From 27c7ab1227b78ffe8d629fa44538c8a6bbfdc16f Mon Sep 17 00:00:00 2001 From: GladysKellogg Date: Tue, 12 Jan 2021 17:45:03 +0800 Subject: [PATCH] add edwards --- Gopkg.lock | 140 -- Gopkg.toml | 86 - go.mod | 1 - go.sum | 4 +- hcec/ed25519/LICENSE | 27 + hcec/ed25519/ed25519.go | 127 ++ hcec/ed25519/ed25519_test.go | 160 ++ hcec/ed25519/edwards25519/const.go | 1411 ++++++++++++++++ hcec/ed25519/edwards25519/edwards25519.go | 1773 ++++++++++++++++++++ hcec/ed25519/extra25519/extra25519.go | 339 ++++ hcec/ed25519/extra25519/extra25519_test.go | 78 + hcec/ed25519/testdata/sign.input.gz | Bin 0 -> 50330 bytes hcec/edwards/const.go | 114 +- hcec/edwards/curve.go | 820 ++++----- hcec/edwards/ecdsa.go | 764 ++++----- hcec/edwards/primitives.go | 592 +++---- hcec/edwards/privkey.go | 406 ++--- 17 files changed, 5265 insertions(+), 1577 deletions(-) delete mode 100644 Gopkg.lock delete mode 100644 Gopkg.toml create mode 100644 hcec/ed25519/LICENSE create mode 100644 hcec/ed25519/ed25519.go create mode 100644 hcec/ed25519/ed25519_test.go create mode 100644 hcec/ed25519/edwards25519/const.go create mode 100644 hcec/ed25519/edwards25519/edwards25519.go create mode 100644 hcec/ed25519/extra25519/extra25519.go create mode 100644 hcec/ed25519/extra25519/extra25519_test.go create mode 100644 hcec/ed25519/testdata/sign.input.gz diff --git a/Gopkg.lock b/Gopkg.lock deleted file mode 100644 index af7e5aa..0000000 --- a/Gopkg.lock +++ /dev/null @@ -1,140 +0,0 @@ -# This file is autogenerated, do not edit; changes may be undone by the next 'dep ensure'. - - -[[projects]] - branch = "master" - name = "github.com/HcashOrg/bitset" - packages = ["."] - revision = "3b5f0c752dfbeeda856fd6af60e997257ca399fc" - -[[projects]] - branch = "master" - name = "github.com/HcashOrg/bliss" - packages = [ - ".", - "huffman", - "params", - "poly", - "sampler" - ] - revision = "f5d53c2a9b7d05ffa1600cad036d3d51dd5423cc" - -[[projects]] - branch = "master" - name = "github.com/HcashOrg/hcrpcclient" - packages = ["."] - revision = "48a5d652f2e17c8ac69e556fc18080e76e4b5c01" - -[[projects]] - branch = "master" - name = "github.com/agl/ed25519" - packages = [ - ".", - "edwards25519" - ] - revision = "5312a61534124124185d41f09206b9fef1d88403" - -[[projects]] - branch = "master" - name = "github.com/btcsuite/btclog" - packages = ["."] - revision = "84c8d2346e9fc8c7b947e243b9c24e6df9fd206a" - -[[projects]] - branch = "master" - name = "github.com/btcsuite/go-socks" - packages = ["socks"] - revision = "4720035b7bfd2a9bb130b1c184f8bbe41b6f0d0f" - -[[projects]] - name = "github.com/btcsuite/goleveldb" - packages = [ - "leveldb", - "leveldb/cache", - "leveldb/comparer", - "leveldb/errors", - "leveldb/filter", - "leveldb/iterator", - "leveldb/journal", - "leveldb/memdb", - "leveldb/opt", - "leveldb/storage", - "leveldb/table", - "leveldb/util" - ] - revision = "3fd0373267b6461dbefe91cef614278064d05465" - version = "v1.0.0" - -[[projects]] - name = "github.com/btcsuite/snappy-go" - packages = ["."] - revision = "b3db38edf0a9a11a115eb6b022d8c946024a9ac0" - version = "v1.0.0" - -[[projects]] - branch = "master" - name = "github.com/btcsuite/websocket" - packages = ["."] - revision = "31079b6807923eb23992c421b114992b95131b55" - -[[projects]] - name = "github.com/btcsuite/winsvc" - packages = [ - "eventlog", - "mgr", - "registry", - "svc", - "winapi" - ] - revision = "f8fb11f83f7e860e3769a08e6811d1b399a43722" - version = "v1.0.0" - -[[projects]] - name = "github.com/davecgh/go-spew" - packages = ["spew"] - revision = "8991bc29aa16c548c550c7ff78260e27b9ab7c73" - version = "v1.1.1" - -[[projects]] - name = "github.com/dchest/blake256" - packages = ["."] - revision = "dee3fe6eb0e98dc774a94fc231f85baf7c29d360" - version = "v1.0.0" - -[[projects]] - name = "github.com/jessevdk/go-flags" - packages = ["."] - revision = "c6ca198ec95c841fdb89fc0de7496fed11ab854e" - version = "v1.4.0" - -[[projects]] - name = "github.com/jrick/logrotate" - packages = ["rotator"] - revision = "a93b200c26cbae3bb09dd0dc2c7c7fe1468a034a" - version = "v1.0.0" - -[[projects]] - branch = "master" - name = "golang.org/x/crypto" - packages = [ - "ripemd160", - "sha3", - "ssh/terminal" - ] - revision = "0709b304e793a5edb4a2c0145f281ecdc20838a4" - -[[projects]] - branch = "master" - name = "golang.org/x/sys" - packages = [ - "unix", - "windows" - ] - revision = "2b024373dcd9800f0cae693839fac6ede8d64a8c" - -[solve-meta] - analyzer-name = "dep" - analyzer-version = 1 - inputs-digest = "ae0cdc70a447260dd5f237fd4ad569c0039b65c290cca3779f90d589b78c41b2" - solver-name = "gps-cdcl" - solver-version = 1 diff --git a/Gopkg.toml b/Gopkg.toml deleted file mode 100644 index e94fac2..0000000 --- a/Gopkg.toml +++ /dev/null @@ -1,86 +0,0 @@ -# Gopkg.toml example -# -# Refer to https://golang.github.io/dep/docs/Gopkg.toml.html -# for detailed Gopkg.toml documentation. -# -# required = ["github.com/user/thing/cmd/thing"] -# ignored = ["github.com/user/project/pkgX", "bitbucket.org/user/project/pkgA/pkgY"] -# -# [[constraint]] -# name = "github.com/user/project" -# version = "1.0.0" -# -# [[constraint]] -# name = "github.com/user/project2" -# branch = "dev" -# source = "github.com/myfork/project2" -# -# [[override]] -# name = "github.com/x/y" -# version = "2.4.0" -# -# [prune] -# non-go = false -# go-tests = true -# unused-packages = true - - -[[constraint]] - branch = "master" - name = "github.com/HcashOrg/bitset" - -[[constraint]] - branch = "master" - name = "github.com/HcashOrg/bliss" - -[[constraint]] - branch = "master" - name = "github.com/HcashOrg/hcrpcclient" - -[[constraint]] - branch = "master" - name = "github.com/agl/ed25519" - -[[constraint]] - branch = "master" - name = "github.com/btcsuite/btclog" - -[[constraint]] - branch = "master" - name = "github.com/btcsuite/go-socks" - -[[constraint]] - name = "github.com/btcsuite/goleveldb" - version = "1.0.0" - -[[constraint]] - branch = "master" - name = "github.com/btcsuite/websocket" - -[[constraint]] - name = "github.com/btcsuite/winsvc" - version = "1.0.0" - -[[constraint]] - name = "github.com/davecgh/go-spew" - version = "1.1.1" - -[[constraint]] - name = "github.com/dchest/blake256" - version = "1.0.0" - -[[constraint]] - name = "github.com/jessevdk/go-flags" - version = "1.4.0" - -[[constraint]] - name = "github.com/jrick/logrotate" - version = "1.0.0" - -[[constraint]] - branch = "master" - name = "golang.org/x/crypto" - -[prune] - go-tests = true - unused-packages = true diff --git a/go.mod b/go.mod index a4635eb..4a0ee9f 100644 --- a/go.mod +++ b/go.mod @@ -5,7 +5,6 @@ go 1.13 require ( github.com/HcashOrg/bitset v0.0.0-20170930031026-3b5f0c752dfb github.com/HcashOrg/bliss v0.0.0-20180719035130-f5d53c2a9b7d - github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412 github.com/btcsuite/btclog v0.0.0-20170628155309-84c8d2346e9f github.com/btcsuite/go-socks v0.0.0-20170105172521-4720035b7bfd github.com/btcsuite/goleveldb v1.0.0 diff --git a/go.sum b/go.sum index 11384fb..6057e7f 100644 --- a/go.sum +++ b/go.sum @@ -2,8 +2,8 @@ github.com/HcashOrg/bitset v0.0.0-20170930031026-3b5f0c752dfb h1:XmMHZh7XHUj2TNE github.com/HcashOrg/bitset v0.0.0-20170930031026-3b5f0c752dfb/go.mod h1:wpl2yM06pqJmmK6QNjF8xLY7hpmG+Dueop4ehfzQ3/w= github.com/HcashOrg/bliss v0.0.0-20180719035130-f5d53c2a9b7d h1:uBrdipThpidikHT2aB/v9QZoW8ehVNaK3CvbEKBx7Ak= github.com/HcashOrg/bliss v0.0.0-20180719035130-f5d53c2a9b7d/go.mod h1:Ey5JSoZdhxhRcRZnLGrOD9Q1sUzl4gpQkF14F4NVlE4= -github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412 h1:w1UutsfOrms1J05zt7ISrnJIXKzwaspym5BTKGx93EI= -github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412/go.mod h1:WPjqKcmVOxf0XSf3YxCJs6N6AOSrOx3obionmG7T0y0= +github.com/HcashOrg/hcd/ed25519 v0.0.0-20170116200512-5312a6153412 h1:w1UutsfOrms1J05zt7ISrnJIXKzwaspym5BTKGx93EI= +github.com/HcashOrg/hcd/ed25519 v0.0.0-20170116200512-5312a6153412/go.mod h1:WPjqKcmVOxf0XSf3YxCJs6N6AOSrOx3obionmG7T0y0= github.com/btcsuite/btclog v0.0.0-20170628155309-84c8d2346e9f h1:bAs4lUbRJpnnkd9VhRV3jjAVU7DJVjMaK+IsvSeZvFo= github.com/btcsuite/btclog v0.0.0-20170628155309-84c8d2346e9f/go.mod h1:TdznJufoqS23FtqVCzL0ZqgP5MqXbb4fg/WgDys70nA= github.com/btcsuite/go-socks v0.0.0-20170105172521-4720035b7bfd h1:R/opQEbFEy9JGkIguV40SvRY1uliPX8ifOvi6ICsFCw= diff --git a/hcec/ed25519/LICENSE b/hcec/ed25519/LICENSE new file mode 100644 index 0000000..7448756 --- /dev/null +++ b/hcec/ed25519/LICENSE @@ -0,0 +1,27 @@ +Copyright (c) 2012 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. diff --git a/hcec/ed25519/ed25519.go b/hcec/ed25519/ed25519.go new file mode 100644 index 0000000..df2fd2b --- /dev/null +++ b/hcec/ed25519/ed25519.go @@ -0,0 +1,127 @@ +// Copyright 2013 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 ed25519 implements the Ed25519 signature algorithm. See +// http://ed25519.cr.yp.to/. +package ed25519 + +// This code is a port of the public domain, "ref10" implementation of ed25519 +// from SUPERCOP. + +import ( + "crypto/sha512" + "crypto/subtle" + "io" + + "github.com/HcashOrg/hcd/hcec/ed25519/edwards25519" +) + +const ( + PublicKeySize = 32 + PrivateKeySize = 64 + SignatureSize = 64 +) + +// GenerateKey generates a public/private key pair using randomness from rand. +func GenerateKey(rand io.Reader) (publicKey *[PublicKeySize]byte, privateKey *[PrivateKeySize]byte, err error) { + privateKey = new([64]byte) + publicKey = new([32]byte) + _, err = io.ReadFull(rand, privateKey[:32]) + if err != nil { + return nil, nil, err + } + + h := sha512.New() + h.Write(privateKey[:32]) + digest := h.Sum(nil) + + digest[0] &= 248 + digest[31] &= 127 + digest[31] |= 64 + + var A edwards25519.ExtendedGroupElement + var hBytes [32]byte + copy(hBytes[:], digest) + edwards25519.GeScalarMultBase(&A, &hBytes) + A.ToBytes(publicKey) + + copy(privateKey[32:], publicKey[:]) + return +} + +// Sign signs the message with privateKey and returns a signature. +func Sign(privateKey *[PrivateKeySize]byte, message []byte) *[SignatureSize]byte { + h := sha512.New() + h.Write(privateKey[:32]) + + var digest1, messageDigest, hramDigest [64]byte + var expandedSecretKey [32]byte + h.Sum(digest1[:0]) + copy(expandedSecretKey[:], digest1[:]) + expandedSecretKey[0] &= 248 + expandedSecretKey[31] &= 63 + expandedSecretKey[31] |= 64 + + h.Reset() + h.Write(digest1[32:]) + h.Write(message) + h.Sum(messageDigest[:0]) + + var messageDigestReduced [32]byte + edwards25519.ScReduce(&messageDigestReduced, &messageDigest) + var R edwards25519.ExtendedGroupElement + edwards25519.GeScalarMultBase(&R, &messageDigestReduced) + + var encodedR [32]byte + R.ToBytes(&encodedR) + + h.Reset() + h.Write(encodedR[:]) + h.Write(privateKey[32:]) + h.Write(message) + h.Sum(hramDigest[:0]) + var hramDigestReduced [32]byte + edwards25519.ScReduce(&hramDigestReduced, &hramDigest) + + var s [32]byte + edwards25519.ScMulAdd(&s, &hramDigestReduced, &expandedSecretKey, &messageDigestReduced) + + signature := new([64]byte) + copy(signature[:], encodedR[:]) + copy(signature[32:], s[:]) + return signature +} + +// Verify returns true iff sig is a valid signature of message by publicKey. +func Verify(publicKey *[PublicKeySize]byte, message []byte, sig *[SignatureSize]byte) bool { + if sig[63]&224 != 0 { + return false + } + + var A edwards25519.ExtendedGroupElement + if !A.FromBytes(publicKey) { + return false + } + edwards25519.FeNeg(&A.X, &A.X) + edwards25519.FeNeg(&A.T, &A.T) + + h := sha512.New() + h.Write(sig[:32]) + h.Write(publicKey[:]) + h.Write(message) + var digest [64]byte + h.Sum(digest[:0]) + + var hReduced [32]byte + edwards25519.ScReduce(&hReduced, &digest) + + var R edwards25519.ProjectiveGroupElement + var b [32]byte + copy(b[:], sig[32:]) + edwards25519.GeDoubleScalarMultVartime(&R, &hReduced, &A, &b) + + var checkR [32]byte + R.ToBytes(&checkR) + return subtle.ConstantTimeCompare(sig[:32], checkR[:]) == 1 +} diff --git a/hcec/ed25519/ed25519_test.go b/hcec/ed25519/ed25519_test.go new file mode 100644 index 0000000..77af378 --- /dev/null +++ b/hcec/ed25519/ed25519_test.go @@ -0,0 +1,160 @@ +// 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 ed25519 + +import ( + "bufio" + "bytes" + "compress/gzip" + "crypto/rand" + "encoding/hex" + "io" + "os" + "strings" + "testing" + + "github.com/HcashOrg/hcd/ed25519/edwards25519" +) + +type zeroReader struct{} + +func (zeroReader) Read(buf []byte) (int, error) { + for i := range buf { + buf[i] = 0 + } + return len(buf), nil +} + +func TestUnmarshalMarshal(t *testing.T) { + pub, _, _ := GenerateKey(rand.Reader) + + var A edwards25519.ExtendedGroupElement + if !A.FromBytes(pub) { + t.Fatalf("ExtendedGroupElement.FromBytes failed") + } + + var pub2 [32]byte + A.ToBytes(&pub2) + + if *pub != pub2 { + t.Errorf("FromBytes(%v)->ToBytes does not round-trip, got %x\n", *pub, pub2) + } +} + +func TestSignVerify(t *testing.T) { + var zero zeroReader + public, private, _ := GenerateKey(zero) + + message := []byte("test message") + sig := Sign(private, message) + if !Verify(public, message, sig) { + t.Errorf("valid signature rejected") + } + + wrongMessage := []byte("wrong message") + if Verify(public, wrongMessage, sig) { + t.Errorf("signature of different message accepted") + } +} + +func TestGolden(t *testing.T) { + // sign.input.gz is a selection of test cases from + // http://ed25519.cr.yp.to/python/sign.input + testDataZ, err := os.Open("testdata/sign.input.gz") + if err != nil { + t.Fatal(err) + } + defer testDataZ.Close() + testData, err := gzip.NewReader(testDataZ) + if err != nil { + t.Fatal(err) + } + defer testData.Close() + + in := bufio.NewReaderSize(testData, 1<<12) + lineNo := 0 + for { + lineNo++ + lineBytes, isPrefix, err := in.ReadLine() + if isPrefix { + t.Fatal("bufio buffer too small") + } + if err != nil { + if err == io.EOF { + break + } + t.Fatalf("error reading test data: %s", err) + } + + line := string(lineBytes) + parts := strings.Split(line, ":") + if len(parts) != 5 { + t.Fatalf("bad number of parts on line %d", lineNo) + } + + privBytes, _ := hex.DecodeString(parts[0]) + pubKeyBytes, _ := hex.DecodeString(parts[1]) + msg, _ := hex.DecodeString(parts[2]) + sig, _ := hex.DecodeString(parts[3]) + // The signatures in the test vectors also include the message + // at the end, but we just want R and S. + sig = sig[:SignatureSize] + + if l := len(pubKeyBytes); l != PublicKeySize { + t.Fatalf("bad public key length on line %d: got %d bytes", lineNo, l) + } + + var priv [PrivateKeySize]byte + copy(priv[:], privBytes) + copy(priv[32:], pubKeyBytes) + + sig2 := Sign(&priv, msg) + if !bytes.Equal(sig, sig2[:]) { + t.Errorf("different signature result on line %d: %x vs %x", lineNo, sig, sig2) + } + + var pubKey [PublicKeySize]byte + copy(pubKey[:], pubKeyBytes) + if !Verify(&pubKey, msg, sig2) { + t.Errorf("signature failed to verify on line %d", lineNo) + } + } +} + +func BenchmarkKeyGeneration(b *testing.B) { + var zero zeroReader + for i := 0; i < b.N; i++ { + if _, _, err := GenerateKey(zero); err != nil { + b.Fatal(err) + } + } +} + +func BenchmarkSigning(b *testing.B) { + var zero zeroReader + _, priv, err := GenerateKey(zero) + if err != nil { + b.Fatal(err) + } + message := []byte("Hello, world!") + b.ResetTimer() + for i := 0; i < b.N; i++ { + Sign(priv, message) + } +} + +func BenchmarkVerification(b *testing.B) { + var zero zeroReader + pub, priv, err := GenerateKey(zero) + if err != nil { + b.Fatal(err) + } + message := []byte("Hello, world!") + signature := Sign(priv, message) + b.ResetTimer() + for i := 0; i < b.N; i++ { + Verify(pub, message, signature) + } +} diff --git a/hcec/ed25519/edwards25519/const.go b/hcec/ed25519/edwards25519/const.go new file mode 100644 index 0000000..ea5b77a --- /dev/null +++ b/hcec/ed25519/edwards25519/const.go @@ -0,0 +1,1411 @@ +// Copyright 2013 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 edwards25519 + +var d = FieldElement{ + -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116, +} + +var d2 = FieldElement{ + -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199, +} + +var SqrtM1 = FieldElement{ + -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482, +} + +var A = FieldElement{ + 486662, 0, 0, 0, 0, 0, 0, 0, 0, 0, +} + +var bi = [8]PreComputedGroupElement{ + { + FieldElement{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605}, + FieldElement{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378}, + FieldElement{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546}, + }, + { + FieldElement{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024}, + FieldElement{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574}, + FieldElement{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357}, + }, + { + FieldElement{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380}, + FieldElement{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306}, + FieldElement{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942}, + }, + { + FieldElement{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766}, + FieldElement{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701}, + FieldElement{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300}, + }, + { + FieldElement{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877}, + FieldElement{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951}, + FieldElement{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784}, + }, + { + FieldElement{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436}, + FieldElement{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918}, + FieldElement{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877}, + }, + { + FieldElement{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800}, + FieldElement{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 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-28812189, -4920970, -18275391, -14621414, 13040862, -12112948}, + }, + { + FieldElement{11293895, 12478086, -27136401, 15083750, -29307421, 14748872, 14555558, -13417103, 1613711, 4896935}, + FieldElement{-25894883, 15323294, -8489791, -8057900, 25967126, -13425460, 2825960, -4897045, -23971776, -11267415}, + FieldElement{-15924766, -5229880, -17443532, 6410664, 3622847, 10243618, 20615400, 12405433, -23753030, -8436416}, + }, + { + FieldElement{-7091295, 12556208, -20191352, 9025187, -17072479, 4333801, 4378436, 2432030, 23097949, -566018}, + FieldElement{4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, 10103221, -18512313, 2424778}, + FieldElement{366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, 1344109, -3642553, 12412659}, + }, + { + FieldElement{-24001791, 7690286, 14929416, -168257, -32210835, -13412986, 24162697, -15326504, -3141501, 11179385}, + FieldElement{18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -6001441, -1486897, -18684645, -11443503}, + FieldElement{476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, 13403813, 11052904, 5219329}, + }, + }, + { + { + FieldElement{20678546, -8375738, -32671898, 8849123, -5009758, 14574752, 31186971, -3973730, 9014762, -8579056}, + FieldElement{-13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -33102500, 9160280, 8473550, -3256838}, + FieldElement{24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -7689309, -16335821, -24568481, 11788948}, + }, + { + FieldElement{-3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -20037437, 10410733, -24568470, -1458691}, + FieldElement{-15659161, 16736706, -22467150, 10215878, -9097177, 7563911, 11871841, -12505194, -18513325, 8464118}, + FieldElement{-23400612, 8348507, -14585951, -861714, -3950205, -6373419, 14325289, 8628612, 33313881, -8370517}, + }, + { + FieldElement{-20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -24805667, -10236854, -8940735, -5818269}, + FieldElement{-6948785, -1795212, -32625683, -16021179, 32635414, -7374245, 15989197, -12838188, 28358192, -4253904}, + FieldElement{-23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -16637684, 4072016, -5351664, 5596589}, + }, + { + FieldElement{-28236598, -3390048, 12312896, 6213178, 3117142, 16078565, 29266239, 2557221, 1768301, 15373193}, + FieldElement{-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -4504991, -24660491, 3442910}, + FieldElement{-30210571, 5124043, 14181784, 8197961, 18964734, -11939093, 22597931, 7176455, -18585478, 