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crypto/bls12381: update kilic library

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This commit is contained in:
Marius van der Wijden 2024-02-05 15:33:47 +01:00
parent c170cc0ab0
commit 00a3896dc5
35 changed files with 18210 additions and 2701 deletions
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122
core/vm/contracts.go
View file

@ -679,11 +679,11 @@ func (c *bls12381G1Add) Run(input []byte) ([]byte, error) {
g := bls12381.NewG1()
// Decode G1 point p_0
if p0, err = g.DecodePoint(input[:128]); err != nil {
if p0, err = decodePointG1(g, input[:128]); err != nil {
return nil, err
}
// Decode G1 point p_1
if p1, err = g.DecodePoint(input[128:]); err != nil {
if p1, err = decodePointG1(g, input[128:]); err != nil {
return nil, err
}
@ -692,7 +692,7 @@ func (c *bls12381G1Add) Run(input []byte) ([]byte, error) {
g.Add(r, p0, p1)
// Encode the G1 point result into 128 bytes
return g.EncodePoint(r), nil
return encodePointG1(g, r), nil
}
// bls12381G1Mul implements EIP-2537 G1Mul precompile.
@ -717,7 +717,7 @@ func (c *bls12381G1Mul) Run(input []byte) ([]byte, error) {
g := bls12381.NewG1()
// Decode G1 point
if p0, err = g.DecodePoint(input[:128]); err != nil {
if p0, err = decodePointG1(g, input[:128]); err != nil {
return nil, err
}
// Decode scalar value
@ -725,10 +725,10 @@ func (c *bls12381G1Mul) Run(input []byte) ([]byte, error) {
// Compute r = e * p_0
r := g.New()
g.MulScalar(r, p0, e)
g.MulScalarBig(r, p0, e)
// Encode the G1 point into 128 bytes
return g.EncodePoint(r), nil
return encodePointG1(g, r), nil
}
// bls12381G1MultiExp implements EIP-2537 G1MultiExp precompile.
@ -773,7 +773,7 @@ func (c *bls12381G1MultiExp) Run(input []byte) ([]byte, error) {
off := 160 * i
t0, t1, t2 := off, off+128, off+160
// Decode G1 point
if points[i], err = g.DecodePoint(input[t0:t1]); err != nil {
if points[i], err = decodePointG1(g, input[t0:t1]); err != nil {
return nil, err
}
// Decode scalar value
@ -782,10 +782,10 @@ func (c *bls12381G1MultiExp) Run(input []byte) ([]byte, error) {
// Compute r = e_0 * p_0 + e_1 * p_1 + ... + e_(k-1) * p_(k-1)
r := g.New()
g.MultiExp(r, points, scalars)
g.MultiExpBig(r, points, scalars)
// Encode the G1 point to 128 bytes
return g.EncodePoint(r), nil
return encodePointG1(g, r), nil
}
// bls12381G2Add implements EIP-2537 G2Add precompile.
@ -811,11 +811,11 @@ func (c *bls12381G2Add) Run(input []byte) ([]byte, error) {
r := g.New()
// Decode G2 point p_0
if p0, err = g.DecodePoint(input[:256]); err != nil {
if p0, err = decodePointG2(g, input[:256]); err != nil {
return nil, err
}
// Decode G2 point p_1
if p1, err = g.DecodePoint(input[256:]); err != nil {
if p1, err = decodePointG2(g, input[256:]); err != nil {
return nil, err
}
@ -823,7 +823,7 @@ func (c *bls12381G2Add) Run(input []byte) ([]byte, error) {
g.Add(r, p0, p1)
// Encode the G2 point into 256 bytes
return g.EncodePoint(r), nil
return encodePointG2(g, r), nil
}
// bls12381G2Mul implements EIP-2537 G2Mul precompile.
@ -848,7 +848,7 @@ func (c *bls12381G2Mul) Run(input []byte) ([]byte, error) {
g := bls12381.NewG2()
// Decode G2 point
if p0, err = g.DecodePoint(input[:256]); err != nil {
if p0, err = decodePointG2(g, input[:256]); err != nil {
return nil, err
}
// Decode scalar value
@ -856,10 +856,10 @@ func (c *bls12381G2Mul) Run(input []byte) ([]byte, error) {
// Compute r = e * p_0
r := g.New()
g.MulScalar(r, p0, e)
g.MulScalarBig(r, p0, e)
// Encode the G2 point into 256 bytes
return g.EncodePoint(r), nil
return encodePointG2(g, r), nil
}
// bls12381G2MultiExp implements EIP-2537 G2MultiExp precompile.
@ -903,8 +903,8 @@ func (c *bls12381G2MultiExp) Run(input []byte) ([]byte, error) {
for i := 0; i < k; i++ {
off := 288 * i
t0, t1, t2 := off, off+256, off+288
// Decode G1 point
if points[i], err = g.DecodePoint(input[t0:t1]); err != nil {
// Decode G2 point
if points[i], err = decodePointG2(g, input[t0:t1]); err != nil {
return nil, err
}
// Decode scalar value
@ -913,10 +913,10 @@ func (c *bls12381G2MultiExp) Run(input []byte) ([]byte, error) {
// Compute r = e_0 * p_0 + e_1 * p_1 + ... + e_(k-1) * p_(k-1)
r := g.New()
g.MultiExp(r, points, scalars)
g.MultiExpBig(r, points, scalars)
// Encode the G2 point to 256 bytes.
return g.EncodePoint(r), nil
return encodePointG2(g, r), nil
}
// bls12381Pairing implements EIP-2537 Pairing precompile.
@ -940,7 +940,7 @@ func (c *bls12381Pairing) Run(input []byte) ([]byte, error) {
}
// Initialize BLS12-381 pairing engine
e := bls12381.NewPairingEngine()
e := bls12381.NewEngine()
g1, g2 := e.G1, e.G2
// Decode pairs
@ -949,12 +949,12 @@ func (c *bls12381Pairing) Run(input []byte) ([]byte, error) {
t0, t1, t2 := off, off+128, off+384
// Decode G1 point
p1, err := g1.DecodePoint(input[t0:t1])
p1, err := decodePointG1(g1, input[t0:t1])
if err != nil {
return nil, err
}
// Decode G2 point
p2, err := g2.DecodePoint(input[t1:t2])
p2, err := decodePointG2(g2, input[t1:t2])
if err != nil {
return nil, err
}
@ -981,6 +981,55 @@ func (c *bls12381Pairing) Run(input []byte) ([]byte, error) {
return out, nil
}
func decodePointG1(g *bls12381.G1, in []byte) (*bls12381.PointG1, error) {
if len(in) != 128 {
return nil, errors.New("invalid g1 point length")
}
pointBytes := make([]byte, 96)
// decode x
xBytes, err := decodeBLS12381FieldElement(in[:64])
if err != nil {
return nil, err
}
// decode y
yBytes, err := decodeBLS12381FieldElement(in[64:])
if err != nil {
return nil, err
}
copy(pointBytes[:48], xBytes)
copy(pointBytes[48:], yBytes)
return g.FromBytes(pointBytes)
}
// decodePointG2 given encoded (x, y) coordinates in 256 bytes returns a valid G2 Point.
func decodePointG2(g *bls12381.G2, in []byte) (*bls12381.PointG2, error) {
if len(in) != 256 {
return nil, errors.New("invalid g2 point length")
}
pointBytes := make([]byte, 192)
x0Bytes, err := decodeBLS12381FieldElement(in[:64])
if err != nil {
return nil, err
}
x1Bytes, err := decodeBLS12381FieldElement(in[64:128])
if err != nil {
return nil, err
}
y0Bytes, err := decodeBLS12381FieldElement(in[128:192])
if err != nil {
return nil, err
}
y1Bytes, err := decodeBLS12381FieldElement(in[192:])
if err != nil {
return nil, err
}
copy(pointBytes[:48], x1Bytes)
copy(pointBytes[48:96], x0Bytes)
copy(pointBytes[96:144], y1Bytes)
copy(pointBytes[144:192], y0Bytes)
return g.FromBytes(pointBytes)
}
// decodeBLS12381FieldElement decodes BLS12-381 elliptic curve field element.
// Removes top 16 bytes of 64 byte input.
func decodeBLS12381FieldElement(in []byte) ([]byte, error) {
@ -998,6 +1047,31 @@ func decodeBLS12381FieldElement(in []byte) ([]byte, error) {
return out, nil
}
// encodePointG1 encodes a point into 128 bytes.
func encodePointG1(g *bls12381.G1, p *bls12381.PointG1) []byte {
outRaw := g.ToBytes(p)
out := make([]byte, 128)
// encode x
copy(out[16:], outRaw[:48])
// encode y
copy(out[64+16:], outRaw[48:])
return out
}
// encodePointG2 encodes a point into 256 bytes.
func encodePointG2(g *bls12381.G2, p *bls12381.PointG2) []byte {
// outRaw is 96 bytes
outRaw := g.ToBytes(p)
out := make([]byte, 256)
// encode x
copy(out[16:16+48], outRaw[48:96])
copy(out[80:80+48], outRaw[:48])
// encode y
copy(out[144:144+48], outRaw[144:])
copy(out[208:208+48], outRaw[96:144])
return out
}
// bls12381MapG1 implements EIP-2537 MapG1 precompile.
type bls12381MapG1 struct{}
@ -1030,7 +1104,7 @@ func (c *bls12381MapG1) Run(input []byte) ([]byte, error) {
}
// Encode the G1 point to 128 bytes
return g.EncodePoint(r), nil
return encodePointG1(g, r), nil
}
// bls12381MapG2 implements EIP-2537 MapG2 precompile.
@ -1072,7 +1146,7 @@ func (c *bls12381MapG2) Run(input []byte) ([]byte, error) {
}
// Encode the G2 point to 256 bytes
return g.EncodePoint(r), nil
return encodePointG2(g, r), nil
}
// kzgPointEvaluation implements the EIP-4844 point evaluation precompile.

