, 0xb3, 0x19, 0xd8, 0x2b, 0x36, 0xf2, 0x2c, 0x2c, 0x6f, 0x36, 0xc6, 0x3c,
+	/* (2^337)P */ 0x05, 0x74, 0x43, 0x10, 0xb6, 0xb0, 0xf8, 0xbf, 0x02, 0x46, 0x9a, 0xee, 0xc1, 0xaf, 0xc1, 0xe5, 0x5a, 0x2e, 0xbb, 0xe1, 0xdc, 0xc6, 0xce, 0x51, 0x29, 0x50, 0xbf, 0x1b, 0xde, 0xff, 0xba, 0x4d, 0x8d, 0x8b, 0x7e, 0xe7, 0xbd, 0x5b, 0x8f, 0xbe, 0xe3, 0x75, 0x71, 0xff, 0x37, 0x05, 0x5a, 0x10, 0xeb, 0x54, 0x7e, 0x44, 0x72, 0x2c, 0xd4, 0xfc,
+	/* (2^338)P */ 0x03, 0x12, 0x1c, 0xb2, 0x08, 0x90, 0xa1, 0x2d, 0x50, 0xa0, 0xad, 0x7f, 0x8d, 0xa6, 0x97, 0xc1, 0xbd, 0xdc, 0xc3, 0xa7, 0xad, 0x31, 0xdf, 0xb8, 0x03, 0x84, 0xc3, 0xb9, 0x29, 0x3d, 0x92, 0x2e, 0xc3, 0x90, 0x07, 0xe8, 0xa7, 0xc7, 0xbc, 0x61, 0xe9, 0x3e, 0xa0, 0x35, 0xda, 0x1d, 0xab, 0x48, 0xfe, 0x50, 0xc9, 0x25, 0x59, 0x23, 0x69, 0x3f,
+	/* (2^339)P */ 0x8e, 0x91, 0xab, 0x6b, 0x91, 0x4f, 0x89, 0x76, 0x67, 0xad, 0xb2, 0x65, 0x9d, 0xad, 0x02, 0x36, 0xdc, 0xac, 0x96, 0x93, 0x97, 0x21, 0x14, 0xd0, 0xe8, 0x11, 0x60, 0x1e, 0xeb, 0x96, 0x06, 0xf2, 0x53, 0xf2, 0x6d, 0xb7, 0x93, 0x6f, 0x26, 0x91, 0x23, 0xe3, 0x34, 0x04, 0x92, 0x91, 0x37, 0x08, 0x50, 0xd6, 0x28, 0x09, 0x27, 0xa1, 0x0c, 0x00,
+	/* (2^340)P */ 0x1f, 0xbb, 0x21, 0x26, 0x33, 0xcb, 0xa4, 0xd1, 0xee, 0x85, 0xf9, 0xd9, 0x3c, 0x90, 0xc3, 0xd1, 0x26, 0xa2, 0x25, 0x93, 0x43, 0x61, 0xed, 0x91, 0x6e, 0x54, 0x03, 0x2e, 0x42, 0x9d, 0xf7, 0xa6, 0x02, 0x0f, 0x2f, 0x9c, 0x7a, 0x8d, 0x12, 0xc2, 0x18, 0xfc, 0x41, 0xff, 0x85, 0x26, 0x1a, 0x44, 0x55, 0x0b, 0x89, 0xab, 0x6f, 0x62, 0x33, 0x8c,
+	/* (2^341)P */ 0xe0, 0x3c, 0x5d, 0x70, 0x64, 0x87, 0x81, 0x35, 0xf2, 0x37, 0xa6, 0x24, 0x3e, 0xe0, 0x62, 0xd5, 0x71, 0xe7, 0x93, 0xfb, 0xac, 0xc3, 0xe7, 0xc7, 0x04, 0xe2, 0x70, 0xd3, 0x29, 0x5b, 0x21, 0xbf, 0xf4, 0x26, 0x5d, 0xf3, 0x95, 0xb4, 0x2a, 0x6a, 0x07, 0x55, 0xa6, 0x4b, 0x3b, 0x15, 0xf2, 0x25, 0x8a, 0x95, 0x3f, 0x63, 0x2f, 0x7a, 0x23, 0x96,
+	/* (2^342)P */ 0x0d, 0x3d, 0xd9, 0x13, 0xa7, 0xb3, 0x5e, 0x67, 0xf7, 0x02, 0x23, 0xee, 0x84, 0xff, 0x99, 0xda, 0xb9, 0x53, 0xf8, 0xf0, 0x0e, 0x39, 0x2f, 0x3c, 0x64, 0x34, 0xe3, 0x09, 0xfd, 0x2b, 0x33, 0xc7, 0xfe, 0x62, 0x2b, 0x84, 0xdf, 0x2b, 0xd2, 0x7c, 0x26, 0x01, 0x70, 0x66, 0x5b, 0x85, 0xc2, 0xbe, 0x88, 0x37, 0xf1, 0x30, 0xac, 0xb8, 0x76, 0xa3,
+	/* (2^343)P */ 0x6e, 0x01, 0xf0, 0x55, 0x35, 0xe4, 0xbd, 0x43, 0x62, 0x9d, 0xd6, 0x11, 0xef, 0x6f, 0xb8, 0x8c, 0xaa, 0x98, 0x87, 0xc6, 0x6d, 0xc4, 0xcc, 0x74, 0x92, 0x53, 0x4a, 0xdf, 0xe4, 0x08, 0x89, 0x17, 0xd0, 0x0f, 0xf4, 0x00, 0x60, 0x78, 0x08, 0x44, 0xb5, 0xda, 0x18, 0xed, 0x98, 0xc8, 0x61, 0x3d, 0x39, 0xdb, 0xcf, 0x1d, 0x49, 0x40, 0x65, 0x75,
+	/* (2^344)P */ 0x8e, 0x10, 0xae, 0x5f, 0x06, 0xd2, 0x95, 0xfd, 0x20, 0x16, 0x49, 0x5b, 0x57, 0xbe, 0x22, 0x8b, 0x43, 0xfb, 0xe6, 0xcc, 0x26, 0xa5, 0x5d, 0xd3, 0x68, 0xc5, 0xf9, 0x5a, 0x86, 0x24, 0x87, 0x27, 0x05, 0xfd, 0xe2, 0xff, 0xb3, 0xa3, 0x7b, 0x37, 0x59, 0xc5, 0x4e, 0x14, 0x94, 0xf9, 0x3b, 0xcb, 0x7c, 0xed, 0xca, 0x1d, 0xb2, 0xac, 0x05, 0x4a,
+	/* (2^345)P */ 0xf4, 0xd1, 0x81, 0xeb, 0x89, 0xbf, 0xfe, 0x1e, 0x41, 0x92, 0x29, 0xee, 0xe1, 0x43, 0xf5, 0x86, 0x1d, 0x2f, 0xbb, 0x1e, 0x84, 0x5d, 0x7b, 0x8d, 0xd5, 0xda, 0xee, 0x1e, 0x8a, 0xd0, 0x27, 0xf2, 0x60, 0x51, 0x59, 0x82, 0xf4, 0x84, 0x2b, 0x5b, 0x14, 0x2d, 0x81, 0x82, 0x3e, 0x2b, 0xb4, 0x6d, 0x51, 0x4f, 0xc5, 0xcb, 0xbf, 0x74, 0xe3, 0xb4,
+	/* (2^346)P */ 0x19, 0x2f, 0x22, 0xb3, 0x04, 0x5f, 0x81, 0xca, 0x05, 0x60, 0xb9, 0xaa, 0xee, 0x0e, 0x2f, 0x48, 0x38, 0xf9, 0x91, 0xb4, 0x66, 0xe4, 0x57, 0x28, 0x54, 0x10, 0xe9, 0x61, 0x9d, 0xd4, 0x90, 0x75, 0xb1, 0x39, 0x23, 0xb6, 0xfc, 0x82, 0xe0, 0xfa, 0xbb, 0x5c, 0x6e, 0xc3, 0x44, 0x13, 0x00, 0x83, 0x55, 0x9e, 0x8e, 0x10, 0x61, 0x81, 0x91, 0x04,
+	/* (2^347)P */ 0x5f, 0x2a, 0xd7, 0x81, 0xd9, 0x9c, 0xbb, 0x79, 0xbc, 0x62, 0x56, 0x98, 0x03, 0x5a, 0x18, 0x85, 0x2a, 0x9c, 0xd0, 0xfb, 0xd2, 0xb1, 0xaf, 0xef, 0x0d, 0x24, 0xc5, 0xfa, 0x39, 0xbb, 0x6b, 0xed, 0xa4, 0xdf, 0xe4, 0x87, 0xcd, 0x41, 0xd3, 0x72, 0x32, 0xc6, 0x28, 0x21, 0xb1, 0xba, 0x8b, 0xa3, 0x91, 0x79, 0x76, 0x22, 0x25, 0x10, 0x61, 0xd1,
+	/* (2^348)P */ 0x73, 0xb5, 0x32, 0x97, 0xdd, 0xeb, 0xdd, 0x22, 0x22, 0xf1, 0x33, 0x3c, 0x77, 0x56, 0x7d, 0x6b, 0x48, 0x2b, 0x05, 0x81, 0x03, 0x03, 0x91, 0x9a, 0xe3, 0x5e, 0xd4, 0xee, 0x3f, 0xf8, 0xbb, 0x50, 0x21, 0x32, 0x4c, 0x4a, 0x58, 0x49, 0xde, 0x0c, 0xde, 0x30, 0x82, 0x3d, 0x92, 0xf0, 0x6c, 0xcc, 0x32, 0x3e, 0xd2, 0x78, 0x8a, 0x6e, 0x2c, 0xd0,
+	/* (2^349)P */ 0xf0, 0xf7, 0xa1, 0x0b, 0xc1, 0x74, 0x85, 0xa8, 0xe9, 0xdd, 0x48, 0xa1, 0xc0, 0x16, 0xd8, 0x2b, 0x61, 0x08, 0xc2, 0x2b, 0x30, 0x26, 0x79, 0xce, 0x9e, 0xfd, 0x39, 0xd7, 0x81, 0xa4, 0x63, 0x8c, 0xd5, 0x74, 0xa0, 0x88, 0xfa, 0x03, 0x30, 0xe9, 0x7f, 0x2b, 0xc6, 0x02, 0xc9, 0x5e, 0xe4, 0xd5, 0x4d, 0x92, 0xd0, 0xf6, 0xf2, 0x5b, 0x79, 0x08,
+	/* (2^350)P */ 0x34, 0x89, 0x81, 0x43, 0xd1, 0x94, 0x2c, 0x10, 0x54, 0x9b, 0xa0, 0xe5, 0x44, 0xe8, 0xc2, 0x2f, 0x3e, 0x0e, 0x74, 0xae, 0xba, 0xe2, 0xac, 0x85, 0x6b, 0xd3, 0x5c, 0x97, 0xf7, 0x90, 0xf1, 0x12, 0xc0, 0x03, 0xc8, 0x1f, 0x37, 0x72, 0x8c, 0x9b, 0x9c, 0x17, 0x96, 0x9d, 0xc7, 0xbf, 0xa3, 0x3f, 0x44, 0x3d, 0x87, 0x81, 0xbd, 0x81, 0xa6, 0x5f,
+	/* (2^351)P */ 0xe4, 0xff, 0x78, 0x62, 0x82, 0x5b, 0x76, 0x58, 0xf5, 0x5b, 0xa6, 0xc4, 0x53, 0x11, 0x3b, 0x7b, 0xaa, 0x67, 0xf8, 0xea, 0x3b, 0x5d, 0x9a, 0x2e, 0x04, 0xeb, 0x4a, 0x24, 0xfb, 0x56, 0xf0, 0xa8, 0xd4, 0x14, 0xed, 0x0f, 0xfd, 0xc5, 0x26, 0x17, 0x2a, 0xf0, 0xb9, 0x13, 0x8c, 0xbd, 0x65, 0x14, 0x24, 0x95, 0x27, 0x12, 0x63, 0x2a, 0x09, 0x18,
+	/* (2^352)P */ 0xe1, 0x5c, 0xe7, 0xe0, 0x00, 0x6a, 0x96, 0xf2, 0x49, 0x6a, 0x39, 0xa5, 0xe0, 0x17, 0x79, 0x4a, 0x63, 0x07, 0x62, 0x09, 0x61, 0x1b, 0x6e, 0xa9, 0xb5, 0x62, 0xb7, 0xde, 0xdf, 0x80, 0x4c, 0x5a, 0x99, 0x73, 0x59, 0x9d, 0xfb, 0xb1, 0x5e, 0xbe, 0xb8, 0xb7, 0x63, 0x93, 0xe8, 0xad, 0x5e, 0x1f, 0xae, 0x59, 0x1c, 0xcd, 0xb4, 0xc2, 0xb3, 0x8a,
+	/* (2^353)P */ 0x78, 0x53, 0xa1, 0x4c, 0x70, 0x9c, 0x63, 0x7e, 0xb3, 0x12, 0x40, 0x5f, 0xbb, 0x23, 0xa7, 0xf7, 0x77, 0x96, 0x5b, 0x4d, 0x91, 0x10, 0x52, 0x85, 0x9e, 0xa5, 0x38, 0x0b, 0xfd, 0x25, 0x01, 0x4b, 0xfa, 0x4d, 0xd3, 0x3f, 0x78, 0x74, 0x42, 0xff, 0x62, 0x2d, 0x27, 0xdc, 0x9d, 0xd1, 0x29, 0x76, 0x2e, 0x78, 0xb3, 0x35, 0xfa, 0x15, 0xd5, 0x38,
+	/* (2^354)P */ 0x8b, 0xc7, 0x43, 0xce, 0xf0, 0x5e, 0xf1, 0x0d, 0x02, 0x38, 0xe8, 0x82, 0xc9, 0x25, 0xad, 0x2d, 0x27, 0xa4, 0x54, 0x18, 0xb2, 0x30, 0x73, 0xa4, 0x41, 0x08, 0xe4, 0x86, 0xe6, 0x8c, 0xe9, 0x2a, 0x34, 0xb3, 0xd6, 0x61, 0x8f, 0x66, 0x26, 0x08, 0xb6, 0x06, 0x33, 0xaa, 0x12, 0xac, 0x72, 0xec, 0x2e, 0x52, 0xa3, 0x25, 0x3e, 0xd7, 0x62, 0xe8,
+	/* (2^355)P */ 0xc4, 0xbb, 0x89, 0xc8, 0x40, 0xcc, 0x84, 0xec, 0x4a, 0xd9, 0xc4, 0x55, 0x78, 0x00, 0xcf, 0xd8, 0xe9, 0x24, 0x59, 0xdc, 0x5e, 0xf0, 0x66, 0xa1, 0x83, 0xae, 0x97, 0x18, 0xc5, 0x54, 0x27, 0xa2, 0x21, 0x52, 0x03, 0x31, 0x5b, 0x11, 0x67, 0xf6, 0x12, 0x00, 0x87, 0x2f, 0xff, 0x59, 0x70, 0x8f, 0x6d, 0x71, 0xab, 0xab, 0x24, 0xb8, 0xba, 0x35,
+	/* (2^356)P */ 0x69, 0x43, 0xa7, 0x14, 0x06, 0x96, 0xe9, 0xc2, 0xe3, 0x2b, 0x45, 0x22, 0xc0, 0xd0, 0x2f, 0x34, 0xd1, 0x01, 0x99, 0xfc, 0x99, 0x38, 0xa1, 0x25, 0x2e, 0x59, 0x6c, 0x27, 0xc9, 0xeb, 0x7b, 0xdc, 0x4e, 0x26, 0x68, 0xba, 0xfa, 0xec, 0x02, 0x05, 0x64, 0x80, 0x30, 0x20, 0x5c, 0x26, 0x7f, 0xaf, 0x95, 0x17, 0x3d, 0x5c, 0x9e, 0x96, 0x96, 0xaf,
+	/* (2^357)P */ 0xa6, 0xba, 0x21, 0x29, 0x32, 0xe2, 0x98, 0xde, 0x9b, 0x6d, 0x0b, 0x44, 0x91, 0xa8, 0x3e, 0xd4, 0xb8, 0x04, 0x6c, 0xf6, 0x04, 0x39, 0xbd, 0x52, 0x05, 0x15, 0x27, 0x78, 0x8e, 0x55, 0xac, 0x79, 0xc5, 0xe6, 0x00, 0x7f, 0x90, 0xa2, 0xdd, 0x07, 0x13, 0xe0, 0x24, 0x70, 0x5c, 0x0f, 0x4d, 0xa9, 0xf9, 0xae, 0xcb, 0x34, 0x10, 0x9d, 0x89, 0x9d,
+	/* (2^358)P */ 0x12, 0xe0, 0xb3, 0x9f, 0xc4, 0x96, 0x1d, 0xcf, 0xed, 0x99, 0x64, 0x28, 0x8d, 0xc7, 0x31, 0x82, 0xee, 0x5e, 0x75, 0x48, 0xff, 0x3a, 0xf2, 0x09, 0x34, 0x03, 0x93, 0x52, 0x19, 0xb2, 0xc5, 0x81, 0x93, 0x45, 0x5e, 0x59, 0x21, 0x2b, 0xec, 0x89, 0xba, 0x36, 0x6e, 0xf9, 0x82, 0x75, 0x7e, 0x82, 0x3f, 0xaa, 0xe2, 0xe3, 0x3b, 0x94, 0xfd, 0x98,