13365930}, + }, + { + FieldElement{-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -8570186, -9689599, -3031667}, + FieldElement{25008904, -10771599, -4305031, -9638010, 16265036, 15721635, 683793, -11823784, 15723479, -15163481}, + FieldElement{-9660625, 12374379, -27006999, -7026148, -7724114, -12314514, 11879682, 5400171, 519526, -1235876}, + }, + { + FieldElement{22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -20353881, 7315967, 16648397, 7605640}, + FieldElement{-8081308, -8464597, -8223311, 9719710, 19259459, -15348212, 23994942, -5281555, -9468848, 4763278}, + FieldElement{-21699244, 9220969, -15730624, 1084137, -25476107, -2852390, 31088447, -7764523, -11356529, 728112}, + }, + { + FieldElement{26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -4273545, -12555558, -29365436, -5498272}, + FieldElement{17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, 12327945, 10750447, 10014012}, + FieldElement{-10312768, 3936952, 9156313, -8897683, 16498692, -994647, -27481051, -666732, 3424691, 7540221}, + }, + { + FieldElement{30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -16317219, -9244265, 15258046}, + FieldElement{13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345}, + FieldElement{-19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310}, + }, + }, + { + { + FieldElement{19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937}, + FieldElement{31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636}, + FieldElement{-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008}, + }, + { + FieldElement{-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429}, + FieldElement{-15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576}, + FieldElement{31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066}, + }, + { + FieldElement{-9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490}, + FieldElement{-12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104}, + FieldElement{33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053}, + }, + { + FieldElement{31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275}, + FieldElement{-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511}, + FieldElement{22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095}, + }, + { + FieldElement{-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439}, + FieldElement{23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939}, + FieldElement{-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424}, + }, + { + FieldElement{2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310}, + FieldElement{3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608}, + FieldElement{-32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079}, + }, + { + FieldElement{-23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101}, + FieldElement{21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418}, + FieldElement{18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576}, + }, + { + FieldElement{30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356}, + FieldElement{9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996}, + FieldElement{-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099}, + }, + }, + { + { + FieldElement{-26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728}, + FieldElement{-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658}, + FieldElement{-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242}, + }, + { + FieldElement{-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001}, + FieldElement{-4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766}, + FieldElement{18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373}, + }, + { + FieldElement{26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458}, + FieldElement{-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628}, + FieldElement{-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657}, + }, + { + FieldElement{-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062}, + FieldElement{25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616}, + FieldElement{31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014}, + }, + { + FieldElement{24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383}, + FieldElement{-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814}, + FieldElement{-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718}, + }, + { + FieldElement{30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417}, + FieldElement{2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222}, + FieldElement{33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444}, + }, + { + FieldElement{-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597}, + FieldElement{23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970}, + FieldElement{1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799}, + }, + { + FieldElement{-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647}, + FieldElement{13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511}, + FieldElement{-29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032}, + }, + }, + { + { + FieldElement{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834}, + FieldElement{-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461}, + FieldElement{29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062}, + }, + { + FieldElement{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516}, + FieldElement{-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547}, + FieldElement{-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240}, + }, + { + FieldElement{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038}, + FieldElement{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741}, + FieldElement{16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103}, + }, + { + FieldElement{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747}, + FieldElement{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323}, + FieldElement{31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016}, + }, + { + FieldElement{-14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373}, + FieldElement{15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228}, + FieldElement{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141}, + }, + { + FieldElement{16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399}, + FieldElement{11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831}, + FieldElement{-185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376}, + }, + { + FieldElement{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313}, + FieldElement{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958}, + FieldElement{-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577}, + }, + { + FieldElement{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743}, + FieldElement{29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684}, + FieldElement{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476}, + }, + }, +} diff --git a/hcec/ed25519/edwards25519/edwards25519.go b/hcec/ed25519/edwards25519/edwards25519.go new file mode 100644 index 0000000..9079818 --- /dev/null +++ b/hcec/ed25519/edwards25519/edwards25519.go @@ -0,0 +1,1773 @@ +// Copyright 2013 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 edwards25519 implements operations in GF(2**255-19) and on an +// Edwards curve that is isomorphic to curve25519. See +// http://ed25519.cr.yp.to/. +package edwards25519 + +// This code is a port of the public domain, "ref10" implementation of ed25519 +// from SUPERCOP. + +// FieldElement represents an element of the field GF(2^255 - 19). An element +// t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 +// t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on +// context. +type FieldElement [10]int32 + +var zero FieldElement + +func FeZero(fe *FieldElement) { + copy(fe[:], zero[:]) +} + +func FeOne(fe *FieldElement) { + FeZero(fe) + fe[0] = 1 +} + +func FeAdd(dst, a, b *FieldElement) { + dst[0] = a[0] + b[0] + dst[1] = a[1] + b[1] + dst[2] = a[2] + b[2] + dst[3] = a[3] + b[3] + dst[4] = a[4] + b[4] + dst[5] = a[5] + b[5] + dst[6] = a[6] + b[6] + dst[7] = a[7] + b[7] + dst[8] = a[8] + b[8] + dst[9] = a[9] + b[9] +} + +func FeSub(dst, a, b *FieldElement) { + dst[0] = a[0] - b[0] + dst[1] = a[1] - b[1] + dst[2] = a[2] - b[2] + dst[3] = a[3] - b[3] + dst[4] = a[4] - b[4] + dst[5] = a[5] - b[5] + dst[6] = a[6] - b[6] + dst[7] = a[7] - b[7] + dst[8] = a[8] - b[8] + dst[9] = a[9] - b[9] +} + +func FeCopy(dst, src *FieldElement) { + copy(dst[:], src[:]) +} + +// Replace (f,g) with (g,g) if b == 1; +// replace (f,g) with (f,g) if b == 0. +// +// Preconditions: b in {0,1}. +func FeCMove(f, g *FieldElement, b int32) { + b = -b + f[0] ^= b & (f[0] ^ g[0]) + f[1] ^= b & (f[1] ^ g[1]) + f[2] ^= b & (f[2] ^ g[2]) + f[3] ^= b & (f[3] ^ g[3]) + f[4] ^= b & (f[4] ^ g[4]) + f[5] ^= b & (f[5] ^ g[5]) + f[6] ^= b & (f[6] ^ g[6]) + f[7] ^= b & (f[7] ^ g[7]) + f[8] ^= b & (f[8] ^ g[8]) + f[9] ^= b & (f[9] ^ g[9]) +} + +func load3(in []byte) int64 { + var r int64 + r = int64(in[0]) + r |= int64(in[1]) << 8 + r |= int64(in[2]) << 16 + return r +} + +func load4(in []byte) int64 { + var r int64 + r = int64(in[0]) + r |= int64(in[1]) << 8 + r |= int64(in[2]) << 16 + r |= int64(in[3]) << 24 + return r +} + +func FeFromBytes(dst *FieldElement, src *[32]byte) { + h0 := load4(src[:]) + h1 := load3(src[4:]) << 6 + h2 := load3(src[7:]) << 5 + h3 := load3(src[10:]) << 3 + h4 := load3(src[13:]) << 2 + h5 := load4(src[16:]) + h6 := load3(src[20:]) << 7 + h7 := load3(src[23:]) << 5 + h8 := load3(src[26:]) << 4 + h9 := (load3(src[29:]) & 8388607) << 2 + + FeCombine(dst, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9) +} + +// FeToBytes marshals h to s. +// Preconditions: +// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +// +// Write p=2^255-19; q=floor(h/p). +// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). +// +// Proof: +// Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. +// Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4. +// +// Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). +// Then 0> 25 + q = (h[0] + q) >> 26 + q = (h[1] + q) >> 25 + q = (h[2] + q) >> 26 + q = (h[3] + q) >> 25 + q = (h[4] + q) >> 26 + q = (h[5] + q) >> 25 + q = (h[6] + q) >> 26 + q = (h[7] + q) >> 25 + q = (h[8] + q) >> 26 + q = (h[9] + q) >> 25 + + // Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. + h[0] += 19 * q + // Goal: Output h-2^255 q, which is between 0 and 2^255-20. + + carry[0] = h[0] >> 26 + h[1] += carry[0] + h[0] -= carry[0] << 26 + carry[1] = h[1] >> 25 + h[2] += carry[1] + h[1] -= carry[1] << 25 + carry[2] = h[2] >> 26 + h[3] += carry[2] + h[2] -= carry[2] << 26 + carry[3] = h[3] >> 25 + h[4] += carry[3] + h[3] -= carry[3] << 25 + carry[4] = h[4] >> 26 + h[5] += carry[4] + h[4] -= carry[4] << 26 + carry[5] = h[5] >> 25 + h[6] += carry[5] + h[5] -= carry[5] << 25 + carry[6] = h[6] >> 26 + h[7] += carry[6] + h[6] -= carry[6] << 26 + carry[7] = h[7] >> 25 + h[8] += carry[7] + h[7] -= carry[7] << 25 + carry[8] = h[8] >> 26 + h[9] += carry[8] + h[8] -= carry[8] << 26 + carry[9] = h[9] >> 25 + h[9] -= carry[9] << 25 + // h10 = carry9 + + // Goal: Output h[0]+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. + // Have h[0]+...+2^230 h[9] between 0 and 2^255-1; + // evidently 2^255 h10-2^255 q = 0. + // Goal: Output h[0]+...+2^230 h[9]. + + s[0] = byte(h[0] >> 0) + s[1] = byte(h[0] >> 8) + s[2] = byte(h[0] >> 16) + s[3] = byte((h[0] >> 24) | (h[1] << 2)) + s[4] = byte(h[1] >> 6) + s[5] = byte(h[1] >> 14) + s[6] = byte((h[1] >> 22) | (h[2] << 3)) + s[7] = byte(h[2] >> 5) + s[8] = byte(h[2] >> 13) + s[9] = byte((h[2] >> 21) | (h[3] << 5)) + s[10] = byte(h[3] >> 3) + s[11] = byte(h[3] >> 11) + s[12] = byte((h[3] >> 19) | (h[4] << 6)) + s[13] = byte(h[4] >> 2) + s[14] = byte(h[4] >> 10) + s[15] = byte(h[4] >> 18) + s[16] = byte(h[5] >> 0) + s[17] = byte(h[5] >> 8) + s[18] = byte(h[5] >> 16) + s[19] = byte((h[5] >> 24) | (h[6] << 1)) + s[20] = byte(h[6] >> 7) + s[21] = byte(h[6] >> 15) + s[22] = byte((h[6] >> 23) | (h[7] << 3)) + s[23] = byte(h[7] >> 5) + s[24] = byte(h[7] >> 13) + s[25] = byte((h[7] >> 21) | (h[8] << 4)) + s[26] = byte(h[8] >> 4) + s[27] = byte(h[8] >> 12) + s[28] = byte((h[8] >> 20) | (h[9] << 6)) + s[29] = byte(h[9] >> 2) + s[30] = byte(h[9] >> 10) + s[31] = byte(h[9] >> 18) +} + +func FeIsNegative(f *FieldElement) byte { + var s [32]byte + FeToBytes(&s, f) + return s[0] & 1 +} + +func FeIsNonZero(f *FieldElement) int32 { + var s [32]byte + FeToBytes(&s, f) + var x uint8 + for _, b := range s { + x |= b + } + x |= x >> 4 + x |= x >> 2 + x |= x >> 1 + return int32(x & 1) +} + +// FeNeg sets h = -f +// +// Preconditions: +// |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +// +// Postconditions: +// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +func FeNeg(h, f *FieldElement) { + h[0] = -f[0] + h[1] = -f[1] + h[2] = -f[2] + h[3] = -f[3] + h[4] = -f[4] + h[5] = -f[5] + h[6] = -f[6] + h[7] = -f[7] + h[8] = -f[8] + h[9] = -f[9] +} + +func FeCombine(h *FieldElement, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) { + var c0, c1, c2, c3, c4, c5, c6, c7, c8, c9 int64 + + /* + |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38)) + i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8 + |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19)) + i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9 + */ + + c0 = (h0 + (1 << 25)) >> 26 + h1 += c0 + h0 -= c0 << 26 + c4 = (h4 + (1 << 25)) >> 26 + h5 += c4 + h4 -= c4 << 26 + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.51*2^58 */ + /* |h5| <= 1.51*2^58 */ + + c1 = (h1 + (1 << 24)) >> 25 + h2 += c1 + h1 -= c1 << 25 + c5 = (h5 + (1 << 24)) >> 25 + h6 += c5 + h5 -= c5 << 25 + /* |h1| <= 2^24; from now on fits into int32 */ + /* |h5| <= 2^24; from now on fits into int32 */ + /* |h2| <= 1.21*2^59 */ + /* |h6| <= 1.21*2^59 */ + + c2 = (h2 + (1 << 25)) >> 26 + h3 += c2 + h2 -= c2 << 26 + c6 = (h6 + (1 << 25)) >> 26 + h7 += c6 + h6 -= c6 << 26 + /* |h2| <= 2^25; from now on fits into int32 unchanged */ + /* |h6| <= 2^25; from now on fits into int32 unchanged */ + /* |h3| <= 1.51*2^58 */ + /* |h7| <= 1.51*2^58 */ + + c3 = (h3 + (1 << 24)) >> 25 + h4 += c3 + h3 -= c3 << 25 + c7 = (h7 + (1 << 24)) >> 25 + h8 += c7 + h7 -= c7 << 25 + /* |h3| <= 2^24; from now on fits into int32 unchanged */ + /* |h7| <= 2^24; from now on fits into int32 unchanged */ + /* |h4| <= 1.52*2^33 */ + /* |h8| <= 1.52*2^33 */ + + c4 = (h4 + (1 << 25)) >> 26 + h5 += c4 + h4 -= c4 << 26 + c8 = (h8 + (1 << 25)) >> 26 + h9 += c8 + h8 -= c8 << 26 + /* |h4| <= 2^25; from now on fits into int32 unchanged */ + /* |h8| <= 2^25; from now on fits into int32 unchanged */ + /* |h5| <= 1.01*2^24 */ + /* |h9| <= 1.51*2^58 */ + + c9 = (h9 + (1 << 24)) >> 25 + h0 += c9 * 19 + h9 -= c9 << 25 + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.8*2^37 */ + + c0 = (h0 + (1 << 25)) >> 26 + h1 += c0 + h0 -= c0 << 26 + /* |h0| <= 2^25; from now on fits into int32 unchanged */ + /* |h1| <= 1.01*2^24 */ + + h[0] = int32(h0) + h[1] = int32(h1) + h[2] = int32(h2) + h[3] = int32(h3) + h[4] = int32(h4) + h[5] = int32(h5) + h[6] = int32(h6) + h[7] = int32(h7) + h[8] = int32(h8) + h[9] = int32(h9) +} + +// FeMul calculates h = f * g +// Can overlap h with f or g. +// +// Preconditions: +// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +// |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +// +// Postconditions: +// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +// +// Notes on implementation strategy: +// +// Using schoolbook multiplication. +// Karatsuba would save a little in some cost models. +// +// Most multiplications by 2 and 19 are 32-bit precomputations; +// cheaper than 64-bit postcomputations. +// +// There is one remaining multiplication by 19 in the carry chain; +// one *19 precomputation can be merged into this, +// but the resulting data flow is considerably less clean. +// +// There are 12 carries below. +// 10 of them are 2-way parallelizable and vectorizable. +// Can get away with 11 carries, but then data flow is much deeper. +// +// With tighter constraints on inputs can squeeze carries into int32. +func FeMul(h, f, g *FieldElement) { + f0 := int64(f[0]) + f1 := int64(f[1]) + f2 := int64(f[2]) + f3 := int64(f[3]) + f4 := int64(f[4]) + f5 := int64(f[5]) + f6 := int64(f[6]) + f7 := int64(f[7]) + f8 := int64(f[8]) + f9 := int64(f[9]) + + f1_2 := int64(2 * f[1]) + f3_2 := int64(2 * f[3]) + f5_2 := int64(2 * f[5]) + f7_2 := int64(2 * f[7]) + f9_2 := int64(2 * f[9]) + + g0 := int64(g[0]) + g1 := int64(g[1]) + g2 := int64(g[2]) + g3 := int64(g[3]) + g4 := int64(g[4]) + g5 := int64(g[5]) + g6 := int64(g[6]) + g7 := int64(g[7]) + g8 := int64(g[8]) + g9 := int64(g[9]) + + g1_19 := int64(19 * g[1]) /* 1.4*2^29 */ + g2_19 := int64(19 * g[2]) /* 1.4*2^30; still ok */ + g3_19 := int64(19 * g[3]) + g4_19 := int64(19 * g[4]) + g5_19 := int64(19 * g[5]) + g6_19 := int64(19 * g[6]) + g7_19 := int64(19 * g[7]) + g8_19 := int64(19 * g[8]) + g9_19 := int64(19 * g[9]) + + h0 := f0*g0 + f1_2*g9_19 + f2*g8_19 + f3_2*g7_19 + f4*g6_19 + f5_2*g5_19 + f6*g4_19 + f7_2*g3_19 + f8*g2_19 + f9_2*g1_19 + h1 := f0*g1 + f1*g0 + f2*g9_19 + f3*g8_19 + f4*g7_19 + f5*g6_19 + f6*g5_19 + f7*g4_19 + f8*g3_19 + f9*g2_19 + h2 := f0*g2 + f1_2*g1 + f2*g0 + f3_2*g9_19 + f4*g8_19 + f5_2*g7_19 + f6*g6_19 + f7_2*g5_19 + f8*g4_19 + f9_2*g3_19 + h3 := f0*g3 + f1*g2 + f2*g1 + f3*g0 + f4*g9_19 + f5*g8_19 + f6*g7_19 + f7*g6_19 + f8*g5_19 + f9*g4_19 + h4 := f0*g4 + f1_2*g3 + f2*g2 + f3_2*g1 + f4*g0 + f5_2*g9_19 + f6*g8_19 + f7_2*g7_19 + f8*g6_19 + f9_2*g5_19 + h5 := f0*g5 + f1*g4 + f2*g3 + f3*g2 + f4*g1 + f5*g0 + f6*g9_19 + f7*g8_19 + f8*g7_19 + f9*g6_19 + h6 := f0*g6 + f1_2*g5 + f2*g4 + f3_2*g3 + f4*g2 + f5_2*g1 + f6*g0 + f7_2*g9_19 + f8*g8_19 + f9_2*g7_19 + h7 := f0*g7 + f1*g6 + f2*g5 + f3*g4 + f4*g3 + f5*g2 + f6*g1 + f7*g0 + f8*g9_19 + f9*g8_19 + h8 := f0*g8 + f1_2*g7 + f2*g6 + f3_2*g5 + f4*g4 + f5_2*g3 + f6*g2 + f7_2*g1 + f8*g0 + f9_2*g9_19 + h9 := f0*g9 + f1*g8 + f2*g7 + f3*g6 + f4*g5 + f5*g4 + f6*g3 + f7*g2 + f8*g1 + f9*g0 + + FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9) +} + +func feSquare(f *FieldElement) (h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) { + f0 := int64(f[0]) + f1 := int64(f[1]) + f2 := int64(f[2]) + f3 := int64(f[3]) + f4 := int64(f[4]) + f5 := int64(f[5]) + f6 := int64(f[6]) + f7 := int64(f[7]) + f8 := int64(f[8]) + f9 := int64(f[9]) + f0_2 := int64(2 * f[0]) + f1_2 := int64(2 * f[1]) + f2_2 := int64(2 * f[2]) + f3_2 := int64(2 * f[3]) + f4_2 := int64(2 * f[4]) + f5_2 := int64(2 * f[5]) + f6_2 := int64(2 * f[6]) + f7_2 := int64(2 * f[7]) + f5_38 := 38 * f5 // 1.31*2^30 + f6_19 := 19 * f6 // 1.31*2^30 + f7_38 := 38 * f7 // 1.31*2^30 + f8_19 := 19 * f8 // 1.31*2^30 + f9_38 := 38 * f9 // 1.31*2^30 + + h0 = f0*f0 + f1_2*f9_38 + f2_2*f8_19 + f3_2*f7_38 + f4_2*f6_19 + f5*f5_38 + h1 = f0_2*f1 + f2*f9_38 + f3_2*f8_19 + f4*f7_38 + f5_2*f6_19 + h2 = f0_2*f2 + f1_2*f1 + f3_2*f9_38 + f4_2*f8_19 + f5_2*f7_38 + f6*f6_19 + h3 = f0_2*f3 + f1_2*f2 + f4*f9_38 + f5_2*f8_19 + f6*f7_38 + h4 = f0_2*f4 + f1_2*f3_2 + f2*f2 + f5_2*f9_38 + f6_2*f8_19 + f7*f7_38 + h5 = f0_2*f5 + f1_2*f4 + f2_2*f3 + f6*f9_38 + f7_2*f8_19 + h6 = f0_2*f6 + f1_2*f5_2 + f2_2*f4 + f3_2*f3 + f7_2*f9_38 + f8*f8_19 + h7 = f0_2*f7 + f1_2*f6 + f2_2*f5 + f3_2*f4 + f8*f9_38 + h8 = f0_2*f8 + f1_2*f7_2 + f2_2*f6 + f3_2*f5_2 + f4*f4 + f9*f9_38 + h9 = f0_2*f9 + f1_2*f8 + f2_2*f7 + f3_2*f6 + f4_2*f5 + + return +} + +// FeSquare calculates h = f*f. Can overlap h with f. +// +// Preconditions: +// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +// +// Postconditions: +// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +func FeSquare(h, f *FieldElement) { + h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f) + FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9) +} + +// FeSquare2 sets h = 2 * f * f +// +// Can overlap h with f. +// +// Preconditions: +// |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. +// +// Postconditions: +// |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. +// See fe_mul.c for discussion of implementation strategy. +func FeSquare2(h, f *FieldElement) { + h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f) + + h0 += h0 + h1 += h1 + h2 += h2 + h3 += h3 + h4 += h4 + h5 += h5 + h6 += h6 + h7 += h7 + h8 += h8 + h9 += h9 + + FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9) +} + +func FeInvert(out, z *FieldElement) { + var t0, t1, t2, t3 FieldElement + var i int + + FeSquare(&t0, z) // 2^1 + FeSquare(&t1, &t0) // 2^2 + for i = 1; i < 2; i++ { // 2^3 + FeSquare(&t1, &t1) + } + FeMul(&t1, z, &t1) // 2^3 + 2^0 + FeMul(&t0, &t0, &t1) // 2^3 + 2^1 + 2^0 + FeSquare(&t2, &t0) // 2^4 + 2^2 + 2^1 + FeMul(&t1, &t1, &t2) // 2^4 + 2^3 + 2^2 + 2^1 + 2^0 + FeSquare(&t2, &t1) // 5,4,3,2,1 + for i = 1; i < 5; i++ { // 9,8,7,6,5 + FeSquare(&t2, &t2) + } + FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0 + FeSquare(&t2, &t1) // 10..1 + for i = 1; i < 10; i++ { // 19..10 + FeSquare(&t2, &t2) + } + FeMul(&t2, &t2, &t1) // 19..0 + FeSquare(&t3, &t2) // 20..1 + for i = 1; i < 20; i++ { // 39..20 + FeSquare(&t3, &t3) + } + FeMul(&t2, &t3, &t2) // 39..0 + FeSquare(&t2, &t2) // 40..1 + for i = 1; i < 10; i++ { // 49..10 + FeSquare(&t2, &t2) + } + FeMul(&t1, &t2, &t1) // 49..0 + FeSquare(&t2, &t1) // 50..1 + for i = 1; i < 50; i++ { // 99..50 + FeSquare(&t2, &t2) + } + FeMul(&t2, &t2, &t1) // 99..0 + FeSquare(&t3, &t2) // 100..1 + for i = 1; i < 100; i++ { // 199..100 + FeSquare(&t3, &t3) + } + FeMul(&t2, &t3, &t2) // 199..0 + FeSquare(&t2, &t2) // 200..1 + for i = 1; i < 50; i++ { // 249..50 + FeSquare(&t2, &t2) + } + FeMul(&t1, &t2, &t1) // 249..0 + FeSquare(&t1, &t1) // 250..1 + for i = 1; i < 5; i++ { // 254..5 + FeSquare(&t1, &t1) + } + FeMul(out, &t1, &t0) // 254..5,3,1,0 +} + +func fePow22523(out, z *FieldElement) { + var t0, t1, t2 FieldElement + var i int + + FeSquare(&t0, z) + for i = 1; i < 1; i++ { + FeSquare(&t0, &t0) + } + FeSquare(&t1, &t0) + for i = 1; i < 2; i++ { + FeSquare(&t1, &t1) + } + FeMul(&t1, z, &t1) + FeMul(&t0, &t0, &t1) + FeSquare(&t0, &t0) + for i = 1; i < 1; i++ { + FeSquare(&t0, &t0) + } + FeMul(&t0, &t1, &t0) + FeSquare(&t1, &t0) + for i = 1; i < 5; i++ { + FeSquare(&t1, &t1) + } + FeMul(&t0, &t1, &t0) + FeSquare(&t1, &t0) + for i = 1; i < 10; i++ { + FeSquare(&t1, &t1) + } + FeMul(&t1, &t1, &t0) + FeSquare(&t2, &t1) + for i = 1; i < 20; i++ { + FeSquare(&t2, &t2) + } + FeMul(&t1, &t2, &t1) + FeSquare(&t1, &t1) + for i = 1; i < 10; i++ { + FeSquare(&t1, &t1) + } + FeMul(&t0, &t1, &t0) + FeSquare(&t1, &t0) + for i = 1; i < 50; i++ { + FeSquare(&t1, &t1) + } + FeMul(&t1, &t1, &t0) + FeSquare(&t2, &t1) + for i = 1; i < 100; i++ { + FeSquare(&t2, &t2) + } + FeMul(&t1, &t2, &t1) + FeSquare(&t1, &t1) + for i = 1; i < 50; i++ { + FeSquare(&t1, &t1) + } + FeMul(&t0, &t1, &t0) + FeSquare(&t0, &t0) + for i = 1; i < 2; i++ { + FeSquare(&t0, &t0) + } + FeMul(out, &t0, z) +} + +// Group elements are members of the elliptic curve -x^2 + y^2 = 1 + d * x^2 * +// y^2 where d = -121665/121666. +// +// Several representations are used: +// ProjectiveGroupElement: (X:Y:Z) satisfying x=X/Z, y=Y/Z +// ExtendedGroupElement: (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT +// CompletedGroupElement: ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T +// PreComputedGroupElement: (y+x,y-x,2dxy) + +type ProjectiveGroupElement struct { + X, Y, Z FieldElement +} + +type ExtendedGroupElement struct { + X, Y, Z, T FieldElement +} + +type CompletedGroupElement struct { + X, Y, Z, T FieldElement +} + +type PreComputedGroupElement struct { + yPlusX, yMinusX, xy2d FieldElement +} + +type CachedGroupElement struct { + yPlusX, yMinusX, Z, T2d FieldElement +} + +func (p *ProjectiveGroupElement) Zero() { + FeZero(&p.X) + FeOne(&p.Y) + FeOne(&p.Z) +} + +func (p *ProjectiveGroupElement) Double(r *CompletedGroupElement) { + var t0 FieldElement + + FeSquare(&r.X, &p.X) + FeSquare(&r.Z, &p.Y) + FeSquare2(&r.T, &p.Z) + FeAdd(&r.Y, &p.X, &p.Y) + FeSquare(&t0, &r.Y) + FeAdd(&r.Y, &r.Z, &r.X) + FeSub(&r.Z, &r.Z, &r.X) + FeSub(&r.X, &t0, &r.Y) + FeSub(&r.T, &r.T, &r.Z) +} + +func (p *ProjectiveGroupElement) ToBytes(s *[32]byte) { + var recip, x, y FieldElement + + FeInvert(&recip, &p.Z) + FeMul(&x, &p.X, &recip) + FeMul(&y, &p.Y, &recip) + FeToBytes(s, &y) + s[31] ^= FeIsNegative(&x) << 7 +} + +func (p *ExtendedGroupElement) Zero() { + FeZero(&p.X) + FeOne(&p.Y) + FeOne(&p.Z) + FeZero(&p.T) +} + +func (p *ExtendedGroupElement) Double(r *CompletedGroupElement) { + var q ProjectiveGroupElement + p.ToProjective(&q) + q.Double(r) +} + +func (p *ExtendedGroupElement) ToCached(r *CachedGroupElement) { + FeAdd(&r.yPlusX, &p.Y, &p.X) + FeSub(&r.yMinusX, &p.Y, &p.X) + FeCopy(&r.Z, &p.Z) + FeMul(&r.T2d, &p.T, &d2) +} + +func (p *ExtendedGroupElement) ToProjective(r *ProjectiveGroupElement) { + FeCopy(&r.X, &p.X) + FeCopy(&r.Y, &p.Y) + FeCopy(&r.Z, &p.Z) +} + +func (p *ExtendedGroupElement) ToBytes(s *[32]byte) { + var recip, x, y FieldElement + + FeInvert(&recip, &p.Z) + FeMul(&x, &p.X, &recip) + FeMul(&y, &p.Y, &recip) + FeToBytes(s, &y) + s[31] ^= FeIsNegative(&x) << 7 +} + +func (p *ExtendedGroupElement) FromBytes(s *[32]byte) bool { + var u, v, v3, vxx, check FieldElement + + FeFromBytes(&p.Y, s) + FeOne(&p.Z) + FeSquare(&u, &p.Y) + FeMul(&v, &u, &d) + FeSub(&u, &u, &p.Z) // y = y^2-1 + FeAdd(&v, &v, &p.Z) // v = dy^2+1 + + FeSquare(&v3, &v) + FeMul(&v3, &v3, &v) // v3 = v^3 + FeSquare(&p.X, &v3) + FeMul(&p.X, &p.X, &v) + FeMul(&p.X, &p.X, &u) // x = uv^7 + + fePow22523(&p.X, &p.X) // x = (uv^7)^((q-5)/8) + FeMul(&p.X, &p.X, &v3) + FeMul(&p.X, &p.X, &u) // x = uv^3(uv^7)^((q-5)/8) + + var tmpX, tmp2 [32]byte + + FeSquare(&vxx, &p.X) + FeMul(&vxx, &vxx, &v) + FeSub(&check, &vxx, &u) // vx^2-u + if FeIsNonZero(&check) == 1 { + FeAdd(&check, &vxx, &u) // vx^2+u + if FeIsNonZero(&check) == 1 { + return false + } + FeMul(&p.X, &p.X, &SqrtM1) + + FeToBytes(&tmpX, &p.X) + for i, v := range tmpX { + tmp2[31-i] = v + } + } + + if FeIsNegative(&p.X) != (s[31] >> 7) { + FeNeg(&p.X, &p.X) + } + + FeMul(&p.T, &p.X, &p.Y) + return true +} + +func (p *CompletedGroupElement) ToProjective(r *ProjectiveGroupElement) { + FeMul(&r.X, &p.X, &p.T) + FeMul(&r.Y, &p.Y, &p.Z) + FeMul(&r.Z, &p.Z, &p.T) +} + +func (p *CompletedGroupElement) ToExtended(r *ExtendedGroupElement) { + FeMul(&r.X, &p.X, &p.T) + FeMul(&r.Y, &p.Y, &p.Z) + FeMul(&r.Z, &p.Z, &p.T) + FeMul(&r.T, &p.X, &p.Y) +} + +func (p *PreComputedGroupElement) Zero() { + FeOne(&p.yPlusX) + FeOne(&p.yMinusX) + FeZero(&p.xy2d) +} + +func geAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) { + var t0 FieldElement + + FeAdd(&r.X, &p.Y, &p.X) + FeSub(&r.Y, &p.Y, &p.X) + FeMul(&r.Z, &r.X, &q.yPlusX) + FeMul(&r.Y, &r.Y, &q.yMinusX) + FeMul(&r.T, &q.T2d, &p.T) + FeMul(&r.X, &p.Z, &q.Z) + FeAdd(&t0, &r.X, &r.X) + FeSub(&r.X, &r.Z, &r.Y) + FeAdd(&r.Y, &r.Z, &r.Y) + FeAdd(&r.Z, &t0, &r.T) + FeSub(&r.T, &t0, &r.T) +} + +func geSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) { + var t0 FieldElement + + FeAdd(&r.X, &p.Y, &p.X) + FeSub(&r.Y, &p.Y, &p.X) + FeMul(&r.Z, &r.X, &q.yMinusX) + FeMul(&r.Y, &r.Y, &q.yPlusX) + FeMul(&r.T, &q.T2d, &p.T) + FeMul(&r.X, &p.Z, &q.Z) + FeAdd(&t0, &r.X, &r.X) + FeSub(&r.X, &r.Z, &r.Y) + FeAdd(&r.Y, &r.Z, &r.Y) + FeSub(&r.Z, &t0, &r.T) + FeAdd(&r.T, &t0, &r.T) +} + +func geMixedAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) { + var t0 FieldElement + + FeAdd(&r.X, &p.Y, &p.X) + FeSub(&r.Y, &p.Y, &p.X) + FeMul(&r.Z, &r.X, &q.yPlusX) + FeMul(&r.Y, &r.Y, &q.yMinusX) + FeMul(&r.T, &q.xy2d, &p.T) + FeAdd(&t0, &p.Z, &p.Z) + FeSub(&r.X, &r.Z, &r.Y) + FeAdd(&r.Y, &r.Z, &r.Y) + FeAdd(&r.Z, &t0, &r.T) + FeSub(&r.T, &t0, &r.T) +} + +func geMixedSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) { + var t0 FieldElement + + FeAdd(&r.X, &p.Y, &p.X) + FeSub(&r.Y, &p.Y, &p.X) + FeMul(&r.Z, &r.X, &q.yMinusX) + FeMul(&r.Y, &r.Y, &q.yPlusX) + FeMul(&r.T, &q.xy2d, &p.T) + FeAdd(&t0, &p.Z, &p.Z) + FeSub(&r.X, &r.Z, &r.Y) + FeAdd(&r.Y, &r.Z, &r.Y) + FeSub(&r.Z, &t0, &r.T) + FeAdd(&r.T, &t0, &r.T) +} + +func slide(r *[256]int8, a *[32]byte) { + for i := range r { + r[i] = int8(1 & (a[i>>3] >> uint(i&7))) + } + + for i := range r { + if r[i] != 0 { + for b := 1; b <= 6 && i+b < 256; b++ { + if r[i+b] != 0 { + if r[i]+(r[i+b]<= -15 { + r[i] -= r[i+b] << uint(b) + for k := i + b; k < 256; k++ { + if r[k] == 0 { + r[k] = 1 + break + } + r[k] = 0 + } + } else { + break + } + } + } + } + } +} + +// GeDoubleScalarMultVartime sets r = a*A + b*B +// where a = a[0]+256*a[1]+...+256^31 a[31]. +// and b = b[0]+256*b[1]+...+256^31 b[31]. +// B is the Ed25519 base point (x,4/5) with x positive. +func GeDoubleScalarMultVartime(r *ProjectiveGroupElement, a *[32]byte, A *ExtendedGroupElement, b *[32]byte) { + var aSlide, bSlide [256]int8 + var Ai [8]CachedGroupElement // A,3A,5A,7A,9A,11A,13A,15A + var t CompletedGroupElement + var u, A2 ExtendedGroupElement + var i int + + slide(&aSlide, a) + slide(&bSlide, b) + + A.ToCached(&Ai[0]) + A.Double(&t) + t.ToExtended(&A2) + + for i := 0; i < 7; i++ { + geAdd(&t, &A2, &Ai[i]) + t.ToExtended(&u) + u.ToCached(&Ai[i+1]) + } + + r.Zero() + + for i = 255; i >= 0; i-- { + if aSlide[i] != 0 || bSlide[i] != 0 { + break + } + } + + for ; i >= 0; i-- { + r.Double(&t) + + if aSlide[i] > 0 { + t.ToExtended(&u) + geAdd(&t, &u, &Ai[aSlide[i]/2]) + } else if aSlide[i] < 0 { + t.ToExtended(&u) + geSub(&t, &u, &Ai[(-aSlide[i])/2]) + } + + if bSlide[i] > 0 { + t.ToExtended(&u) + geMixedAdd(&t, &u, &bi[bSlide[i]/2]) + } else if bSlide[i] < 0 { + t.ToExtended(&u) + geMixedSub(&t, &u, &bi[(-bSlide[i])/2]) + } + + t.ToProjective(r) + } +} + +// equal returns 1 if b == c and 0 otherwise. +func equal(b, c int32) int32 { + x := uint32(b ^ c) + x-- + return int32(x >> 31) +} + +// negative returns 1 if b < 0 and 0 otherwise. +func negative(b int32) int32 { + return (b >> 31) & 1 +} + +func PreComputedGroupElementCMove(t, u *PreComputedGroupElement, b int32) { + FeCMove(&t.yPlusX, &u.yPlusX, b) + FeCMove(&t.yMinusX, &u.yMinusX, b) + FeCMove(&t.xy2d, &u.xy2d, b) +} + +func selectPoint(t *PreComputedGroupElement, pos int32, b int32) { + var minusT PreComputedGroupElement + bNegative := negative(b) + bAbs := b - (((-bNegative) & b) << 1) + + t.Zero() + for i := int32(0); i < 8; i++ { + PreComputedGroupElementCMove(t, &base[pos][i], equal(bAbs, i+1)) + } + FeCopy(&minusT.yPlusX, &t.yMinusX) + FeCopy(&minusT.yMinusX, &t.yPlusX) + FeNeg(&minusT.xy2d, &t.xy2d) + PreComputedGroupElementCMove(t, &minusT, bNegative) +} + +// GeScalarMultBase computes h = a*B, where +// a = a[0]+256*a[1]+...+256^31 a[31] +// B is the Ed25519 base point (x,4/5) with x positive. +// +// Preconditions: +// a[31] <= 127 +func GeScalarMultBase(h *ExtendedGroupElement, a *[32]byte) { + var e [64]int8 + + for i, v := range a { + e[2*i] = int8(v & 15) + e[2*i+1] = int8((v >> 4) & 15) + } + + // each e[i] is between 0 and 15 and e[63] is between 0 and 7. + + carry := int8(0) + for i := 0; i < 63; i++ { + e[i] += carry + carry = (e[i] + 8) >> 4 + e[i] -= carry << 4 + } + e[63] += carry + // each e[i] is between -8 and 8. + + h.Zero() + var t PreComputedGroupElement + var r CompletedGroupElement + for i := int32(1); i < 64; i += 2 { + selectPoint(&t, i/2, int32(e[i])) + geMixedAdd(&r, h, &t) + r.ToExtended(h) + } + + var s ProjectiveGroupElement + + h.Double(&r) + r.ToProjective(&s) + s.Double(&r) + r.ToProjective(&s) + s.Double(&r) + r.ToProjective(&s) + s.Double(&r) + r.ToExtended(h) + + for i := int32(0); i < 64; i += 2 { + selectPoint(&t, i/2, int32(e[i])) + geMixedAdd(&r, h, &t) + r.ToExtended(h) + } +} + +// The scalars are GF(2^252 + 27742317777372353535851937790883648493). + +// Input: +// a[0]+256*a[1]+...+256^31*a[31] = a +// b[0]+256*b[1]+...+256^31*b[31] = b +// c[0]+256*c[1]+...+256^31*c[31] = c +// +// Output: +// s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l +// where l = 2^252 + 27742317777372353535851937790883648493. +func ScMulAdd(s, a, b, c *[32]byte) { + a0 := 2097151 & load3(a[:]) + a1 := 2097151 & (load4(a[2:]) >> 5) + a2 := 2097151 & (load3(a[5:]) >> 2) + a3 := 2097151 & (load4(a[7:]) >> 7) + a4 := 2097151 & (load4(a[10:]) >> 4) + a5 := 2097151 & (load3(a[13:]) >> 1) + a6 := 2097151 & (load4(a[15:]) >> 6) + a7 := 2097151 & (load3(a[18:]) >> 3) + a8 := 2097151 & load3(a[21:]) + a9 := 2097151 & (load4(a[23:]) >> 5) + a10 := 2097151 & (load3(a[26:]) >> 2) + a11 := (load4(a[28:]) >> 7) + b0 := 2097151 & load3(b[:]) + b1 := 2097151 & (load4(b[2:]) >> 5) + b2 := 2097151 & (load3(b[5:]) >> 2) + b3 := 2097151 & (load4(b[7:]) >> 7) + b4 := 2097151 & (load4(b[10:]) >> 4) + b5 := 2097151 & (load3(b[13:]) >> 1) + b6 := 2097151 & (load4(b[15:]) >> 6) + b7 := 2097151 & (load3(b[18:]) >> 3) + b8 := 2097151 & load3(b[21:]) + b9 := 2097151 & (load4(b[23:]) >> 5) + b10 := 2097151 & (load3(b[26:]) >> 2) + b11 := (load4(b[28:]) >> 7) + c0 := 2097151 & load3(c[:]) + c1 := 2097151 & (load4(c[2:]) >> 5) + c2 := 2097151 & (load3(c[5:]) >> 2) + c3 := 2097151 & (load4(c[7:]) >> 7) + c4 := 2097151 & (load4(c[10:]) >> 4) + c5 := 2097151 & (load3(c[13:]) >> 1) + c6 := 2097151 & (load4(c[15:]) >> 6) + c7 := 2097151 & (load3(c[18:]) >> 3) + c8 := 2097151 & load3(c[21:]) + c9 := 2097151 & (load4(c[23:]) >> 5) + c10 := 2097151 & (load3(c[26:]) >> 2) + c11 := (load4(c[28:]) >> 7) + var carry [23]int64 + + s0 := c0 + a0*b0 + s1 := c1 + a0*b1 + a1*b0 + s2 := c2 + a0*b2 + a1*b1 + a2*b0 + s3 := c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0 + s4 := c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0 + s5 := c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0 + s6 := c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0 + s7 := c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0 + s8 := c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0 + s9 := c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0 + s10 := c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0 + s11 := c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0 + s12 := a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1 + s13 := a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2 + s14 := a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3 + s15 := a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4 + s16 := a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5 + s17 := a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6 + s18 := a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7 + s19 := a8*b11 + a9*b10 + a10*b9 + a11*b8 + s20 := a9*b11 + a10*b10 + a11*b9 + s21 := a10*b11 + a11*b10 + s22 := a11 * b11 + s23 := int64(0) + + carry[0] = (s0 + (1 << 20)) >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[2] = (s2 + (1 << 20)) >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[4] = (s4 + (1 << 20)) >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[6] = (s6 + (1 << 20)) >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[8] = (s8 + (1 << 20)) >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[10] = (s10 + (1 << 20)) >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + carry[12] = (s12 + (1 << 20)) >> 21 + s13 += carry[12] + s12 -= carry[12] << 21 + carry[14] = (s14 + (1 << 20)) >> 21 + s15 += carry[14] + s14 -= carry[14] << 21 + carry[16] = (s16 + (1 << 20)) >> 21 + s17 += carry[16] + s16 -= carry[16] << 21 + carry[18] = (s18 + (1 << 20)) >> 21 + s19 += carry[18] + s18 -= carry[18] << 21 + carry[20] = (s20 + (1 << 20)) >> 21 + s21 += carry[20] + s20 -= carry[20] << 21 + carry[22] = (s22 + (1 << 20)) >> 21 + s23 += carry[22] + s22 -= carry[22] << 21 + + carry[1] = (s1 + (1 << 20)) >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[3] = (s3 + (1 << 20)) >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[5] = (s5 + (1 << 20)) >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[7] = (s7 + (1 << 20)) >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[9] = (s9 + (1 << 20)) >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[11] = (s11 + (1 << 20)) >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + carry[13] = (s13 + (1 << 20)) >> 21 + s14 += carry[13] + s13 -= carry[13] << 21 + carry[15] = (s15 + (1 << 20)) >> 21 + s16 += carry[15] + s15 -= carry[15] << 21 + carry[17] = (s17 + (1 << 20)) >> 21 + s18 += carry[17] + s17 -= carry[17] << 21 + carry[19] = (s19 + (1 << 20)) >> 21 + s20 += carry[19] + s19 -= carry[19] << 21 + carry[21] = (s21 + (1 << 20)) >> 21 + s22 += carry[21] + s21 -= carry[21] << 21 + + s11 += s23 * 666643 + s12 += s23 * 470296 + s13 += s23 * 654183 + s14 -= s23 * 997805 + s15 += s23 * 136657 + s16 -= s23 * 683901 + s23 = 0 + + s10 += s22 * 666643 + s11 += s22 * 470296 + s12 += s22 * 654183 + s13 -= s22 * 997805 + s14 += s22 * 136657 + s15 -= s22 * 683901 + s22 = 0 + + s9 += s21 * 666643 + s10 += s21 * 470296 + s11 += s21 * 654183 + s12 -= s21 * 997805 + s13 += s21 * 136657 + s14 -= s21 * 683901 + s21 = 0 + + s8 += s20 * 666643 + s9 += s20 * 470296 + s10 += s20 * 654183 + s11 -= s20 * 997805 + s12 += s20 * 136657 + s13 -= s20 * 683901 + s20 = 0 + + s7 += s19 * 666643 + s8 += s19 * 470296 + s9 += s19 * 654183 + s10 -= s19 * 997805 + s11 += s19 * 136657 + s12 -= s19 * 683901 + s19 = 0 + + s6 += s18 * 666643 + s7 += s18 * 470296 + s8 += s18 * 654183 + s9 -= s18 * 997805 + s10 += s18 * 136657 + s11 -= s18 * 683901 + s18 = 0 + + carry[6] = (s6 + (1 << 20)) >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[8] = (s8 + (1 << 20)) >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[10] = (s10 + (1 << 20)) >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + carry[12] = (s12 + (1 << 20)) >> 21 + s13 += carry[12] + s12 -= carry[12] << 21 + carry[14] = (s14 + (1 << 20)) >> 21 + s15 += carry[14] + s14 -= carry[14] << 21 + carry[16] = (s16 + (1 << 20)) >> 21 + s17 += carry[16] + s16 -= carry[16] << 21 + + carry[7] = (s7 + (1 << 20)) >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[9] = (s9 + (1 << 20)) >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[11] = (s11 + (1 << 20)) >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + carry[13] = (s13 + (1 << 20)) >> 21 + s14 += carry[13] + s13 -= carry[13] << 21 + carry[15] = (s15 + (1 << 20)) >> 21 + s16 += carry[15] + s15 -= carry[15] << 21 + + s5 += s17 * 666643 + s6 += s17 * 470296 + s7 += s17 * 654183 + s8 -= s17 * 997805 + s9 += s17 * 136657 + s10 -= s17 * 683901 + s17 = 0 + + s4 += s16 * 666643 + s5 += s16 * 470296 + s6 += s16 * 654183 + s7 -= s16 * 997805 + s8 += s16 * 136657 + s9 -= s16 * 683901 + s16 = 0 + + s3 += s15 * 666643 + s4 += s15 * 470296 + s5 += s15 * 654183 + s6 -= s15 * 997805 + s7 += s15 * 136657 + s8 -= s15 * 683901 + s15 = 0 + + s2 += s14 * 666643 + s3 += s14 * 470296 + s4 += s14 * 654183 + s5 -= s14 * 997805 + s6 += s14 * 136657 + s7 -= s14 * 683901 + s14 = 0 + + s1 += s13 * 666643 + s2 += s13 * 470296 + s3 += s13 * 654183 + s4 -= s13 * 997805 + s5 += s13 * 136657 + s6 -= s13 * 683901 + s13 = 0 + + s0 += s12 * 666643 + s1 += s12 * 470296 + s2 += s12 * 654183 + s3 -= s12 * 997805 + s4 += s12 * 136657 + s5 -= s12 * 683901 + s12 = 0 + + carry[0] = (s0 + (1 << 20)) >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[2] = (s2 + (1 << 20)) >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[4] = (s4 + (1 << 20)) >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[6] = (s6 + (1 << 20)) >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[8] = (s8 + (1 << 20)) >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[10] = (s10 + (1 << 20)) >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + + carry[1] = (s1 + (1 << 20)) >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[3] = (s3 + (1 << 20)) >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[5] = (s5 + (1 << 20)) >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[7] = (s7 + (1 << 20)) >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[9] = (s9 + (1 << 20)) >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[11] = (s11 + (1 << 20)) >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + + s0 += s12 * 666643 + s1 += s12 * 470296 + s2 += s12 * 654183 + s3 -= s12 * 997805 + s4 += s12 * 136657 + s5 -= s12 * 683901 + s12 = 0 + + carry[0] = s0 >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[1] = s1 >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[2] = s2 >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[3] = s3 >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[4] = s4 >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[5] = s5 >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[6] = s6 >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[7] = s7 >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[8] = s8 >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[9] = s9 >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[10] = s10 >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + carry[11] = s11 >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + + s0 += s12 * 666643 + s1 += s12 * 470296 + s2 += s12 * 654183 + s3 -= s12 * 997805 + s4 += s12 * 136657 + s5 -= s12 * 683901 + s12 = 0 + + carry[0] = s0 >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[1] = s1 >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[2] = s2 >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[3] = s3 >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[4] = s4 >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[5] = s5 >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[6] = s6 >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[7] = s7 >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[8] = s8 >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[9] = s9 >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[10] = s10 >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + + s[0] = byte(s0 >> 0) + s[1] = byte(s0 >> 8) + s[2] = byte((s0 >> 16) | (s1 << 5)) + s[3] = byte(s1 >> 3) + s[4] = byte(s1 >> 11) + s[5] = byte((s1 >> 19) | (s2 << 2)) + s[6] = byte(s2 >> 6) + s[7] = byte((s2 >> 14) | (s3 << 7)) + s[8] = byte(s3 >> 1) + s[9] = byte(s3 >> 9) + s[10] = byte((s3 >> 17) | (s4 << 4)) + s[11] = byte(s4 >> 4) + s[12] = byte(s4 >> 12) + s[13] = byte((s4 >> 20) | (s5 << 1)) + s[14] = byte(s5 >> 7) + s[15] = byte((s5 >> 15) | (s6 << 6)) + s[16] = byte(s6 >> 2) + s[17] = byte(s6 >> 10) + s[18] = byte((s6 >> 18) | (s7 << 3)) + s[19] = byte(s7 >> 5) + s[20] = byte(s7 >> 13) + s[21] = byte(s8 >> 0) + s[22] = byte(s8 >> 8) + s[23] = byte((s8 >> 16) | (s9 << 5)) + s[24] = byte(s9 >> 3) + s[25] = byte(s9 >> 11) + s[26] = byte((s9 >> 19) | (s10 << 2)) + s[27] = byte(s10 >> 6) + s[28] = byte((s10 >> 14) | (s11 << 7)) + s[29] = byte(s11 >> 1) + s[30] = byte(s11 >> 9) + s[31] = byte(s11 >> 17) +} + +// Input: +// s[0]+256*s[1]+...