4
core/vm/contracts_test.go
View file

@ -372,7 +372,7 @@ func BenchmarkPrecompiledBLS12381G1MultiExpWorstCase(b *testing.B) {
Name: "WorstCaseG1",
NoBenchmark: false,
}
benchmarkPrecompiled("0c", testcase, b)
benchmarkPrecompiled("f0c", testcase, b)
}
// BenchmarkPrecompiledBLS12381G2MultiExpWorstCase benchmarks the worst case we could find that still fits a gaslimit of 10MGas.
@ -393,5 +393,5 @@ func BenchmarkPrecompiledBLS12381G2MultiExpWorstCase(b *testing.B) {
Name: "WorstCaseG2",
NoBenchmark: false,
}
benchmarkPrecompiled("0f", testcase, b)
benchmarkPrecompiled("f0f", testcase, b)
}

197
crypto/bls12381/arithmetic_decl.go
View file

@ -1,21 +1,4 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
//go:build (amd64 && blsasm) || (amd64 && blsadx)
// +build amd64,blsasm amd64,blsadx
// +build amd64,!generic
package bls12381
@ -24,13 +7,22 @@ import (
)
func init() {
if !enableADX || !cpu.X86.HasADX || !cpu.X86.HasBMI2 {
if !cpu.X86.HasADX || !cpu.X86.HasBMI2 {
mul = mulNoADX
wmul = wmulNoADX
fromWide = montRedNoADX
mulFR = mulNoADXFR
wmulFR = wmulNoADXFR
wfp2Mul = wfp2MulGeneric
wfp2Square = wfp2SquareGeneric
}
}
// Use ADX backend for default
var mul func(c, a, b *fe) = mulADX
var wmul func(c *wfe, a, b *fe) = wmulADX
var fromWide func(c *fe, w *wfe) = montRedADX
var wfp2Mul func(c *wfe2, a, b *fe2) = wfp2MulADX
var wfp2Square func(c *wfe2, b *fe2) = wfp2SquareADX
func square(c, a *fe) {
mul(c, a, a)
@ -65,6 +57,9 @@ func doubleAssign(a *fe)
//go:noescape
func ldouble(c, a *fe)
//go:noescape
func ldoubleAssign(a *fe)
//go:noescape
func sub(c, a, b *fe)
@ -82,3 +77,165 @@ func mulNoADX(c, a, b *fe)
//go:noescape
func mulADX(c, a, b *fe)
//go:noescape
func wmulNoADX(c *wfe, a, b *fe)
//go:noescape
func wmulADX(c *wfe, a, b *fe)
//go:noescape
func montRedNoADX(a *fe, w *wfe)
//go:noescape
func montRedADX(a *fe, w *wfe)
//go:noescape
func lwadd(c, a, b *wfe)
//go:noescape
func lwaddAssign(a, b *wfe)
//go:noescape
func wadd(c, a, b *wfe)
//go:noescape
func lwdouble(c, a *wfe)
//go:noescape
func wdouble(c, a *wfe)
//go:noescape
func lwsub(c, a, b *wfe)
//go:noescape
func lwsubAssign(a, b *wfe)
//go:noescape
func wsub(c, a, b *wfe)
//go:noescape
func fp2Add(c, a, b *fe2)
//go:noescape
func fp2AddAssign(a, b *fe2)
//go:noescape
func fp2Ladd(c, a, b *fe2)
//go:noescape
func fp2LaddAssign(a, b *fe2)
//go:noescape
func fp2DoubleAssign(a *fe2)
//go:noescape
func fp2Double(c, a *fe2)
//go:noescape
func fp2Sub(c, a, b *fe2)
//go:noescape
func fp2SubAssign(a, b *fe2)
//go:noescape
func mulByNonResidue(c, a *fe2)
//go:noescape
func mulByNonResidueAssign(a *fe2)
//go:noescape
func wfp2Add(c, a, b *wfe2)
//go:noescape
func wfp2AddAssign(a, b *wfe2)
//go:noescape
func wfp2Ladd(c, a, b *wfe2)
//go:noescape
func wfp2LaddAssign(a, b *wfe2)
//go:noescape
func wfp2AddMixed(c, a, b *wfe2)
//go:noescape
func wfp2AddMixedAssign(a, b *wfe2)
//go:noescape
func wfp2Sub(c, a, b *wfe2)
//go:noescape
func wfp2SubAssign(a, b *wfe2)
//go:noescape
func wfp2SubMixed(c, a, b *wfe2)
//go:noescape
func wfp2SubMixedAssign(a, b *wfe2)
//go:noescape
func wfp2Double(c, a *wfe2)
//go:noescape
func wfp2DoubleAssign(a *wfe2)
//go:noescape
func wfp2MulByNonResidue(c, a *wfe2)
//go:noescape
func wfp2MulByNonResidueAssign(a *wfe2)
//go:noescape
func wfp2SquareADX(c *wfe2, a *fe2)
//go:noescape
func wfp2MulADX(c *wfe2, a, b *fe2)
var mulFR func(c, a, b *Fr) = mulADXFR
var wmulFR func(c *wideFr, a, b *Fr) = wmulADXFR
func squareFR(c, a *Fr) {
mulFR(c, a, a)
}
func negFR(c, a *Fr) {
if a.IsZero() {
c.Set(a)
} else {
_negFR(c, a)
}
}
//go:noescape
func addFR(c, a, b *Fr)
//go:noescape
func laddAssignFR(a, b *Fr)
//go:noescape
func doubleFR(c, a *Fr)
//go:noescape
func subFR(c, a, b *Fr)
//go:noescape
func lsubAssignFR(a, b *Fr)
//go:noescape
func _negFR(c, a *Fr)
//go:noescape
func mulNoADXFR(c, a, b *Fr)
//go:noescape
func mulADXFR(c, a, b *Fr)
//go:noescape
func wmulADXFR(c *wideFr, a, b *Fr)
//go:noescape
func wmulNoADXFR(c *wideFr, a, b *Fr)
//go:noescape
func waddFR(a, b *wideFr)