+	/* (2^359)P */ 0x7c, 0xdb, 0x75, 0x31, 0x61, 0xfb, 0x15, 0x28, 0x94, 0xd7, 0xc3, 0x5a, 0xa9, 0xa1, 0x0a, 0x66, 0x0f, 0x2b, 0x13, 0x3e, 0x42, 0xb5, 0x28, 0x3a, 0xca, 0x83, 0xf3, 0x61, 0x22, 0xf4, 0x40, 0xc5, 0xdf, 0xe7, 0x31, 0x9f, 0x7e, 0x51, 0x75, 0x06, 0x9d, 0x51, 0xc8, 0xe7, 0x9f, 0xc3, 0x71, 0x4f, 0x3d, 0x5b, 0xfb, 0xe9, 0x8e, 0x08, 0x40, 0x8e,
+	/* (2^360)P */ 0xf7, 0x31, 0xad, 0x50, 0x5d, 0x25, 0x93, 0x73, 0x68, 0xf6, 0x7c, 0x89, 0x5a, 0x3d, 0x9f, 0x9b, 0x05, 0x82, 0xe7, 0x70, 0x4b, 0x19, 0xaa, 0xcf, 0xff, 0xde, 0x50, 0x8f, 0x2f, 0x69, 0xd3, 0xf0, 0x99, 0x51, 0x6b, 0x9d, 0xb6, 0x56, 0x6f, 0xf8, 0x4c, 0x74, 0x8b, 0x4c, 0x91, 0xf9, 0xa9, 0xb1, 0x3e, 0x07, 0xdf, 0x0b, 0x27, 0x8a, 0xb1, 0xed,
+	/* (2^361)P */ 0xfb, 0x67, 0xd9, 0x48, 0xd2, 0xe4, 0x44, 0x9b, 0x43, 0x15, 0x8a, 0xeb, 0x00, 0x53, 0xad, 0x25, 0xc7, 0x7e, 0x19, 0x30, 0x87, 0xb7, 0xd5, 0x5f, 0x04, 0xf8, 0xaa, 0xdd, 0x57, 0xae, 0x34, 0x75, 0xe2, 0x84, 0x4b, 0x54, 0x60, 0x37, 0x95, 0xe4, 0xd3, 0xec, 0xac, 0xef, 0x47, 0x31, 0xa3, 0xc8, 0x31, 0x22, 0xdb, 0x26, 0xe7, 0x6a, 0xb5, 0xad,
+	/* (2^362)P */ 0x44, 0x09, 0x5c, 0x95, 0xe4, 0x72, 0x3c, 0x1a, 0xd1, 0xac, 0x42, 0x51, 0x99, 0x6f, 0xfa, 0x1f, 0xf2, 0x22, 0xbe, 0xff, 0x7b, 0x66, 0xf5, 0x6c, 0xb3, 0x66, 0xc7, 0x4d, 0x78, 0x31, 0x83, 0x80, 0xf5, 0x41, 0xe9, 0x7f, 0xbe, 0xf7, 0x23, 0x49, 0x6b, 0x84, 0x4e, 0x7e, 0x47, 0x07, 0x6e, 0x74, 0xdf, 0xe5, 0x9d, 0x9e, 0x56, 0x2a, 0xc0, 0xbc,
+	/* (2^363)P */ 0xac, 0x10, 0x80, 0x8c, 0x7c, 0xfa, 0x83, 0xdf, 0xb3, 0xd0, 0xc4, 0xbe, 0xfb, 0x9f, 0xac, 0xc9, 0xc3, 0x40, 0x95, 0x0b, 0x09, 0x23, 0xda, 0x63, 0x67, 0xcf, 0xe7, 0x9f, 0x7d, 0x7b, 0x6b, 0xe2, 0xe6, 0x6d, 0xdb, 0x87, 0x9e, 0xa6, 0xff, 0x6d, 0xab, 0xbd, 0xfb, 0x54, 0x84, 0x68, 0xcf, 0x89, 0xf1, 0xd0, 0xe2, 0x85, 0x61, 0xdc, 0x22, 0xd1,
+	/* (2^364)P */ 0xa8, 0x48, 0xfb, 0x8c, 0x6a, 0x63, 0x01, 0x72, 0x43, 0x43, 0xeb, 0x21, 0xa3, 0x00, 0x8a, 0xc0, 0x87, 0x51, 0x9e, 0x86, 0x75, 0x16, 0x79, 0xf9, 0x6b, 0x11, 0x80, 0x62, 0xc2, 0x9d, 0xb8, 0x8c, 0x30, 0x8e, 0x8d, 0x03, 0x52, 0x7e, 0x31, 0x59, 0x38, 0xf9, 0x25, 0xc7, 0x0f, 0xc7, 0xa8, 0x2b, 0x5c, 0x80, 0xfa, 0x90, 0xa2, 0x63, 0xca, 0xe7,
+	/* (2^365)P */ 0xf1, 0x5d, 0xb5, 0xd9, 0x20, 0x10, 0x7d, 0x0f, 0xc5, 0x50, 0x46, 0x07, 0xff, 0x02, 0x75, 0x2b, 0x4a, 0xf3, 0x39, 0x91, 0x72, 0xb7, 0xd5, 0xcc, 0x38, 0xb8, 0xe7, 0x36, 0x26, 0x5e, 0x11, 0x97, 0x25, 0xfb, 0x49, 0x68, 0xdc, 0xb4, 0x46, 0x87, 0x5c, 0xc2, 0x7f, 0xaa, 0x7d, 0x36, 0x23, 0xa6, 0xc6, 0x53, 0xec, 0xbc, 0x57, 0x47, 0xc1, 0x2b,
+	/* (2^366)P */ 0x25, 0x5d, 0x7d, 0x95, 0xda, 0x0b, 0x8f, 0x78, 0x1e, 0x19, 0x09, 0xfa, 0x67, 0xe0, 0xa0, 0x17, 0x24, 0x76, 0x6c, 0x30, 0x1f, 0x62, 0x3d, 0xbe, 0x45, 0x70, 0xcc, 0xb6, 0x1e, 0x68, 0x06, 0x25, 0x68, 0x16, 0x1a, 0x33, 0x3f, 0x90, 0xc7, 0x78, 0x2d, 0x98, 0x3c, 0x2f, 0xb9, 0x2d, 0x94, 0x0b, 0xfb, 0x49, 0x56, 0x30, 0xd7, 0xc1, 0xe6, 0x48,
+	/* (2^367)P */ 0x7a, 0xd1, 0xe0, 0x8e, 0x67, 0xfc, 0x0b, 0x50, 0x1f, 0x84, 0x98, 0xfa, 0xaf, 0xae, 0x2e, 0x31, 0x27, 0xcf, 0x3f, 0xf2, 0x6e, 0x8d, 0x81, 0x8f, 0xd2, 0x5f, 0xde, 0xd3, 0x5e, 0xe9, 0xe7, 0x13, 0x48, 0x83, 0x5a, 0x4e, 0x84, 0xd1, 0x58, 0xcf, 0x6b, 0x84, 0xdf, 0x13, 0x1d, 0x91, 0x85, 0xe8, 0xcb, 0x29, 0x79, 0xd2, 0xca, 0xac, 0x6a, 0x93,
+	/* (2^368)P */ 0x53, 0x82, 0xce, 0x61, 0x96, 0x88, 0x6f, 0xe1, 0x4a, 0x4c, 0x1e, 0x30, 0x73, 0xe8, 0x74, 0xde, 0x40, 0x2b, 0xe0, 0xc4, 0xb5, 0xd8, 0x7c, 0x15, 0xe7, 0xe1, 0xb1, 0xe0, 0xd6, 0x88, 0xb1, 0x6a, 0x57, 0x19, 0x6a, 0x22, 0x66, 0x57, 0xf6, 0x8d, 0xfd, 0xc0, 0xf2, 0xa3, 0x03, 0x56, 0xfb, 0x2e, 0x75, 0x5e, 0xc7, 0x8e, 0x22, 0x96, 0x5c, 0x06,
+	/* (2^369)P */ 0x98, 0x7e, 0xbf, 0x3e, 0xbf, 0x24, 0x9d, 0x15, 0xd3, 0xf6, 0xd3, 0xd2, 0xf0, 0x11, 0xf2, 0xdb, 0x36, 0x23, 0x38, 0xf7, 0x1d, 0x71, 0x20, 0xd2, 0x54, 0x7f, 0x1e, 0x24, 0x8f, 0xe2, 0xaa, 0xf7, 0x3f, 0x6b, 0x41, 0x4e, 0xdc, 0x0e, 0xec, 0xe8, 0x35, 0x0a, 0x08, 0x6d, 0x89, 0x5b, 0x32, 0x91, 0x01, 0xb6, 0xe0, 0x2c, 0xc6, 0xa1, 0xbe, 0xb4,
+	/* (2^370)P */ 0x29, 0xf2, 0x1e, 0x1c, 0xdc, 0x68, 0x8a, 0x43, 0x87, 0x2c, 0x48, 0xb3, 0x9e, 0xed, 0xd2, 0x82, 0x46, 0xac, 0x2f, 0xef, 0x93, 0x34, 0x37, 0xca, 0x64, 0x8d, 0xc9, 0x06, 0x90, 0xbb, 0x78, 0x0a, 0x3c, 0x4c, 0xcf, 0x35, 0x7a, 0x0f, 0xf7, 0xa7, 0xf4, 0x2f, 0x45, 0x69, 0x3f, 0xa9, 0x5d, 0xce, 0x7b, 0x8a, 0x84, 0xc3, 0xae, 0xf4, 0xda, 0xd5,
+	/* (2^371)P */ 0xca, 0xba, 0x95, 0x43, 0x05, 0x7b, 0x06, 0xd9, 0x5c, 0x0a, 0x18, 0x5f, 0x6a, 0x6a, 0xce, 0xc0, 0x3d, 0x95, 0x51, 0x0e, 0x1a, 0xbe, 0x85, 0x7a, 0xf2, 0x69, 0xec, 0xc0, 0x8c, 0xca, 0xa3, 0x32, 0x0a, 0x76, 0x50, 0xc6, 0x76, 0x61, 0x00, 0x89, 0xbf, 0x6e, 0x0f, 0x48, 0x90, 0x31, 0x93, 0xec, 0x34, 0x70, 0xf0, 0xc3, 0x8d, 0xf0, 0x0f, 0xb5,
+	/* (2^372)P */ 0xbe, 0x23, 0xe2, 0x18, 0x99, 0xf1, 0xed, 0x8a, 0xf6, 0xc9, 0xac, 0xb8, 0x1e, 0x9a, 0x3c, 0x15, 0xae, 0xd7, 0x6d, 0xb3, 0x04, 0xee, 0x5b, 0x0d, 0x1e, 0x79, 0xb7, 0xf9, 0xf9, 0x8d, 0xad, 0xf9, 0x8f, 0x5a, 0x6a, 0x7b, 0xd7, 0x9b, 0xca, 0x62, 0xfe, 0x9c, 0xc0, 0x6f, 0x6d, 0x9d, 0x76, 0xa3, 0x69, 0xb9, 0x4c, 0xa1, 0xc4, 0x0c, 0x76, 0xaa,
+	/* (2^373)P */ 0x1c, 0x06, 0xfe, 0x3f, 0x45, 0x70, 0xcd, 0x97, 0xa9, 0xa2, 0xb1, 0xd3, 0xf2, 0xa5, 0x0c, 0x49, 0x2c, 0x75, 0x73, 0x1f, 0xcf, 0x00, 0xaf, 0xd5, 0x2e, 0xde, 0x0d, 0x8f, 0x8f, 0x7c, 0xc4, 0x58, 0xce, 0xd4, 0xf6, 0x24, 0x19, 0x2e, 0xd8, 0xc5, 0x1d, 0x1a, 0x3f, 0xb8, 0x4f, 0xbc, 0x7d, 0xbd, 0x68, 0xe3, 0x81, 0x98, 0x1b, 0xa8, 0xc9, 0xd9,
+	/* (2^374)P */ 0x39, 0x95, 0x78, 0x24, 0x6c, 0x38, 0xe4, 0xe7, 0xd0, 0x8d, 0xb9, 0x38, 0x71, 0x5e, 0xc1, 0x62, 0x80, 0xcc, 0xcb, 0x8c, 0x97, 0xca, 0xf8, 0xb9, 0xd9, 0x9c, 0xce, 0x72, 0x7b, 0x70, 0xee, 0x5f, 0xea, 0xa2, 0xdf, 0xa9, 0x14, 0x10, 0xf9, 0x6e, 0x59, 0x9f, 0x9c, 0xe0, 0x0c, 0xb2, 0x07, 0x97, 0xcd, 0xd2, 0x89, 0x16, 0xfd, 0x9c, 0xa8, 0xa5,
+	/* (2^375)P */ 0x5a, 0x61, 0xf1, 0x59, 0x7c, 0x38, 0xda, 0xe2, 0x85, 0x99, 0x68, 0xe9, 0xc9, 0xf7, 0x32, 0x7e, 0xc4, 0xca, 0xb7, 0x11, 0x08, 0x69, 0x2b, 0x66, 0x02, 0xf7, 0x2e, 0x18, 0xc3, 0x8e, 0xe1, 0xf9, 0xc5, 0x19, 0x9a, 0x0a, 0x9c, 0x07, 0xba, 0xc7, 0x9c, 0x03, 0x34, 0x89, 0x99, 0x67, 0x0b, 0x16, 0x4b, 0x07, 0x36, 0x16, 0x36, 0x2c, 0xe2, 0xa1,
+	/* (2^376)P */ 0x70, 0x10, 0x91, 0x27, 0xa8, 0x24, 0x8e, 0x29, 0x04, 0x6f, 0x79, 0x1f, 0xd3, 0xa5, 0x68, 0xd3, 0x0b, 0x7d, 0x56, 0x4d, 0x14, 0x57, 0x7b, 0x2e, 0x00, 0x9f, 0x9a, 0xfd, 0x6c, 0x63, 0x18, 0x81, 0xdb, 0x9d, 0xb7, 0xd7, 0xa4, 0x1e, 0xe8, 0x40, 0xf1, 0x4c, 0xa3, 0x01, 0xd5, 0x4b, 0x75, 0xea, 0xdd, 0x97, 0xfd, 0x5b, 0xb2, 0x66, 0x6a, 0x24,
+	/* (2^377)P */ 0x72, 0x11, 0xfe, 0x73, 0x1b, 0xd3, 0xea, 0x7f, 0x93, 0x15, 0x15, 0x05, 0xfe, 0x40, 0xe8, 0x28, 0xd8, 0x50, 0x47, 0x66, 0xfa, 0xb7, 0xb5, 0x04, 0xba, 0x35, 0x1e, 0x32, 0x9f, 0x5f, 0x32, 0xba, 0x3d, 0xd1, 0xed, 0x9a, 0x76, 0xca, 0xa3, 0x3e, 0x77, 0xd8, 0xd8, 0x7c, 0x5f, 0x68, 0x42, 0xb5, 0x86, 0x7f, 0x3b, 0xc9, 0xc1, 0x89, 0x64, 0xda,
+	/* (2^378)P */ 0xd5, 0xd4, 0x17, 0x31, 0xfc, 0x6a, 0xfd, 0xb8, 0xe8, 0xe5, 0x3e, 0x39, 0x06, 0xe4, 0xd1, 0x90, 0x2a, 0xca, 0xf6, 0x54, 0x6c, 0x1b, 0x2f, 0x49, 0x97, 0xb1, 0x2a, 0x82, 0x43, 0x3d, 0x1f, 0x8b, 0xe2, 0x47, 0xc5, 0x24, 0xa8, 0xd5, 0x53, 0x29, 0x7d, 0xc6, 0x87, 0xa6, 0x25, 0x3a, 0x64, 0xdd, 0x71, 0x08, 0x9e, 0xcd, 0xe9, 0x45, 0xc7, 0xba,
+	/* (2^379)P */ 0x37, 0x72, 0x6d, 0x13, 0x7a, 0x8d, 0x04, 0x31, 0xe6, 0xe3, 0x9e, 0x36, 0x71, 0x3e, 0xc0, 0x1e, 0xe3, 0x71, 0xd3, 0x49, 0x4e, 0x4a, 0x36, 0x42, 0x68, 0x68, 0x61, 0xc7, 0x3c, 0xdb, 0x81, 0x49, 0xf7, 0x91, 0x4d, 0xea, 0x4c, 0x4f, 0x98, 0xc6, 0x7e, 0x60, 0x84, 0x4b, 0x6a, 0x37, 0xbb, 0x52, 0xf7, 0xce, 0x02, 0xe4, 0xad, 0xd1, 0x3c, 0xa7,
+	/* (2^380)P */ 0x51, 0x06, 0x2d, 0xf8, 0x08, 0xe8, 0xf1, 0x0c, 0xe5, 0xa9, 0xac, 0x29, 0x73, 0x3b, 0xed, 0x98, 0x5f, 0x55, 0x08, 0x38, 0x51, 0x44, 0x36, 0x5d, 0xea, 0xc3, 0xb8, 0x0e, 0xa0, 0x4f, 0xd2, 0x79, 0xe9, 0x98, 0xc3, 0xf5, 0x00, 0xb9, 0x26, 0x27, 0x42, 0xa8, 0x07, 0xc1, 0x12, 0x31, 0xc1, 0xc3, 0x3c, 0x3b, 0x7a, 0x72, 0x97, 0xc2, 0x70, 0x3a,