+256^63*s[63] = s +// +// Output: +// s[0]+256*s[1]+...+256^31*s[31] = s mod l +// where l = 2^252 + 27742317777372353535851937790883648493. +func ScReduce(out *[32]byte, s *[64]byte) { + s0 := 2097151 & load3(s[:]) + s1 := 2097151 & (load4(s[2:]) >> 5) + s2 := 2097151 & (load3(s[5:]) >> 2) + s3 := 2097151 & (load4(s[7:]) >> 7) + s4 := 2097151 & (load4(s[10:]) >> 4) + s5 := 2097151 & (load3(s[13:]) >> 1) + s6 := 2097151 & (load4(s[15:]) >> 6) + s7 := 2097151 & (load3(s[18:]) >> 3) + s8 := 2097151 & load3(s[21:]) + s9 := 2097151 & (load4(s[23:]) >> 5) + s10 := 2097151 & (load3(s[26:]) >> 2) + s11 := 2097151 & (load4(s[28:]) >> 7) + s12 := 2097151 & (load4(s[31:]) >> 4) + s13 := 2097151 & (load3(s[34:]) >> 1) + s14 := 2097151 & (load4(s[36:]) >> 6) + s15 := 2097151 & (load3(s[39:]) >> 3) + s16 := 2097151 & load3(s[42:]) + s17 := 2097151 & (load4(s[44:]) >> 5) + s18 := 2097151 & (load3(s[47:]) >> 2) + s19 := 2097151 & (load4(s[49:]) >> 7) + s20 := 2097151 & (load4(s[52:]) >> 4) + s21 := 2097151 & (load3(s[55:]) >> 1) + s22 := 2097151 & (load4(s[57:]) >> 6) + s23 := (load4(s[60:]) >> 3) + + s11 += s23 * 666643 + s12 += s23 * 470296 + s13 += s23 * 654183 + s14 -= s23 * 997805 + s15 += s23 * 136657 + s16 -= s23 * 683901 + s23 = 0 + + s10 += s22 * 666643 + s11 += s22 * 470296 + s12 += s22 * 654183 + s13 -= s22 * 997805 + s14 += s22 * 136657 + s15 -= s22 * 683901 + s22 = 0 + + s9 += s21 * 666643 + s10 += s21 * 470296 + s11 += s21 * 654183 + s12 -= s21 * 997805 + s13 += s21 * 136657 + s14 -= s21 * 683901 + s21 = 0 + + s8 += s20 * 666643 + s9 += s20 * 470296 + s10 += s20 * 654183 + s11 -= s20 * 997805 + s12 += s20 * 136657 + s13 -= s20 * 683901 + s20 = 0 + + s7 += s19 * 666643 + s8 += s19 * 470296 + s9 += s19 * 654183 + s10 -= s19 * 997805 + s11 += s19 * 136657 + s12 -= s19 * 683901 + s19 = 0 + + s6 += s18 * 666643 + s7 += s18 * 470296 + s8 += s18 * 654183 + s9 -= s18 * 997805 + s10 += s18 * 136657 + s11 -= s18 * 683901 + s18 = 0 + + var carry [17]int64 + + carry[6] = (s6 + (1 << 20)) >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[8] = (s8 + (1 << 20)) >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[10] = (s10 + (1 << 20)) >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + carry[12] = (s12 + (1 << 20)) >> 21 + s13 += carry[12] + s12 -= carry[12] << 21 + carry[14] = (s14 + (1 << 20)) >> 21 + s15 += carry[14] + s14 -= carry[14] << 21 + carry[16] = (s16 + (1 << 20)) >> 21 + s17 += carry[16] + s16 -= carry[16] << 21 + + carry[7] = (s7 + (1 << 20)) >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[9] = (s9 + (1 << 20)) >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[11] = (s11 + (1 << 20)) >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + carry[13] = (s13 + (1 << 20)) >> 21 + s14 += carry[13] + s13 -= carry[13] << 21 + carry[15] = (s15 + (1 << 20)) >> 21 + s16 += carry[15] + s15 -= carry[15] << 21 + + s5 += s17 * 666643 + s6 += s17 * 470296 + s7 += s17 * 654183 + s8 -= s17 * 997805 + s9 += s17 * 136657 + s10 -= s17 * 683901 + s17 = 0 + + s4 += s16 * 666643 + s5 += s16 * 470296 + s6 += s16 * 654183 + s7 -= s16 * 997805 + s8 += s16 * 136657 + s9 -= s16 * 683901 + s16 = 0 + + s3 += s15 * 666643 + s4 += s15 * 470296 + s5 += s15 * 654183 + s6 -= s15 * 997805 + s7 += s15 * 136657 + s8 -= s15 * 683901 + s15 = 0 + + s2 += s14 * 666643 + s3 += s14 * 470296 + s4 += s14 * 654183 + s5 -= s14 * 997805 + s6 += s14 * 136657 + s7 -= s14 * 683901 + s14 = 0 + + s1 += s13 * 666643 + s2 += s13 * 470296 + s3 += s13 * 654183 + s4 -= s13 * 997805 + s5 += s13 * 136657 + s6 -= s13 * 683901 + s13 = 0 + + s0 += s12 * 666643 + s1 += s12 * 470296 + s2 += s12 * 654183 + s3 -= s12 * 997805 + s4 += s12 * 136657 + s5 -= s12 * 683901 + s12 = 0 + + carry[0] = (s0 + (1 << 20)) >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[2] = (s2 + (1 << 20)) >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[4] = (s4 + (1 << 20)) >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[6] = (s6 + (1 << 20)) >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[8] = (s8 + (1 << 20)) >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[10] = (s10 + (1 << 20)) >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + + carry[1] = (s1 + (1 << 20)) >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[3] = (s3 + (1 << 20)) >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[5] = (s5 + (1 << 20)) >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[7] = (s7 + (1 << 20)) >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[9] = (s9 + (1 << 20)) >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[11] = (s11 + (1 << 20)) >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + + s0 += s12 * 666643 + s1 += s12 * 470296 + s2 += s12 * 654183 + s3 -= s12 * 997805 + s4 += s12 * 136657 + s5 -= s12 * 683901 + s12 = 0 + + carry[0] = s0 >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[1] = s1 >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[2] = s2 >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[3] = s3 >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[4] = s4 >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[5] = s5 >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[6] = s6 >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[7] = s7 >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[8] = s8 >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[9] = s9 >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[10] = s10 >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + carry[11] = s11 >> 21 + s12 += carry[11] + s11 -= carry[11] << 21 + + s0 += s12 * 666643 + s1 += s12 * 470296 + s2 += s12 * 654183 + s3 -= s12 * 997805 + s4 += s12 * 136657 + s5 -= s12 * 683901 + s12 = 0 + + carry[0] = s0 >> 21 + s1 += carry[0] + s0 -= carry[0] << 21 + carry[1] = s1 >> 21 + s2 += carry[1] + s1 -= carry[1] << 21 + carry[2] = s2 >> 21 + s3 += carry[2] + s2 -= carry[2] << 21 + carry[3] = s3 >> 21 + s4 += carry[3] + s3 -= carry[3] << 21 + carry[4] = s4 >> 21 + s5 += carry[4] + s4 -= carry[4] << 21 + carry[5] = s5 >> 21 + s6 += carry[5] + s5 -= carry[5] << 21 + carry[6] = s6 >> 21 + s7 += carry[6] + s6 -= carry[6] << 21 + carry[7] = s7 >> 21 + s8 += carry[7] + s7 -= carry[7] << 21 + carry[8] = s8 >> 21 + s9 += carry[8] + s8 -= carry[8] << 21 + carry[9] = s9 >> 21 + s10 += carry[9] + s9 -= carry[9] << 21 + carry[10] = s10 >> 21 + s11 += carry[10] + s10 -= carry[10] << 21 + + out[0] = byte(s0 >> 0) + out[1] = byte(s0 >> 8) + out[2] = byte((s0 >> 16) | (s1 << 5)) + out[3] = byte(s1 >> 3) + out[4] = byte(s1 >> 11) + out[5] = byte((s1 >> 19) | (s2 << 2)) + out[6] = byte(s2 >> 6) + out[7] = byte((s2 >> 14) | (s3 << 7)) + out[8] = byte(s3 >> 1) + out[9] = byte(s3 >> 9) + out[10] = byte((s3 >> 17) | (s4 << 4)) + out[11] = byte(s4 >> 4) + out[12] = byte(s4 >> 12) + out[13] = byte((s4 >> 20) | (s5 << 1)) + out[14] = byte(s5 >> 7) + out[15] = byte((s5 >> 15) | (s6 << 6)) + out[16] = byte(s6 >> 2) + out[17] = byte(s6 >> 10) + out[18] = byte((s6 >> 18) | (s7 << 3)) + out[19] = byte(s7 >> 5) + out[20] = byte(s7 >> 13) + out[21] = byte(s8 >> 0) + out[22] = byte(s8 >> 8) + out[23] = byte((s8 >> 16) | (s9 << 5)) + out[24] = byte(s9 >> 3) + out[25] = byte(s9 >> 11) + out[26] = byte((s9 >> 19) | (s10 << 2)) + out[27] = byte(s10 >> 6) + out[28] = byte((s10 >> 14) | (s11 << 7)) + out[29] = byte(s11 >> 1) + out[30] = byte(s11 >> 9) + out[31] = byte(s11 >> 17) +} diff --git a/hcec/ed25519/extra25519/extra25519.go b/hcec/ed25519/extra25519/extra25519.go new file mode 100644 index 0000000..aef9f51 --- /dev/null +++ b/hcec/ed25519/extra25519/extra25519.go @@ -0,0 +1,339 @@ +// Copyright 2013 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 extra25519 + +import ( + "crypto/sha512" + "github.com/HcashOrg/hcd/hcec/ed25519/edwards25519" +) + +// PrivateKeyToCurve25519 converts an ed25519 private key into a corresponding +// curve25519 private key such that the resulting curve25519 public key will +// equal the result from PublicKeyToCurve25519. +func PrivateKeyToCurve25519(curve25519Private *[32]byte, privateKey *[64]byte) { + h := sha512.New() + h.Write(privateKey[:32]) + digest := h.Sum(nil) + + digest[0] &= 248 + digest[31] &= 127 + digest[31] |= 64 + + copy(curve25519Private[:], digest) +} + +func edwardsToMontgomeryX(outX, y *edwards25519.FieldElement) { + // We only need the x-coordinate of the curve25519 point, which I'll + // call u. The isomorphism is u=(y+1)/(1-y), since y=Y/Z, this gives + // u=(Y+Z)/(Z-Y). We know that Z=1, thus u=(Y+1)/(1-Y). + var oneMinusY edwards25519.FieldElement + edwards25519.FeOne(&oneMinusY) + edwards25519.FeSub(&oneMinusY, &oneMinusY, y) + edwards25519.FeInvert(&oneMinusY, &oneMinusY) + + edwards25519.FeOne(outX) + edwards25519.FeAdd(outX, outX, y) + + edwards25519.FeMul(outX, outX, &oneMinusY) +} + +// PublicKeyToCurve25519 converts an Ed25519 public key into the curve25519 +// public key that would be generated from the same private key. +func PublicKeyToCurve25519(curve25519Public *[32]byte, publicKey *[32]byte) bool { + var A edwards25519.ExtendedGroupElement + if !A.FromBytes(publicKey) { + return false + } + + // A.Z = 1 as a postcondition of FromBytes. + var x edwards25519.FieldElement + edwardsToMontgomeryX(&x, &A.Y) + edwards25519.FeToBytes(curve25519Public, &x) + return true +} + +// sqrtMinusAPlus2 is sqrt(-(486662+2)) +var sqrtMinusAPlus2 = edwards25519.FieldElement{ + -12222970, -8312128, -11511410, 9067497, -15300785, -241793, 25456130, 14121551, -12187136, 3972024, +} + +// sqrtMinusHalf is sqrt(-1/2) +var sqrtMinusHalf = edwards25519.FieldElement{ + -17256545, 3971863, 28865457, -1750208, 27359696, -16640980, 12573105, 1002827, -163343, 11073975, +} + +// halfQMinus1Bytes is (2^255-20)/2 expressed in little endian form. +var halfQMinus1Bytes = [32]byte{ + 0xf6, 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, 0x3f, +} + +// feBytesLess returns one if a <= b and zero otherwise. +func feBytesLE(a, b *[32]byte) int32 { + equalSoFar := int32(-1) + greater := int32(0) + + for i := uint(31); i < 32; i-- { + x := int32(a[i]) + y := int32(b[i]) + + greater = (^equalSoFar & greater) | (equalSoFar & ((x - y) >> 31)) + equalSoFar = equalSoFar & (((x ^ y) - 1) >> 31) + } + + return int32(^equalSoFar & 1 & greater) +} + +// ScalarBaseMult computes a curve25519 public key from a private key and also +// a uniform representative for that public key. Note that this function will +// fail and return false for about half of private keys. +// See http://elligator.cr.yp.to/elligator-20130828.pdf. +func ScalarBaseMult(publicKey, representative, privateKey *[32]byte) bool { + var maskedPrivateKey [32]byte + copy(maskedPrivateKey[:], privateKey[:]) + + maskedPrivateKey[0] &= 248 + maskedPrivateKey[31] &= 127 + maskedPrivateKey[31] |= 64 + + var A edwards25519.ExtendedGroupElement + edwards25519.GeScalarMultBase(&A, &maskedPrivateKey) + + var inv1 edwards25519.FieldElement + edwards25519.FeSub(&inv1, &A.Z, &A.Y) + edwards25519.FeMul(&inv1, &inv1, &A.X) + edwards25519.FeInvert(&inv1, &inv1) + + var t0, u edwards25519.FieldElement + edwards25519.FeMul(&u, &inv1, &A.X) + edwards25519.FeAdd(&t0, &A.Y, &A.Z) + edwards25519.FeMul(&u, &u, &t0) + + var v edwards25519.FieldElement + edwards25519.FeMul(&v, &t0, &inv1) + edwards25519.FeMul(&v, &v, &A.Z) + edwards25519.FeMul(&v, &v, &sqrtMinusAPlus2) + + var b edwards25519.FieldElement + edwards25519.FeAdd(&b, &u, &edwards25519.A) + + var c, b3, b7, b8 edwards25519.FieldElement + edwards25519.FeSquare(&b3, &b) // 2 + edwards25519.FeMul(&b3, &b3, &b) // 3 + edwards25519.FeSquare(&c, &b3) // 6 + edwards25519.FeMul(&b7, &c, &b) // 7 + edwards25519.FeMul(&b8, &b7, &b) // 8 + edwards25519.FeMul(&c, &b7, &u) + q58(&c, &c) + + var chi edwards25519.FieldElement + edwards25519.FeSquare(&chi, &c) + edwards25519.FeSquare(&chi, &chi) + + edwards25519.FeSquare(&t0, &u) + edwards25519.FeMul(&chi, &chi, &t0) + + edwards25519.FeSquare(&t0, &b7) // 14 + edwards25519.FeMul(&chi, &chi, &t0) + edwards25519.FeNeg(&chi, &chi) + + var chiBytes [32]byte + edwards25519.FeToBytes(&chiBytes, &chi) + // chi[1] is either 0 or 0xff + if chiBytes[1] == 0xff { + return false + } + + // Calculate r1 = sqrt(-u/(2*(u+A))) + var r1 edwards25519.FieldElement + edwards25519.FeMul(&r1, &c, &u) + edwards25519.FeMul(&r1, &r1, &b3) + edwards25519.FeMul(&r1, &r1, &sqrtMinusHalf) + + var maybeSqrtM1 edwards25519.FieldElement + edwards25519.FeSquare(&t0, &r1) + edwards25519.FeMul(&t0, &t0, &b) + edwards25519.FeAdd(&t0, &t0, &t0) + edwards25519.FeAdd(&t0, &t0, &u) + + edwards25519.FeOne(&maybeSqrtM1) + edwards25519.FeCMove(&maybeSqrtM1, &edwards25519.SqrtM1, edwards25519.FeIsNonZero(&t0)) + edwards25519.FeMul(&r1, &r1, &maybeSqrtM1) + + // Calculate r = sqrt(-(u+A)/(2u)) + var r edwards25519.FieldElement + edwards25519.FeSquare(&t0, &c) // 2 + edwards25519.FeMul(&t0, &t0, &c) // 3 + edwards25519.FeSquare(&t0, &t0) // 6 + edwards25519.FeMul(&r, &t0, &c) // 7 + + edwards25519.FeSquare(&t0, &u) // 2 + edwards25519.FeMul(&t0, &t0, &u) // 3 + edwards25519.FeMul(&r, &r, &t0) + + edwards25519.FeSquare(&t0, &b8) // 16 + edwards25519.FeMul(&t0, &t0, &b8) // 24 + edwards25519.FeMul(&t0, &t0, &b) // 25 + edwards25519.FeMul(&r, &r, &t0) + edwards25519.FeMul(&r, &r, &sqrtMinusHalf) + + edwards25519.FeSquare(&t0, &r) + edwards25519.FeMul(&t0, &t0, &u) + edwards25519.FeAdd(&t0, &t0, &t0) + edwards25519.FeAdd(&t0, &t0, &b) + edwards25519.FeOne(&maybeSqrtM1) + edwards25519.FeCMove(&maybeSqrtM1, &edwards25519.SqrtM1, edwards25519.FeIsNonZero(&t0)) + edwards25519.FeMul(&r, &r, &maybeSqrtM1) + + var vBytes [32]byte + edwards25519.FeToBytes(&vBytes, &v) + vInSquareRootImage := feBytesLE(&vBytes, &halfQMinus1Bytes) + edwards25519.FeCMove(&r, &r1, vInSquareRootImage) + + edwards25519.FeToBytes(publicKey, &u) + edwards25519.FeToBytes(representative, &r) + return true +} + +// q58 calculates out = z^((p-5)/8). +func q58(out, z *edwards25519.FieldElement) { + var t1, t2, t3 edwards25519.FieldElement + var i int + + edwards25519.FeSquare(&t1, z) // 2^1 + edwards25519.FeMul(&t1, &t1, z) // 2^1 + 2^0 + edwards25519.FeSquare(&t1, &t1) // 2^2 + 2^1 + edwards25519.FeSquare(&t2, &t1) // 2^3 + 2^2 + edwards25519.FeSquare(&t2, &t2) // 2^4 + 2^3 + edwards25519.FeMul(&t2, &t2, &t1) // 4,3,2,1 + edwards25519.FeMul(&t1, &t2, z) // 4..0 + edwards25519.FeSquare(&t2, &t1) // 5..1 + for i = 1; i < 5; i++ { // 9,8,7,6,5 + edwards25519.FeSquare(&t2, &t2) + } + edwards25519.FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0 + edwards25519.FeSquare(&t2, &t1) // 10..1 + for i = 1; i < 10; i++ { // 19..10 + edwards25519.FeSquare(&t2, &t2) + } + edwards25519.FeMul(&t2, &t2, &t1) // 19..0 + edwards25519.FeSquare(&t3, &t2) // 20..1 + for i = 1; i < 20; i++ { // 39..20 + edwards25519.FeSquare(&t3, &t3) + } + edwards25519.FeMul(&t2, &t3, &t2) // 39..0 + edwards25519.FeSquare(&t2, &t2) // 40..1 + for i = 1; i < 10; i++ { // 49..10 + edwards25519.FeSquare(&t2, &t2) + } + edwards25519.FeMul(&t1, &t2, &t1) // 49..0 + edwards25519.FeSquare(&t2, &t1) // 50..1 + for i = 1; i < 50; i++ { // 99..50 + edwards25519.FeSquare(&t2, &t2) + } + edwards25519.FeMul(&t2, &t2, &t1) // 99..0 + edwards25519.FeSquare(&t3, &t2) // 100..1 + for i = 1; i < 100; i++ { // 199..100 + edwards25519.FeSquare(&t3, &t3) + } + edwards25519.FeMul(&t2, &t3, &t2) // 199..0 + edwards25519.FeSquare(&t2, &t2) // 200..1 + for i = 1; i < 50; i++ { // 249..50 + edwards25519.FeSquare(&t2, &t2) + } + edwards25519.FeMul(&t1, &t2, &t1) // 249..0 + edwards25519.FeSquare(&t1, &t1) // 250..1 + edwards25519.FeSquare(&t1, &t1) // 251..2 + edwards25519.FeMul(out, &t1, z) // 251..2,0 +} + +// chi calculates out = z^((p-1)/2). The result is either 1, 0, or -1 depending +// on whether z is a non-zero square, zero, or a non-square. +func chi(out, z *edwards25519.FieldElement) { + var t0, t1, t2, t3 edwards25519.FieldElement + var i int + + edwards25519.FeSquare(&t0, z) // 2^1 + edwards25519.FeMul(&t1, &t0, z) // 2^1 + 2^0 + edwards25519.FeSquare(&t0, &t1) // 2^2 + 2^1 + edwards25519.FeSquare(&t2, &t0) // 2^3 + 2^2 + edwards25519.FeSquare(&t2, &t2) // 4,3 + edwards25519.FeMul(&t2, &t2, &t0) // 4,3,2,1 + edwards25519.FeMul(&t1, &t2, z) // 4..0 + edwards25519.FeSquare(&t2, &t1) // 5..1 + for i = 1; i < 5; i++ { // 9,8,7,6,5 + edwards25519.FeSquare(&t2, &t2) + } + edwards25519.FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0 + edwards25519.FeSquare(&t2, &t1) // 10..1 + for i = 1; i < 10; i++ { // 19..10 + edwards25519.FeSquare(&t2, &t2) + } + edwards25519.FeMul(&t2, &t2, &t1) // 19..0 + edwards25519.FeSquare(&t3, &t2) // 20..1 + for i = 1; i < 20; i++ { // 39..20 + edwards25519.FeSquare(&t3, &t3) + } + edwards25519.FeMul(&t2, &t3, &t2) // 39..0 + edwards25519.FeSquare(&t2, &t2) // 40..1 + for i = 1; i < 10; i++ { // 49..10 + edwards25519.FeSquare(&t2, &t2) + } + edwards25519.FeMul(&t1, &t2, &t1) // 49..0 + edwards25519.FeSquare(&t2, &t1) // 50..1 + for i = 1; i < 50; i++ { // 99..50 + edwards25519.FeSquare(&t2, &t2) + } + edwards25519.FeMul(&t2, &t2, &t1) // 99..0 + edwards25519.FeSquare(&t3, &t2) // 100..1 + for i = 1; i < 100; i++ { // 199..100 + edwards25519.FeSquare(&t3, &t3) + } + edwards25519.FeMul(&t2, &t3, &t2) // 199..0 + edwards25519.FeSquare(&t2, &t2) // 200..1 + for i = 1; i < 50; i++ { // 249..50 + edwards25519.FeSquare(&t2, &t2) + } + edwards25519.FeMul(&t1, &t2, &t1) // 249..0 + edwards25519.FeSquare(&t1, &t1) // 250..1 + for i = 1; i < 4; i++ { // 253..4 + edwards25519.FeSquare(&t1, &t1) + } + edwards25519.FeMul(out, &t1, &t0) // 253..4,2,1 +} + +// RepresentativeToPublicKey converts a uniform representative value for a +// curve25519 public key, as produced by ScalarBaseMult, to a curve25519 public +// key. +func RepresentativeToPublicKey(publicKey, representative *[32]byte) { + var rr2, v, e edwards25519.FieldElement + edwards25519.FeFromBytes(&rr2, representative) + + edwards25519.FeSquare2(&rr2, &rr2) + rr2[0]++ + edwards25519.FeInvert(&rr2, &rr2) + edwards25519.FeMul(&v, &edwards25519.A, &rr2) + edwards25519.FeNeg(&v, &v) + + var v2, v3 edwards25519.FieldElement + edwards25519.FeSquare(&v2, &v) + edwards25519.FeMul(&v3, &v, &v2) + edwards25519.FeAdd(&e, &v3, &v) + edwards25519.FeMul(&v2, &v2, &edwards25519.A) + edwards25519.FeAdd(&e, &v2, &e) + chi(&e, &e) + var eBytes [32]byte + edwards25519.FeToBytes(&eBytes, &e) + // eBytes[1] is either 0 (for e = 1) or 0xff (for e = -1) + eIsMinus1 := int32(eBytes[1]) & 1 + var negV edwards25519.FieldElement + edwards25519.FeNeg(&negV, &v) + edwards25519.FeCMove(&v, &negV, eIsMinus1) + + edwards25519.FeZero(&v2) + edwards25519.FeCMove(&v2, &edwards25519.A, eIsMinus1) + edwards25519.FeSub(&v, &v, &v2) + + edwards25519.FeToBytes(publicKey, &v) +} diff --git a/hcec/ed25519/extra25519/extra25519_test.go b/hcec/ed25519/extra25519/extra25519_test.go new file mode 100644 index 0000000..0faa93f --- /dev/null +++ b/hcec/ed25519/extra25519/extra25519_test.go @@ -0,0 +1,78 @@ +// Copyright 2013 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 extra25519 + +import ( + "bytes" + "crypto/rand" + "testing" + + "github.com/HcashOrg/hcd/ed25519" + "golang.org/x/crypto/curve25519" +) + +func TestCurve25519Conversion(t *testing.T) { + public, private, _ := ed25519.GenerateKey(rand.Reader) + + var curve25519Public, curve25519Public2, curve25519Private [32]byte + PrivateKeyToCurve25519(&curve25519Private, private) + curve25519.ScalarBaseMult(&curve25519Public, &curve25519Private) + + if !PublicKeyToCurve25519(&curve25519Public2, public) { + t.Fatalf("PublicKeyToCurve25519 failed") + } + + if !bytes.Equal(curve25519Public[:], curve25519Public2[:]) { + t.Errorf("Values didn't match: curve25519 produced %x, conversion produced %x", curve25519Public[:], curve25519Public2[:]) + } +} + +func TestElligator(t *testing.T) { + var publicKey, publicKey2, publicKey3, representative, privateKey [32]byte + + for i := 0; i < 1000; i++ { + rand.Reader.Read(privateKey[:]) + + if !ScalarBaseMult(&publicKey, &representative, &privateKey) { + continue + } + RepresentativeToPublicKey(&publicKey2, &representative) + if !bytes.Equal(publicKey[:], publicKey2[:]) { + t.Fatal("The resulting public key doesn't match the initial one.") + } + + curve25519.ScalarBaseMult(&publicKey3, &privateKey) + if !bytes.Equal(publicKey[:], publicKey3[:]) { + t.Fatal("The public key doesn't match the value that curve25519 produced.") + } + } +} + +func BenchmarkKeyGeneration(b *testing.B) { + var publicKey, representative, privateKey [32]byte + + // Find the private key that results in a point that's in the image of the map. + for { + rand.Reader.Read(privateKey[:]) + if ScalarBaseMult(&publicKey, &representative, &privateKey) { + break + } + } + + b.ResetTimer() + for i := 0; i < b.N; i++ { + ScalarBaseMult(&publicKey, &representative, &privateKey) + } +} + +func BenchmarkMap(b *testing.B) { + var publicKey, representative [32]byte + rand.Reader.Read(representative[:]) + + b.ResetTimer() + for i := 0; i < b.N; i++ { + RepresentativeToPublicKey(&publicKey, &representative) + } +} diff --git a/hcec/ed25519/testdata/sign.input.gz b/hcec/ed25519/testdata/sign.input.gz new file mode 100644 index 0000000000000000000000000000000000000000..41030690c0db39a0279304a46f002a625caa9080 GIT binary patch literal 50330 zcmV*3Kz6?$iwFoTsc=vL19NF-ZZ2tVaCLM5?EPz!AU%?02mX)M0EV~k28PG}moVqp z*D^9gA!nNH)m2%^C^oAyBf`zi0DW8qRPPrlJ!@tDXRK03 zd(%@#94(}Gu8`uIr`;NMD|7S^`}4*y-?mGB@7ZaMnnO!7oDj z{=_oEOn%&|@gzPpt~=gb-~E*LmK(|_?|YtHONlw=)K8l+g!ku9UTcRw-lyL?>Yii2 zb){U-iZP#X%iCv)rTC-5?Z}sL=BXEA5vhDdjGp(ZW#rjbEN3)d z=IMI{cIK>eW@LlecwgcV`#3{+aia3fl2bjghg7gnA9(HzDVNKly|J{Xw9?vhdI;s< zCH;(3)eNZoOLxeVYHgo8M*BAKK$=ivGKig4)4NCp1tCnrG?Ude*J*;uGZe4 zJ$miCJnMO}zD6s(JQ!;s ztfctj_WbP3u3=JU>(G`=U) z`QTXie#*qB)AAa3g?#X(_g!JLx8Yg2q!bNOWv`r~cJQQ<&YbvCZ=DUnLx@))#5s|E?n-JDB3pP%R?=C6SN{H;ZVaLz*t%U!5_Qf~}514x* 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zMN`&!i@hX7L#dsYxu0q3;+*5v+4S|sX`9LPzK@KD-05Mlq;-|A>z+rtRx-m}In;!2xtyod`(i$3D97s^CVTCFOP8;-%Gw#ax`qI;qUnbRFa?!PUSbKJQm=j{_ zMd8a3BnGU6f|Wj|y5nsqA%vqQ{wTSWtUns7^GEgVjU)k(vnB?whE-9*nBMD!z5*iQ z8%+fvO$T|-?N$k2&ZF5PK|v6KX#|I42*#wiX{g$Q>&&lAhWqj}#e_BdhTq@t`x}0L T!|y*De*gRjX1oxufGGk1?cM`* literal 0 HcmV?d00001 diff --git a/hcec/edwards/const.go b/hcec/edwards/const.go index c957543..83440df 100644 --- a/hcec/edwards/const.go +++ b/hcec/edwards/const.go @@ -1,57 +1,57 @@ -// Copyright (c) 2015-2017 The Decred developers -// Copyright (c) 2018-2020 The Hc developers -// Use of this source code is governed by an ISC -// license that can be found in the LICENSE file. - -package edwards - -import ( - "math/big" - - "github.com/agl/ed25519/edwards25519" -) - -var ( - // zero through eight are big.Int numbers useful in - // elliptical curve math. - zero = new(big.Int).SetInt64(0) - one = new(big.Int).SetInt64(1) - two = new(big.Int).SetInt64(2) - three = new(big.Int).SetInt64(3) - four = new(big.Int).SetInt64(4) - eight = new(big.Int).SetInt64(8) - - // fieldIntSize is the size of a field element encoded - // as bytes. - fieldIntSize = 32 -) - -// feOne is the field element representation of one. This is -// also the neutral (null) element. -var feOne = edwards25519.FieldElement{ - 1, 0, 0, 0, 0, - 0, 0, 0, 0, 0, -} - -// feA is the field element representation of one. -var feA = edwards25519.FieldElement{ - 486662, 0, 0, 0, 0, 0, 0, 0, 0, 0, -} - -// fed is the field element representation of D. -var fed = edwards25519.FieldElement{ - -10913610, 13857413, -15372611, 6949391, 114729, - -8787816, -6275908, -3247719, -18696448, -12055116, -} - -// fed2 is the field element representation of D^2. -var fed2 = edwards25519.FieldElement{ - -21827239, -5839606, -30745221, 13898782, 229458, - 15978800, -12551817, -6495438, 29715968, 9444199, -} - -// feI is the field element representation of I. -var feI = edwards25519.FieldElement{ - -32595792, -7943725, 9377950, 3500415, 12389472, - -272473, -25146209, -2005654, 326686, 11406482, -} +// Copyright (c) 2015-2017 The Decred developers +// Copyright (c) 2018-2020 The Hc developers +// Use of this source code is governed by an ISC +// license that can be found in the LICENSE file. + +package edwards + +import ( + "math/big" + + "github.com/HcashOrg/hcd/hcec/ed25519/edwards25519" +) + +var ( + // zero through eight are big.Int numbers useful in + // elliptical curve math. + zero = new(big.Int).SetInt64(0) + one = new(big.Int).SetInt64(1) + two = new(big.Int).SetInt64(2) + three = new(big.Int).SetInt64(3) + four = new(big.Int).SetInt64(4) + eight = new(big.Int).SetInt64(8) + + // fieldIntSize is the size of a field element encoded + // as bytes. + fieldIntSize = 32 +) + +// feOne is the field element representation of one. This is +// also the neutral (null) element. +var feOne = edwards25519.FieldElement{ + 1, 0, 0, 0, 0, + 0, 0, 0, 0, 0, +} + +// feA is the field element representation of one. +var feA = edwards25519.FieldElement{ + 486662, 0, 0, 0, 0, 0, 0, 0, 0, 0, +} + +// fed is the field element representation of D. +var fed = edwards25519.FieldElement{ + -10913610, 13857413, -15372611, 6949391, 114729, + -8787816, -6275908, -3247719, -18696448, -12055116, +} + +// fed2 is the field element representation of D^2. +var fed2 = edwards25519.FieldElement{ + -21827239, -5839606, -30745221, 13898782, 229458, + 15978800, -12551817, -6495438, 29715968, 9444199, +} + +// feI is the field element representation of I. +var feI = edwards25519.FieldElement{ + -32595792, -7943725, 9377950, 3500415, 12389472, + -272473, -25146209, -2005654, 326686, 11406482, +} diff --git a/hcec/edwards/curve.go b/hcec/edwards/curve.go index 710bdc6..ee45b10 100644 --- a/hcec/edwards/curve.go +++ b/hcec/edwards/curve.go @@ -1,410 +1,410 @@ -// Copyright (c) 2015-2017 The Decred developers -// Copyright (c) 2018-2020 The Hc developers -// Use of this source code is governed by an ISC -// license that can be found in the LICENSE file. - -package edwards - -import ( - "crypto/elliptic" - "math/big" - - "github.com/agl/ed25519/edwards25519" -) - -// TwistedEdwardsCurve extended an elliptical curve set of -// parameters to satisfy the interface of the elliptic package. -type TwistedEdwardsCurve struct { - *elliptic.CurveParams - H int // Cofactor of the curve - - A, D, I *big.Int // Edwards curve equation parameter constants - - // byteSize is simply the bit size / 8 and is provided for convenience - // since it is calculated repeatedly. - byteSize int -} - -// Params returns the parameters for the curve. -func (curve TwistedEdwardsCurve) Params() *elliptic.CurveParams { - return curve.CurveParams -} - -// Marshal converts a point into the 32 byte encoded Ed25519 form. -func Marshal(curve TwistedEdwardsCurve, x, y *big.Int) []byte { - return BigIntPointToEncodedBytes(x, y)[:] -} - -// Unmarshal converts a point into the 32 byte encoded Ed25519 form. -func Unmarshal(curve *TwistedEdwardsCurve, data []byte) (x, y *big.Int) { - var err error - x, y, err = curve.EncodedBytesToBigIntPoint(copyBytes(data)) - if err != nil { - x = nil - y = nil - } - return -} - -// RecoverXBigInt recovers the X value for some Y value, for a coordinate -// on the Ed25519 curve given as a big integer Y value. -func (curve *TwistedEdwardsCurve) RecoverXBigInt(xIsNeg bool, - y *big.Int) *big.Int { - // (y^2 - 1) - l := new(big.Int).Mul(y, y) - l.Sub(l, one) - - // inv(d*y^2+1) - temp := new(big.Int).Mul(y, y) - temp.Mul(temp, curve.D) - temp.Add(temp, one) - r := curve.invert(temp) - - // x2 = (y^2 - 1) * invert(d*y^2+1) - x2 := new(big.Int).Mul(r, l) - - // x = exp(x^2,(P+3)/8, P) - qp3 := new(big.Int).Add(curve.P, three) - qp3.Div(qp3, eight) // /= curve.H - x := new(big.Int).Exp(x2, qp3, curve.P) - - // check (x^2 - x2) % q != 0 - x22 := new(big.Int).Mul(x, x) - xsub := new(big.Int).Sub(x22, x2) - xsub.Mod(xsub, curve.P) - if xsub.Cmp(zero) != 0 { - ximod := new(big.Int) - ximod.Mul(x, curve.I) - ximod.Mod(ximod, curve.P) - x.Set(ximod) - } - - xmod2 := new(big.Int).Mod(x, two) - if xmod2.Cmp(zero) != 0 { - x.Sub(curve.P, x) - } - - // We got the wrong x, negate it to get the right one. - if xIsNeg != (x.Bit(0) == 1) { - x.Sub(curve.P, x) - } - - return x -} - -// RecoverXFieldElement recovers the X value for some Y value, for a coordinate -// on the Ed25519 curve given as a field element. Y value. Probably the fastest -// way to get your respective X from Y. -func (curve *TwistedEdwardsCurve) RecoverXFieldElement(xIsNeg bool, - y *edwards25519.FieldElement) *edwards25519.FieldElement { - // (y^2 - 1) - l := new(edwards25519.FieldElement) - edwards25519.FeSquare(l, y) - edwards25519.FeSub(l, l, &feOne) - - // inv(d*y^2+1) - r := new(edwards25519.FieldElement) - edwards25519.FeSquare(r, y) - edwards25519.FeMul(r, r, &fed) - edwards25519.FeAdd(r, r, &feOne) - edwards25519.FeInvert(r, r) - - x2 := new(edwards25519.FieldElement) - edwards25519.FeMul(x2, r, l) - - // Get a big int so we can do the exponentiation. - x2Big := FieldElementToBigInt(x2) - - // x = exp(x^2,(P+3)/8, P) - qp3 := new(big.Int).Add(curve.P, three) - qp3.Div(qp3, eight) // /= curve.H - xBig := new(big.Int).Exp(x2Big, qp3, curve.P) - - // Convert back to a field element and do - // the rest. - x := BigIntToFieldElement(xBig) - - // check (x^2 - x2) % q != 0 - x22 := new(edwards25519.FieldElement) - edwards25519.FeSquare(x22, x) - xsub := new(edwards25519.FieldElement) - edwards25519.FeSub(xsub, x22, x2) - xsubBig := FieldElementToBigInt(xsub) - xsubBig.Mod(xsubBig, curve.P) - - if xsubBig.Cmp(zero) != 0 { - xi := new(edwards25519.FieldElement) - edwards25519.FeMul(xi, x, &feI) - xiModBig := FieldElementToBigInt(xi) - xiModBig.Mod(xiModBig, curve.P) - xiMod := BigIntToFieldElement(xiModBig) - - x = xiMod - } - - xBig = FieldElementToBigInt(x) - xmod2 := new(big.Int).Mod(xBig, two) - if xmod2.Cmp(zero) != 0 { - // TODO replace this with FeSub - xBig.Sub(curve.P, xBig) - x = BigIntToFieldElement(xBig) - } - - // We got the wrong x, negate it to get the right one. - isNegative := edwards25519.FeIsNegative(x) == 1 - if xIsNeg != isNegative { - edwards25519.FeNeg(x, x) - } - - return x -} - -// IsOnCurve returns bool to say if the point (x,y) is on the curve by -// checking (y^2 - x^2 - 1 - dx^2y^2) % P == 0. -func (curve *TwistedEdwardsCurve) IsOnCurve(x *big.Int, y *big.Int) bool { - // Convert to field elements. - xB := BigIntToEncodedBytes(x) - yB := BigIntToEncodedBytes(y) - - yfe := new(edwards25519.FieldElement) - xfe := new(edwards25519.FieldElement) - edwards25519.FeFromBytes(yfe, yB) - edwards25519.FeFromBytes(xfe, xB) - - x2 := new(edwards25519.FieldElement) - edwards25519.FeSquare(x2, xfe) - y2 := new(edwards25519.FieldElement) - edwards25519.FeSquare(y2, yfe) - - dx2y2 := new(edwards25519.FieldElement) - edwards25519.FeMul(dx2y2, &fed, x2) - edwards25519.FeMul(dx2y2, dx2y2, y2) - - enum := new(edwards25519.FieldElement) - edwards25519.FeSub(enum, y2, x2) - edwards25519.FeSub(enum, enum, &feOne) - edwards25519.FeSub(enum, enum, dx2y2) - - enumBig := FieldElementToBigInt(enum) - enumBig.Mod(enumBig, curve.P) - - if enumBig.Cmp(zero) != 0 { - return false - } - - // Check if we're in the cofactor of the curve (8). - modEight := new(big.Int) - modEight.Mod(enumBig, eight) - - return modEight.Cmp(zero) == 0 -} - -// cachedGroupElement is a cached extended group element derived from -// another extended group element, for use in computation. -type cachedGroupElement struct { - yPlusX, yMinusX, Z, T2d edwards25519.FieldElement -} - -// toCached converts an extended group element to a useful intermediary -// containing precalculated values. -func toCached(r *cachedGroupElement, p *edwards25519.ExtendedGroupElement) { - edwards25519.FeAdd(&r.yPlusX, &p.Y, &p.X) - edwards25519.FeSub(&r.yMinusX, &p.Y, &p.X) - edwards25519.FeCopy(&r.Z, &p.Z) - edwards25519.FeMul(&r.T2d, &p.T, &fed2) -} - -// Add adds two points represented by pairs of big integers on the elliptical -// curve. -func (curve *TwistedEdwardsCurve) Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int) { - // Convert to extended from affine. - a := BigIntPointToEncodedBytes(x1, y1) - aEGE := new(edwards25519.ExtendedGroupElement) - aEGE.FromBytes(a) - - b := BigIntPointToEncodedBytes(x2, y2) - bEGE := new(edwards25519.ExtendedGroupElement) - bEGE.FromBytes(b) - - // Cache b for use in group element addition. - bCached := new(cachedGroupElement) - toCached(bCached, bEGE) - - p := aEGE - q := bCached - - // geAdd(r*CompletedGroupElement, p*ExtendedGroupElement, - // q*CachedGroupElement) - // r is the result. - r := new(edwards25519.CompletedGroupElement) - var t0 edwards25519.FieldElement - - edwards25519.FeAdd(&r.X, &p.Y, &p.X) - edwards25519.FeSub(&r.Y, &p.Y, &p.X) - edwards25519.FeMul(&r.Z, &r.X, &q.yPlusX) - edwards25519.FeMul(&r.Y, &r.Y, &q.yMinusX) - edwards25519.FeMul(&r.T, &q.T2d, &p.T) - edwards25519.FeMul(&r.X, &p.Z, &q.Z) - edwards25519.FeAdd(&t0, &r.X, &r.X) - edwards25519.FeSub(&r.X, &r.Z, &r.Y) - edwards25519.FeAdd(&r.Y, &r.Z, &r.Y) - edwards25519.FeAdd(&r.Z, &t0, &r.T) - edwards25519.FeSub(&r.T, &t0, &r.T) - - rEGE := new(edwards25519.ExtendedGroupElement) - r.ToExtended(rEGE) - - s := new([32]byte) - rEGE.ToBytes(s) - - x, y, _ = curve.EncodedBytesToBigIntPoint(s) - - return -} - -// Double adds the same pair of big integer coordinates to itself on the -// elliptical curve. -func (curve *TwistedEdwardsCurve) Double(x1, y1 *big.Int) (x, y *big.Int) { - // Convert to extended projective coordinates. - a := BigIntPointToEncodedBytes(x1, y1) - aEGE := new(edwards25519.ExtendedGroupElement) - aEGE.FromBytes(a) - - r := new(edwards25519.CompletedGroupElement) - aEGE.Double(r) - rEGE := new(edwards25519.ExtendedGroupElement) - r.ToExtended(rEGE) - - s := new([32]byte) - rEGE.ToBytes(s) - x, y, _ = curve.EncodedBytesToBigIntPoint(s) - - return -} - -// ScalarMult returns k*(Bx,By) where k is a number in big-endian form. This -// uses the repeated doubling method, which is variable time. -// TODO use a constant time method to prevent side channel attacks. -func (curve *TwistedEdwardsCurve) ScalarMult(x1, y1 *big.Int, - k []byte) (x, y *big.Int) { - // Convert the scalar to a big int. - s := new(big.Int).SetBytes(k) - - // Get a new group element to do cached doubling - // calculations in. - dEGE := new(edwards25519.ExtendedGroupElement) - dEGE.Zero() - - // Use the doubling method for the multiplication. - // p := given point - // q := point(zero) - // for each bit in the scalar, descending: - // double(q) - // if bit == 1: - // add(q, p) - // return q - // - // Note that the addition is skipped for zero bits, - // making this variable time and thus vulnerable to - // side channel attack vectors. - for i := s.BitLen() - 1; i >= 0; i-- { - dCGE := new(edwards25519.CompletedGroupElement) - dEGE.Double(dCGE) - dCGE.ToExtended(dEGE) - if s.Bit(i) == 1 { - ss := new([32]byte) - dEGE.ToBytes(ss) - var err error - xi, yi, err := curve.EncodedBytesToBigIntPoint(ss) - if err != nil { - return nil, nil - } - xAdd, yAdd := curve.Add(xi, yi, x1, y1) - dTempBytes := BigIntPointToEncodedBytes(xAdd, yAdd) - dEGE.FromBytes(dTempBytes) - } - } - - finalBytes := new([32]byte) - dEGE.ToBytes(finalBytes) - - var err error - x, y, err = curve.EncodedBytesToBigIntPoint(finalBytes) - if err != nil { - return nil, nil - } - - return -} - -// ScalarBaseMult returns k*G, where G is the base point of the group -// and k is an integer in big-endian form. -// TODO Optimize this with field elements -func (curve *TwistedEdwardsCurve) ScalarBaseMult(k []byte) (x, y *big.Int) { - return curve.ScalarMult(curve.Gx, curve.Gy, k) -} - -// ScalarAdd adds two scalars and returns the sum mod N. -func ScalarAdd(a, b *big.Int) *big.Int { - feA := BigIntToFieldElement(a) - feB := BigIntToFieldElement(b) - sum := new(edwards25519.FieldElement) - - edwards25519.FeAdd(sum, feA, feB) - sumArray := new([32]byte) - edwards25519.FeToBytes(sumArray, sum) - - return EncodedBytesToBigInt(sumArray) -} - -// InitParam25519 initializes an instance of the Ed25519 curve. -func (curve *TwistedEdwardsCurve) InitParam25519() { - // The prime modulus of the field. - // P = 2^255-19 - curve.CurveParams = new(elliptic.CurveParams) - curve.P = new(big.Int) - curve.P.SetBit(zero, 255, 1).Sub(curve.P, big.NewInt(19)) - - // The prime order for the base point. - // N = 2^252 + 27742317777372353535851937790883648493 - qs, _ := new(big.Int).SetString("27742317777372353535851937790883648493", 10) - curve.N = new(big.Int) - curve.N.SetBit(zero, 252, 1).Add(curve.N, qs) // AKA Q - - curve.A = new(big.Int) - curve.A.SetInt64(-1).Add(curve.P, curve.A) - - // d = -121665 * inv(121666) - da := new(big.Int).SetInt64(-121665) - ds := new(big.Int).SetInt64(121666) - di := curve.invert(ds) - curve.D = new(big.Int).Mul(da, di) - - // I = expmod(2,(q-1)/4,q) - psn := new(big.Int) - psn.SetBit(zero, 255, 1).Sub(psn, big.NewInt(19)) - psn.Sub(psn, one) - psn.Div(psn, four) - curve.I = psn.Exp(two, psn, curve.P) - - // The base point. - curve.Gx = new(big.Int) - curve.Gx.SetString("151122213495354007725011514095885315"+ - "11454012693041857206046113283949847762202", 10) - curve.Gy = new(big.Int) - curve.Gy.SetString("463168356949264781694283940034751631"+ - "41307993866256225615783033603165251855960", 10) - - curve.BitSize = 256 - curve.H = 8 - - // Provided for convenience since this gets computed repeatedly. - curve.byteSize = curve.BitSize / 8 -} - -// Edwards returns a Curve which implements Ed25519. -func Edwards() *TwistedEdwardsCurve { - c := new(TwistedEdwardsCurve) - c.InitParam25519() - return c -} +// Copyright (c) 2015-2017 The Decred developers +// Copyright (c) 2018-2020 The Hc developers +// Use of this source code is governed by an ISC +// license that can be found in the LICENSE file. + +package edwards + +import ( + "crypto/elliptic" + "math/big" + + "github.com/HcashOrg/hcd/hcec/ed25519/edwards25519" +) + +// TwistedEdwardsCurve extended an elliptical curve set of +// parameters to satisfy the interface of the elliptic package. +type TwistedEdwardsCurve struct { + *elliptic.CurveParams + H int // Cofactor of the curve + + A, D, I *big.Int // Edwards curve equation parameter constants + + // byteSize is simply the bit size / 8 and is provided for convenience + // since it is calculated repeatedly. + byteSize int +} + +// Params returns the parameters for the curve. +func (curve TwistedEdwardsCurve) Params() *elliptic.CurveParams { + return curve.CurveParams +} + +// Marshal converts