511
crypto/bls12381/arithmetic_fallback.go
View file

@ -1,8 +1,6 @@
// Native go field arithmetic code is generated with 'goff'
// https://github.com/ConsenSys/goff
// Many function signature of field operations are renamed.
// +build !amd64 generic
// Copyright 2020 ConsenSys AG
// Copyright 2020 ConsenSys Software Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
@ -16,23 +14,7 @@
// See the License for the specific language governing permissions and
// limitations under the License.
// field modulus q =
//
// 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787
// Code generated by goff DO NOT EDIT
// goff version: v0.1.0 - build: 790f1f56eac432441e043abff8819eacddd1d668
// fe are assumed to be in Montgomery form in all methods
// /!\ WARNING /!\
// this code has not been audited and is provided as-is. In particular,
// there is no security guarantees such as constant time implementation
// or side-channel attack resistance
// /!\ WARNING /!\
// Package bls (generated by goff) contains field arithmetics operations
//go:build !amd64 || (!blsasm && !blsadx)
// +build !amd64 !blsasm,!blsadx
// Code generated by goff (v0.3.5) DO NOT EDIT
package bls12381
@ -40,440 +22,6 @@ import (
"math/bits"
)
func add(z, x, y *fe) {
var carry uint64
z[0], carry = bits.Add64(x[0], y[0], 0)
z[1], carry = bits.Add64(x[1], y[1], carry)
z[2], carry = bits.Add64(x[2], y[2], carry)
z[3], carry = bits.Add64(x[3], y[3], carry)
z[4], carry = bits.Add64(x[4], y[4], carry)
z[5], _ = bits.Add64(x[5], y[5], carry)
// if z > q --> z -= q
// note: this is NOT constant time
if !(z[5] < 1873798617647539866 || (z[5] == 1873798617647539866 && (z[4] < 5412103778470702295 || (z[4] == 5412103778470702295 && (z[3] < 7239337960414712511 || (z[3] == 7239337960414712511 && (z[2] < 7435674573564081700 || (z[2] == 7435674573564081700 && (z[1] < 2210141511517208575 || (z[1] == 2210141511517208575 && (z[0] < 13402431016077863595))))))))))) {
var b uint64
z[0], b = bits.Sub64(z[0], 13402431016077863595, 0)
z[1], b = bits.Sub64(z[1], 2210141511517208575, b)
z[2], b = bits.Sub64(z[2], 7435674573564081700, b)
z[3], b = bits.Sub64(z[3], 7239337960414712511, b)
z[4], b = bits.Sub64(z[4], 5412103778470702295, b)
z[5], _ = bits.Sub64(z[5], 1873798617647539866, b)
}
}
func addAssign(x, y *fe) {
var carry uint64
x[0], carry = bits.Add64(x[0], y[0], 0)
x[1], carry = bits.Add64(x[1], y[1], carry)
x[2], carry = bits.Add64(x[2], y[2], carry)
x[3], carry = bits.Add64(x[3], y[3], carry)
x[4], carry = bits.Add64(x[4], y[4], carry)
x[5], _ = bits.Add64(x[5], y[5], carry)
// if z > q --> z -= q
// note: this is NOT constant time
if !(x[5] < 1873798617647539866 || (x[5] == 1873798617647539866 && (x[4] < 5412103778470702295 || (x[4] == 5412103778470702295 && (x[3] < 7239337960414712511 || (x[3] == 7239337960414712511 && (x[2] < 7435674573564081700 || (x[2] == 7435674573564081700 && (x[1] < 2210141511517208575 || (x[1] == 2210141511517208575 && (x[0] < 13402431016077863595))))))))))) {
var b uint64
x[0], b = bits.Sub64(x[0], 13402431016077863595, 0)
x[1], b = bits.Sub64(x[1], 2210141511517208575, b)
x[2], b = bits.Sub64(x[2], 7435674573564081700, b)
x[3], b = bits.Sub64(x[3], 7239337960414712511, b)
x[4], b = bits.Sub64(x[4], 5412103778470702295, b)
x[5], _ = bits.Sub64(x[5], 1873798617647539866, b)
}
}
func ladd(z, x, y *fe) {
var carry uint64
z[0], carry = bits.Add64(x[0], y[0], 0)
z[1], carry = bits.Add64(x[1], y[1], carry)
z[2], carry = bits.Add64(x[2], y[2], carry)
z[3], carry = bits.Add64(x[3], y[3], carry)
z[4], carry = bits.Add64(x[4], y[4], carry)
z[5], _ = bits.Add64(x[5], y[5], carry)
}
func laddAssign(x, y *fe) {
var carry uint64
x[0], carry = bits.Add64(x[0], y[0], 0)
x[1], carry = bits.Add64(x[1], y[1], carry)
x[2], carry = bits.Add64(x[2], y[2], carry)
x[3], carry = bits.Add64(x[3], y[3], carry)
x[4], carry = bits.Add64(x[4], y[4], carry)
x[5], _ = bits.Add64(x[5], y[5], carry)
}
func double(z, x *fe) {
var carry uint64
z[0], carry = bits.Add64(x[0], x[0], 0)
z[1], carry = bits.Add64(x[1], x[1], carry)
z[2], carry = bits.Add64(x[2], x[2], carry)
z[3], carry = bits.Add64(x[3], x[3], carry)
z[4], carry = bits.Add64(x[4], x[4], carry)
z[5], _ = bits.Add64(x[5], x[5], carry)
// if z > q --> z -= q
// note: this is NOT constant time
if !(z[5] < 1873798617647539866 || (z[5] == 1873798617647539866 && (z[4] < 5412103778470702295 || (z[4] == 5412103778470702295 && (z[3] < 7239337960414712511 || (z[3] == 7239337960414712511 && (z[2] < 7435674573564081700 || (z[2] == 7435674573564081700 && (z[1] < 2210141511517208575 || (z[1] == 2210141511517208575 && (z[0] < 13402431016077863595))))))))))) {
var b uint64
z[0], b = bits.Sub64(z[0], 13402431016077863595, 0)
z[1], b = bits.Sub64(z[1], 2210141511517208575, b)
z[2], b = bits.Sub64(z[2], 7435674573564081700, b)
z[3], b = bits.Sub64(z[3], 7239337960414712511, b)
z[4], b = bits.Sub64(z[4], 5412103778470702295, b)
z[5], _ = bits.Sub64(z[5], 1873798617647539866, b)
}
}
func doubleAssign(z *fe) {
var carry uint64
z[0], carry = bits.Add64(z[0], z[0], 0)
z[1], carry = bits.Add64(z[1], z[1], carry)
z[2], carry = bits.Add64(z[2], z[2], carry)
z[3], carry = bits.Add64(z[3], z[3], carry)
z[4], carry = bits.Add64(z[4], z[4], carry)
z[5], _ = bits.Add64(z[5], z[5], carry)
// if z > q --> z -= q
// note: this is NOT constant time
if !(z[5] < 1873798617647539866 || (z[5] == 1873798617647539866 && (z[4] < 5412103778470702295 || (z[4] == 5412103778470702295 && (z[3] < 7239337960414712511 || (z[3] == 7239337960414712511 && (z[2] < 7435674573564081700 || (z[2] == 7435674573564081700 && (z[1] < 2210141511517208575 || (z[1] == 2210141511517208575 && (z[0] < 13402431016077863595))))))))))) {
var b uint64
z[0], b = bits.Sub64(z[0], 13402431016077863595, 0)
z[1], b = bits.Sub64(z[1], 2210141511517208575, b)
z[2], b = bits.Sub64(z[2], 7435674573564081700, b)
z[3], b = bits.Sub64(z[3], 7239337960414712511, b)
z[4], b = bits.Sub64(z[4], 5412103778470702295, b)
z[5], _ = bits.Sub64(z[5], 1873798617647539866, b)
}
}
func ldouble(z, x *fe) {
var carry uint64