+	/* (2^381)P */ 0xf4, 0xb2, 0xba, 0x32, 0xbc, 0xa9, 0x2f, 0x87, 0xc7, 0x3c, 0x45, 0xcd, 0xae, 0xe2, 0x13, 0x6d, 0x3a, 0xf2, 0xf5, 0x66, 0x97, 0x29, 0xaf, 0x53, 0x9f, 0xda, 0xea, 0x14, 0xdf, 0x04, 0x98, 0x19, 0x95, 0x9e, 0x2a, 0x00, 0x5c, 0x9d, 0x1d, 0xf0, 0x39, 0x23, 0xff, 0xfc, 0xca, 0x36, 0xb7, 0xde, 0xdf, 0x37, 0x78, 0x52, 0x21, 0xfa, 0x19, 0x10,
+	/* (2^382)P */ 0x50, 0x20, 0x73, 0x74, 0x62, 0x21, 0xf2, 0xf7, 0x9b, 0x66, 0x85, 0x34, 0x74, 0xd4, 0x9d, 0x60, 0xd7, 0xbc, 0xc8, 0x46, 0x3b, 0xb8, 0x80, 0x42, 0x15, 0x0a, 0x6c, 0x35, 0x1a, 0x69, 0xf0, 0x1d, 0x4b, 0x29, 0x54, 0x5a, 0x9a, 0x48, 0xec, 0x9f, 0x37, 0x74, 0x91, 0xd0, 0xd1, 0x9e, 0x00, 0xc2, 0x76, 0x56, 0xd6, 0xa0, 0x15, 0x14, 0x83, 0x59,
+	/* (2^383)P */ 0xc2, 0xf8, 0x22, 0x20, 0x23, 0x07, 0xbd, 0x1d, 0x6f, 0x1e, 0x8c, 0x56, 0x06, 0x6a, 0x4b, 0x9f, 0xe2, 0xa9, 0x92, 0x46, 0x4b, 0x46, 0x59, 0xd7, 0xe1, 0xda, 0x14, 0x98, 0x07, 0x65, 0x7e, 0x28, 0x20, 0xf2, 0x9d, 0x4f, 0x36, 0x5c, 0x92, 0xe0, 0x9d, 0xfe, 0x3e, 0xda, 0xe4, 0x47, 0x19, 0x3c, 0x00, 0x7f, 0x22, 0xf2, 0x9e, 0x51, 0xae, 0x4d,
+	/* (2^384)P */ 0xbe, 0x8c, 0x1b, 0x10, 0xb6, 0xad, 0xcc, 0xcc, 0xd8, 0x5e, 0x21, 0xa6, 0xfb, 0xf1, 0xf6, 0xbd, 0x0a, 0x24, 0x67, 0xb4, 0x57, 0x7a, 0xbc, 0xe8, 0xe9, 0xff, 0xee, 0x0a, 0x1f, 0xee, 0xbd, 0xc8, 0x44, 0xed, 0x2b, 0xbb, 0x55, 0x1f, 0xdd, 0x7c, 0xb3, 0xeb, 0x3f, 0x63, 0xa1, 0x28, 0x91, 0x21, 0xab, 0x71, 0xc6, 0x4c, 0xd0, 0xe9, 0xb0, 0x21,
+	/* (2^385)P */ 0xad, 0xc9, 0x77, 0x2b, 0xee, 0x89, 0xa4, 0x7b, 0xfd, 0xf9, 0xf6, 0x14, 0xe4, 0xed, 0x1a, 0x16, 0x9b, 0x78, 0x41, 0x43, 0xa8, 0x83, 0x72, 0x06, 0x2e, 0x7c, 0xdf, 0xeb, 0x7e, 0xdd, 0xd7, 0x8b, 0xea, 0x9a, 0x2b, 0x03, 0xba, 0x57, 0xf3, 0xf1, 0xd9, 0xe5, 0x09, 0xc5, 0x98, 0x61, 0x1c, 0x51, 0x6d, 0x5d, 0x6e, 0xfb, 0x5e, 0x95, 0x9f, 0xb5,
+	/* (2^386)P */ 0x23, 0xe2, 0x1e, 0x95, 0xa3, 0x5e, 0x42, 0x10, 0xc7, 0xc3, 0x70, 0xbf, 0x4b, 0x6b, 0x83, 0x36, 0x93, 0xb7, 0x68, 0x47, 0x88, 0x3a, 0x10, 0x88, 0x48, 0x7f, 0x8c, 0xae, 0x54, 0x10, 0x02, 0xa4, 0x52, 0x8f, 0x8d, 0xf7, 0x26, 0x4f, 0x50, 0xc3, 0x6a, 0xe2, 0x4e, 0x3b, 0x4c, 0xb9, 0x8a, 0x14, 0x15, 0x6d, 0x21, 0x29, 0xb3, 0x6e, 0x4e, 0xd0,
+	/* (2^387)P */ 0x4c, 0x8a, 0x18, 0x3f, 0xb7, 0x20, 0xfd, 0x3e, 0x54, 0xca, 0x68, 0x3c, 0xea, 0x6f, 0xf4, 0x6b, 0xa2, 0xbd, 0x01, 0xbd, 0xfe, 0x08, 0xa8, 0xd8, 0xc2, 0x20, 0x36, 0x05, 0xcd, 0xe9, 0xf3, 0x9e, 0xfa, 0x85, 0x66, 0x8f, 0x4b, 0x1d, 0x8c, 0x64, 0x4f, 0xb8, 0xc6, 0x0f, 0x5b, 0x57, 0xd8, 0x24, 0x19, 0x5a, 0x14, 0x4b, 0x92, 0xd3, 0x96, 0xbc,
+	/* (2^388)P */ 0xa9, 0x3f, 0xc9, 0x6c, 0xca, 0x64, 0x1e, 0x6f, 0xdf, 0x65, 0x7f, 0x9a, 0x47, 0x6b, 0x8a, 0x60, 0x31, 0xa6, 0x06, 0xac, 0x69, 0x30, 0xe6, 0xea, 0x63, 0x42, 0x26, 0x5f, 0xdb, 0xd0, 0xf2, 0x8e, 0x34, 0x0a, 0x3a, 0xeb, 0xf3, 0x79, 0xc8, 0xb7, 0x60, 0x56, 0x5c, 0x37, 0x95, 0x71, 0xf8, 0x7f, 0x49, 0x3e, 0x9e, 0x01, 0x26, 0x1e, 0x80, 0x9f,
+	/* (2^389)P */ 0xf8, 0x16, 0x9a, 0xaa, 0xb0, 0x28, 0xb5, 0x8e, 0xd0, 0x60, 0xe5, 0x26, 0xa9, 0x47, 0xc4, 0x5c, 0xa9, 0x39, 0xfe, 0x0a, 0xd8, 0x07, 0x2b, 0xb3, 0xce, 0xf1, 0xea, 0x1a, 0xf4, 0x7b, 0x98, 0x31, 0x3d, 0x13, 0x29, 0x80, 0xe8, 0x0d, 0xcf, 0x56, 0x39, 0x86, 0x50, 0x0c, 0xb3, 0x18, 0xf4, 0xc5, 0xca, 0xf2, 0x6f, 0xcd, 0x8d, 0xd5, 0x02, 0xb0,
+	/* (2^390)P */ 0xbf, 0x39, 0x3f, 0xac, 0x6d, 0x1a, 0x6a, 0xe4, 0x42, 0x24, 0xd6, 0x41, 0x9d, 0xb9, 0x5b, 0x46, 0x73, 0x93, 0x76, 0xaa, 0xb7, 0x37, 0x36, 0xa6, 0x09, 0xe5, 0x04, 0x3b, 0x66, 0xc4, 0x29, 0x3e, 0x41, 0xc2, 0xcb, 0xe5, 0x17, 0xd7, 0x34, 0x67, 0x1d, 0x2c, 0x12, 0xec, 0x24, 0x7a, 0x40, 0xa2, 0x45, 0x41, 0xf0, 0x75, 0xed, 0x43, 0x30, 0xc9,
+	/* (2^391)P */ 0x80, 0xf6, 0x47, 0x5b, 0xad, 0x54, 0x02, 0xbc, 0xdd, 0xa4, 0xb2, 0xd7, 0x42, 0x95, 0xf2, 0x0d, 0x1b, 0xef, 0x37, 0xa7, 0xb4, 0x34, 0x04, 0x08, 0x71, 0x1b, 0xd3, 0xdf, 0xa1, 0xf0, 0x2b, 0xfa, 0xc0, 0x1f, 0xf3, 0x44, 0xb5, 0xc6, 0x47, 0x3d, 0x65, 0x67, 0x45, 0x4d, 0x2f, 0xde, 0x52, 0x73, 0xfc, 0x30, 0x01, 0x6b, 0xc1, 0x03, 0xd8, 0xd7,
+	/* (2^392)P */ 0x1c, 0x67, 0x55, 0x3e, 0x01, 0x17, 0x0f, 0x3e, 0xe5, 0x34, 0x58, 0xfc, 0xcb, 0x71, 0x24, 0x74, 0x5d, 0x36, 0x1e, 0x89, 0x2a, 0x63, 0xf8, 0xf8, 0x9f, 0x50, 0x9f, 0x32, 0x92, 0x29, 0xd8, 0x1a, 0xec, 0x76, 0x57, 0x6c, 0x67, 0x12, 0x6a, 0x6e, 0xef, 0x97, 0x1f, 0xc3, 0x77, 0x60, 0x3c, 0x22, 0xcb, 0xc7, 0x04, 0x1a, 0x89, 0x2d, 0x10, 0xa6,
+	/* (2^393)P */ 0x12, 0xf5, 0xa9, 0x26, 0x16, 0xd9, 0x3c, 0x65, 0x5d, 0x83, 0xab, 0xd1, 0x70, 0x6b, 0x1c, 0xdb, 0xe7, 0x86, 0x0d, 0xfb, 0xe7, 0xf8, 0x2a, 0x58, 0x6e, 0x7a, 0x66, 0x13, 0x53, 0x3a, 0x6f, 0x8d, 0x43, 0x5f, 0x14, 0x23, 0x14, 0xff, 0x3d, 0x52, 0x7f, 0xee, 0xbd, 0x7a, 0x34, 0x8b, 0x35, 0x24, 0xc3, 0x7a, 0xdb, 0xcf, 0x22, 0x74, 0x9a, 0x8f,
+	/* (2^394)P */ 0xdb, 0x20, 0xfc, 0xe5, 0x39, 0x4e, 0x7d, 0x78, 0xee, 0x0b, 0xbf, 0x1d, 0x80, 0xd4, 0x05, 0x4f, 0xb9, 0xd7, 0x4e, 0x94, 0x88, 0x9a, 0x50, 0x78, 0x1a, 0x70, 0x8c, 0xcc, 0x25, 0xb6, 0x61, 0x09, 0xdc, 0x7b, 0xea, 0x3f, 0x7f, 0xea, 0x2a, 0x0d, 0x47, 0x1c, 0x8e, 0xa6, 0x5b, 0xd2, 0xa3, 0x61, 0x93, 0x3c, 0x68, 0x9f, 0x8b, 0xea, 0xb0, 0xcb,
+	/* (2^395)P */ 0xff, 0x54, 0x02, 0x19, 0xae, 0x8b, 0x4c, 0x2c, 0x3a, 0xe0, 0xe4, 0xac, 0x87, 0xf7, 0x51, 0x45, 0x41, 0x43, 0xdc, 0xaa, 0xcd, 0xcb, 0xdc, 0x40, 0xe3, 0x44, 0x3b, 0x1d, 0x9e, 0x3d, 0xb9, 0x82, 0xcc, 0x7a, 0xc5, 0x12, 0xf8, 0x1e, 0xdd, 0xdb, 0x8d, 0xb0, 0x2a, 0xe8, 0xe6, 0x6c, 0x94, 0x3b, 0xb7, 0x2d, 0xba, 0x79, 0x3b, 0xb5, 0x86, 0xfb,
+	/* (2^396)P */ 0x82, 0x88, 0x13, 0xdd, 0x6c, 0xcd, 0x85, 0x2b, 0x90, 0x86, 0xb7, 0xac, 0x16, 0xa6, 0x6e, 0x6a, 0x94, 0xd8, 0x1e, 0x4e, 0x41, 0x0f, 0xce, 0x81, 0x6a, 0xa8, 0x26, 0x56, 0x43, 0x52, 0x52, 0xe6, 0xff, 0x88, 0xcf, 0x47, 0x05, 0x1d, 0xff, 0xf3, 0xa0, 0x10, 0xb2, 0x97, 0x87, 0xeb, 0x47, 0xbb, 0xfa, 0x1f, 0xe8, 0x4c, 0xce, 0xc4, 0xcd, 0x93,
+	/* (2^397)P */ 0xf4, 0x11, 0xf5, 0x8d, 0x89, 0x29, 0x79, 0xb3, 0x59, 0x0b, 0x29, 0x7d, 0x9c, 0x12, 0x4a, 0x65, 0x72, 0x3a, 0xf9, 0xec, 0x37, 0x18, 0x86, 0xef, 0x44, 0x07, 0x25, 0x74, 0x76, 0x53, 0xed, 0x51, 0x01, 0xc6, 0x28, 0xc5, 0xc3, 0x4a, 0x0f, 0x99, 0xec, 0xc8, 0x40, 0x5a, 0x83, 0x30, 0x79, 0xa2, 0x3e, 0x63, 0x09, 0x2d, 0x6f, 0x23, 0x54, 0x1c,
+	/* (2^398)P */ 0x5c, 0x6f, 0x3b, 0x1c, 0x30, 0x77, 0x7e, 0x87, 0x66, 0x83, 0x2e, 0x7e, 0x85, 0x50, 0xfd, 0xa0, 0x7a, 0xc2, 0xf5, 0x0f, 0xc1, 0x64, 0xe7, 0x0b, 0xbd, 0x59, 0xa7, 0xe7, 0x65, 0x53, 0xc3, 0xf5, 0x55, 0x5b, 0xe1, 0x82, 0x30, 0x5a, 0x61, 0xcd, 0xa0, 0x89, 0x32, 0xdb, 0x87, 0xfc, 0x21, 0x8a, 0xab, 0x6d, 0x82, 0xa8, 0x42, 0x81, 0x4f, 0xf2,
+	/* (2^399)P */ 0xb3, 0xeb, 0x88, 0x18, 0xf6, 0x56, 0x96, 0xbf, 0xba, 0x5d, 0x71, 0xa1, 0x5a, 0xd1, 0x04, 0x7b, 0xd5, 0x46, 0x01, 0x74, 0xfe, 0x15, 0x25, 0xb7, 0xff, 0x0c, 0x24, 0x47, 0xac, 0xfd, 0xab, 0x47, 0x32, 0xe1, 0x6a, 0x4e, 0xca, 0xcf, 0x7f, 0xdd, 0xf8, 0xd2, 0x4b, 0x3b, 0xf5, 0x17, 0xba, 0xba, 0x8b, 0xa1, 0xec, 0x28, 0x3f, 0x97, 0xab, 0x2a,
+	/* (2^400)P */ 0x51, 0x38, 0xc9, 0x5e, 0xc6, 0xb3, 0x64, 0xf2, 0x24, 0x4d, 0x04, 0x7d, 0xc8, 0x39, 0x0c, 0x4a, 0xc9, 0x73, 0x74, 0x1b, 0x5c, 0xb2, 0xc5, 0x41, 0x62, 0xa0, 0x4c, 0x6d, 0x8d, 0x91, 0x9a, 0x7b, 0x88, 0xab, 0x9c, 0x7e, 0x23, 0xdb, 0x6f, 0xb5, 0x72, 0xd6, 0x47, 0x40, 0xef, 0x22, 0x58, 0x62, 0x19, 0x6c, 0x38, 0xba, 0x5b, 0x00, 0x30, 0x9f,
+	/* (2^401)P */ 0x65, 0xbb, 0x3b, 0x9b, 0xe9, 0xae, 0xbf, 0xbe, 0xe4, 0x13, 0x95, 0xf3, 0xe3, 0x77, 0xcb, 0xe4, 0x9a, 0x22, 0xb5, 0x4a, 0x08, 0x9d, 0xb3, 0x9e, 0x27, 0xe0, 0x15, 0x6c, 0x9f, 0x7e, 0x9a, 0x5e, 0x15, 0x45, 0x25, 0x8d, 0x01, 0x0a, 0xd2, 0x2b, 0xbd, 0x48, 0x06, 0x0d, 0x18, 0x97, 0x4b, 0xdc, 0xbc, 0xf0, 0xcd, 0xb2, 0x52, 0x3c, 0xac, 0xf5,
+	/* (2^402)P */ 0x3e, 0xed, 0x47, 0x6b, 0x5c, 0xf6, 0x76, 0xd0, 0xe9, 0x15, 0xa3, 0xcb, 0x36, 0x00, 0x21, 0xa3, 0x79, 0x20, 0xa5, 0x3e, 0x88, 0x03, 0xcb, 0x7e, 0x63, 0xbb, 0xed, 0xa9, 0x13, 0x35, 0x16, 0xaf, 0x2e, 0xb4, 0x70, 0x14, 0x93, 0xfb, 0xc4, 0x9b, 0xd8, 0xb1, 0xbe, 0x43, 0xd1, 0x85, 0xb8, 0x97, 0xef, 0xea, 0x88, 0xa1, 0x25, 0x52, 0x62, 0x75,
+	/* (2^403)P */ 0x8e, 0x4f, 0xaa, 0x23, 0x62, 0x7e, 0x2b, 0x37, 0x89, 0x00, 0x11, 0x30, 0xc5, 0x33, 0x4a, 0x89, 0x8a, 0xe2, 0xfc, 0x5c, 0x6a, 0x75, 0xe5, 0xf7, 0x02, 0x4a, 0x9b, 0xf7, 0xb5, 0x6a, 0x85, 0x31, 0xd3, 0x5a, 0xcf, 0xc3, 0xf8, 0xde, 0x2f, 0xcf, 0xb5, 0x24, 0xf4, 0xe3, 0xa1, 0xad, 0x42, 0xae, 0x09, 0xb9, 0x2e, 0x04, 0x2d, 0x01, 0x22, 0x3f,