a point into the 32 byte encoded Ed25519 form. +func Marshal(curve TwistedEdwardsCurve, x, y *big.Int) []byte { + return BigIntPointToEncodedBytes(x, y)[:] +} + +// Unmarshal converts a point into the 32 byte encoded Ed25519 form. +func Unmarshal(curve *TwistedEdwardsCurve, data []byte) (x, y *big.Int) { + var err error + x, y, err = curve.EncodedBytesToBigIntPoint(copyBytes(data)) + if err != nil { + x = nil + y = nil + } + return +} + +// RecoverXBigInt recovers the X value for some Y value, for a coordinate +// on the Ed25519 curve given as a big integer Y value. +func (curve *TwistedEdwardsCurve) RecoverXBigInt(xIsNeg bool, + y *big.Int) *big.Int { + // (y^2 - 1) + l := new(big.Int).Mul(y, y) + l.Sub(l, one) + + // inv(d*y^2+1) + temp := new(big.Int).Mul(y, y) + temp.Mul(temp, curve.D) + temp.Add(temp, one) + r := curve.invert(temp) + + // x2 = (y^2 - 1) * invert(d*y^2+1) + x2 := new(big.Int).Mul(r, l) + + // x = exp(x^2,(P+3)/8, P) + qp3 := new(big.Int).Add(curve.P, three) + qp3.Div(qp3, eight) // /= curve.H + x := new(big.Int).Exp(x2, qp3, curve.P) + + // check (x^2 - x2) % q != 0 + x22 := new(big.Int).Mul(x, x) + xsub := new(big.Int).Sub(x22, x2) + xsub.Mod(xsub, curve.P) + if xsub.Cmp(zero) != 0 { + ximod := new(big.Int) + ximod.Mul(x, curve.I) + ximod.Mod(ximod, curve.P) + x.Set(ximod) + } + + xmod2 := new(big.Int).Mod(x, two) + if xmod2.Cmp(zero) != 0 { + x.Sub(curve.P, x) + } + + // We got the wrong x, negate it to get the right one. + if xIsNeg != (x.Bit(0) == 1) { + x.Sub(curve.P, x) + } + + return x +} + +// RecoverXFieldElement recovers the X value for some Y value, for a coordinate +// on the Ed25519 curve given as a field element. Y value. Probably the fastest +// way to get your respective X from Y. +func (curve *TwistedEdwardsCurve) RecoverXFieldElement(xIsNeg bool, + y *edwards25519.FieldElement) *edwards25519.FieldElement { + // (y^2 - 1) + l := new(edwards25519.FieldElement) + edwards25519.FeSquare(l, y) + edwards25519.FeSub(l, l, &feOne) + + // inv(d*y^2+1) + r := new(edwards25519.FieldElement) + edwards25519.FeSquare(r, y) + edwards25519.FeMul(r, r, &fed) + edwards25519.FeAdd(r, r, &feOne) + edwards25519.FeInvert(r, r) + + x2 := new(edwards25519.FieldElement) + edwards25519.FeMul(x2, r, l) + + // Get a big int so we can do the exponentiation. + x2Big := FieldElementToBigInt(x2) + + // x = exp(x^2,(P+3)/8, P) + qp3 := new(big.Int).Add(curve.P, three) + qp3.Div(qp3, eight) // /= curve.H + xBig := new(big.Int).Exp(x2Big, qp3, curve.P) + + // Convert back to a field element and do + // the rest. + x := BigIntToFieldElement(xBig) + + // check (x^2 - x2) % q != 0 + x22 := new(edwards25519.FieldElement) + edwards25519.FeSquare(x22, x) + xsub := new(edwards25519.FieldElement) + edwards25519.FeSub(xsub, x22, x2) + xsubBig := FieldElementToBigInt(xsub) + xsubBig.Mod(xsubBig, curve.P) + + if xsubBig.Cmp(zero) != 0 { + xi := new(edwards25519.FieldElement) + edwards25519.FeMul(xi, x, &feI) + xiModBig := FieldElementToBigInt(xi) + xiModBig.Mod(xiModBig, curve.P) + xiMod := BigIntToFieldElement(xiModBig) + + x = xiMod + } + + xBig = FieldElementToBigInt(x) + xmod2 := new(big.Int).Mod(xBig, two) + if xmod2.Cmp(zero) != 0 { + // TODO replace this with FeSub + xBig.Sub(curve.P, xBig) + x = BigIntToFieldElement(xBig) + } + + // We got the wrong x, negate it to get the right one. + isNegative := edwards25519.FeIsNegative(x) == 1 + if xIsNeg != isNegative { + edwards25519.FeNeg(x, x) + } + + return x +} + +// IsOnCurve returns bool to say if the point (x,y) is on the curve by +// checking (y^2 - x^2 - 1 - dx^2y^2) % P == 0. +func (curve *TwistedEdwardsCurve) IsOnCurve(x *big.Int, y *big.Int) bool { + // Convert to field elements. + xB := BigIntToEncodedBytes(x) + yB := BigIntToEncodedBytes(y) + + yfe := new(edwards25519.FieldElement) + xfe := new(edwards25519.FieldElement) + edwards25519.FeFromBytes(yfe, yB) + edwards25519.FeFromBytes(xfe, xB) + + x2 := new(edwards25519.FieldElement) + edwards25519.FeSquare(x2, xfe) + y2 := new(edwards25519.FieldElement) + edwards25519.FeSquare(y2, yfe) + + dx2y2 := new(edwards25519.FieldElement) + edwards25519.FeMul(dx2y2, &fed, x2) + edwards25519.FeMul(dx2y2, dx2y2, y2) + + enum := new(edwards25519.FieldElement) + edwards25519.FeSub(enum, y2, x2) + edwards25519.FeSub(enum, enum, &feOne) + edwards25519.FeSub(enum, enum, dx2y2) + + enumBig := FieldElementToBigInt(enum) + enumBig.Mod(enumBig, curve.P) + + if enumBig.Cmp(zero) != 0 { + return false + } + + // Check if we're in the cofactor of the curve (8). + modEight := new(big.Int) + modEight.Mod(enumBig, eight) + + return modEight.Cmp(zero) == 0 +} + +// cachedGroupElement is a cached extended group element derived from +// another extended group element, for use in computation. +type cachedGroupElement struct { + yPlusX, yMinusX, Z, T2d edwards25519.FieldElement +} + +// toCached converts an extended group element to a useful intermediary +// containing precalculated values. +func toCached(r *cachedGroupElement, p *edwards25519.ExtendedGroupElement) { + edwards25519.FeAdd(&r.yPlusX, &p.Y, &p.X) + edwards25519.FeSub(&r.yMinusX, &p.Y, &p.X) + edwards25519.FeCopy(&r.Z, &p.Z) + edwards25519.FeMul(&r.T2d, &p.T, &fed2) +} + +// Add adds two points represented by pairs of big integers on the elliptical +// curve. +func (curve *TwistedEdwardsCurve) Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int) { + // Convert to extended from affine. + a := BigIntPointToEncodedBytes(x1, y1) + aEGE := new(edwards25519.ExtendedGroupElement) + aEGE.FromBytes(a) + + b := BigIntPointToEncodedBytes(x2, y2) + bEGE := new(edwards25519.ExtendedGroupElement) + bEGE.FromBytes(b) + + // Cache b for use in group element addition. + bCached := new(cachedGroupElement) + toCached(bCached, bEGE) + + p := aEGE + q := bCached + + // geAdd(r*CompletedGroupElement, p*ExtendedGroupElement, + // q*CachedGroupElement) + // r is the result. + r := new(edwards25519.CompletedGroupElement) + var t0 edwards25519.FieldElement + + edwards25519.FeAdd(&r.X, &p.Y, &p.X) + edwards25519.FeSub(&r.Y, &p.Y, &p.X) + edwards25519.FeMul(&r.Z, &r.X, &q.yPlusX) + edwards25519.FeMul(&r.Y, &r.Y, &q.yMinusX) + edwards25519.FeMul(&r.T, &q.T2d, &p.T) + edwards25519.FeMul(&r.X, &p.Z, &q.Z) + edwards25519.FeAdd(&t0, &r.X, &r.X) + edwards25519.FeSub(&r.X, &r.Z, &r.Y) + edwards25519.FeAdd(&r.Y, &r.Z, &r.Y) + edwards25519.FeAdd(&r.Z, &t0, &r.T) + edwards25519.FeSub(&r.T, &t0, &r.T) + + rEGE := new(edwards25519.ExtendedGroupElement) + r.ToExtended(rEGE) + + s := new([32]byte) + rEGE.ToBytes(s) + + x, y, _ = curve.EncodedBytesToBigIntPoint(s) + + return +} + +// Double adds the same pair of big integer coordinates to itself on the +// elliptical curve. +func (curve *TwistedEdwardsCurve) Double(x1, y1 *big.Int) (x, y *big.Int) { + // Convert to extended projective coordinates. + a := BigIntPointToEncodedBytes(x1, y1) + aEGE := new(edwards25519.ExtendedGroupElement) + aEGE.FromBytes(a) + + r := new(edwards25519.CompletedGroupElement) + aEGE.Double(r) + rEGE := new(edwards25519.ExtendedGroupElement) + r.ToExtended(rEGE) + + s := new([32]byte) + rEGE.ToBytes(s) + x, y, _ = curve.EncodedBytesToBigIntPoint(s) + + return +} + +// ScalarMult returns k*(Bx,By) where k is a number in big-endian form. This +// uses the repeated doubling method, which is variable time. +// TODO use a constant time method to prevent side channel attacks. +func (curve *TwistedEdwardsCurve) ScalarMult(x1, y1 *big.Int, + k []byte) (x, y *big.Int) { + // Convert the scalar to a big int. + s := new(big.Int).SetBytes(k) + + // Get a new group element to do cached doubling + // calculations in. + dEGE := new(edwards25519.ExtendedGroupElement) + dEGE.Zero() + + // Use the doubling method for the multiplication. + // p := given point + // q := point(zero) + // for each bit in the scalar, descending: + // double(q) + // if bit == 1: + // add(q, p) + // return q + // + // Note that the addition is skipped for zero bits, + // making this variable time and thus vulnerable to + // side channel attack vectors. + for i := s.BitLen() - 1; i >= 0; i-- { + dCGE := new(edwards25519.CompletedGroupElement) + dEGE.Double(dCGE) + dCGE.ToExtended(dEGE) + if s.Bit(i) == 1 { + ss := new([32]byte) + dEGE.ToBytes(ss) + var err error + xi, yi, err := curve.EncodedBytesToBigIntPoint(ss) + if err != nil { + return nil, nil + } + xAdd, yAdd := curve.Add(xi, yi, x1, y1) + dTempBytes := BigIntPointToEncodedBytes(xAdd, yAdd) + dEGE.FromBytes(dTempBytes) + } + } + + finalBytes := new([32]byte) + dEGE.ToBytes(finalBytes) + + var err error + x, y, err = curve.EncodedBytesToBigIntPoint(finalBytes) + if err != nil { + return nil, nil + } + + return +} + +// ScalarBaseMult returns k*G, where G is the base point of the group +// and k is an integer in big-endian form. +// TODO Optimize this with field elements +func (curve *TwistedEdwardsCurve) ScalarBaseMult(k []byte) (x, y *big.Int) { + return curve.ScalarMult(curve.Gx, curve.Gy, k) +} + +// ScalarAdd adds two scalars and returns the sum mod N. +func ScalarAdd(a, b *big.Int) *big.Int { + feA := BigIntToFieldElement(a) + feB := BigIntToFieldElement(b) + sum := new(edwards25519.FieldElement) + + edwards25519.FeAdd(sum, feA, feB) + sumArray := new([32]byte) + edwards25519.FeToBytes(sumArray, sum) + + return EncodedBytesToBigInt(sumArray) +} + +// InitParam25519 initializes an instance of the Ed25519 curve. +func (curve *TwistedEdwardsCurve) InitParam25519() { + // The prime modulus of the field. + // P = 2^255-19 + curve.CurveParams = new(elliptic.CurveParams) + curve.P = new(big.Int) + curve.P.SetBit(zero, 255, 1).Sub(curve.P, big.NewInt(19)) + + // The prime order for the base point. + // N = 2^252 + 27742317777372353535851937790883648493 + qs, _ := new(big.Int).SetString("27742317777372353535851937790883648493", 10) + curve.N = new(big.Int) + curve.N.SetBit(zero, 252, 1).Add(curve.N, qs) // AKA Q + + curve.A = new(big.Int) + curve.A.SetInt64(-1).Add(curve.P, curve.A) + + // d = -121665 * inv(121666) + da := new(big.Int).SetInt64(-121665) + ds := new(big.Int).SetInt64(121666) + di := curve.invert(ds) + curve.D = new(big.Int).Mul(da, di) + + // I = expmod(2,(q-1)/4,q) + psn := new(big.Int) + psn.SetBit(zero, 255, 1).Sub(psn, big.NewInt(19)) + psn.Sub(psn, one) + psn.Div(psn, four) + curve.I = psn.Exp(two, psn, curve.P) + + // The base point. + curve.Gx = new(big.Int) + curve.Gx.SetString("151122213495354007725011514095885315"+ + "11454012693041857206046113283949847762202", 10) + curve.Gy = new(big.Int) + curve.Gy.SetString("463168356949264781694283940034751631"+ + "41307993866256225615783033603165251855960", 10) + + curve.BitSize = 256 + curve.H = 8 + + // Provided for convenience since this gets computed repeatedly. + curve.byteSize = curve.BitSize / 8 +} + +// Edwards returns a Curve which implements Ed25519. +func Edwards() *TwistedEdwardsCurve { + c := new(TwistedEdwardsCurve) + c.InitParam25519() + return c +} diff --git a/hcec/edwards/ecdsa.go b/hcec/edwards/ecdsa.go index d7b66b4..d71b60b 100644 --- a/hcec/edwards/ecdsa.go +++ b/hcec/edwards/ecdsa.go @@ -1,382 +1,382 @@ -// Copyright (c) 2015-2017 The Decred developers -// Copyright (c) 2018-2020 The Hc developers -// Use of this source code is governed by an ISC -// license that can be found in the LICENSE file. - -package edwards - -import ( - "bytes" - "crypto/hmac" - "crypto/sha256" - "crypto/sha512" - "fmt" - "hash" - "io" - "math/big" - - "github.com/agl/ed25519" - "github.com/agl/ed25519/edwards25519" -) - -// BIG CAVEAT -// Memory management is kind of sloppy and whether or not your keys or -// nonces can be found in memory later is likely a product of when the -// garbage collector runs. -// Signing/EC mult is also not constant side, so don't use this in any -// application where you think you might be vulnerable to side channel -// attacks. - -var ( - // oneInitializer is used to fill a byte slice with byte 0x01. It is provided - // here to avoid the need to create it multiple times. - oneInitializer = []byte{0x01} - - // ecTypeEdwards is the ECDSA type for the chainec interface. - ecTypeEdwards = 1 -) - -// GenerateKey generates a key using a random number generator, returning -// the private scalar and the corresponding public key points from a -// random secret. -func GenerateKey(curve *TwistedEdwardsCurve, rand io.Reader) (priv []byte, x, - y *big.Int, err error) { - var pub *[PubKeyBytesLen]byte - var privArray *[PrivKeyBytesLen]byte - pub, privArray, err = ed25519.GenerateKey(rand) - priv = privArray[:] - - x, y, err = curve.EncodedBytesToBigIntPoint(pub) - if err != nil { - return nil, nil, nil, err - } - - return -} - -// GenerateKey generates a key using a random number generator, returning -// the private scalar and the corresponding public key points from a -// random secret. -func GenerateKeyNew(rand io.Reader) (priv []byte, x, y *big.Int, err error) { - var pub *[PubKeyBytesLen]byte - var privArray *[PrivKeyBytesLen]byte - pub, privArray, err = ed25519.GenerateKey(rand) - if err != nil { - return nil, nil, nil, err - } - priv = privArray[:] - - curve := new(TwistedEdwardsCurve) - curve.InitParam25519() - - x, y, err = curve.EncodedBytesToBigIntPoint(pub) - if err != nil { - return nil, nil, nil, err - } - - return -} - -// SignFromSecret signs a message 'hash' using the given private key priv. It doesn't -// actually user the random reader (the lib is maybe deterministic???). -func SignFromSecret(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, - err error) { - r, s, err = SignFromSecretNoReader(priv, hash) - - return -} - -// SignFromSecretNoReader signs a message 'hash' using the given private key -// priv. It doesn't actually user the random reader. -func SignFromSecretNoReader(priv *PrivateKey, hash []byte) (r, s *big.Int, - err error) { - privBytes := priv.SerializeSecret() - privArray := copyBytes64(privBytes) - sig := ed25519.Sign(privArray, hash) - - // The signatures are encoded as - // sig[0:32] R, a point encoded as little endian - // sig[32:64] S, scalar multiplication/addition results = (ab+c) mod l - // encoded also as little endian - rBytes := copyBytes(sig[0:32]) - r = EncodedBytesToBigInt(rBytes) - sBytes := copyBytes(sig[32:64]) - s = EncodedBytesToBigInt(sBytes) - - return -} - -// nonceRFC6979 is a local instatiation of deterministic nonce generation -// by the standards of RFC6979. -func nonceRFC6979(curve *TwistedEdwardsCurve, privkey []byte, hash []byte, - extra []byte, version []byte) []byte { - pkD := new(big.Int).SetBytes(privkey) - defer pkD.SetInt64(0) - bigK := NonceRFC6979(curve, pkD, hash, extra, version) - defer bigK.SetInt64(0) - k := BigIntToEncodedBytesNoReverse(bigK) - return k[:] -} - -// NonceRFC6979 generates an ECDSA nonce (`k`) deterministically according to -// RFC 6979. It takes a 32-byte hash as an input and returns 32-byte nonce to -// be used in ECDSA algorithm. -func NonceRFC6979(curve *TwistedEdwardsCurve, privkey *big.Int, hash []byte, - extra []byte, version []byte) *big.Int { - q := curve.Params().N - x := privkey - alg := sha256.New - - qlen := q.BitLen() - holen := alg().Size() - rolen := (qlen + 7) >> 3 - bx := append(int2octets(x, rolen), bits2octets(hash, curve, rolen)...) - if len(extra) == 32 { - bx = append(bx, extra...) - } - if len(version) == 16 && len(extra) == 32 { - bx = append(bx, extra...) - } - if len(version) == 16 && len(extra) != 32 { - bx = append(bx, bytes.Repeat([]byte{0x00}, 32)...) - bx = append(bx, version...) - } - - // Step B - v := bytes.Repeat(oneInitializer, holen) - - // Step C (Go zeroes the all allocated memory) - k := make([]byte, holen) - - // Step D - k = mac(alg, k, append(append(v, 0x00), bx...)) - - // Step E - v = mac(alg, k, v) - - // Step F - k = mac(alg, k, append(append(v, 0x01), bx...)) - - // Step G - v = mac(alg, k, v) - - // Step H - for { - // Step H1 - var t []byte - - // Step H2 - for len(t)*8 < qlen { - v = mac(alg, k, v) - t = append(t, v...) - } - - // Step H3 - secret := hashToInt(t, curve) - if secret.Cmp(one) >= 0 && secret.Cmp(q) < 0 { - return secret - } - k = mac(alg, k, append(v, 0x00)) - v = mac(alg, k, v) - } -} - -// hashToInt converts a hash value to an integer. There is some disagreement -// about how this is done. [NSA] suggests that this is done in the obvious -// manner, but [SECG] truncates the hash to the bit-length of the curve order -// first. We follow [SECG] because that's what OpenSSL does. Additionally, -// OpenSSL right shifts excess bits from the number if the hash is too large -// and we mirror that too. -// This is borrowed from crypto/ecdsa. -func hashToInt(hash []byte, c *TwistedEdwardsCurve) *big.Int { - orderBits := c.Params().N.BitLen() - orderBytes := (orderBits + 7) / 8 - if len(hash) > orderBytes { - hash = hash[:orderBytes] - } - - ret := new(big.Int).SetBytes(hash) - excess := len(hash)*8 - orderBits - if excess > 0 { - ret.Rsh(ret, uint(excess)) - } - return ret -} - -// mac returns an HMAC of the given key and message. -func mac(alg func() hash.Hash, k, m []byte) []byte { - h := hmac.New(alg, k) - h.Write(m) - return h.Sum(nil) -} - -// https://tools.ietf.org/html/rfc6979#section-2.3.3 -func int2octets(v *big.Int, rolen int) []byte { - out := v.Bytes() - - // left pad with zeros if it's too short - if len(out) < rolen { - out2 := make([]byte, rolen) - copy(out2[rolen-len(out):], out) - return out2 - } - - // drop most significant bytes if it's too long - if len(out) > rolen { - out2 := make([]byte, rolen) - copy(out2, out[len(out)-rolen:]) - return out2 - } - - return out -} - -// https://tools.ietf.org/html/rfc6979#section-2.3.4 -func bits2octets(in []byte, curve *TwistedEdwardsCurve, rolen int) []byte { - z1 := hashToInt(in, curve) - z2 := new(big.Int).Sub(z1, curve.Params().N) - if z2.Sign() < 0 { - return int2octets(z1, rolen) - } - return int2octets(z2, rolen) -} - -// SignFromScalar signs a message 'hash' using the given private scalar priv. -// It uses RFC6979 to generate a deterministic nonce. Considered experimental. -// r = kG, where k is the RFC6979 nonce -// s = r + hash512(k || A || M) * a -func SignFromScalar(curve *TwistedEdwardsCurve, priv *PrivateKey, - nonce []byte, hash []byte) (r, s *big.Int, err error) { - publicKey := new([PubKeyBytesLen]byte) - var A edwards25519.ExtendedGroupElement - privateScalar := copyBytes(priv.Serialize()) - reverse(privateScalar) // BE --> LE - edwards25519.GeScalarMultBase(&A, privateScalar) - A.ToBytes(publicKey) - - // For signing from a scalar, r = nonce. - nonceLE := copyBytes(nonce) - reverse(nonceLE) - var R edwards25519.ExtendedGroupElement - edwards25519.GeScalarMultBase(&R, nonceLE) - - var encodedR [32]byte - R.ToBytes(&encodedR) - - // h = hash512(k || A || M) - h := sha512.New() - h.Reset() - h.Write(encodedR[:]) - h.Write(publicKey[:]) - h.Write(hash) - - // s = r + h * a - var hramDigest [64]byte - h.Sum(hramDigest[:0]) - var hramDigestReduced [32]byte - edwards25519.ScReduce(&hramDigestReduced, &hramDigest) - - var localS [32]byte - edwards25519.ScMulAdd(&localS, &hramDigestReduced, privateScalar, - nonceLE) - - signature := new([64]byte) - copy(signature[:], encodedR[:]) - copy(signature[32:], localS[:]) - sigEd, err := ParseSignature(curve, signature[:]) - if err != nil { - return nil, nil, err - } - - return sigEd.GetR(), sigEd.GetS(), nil -} - -// SignThreshold signs a message 'hash' using the given private scalar priv in -// a threshold group signature. It uses RFC6979 to generate a deterministic nonce. -// Considered experimental. -// As opposed to the threshold signing function for secp256k1, this function -// takes the entirety of the public nonce point (all points added) instead of -// the public nonce point with n-1 keys added. -// r = K_Sum -// s = r + hash512(k || A || M) * a -func SignThreshold(curve *TwistedEdwardsCurve, priv *PrivateKey, - groupPub *PublicKey, hash []byte, privNonce *PrivateKey, - pubNonceSum *PublicKey) (r, s *big.Int, err error) { - if priv == nil || hash == nil || privNonce == nil || pubNonceSum == nil { - return nil, nil, fmt.Errorf("nil input") - } - - privateScalar := copyBytes(priv.Serialize()) - reverse(privateScalar) // BE --> LE - - // Threshold variant scheme: - // R = K_Sum - // Where K_Sum is the sum of the public keys corresponding to - // the private nonce