z[0], carry = bits.Add64(x[0], x[0], 0)
z[1], carry = bits.Add64(x[1], x[1], carry)
z[2], carry = bits.Add64(x[2], x[2], carry)
z[3], carry = bits.Add64(x[3], x[3], carry)
z[4], carry = bits.Add64(x[4], x[4], carry)
z[5], _ = bits.Add64(x[5], x[5], carry)
}
func sub(z, x, y *fe) {
var b uint64
z[0], b = bits.Sub64(x[0], y[0], 0)
z[1], b = bits.Sub64(x[1], y[1], b)
z[2], b = bits.Sub64(x[2], y[2], b)
z[3], b = bits.Sub64(x[3], y[3], b)
z[4], b = bits.Sub64(x[4], y[4], b)
z[5], b = bits.Sub64(x[5], y[5], b)
if b != 0 {
var c uint64
z[0], c = bits.Add64(z[0], 13402431016077863595, 0)
z[1], c = bits.Add64(z[1], 2210141511517208575, c)
z[2], c = bits.Add64(z[2], 7435674573564081700, c)
z[3], c = bits.Add64(z[3], 7239337960414712511, c)
z[4], c = bits.Add64(z[4], 5412103778470702295, c)
z[5], _ = bits.Add64(z[5], 1873798617647539866, c)
}
}
func subAssign(z, x *fe) {
var b uint64
z[0], b = bits.Sub64(z[0], x[0], 0)
z[1], b = bits.Sub64(z[1], x[1], b)
z[2], b = bits.Sub64(z[2], x[2], b)
z[3], b = bits.Sub64(z[3], x[3], b)
z[4], b = bits.Sub64(z[4], x[4], b)
z[5], b = bits.Sub64(z[5], x[5], b)
if b != 0 {
var c uint64
z[0], c = bits.Add64(z[0], 13402431016077863595, 0)
z[1], c = bits.Add64(z[1], 2210141511517208575, c)
z[2], c = bits.Add64(z[2], 7435674573564081700, c)
z[3], c = bits.Add64(z[3], 7239337960414712511, c)
z[4], c = bits.Add64(z[4], 5412103778470702295, c)
z[5], _ = bits.Add64(z[5], 1873798617647539866, c)
}
}
func lsubAssign(z, x *fe) {
var b uint64
z[0], b = bits.Sub64(z[0], x[0], 0)
z[1], b = bits.Sub64(z[1], x[1], b)
z[2], b = bits.Sub64(z[2], x[2], b)
z[3], b = bits.Sub64(z[3], x[3], b)
z[4], b = bits.Sub64(z[4], x[4], b)
z[5], _ = bits.Sub64(z[5], x[5], b)
}
func neg(z *fe, x *fe) {
if x.isZero() {
z.zero()
return
}
var borrow uint64
z[0], borrow = bits.Sub64(13402431016077863595, x[0], 0)
z[1], borrow = bits.Sub64(2210141511517208575, x[1], borrow)
z[2], borrow = bits.Sub64(7435674573564081700, x[2], borrow)
z[3], borrow = bits.Sub64(7239337960414712511, x[3], borrow)
z[4], borrow = bits.Sub64(5412103778470702295, x[4], borrow)
z[5], _ = bits.Sub64(1873798617647539866, x[5], borrow)
}
func mul(z, x, y *fe) {
var t [6]uint64
var c [3]uint64
{
// round 0
v := x[0]
c[1], c[0] = bits.Mul64(v, y[0])
m := c[0] * 9940570264628428797
c[2] = madd0(m, 13402431016077863595, c[0])
c[1], c[0] = madd1(v, y[1], c[1])
c[2], t[0] = madd2(m, 2210141511517208575, c[2], c[0])
c[1], c[0] = madd1(v, y[2], c[1])
c[2], t[1] = madd2(m, 7435674573564081700, c[2], c[0])
c[1], c[0] = madd1(v, y[3], c[1])
c[2], t[2] = madd2(m, 7239337960414712511, c[2], c[0])
c[1], c[0] = madd1(v, y[4], c[1])
c[2], t[3] = madd2(m, 5412103778470702295, c[2], c[0])
c[1], c[0] = madd1(v, y[5], c[1])
t[5], t[4] = madd3(m, 1873798617647539866, c[0], c[2], c[1])
}
{
// round 1
v := x[1]
c[1], c[0] = madd1(v, y[0], t[0])
m := c[0] * 9940570264628428797
c[2] = madd0(m, 13402431016077863595, c[0])
c[1], c[0] = madd2(v, y[1], c[1], t[1])
c[2], t[0] = madd2(m, 2210141511517208575, c[2], c[0])
c[1], c[0] = madd2(v, y[2], c[1], t[2])
c[2], t[1] = madd2(m, 7435674573564081700, c[2], c[0])
c[1], c[0] = madd2(v, y[3], c[1], t[3])
c[2], t[2] = madd2(m, 7239337960414712511, c[2], c[0])
c[1], c[0] = madd2(v, y[4], c[1], t[4])
c[2], t[3] = madd2(m, 5412103778470702295, c[2], c[0])
c[1], c[0] = madd2(v, y[5], c[1], t[5])
t[5], t[4] = madd3(m, 1873798617647539866, c[0], c[2], c[1])
}
{
// round 2
v := x[2]
c[1], c[0] = madd1(v, y[0], t[0])
m := c[0] * 9940570264628428797
c[2] = madd0(m, 13402431016077863595, c[0])
c[1], c[0] = madd2(v, y[1], c[1], t[1])
c[2], t[0] = madd2(m, 2210141511517208575, c[2], c[0])
c[1], c[0] = madd2(v, y[2], c[1], t[2])
c[2], t[1] = madd2(m, 7435674573564081700, c[2], c[0])
c[1], c[0] = madd2(v, y[3], c[1], t[3])
c[2], t[2] = madd2(m, 7239337960414712511, c[2], c[0])
c[1], c[0] = madd2(v, y[4], c[1], t[4])
c[2], t[3] = madd2(m, 5412103778470702295, c[2], c[0])
c[1], c[0] = madd2(v, y[5], c[1], t[5])
t[5], t[4] = madd3(m, 1873798617647539866, c[0], c[2], c[1])
}
{
// round 3
v := x[3]
c[1], c[0] = madd1(v, y[0], t[0])
m := c[0] * 9940570264628428797
c[2] = madd0(m, 13402431016077863595, c[0])
c[1], c[0] = madd2(v, y[1], c[1], t[1])
c[2], t[0] = madd2(m, 2210141511517208575, c[2], c[0])
c[1], c[0] = madd2(v, y[2], c[1], t[2])
c[2], t[1] = madd2(m, 7435674573564081700, c[2], c[0])
c[1], c[0] = madd2(v, y[3], c[1], t[3])
c[2], t[2] = madd2(m, 7239337960414712511, c[2], c[0])
c[1], c[0] = madd2(v, y[4], c[1], t[4])
c[2], t[3] = madd2(m, 5412103778470702295, c[2], c[0])
c[1], c[0] = madd2(v, y[5], c[1], t[5])
t[5], t[4] = madd3(m, 1873798617647539866, c[0], c[2], c[1])
}
{
// round 4
v := x[4]
c[1], c[0] = madd1(v, y[0], t[0])
m := c[0] * 9940570264628428797
c[2] = madd0(m, 13402431016077863595, c[0])
c[1], c[0] = madd2(v, y[1], c[1], t[1])
c[2], t[0] = madd2(m, 2210141511517208575, c[2], c[0])
c[1], c[0] = madd2(v, y[2], c[1], t[2])
c[2], t[1] = madd2(m, 7435674573564081700, c[2], c[0])
c[1], c[0] = madd2(v, y[3], c[1], t[3])
c[2], t[2] = madd2(m, 7239337960414712511, c[2], c[0])
c[1], c[0] = madd2(v, y[4], c[1], t[4])
c[2], t[3] = madd2(m, 5412103778470702295, c[2], c[0])
c[1], c[0] = madd2(v, y[5], c[1], t[5])
t[5], t[4] = madd3(m, 1873798617647539866, c[0], c[2], c[1])
}
{
// round 5
v := x[5]
c[1], c[0] = madd1(v, y[0], t[0])
m := c[0] * 9940570264628428797
c[2] = madd0(m, 13402431016077863595, c[0])
c[1], c[0] = madd2(v, y[1], c[1], t[1])
c[2], z[0] = madd2(m, 2210141511517208575, c[2], c[0])
c[1], c[0] = madd2(v, y[2], c[1], t[2])
c[2], z[1] = madd2(m, 7435674573564081700, c[2], c[0])
c[1], c[0] = madd2(v, y[3], c[1], t[3])
c[2], z[2] = madd2(m, 7239337960414712511, c[2], c[0])
c[1], c[0] = madd2(v, y[4], c[1], t[4])
c[2], z[3] = madd2(m, 5412103778470702295, c[2], c[0])
c[1], c[0] = madd2(v, y[5], c[1], t[5])
z[5], z[4] = madd3(m, 1873798617647539866, c[0], c[2], c[1])
}
// if z > q --> z -= q
// note: this is NOT constant time