+	/* (2^404)P */ 0x41, 0x16, 0xfb, 0x7d, 0x50, 0xfd, 0xb5, 0xba, 0x88, 0x24, 0xba, 0xfd, 0x3d, 0xb2, 0x90, 0x15, 0xb7, 0xfa, 0xa2, 0xe1, 0x4c, 0x7d, 0xb9, 0xc6, 0xff, 0x81, 0x57, 0xb6, 0xc2, 0x9e, 0xcb, 0xc4, 0x35, 0xbd, 0x01, 0xb7, 0xaa, 0xce, 0xd0, 0xe9, 0xb5, 0xd6, 0x72, 0xbf, 0xd2, 0xee, 0xc7, 0xac, 0x94, 0xff, 0x29, 0x57, 0x02, 0x49, 0x09, 0xad,
+	/* (2^405)P */ 0x27, 0xa5, 0x78, 0x1b, 0xbf, 0x6b, 0xaf, 0x0b, 0x8c, 0xd9, 0xa8, 0x37, 0xb0, 0x67, 0x18, 0xb6, 0xc7, 0x05, 0x8a, 0x67, 0x03, 0x30, 0x62, 0x6e, 0x56, 0x82, 0xa9, 0x54, 0x3e, 0x0c, 0x4e, 0x07, 0xe1, 0x5a, 0x38, 0xed, 0xfa, 0xc8, 0x55, 0x6b, 0x08, 0xa3, 0x6b, 0x64, 0x2a, 0x15, 0xd6, 0x39, 0x6f, 0x47, 0x99, 0x42, 0x3f, 0x33, 0x84, 0x8f,
+	/* (2^406)P */ 0xbc, 0x45, 0x29, 0x81, 0x0e, 0xa4, 0xc5, 0x72, 0x3a, 0x10, 0xe1, 0xc4, 0x1e, 0xda, 0xc3, 0xfe, 0xb0, 0xce, 0xd2, 0x13, 0x34, 0x67, 0x21, 0xc6, 0x7e, 0xf9, 0x8c, 0xff, 0x39, 0x50, 0xae, 0x92, 0x60, 0x35, 0x2f, 0x8b, 0x6e, 0xc9, 0xc1, 0x27, 0x3a, 0x94, 0x66, 0x3e, 0x26, 0x84, 0x93, 0xc8, 0x6c, 0xcf, 0xd2, 0x03, 0xa1, 0x10, 0xcf, 0xb7,
+	/* (2^407)P */ 0x64, 0xda, 0x19, 0xf6, 0xc5, 0x73, 0x17, 0x44, 0x88, 0x81, 0x07, 0x0d, 0x34, 0xb2, 0x75, 0xf9, 0xd9, 0xe2, 0xe0, 0x8b, 0x71, 0xcf, 0x72, 0x34, 0x83, 0xb4, 0xce, 0xfc, 0xd7, 0x29, 0x09, 0x5a, 0x98, 0xbf, 0x14, 0xac, 0x77, 0x55, 0x38, 0x47, 0x5b, 0x0f, 0x40, 0x24, 0xe5, 0xa5, 0xa6, 0xac, 0x2d, 0xa6, 0xff, 0x9c, 0x73, 0xfe, 0x5c, 0x7e,
+	/* (2^408)P */ 0x1e, 0x33, 0xcc, 0x68, 0xb2, 0xbc, 0x8c, 0x93, 0xaf, 0xcc, 0x38, 0xf8, 0xd9, 0x16, 0x72, 0x50, 0xac, 0xd9, 0xb5, 0x0b, 0x9a, 0xbe, 0x46, 0x7a, 0xf1, 0xee, 0xf1, 0xad, 0xec, 0x5b, 0x59, 0x27, 0x9c, 0x05, 0xa3, 0x87, 0xe0, 0x37, 0x2c, 0x83, 0xce, 0xb3, 0x65, 0x09, 0x8e, 0xc3, 0x9c, 0xbf, 0x6a, 0xa2, 0x00, 0xcc, 0x12, 0x36, 0xc5, 0x95,
+	/* (2^409)P */ 0x36, 0x11, 0x02, 0x14, 0x9c, 0x3c, 0xeb, 0x2f, 0x23, 0x5b, 0x6b, 0x2b, 0x08, 0x54, 0x53, 0xac, 0xb2, 0xa3, 0xe0, 0x26, 0x62, 0x3c, 0xe4, 0xe1, 0x81, 0xee, 0x13, 0x3e, 0xa4, 0x97, 0xef, 0xf9, 0x92, 0x27, 0x01, 0xce, 0x54, 0x8b, 0x3e, 0x31, 0xbe, 0xa7, 0x88, 0xcf, 0x47, 0x99, 0x3c, 0x10, 0x6f, 0x60, 0xb3, 0x06, 0x4e, 0xee, 0x1b, 0xf0,
+	/* (2^410)P */ 0x59, 0x49, 0x66, 0xcf, 0x22, 0xe6, 0xf6, 0x73, 0xfe, 0xa3, 0x1c, 0x09, 0xfa, 0x5f, 0x65, 0xa8, 0xf0, 0x82, 0xc2, 0xef, 0x16, 0x63, 0x6e, 0x79, 0x69, 0x51, 0x39, 0x07, 0x65, 0xc4, 0x81, 0xec, 0x73, 0x0f, 0x15, 0x93, 0xe1, 0x30, 0x33, 0xe9, 0x37, 0x86, 0x42, 0x4c, 0x1f, 0x9b, 0xad, 0xee, 0x3f, 0xf1, 0x2a, 0x8e, 0x6a, 0xa3, 0xc8, 0x35,
+	/* (2^411)P */ 0x1e, 0x49, 0xf1, 0xdd, 0xd2, 0x9c, 0x8e, 0x78, 0xb2, 0x06, 0xe4, 0x6a, 0xab, 0x3a, 0xdc, 0xcd, 0xf4, 0xeb, 0xe1, 0xe7, 0x2f, 0xaa, 0xeb, 0x40, 0x31, 0x9f, 0xb9, 0xab, 0x13, 0xa9, 0x78, 0xbf, 0x38, 0x89, 0x0e, 0x85, 0x14, 0x8b, 0x46, 0x76, 0x14, 0xda, 0xcf, 0x33, 0xc8, 0x79, 0xd3, 0xd5, 0xa3, 0x6a, 0x69, 0x45, 0x70, 0x34, 0xc3, 0xe9,
+	/* (2^412)P */ 0x5e, 0xe7, 0x78, 0xe9, 0x24, 0xcc, 0xe9, 0xf4, 0xc8, 0x6b, 0xe0, 0xfb, 0x3a, 0xbe, 0xcc, 0x42, 0x4a, 0x00, 0x22, 0xf8, 0xe6, 0x32, 0xbe, 0x6d, 0x18, 0x55, 0x60, 0xe9, 0x72, 0x69, 0x50, 0x56, 0xca, 0x04, 0x18, 0x38, 0xa1, 0xee, 0xd8, 0x38, 0x3c, 0xa7, 0x70, 0xe2, 0xb9, 0x4c, 0xa0, 0xc8, 0x89, 0x72, 0xcf, 0x49, 0x7f, 0xdf, 0xbc, 0x67,
+	/* (2^413)P */ 0x1d, 0x17, 0xcb, 0x0b, 0xbd, 0xb2, 0x36, 0xe3, 0xa8, 0x99, 0x31, 0xb6, 0x26, 0x9c, 0x0c, 0x74, 0xaf, 0x4d, 0x24, 0x61, 0xcf, 0x31, 0x7b, 0xed, 0xdd, 0xc3, 0xf6, 0x32, 0x70, 0xfe, 0x17, 0xf6, 0x51, 0x37, 0x65, 0xce, 0x5d, 0xaf, 0xa5, 0x2f, 0x2a, 0xfe, 0x00, 0x71, 0x7c, 0x50, 0xbe, 0x21, 0xc7, 0xed, 0xc6, 0xfc, 0x67, 0xcf, 0x9c, 0xdd,
+	/* (2^414)P */ 0x26, 0x3e, 0xf8, 0xbb, 0xd0, 0xb1, 0x01, 0xd8, 0xeb, 0x0b, 0x62, 0x87, 0x35, 0x4c, 0xde, 0xca, 0x99, 0x9c, 0x6d, 0xf7, 0xb6, 0xf0, 0x57, 0x0a, 0x52, 0x29, 0x6a, 0x3f, 0x26, 0x31, 0x04, 0x07, 0x2a, 0xc9, 0xfa, 0x9b, 0x0e, 0x62, 0x8e, 0x72, 0xf2, 0xad, 0xce, 0xb6, 0x35, 0x7a, 0xc1, 0xae, 0x35, 0xc7, 0xa3, 0x14, 0xcf, 0x0c, 0x28, 0xb7,
+	/* (2^415)P */ 0xa6, 0xf1, 0x32, 0x3a, 0x20, 0xd2, 0x24, 0x97, 0xcf, 0x5d, 0x37, 0x99, 0xaf, 0x33, 0x7a, 0x5b, 0x7a, 0xcc, 0x4e, 0x41, 0x38, 0xb1, 0x4e, 0xad, 0xc9, 0xd9, 0x71, 0x7e, 0xb2, 0xf5, 0xd5, 0x01, 0x6c, 0x4d, 0xfd, 0xa1, 0xda, 0x03, 0x38, 0x9b, 0x3d, 0x92, 0x92, 0xf2, 0xca, 0xbf, 0x1f, 0x24, 0xa4, 0xbb, 0x30, 0x6a, 0x74, 0x56, 0xc8, 0xce,
+	/* (2^416)P */ 0x27, 0xf4, 0xed, 0xc9, 0xc3, 0xb1, 0x79, 0x85, 0xbe, 0xf6, 0xeb, 0xf3, 0x55, 0xc7, 0xaa, 0xa6, 0xe9, 0x07, 0x5d, 0xf4, 0xeb, 0xa6, 0x81, 0xe3, 0x0e, 0xcf, 0xa3, 0xc1, 0xef, 0xe7, 0x34, 0xb2, 0x03, 0x73, 0x8a, 0x91, 0xf1, 0xad, 0x05, 0xc7, 0x0b, 0x43, 0x99, 0x12, 0x31, 0xc8, 0xc7, 0xc5, 0xa4, 0x3d, 0xcd, 0xe5, 0x4e, 0x6d, 0x24, 0xdd,
+	/* (2^417)P */ 0x61, 0x54, 0xd0, 0x95, 0x2c, 0x45, 0x75, 0xac, 0xb5, 0x1a, 0x9d, 0x11, 0xeb, 0xed, 0x6b, 0x57, 0xa3, 0xe6, 0xcd, 0x77, 0xd4, 0x83, 0x8e, 0x39, 0xf1, 0x0f, 0x98, 0xcb, 0x40, 0x02, 0x6e, 0x10, 0x82, 0x9e, 0xb4, 0x93, 0x76, 0xd7, 0x97, 0xa3, 0x53, 0x12, 0x86, 0xc6, 0x15, 0x78, 0x73, 0x93, 0xe7, 0x7f, 0xcf, 0x1f, 0xbf, 0xcd, 0xd2, 0x7a,
+	/* (2^418)P */ 0xc2, 0x21, 0xdc, 0xd5, 0x69, 0xff, 0xca, 0x49, 0x3a, 0xe1, 0xc3, 0x69, 0x41, 0x56, 0xc1, 0x76, 0x63, 0x24, 0xbd, 0x64, 0x1b, 0x3d, 0x92, 0xf9, 0x13, 0x04, 0x25, 0xeb, 0x27, 0xa6, 0xef, 0x39, 0x3a, 0x80, 0xe0, 0xf8, 0x27, 0xee, 0xc9, 0x49, 0x77, 0xef, 0x3f, 0x29, 0x3d, 0x5e, 0xe6, 0x66, 0x83, 0xd1, 0xf6, 0xfe, 0x9d, 0xbc, 0xf1, 0x96,
+	/* (2^419)P */ 0x6b, 0xc6, 0x99, 0x26, 0x3c, 0xf3, 0x63, 0xf9, 0xc7, 0x29, 0x8c, 0x52, 0x62, 0x2d, 0xdc, 0x8a, 0x66, 0xce, 0x2c, 0xa7, 0xe4, 0xf0, 0xd7, 0x37, 0x17, 0x1e, 0xe4, 0xa3, 0x53, 0x7b, 0x29, 0x8e, 0x60, 0x99, 0xf9, 0x0c, 0x7c, 0x6f, 0xa2, 0xcc, 0x9f, 0x80, 0xdd, 0x5e, 0x46, 0xaa, 0x0d, 0x6c, 0xc9, 0x6c, 0xf7, 0x78, 0x5b, 0x38, 0xe3, 0x24,
+	/* (2^420)P */ 0x4b, 0x75, 0x6a, 0x2f, 0x08, 0xe1, 0x72, 0x76, 0xab, 0x82, 0x96, 0xdf, 0x3b, 0x1f, 0x9b, 0xd8, 0xed, 0xdb, 0xcd, 0x15, 0x09, 0x5a, 0x1e, 0xb7, 0xc5, 0x26, 0x72, 0x07, 0x0c, 0x50, 0xcd, 0x3b, 0x4d, 0x3f, 0xa2, 0x67, 0xc2, 0x02, 0x61, 0x2e, 0x68, 0xe9, 0x6f, 0xf0, 0x21, 0x2a, 0xa7, 0x3b, 0x88, 0x04, 0x11, 0x64, 0x49, 0x0d, 0xb4, 0x46,
+	/* (2^421)P */ 0x63, 0x85, 0xf3, 0xc5, 0x2b, 0x5a, 0x9f, 0xf0, 0x17, 0xcb, 0x45, 0x0a, 0xf3, 0x6e, 0x7e, 0xb0, 0x7c, 0xbc, 0xf0, 0x4f, 0x3a, 0xb0, 0xbc, 0x36, 0x36, 0x52, 0x51, 0xcb, 0xfe, 0x9a, 0xcb, 0xe8, 0x7e, 0x4b, 0x06, 0x7f, 0xaa, 0x35, 0xc8, 0x0e, 0x7a, 0x30, 0xa3, 0xb1, 0x09, 0xbb, 0x86, 0x4c, 0xbe, 0xb8, 0xbd, 0xe0, 0x32, 0xa5, 0xd4, 0xf7,
+	/* (2^422)P */ 0x7d, 0x50, 0x37, 0x68, 0x4e, 0x22, 0xb2, 0x2c, 0xd5, 0x0f, 0x2b, 0x6d, 0xb1, 0x51, 0xf2, 0x82, 0xe9, 0x98, 0x7c, 0x50, 0xc7, 0x96, 0x7e, 0x0e, 0xdc, 0xb1, 0x0e, 0xb2, 0x63, 0x8c, 0x30, 0x37, 0x72, 0x21, 0x9c, 0x61, 0xc2, 0xa7, 0x33, 0xd9, 0xb2, 0x63, 0x93, 0xd1, 0x6b, 0x6a, 0x73, 0xa5, 0x58, 0x80, 0xff, 0x04, 0xc7, 0x83, 0x21, 0x29,
+	/* (2^423)P */ 0x29, 0x04, 0xbc, 0x99, 0x39, 0xc9, 0x58, 0xc9, 0x6b, 0x17, 0xe8, 0x90, 0xb3, 0xe6, 0xa9, 0xb6, 0x28, 0x9b, 0xcb, 0x3b, 0x28, 0x90, 0x68, 0x71, 0xff, 0xcf, 0x08, 0x78, 0xc9, 0x8d, 0xa8, 0x4e, 0x43, 0xd1, 0x1c, 0x9e, 0xa4, 0xe3, 0xdf, 0xbf, 0x92, 0xf4, 0xf9, 0x41, 0xba, 0x4d, 0x1c, 0xf9, 0xdd, 0x74, 0x76, 0x1c, 0x6e, 0x3e, 0x94, 0x87,
+	/* (2^424)P */ 0xe4, 0xda, 0xc5, 0xd7, 0xfb, 0x87, 0xc5, 0x4d, 0x6b, 0x19, 0xaa, 0xb9, 0xbc, 0x8c, 0xf2, 0x8a, 0xd8, 0x5d, 0xdb, 0x4d, 0xef, 0xa6, 0xf2, 0x65, 0xf1, 0x22, 0x9c, 0xf1, 0x46, 0x30, 0x71, 0x7c, 0xe4, 0x53, 0x8e, 0x55, 0x2e, 0x9c, 0x9a, 0x31, 0x2a, 0xc3, 0xab, 0x0f, 0xde, 0xe4, 0xbe, 0xd8, 0x96, 0x50, 0x6e, 0x0c, 0x54, 0x49, 0xe6, 0xec,
+	/* (2^425)P */ 0x3c, 0x1d, 0x5a, 0xa5, 0xda, 0xad, 0xdd, 0xc2, 0xae, 0xac, 0x6f, 0x86, 0x75, 0x31, 0x91, 0x64, 0x45, 0x9d, 0xa4, 0xf0, 0x81, 0xf1, 0x0e, 0xba, 0x74, 0xaf, 0x7b, 0xcd, 0x6f, 0xfe, 0xac, 0x4e, 0xdb, 0x4e, 0x45, 0x35, 0x36, 0xc5, 0xc0, 0x6c, 0x3d, 0x64, 0xf4, 0xd8, 0x07, 0x62, 0xd1, 0xec, 0xf3, 0xfc, 0x93, 0xc9, 0x28, 0x0c, 0x2c, 0xf3,