scalars of each group signature member. - // That is, R = k1G + ... + knG. - encodedGroupR := BigIntPointToEncodedBytes(pubNonceSum.GetX(), - pubNonceSum.GetY()) - - // h = hash512(k || A || M) - var hramDigest [64]byte - h := sha512.New() - h.Reset() - h.Write(encodedGroupR[:]) - h.Write(groupPub.Serialize()[:]) - h.Write(hash) - h.Sum(hramDigest[:0]) - var hramDigestReduced [32]byte - edwards25519.ScReduce(&hramDigestReduced, &hramDigest) - - // s = r + h * a - var localS [32]byte - privNonceLE := copyBytes(privNonce.Serialize()) - reverse(privNonceLE) // BE --> LE - edwards25519.ScMulAdd(&localS, &hramDigestReduced, privateScalar, - privNonceLE) - - signature := new([64]byte) - copy(signature[:], encodedGroupR[:]) - copy(signature[32:], localS[:]) - sigEd, err := ParseSignature(curve, signature[:]) - if err != nil { - return nil, nil, err - } - - return sigEd.GetR(), sigEd.GetS(), nil -} - -// Sign is the generalized and exported version of Ed25519 signing, that -// handles both standard private secrets and non-standard scalars. -func Sign(curve *TwistedEdwardsCurve, priv *PrivateKey, hash []byte) (r, - s *big.Int, err error) { - if priv == nil { - return nil, nil, fmt.Errorf("private key is nil") - } - if hash == nil { - return nil, nil, fmt.Errorf("message key is nil") - } - - if priv.secret == nil { - privLE := copyBytes(priv.Serialize()) - reverse(privLE) - nonce := nonceRFC6979(curve, privLE[:], hash, nil, nil) - return SignFromScalar(curve, priv, nonce, hash) - } - - return SignFromSecretNoReader(priv, hash) -} - -// Verify verifies a message 'hash' using the given public keys and signature. -func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool { - if pub == nil || hash == nil || r == nil || s == nil { - return false - } - - pubBytes := pub.Serialize() - sig := &Signature{r, s} - sigBytes := sig.Serialize() - pubArray := copyBytes(pubBytes) - sigArray := copyBytes64(sigBytes) - return ed25519.Verify(pubArray, hash, sigArray) -} +// Copyright (c) 2015-2017 The Decred developers +// Copyright (c) 2018-2020 The Hc developers +// Use of this source code is governed by an ISC +// license that can be found in the LICENSE file. + +package edwards + +import ( + "bytes" + "crypto/hmac" + "crypto/sha256" + "crypto/sha512" + "fmt" + "hash" + "io" + "math/big" + + "github.com/HcashOrg/hcd/hcec/ed25519" + "github.com/HcashOrg/hcd/hcec/ed25519/edwards25519" +) + +// BIG CAVEAT +// Memory management is kind of sloppy and whether or not your keys or +// nonces can be found in memory later is likely a product of when the +// garbage collector runs. +// Signing/EC mult is also not constant side, so don't use this in any +// application where you think you might be vulnerable to side channel +// attacks. + +var ( + // oneInitializer is used to fill a byte slice with byte 0x01. It is provided + // here to avoid the need to create it multiple times. + oneInitializer = []byte{0x01} + + // ecTypeEdwards is the ECDSA type for the chainec interface. + ecTypeEdwards = 1 +) + +// GenerateKey generates a key using a random number generator, returning +// the private scalar and the corresponding public key points from a +// random secret. +func GenerateKey(curve *TwistedEdwardsCurve, rand io.Reader) (priv []byte, x, + y *big.Int, err error) { + var pub *[PubKeyBytesLen]byte + var privArray *[PrivKeyBytesLen]byte + pub, privArray, err = ed25519.GenerateKey(rand) + priv = privArray[:] + + x, y, err = curve.EncodedBytesToBigIntPoint(pub) + if err != nil { + return nil, nil, nil, err + } + + return +} + +// GenerateKey generates a key using a random number generator, returning +// the private scalar and the corresponding public key points from a +// random secret. +func GenerateKeyNew(rand io.Reader) (priv []byte, x, y *big.Int, err error) { + var pub *[PubKeyBytesLen]byte + var privArray *[PrivKeyBytesLen]byte + pub, privArray, err = ed25519.GenerateKey(rand) + if err != nil { + return nil, nil, nil, err + } + priv = privArray[:] + + curve := new(TwistedEdwardsCurve) + curve.InitParam25519() + + x, y, err = curve.EncodedBytesToBigIntPoint(pub) + if err != nil { + return nil, nil, nil, err + } + + return +} + +// SignFromSecret signs a message 'hash' using the given private key priv. It doesn't +// actually user the random reader (the lib is maybe deterministic???). +func SignFromSecret(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, + err error) { + r, s, err = SignFromSecretNoReader(priv, hash) + + return +} + +// SignFromSecretNoReader signs a message 'hash' using the given private key +// priv. It doesn't actually user the random reader. +func SignFromSecretNoReader(priv *PrivateKey, hash []byte) (r, s *big.Int, + err error) { + privBytes := priv.SerializeSecret() + privArray := copyBytes64(privBytes) + sig := ed25519.Sign(privArray, hash) + + // The signatures are encoded as + // sig[0:32] R, a point encoded as little endian + // sig[32:64] S, scalar multiplication/addition results = (ab+c) mod l + // encoded also as little endian + rBytes := copyBytes(sig[0:32]) + r = EncodedBytesToBigInt(rBytes) + sBytes := copyBytes(sig[32:64]) + s = EncodedBytesToBigInt(sBytes) + + return +} + +// nonceRFC6979 is a local instatiation of deterministic nonce generation +// by the standards of RFC6979. +func nonceRFC6979(curve *TwistedEdwardsCurve, privkey []byte, hash []byte, + extra []byte, version []byte) []byte { + pkD := new(big.Int).SetBytes(privkey) + defer pkD.SetInt64(0) + bigK := NonceRFC6979(curve, pkD, hash, extra, version) + defer bigK.SetInt64(0) + k := BigIntToEncodedBytesNoReverse(bigK) + return k[:] +} + +// NonceRFC6979 generates an ECDSA nonce (`k`) deterministically according to +// RFC 6979. It takes a 32-byte hash as an input and returns 32-byte nonce to +// be used in ECDSA algorithm. +func NonceRFC6979(curve *TwistedEdwardsCurve, privkey *big.Int, hash []byte, + extra []byte, version []byte) *big.Int { + q := curve.Params().N + x := privkey + alg := sha256.New + + qlen := q.BitLen() + holen := alg().Size() + rolen := (qlen + 7) >> 3 + bx := append(int2octets(x, rolen), bits2octets(hash, curve, rolen)...) + if len(extra) == 32 { + bx = append(bx, extra...) + } + if len(version) == 16 && len(extra) == 32 { + bx = append(bx, extra...) + } + if len(version) == 16 && len(extra) != 32 { + bx = append(bx, bytes.Repeat([]byte{0x00}, 32)...) + bx = append(bx, version...) + } + + // Step B + v := bytes.Repeat(oneInitializer, holen) + + // Step C (Go zeroes the all allocated memory) + k := make([]byte, holen) + + // Step D + k = mac(alg, k, append(append(v, 0x00), bx...)) + + // Step E + v = mac(alg, k, v) + + // Step F + k = mac(alg, k, append(append(v, 0x01), bx...)) + + // Step G + v = mac(alg, k, v) + + // Step H + for { + // Step H1 + var t []byte + + // Step H2 + for len(t)*8 < qlen { + v = mac(alg, k, v) + t = append(t, v...) + } + + // Step H3 + secret := hashToInt(t, curve) + if secret.Cmp(one) >= 0 && secret.Cmp(q) < 0 { + return secret + } + k = mac(alg, k, append(v, 0x00)) + v = mac(alg, k, v) + } +} + +// hashToInt converts a hash value to an integer. There is some disagreement +// about how this is done. [NSA] suggests that this is done in the obvious +// manner, but [SECG] truncates the hash to the bit-length of the curve order +// first. We follow [SECG] because that's what OpenSSL does. Additionally, +// OpenSSL right shifts excess bits from the number if the hash is too large +// and we mirror that too. +// This is borrowed from crypto/ecdsa. +func hashToInt(hash []byte, c *TwistedEdwardsCurve) *big.Int { + orderBits := c.Params().N.BitLen() + orderBytes := (orderBits + 7) / 8 + if len(hash) > orderBytes { + hash = hash[:orderBytes] + } + + ret := new(big.Int).SetBytes(hash) + excess := len(hash)*8 - orderBits + if excess > 0 { + ret.Rsh(ret, uint(excess)) + } + return ret +} + +// mac returns an HMAC of the given key and message. +func mac(alg func() hash.Hash, k, m []byte) []byte { + h := hmac.New(alg, k) + h.Write(m) + return h.Sum(nil) +} + +// https://tools.ietf.org/html/rfc6979#section-2.3.3 +func int2octets(v *big.Int, rolen int) []byte { + out := v.Bytes() + + // left pad with zeros if it's too short + if len(out) < rolen { + out2 := make([]byte, rolen) + copy(out2[rolen-len(out):], out) + return out2 + } + + // drop most significant bytes if it's too long + if len(out) > rolen { + out2 := make([]byte, rolen) + copy(out2, out[len(out)-rolen:]) + return out2 + } + + return out +} + +// https://tools.ietf.org/html/rfc6979#section-2.3.4 +func bits2octets(in []byte, curve *TwistedEdwardsCurve, rolen int) []byte { + z1 := hashToInt(in, curve) + z2 := new(big.Int).Sub(z1, curve.Params().N) + if z2.Sign() < 0 { + return int2octets(z1, rolen) + } + return int2octets(z2, rolen) +} + +// SignFromScalar signs a message 'hash' using the given private scalar priv. +// It uses RFC6979 to generate a deterministic nonce. Considered experimental. +// r = kG, where k is the RFC6979 nonce +// s = r + hash512(k || A || M) * a +func SignFromScalar(curve *TwistedEdwardsCurve, priv *PrivateKey, + nonce []byte, hash []byte) (r, s *big.Int, err error) { + publicKey := new([PubKeyBytesLen]byte) + var A edwards25519.ExtendedGroupElement + privateScalar := copyBytes(priv.Serialize()) + reverse(privateScalar) // BE --> LE + edwards25519.GeScalarMultBase(&A, privateScalar) + A.ToBytes(publicKey) + + // For signing from a scalar, r = nonce. + nonceLE := copyBytes(nonce) + reverse(nonceLE) + var R edwards25519.ExtendedGroupElement + edwards25519.GeScalarMultBase(&R, nonceLE) + + var encodedR [32]byte + R.ToBytes(&encodedR) + + // h = hash512(k || A || M) + h := sha512.New() + h.Reset() + h.Write(encodedR[:]) + h.Write(publicKey[:]) + h.Write(hash) + + // s = r + h * a + var hramDigest [64]byte + h.Sum(hramDigest[:0]) + var hramDigestReduced [32]byte + edwards25519.ScReduce(&hramDigestReduced, &hramDigest) + + var localS [32]byte + edwards25519.ScMulAdd(&localS, &hramDigestReduced, privateScalar, + nonceLE) + + signature := new([64]byte) + copy(signature[:], encodedR[:]) + copy(signature[32:], localS[:]) + sigEd, err := ParseSignature(curve, signature[:]) + if err != nil { + return nil, nil, err + } + + return sigEd.GetR(), sigEd.GetS(), nil +} + +// SignThreshold signs a message 'hash' using the given private scalar priv in +// a threshold group signature. It uses RFC6979 to generate a deterministic nonce. +// Considered experimental. +// As opposed to the threshold signing function for secp256k1, this function +// takes the entirety of the public nonce point (all points added) instead of +// the public nonce point with n-1 keys added. +// r = K_Sum +// s = r + hash512(k || A || M) * a +func SignThreshold(curve *TwistedEdwardsCurve, priv *PrivateKey, + groupPub *PublicKey, hash []byte, privNonce *PrivateKey, + pubNonceSum *PublicKey) (r, s *big.Int, err error) { + if priv == nil || hash == nil || privNonce == nil || pubNonceSum == nil { + return nil, nil, fmt.Errorf("nil input") + } + + privateScalar := copyBytes(priv.Serialize()) + reverse(privateScalar) // BE --> LE + + // Threshold variant scheme: + // R = K_Sum + // Where K_Sum is the sum of the public keys corresponding to + // the private nonce scalars of each group signature member. + // That is, R = k1G + ... + knG. + encodedGroupR := BigIntPointToEncodedBytes(pubNonceSum.GetX(), + pubNonceSum.GetY()) + + // h = hash512(k || A || M) + var hramDigest [64]byte + h := sha512.New() + h.Reset() + h.Write(encodedGroupR[:]) + h.Write(groupPub.Serialize()[:]) + h.Write(hash) + h.Sum(hramDigest[:0]) + var hramDigestReduced [32]byte + edwards25519.ScReduce(&hramDigestReduced, &hramDigest) + + // s = r + h * a + var localS [32]byte + privNonceLE := copyBytes(privNonce.Serialize()) + reverse(privNonceLE) // BE --> LE + edwards25519.ScMulAdd(&localS, &hramDigestReduced, privateScalar, + privNonceLE) + + signature := new([64]byte) + copy(signature[:], encodedGroupR[:]) + copy(signature[32:], localS[:]) + sigEd, err := ParseSignature(curve, signature[:]) + if err != nil { + return nil, nil, err + } + + return sigEd.GetR(), sigEd.GetS(), nil +} + +// Sign is the generalized and exported version of Ed25519 signing, that +// handles both standard private secrets and non-standard scalars. +func Sign(curve *TwistedEdwardsCurve, priv *PrivateKey, hash []byte) (r, + s *big.Int, err error) { + if priv == nil { + return nil, nil, fmt.Errorf("private key is nil") + } + if hash == nil { + return nil, nil, fmt.Errorf("message key is nil") + } + + if priv.secret == nil { + privLE := copyBytes(priv.Serialize()) + reverse(privLE) + nonce := nonceRFC6979(curve, privLE[:], hash, nil, nil) + return SignFromScalar(curve, priv, nonce, hash) + } + + return SignFromSecretNoReader(priv, hash) +} + +// Verify verifies a message 'hash' using the given public keys and signature. +func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool { + if pub == nil || hash == nil || r == nil || s == nil { + return false + } + + pubBytes := pub.Serialize() + sig := &Signature{r, s} + sigBytes := sig.Serialize() + pubArray := copyBytes(pubBytes) + sigArray := copyBytes64(sigBytes) + return ed25519.Verify(pubArray, hash, sigArray) +} diff --git a/hcec/edwards/primitives.go b/hcec/edwards/primitives.go index 59fd089..a84986a 100644 --- a/hcec/edwards/primitives.go +++ b/hcec/edwards/primitives.go @@ -1,296 +1,296 @@ -// Copyright (c) 2015-2017 The Decred developers -// Copyright (c) 2018-2020 The Hc developers -// Use of this source code is governed by an ISC -// license that can be found in the LICENSE file. - -package edwards - -import ( - "fmt" - "math/big" - - "github.com/agl/ed25519/edwards25519" -) - -// Some notes on primitives in Ed25519: -// 1) The integers themselves are stored as 32-byte little endian -// representations. If the store value is a point, the bit in -// the 31st byte, seventh position (b[31]>>7) represents whether -// or not the X value retrieved from the Y value should be -// negative or not. Remember, in affine EC space, the negative -// is P - positiveX. The rest of the 255 bits then represent -// the Y-value in little endian. -// 2) For high effiency, 40 byte field elements (10x int32s) are -// often used to represent integers. -// 3) For further increases in efficiency, the affine (cartesian) -// coordinates are converted into projective (extended or non- -// extended) formats, which include a Z and T or Z value -// respectively. -// 4) Almost *everything* is encoded in little endian, with the -// exception of ECDSA X and Y values of points in affine space. - -// reverse reverses a byte string. -func reverse(s *[32]byte) { - for i, j := 0, len(s)-1; i < j; i, j = i+1, j-1 { - s[i], s[j] = s[j], s[i] - } -} - -// copyBytes copies a byte slice to a 32 byte array. -func copyBytes(aB []byte) *[32]byte { - if aB == nil { - return nil - } - s := new([32]byte) - - // If we have a short byte string, expand - // it so that it's long enough. - aBLen := len(aB) - if aBLen < fieldIntSize { - diff := fieldIntSize - aBLen - for i := 0; i < diff; i++ { - aB = append([]byte{0x00}, aB...) - } - } - - for i := 0; i < fieldIntSize; i++ { - s[i] = aB[i] - } - - return s -} - -// copyBytes64 copies a byte slice to a 64 byte array. -func copyBytes64(aB []byte) *[64]byte { - if aB == nil { - return nil - } - - s := new([64]byte) - - // If we have a short byte string, expand - // it so that it's long enough. - aBLen := len(aB) - if aBLen < 64 { - diff := 64 - aBLen - for i := 0; i < diff; i++ { - aB = append([]byte{0x00}, aB...) - } - } - - for i := 0; i < 64; i++ { - s[i] = aB[i] - } - - return s -} - -// zeroSlice zeroes the memory of a scalar byte slice. -func zeroSlice(s []byte) { - for i := 0; i < PrivScalarSize; i++ { - s[i] = 0x00 - } - - return -} - -// BigIntToEncodedBytes converts a big integer into its corresponding -// 32 byte little endian representation. -func BigIntToEncodedBytes(a *big.Int) *[32]byte { - s := new([32]byte) - if a == nil { - return s - } - // Caveat: a can be longer than 32 bytes. - aB := a.Bytes() - - // If we have a short byte string, expand - // it so that it's long enough. - aBLen := len(aB) - if aBLen < fieldIntSize { - diff := fieldIntSize - aBLen - for i := 0; i < diff; i++ { - aB = append([]byte{0x00}, aB...) - } - } - - for i := 0; i < fieldIntSize; i++ { - s[i] = aB[i] - } - - // Reverse the byte string --> little endian after - // encoding. - reverse(s) - - return s -} - -// BigIntToEncodedBytesNoReverse converts a big integer into its corresponding -// 32 byte big endian representation. -func BigIntToEncodedBytesNoReverse(a *big.Int) *[32]byte { - s := new([32]byte) - if a == nil { - return s - } - // Caveat: a can be longer than 32 bytes. - aB := a.Bytes() - - // If we have a short byte string, expand - // it so that it's long enough. - aBLen := len(aB) - if aBLen < fieldIntSize { - diff := fieldIntSize - aBLen - for i := 0; i < diff; i++ { - aB = append([]byte{0x00}, aB...) - } - } - - for i := 0; i < fieldIntSize; i++ { - s[i] = aB[i] - } - - return s -} - -// BigIntToFieldElement converts a big little endian integer into its corresponding -// 40 byte field representation. -func BigIntToFieldElement(a *big.Int) *edwards25519.FieldElement { - aB := BigIntToEncodedBytes(a) - fe := new(edwards25519.FieldElement) - edwards25519.FeFromBytes(fe, aB) - return fe -} - -// BigIntPointToEncodedBytes converts an affine point to a compressed -// 32 byte integer representation. -func BigIntPointToEncodedBytes(x *big.Int, y *big.Int) *[32]byte { - s := BigIntToEncodedBytes(y) - xB := BigIntToEncodedBytes(x) - xFE := new(edwards25519.FieldElement) - edwards25519.FeFromBytes(xFE, xB) - isNegative := edwards25519.FeIsNegative(xFE) == 1 - - if isNegative { - s[31] |= (1 << 7) - } else { - s[31] &^= (1 << 7) - } - - return s -} - -// EncodedBytesToBigInt converts a 32 byte little endian representation of -// an integer into a big, big endian integer. -func EncodedBytesToBigInt(s *[32]byte) *big.Int { - // Use a copy so we don't screw up our original - // memory. - sCopy := new([32]byte) - for i := 0; i < fieldIntSize; i++ { - sCopy[i] = s[i] - } - reverse(sCopy) - - bi := new(big.Int).SetBytes(sCopy[:]) - - return bi -} - -// EncodedBytesToBigIntNoReverse converts a 32 byte big endian representation of -// an integer into a big little endian integer. -func EncodedBytesToBigIntNoReverse(s *[32]byte) *big.Int { - // Use a copy so we don't screw up our original - // memory. - sCopy := new([32]byte) - for i := 0; i < fieldIntSize; i++ { - sCopy[i] = s[i] - } - - bi := new(big.Int).SetBytes(sCopy[:]) - - return bi -} - -// extendedToBigAffine converts projective x, y, and z field elements into -// affine x and y coordinates, and returns whether or not the x value -// returned is negative. -func (curve *TwistedEdwardsCurve) extendedToBigAffine(xi, yi, - zi *edwards25519.FieldElement) (*big.Int, *big.Int, bool) { - var recip, x, y edwards25519.FieldElement - - // Normalize to Z=1. - edwards25519.FeInvert(&recip, zi) - edwards25519.FeMul(&x, xi, &recip) - edwards25519.FeMul(&y, yi, &recip) - - isNegative := edwards25519.FeIsNegative(&x) == 1 - - return FieldElementToBigInt(&x), FieldElementToBigInt(&y), isNegative -} - -// EncodedBytesToBigIntPoint converts a 32 byte representation of a point -// on the elliptical curve into a big integer point. It returns an error -// if the point does not fall on the curve. -func (curve *TwistedEdwardsCurve) EncodedBytesToBigIntPoint(s *[32]byte) (*big.Int, - *big.Int, error) { - sCopy := new([32]byte) - for i := 0; i < fieldIntSize; i++ { - sCopy[i] = s[i] - } - - xIsNegBytes := sCopy[31]>>7 == 1 - p := new(edwards25519.ExtendedGroupElement) - if !p.FromBytes(sCopy) { - return nil, nil, fmt.Errorf("point not on curve") - } - - // Normalize the X and Y coordinates in affine space. - x, y, isNegative := curve.extendedToBigAffine(&p.X, &p.Y, &p.Z) - - // We got the wrong sign; flip the bit and recalculate. - if xIsNegBytes != isNegative { - x.Sub(curve.P, x) - } - - // This should hopefully never happen, since the - // library itself should never let us create a bad - // point. - if !curve.IsOnCurve(x, y) { - return nil, nil, fmt.Errorf("point not on curve") - } - - return x, y, nil -} - -// EncodedBytesToFieldElement converts a 32 byte