if !(z[5] < 1873798617647539866 || (z[5] == 1873798617647539866 && (z[4] < 5412103778470702295 || (z[4] == 5412103778470702295 && (z[3] < 7239337960414712511 || (z[3] == 7239337960414712511 && (z[2] < 7435674573564081700 || (z[2] == 7435674573564081700 && (z[1] < 2210141511517208575 || (z[1] == 2210141511517208575 && (z[0] < 13402431016077863595))))))))))) {
var b uint64
z[0], b = bits.Sub64(z[0], 13402431016077863595, 0)
z[1], b = bits.Sub64(z[1], 2210141511517208575, b)
z[2], b = bits.Sub64(z[2], 7435674573564081700, b)
z[3], b = bits.Sub64(z[3], 7239337960414712511, b)
z[4], b = bits.Sub64(z[4], 5412103778470702295, b)
z[5], _ = bits.Sub64(z[5], 1873798617647539866, b)
}
}
func square(z, x *fe) {
var p [6]uint64
var u, v uint64
{
// round 0
u, p[0] = bits.Mul64(x[0], x[0])
m := p[0] * 9940570264628428797
C := madd0(m, 13402431016077863595, p[0])
var t uint64
t, u, v = madd1sb(x[0], x[1], u)
C, p[0] = madd2(m, 2210141511517208575, v, C)
t, u, v = madd1s(x[0], x[2], t, u)
C, p[1] = madd2(m, 7435674573564081700, v, C)
t, u, v = madd1s(x[0], x[3], t, u)
C, p[2] = madd2(m, 7239337960414712511, v, C)
t, u, v = madd1s(x[0], x[4], t, u)
C, p[3] = madd2(m, 5412103778470702295, v, C)
_, u, v = madd1s(x[0], x[5], t, u)
p[5], p[4] = madd3(m, 1873798617647539866, v, C, u)
}
{
// round 1
m := p[0] * 9940570264628428797
C := madd0(m, 13402431016077863595, p[0])
u, v = madd1(x[1], x[1], p[1])
C, p[0] = madd2(m, 2210141511517208575, v, C)
var t uint64
t, u, v = madd2sb(x[1], x[2], p[2], u)
C, p[1] = madd2(m, 7435674573564081700, v, C)
t, u, v = madd2s(x[1], x[3], p[3], t, u)
C, p[2] = madd2(m, 7239337960414712511, v, C)
t, u, v = madd2s(x[1], x[4], p[4], t, u)
C, p[3] = madd2(m, 5412103778470702295, v, C)
_, u, v = madd2s(x[1], x[5], p[5], t, u)
p[5], p[4] = madd3(m, 1873798617647539866, v, C, u)
}
{
// round 2
m := p[0] * 9940570264628428797
C := madd0(m, 13402431016077863595, p[0])
C, p[0] = madd2(m, 2210141511517208575, p[1], C)
u, v = madd1(x[2], x[2], p[2])
C, p[1] = madd2(m, 7435674573564081700, v, C)
var t uint64
t, u, v = madd2sb(x[2], x[3], p[3], u)
C, p[2] = madd2(m, 7239337960414712511, v, C)
t, u, v = madd2s(x[2], x[4], p[4], t, u)
C, p[3] = madd2(m, 5412103778470702295, v, C)
_, u, v = madd2s(x[2], x[5], p[5], t, u)
p[5], p[4] = madd3(m, 1873798617647539866, v, C, u)
}
{
// round 3
m := p[0] * 9940570264628428797
C := madd0(m, 13402431016077863595, p[0])
C, p[0] = madd2(m, 2210141511517208575, p[1], C)
C, p[1] = madd2(m, 7435674573564081700, p[2], C)
u, v = madd1(x[3], x[3], p[3])
C, p[2] = madd2(m, 7239337960414712511, v, C)
var t uint64
t, u, v = madd2sb(x[3], x[4], p[4], u)
C, p[3] = madd2(m, 5412103778470702295, v, C)
_, u, v = madd2s(x[3], x[5], p[5], t, u)
p[5], p[4] = madd3(m, 1873798617647539866, v, C, u)
}
{
// round 4
m := p[0] * 9940570264628428797
C := madd0(m, 13402431016077863595, p[0])
C, p[0] = madd2(m, 2210141511517208575, p[1], C)
C, p[1] = madd2(m, 7435674573564081700, p[2], C)
C, p[2] = madd2(m, 7239337960414712511, p[3], C)
u, v = madd1(x[4], x[4], p[4])
C, p[3] = madd2(m, 5412103778470702295, v, C)
_, u, v = madd2sb(x[4], x[5], p[5], u)
p[5], p[4] = madd3(m, 1873798617647539866, v, C, u)
}
{
// round 5
m := p[0] * 9940570264628428797
C := madd0(m, 13402431016077863595, p[0])
C, z[0] = madd2(m, 2210141511517208575, p[1], C)
C, z[1] = madd2(m, 7435674573564081700, p[2], C)
C, z[2] = madd2(m, 7239337960414712511, p[3], C)
C, z[3] = madd2(m, 5412103778470702295, p[4], C)
u, v = madd1(x[5], x[5], p[5])
z[5], z[4] = madd3(m, 1873798617647539866, v, C, u)
}
// if z > q --> z -= q
// note: this is NOT constant time
if !(z[5] < 1873798617647539866 || (z[5] == 1873798617647539866 && (z[4] < 5412103778470702295 || (z[4] == 5412103778470702295 && (z[3] < 7239337960414712511 || (z[3] == 7239337960414712511 && (z[2] < 7435674573564081700 || (z[2] == 7435674573564081700 && (z[1] < 2210141511517208575 || (z[1] == 2210141511517208575 && (z[0] < 13402431016077863595))))))))))) {
var b uint64
z[0], b = bits.Sub64(z[0], 13402431016077863595, 0)
z[1], b = bits.Sub64(z[1], 2210141511517208575, b)
z[2], b = bits.Sub64(z[2], 7435674573564081700, b)
z[3], b = bits.Sub64(z[3], 7239337960414712511, b)
z[4], b = bits.Sub64(z[4], 5412103778470702295, b)
z[5], _ = bits.Sub64(z[5], 1873798617647539866, b)
}
}
// arith.go
// Copyright 2020 ConsenSys AG
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// Code generated by goff DO NOT EDIT
func madd(a, b, t, u, v uint64) (uint64, uint64, uint64) {
var carry uint64
hi, lo := bits.Mul64(a, b)
v, carry = bits.Add64(lo, v, 0)
u, carry = bits.Add64(hi, u, carry)
t, _ = bits.Add64(t, 0, carry)
return t, u, v
}
// madd0 hi = a*b + c (discards lo bits)
func madd0(a, b, c uint64) (hi uint64) {
var carry, lo uint64
@ -503,59 +51,6 @@ func madd2(a, b, c, d uint64) (hi uint64, lo uint64) {
return
}
// madd2s superhi, hi, lo = 2*a*b + c + d + e
func madd2s(a, b, c, d, e uint64) (superhi, hi, lo uint64) {
var carry, sum uint64
hi, lo = bits.Mul64(a, b)
lo, carry = bits.Add64(lo, lo, 0)
hi, superhi = bits.Add64(hi, hi, carry)
sum, carry = bits.Add64(c, e, 0)
hi, _ = bits.Add64(hi, 0, carry)
lo, carry = bits.Add64(lo, sum, 0)
hi, _ = bits.Add64(hi, 0, carry)
hi, _ = bits.Add64(hi, 0, d)
return
}
func madd1s(a, b, d, e uint64) (superhi, hi, lo uint64) {
var carry uint64
hi, lo = bits.Mul64(a, b)
lo, carry = bits.Add64(lo, lo, 0)
hi, superhi = bits.Add64(hi, hi, carry)
lo, carry = bits.Add64(lo, e, 0)
hi, _ = bits.Add64(hi, 0, carry)
hi, _ = bits.Add64(hi, 0, d)
return
}
func madd2sb(a, b, c, e uint64) (superhi, hi, lo uint64) {
var carry, sum uint64
hi, lo = bits.Mul64(a, b)
lo, carry = bits.Add64(lo, lo, 0)
hi, superhi = bits.Add64(hi, hi, carry)
sum, carry = bits.Add64(c, e, 0)
hi, _ = bits.Add64(hi, 0, carry)
lo, carry = bits.Add64(lo, sum, 0)
hi, _ = bits.Add64(hi, 0, carry)
return
}
func madd1sb(a, b, e uint64) (superhi, hi, lo uint64) {
var carry uint64
hi, lo = bits.Mul64(a, b)
lo, carry = bits.Add64(lo, lo, 0)
hi, superhi = bits.Add64(hi, hi, carry)
lo, carry = bits.Add64(lo, e, 0)
hi, _ = bits.Add64(hi, 0, carry)
return
}
func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
var carry uint64
hi, lo = bits.Mul64(a, b)