+	/* (2^426)P */ 0x0c, 0x69, 0x2b, 0x5c, 0xb6, 0x41, 0x69, 0xf1, 0xa4, 0xf1, 0x5b, 0x75, 0x4c, 0x42, 0x8b, 0x47, 0xeb, 0x69, 0xfb, 0xa8, 0xe6, 0xf9, 0x7b, 0x48, 0x50, 0xaf, 0xd3, 0xda, 0xb2, 0x35, 0x10, 0xb5, 0x5b, 0x40, 0x90, 0x39, 0xc9, 0x07, 0x06, 0x73, 0x26, 0x20, 0x95, 0x01, 0xa4, 0x2d, 0xf0, 0xe7, 0x2e, 0x00, 0x7d, 0x41, 0x09, 0x68, 0x13, 0xc4,
+	/* (2^427)P */ 0xbe, 0x38, 0x78, 0xcf, 0xc9, 0x4f, 0x36, 0xca, 0x09, 0x61, 0x31, 0x3c, 0x57, 0x2e, 0xec, 0x17, 0xa4, 0x7d, 0x19, 0x2b, 0x9b, 0x5b, 0xbe, 0x8f, 0xd6, 0xc5, 0x2f, 0x86, 0xf2, 0x64, 0x76, 0x17, 0x00, 0x6e, 0x1a, 0x8c, 0x67, 0x1b, 0x68, 0xeb, 0x15, 0xa2, 0xd6, 0x09, 0x91, 0xdd, 0x23, 0x0d, 0x98, 0xb2, 0x10, 0x19, 0x55, 0x9b, 0x63, 0xf2,
+	/* (2^428)P */ 0x51, 0x1f, 0x93, 0xea, 0x2a, 0x3a, 0xfa, 0x41, 0xc0, 0x57, 0xfb, 0x74, 0xa6, 0x65, 0x09, 0x56, 0x14, 0xb6, 0x12, 0xaa, 0xb3, 0x1a, 0x8d, 0x3b, 0x76, 0x91, 0x7a, 0x23, 0x56, 0x9c, 0x6a, 0xc0, 0xe0, 0x3c, 0x3f, 0xb5, 0x1a, 0xf4, 0x57, 0x71, 0x93, 0x2b, 0xb1, 0xa7, 0x70, 0x57, 0x22, 0x80, 0xf5, 0xb8, 0x07, 0x77, 0x87, 0x0c, 0xbe, 0x83,
+	/* (2^429)P */ 0x07, 0x9b, 0x0e, 0x52, 0x38, 0x63, 0x13, 0x86, 0x6a, 0xa6, 0xb4, 0xd2, 0x60, 0x68, 0x9a, 0x99, 0x82, 0x0a, 0x04, 0x5f, 0x89, 0x7a, 0x1a, 0x2a, 0xae, 0x2d, 0x35, 0x0c, 0x1e, 0xad, 0xef, 0x4f, 0x9a, 0xfc, 0xc8, 0xd9, 0xcf, 0x9d, 0x48, 0x71, 0xa5, 0x55, 0x79, 0x73, 0x39, 0x1b, 0xd8, 0x73, 0xec, 0x9b, 0x03, 0x16, 0xd8, 0x82, 0xf7, 0x67,
+	/* (2^430)P */ 0x52, 0x67, 0x42, 0x21, 0xc9, 0x40, 0x78, 0x82, 0x2b, 0x95, 0x2d, 0x20, 0x92, 0xd1, 0xe2, 0x61, 0x25, 0xb0, 0xc6, 0x9c, 0x20, 0x59, 0x8e, 0x28, 0x6f, 0xf3, 0xfd, 0xd3, 0xc1, 0x32, 0x43, 0xc9, 0xa6, 0x08, 0x7a, 0x77, 0x9c, 0x4c, 0x8c, 0x33, 0x71, 0x13, 0x69, 0xe3, 0x52, 0x30, 0xa7, 0xf5, 0x07, 0x67, 0xac, 0xad, 0x46, 0x8a, 0x26, 0x25,
+	/* (2^431)P */ 0xda, 0x86, 0xc4, 0xa2, 0x71, 0x56, 0xdd, 0xd2, 0x48, 0xd3, 0xde, 0x42, 0x63, 0x01, 0xa7, 0x2c, 0x92, 0x83, 0x6f, 0x2e, 0xd8, 0x1e, 0x3f, 0xc1, 0xc5, 0x42, 0x4e, 0x34, 0x19, 0x54, 0x6e, 0x35, 0x2c, 0x51, 0x2e, 0xfd, 0x0f, 0x9a, 0x45, 0x66, 0x5e, 0x4a, 0x83, 0xda, 0x0a, 0x53, 0x68, 0x63, 0xfa, 0xce, 0x47, 0x20, 0xd3, 0x34, 0xba, 0x0d,
+	/* (2^432)P */ 0xd0, 0xe9, 0x64, 0xa4, 0x61, 0x4b, 0x86, 0xe5, 0x93, 0x6f, 0xda, 0x0e, 0x31, 0x7e, 0x6e, 0xe3, 0xc6, 0x73, 0xd8, 0xa3, 0x08, 0x57, 0x52, 0xcd, 0x51, 0x63, 0x1d, 0x9f, 0x93, 0x00, 0x62, 0x91, 0x26, 0x21, 0xa7, 0xdd, 0x25, 0x0f, 0x09, 0x0d, 0x35, 0xad, 0xcf, 0x11, 0x8e, 0x6e, 0xe8, 0xae, 0x1d, 0x95, 0xcb, 0x88, 0xf8, 0x70, 0x7b, 0x91,
+	/* (2^433)P */ 0x0c, 0x19, 0x5c, 0xd9, 0x8d, 0xda, 0x9d, 0x2c, 0x90, 0x54, 0x65, 0xe8, 0xb6, 0x35, 0x50, 0xae, 0xea, 0xae, 0x43, 0xb7, 0x1e, 0x99, 0x8b, 0x4c, 0x36, 0x4e, 0xe4, 0x1e, 0xc4, 0x64, 0x43, 0xb6, 0xeb, 0xd4, 0xe9, 0x60, 0x22, 0xee, 0xcf, 0xb8, 0x52, 0x1b, 0xf0, 0x04, 0xce, 0xbc, 0x2b, 0xf0, 0xbe, 0xcd, 0x44, 0x74, 0x1e, 0x1f, 0x63, 0xf9,
+	/* (2^434)P */ 0xe1, 0x3f, 0x95, 0x94, 0xb2, 0xb6, 0x31, 0xa9, 0x1b, 0xdb, 0xfd, 0x0e, 0xdb, 0xdd, 0x1a, 0x22, 0x78, 0x60, 0x9f, 0x75, 0x5f, 0x93, 0x06, 0x0c, 0xd8, 0xbb, 0xa2, 0x85, 0x2b, 0x5e, 0xc0, 0x9b, 0xa8, 0x5d, 0xaf, 0x93, 0x91, 0x91, 0x47, 0x41, 0x1a, 0xfc, 0xb4, 0x51, 0x85, 0xad, 0x69, 0x4d, 0x73, 0x69, 0xd5, 0x4e, 0x82, 0xfb, 0x66, 0xcb,
+	/* (2^435)P */ 0x7c, 0xbe, 0xc7, 0x51, 0xc4, 0x74, 0x6e, 0xab, 0xfd, 0x41, 0x4f, 0x76, 0x4f, 0x24, 0x03, 0xd6, 0x2a, 0xb7, 0x42, 0xb4, 0xda, 0x41, 0x2c, 0x82, 0x48, 0x4c, 0x7f, 0x6f, 0x25, 0x5d, 0x36, 0xd4, 0x69, 0xf5, 0xef, 0x02, 0x81, 0xea, 0x6f, 0x19, 0x69, 0xe8, 0x6f, 0x5b, 0x2f, 0x14, 0x0e, 0x6f, 0x89, 0xb4, 0xb5, 0xd8, 0xae, 0xef, 0x7b, 0x87,
+	/* (2^436)P */ 0xe9, 0x91, 0xa0, 0x8b, 0xc9, 0xe0, 0x01, 0x90, 0x37, 0xc1, 0x6f, 0xdc, 0x5e, 0xf7, 0xbf, 0x43, 0x00, 0xaa, 0x10, 0x76, 0x76, 0x18, 0x6e, 0x19, 0x1e, 0x94, 0x50, 0x11, 0x0a, 0xd1, 0xe2, 0xdb, 0x08, 0x21, 0xa0, 0x1f, 0xdb, 0x54, 0xfe, 0xea, 0x6e, 0xa3, 0x68, 0x56, 0x87, 0x0b, 0x22, 0x4e, 0x66, 0xf3, 0x82, 0x82, 0x00, 0xcd, 0xd4, 0x12,
+	/* (2^437)P */ 0x25, 0x8e, 0x24, 0x77, 0x64, 0x4c, 0xe0, 0xf8, 0x18, 0xc0, 0xdc, 0xc7, 0x1b, 0x35, 0x65, 0xde, 0x67, 0x41, 0x5e, 0x6f, 0x90, 0x82, 0xa7, 0x2e, 0x6d, 0xf1, 0x47, 0xb4, 0x92, 0x9c, 0xfd, 0x6a, 0x9a, 0x41, 0x36, 0x20, 0x24, 0x58, 0xc3, 0x59, 0x07, 0x9a, 0xfa, 0x9f, 0x03, 0xcb, 0xc7, 0x69, 0x37, 0x60, 0xe1, 0xab, 0x13, 0x72, 0xee, 0xa2,
+	/* (2^438)P */ 0x74, 0x78, 0xfb, 0x13, 0xcb, 0x8e, 0x37, 0x1a, 0xf6, 0x1d, 0x17, 0x83, 0x06, 0xd4, 0x27, 0x06, 0x21, 0xe8, 0xda, 0xdf, 0x6b, 0xf3, 0x83, 0x6b, 0x34, 0x8a, 0x8c, 0xee, 0x01, 0x05, 0x5b, 0xed, 0xd3, 0x1b, 0xc9, 0x64, 0x83, 0xc9, 0x49, 0xc2, 0x57, 0x1b, 0xdd, 0xcf, 0xf1, 0x9d, 0x63, 0xee, 0x1c, 0x0d, 0xa0, 0x0a, 0x73, 0x1f, 0x5b, 0x32,
+	/* (2^439)P */ 0x29, 0xce, 0x1e, 0xc0, 0x6a, 0xf5, 0xeb, 0x99, 0x5a, 0x39, 0x23, 0xe9, 0xdd, 0xac, 0x44, 0x88, 0xbc, 0x80, 0x22, 0xde, 0x2c, 0xcb, 0xa8, 0x3b, 0xff, 0xf7, 0x6f, 0xc7, 0x71, 0x72, 0xa8, 0xa3, 0xf6, 0x4d, 0xc6, 0x75, 0xda, 0x80, 0xdc, 0xd9, 0x30, 0xd9, 0x07, 0x50, 0x5a, 0x54, 0x7d, 0xda, 0x39, 0x6f, 0x78, 0x94, 0xbf, 0x25, 0x98, 0xdc,
+	/* (2^440)P */ 0x01, 0x26, 0x62, 0x44, 0xfb, 0x0f, 0x11, 0x72, 0x73, 0x0a, 0x16, 0xc7, 0x16, 0x9c, 0x9b, 0x37, 0xd8, 0xff, 0x4f, 0xfe, 0x57, 0xdb, 0xae, 0xef, 0x7d, 0x94, 0x30, 0x04, 0x70, 0x83, 0xde, 0x3c, 0xd4, 0xb5, 0x70, 0xda, 0xa7, 0x55, 0xc8, 0x19, 0xe1, 0x36, 0x15, 0x61, 0xe7, 0x3b, 0x7d, 0x85, 0xbb, 0xf3, 0x42, 0x5a, 0x94, 0xf4, 0x53, 0x2a,
+	/* (2^441)P */ 0x14, 0x60, 0xa6, 0x0b, 0x83, 0xe1, 0x23, 0x77, 0xc0, 0xce, 0x50, 0xed, 0x35, 0x8d, 0x98, 0x99, 0x7d, 0xf5, 0x8d, 0xce, 0x94, 0x25, 0xc8, 0x0f, 0x6d, 0xfa, 0x4a, 0xa4, 0x3a, 0x1f, 0x66, 0xfb, 0x5a, 0x64, 0xaf, 0x8b, 0x54, 0x54, 0x44, 0x3f, 0x5b, 0x88, 0x61, 0xe4, 0x48, 0x45, 0x26, 0x20, 0xbe, 0x0d, 0x06, 0xbb, 0x65, 0x59, 0xe1, 0x36,
+	/* (2^442)P */ 0xb7, 0x98, 0xce, 0xa3, 0xe3, 0xee, 0x11, 0x1b, 0x9e, 0x24, 0x59, 0x75, 0x31, 0x37, 0x44, 0x6f, 0x6b, 0x9e, 0xec, 0xb7, 0x44, 0x01, 0x7e, 0xab, 0xbb, 0x69, 0x5d, 0x11, 0xb0, 0x30, 0x64, 0xea, 0x91, 0xb4, 0x7a, 0x8c, 0x02, 0x4c, 0xb9, 0x10, 0xa7, 0xc7, 0x79, 0xe6, 0xdc, 0x77, 0xe3, 0xc8, 0xef, 0x3e, 0xf9, 0x38, 0x81, 0xce, 0x9a, 0xb2,
+	/* (2^443)P */ 0x91, 0x12, 0x76, 0xd0, 0x10, 0xb4, 0xaf, 0xe1, 0x89, 0x3a, 0x93, 0x6b, 0x5c, 0x19, 0x5f, 0x24, 0xed, 0x04, 0x92, 0xc7, 0xf0, 0x00, 0x08, 0xc1, 0x92, 0xff, 0x90, 0xdb, 0xb2, 0xbf, 0xdf, 0x49, 0xcd, 0xbd, 0x5c, 0x6e, 0xbf, 0x16, 0xbb, 0x61, 0xf9, 0x20, 0x33, 0x35, 0x93, 0x11, 0xbc, 0x59, 0x69, 0xce, 0x18, 0x9f, 0xf8, 0x7b, 0xa1, 0x6e,
+	/* (2^444)P */ 0xa1, 0xf4, 0xaf, 0xad, 0xf8, 0xe6, 0x99, 0xd2, 0xa1, 0x4d, 0xde, 0x56, 0xc9, 0x7b, 0x0b, 0x11, 0x3e, 0xbf, 0x89, 0x1a, 0x9a, 0x90, 0xe5, 0xe2, 0xa6, 0x37, 0x88, 0xa1, 0x68, 0x59, 0xae, 0x8c, 0xec, 0x02, 0x14, 0x8d, 0xb7, 0x2e, 0x25, 0x75, 0x7f, 0x76, 0x1a, 0xd3, 0x4d, 0xad, 0x8a, 0x00, 0x6c, 0x96, 0x49, 0xa4, 0xc3, 0x2e, 0x5c, 0x7b,
+	/* (2^445)P */ 0x26, 0x53, 0xf7, 0xda, 0xa8, 0x01, 0x14, 0xb1, 0x63, 0xe3, 0xc3, 0x89, 0x88, 0xb0, 0x85, 0x40, 0x2b, 0x26, 0x9a, 0x10, 0x1a, 0x70, 0x33, 0xf4, 0x50, 0x9d, 0x4d, 0xd8, 0x64, 0xc6, 0x0f, 0xe1, 0x17, 0xc8, 0x10, 0x4b, 0xfc, 0xa0, 0xc9, 0xba, 0x2c, 0x98, 0x09, 0xf5, 0x84, 0xb6, 0x7c, 0x4e, 0xa3, 0xe3, 0x81, 0x1b, 0x32, 0x60, 0x02, 0xdd,
+	/* (2^446)P */ 0xa3, 0xe5, 0x86, 0xd4, 0x43, 0xa8, 0xd1, 0x98, 0x9d, 0x9d, 0xdb, 0x04, 0xcf, 0x6e, 0x35, 0x05, 0x30, 0x53, 0x3b, 0xbc, 0x90, 0x00, 0x4a, 0xc5, 0x40, 0x2a, 0x0f, 0xde, 0x1a, 0xd7, 0x36, 0x27, 0x44, 0x62, 0xa6, 0xac, 0x9d, 0xd2, 0x70, 0x69, 0x14, 0x39, 0x9b, 0xd1, 0xc3, 0x0a, 0x3a, 0x82, 0x0e, 0xf1, 0x94, 0xd7, 0x42, 0x94, 0xd5, 0x7d,
+	/* (2^447)P */ 0x04, 0xc0, 0x6e, 0x12, 0x90, 0x70, 0xf9, 0xdf, 0xf7, 0xc9, 0x86, 0xc0, 0xe6, 0x92, 0x8b, 0x0a, 0xa1, 0xc1, 0x3b, 0xcc, 0x33, 0xb7, 0xf0, 0xeb, 0x51, 0x50, 0x80, 0x20, 0x69, 0x1c, 0x4f, 0x89, 0x05, 0x1e, 0xe4, 0x7a, 0x0a, 0xc2, 0xf0, 0xf5, 0x78, 0x91, 0x76, 0x34, 0x45, 0xdc, 0x24, 0x53, 0x24, 0x98, 0xe2, 0x73, 0x6f, 0xe6, 0x46, 0x67,
+}