little endian integer into -// a field element. -func EncodedBytesToFieldElement(s *[32]byte) *edwards25519.FieldElement { - fe := new(edwards25519.FieldElement) - edwards25519.FeFromBytes(fe, s) - return fe -} - -// FieldElementToBigInt converts a 40 byte field element into a big int. -func FieldElementToBigInt(fe *edwards25519.FieldElement) *big.Int { - s := new([32]byte) - edwards25519.FeToBytes(s, fe) - reverse(s) - - aBI := new(big.Int).SetBytes(s[:]) - - return aBI -} - -// FieldElementToEncodedBytes converts a 40 byte field element into a 32 byte -// little endian integer. -func FieldElementToEncodedBytes(fe *edwards25519.FieldElement) *[32]byte { - s := new([32]byte) - edwards25519.FeToBytes(s, fe) - return s -} - -// invert inverts a big integer over the Ed25519 curve. -func (curve *TwistedEdwardsCurve) invert(a *big.Int) *big.Int { - sub2 := new(big.Int).Sub(curve.P, two) - inv := new(big.Int).Exp(a, sub2, curve.P) - return inv -} +// Copyright (c) 2015-2017 The Decred developers +// Copyright (c) 2018-2020 The Hc developers +// Use of this source code is governed by an ISC +// license that can be found in the LICENSE file. + +package edwards + +import ( + "fmt" + "math/big" + + "github.com/HcashOrg/hcd/hcec/ed25519/edwards25519" +) + +// Some notes on primitives in Ed25519: +// 1) The integers themselves are stored as 32-byte little endian +// representations. If the store value is a point, the bit in +// the 31st byte, seventh position (b[31]>>7) represents whether +// or not the X value retrieved from the Y value should be +// negative or not. Remember, in affine EC space, the negative +// is P - positiveX. The rest of the 255 bits then represent +// the Y-value in little endian. +// 2) For high effiency, 40 byte field elements (10x int32s) are +// often used to represent integers. +// 3) For further increases in efficiency, the affine (cartesian) +// coordinates are converted into projective (extended or non- +// extended) formats, which include a Z and T or Z value +// respectively. +// 4) Almost *everything* is encoded in little endian, with the +// exception of ECDSA X and Y values of points in affine space. + +// reverse reverses a byte string. +func reverse(s *[32]byte) { + for i, j := 0, len(s)-1; i < j; i, j = i+1, j-1 { + s[i], s[j] = s[j], s[i] + } +} + +// copyBytes copies a byte slice to a 32 byte array. +func copyBytes(aB []byte) *[32]byte { + if aB == nil { + return nil + } + s := new([32]byte) + + // If we have a short byte string, expand + // it so that it's long enough. + aBLen := len(aB) + if aBLen < fieldIntSize { + diff := fieldIntSize - aBLen + for i := 0; i < diff; i++ { + aB = append([]byte{0x00}, aB...) + } + } + + for i := 0; i < fieldIntSize; i++ { + s[i] = aB[i] + } + + return s +} + +// copyBytes64 copies a byte slice to a 64 byte array. +func copyBytes64(aB []byte) *[64]byte { + if aB == nil { + return nil + } + + s := new([64]byte) + + // If we have a short byte string, expand + // it so that it's long enough. + aBLen := len(aB) + if aBLen < 64 { + diff := 64 - aBLen + for i := 0; i < diff; i++ { + aB = append([]byte{0x00}, aB...) + } + } + + for i := 0; i < 64; i++ { + s[i] = aB[i] + } + + return s +} + +// zeroSlice zeroes the memory of a scalar byte slice. +func zeroSlice(s []byte) { + for i := 0; i < PrivScalarSize; i++ { + s[i] = 0x00 + } + + return +} + +// BigIntToEncodedBytes converts a big integer into its corresponding +// 32 byte little endian representation. +func BigIntToEncodedBytes(a *big.Int) *[32]byte { + s := new([32]byte) + if a == nil { + return s + } + // Caveat: a can be longer than 32 bytes. + aB := a.Bytes() + + // If we have a short byte string, expand + // it so that it's long enough. + aBLen := len(aB) + if aBLen < fieldIntSize { + diff := fieldIntSize - aBLen + for i := 0; i < diff; i++ { + aB = append([]byte{0x00}, aB...) + } + } + + for i := 0; i < fieldIntSize; i++ { + s[i] = aB[i] + } + + // Reverse the byte string --> little endian after + // encoding. + reverse(s) + + return s +} + +// BigIntToEncodedBytesNoReverse converts a big integer into its corresponding +// 32 byte big endian representation. +func BigIntToEncodedBytesNoReverse(a *big.Int) *[32]byte { + s := new([32]byte) + if a == nil { + return s + } + // Caveat: a can be longer than 32 bytes. + aB := a.Bytes() + + // If we have a short byte string, expand + // it so that it's long enough. + aBLen := len(aB) + if aBLen < fieldIntSize { + diff := fieldIntSize - aBLen + for i := 0; i < diff; i++ { + aB = append([]byte{0x00}, aB...) + } + } + + for i := 0; i < fieldIntSize; i++ { + s[i] = aB[i] + } + + return s +} + +// BigIntToFieldElement converts a big little endian integer into its corresponding +// 40 byte field representation. +func BigIntToFieldElement(a *big.Int) *edwards25519.FieldElement { + aB := BigIntToEncodedBytes(a) + fe := new(edwards25519.FieldElement) + edwards25519.FeFromBytes(fe, aB) + return fe +} + +// BigIntPointToEncodedBytes converts an affine point to a compressed +// 32 byte integer representation. +func BigIntPointToEncodedBytes(x *big.Int, y *big.Int) *[32]byte { + s := BigIntToEncodedBytes(y) + xB := BigIntToEncodedBytes(x) + xFE := new(edwards25519.FieldElement) + edwards25519.FeFromBytes(xFE, xB) + isNegative := edwards25519.FeIsNegative(xFE) == 1 + + if isNegative { + s[31] |= (1 << 7) + } else { + s[31] &^= (1 << 7) + } + + return s +} + +// EncodedBytesToBigInt converts a 32 byte little endian representation of +// an integer into a big, big endian integer. +func EncodedBytesToBigInt(s *[32]byte) *big.Int { + // Use a copy so we don't screw up our original + // memory. + sCopy := new([32]byte) + for i := 0; i < fieldIntSize; i++ { + sCopy[i] = s[i] + } + reverse(sCopy) + + bi := new(big.Int).SetBytes(sCopy[:]) + + return bi +} + +// EncodedBytesToBigIntNoReverse converts a 32 byte big endian representation of +// an integer into a big little endian integer. +func EncodedBytesToBigIntNoReverse(s *[32]byte) *big.Int { + // Use a copy so we don't screw up our original + // memory. + sCopy := new([32]byte) + for i := 0; i < fieldIntSize; i++ { + sCopy[i] = s[i] + } + + bi := new(big.Int).SetBytes(sCopy[:]) + + return bi +} + +// extendedToBigAffine converts projective x, y, and z field elements into +// affine x and y coordinates, and returns whether or not the x value +// returned is negative. +func (curve *TwistedEdwardsCurve) extendedToBigAffine(xi, yi, + zi *edwards25519.FieldElement) (*big.Int, *big.Int, bool) { + var recip, x, y edwards25519.FieldElement + + // Normalize to Z=1. + edwards25519.FeInvert(&recip, zi) + edwards25519.FeMul(&x, xi, &recip) + edwards25519.FeMul(&y, yi, &recip) + + isNegative := edwards25519.FeIsNegative(&x) == 1 + + return FieldElementToBigInt(&x), FieldElementToBigInt(&y), isNegative +} + +// EncodedBytesToBigIntPoint converts a 32 byte representation of a point +// on the elliptical curve into a big integer point. It returns an error +// if the point does not fall on the curve. +func (curve *TwistedEdwardsCurve) EncodedBytesToBigIntPoint(s *[32]byte) (*big.Int, + *big.Int, error) { + sCopy := new([32]byte) + for i := 0; i < fieldIntSize; i++ { + sCopy[i] = s[i] + } + + xIsNegBytes := sCopy[31]>>7 == 1 + p := new(edwards25519.ExtendedGroupElement) + if !p.FromBytes(sCopy) { + return nil, nil, fmt.Errorf("point not on curve") + } + + // Normalize the X and Y coordinates in affine space. + x, y, isNegative := curve.extendedToBigAffine(&p.X, &p.Y, &p.Z) + + // We got the wrong sign; flip the bit and recalculate. + if xIsNegBytes != isNegative { + x.Sub(curve.P, x) + } + + // This should hopefully never happen, since the + // library itself should never let us create a bad + // point. + if !curve.IsOnCurve(x, y) { + return nil, nil, fmt.Errorf("point not on curve") + } + + return x, y, nil +} + +// EncodedBytesToFieldElement converts a 32 byte little endian integer into +// a field element. +func EncodedBytesToFieldElement(s *[32]byte) *edwards25519.FieldElement { + fe := new(edwards25519.FieldElement) + edwards25519.FeFromBytes(fe, s) + return fe +} + +// FieldElementToBigInt converts a 40 byte field element into a big int. +func FieldElementToBigInt(fe *edwards25519.FieldElement) *big.Int { + s := new([32]byte) + edwards25519.FeToBytes(s, fe) + reverse(s) + + aBI := new(big.Int).SetBytes(s[:]) + + return aBI +} + +// FieldElementToEncodedBytes converts a 40 byte field element into a 32 byte +// little endian integer. +func FieldElementToEncodedBytes(fe *edwards25519.FieldElement) *[32]byte { + s := new([32]byte) + edwards25519.FeToBytes(s, fe) + return s +} + +// invert inverts a big integer over the Ed25519 curve. +func (curve *TwistedEdwardsCurve) invert(a *big.Int) *big.Int { + sub2 := new(big.Int).Sub(curve.P, two) + inv := new(big.Int).Exp(a, sub2, curve.P) + return inv +} diff --git a/hcec/edwards/privkey.go b/hcec/edwards/privkey.go index ac25b3d..9467427 100644 --- a/hcec/edwards/privkey.go +++ b/hcec/edwards/privkey.go @@ -1,203 +1,203 @@ -// Copyright (c) 2013-2014 The btcsuite developers -// Copyright (c) 2015-2017 The Decred developers -// Copyright (c) 2018-2020 The Hc developers -// Use of this source code is governed by an ISC -// license that can be found in the LICENSE file. - -package edwards - -import ( - "bytes" - "crypto/ecdsa" - "crypto/rand" - "crypto/sha512" - "fmt" - "math/big" - - "github.com/agl/ed25519" -) - -// These constants define the lengths of serialized private keys. -const ( - PrivScalarSize = 32 - PrivKeyBytesLen = 64 -) - -// PrivateKey wraps an ecdsa.PrivateKey as a convenience mainly for signing -// things with the the private key without having to directly import the ecdsa -// package. -type PrivateKey struct { - ecPk *ecdsa.PrivateKey - secret *[32]byte -} - -// NewPrivateKey instantiates a new private key from a scalar encoded as a -// big integer. -func NewPrivateKey(curve *TwistedEdwardsCurve, d *big.Int) *PrivateKey { - dArray := BigIntToEncodedBytes(d) - priv, _ := PrivKeyFromSecret(curve, dArray[:]) - return priv -} - -// GeneratePrivateKey is a wrapper for ecdsa.GenerateKey that returns a -// PrivateKey instead of the normal ecdsa.PrivateKey. -func GeneratePrivateKey(curve *TwistedEdwardsCurve) (*PrivateKey, error) { - key, err := ecdsa.GenerateKey(curve, rand.Reader) - if err != nil { - return nil, err - } - - pk := new(PrivateKey) - pk.ecPk = key - - return pk, nil -} - -// computeScalar obtains a private scalar from a private key. -func computeScalar(privateKey *[PrivKeyBytesLen]byte) *[PrivScalarSize]byte { - h := sha512.New() - h.Write(privateKey[:32]) - digest := h.Sum(nil) - - digest[0] &= 248 // Make a multiple of 8 - digest[31] &= 127 // Zero the first bit of this byte - digest[31] |= 64 // Enable the seventh bit - - var hBytes [PrivScalarSize]byte - copy(hBytes[:], digest) - - return &hBytes -} - -// PrivKeyFromBytes returns a private and public key for `curve' based on the -// private key passed as an argument as a byte slice. -func PrivKeyFromBytes(curve *TwistedEdwardsCurve, - pkBytes []byte) (*PrivateKey, *PublicKey) { - if len(pkBytes) != PrivKeyBytesLen { - return nil, nil - } - pk := copyBytes64(pkBytes) - - // The ed25519 library does a weird thing where it generates a - // private key 64 bytes long, and stores the private scalar in - // the first 32 bytes and the public key in the last 32 bytes. - // So, make sure we only grab the actual scalar we care about. - privKeyBytes := pk[0:32] - pubKeyBytes := pk[32:64] - pubKey, err := ParsePubKey(curve, pubKeyBytes) - if err != nil { - return nil, nil - } - - priv := &ecdsa.PrivateKey{ - PublicKey: *pubKey.ToECDSA(), - D: new(big.Int).SetBytes(computeScalar(pk)[:]), - } - privEd := new(PrivateKey) - privEd.ecPk = priv - privEd.secret = copyBytes(privKeyBytes) - - return privEd, (*PublicKey)(&priv.PublicKey) -} - -// PrivKeyFromSecret returns a private and public key for `curve' based on the -// 32-byte private key secret passed as an argument as a byte slice. -func PrivKeyFromSecret(curve *TwistedEdwardsCurve, s []byte) (*PrivateKey, - *PublicKey) { - if len(s) != PrivKeyBytesLen/2 { - return nil, nil - } - - // Instead of using rand to generate our scalar, use the scalar - // itself as a reader. - sReader := bytes.NewReader(s) - _, pk, err := ed25519.GenerateKey(sReader) - if err != nil { - return nil, nil - } - - return PrivKeyFromBytes(curve, pk[:]) -} - -// PrivKeyFromScalar returns a private and public key for `curve' based on the -// 32-byte private scalar passed as an argument as a byte slice (encoded big -// endian int). -func PrivKeyFromScalar(curve *TwistedEdwardsCurve, p []byte) (*PrivateKey, - *PublicKey, error) { - if len(p) != PrivScalarSize { - return nil, nil, fmt.Errorf("bad private scalar size") - } - - pk := new(PrivateKey) - pk.ecPk = new(ecdsa.PrivateKey) - pk.ecPk.D = new(big.Int).SetBytes(p) - - // The scalar must be in the subgroup. - if pk.ecPk.D.Cmp(curve.N) > 0 { - return nil, nil, fmt.Errorf("not on subgroup (>N)") - } - - // The scalar must not be zero or negative. - if pk.ecPk.D.Cmp(zero) <= 0 { - return nil, nil, fmt.Errorf("zero or negative scalar") - } - - pk.ecPk.Curve = curve - pk.ecPk.PublicKey.X, pk.ecPk.PublicKey.Y = - curve.ScalarBaseMult(pk.GetD().Bytes()) - - if pk.ecPk.PublicKey.X == nil || pk.ecPk.PublicKey.Y == nil { - return nil, nil, fmt.Errorf("scalarbase mult failure to get pubkey") - } - pub := PublicKey(pk.ecPk.PublicKey) - - return pk, &pub, nil -} - -// Public returns the PublicKey corresponding to this private key. -func (p PrivateKey) Public() (*big.Int, *big.Int) { - return p.ecPk.PublicKey.X, p.ecPk.PublicKey.Y -} - -// ToECDSA returns the private key as a *ecdsa.PrivateKey. -func (p PrivateKey) ToECDSA() *ecdsa.PrivateKey { - return p.ecPk -} - -// Serialize returns the private key as a 32 byte big endian number. -func (p PrivateKey) Serialize() []byte { - if p.ecPk.D == nil || - p.ecPk.PublicKey.X == nil || - p.ecPk.PublicKey.Y == nil { - return nil - } - privateScalar := copyBytes(p.ecPk.D.Bytes()) - - return privateScalar[:] -} - -// SerializeSecret returns the 32 byte secret along with its public key as 64 -// bytes. -func (p PrivateKey) SerializeSecret() []byte { - if p.secret == nil { - return nil - } - - // This is little endian. - pubX, pubY := p.Public() - spk := BigIntPointToEncodedBytes(pubX, pubY) - - all := append(p.secret[:], spk[:]...) - - return all -} - -// GetD satisfies the chainec PrivateKey interface. -func (p PrivateKey) GetD() *big.Int { - return p.ecPk.D -} - -// GetType satisfies the chainec PrivateKey interface. -func (p PrivateKey) GetType() int { - return ecTypeEdwards -} +// Copyright (c) 2013-2014 The btcsuite developers +// Copyright (c) 2015-2017 The Decred developers +// Copyright (c) 2018-2020 The Hc developers +// Use of this source code is governed by an ISC +// license that can be found in the LICENSE file. + +package edwards + +import ( + "bytes" + "crypto/ecdsa" + "crypto/rand" + "crypto/sha512" + "fmt" + "math/big" + + "github.com/HcashOrg/hcd/hcec/ed25519" +) + +// These constants define the lengths of serialized private keys. +const ( + PrivScalarSize = 32 + PrivKeyBytesLen = 64 +) + +// PrivateKey wraps an ecdsa.PrivateKey as a convenience mainly for signing +// things with the the private key without having to directly import the ecdsa +// package. +type PrivateKey struct { + ecPk *ecdsa.PrivateKey + secret *[32]byte +} + +// NewPrivateKey instantiates a new private key from a scalar encoded as a +// big integer. +func NewPrivateKey(curve *TwistedEdwardsCurve, d *big.Int) *PrivateKey { + dArray := BigIntToEncodedBytes(d) + priv, _ := PrivKeyFromSecret(curve, dArray[:]) + return priv +} + +// GeneratePrivateKey is a wrapper for ecdsa.GenerateKey that returns a +// PrivateKey instead of the normal ecdsa.PrivateKey. +func GeneratePrivateKey(curve *TwistedEdwardsCurve) (*PrivateKey, error) { + key, err := ecdsa.GenerateKey(curve, rand.Reader) + if err != nil { + return nil, err + } + + pk := new(PrivateKey) + pk.ecPk = key + + return pk, nil +} + +// computeScalar obtains a private scalar from a private key. +func computeScalar(privateKey *[PrivKeyBytesLen]byte) *[PrivScalarSize]byte { + h := sha512.New() + h.Write(privateKey[:32]) + digest := h.Sum(nil) + + digest[0] &= 248 // Make a multiple of 8 + digest[31] &= 127 // Zero the first bit of this byte + digest[31] |= 64 // Enable the seventh bit + + var hBytes [PrivScalarSize]byte + copy(hBytes[:], digest) + + return &hBytes +} + +// PrivKeyFromBytes returns a private and public key for `curve' based on the +// private key passed as an argument as a byte slice. +func PrivKeyFromBytes(curve *TwistedEdwardsCurve, + pkBytes []byte) (*PrivateKey, *PublicKey) { + if len(pkBytes) != PrivKeyBytesLen { + return nil, nil + } + pk := copyBytes64(pkBytes) + + // The ed25519 library does a weird thing where it generates a + // private key 64 bytes long, and stores the private scalar in + // the first 32 bytes and the public key in the last 32 bytes. + // So, make sure we only grab the actual scalar we care about. + privKeyBytes := pk[0:32] + pubKeyBytes := pk[32:64] + pubKey, err := ParsePubKey(curve, pubKeyBytes) + if err != nil { + return nil, nil + } + + priv := &ecdsa.PrivateKey{ + PublicKey: *pubKey.ToECDSA(), + D: new(big.Int).SetBytes(computeScalar(pk)[:]), + } + privEd := new(PrivateKey) + privEd.ecPk = priv + privEd.secret = copyBytes(privKeyBytes) + + return privEd, (*PublicKey)(&priv.PublicKey) +} + +// PrivKeyFromSecret returns a private and public key for `curve' based on the +// 32-byte private key secret passed as an argument as a byte slice. +func PrivKeyFromSecret(curve *TwistedEdwardsCurve, s []byte) (*PrivateKey, + *PublicKey) { + if len(s) != PrivKeyBytesLen/2 { + return nil, nil + } + + // Instead of using rand to generate our scalar, use the scalar + // itself as a reader. + sReader := bytes.NewReader(s) + _, pk, err := ed25519.GenerateKey(sReader) + if err != nil { + return nil, nil + } + + return PrivKeyFromBytes(curve, pk[:]) +} + +// PrivKeyFromScalar returns a private and public key for `curve' based on the +// 32-byte private scalar passed as an argument as a byte slice (encoded big +// endian int). +func PrivKeyFromScalar(curve *TwistedEdwardsCurve, p []byte) (*PrivateKey, + *PublicKey, error) { + if len(p) != PrivScalarSize { + return nil, nil, fmt.Errorf("bad private scalar size") + } + + pk := new(PrivateKey) + pk.ecPk = new(ecdsa.PrivateKey) + pk.ecPk.D = new(big.Int).SetBytes(p) + + // The scalar must be in the subgroup. + if pk.ecPk.D.Cmp(curve.N) > 0 { + return nil, nil, fmt.Errorf("not on subgroup (>N)") + } + + // The scalar must not be zero or negative. + if pk.ecPk.D.Cmp(zero) <= 0 { + return nil, nil, fmt.Errorf("zero or negative scalar") + } + + pk.ecPk.Curve = curve + pk.ecPk.PublicKey.X, pk.ecPk.PublicKey.Y = + curve.ScalarBaseMult(pk.GetD().Bytes()) + + if pk.ecPk.PublicKey.X == nil || pk.ecPk.PublicKey.Y == nil { + return nil, nil, fmt.Errorf("scalarbase mult failure to get pubkey") + } + pub := PublicKey(pk.ecPk.PublicKey) + + return pk, &pub, nil +} + +// Public returns the PublicKey corresponding to this private key. +func (p PrivateKey) Public() (*big.Int, *big.Int) { + return p.ecPk.PublicKey.X, p.ecPk.PublicKey.Y +} + +// ToECDSA returns the private key as a *ecdsa.PrivateKey. +func (p PrivateKey) ToECDSA() *ecdsa.PrivateKey { + return p.ecPk +} + +// Serialize returns the private key as a 32 byte big endian number. +func (p PrivateKey) Serialize() []byte { + if p.ecPk.D == nil || + p.ecPk.PublicKey.X == nil || + p.ecPk.PublicKey.Y == nil { + return nil + } + privateScalar := copyBytes(p.ecPk.D.Bytes()) + + return privateScalar[:] +} + +// SerializeSecret returns the 32 byte secret along with its public key as 64 +// bytes. +func (p PrivateKey) SerializeSecret() []byte { + if p.secret == nil { + return nil + } + + // This is little endian. + pubX, pubY := p.Public() + spk := BigIntPointToEncodedBytes(pubX, pubY) + + all := append(p.secret[:], spk[:]...) + + return all +} + +// GetD satisfies the chainec PrivateKey interface. +func (p PrivateKey) GetD() *big.Int { + return p.ecPk.D +} + +// GetType satisfies the chainec PrivateKey interface. +func (p PrivateKey) GetType() int { + return ecTypeEdwards +}