277
crypto/bls12381/bls12_381.go
View file

@ -1,79 +1,89 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
/*
Field Constants
*/
const fpNumberOfLimbs = 6
const fpByteSize = 48
const fpBitSize = 381
const sixWordBitSize = 384
// Base field modulus
// Base Field
// p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
// Size of six words
// r = 2 ^ 384
// modulus = p
var modulus = fe{0xb9feffffffffaaab, 0x1eabfffeb153ffff, 0x6730d2a0f6b0f624, 0x64774b84f38512bf, 0x4b1ba7b6434bacd7, 0x1a0111ea397fe69a}
var (
// -p^(-1) mod 2^64
inp uint64 = 0x89f3fffcfffcfffd
// This value is used in assembly code
_ = inp
)
// -p^(-1) mod 2^64
var inp uint64 = 0x89f3fffcfffcfffd
// r mod p
// r1 = r mod p
var r1 = &fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493}
// r^2 mod p
// one = mod p
var one = r1
// zero = 0
var zero = &fe{}
// r2 = r^2 mod p
var r2 = &fe{
0xf4df1f341c341746, 0x0a76e6a609d104f1, 0x8de5476c4c95b6d5, 0x67eb88a9939d83c0, 0x9a793e85b519952d, 0x11988fe592cae3aa,
}
// -1 + 0 * u
// negativeOne = -r mod p
var negativeOne = &fe{
0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206,
}
// negativeOne2 = -1 + 0 * u
var negativeOne2 = &fe2{
fe{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
}
// 2 ^ (-1)
// twoInv = 2^(-1)
var twoInv = &fe{0x1804000000015554, 0x855000053ab00001, 0x633cb57c253c276f, 0x6e22d1ec31ebb502, 0xd3916126f2d14ca2, 0x17fbb8571a006596}
// (p - 3) / 4
// pMinus3Over4 = (p - 3) / 4
var pMinus3Over4 = bigFromHex("0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc34a83dac3d8907aaffffac54ffffee7fbfffffffeaaa")
// (p + 1) / 4
// pPlus1Over4 = (p + 1) / 4
var pPlus1Over4 = bigFromHex("0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc34a83dac3d8907aaffffac54ffffee7fbfffffffeaab")
// (p - 1) / 2
// pMinus1Over2 = (p - 1) / 2
var pMinus1Over2 = bigFromHex("0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdcff7fffffffd555")
// -1
// nonResidue1 = -1
var nonResidue1 = &fe{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206}
// (1 + 1 * u)
// nonResidue2 = (1 + 1 * u)
var nonResidue2 = &fe2{
fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
}
/*
Curve Constants
*/
// Scalar Field
// q = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
// Size of six words
// qr = 2 ^ 256
var qBig = bigFromHex("0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001")
var q = Fr{0xffffffff00000001, 0x53bda402fffe5bfe, 0x3339d80809a1d805, 0x73eda753299d7d48}
// var qmodulus = Fr{0xffffffff00000001, 0x53bda402fffe5bfe, 0x3339d80809a1d805, 0x73eda753299d7d48}
// -q^(-1) mod 2^64
var qinp uint64 = 0xfffffffeffffffff
// supress warning: qinp is used in assembly code
var _ = qinp
// qr1 = qr mod q
var qr1 = &Fr{0x00000001fffffffe, 0x5884b7fa00034802, 0x998c4fefecbc4ff5, 0x1824b159acc5056f}
// qr2 = qr^2 mod q
var qr2 = &Fr{0xc999e990f3f29c6d, 0x2b6cedcb87925c23, 0x05d314967254398f, 0x0748d9d99f59ff11}
// Curve Constants
// b coefficient for G1
var b = &fe{0xaa270000000cfff3, 0x53cc0032fc34000a, 0x478fe97a6b0a807f, 0xb1d37ebee6ba24d7, 0x8ec9733bbf78ab2f, 0x09d645513d83de7e}
@ -84,21 +94,28 @@ var b2 = &fe2{
fe{0xaa270000000cfff3, 0x53cc0032fc34000a, 0x478fe97a6b0a807f, 0xb1d37ebee6ba24d7, 0x8ec9733bbf78ab2f, 0x09d645513d83de7e},
}
// Curve order
var q = bigFromHex("0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001")
// G1 cofactor
var cofactorG1 = bigFromHex("0x396c8c005555e1568c00aaab0000aaab")
// Efficient cofactor of G1
// G2 cofactor
var cofactorG2 = bigFromHex("5d543a95414e7f1091d50792876a202cd91de4547085abaa68a205b2e5a7ddfa628f1cb4d9e82ef21537e293a6691ae1616ec6e786f0c70cf1c38e31c7238e5")
// Efficient G1 cofactor
var cofactorEFFG1 = bigFromHex("0xd201000000010001")
// Efficient cofactor of G2
// Efficient G2 cofactor
var cofactorEFFG2 = bigFromHex("0x0bc69f08f2ee75b3584c6a0ea91b352888e2a8e9145ad7689986ff031508ffe1329c2f178731db956d82bf015d1212b02ec0ec69d7477c1ae954cbc06689f6a359894c0adebbf6b4e8020005aaa95551")
// G1 generator
var g1One = PointG1{
fe{0x5cb38790fd530c16, 0x7817fc679976fff5, 0x154f95c7143ba1c1, 0xf0ae6acdf3d0e747, 0xedce6ecc21dbf440, 0x120177419e0bfb75},
fe{0xbaac93d50ce72271, 0x8c22631a7918fd8e, 0xdd595f13570725ce, 0x51ac582950405194, 0x0e1c8c3fad0059c0, 0x0bbc3efc5008a26a},
fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
}
var G1One = g1One
// G2 generator
var g2One = PointG2{
fe2{
fe{0xf5f28fa202940a10, 0xb3f5fb2687b4961a, 0xa1a893b53e2ae580, 0x9894999d1a3caee9, 0x6f67b7631863366b, 0x058191924350bcd7},
@ -114,117 +131,179 @@ var g2One = PointG2{
},
}
/*
Frobenious Coeffs
*/
var G2One = g2One
// Psi values for faster cofactor clearing
// psix = 1 / (nr ^ (p - 1)/3)
var psix = fe2{
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
fe{0x890dc9e4867545c3, 0x2af322533285a5d5, 0x50880866309b7e2c, 0xa20d1b8c7e881024, 0x14e4f04fe2db9068, 0x14e56d3f1564853a},
}
// psiy = 1 / (nr ^ (p - 1)/2)
var psiy = fe2{
fe{0x3e2f585da55c9ad1, 0x4294213d86c18183, 0x382844c88b623732, 0x92ad2afd19103e18, 0x1d794e4fac7cf0b9, 0x0bd592fc7d825ec8},
fe{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2},
}
// Frobenius Coeffs
// z = -1
var frobeniusCoeffs2 = [2]fe{
// z ^ (( p ^ 0 - 1) / 2)
{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
// z ^ (( p ^ 1 - 1) / 2)
{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206},
}
// z = u + 1
var frobeniusCoeffs61 = [6]fe2{
// z ^ (( p ^ 0 - 1) / 3)
{
fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ (( p ^ 1 - 1) / 3)
{
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
fe{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741},
},
// z ^ (( p ^ 2 - 1) / 3)
{
fe{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ (( p ^ 3 - 1) / 3)
{
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
},
// z ^ (( p ^ 4 - 1) / 3)
{
fe{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ (( p ^ 5 - 1) / 3)
{
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
fe{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160},
},
}
// z = u + 1
var frobeniusCoeffs62 = [6]fe2{
// z ^ (( 2 * p ^ 0 - 2) / 3)
{
fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ (( 2 * p ^ 1 - 2) / 3)
{
fe{0x890dc9e4867545c3, 0x2af322533285a5d5, 0x50880866309b7e2c, 0xa20d1b8c7e881024, 0x14e4f04fe2db9068, 0x14e56d3f1564853a},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0x890dc9e4867545c3, 0x2af322533285a5d5, 0x50880866309b7e2c, 0xa20d1b8c7e881024, 0x14e4f04fe2db9068, 0x14e56d3f1564853a},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ (( 2 * p ^ 2 - 2) / 3)
{
fe{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ (( 2 * p ^ 3 - 2) / 3)
{
fe{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ (( 2 * p ^ 4 - 2) / 3)
{
fe{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ (( 2 * p ^ 5 - 2) / 3)
{
fe{0xecfb361b798dba3a, 0xc100ddb891865a2c, 0x0ec08ff1232bda8e, 0xd5c13cc6f1ca4721, 0x47222a47bf7b5c04, 0x0110f184e51c5f59},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0xecfb361b798dba3a, 0xc100ddb891865a2c, 0x0ec08ff1232bda8e, 0xd5c13cc6f1ca4721, 0x47222a47bf7b5c04, 0x0110f184e51c5f59},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
}
var frobeniusCoeffs12 = [12]fe2{
// z = u + 1
// z ^ ((p ^ 0 - 1) / 6)
{
fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ ((p ^ 1 - 1) / 6)
{
fe{0x07089552b319d465, 0xc6695f92b50a8313, 0x97e83cccd117228f, 0xa35baecab2dc29ee, 0x1ce393ea5daace4d, 0x08f2220fb0fb66eb},
fe{0xb2f66aad4ce5d646, 0x5842a06bfc497cec, 0xcf4895d42599d394, 0xc11b9cba40a8e8d0, 0x2e3813cbe5a0de89, 0x110eefda88847faf},
{0x07089552b319d465, 0xc6695f92b50a8313, 0x97e83cccd117228f, 0xa35baecab2dc29ee, 0x1ce393ea5daace4d, 0x08f2220fb0fb66eb},
{0xb2f66aad4ce5d646, 0x5842a06bfc497cec, 0xcf4895d42599d394, 0xc11b9cba40a8e8d0, 0x2e3813cbe5a0de89, 0x110eefda88847faf},
},
// z ^ ((p ^ 2 - 1) / 6)
{
fe{0xecfb361b798dba3a, 0xc100ddb891865a2c, 0x0ec08ff1232bda8e, 0xd5c13cc6f1ca4721, 0x47222a47bf7b5c04, 0x0110f184e51c5f59},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0xecfb361b798dba3a, 0xc100ddb891865a2c, 0x0ec08ff1232bda8e, 0xd5c13cc6f1ca4721, 0x47222a47bf7b5c04, 0x0110f184e51c5f59},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ ((p ^ 3 - 1) / 6)
{
fe{0x3e2f585da55c9ad1, 0x4294213d86c18183, 0x382844c88b623732, 0x92ad2afd19103e18, 0x1d794e4fac7cf0b9, 0x0bd592fc7d825ec8},
fe{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2},
{0x3e2f585da55c9ad1, 0x4294213d86c18183, 0x382844c88b623732, 0x92ad2afd19103e18, 0x1d794e4fac7cf0b9, 0x0bd592fc7d825ec8},
{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2},
},
// z ^ ((p ^ 4 - 1) / 6)
{
fe{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ ((p ^ 5 - 1) / 6)
{
fe{0x3726c30af242c66c, 0x7c2ac1aad1b6fe70, 0xa04007fbba4b14a2, 0xef517c3266341429, 0x0095ba654ed2226b, 0x02e370eccc86f7dd},
fe{0x82d83cf50dbce43f, 0xa2813e53df9d018f, 0xc6f0caa53c65e181, 0x7525cf528d50fe95, 0x4a85ed50f4798a6b, 0x171da0fd6cf8eebd},
{0x3726c30af242c66c, 0x7c2ac1aad1b6fe70, 0xa04007fbba4b14a2, 0xef517c3266341429, 0x0095ba654ed2226b, 0x02e370eccc86f7dd},
{0x82d83cf50dbce43f, 0xa2813e53df9d018f, 0xc6f0caa53c65e181, 0x7525cf528d50fe95, 0x4a85ed50f4798a6b, 0x171da0fd6cf8eebd},
},
// z ^ ((p ^ 6 - 1) / 6)
{
fe{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ ((p ^ 7 - 1) / 6)
{
fe{0xb2f66aad4ce5d646, 0x5842a06bfc497cec, 0xcf4895d42599d394, 0xc11b9cba40a8e8d0, 0x2e3813cbe5a0de89, 0x110eefda88847faf},
fe{0x07089552b319d465, 0xc6695f92b50a8313, 0x97e83cccd117228f, 0xa35baecab2dc29ee, 0x1ce393ea5daace4d, 0x08f2220fb0fb66eb},
{0xb2f66aad4ce5d646, 0x5842a06bfc497cec, 0xcf4895d42599d394, 0xc11b9cba40a8e8d0, 0x2e3813cbe5a0de89, 0x110eefda88847faf},
{0x07089552b319d465, 0xc6695f92b50a8313, 0x97e83cccd117228f, 0xa35baecab2dc29ee, 0x1ce393ea5daace4d, 0x08f2220fb0fb66eb},
},
// z ^ ((p ^ 8 - 1) / 6)
{
fe{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ ((p ^ 9 - 1) / 6)
{
fe{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2},
fe{0x3e2f585da55c9ad1, 0x4294213d86c18183, 0x382844c88b623732, 0x92ad2afd19103e18, 0x1d794e4fac7cf0b9, 0x0bd592fc7d825ec8},
{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2},
{0x3e2f585da55c9ad1, 0x4294213d86c18183, 0x382844c88b623732, 0x92ad2afd19103e18, 0x1d794e4fac7cf0b9, 0x0bd592fc7d825ec8},
},
// z ^ ((p ^ 10 - 1) / 6)
{
fe{0x890dc9e4867545c3, 0x2af322533285a5d5, 0x50880866309b7e2c, 0xa20d1b8c7e881024, 0x14e4f04fe2db9068, 0x14e56d3f1564853a},
fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
{0x890dc9e4867545c3, 0x2af322533285a5d5, 0x50880866309b7e2c, 0xa20d1b8c7e881024, 0x14e4f04fe2db9068, 0x14e56d3f1564853a},
{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
},
// z ^ ((p ^ 11 - 1) / 6)
{
fe{0x82d83cf50dbce43f, 0xa2813e53df9d018f, 0xc6f0caa53c65e181, 0x7525cf528d50fe95, 0x4a85ed50f4798a6b, 0x171da0fd6cf8eebd},
fe{0x3726c30af242c66c, 0x7c2ac1aad1b6fe70, 0xa04007fbba4b14a2, 0xef517c3266341429, 0x0095ba654ed2226b, 0x02e370eccc86f7dd},
{0x82d83cf50dbce43f, 0xa2813e53df9d018f, 0xc6f0caa53c65e181, 0x7525cf528d50fe95, 0x4a85ed50f4798a6b, 0x171da0fd6cf8eebd},
{0x3726c30af242c66c, 0x7c2ac1aad1b6fe70, 0xa04007fbba4b14a2, 0xef517c3266341429, 0x0095ba654ed2226b, 0x02e370eccc86f7dd},
},
}
/*
x
*/
// x
var x = bigFromHex("0xd201000000010000")
// var x = bigFromHex("0xd201000000010000")
var x uint64 = 0xd201000000010000
// square root
var sqrtMinus1 = &fe2{*new(fe).zero(), *new(fe).one()}
var sqrtSqrtMinus1 = &fe2{
fe{0x3e2f585da55c9ad1, 0x4294213d86c18183, 0x382844c88b623732, 0x92ad2afd19103e18, 0x1d794e4fac7cf0b9, 0x0bd592fc7d825ec8},
fe{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2},
}
var sqrtMinusSqrtMinus1 = &fe2{
fe{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2},
fe{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2},
}