vendor/github.com/cloudflare/circl/ecc/goldilocks/constants.go

@@ -0,0 +1,71 @@
+package goldilocks
+
+import fp "github.com/cloudflare/circl/math/fp448"
+
+var (
+	// genX is the x-coordinate of the generator of Goldilocks curve.
+	genX = fp.Elt{
+		0x5e, 0xc0, 0x0c, 0xc7, 0x2b, 0xa8, 0x26, 0x26,
+		0x8e, 0x93, 0x00, 0x8b, 0xe1, 0x80, 0x3b, 0x43,
+		0x11, 0x65, 0xb6, 0x2a, 0xf7, 0x1a, 0xae, 0x12,
+		0x64, 0xa4, 0xd3, 0xa3, 0x24, 0xe3, 0x6d, 0xea,
+		0x67, 0x17, 0x0f, 0x47, 0x70, 0x65, 0x14, 0x9e,
+		0xda, 0x36, 0xbf, 0x22, 0xa6, 0x15, 0x1d, 0x22,
+		0xed, 0x0d, 0xed, 0x6b, 0xc6, 0x70, 0x19, 0x4f,
+	}
+	// genY is the y-coordinate of the generator of Goldilocks curve.
+	genY = fp.Elt{
+		0x14, 0xfa, 0x30, 0xf2, 0x5b, 0x79, 0x08, 0x98,
+		0xad, 0xc8, 0xd7, 0x4e, 0x2c, 0x13, 0xbd, 0xfd,
+		0xc4, 0x39, 0x7c, 0xe6, 0x1c, 0xff, 0xd3, 0x3a,
+		0xd7, 0xc2, 0xa0, 0x05, 0x1e, 0x9c, 0x78, 0x87,
+		0x40, 0x98, 0xa3, 0x6c, 0x73, 0x73, 0xea, 0x4b,
+		0x62, 0xc7, 0xc9, 0x56, 0x37, 0x20, 0x76, 0x88,
+		0x24, 0xbc, 0xb6, 0x6e, 0x71, 0x46, 0x3f, 0x69,
+	}
+	// paramD is -39081 in Fp.
+	paramD = fp.Elt{
+		0x56, 0x67, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	}
+	// order is 2^446-0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d,
+	// which is the number of points in the prime subgroup.
+	order = Scalar{
+		0xf3, 0x44, 0x58, 0xab, 0x92, 0xc2, 0x78, 0x23,
+		0x55, 0x8f, 0xc5, 0x8d, 0x72, 0xc2, 0x6c, 0x21,
+		0x90, 0x36, 0xd6, 0xae, 0x49, 0xdb, 0x4e, 0xc4,
+		0xe9, 0x23, 0xca, 0x7c, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f,
+	}
+	// residue448 is 2^448 mod order.
+	residue448 = [4]uint64{
+		0x721cf5b5529eec34, 0x7a4cf635c8e9c2ab, 0xeec492d944a725bf, 0x20cd77058,
+	}
+	// invFour is 1/4 mod order.
+	invFour = Scalar{
+		0x3d, 0x11, 0xd6, 0xaa, 0xa4, 0x30, 0xde, 0x48,
+		0xd5, 0x63, 0x71, 0xa3, 0x9c, 0x30, 0x5b, 0x08,
+		0xa4, 0x8d, 0xb5, 0x6b, 0xd2, 0xb6, 0x13, 0x71,
+		0xfa, 0x88, 0x32, 0xdf, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f,
+	}
+	// paramDTwist is -39082 in Fp. The D parameter of the twist curve.
+	paramDTwist = fp.Elt{
+		0x55, 0x67, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	}
+)

vendor/github.com/cloudflare/circl/ecc/goldilocks/curve.go

@@ -0,0 +1,80 @@
+// Package goldilocks provides elliptic curve operations over the goldilocks curve.
+package goldilocks
+
+import fp "github.com/cloudflare/circl/math/fp448"
+
+// Curve is the Goldilocks curve x^2+y^2=z^2-39081x^2y^2.
+type Curve struct{}
+
+// Identity returns the identity point.
+func (Curve) Identity() *Point {
+	return &Point{
+		y: fp.One(),
+		z: fp.One(),
+	}
+}
+
+// IsOnCurve returns true if the point lies on the curve.
+func (Curve) IsOnCurve(P *Point) bool {
+	x2, y2, t, t2, z2 := &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{}, &fp.Elt{}
+	rhs, lhs := &fp.Elt{}, &fp.Elt{}
+	fp.Mul(t, &P.ta, &P.tb)  // t = ta*tb
+	fp.Sqr(x2, &P.x)         // x^2
+	fp.Sqr(y2, &P.y)         // y^2
+	fp.Sqr(z2, &P.z)         // z^2
+	fp.Sqr(t2, t)            // t^2
+	fp.Add(lhs, x2, y2)      // x^2 + y^2
+	fp.Mul(rhs, t2, &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)))
+}

vendor/github.com/cloudflare/circl/ecc/goldilocks/isogeny.go

@@ -0,0 +1,52 @@
+package goldilocks
+
+import fp "github.com/cloudflare/circl/math/fp448"
+
+func (Curve) pull(P *twistPoint) *Point      { return twistCurve{}.push(P) }
+func (twistCurve) pull(P *Point) *twistPoint { return Curve{}.push(P) }
+
+// push sends a point on the Goldilocks curve to a point on the twist curve.
+func (Curve) push(P *Point) *twistPoint {
+	Q := &twistPoint{}
+	Px, Py, Pz := &P.x, &P.y, &P.z
+	a, b, c, d, e, f, g, h := &Q.x, &Q.y, &Q.z, &fp.Elt{}, &Q.ta, &Q.x, &Q.y, &Q.tb
+	fp.Add(e, Px, Py)  // x+y
+	fp.Sqr(a, Px)      // A = x^2
+	fp.Sqr(b, Py)      // B = y^2
+	fp.Sqr(c, Pz)      // z^2
+	fp.Add(c, c, c)    // C = 2*z^2
+	*d = *a            // D = A
+	fp.Sqr(e, e)       // (x+y)^2
+	fp.Sub(e, e, a)    // (x+y)^2-A
+	fp.Sub(e, e, b)    // E = (x+y)^2-A-B
+	fp.Add(h, b, d)    // H = B+D
+	fp.Sub(g, b, d)    // G = B-D
+	fp.Sub(f, c, h)    // F = C-H
+	fp.Mul(&Q.z, f, g) // Z = F * G
+	fp.Mul(&Q.x, e, f) // X = E * F
+	fp.Mul(&Q.y, g, h) // Y = G * H, // T = E * H
+	return Q
+}
+
+// push sends a point on the twist curve to a point on the Goldilocks curve.
+func (twistCurve) push(P *twistPoint) *Point {
+	Q := &Point{}
+	Px, Py, Pz := &P.x, &P.y, &P.z
+	a, b, c, d, e, f, g, h := &Q.x, &Q.y, &Q.z, &fp.Elt{}, &Q.ta, &Q.x, &Q.y, &Q.tb
+	fp.Add(e, Px, Py)  // x+y
+	fp.Sqr(a, Px)      // A = x^2
+	fp.Sqr(b, Py)      // B = y^2
+	fp.Sqr(c, Pz)      // z^2
+	fp.Add(c, c, c)    // C = 2*z^2
+	fp.Neg(d, a)       // D = -A
+	fp.Sqr(e, e)       // (x+y)^2
+	fp.Sub(e, e, a)    // (x+y)^2-A
+	fp.Sub(e, e, b)    // E = (x+y)^2-A-B
+	fp.Add(h, b, d)    // H = B+D
+	fp.Sub(g, b, d)    // G = B-D
+	fp.Sub(f, c, h)    // F = C-H
+	fp.Mul(&Q.z, f, g) // Z = F * G
+	fp.Mul(&Q.x, e, f) // X = E * F
+	fp.Mul(&Q.y, g, h) // Y = G * H, // T = E * H
+	return Q
+}