58
crypto/bls12381/bls12_381_test.go
View file

@ -2,12 +2,66 @@ package bls12381
import (
"crypto/rand"
"encoding/hex"
"errors"
"flag"
"math/big"
"os"
"testing"
)
var fuz = 10
var fuz int
func TestMain(m *testing.M) {
_fuz := flag.Int("fuzz", 10, "# of iterations")
flag.Parse()
fuz = *_fuz
os.Exit(m.Run())
}
func randScalar(max *big.Int) *big.Int {
a, _ := rand.Int(rand.Reader, max)
a, err := rand.Int(rand.Reader, max)
if err != nil {
panic(errors.New(""))
}
return a
}
func fromHex(size int, hexStrs ...string) []byte {
var out []byte
if size > 0 {
out = make([]byte, size*len(hexStrs))
}
for i := 0; i < len(hexStrs); i++ {
hexStr := hexStrs[i]
if hexStr[:2] == "0x" {
hexStr = hexStr[2:]
}
if len(hexStr)%2 == 1 {
hexStr = "0" + hexStr
}
bytes, err := hex.DecodeString(hexStr)
if err != nil {
return nil
}
if size <= 0 {
out = append(out, bytes...)
} else {
if len(bytes) > size {
return nil
}
offset := i*size + (size - len(bytes))
copy(out[offset:], bytes)
}
}
return out
}
func padBytes(in []byte, size int) []byte {
out := make([]byte, size)
if len(in) > size {
panic("bad input for padding")
}
copy(out[size-len(in):], in)
return out
}