vendor/github.com/cloudflare/circl/ecc/goldilocks/point.go

@@ -0,0 +1,171 @@
+package goldilocks
+
+import (
+	"errors"
+	"fmt"
+
+	fp "github.com/cloudflare/circl/math/fp448"
+)
+
+// Point is a point on the Goldilocks Curve.
+type Point struct{ x, y, z, ta, tb fp.Elt }
+
+func (P Point) String() string {
+	return fmt.Sprintf("x: %v\ny: %v\nz: %v\nta: %v\ntb: %v", P.x, P.y, P.z, P.ta, P.tb)
+}
+
+// FromAffine creates a point from affine coordinates.
+func FromAffine(x, y *fp.Elt) (*Point, error) {
+	P := &Point{
+		x:  *x,
+		y:  *y,
+		z:  fp.One(),
+		ta: *x,
+		tb: *y,
+	}
+	if !(Curve{}).IsOnCurve(P) {
+		return P, errors.New("point not on curve")
+	}
+	return P, nil
+}
+
+// isLessThan returns true if 0 <= x < y, and assumes that slices are of the
+// same length and are interpreted in little-endian order.
+func isLessThan(x, y []byte) bool {
+	i := len(x) - 1
+	for i > 0 && x[i] == y[i] {
+		i--
+	}
+	return x[i] < y[i]
+}
+
+// FromBytes returns a point from the input buffer.
+func FromBytes(in []byte) (*Point, error) {
+	if len(in) < fp.Size+1 {
+		return nil, errors.New("wrong input length")
+	}
+	err := errors.New("invalid decoding")
+	P := &Point{}
+	signX := in[fp.Size] >> 7
+	copy(P.y[:], in[:fp.Size])
+	p := fp.P()
+	if !isLessThan(P.y[:], p[:]) {
+		return nil, err
+	}
+
+	u, v := &fp.Elt{}, &fp.Elt{}
+	one := fp.One()
+	fp.Sqr(u, &P.y)                // u = y^2
+	fp.Mul(v, u, &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
+}

vendor/github.com/cloudflare/circl/ecc/goldilocks/scalar.go

@@ -0,0 +1,203 @@
+package goldilocks
+
+import (
+	"encoding/binary"
+	"math/bits"
+)
+
+// ScalarSize is the size (in bytes) of scalars.
+const ScalarSize = 56 // 448 / 8
+
+// _N is the number of 64-bit words to store scalars.
+const _N = 7 // 448 / 64
+
+// Scalar represents a positive integer stored in little-endian order.
+type Scalar [ScalarSize]byte
+
+type scalar64 [_N]uint64
+
+func (z *scalar64) fromScalar(x *Scalar) {
+	z[0] = binary.LittleEndian.Uint64(x[0*8 : 1*8])
+	z[1] = binary.LittleEndian.Uint64(x[1*8 : 2*8])
+	z[2] = binary.LittleEndian.Uint64(x[2*8 : 3*8])
+	z[3] = binary.LittleEndian.Uint64(x[3*8 : 4*8])
+	z[4] = binary.LittleEndian.Uint64(x[4*8 : 5*8])
+	z[5] = binary.LittleEndian.Uint64(x[5*8 : 6*8])
+	z[6] = binary.LittleEndian.Uint64(x[6*8 : 7*8])
+}
+
+func (z *scalar64) toScalar(x *Scalar) {
+	binary.LittleEndian.PutUint64(x[0*8:1*8], z[0])
+	binary.LittleEndian.PutUint64(x[1*8:2*8], z[1])
+	binary.LittleEndian.PutUint64(x[2*8:3*8], z[2])
+	binary.LittleEndian.PutUint64(x[3*8:4*8], z[3])
+	binary.LittleEndian.PutUint64(x[4*8:5*8], z[4])
+	binary.LittleEndian.PutUint64(x[5*8:6*8], z[5])
+	binary.LittleEndian.PutUint64(x[6*8:7*8], z[6])
+}
+
+// add calculates z = x + y. Assumes len(z) > max(len(x),len(y)).
+func add(z, x, y []uint64) uint64 {
+	l, L, zz := len(x), len(y), y
+	if l > L {
+		l, L, zz = L, l, x
+	}
+	c := uint64(0)
+	for i := 0; i < l; i++ {
+		z[i], c = bits.Add64(x[i], y[i], c)
+	}
+	for i := l; i < L; i++ {
+		z[i], c = bits.Add64(zz[i], 0, c)
+	}
+	return c
+}
+
+// sub calculates z = x - y. Assumes len(z) > max(len(x),len(y)).
+func sub(z, x, y []uint64) uint64 {
+	l, L, zz := len(x), len(y), y
+	if l > L {
+		l, L, zz = L, l, x
+	}
+	c := uint64(0)
+	for i := 0; i < l; i++ {
+		z[i], c = bits.Sub64(x[i], y[i], c)
+	}
+	for i := l; i < L; i++ {
+		z[i], c = bits.Sub64(zz[i], 0, c)
+	}
+	return c
+}
+
+// mulWord calculates z = x * y. Assumes len(z) >= len(x)+1.
+func mulWord(z, x []uint64, y uint64) {
+	for i := range z {
+		z[i] = 0
+	}
+	carry := uint64(0)
+	for i := range x {
+		hi, lo := bits.Mul64(x[i], y)
+		lo, cc := bits.Add64(lo, z[i], 0)
+		hi, _ = bits.Add64(hi, 0, cc)
+		z[i], cc = bits.Add64(lo, carry, 0)
+		carry, _ = bits.Add64(hi, 0, cc)
+	}
+	z[len(x)] = carry
+}
+
+// Cmov moves x into z if b=1.
+func (z *scalar64) Cmov(b uint64, x *scalar64) {
+	m := uint64(0) - b
+	for i := range z {
+		z[i] = (z[i] &^ m) | (x[i] & m)
+	}
+}
+
+// leftShift shifts to the left the words of z returning the more significant word.
+func (z *scalar64) leftShift(low uint64) uint64 {
+	high := z[_N-1]
+	for i := _N - 1; i > 0; i-- {
+		z[i] = z[i-1]
+	}
+	z[0] = low
+	return high
+}
+
+// reduceOneWord calculates z = z + 2^448*x such that the result fits in a Scalar.
+func (z *scalar64) reduceOneWord(x uint64) {
+	prod := (&scalar64{})[:]
+	mulWord(prod, residue448[:], x)
+	cc := add(z[:], z[:], prod)
+	mulWord(prod, residue448[:], cc)
+	add(z[:], z[:], prod)
+}
+
+// modOrder reduces z mod order.
+func (z *scalar64) modOrder() {
+	var o64, x scalar64
+	o64.fromScalar(&order)
+	// Performs: while (z >= order) { z = z-order }
+	// At most 8 (eight) iterations reduce 3 bits by subtracting.
+	for i := 0; i < 8; i++ {
+		c := sub(x[:], z[:], o64[:]) // (c || x) = z-order
+		z.Cmov(1-c, &x)              // if c != 0 { z = x }
+	}
+}
+
+// FromBytes stores z = x mod order, where x is a number stored in little-endian order.
+func (z *Scalar) FromBytes(x []byte) {
+	n := len(x)
+	nCeil := (n + 7) >> 3
+	for i := range z {
+		z[i] = 0
+	}
+	if nCeil < _N {
+		copy(z[:], x)
+		return
+	}
+	copy(z[:], x[8*(nCeil-_N):])
+	var z64 scalar64
+	z64.fromScalar(z)
+	for i := nCeil - _N - 1; i >= 0; i-- {
+		low := binary.LittleEndian.Uint64(x[8*i:])
+		high := z64.leftShift(low)
+		z64.reduceOneWord(high)
+	}
+	z64.modOrder()
+	z64.toScalar(z)
+}
+
+// divBy4 calculates z = x/4 mod order.
+func (z *Scalar) divBy4(x *Scalar) { z.Mul(x, &invFour) }
+
+// Red reduces z mod order.
+func (z *Scalar) Red() { var t scalar64; t.fromScalar(z); t.modOrder(); t.toScalar(z) }
+
+// Neg calculates z = -z mod order.
+func (z *Scalar) Neg() { z.Sub(&order, z) }
+
+// Add calculates z = x+y mod order.
+func (z *Scalar) Add(x, y *Scalar) {
+	var z64, x64, y64, t scalar64
+	x64.fromScalar(x)
+	y64.fromScalar(y)
+	c := add(z64[:], x64[:], y64[:])
+	add(t[:], z64[:], residue448[:])
+	z64.Cmov(c, &t)
+	z64.modOrder()
+	z64.toScalar(z)
+}
+
+// Sub calculates z = x-y mod order.
+func (z *Scalar) Sub(x, y *Scalar) {
+	var z64, x64, y64, t scalar64
+	x64.fromScalar(x)
+	y64.fromScalar(y)
+	c := sub(z64[:], x64[:], y64[:])
+	sub(t[:], z64[:], residue448[:])
+	z64.Cmov(c, &t)
+	z64.modOrder()
+	z64.toScalar(z)
+}
+
+// Mul calculates z = x*y mod order.
+func (z *Scalar) Mul(x, y *Scalar) {
+	var z64, x64, y64 scalar64
+	prod := (&[_N + 1]uint64{})[:]
+	x64.fromScalar(x)
+	y64.fromScalar(y)
+	mulWord(prod, x64[:], y64[_N-1])
+	copy(z64[:], prod[:_N])
+	z64.reduceOneWord(prod[_N])
+	for i := _N - 2; i >= 0; i-- {
+		h := z64.leftShift(0)
+		z64.reduceOneWord(h)
+		mulWord(prod, x64[:], y64[i])
+		c := add(z64[:], z64[:], prod[:_N])
+		z64.reduceOneWord(prod[_N] + c)
+	}
+	z64.modOrder()
+	z64.toScalar(z)
+}
+
+// IsZero returns true if z=0.
+func (z *Scalar) IsZero() bool { z.Red(); return *z == Scalar{} }

vendor/github.com/cloudflare/circl/ecc/goldilocks/twist.go

@@ -0,0 +1,138 @@
+package goldilocks
+
+import (
+	"crypto/subtle"
+	"math/bits"
+
+	"github.com/cloudflare/circl/internal/conv"
+	"github.com/cloudflare/circl/math"
+	fp "github.com/cloudflare/circl/math/fp448"
+)
+
+// twistCurve is -x^2+y^2=1-39082x^2y^2 and is 4-isogeneous to Goldilocks.
+type twistCurve struct{}
+
+// Identity returns the identity point.
+func (twistCurve) Identity() *twistPoint {
+	return &twistPoint{
+		y: fp.One(),
+		z: fp.One(),
+	}
+}
+
+// subYDiv16 update x = (x - y) / 16.
+func subYDiv16(x *scalar64, y int64) {
+	s := uint64(y >> 63)
+	x0, b0 := bits.Sub64((*x)[0], uint64(y), 0)
+	x1, b1 := bits.Sub64((*x)[1], s, b0)
+	x2, b2 := bits.Sub64((*x)[2], s, b1)
+	x3, b3 := bits.Sub64((*x)[3], s, b2)
+	x4, b4 := bits.Sub64((*x)[4], s, b3)
+	x5, b5 := bits.Sub64((*x)[5], s, b4)
+	x6, _ := bits.Sub64((*x)[6], s, b5)
+	x[0] = (x0 >> 4) | (x1 << 60)
+	x[1] = (x1 >> 4) | (x2 << 60)
+	x[2] = (x2 >> 4) | (x3 << 60)
+	x[3] = (x3 >> 4) | (x4 << 60)
+	x[4] = (x4 >> 4) | (x5 << 60)
+	x[5] = (x5 >> 4) | (x6 << 60)
+	x[6] = (x6 >> 4)
+}
+
+func recodeScalar(d *[113]int8, k *Scalar) {
+	var k64 scalar64
+	k64.fromScalar(k)
+	for i := 0; i < 112; i++ {
+		d[i] = int8((k64[0] & 0x1f) - 16)
+		subYDiv16(&k64, int64(d[i]))
+	}
+	d[112] = int8(k64[0])
+}
+
+// ScalarMult returns kP.
+func (e twistCurve) ScalarMult(k *Scalar, P *twistPoint) *twistPoint {
+	var TabP [8]preTwistPointProy
+	var S preTwistPointProy
+	var d [113]int8
+
+	var isZero int
+	if k.IsZero() {
+		isZero = 1
+	}
+	subtle.ConstantTimeCopy(isZero, k[:], order[:])
+
+	minusK := *k
+	isEven := 1 - int(k[0]&0x1)
+	minusK.Neg()
+	subtle.ConstantTimeCopy(isEven, k[:], minusK[:])
+	recodeScalar(&d, k)
+
+	P.oddMultiples(TabP[:])
+	Q := e.Identity()
+	for i := 112; i >= 0; i-- {
+		Q.Double()
+		Q.Double()
+		Q.Double()
+		Q.Double()
+		mask := d[i] >> 7
+		absDi := (d[i] + mask) ^ mask
+		inx := int32((absDi - 1) >> 1)
+		sig := int((d[i] >> 7) & 0x1)
+		for j := range TabP {
+			S.cmov(&TabP[j], uint(subtle.ConstantTimeEq(inx, int32(j))))
+		}
+		S.cneg(sig)
+		Q.mixAdd(&S)
+	}
+	Q.cneg(uint(isEven))
+	return Q
+}
+
+const (
+	omegaFix = 7
+	omegaVar = 5
+)
+
+// CombinedMult returns mG+nP.
+func (e twistCurve) CombinedMult(m, n *Scalar, P *twistPoint) *twistPoint {
+	nafFix := math.OmegaNAF(conv.BytesLe2BigInt(m[:]), omegaFix)
+	nafVar := math.OmegaNAF(conv.BytesLe2BigInt(n[:]), omegaVar)
+
+	if len(nafFix) > len(nafVar) {
+		nafVar = append(nafVar, make([]int32, len(nafFix)-len(nafVar))...)
+	} else if len(nafFix) < len(nafVar) {
+		nafFix = append(nafFix, make([]int32, len(nafVar)-len(nafFix))...)
+	}
+
+	var TabQ [1 << (omegaVar - 2)]preTwistPointProy
+	P.oddMultiples(TabQ[:])
+	Q := e.Identity()
+	for i := len(nafFix) - 1; i >= 0; i-- {
+		Q.Double()
+		// Generator point
+		if nafFix[i] != 0 {
+			idxM := absolute(nafFix[i]) >> 1
+			R := tabVerif[idxM]
+			if nafFix[i] < 0 {
+				R.neg()
+			}
+			Q.mixAddZ1(&R)
+		}
+		// Variable input point
+		if nafVar[i] != 0 {
+			idxN := absolute(nafVar[i]) >> 1
+			S := TabQ[idxN]
+			if nafVar[i] < 0 {
+				S.neg()
+			}
+			Q.mixAdd(&S)
+		}
+	}
+	return Q
+}
+
+// absolute returns always a positive value.
+func absolute(x int32) int32 {
+	mask := x >> 31
+	return (x + mask) ^ mask
+}

vendor/github.com/cloudflare/circl/ecc/goldilocks/twistPoint.go

@@ -0,0 +1,135 @@
+package goldilocks
+
+import (
+	"fmt"
+
+	fp "github.com/cloudflare/circl/math/fp448"
+)
+
+type twistPoint struct{ x, y, z, ta, tb fp.Elt }
+
+type preTwistPointAffine struct{ addYX, subYX, dt2 fp.Elt }
+
+type preTwistPointProy struct {
+	preTwistPointAffine
+	z2 fp.Elt
+}
+
+func (P *twistPoint) String() string {
+	return fmt.Sprintf("x: %v\ny: %v\nz: %v\nta: %v\ntb: %v", P.x, P.y, P.z, P.ta, P.tb)
+}
+
+// cneg conditionally negates the point if b=1.
+func (P *twistPoint) cneg(b uint) {
+	t := &fp.Elt{}
+	fp.Neg(t, &P.x)
+	fp.Cmov(&P.x, t, b)
+	fp.Neg(t, &P.ta)
+	fp.Cmov(&P.ta, t, b)
+}
+
+// Double updates P with 2P.
+func (P *twistPoint) Double() {
+	// This is formula (7) from "Twisted Edwards Curves Revisited" by
+	// Hisil H., Wong K.KH., Carter G., Dawson E. (2008)
+	// https://doi.org/10.1007/978-3-540-89255-7_20
+	Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb
+	a, b, c, e, f, g, h := Px, Py, Pz, Pta, Px, Py, Ptb
+	fp.Add(e, Px, Py) // x+y
+	fp.Sqr(a, Px)     // A = x^2
+	fp.Sqr(b, Py)     // B = y^2
+	fp.Sqr(c, Pz)     // z^2
+	fp.Add(c, c, c)   // C = 2*z^2
+	fp.Add(h, a, b)   // H = A+B
+	fp.Sqr(e, e)      // (x+y)^2
+	fp.Sub(e, e, h)   // E = (x+y)^2-A-B
+	fp.Sub(g, b, a)   // G = B-A
+	fp.Sub(f, c, g)   // F = C-G
+	fp.Mul(Pz, f, g)  // Z = F * G
+	fp.Mul(Px, e, f)  // X = E * F
+	fp.Mul(Py, g, h)  // Y = G * H, T = E * H
+}
+
+// mixAdd calculates P= P+Q, where Q is a precomputed point with Z_Q = 1.
+func (P *twistPoint) mixAddZ1(Q *preTwistPointAffine) {
+	fp.Add(&P.z, &P.z, &P.z) // D = 2*z1 (z2=1)
+	P.coreAddition(Q)
+}
+
+// coreAddition calculates P=P+Q for curves with A=-1.
+func (P *twistPoint) coreAddition(Q *preTwistPointAffine) {
+	// This is the formula following (5) from "Twisted Edwards Curves Revisited" by
+	// Hisil H., Wong K.KH., Carter G., Dawson E. (2008)
+	// https://doi.org/10.1007/978-3-540-89255-7_20
+	Px, Py, Pz, Pta, Ptb := &P.x, &P.y, &P.z, &P.ta, &P.tb
+	addYX2, subYX2, dt2 := &Q.addYX, &Q.subYX, &Q.dt2
+	a, b, c, d, e, f, g, h := Px, Py, &fp.Elt{}, Pz, Pta, Px, Py, Ptb
+	fp.Mul(c, Pta, Ptb)  // t1 = ta*tb
+	fp.Sub(h, Py, Px)    // y1-x1
+	fp.Add(b, Py, Px)    // y1+x1
+	fp.Mul(a, h, subYX2) // A = (y1-x1)*(y2-x2)
+	fp.Mul(b, b, addYX2) // B = (y1+x1)*(y2+x2)
+	fp.Mul(c, c, dt2)    // C = 2*D*t1*t2
+	fp.Sub(e, b, a)      // E = B-A
+	fp.Add(h, b, a)      // H = B+A
+	fp.Sub(f, d, c)      // F = D-C
+	fp.Add(g, d, c)      // G = D+C
+	fp.Mul(Pz, f, g)     // Z = F * G
+	fp.Mul(Px, e, f)     // X = E * F
+	fp.Mul(Py, g, h)     // Y = G * H, T = E * H
+}
+
+func (P *preTwistPointAffine) neg() {
+	P.addYX, P.subYX = P.subYX, P.addYX
+	fp.Neg(&P.dt2, &P.dt2)
+}
+
+func (P *preTwistPointAffine) cneg(b int) {
+	t := &fp.Elt{}
+	fp.Cswap(&P.addYX, &P.subYX, uint(b))
+	fp.Neg(t, &P.dt2)
+	fp.Cmov(&P.dt2, t, uint(b))
+}
+
+func (P *preTwistPointAffine) cmov(Q *preTwistPointAffine, b uint) {
+	fp.Cmov(&P.addYX, &Q.addYX, b)
+	fp.Cmov(&P.subYX, &Q.subYX, b)
+	fp.Cmov(&P.dt2, &Q.dt2, b)
+}
+
+// mixAdd calculates P= P+Q, where Q is a precomputed point with Z_Q != 1.
+func (P *twistPoint) mixAdd(Q *preTwistPointProy) {
+	fp.Mul(&P.z, &P.z, &Q.z2) // D = 2*z1*z2
+	P.coreAddition(&Q.preTwistPointAffine)
+}
+
+// oddMultiples calculates T[i] = (2*i-1)P for 0 < i < len(T).
+func (P *twistPoint) oddMultiples(T []preTwistPointProy) {
+	if n := len(T); n > 0 {
+		T[0].FromTwistPoint(P)
+		_2P := *P
+		_2P.Double()
+		R := &preTwistPointProy{}
+		R.FromTwistPoint(&_2P)
+		for i := 1; i < n; i++ {
+			P.mixAdd(R)
+			T[i].FromTwistPoint(P)
+		}
+	}
+}
+
+// cmov conditionally moves Q into P if b=1.
+func (P *preTwistPointProy) cmov(Q *preTwistPointProy, b uint) {
+	P.preTwistPointAffine.cmov(&Q.preTwistPointAffine, b)
+	fp.Cmov(&P.z2, &Q.z2, b)
+}
+
+// FromTwistPoint precomputes some coordinates of Q for missed addition.
+func (P *preTwistPointProy) FromTwistPoint(Q *twistPoint) {
+	fp.Add(&P.addYX, &Q.y, &Q.x)         // addYX = X + Y
+	fp.Sub(&P.subYX, &Q.y, &Q.x)         // subYX = Y - X
+	fp.Mul(&P.dt2, &Q.ta, &Q.tb)         // T = ta*tb
+	fp.Mul(&P.dt2, &P.dt2, &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
+}

vendor/github.com/cloudflare/circl/ecc/goldilocks/twistTables.go

@@ -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},
+	},
+}

vendor/github.com/cloudflare/circl/ecc/goldilocks/twist_basemult.go

@@ -0,0 +1,62 @@
+package goldilocks
+
+import (
+	"crypto/subtle"
+
+	mlsb "github.com/cloudflare/circl/math/mlsbset"
+)
+
+const (
+	// MLSBRecoding parameters
+	fxT   = 448
+	fxV   = 2
+	fxW   = 3
+	fx2w1 = 1 << (uint(fxW) - 1)
+)
+
+// ScalarBaseMult returns kG where G is the generator point.
+func (e twistCurve) ScalarBaseMult(k *Scalar) *twistPoint {
+	m, err := mlsb.New(fxT, fxV, fxW)
+	if err != nil {
+		panic(err)
+	}
+	if m.IsExtended() {
+		panic("not extended")
+	}
+
+	var isZero int
+	if k.IsZero() {
+		isZero = 1
+	}
+	subtle.ConstantTimeCopy(isZero, k[:], order[:])
+
+	minusK := *k
+	isEven := 1 - int(k[0]&0x1)
+	minusK.Neg()
+	subtle.ConstantTimeCopy(isEven, k[:], minusK[:])
+	c, err := m.Encode(k[:])
+	if err != nil {
+		panic(err)
+	}
+
+	gP := c.Exp(groupMLSB{})
+	P := gP.(*twistPoint)
+	P.cneg(uint(isEven))
+	return P
+}
+
+type groupMLSB struct{}
+
+func (e groupMLSB) ExtendedEltP() mlsb.EltP      { return nil }
+func (e groupMLSB) Sqr(x mlsb.EltG)              { x.(*twistPoint).Double() }
+func (e groupMLSB) Mul(x mlsb.EltG, y mlsb.EltP) { x.(*twistPoint).mixAddZ1(y.(*preTwistPointAffine)) }
+func (e groupMLSB) Identity() mlsb.EltG          { return twistCurve{}.Identity() }
+func (e groupMLSB) NewEltP() mlsb.EltP           { return &preTwistPointAffine{} }
+func (e groupMLSB) Lookup(a mlsb.EltP, v uint, s, u int32) {
+	Tabj := &tabFixMult[v]
+	P := a.(*preTwistPointAffine)
+	for k := range Tabj {
+		P.cmov(&Tabj[k], uint(subtle.ConstantTimeEq(int32(k), u)))
+	}
+	P.cneg(int(s >> 31))
+}

vendor/github.com/cloudflare/circl/internal/conv/conv.go

@@ -0,0 +1,140 @@
+package conv
+
+import (
+	"encoding/binary"
+	"fmt"
+	"math/big"
+	"strings"
+)
+
+// BytesLe2Hex returns an hexadecimal string of a number stored in a
+// little-endian order slice x.
+func BytesLe2Hex(x []byte) string {
+	b := &strings.Builder{}
+	b.Grow(2*len(x) + 2)
+	fmt.Fprint(b, "0x")
+	if len(x) == 0 {
+		fmt.Fprint(b, "00")
+	}
+	for i := len(x) - 1; i >= 0; i-- {
+		fmt.Fprintf(b, "%02x", x[i])
+	}
+	return b.String()
+}
+
+// BytesLe2BigInt converts a little-endian slice x into a big-endian
+// math/big.Int.
+func BytesLe2BigInt(x []byte) *big.Int {
+	n := len(x)
+	b := new(big.Int)
+	if len(x) > 0 {
+		y := make([]byte, n)
+		for i := 0; i < n; i++ {
+			y[n-1-i] = x[i]
+		}
+		b.SetBytes(y)
+	}
+	return b
+}
+
+// BytesBe2Uint64Le converts a big-endian slice x to a little-endian slice of uint64.
+func BytesBe2Uint64Le(x []byte) []uint64 {
+	l := len(x)
+	z := make([]uint64, (l+7)/8)
+	blocks := l / 8
+	for i := 0; i < blocks; i++ {
+		z[i] = binary.BigEndian.Uint64(x[l-8*(i+1):])
+	}
+	remBytes := l % 8
+	for i := 0; i < remBytes; i++ {
+		z[blocks] |= uint64(x[l-1-8*blocks-i]) << uint(8*i)
+	}
+	return z
+}
+
+// BigInt2BytesLe stores a positive big.Int number x into a little-endian slice z.
+// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros).
+// If x does not fit in the slice or is negative, z is not modified.
+func BigInt2BytesLe(z []byte, x *big.Int) {
+	xLen := (x.BitLen() + 7) >> 3
+	zLen := len(z)
+	if zLen >= xLen && x.Sign() >= 0 {
+		y := x.Bytes()
+		for i := 0; i < xLen; i++ {
+			z[i] = y[xLen-1-i]
+		}
+		for i := xLen; i < zLen; i++ {
+			z[i] = 0
+		}
+	}
+}
+
+// Uint64Le2BigInt converts a little-endian slice x into a big number.
+func Uint64Le2BigInt(x []uint64) *big.Int {
+	n := len(x)
+	b := new(big.Int)
+	var bi big.Int
+	for i := n - 1; i >= 0; i-- {
+		bi.SetUint64(x[i])
+		b.Lsh(b, 64)
+		b.Add(b, &bi)
+	}
+	return b
+}
+
+// Uint64Le2BytesLe converts a little-endian slice x to a little-endian slice of bytes.
+func Uint64Le2BytesLe(x []uint64) []byte {
+	b := make([]byte, 8*len(x))
+	n := len(x)
+	for i := 0; i < n; i++ {
+		binary.LittleEndian.PutUint64(b[i*8:], x[i])
+	}
+	return b
+}
+
+// Uint64Le2BytesBe converts a little-endian slice x to a big-endian slice of bytes.
+func Uint64Le2BytesBe(x []uint64) []byte {
+	b := make([]byte, 8*len(x))
+	n := len(x)
+	for i := 0; i < n; i++ {
+		binary.BigEndian.PutUint64(b[i*8:], x[n-1-i])
+	}
+	return b
+}
+
+// Uint64Le2Hex returns an hexadecimal string of a number stored in a
+// little-endian order slice x.
+func Uint64Le2Hex(x []uint64) string {
+	b := new(strings.Builder)
+	b.Grow(16*len(x) + 2)
+	fmt.Fprint(b, "0x")
+	if len(x) == 0 {
+		fmt.Fprint(b, "00")
+	}
+	for i := len(x) - 1; i >= 0; i-- {
+		fmt.Fprintf(b, "%016x", x[i])
+	}
+	return b.String()
+}
+
+// BigInt2Uint64Le stores a positive big.Int number x into a little-endian slice z.
+// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros).
+// If x does not fit in the slice or is negative, z is not modified.
+func BigInt2Uint64Le(z []uint64, x *big.Int) {
+	xLen := (x.BitLen() + 63) >> 6 // number of 64-bit words
+	zLen := len(z)
+	if zLen >= xLen && x.Sign() > 0 {
+		var y, yi big.Int
+		y.Set(x)
+		two64 := big.NewInt(1)
+		two64.Lsh(two64, 64).Sub(two64, big.NewInt(1))
+		for i := 0; i < xLen; i++ {
+			yi.And(&y, two64)
+			z[i] = yi.Uint64()
+			y.Rsh(&y, 64)
+		}
+	}
+	for i := xLen; i < zLen; i++ {
+		z[i] = 0
+	}
+}

vendor/github.com/cloudflare/circl/internal/sha3/doc.go

@@ -0,0 +1,62 @@
+// Copyright 2014 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package sha3 implements the SHA-3 fixed-output-length hash functions and
+// the SHAKE variable-output-length hash functions defined by FIPS-202.
+//
+// Both types of hash function use the "sponge" construction and the Keccak
+// permutation. For a detailed specification see http://keccak.noekeon.org/
+//
+// # Guidance
+//
+// If you aren't sure what function you need, use SHAKE256 with at least 64
+// bytes of output. The SHAKE instances are faster than the SHA3 instances;
+// the latter have to allocate memory to conform to the hash.Hash interface.
+//
+// If you need a secret-key MAC (message authentication code), prepend the
+// secret key to the input, hash with SHAKE256 and read at least 32 bytes of
+// output.
+//
+// # Security strengths
+//
+// The SHA3-x (x equals 224, 256, 384, or 512) functions have a security
+// strength against preimage attacks of x bits. Since they only produce "x"
+// bits of output, their collision-resistance is only "x/2" bits.
+//
+// The SHAKE-256 and -128 functions have a generic security strength of 256 and
+// 128 bits against all attacks, provided that at least 2x bits of their output
+// is used.  Requesting more than 64 or 32 bytes of output, respectively, does
+// not increase the collision-resistance of the SHAKE functions.
+//
+// # The sponge construction
+//
+// A sponge builds a pseudo-random function from a public pseudo-random
+// permutation, by applying the permutation to a state of "rate + capacity"
+// bytes, but hiding "capacity" of the bytes.
+//
+// A sponge starts out with a zero state. To hash an input using a sponge, up
+// to "rate" bytes of the input are XORed into the sponge's state. The sponge
+// is then "full" and the permutation is applied to "empty" it. This process is
+// repeated until all the input has been "absorbed". The input is then padded.
+// The digest is "squeezed" from the sponge in the same way, except that output
+// is copied out instead of input being XORed in.
+//
+// A sponge is parameterized by its generic security strength, which is equal
+// to half its capacity; capacity + rate is equal to the permutation's width.
+// Since the KeccakF-1600 permutation is 1600 bits (200 bytes) wide, this means
+// that the security strength of a sponge instance is equal to (1600 - bitrate) / 2.
+//
+// # Recommendations
+//
+// The SHAKE functions are recommended for most new uses. They can produce
+// output of arbitrary length. SHAKE256, with an output length of at least
+// 64 bytes, provides 256-bit security against all attacks.  The Keccak team
+// recommends it for most applications upgrading from SHA2-512. (NIST chose a
+// much stronger, but much slower, sponge instance for SHA3-512.)
+//
+// The SHA-3 functions are "drop-in" replacements for the SHA-2 functions.
+// They produce output of the same length, with the same security strengths
+// against all attacks. This means, in particular, that SHA3-256 only has
+// 128-bit collision resistance, because its output length is 32 bytes.
+package sha3