174
crypto/bls12381/field_element.go
View file

@ -1,19 +1,3 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
import (
@ -25,31 +9,34 @@ import (
)
// fe is base field element representation
type fe [6]uint64
type fe /*** ***/ [fpNumberOfLimbs]uint64
// fe2 is element representation of 'fp2' which is quadratic extension of base field 'fp'
// fe2 is element representation of 'fp2' which is quadratic extention of base field 'fp'
// Representation follows c[0] + c[1] * u encoding order.
type fe2 [2]fe
type fe2 /** ***/ [2]fe
// fe6 is element representation of 'fp6' field which is cubic extension of 'fp2'
// fe6 is element representation of 'fp6' field which is cubic extention of 'fp2'
// Representation follows c[0] + c[1] * v + c[2] * v^2 encoding order.
type fe6 [3]fe2
type fe6 /** ***/ [3]fe2
// fe12 is element representation of 'fp12' field which is quadratic extension of 'fp6'
// fe12 is element representation of 'fp12' field which is quadratic extention of 'fp6'
// Representation follows c[0] + c[1] * w encoding order.
type fe12 [2]fe6
type fe12 /** ***/ [2]fe6
type wfe /*** ***/ [fpNumberOfLimbs * 2]uint64
type wfe2 /** ***/ [2]wfe
type wfe6 /** ***/ [3]wfe2
func (fe *fe) setBytes(in []byte) *fe {
size := 48
l := len(in)
if l >= size {
l = size
if l >= fpByteSize {
l = fpByteSize
}
padded := make([]byte, size)
copy(padded[size-l:], in[:])
padded := make([]byte, fpByteSize)
copy(padded[fpByteSize-l:], in[:])
var a int
for i := 0; i < 6; i++ {
a = size - i*8
for i := 0; i < fpNumberOfLimbs; i++ {
a = fpByteSize - i*8
fe[i] = uint64(padded[a-1]) | uint64(padded[a-2])<<8 |
uint64(padded[a-3])<<16 | uint64(padded[a-4])<<24 |
uint64(padded[a-5])<<32 | uint64(padded[a-6])<<40 |
@ -84,10 +71,10 @@ func (fe *fe) set(fe2 *fe) *fe {
}
func (fe *fe) bytes() []byte {
out := make([]byte, 48)
out := make([]byte, fpByteSize)
var a int
for i := 0; i < 6; i++ {
a = 48 - i*8
for i := 0; i < fpNumberOfLimbs; i++ {
a = fpByteSize - i*8
out[a-1] = byte(fe[i])
out[a-2] = byte(fe[i] >> 8)
out[a-3] = byte(fe[i] >> 16)
@ -105,7 +92,7 @@ func (fe *fe) big() *big.Int {
}
func (fe *fe) string() (s string) {
for i := 5; i >= 0; i-- {
for i := fpNumberOfLimbs - 1; i >= 0; i-- {
s = fmt.Sprintf("%s%16.16x", s, fe[i])
}
return "0x" + s
@ -134,7 +121,7 @@ func (fe *fe) rand(r io.Reader) (*fe, error) {
}
func (fe *fe) isValid() bool {
return fe.cmp(&modulus) < 0
return fe.cmp(&modulus) == -1
}
func (fe *fe) isOdd() bool {
@ -156,7 +143,7 @@ func (fe *fe) isOne() bool {
}
func (fe *fe) cmp(fe2 *fe) int {
for i := 5; i >= 0; i-- {
for i := fpNumberOfLimbs - 1; i >= 0; i-- {
if fe[i] > fe2[i] {
return 1
} else if fe[i] < fe2[i] {
@ -170,30 +157,37 @@ func (fe *fe) equal(fe2 *fe) bool {
return fe2[0] == fe[0] && fe2[1] == fe[1] && fe2[2] == fe[2] && fe2[3] == fe[3] && fe2[4] == fe[4] && fe2[5] == fe[5]
}
func (e *fe) signBE() bool {
negZ, z := new(fe), new(fe)
fromMont(z, e)
neg(negZ, z)
return negZ.cmp(z) > -1
}
func (e *fe) sign() bool {
r := new(fe)
fromMont(r, e)
return r[0]&1 == 0
}
func (fe *fe) div2(e uint64) {
fe[0] = fe[0]>>1 | fe[1]<<63
fe[1] = fe[1]>>1 | fe[2]<<63
fe[2] = fe[2]>>1 | fe[3]<<63
fe[3] = fe[3]>>1 | fe[4]<<63
fe[4] = fe[4]>>1 | fe[5]<<63
fe[5] = fe[5]>>1 | e<<63
func (e *fe) div2(u uint64) {
e[0] = e[0]>>1 | e[1]<<63
e[1] = e[1]>>1 | e[2]<<63
e[2] = e[2]>>1 | e[3]<<63
e[3] = e[3]>>1 | e[4]<<63
e[4] = e[4]>>1 | e[5]<<63
e[5] = e[5]>>1 | u<<63
}
func (fe *fe) mul2() uint64 {
e := fe[5] >> 63
fe[5] = fe[5]<<1 | fe[4]>>63
fe[4] = fe[4]<<1 | fe[3]>>63
fe[3] = fe[3]<<1 | fe[2]>>63
fe[2] = fe[2]<<1 | fe[1]>>63
fe[1] = fe[1]<<1 | fe[0]>>63
fe[0] = fe[0] << 1
return e
func (e *fe) mul2() uint64 {
u := e[5] >> 63
e[5] = e[5]<<1 | e[4]>>63
e[4] = e[4]<<1 | e[3]>>63
e[3] = e[3]<<1 | e[2]>>63
e[2] = e[2]<<1 | e[1]>>63
e[1] = e[1]<<1 | e[0]>>63
e[0] = e[0] << 1
return u
}
func (e *fe2) zero() *fe2 {
@ -214,16 +208,28 @@ func (e *fe2) set(e2 *fe2) *fe2 {
return e
}
func (e *fe2) fromMont(a *fe2) {
fromMont(&e[0], &a[0])
fromMont(&e[1], &a[1])
}
func (e *fe2) fromWide(w *wfe2) {
fromWide(&e[0], &w[0])
fromWide(&e[1], &w[1])
}
func (e *fe2) rand(r io.Reader) (*fe2, error) {
a0, err := new(fe).rand(r)
if err != nil {
return nil, err
}
e[0].set(a0)
a1, err := new(fe).rand(r)
if err != nil {
return nil, err
}
return &fe2{*a0, *a1}, nil
e[1].set(a1)
return e, nil
}
func (e *fe2) isOne() bool {
@ -238,6 +244,13 @@ func (e *fe2) equal(e2 *fe2) bool {
return e[0].equal(&e2[0]) && e[1].equal(&e2[1])
}
func (e *fe2) signBE() bool {
if !e[1].isZero() {
return e[1].signBE()
}
return e[0].signBE()
}
func (e *fe2) sign() bool {
r := new(fe)
if !e[0].isZero() {
@ -269,20 +282,35 @@ func (e *fe6) set(e2 *fe6) *fe6 {
return e
}
func (e *fe6) fromMont(a *fe6) {
e[0].fromMont(&a[0])
e[1].fromMont(&a[1])
e[2].fromMont(&a[2])
}
func (e *fe6) fromWide(w *wfe6) {
e[0].fromWide(&w[0])
e[1].fromWide(&w[1])
e[2].fromWide(&w[2])
}
func (e *fe6) rand(r io.Reader) (*fe6, error) {
a0, err := new(fe2).rand(r)
if err != nil {
return nil, err
}
e[0].set(a0)
a1, err := new(fe2).rand(r)
if err != nil {
return nil, err
}
e[1].set(a1)
a2, err := new(fe2).rand(r)
if err != nil {
return nil, err
}
return &fe6{*a0, *a1, *a2}, nil
e[2].set(a2)
return e, nil
}
func (e *fe6) isOne() bool {
@ -315,16 +343,23 @@ func (e *fe12) set(e2 *fe12) *fe12 {
return e
}
func (e *fe12) fromMont(a *fe12) {
e[0].fromMont(&a[0])
e[1].fromMont(&a[1])
}
func (e *fe12) rand(r io.Reader) (*fe12, error) {
a0, err := new(fe6).rand(r)
if err != nil {
return nil, err
}
e[0].set(a0)
a1, err := new(fe6).rand(r)
if err != nil {
return nil, err
}
return &fe12{*a0, *a1}, nil
e[1].set(a1)
return e, nil
}
func (e *fe12) isOne() bool {
@ -338,3 +373,32 @@ func (e *fe12) isZero() bool {
func (e *fe12) equal(e2 *fe12) bool {
return e[0].equal(&e2[0]) && e[1].equal(&e2[1])
}
func (fe *wfe) set(fe2 *wfe) *wfe {
fe[0] = fe2[0]
fe[1] = fe2[1]
fe[2] = fe2[2]
fe[3] = fe2[3]
fe[4] = fe2[4]
fe[5] = fe2[5]
fe[6] = fe2[6]
fe[7] = fe2[7]
fe[8] = fe2[8]
fe[9] = fe2[9]
fe[10] = fe2[10]
fe[11] = fe2[11]
return fe
}
func (fe *wfe2) set(fe2 *wfe2) *wfe2 {
fe[0].set(&fe2[0])
fe[1].set(&fe2[1])
return fe
}
func (fe *wfe6) set(fe2 *wfe6) *wfe6 {
fe[0].set(&fe2[0])
fe[1].set(&fe2[1])
fe[2].set(&fe2[2])
return fe
}

47
crypto/bls12381/field_element_test.go
View file

@ -8,6 +8,7 @@ import (
)
func TestFieldElementValidation(t *testing.T) {
// fe
zero := new(fe).zero()
if !zero.isValid() {
t.Fatal("zero must be valid")
@ -59,8 +60,7 @@ func TestFieldElementEquality(t *testing.T) {
t.Fatal("a == a")
}
b2 := new(fe2)
fp2 := newFp2()
fp2.add(b2, a2, one2)
fp2Add(b2, a2, one2)
if a2.equal(b2) {
t.Fatal("a != a + 1")
}
@ -78,8 +78,7 @@ func TestFieldElementEquality(t *testing.T) {
t.Fatal("a == a")
}
b6 := new(fe6)
fp6 := newFp6(fp2)
fp6.add(b6, a6, one6)
fp6Add(b6, a6, one6)
if a6.equal(b6) {
t.Fatal("a != a + 1")
}
@ -97,11 +96,11 @@ func TestFieldElementEquality(t *testing.T) {
t.Fatal("a == a")
}
b12 := new(fe12)
fp12 := newFp12(fp6)
fp12.add(b12, a12, one12)
fp12Add(b12, a12, one12)
if a12.equal(b12) {
t.Fatal("a != a + 1")
}
}
func TestFieldElementHelpers(t *testing.T) {
@ -159,13 +158,13 @@ func TestFieldElementHelpers(t *testing.T) {
func TestFieldElementSerialization(t *testing.T) {
t.Run("zero", func(t *testing.T) {
in := make([]byte, 48)
in := make([]byte, fpByteSize)
fe := new(fe).setBytes(in)
if !fe.isZero() {
t.Fatal("bad serialization")
t.Fatal("serialization failed")
}
if !bytes.Equal(in, fe.bytes()) {
t.Fatal("bad serialization")
t.Fatal("serialization failed")
}
})
t.Run("bytes", func(t *testing.T) {
@ -173,7 +172,7 @@ func TestFieldElementSerialization(t *testing.T) {
a, _ := new(fe).rand(rand.Reader)
b := new(fe).setBytes(a.bytes())
if !a.equal(b) {
t.Fatal("bad serialization")
t.Fatal("serialization failed")
}
}
})
@ -182,7 +181,7 @@ func TestFieldElementSerialization(t *testing.T) {
a, _ := new(fe).rand(rand.Reader)
b := new(fe).setBig(a.big())
if !a.equal(b) {
t.Fatal("bad encoding or decoding")
t.Fatal("encoding or decoding failed")
}
}
})
@ -194,7 +193,7 @@ func TestFieldElementSerialization(t *testing.T) {
t.Fatal(err)
}
if !a.equal(b) {
t.Fatal("bad encoding or decoding")
t.Fatal("encoding or decoding failed")
}
}
})
@ -205,24 +204,24 @@ func TestFieldElementByteInputs(t *testing.T) {
in := make([]byte, 0)
a := new(fe).setBytes(in)
if !a.equal(zero) {
t.Fatal("bad serialization")
t.Fatal("serialization failed")
}
in = make([]byte, 48)
in = make([]byte, fpByteSize)
a = new(fe).setBytes(in)
if !a.equal(zero) {
t.Fatal("bad serialization")
t.Fatal("serialization failed")
}
in = make([]byte, 64)
in = make([]byte, fpByteSize+200)
a = new(fe).setBytes(in)
if !a.equal(zero) {
t.Fatal("bad serialization")
t.Fatal("serialization failed")
}
in = make([]byte, 49)
in[47] = 1
in = make([]byte, fpByteSize+1)
in[fpByteSize-1] = 1
normalOne := &fe{1, 0, 0, 0, 0, 0}
a = new(fe).setBytes(in)
if !a.equal(normalOne) {
t.Fatal("bad serialization")
t.Fatal("serialization failed")
}
}
@ -230,21 +229,21 @@ func TestFieldElementCopy(t *testing.T) {
a, _ := new(fe).rand(rand.Reader)
b := new(fe).set(a)
if !a.equal(b) {
t.Fatal("bad copy, 1")
t.Fatal("copy failed")
}
a2, _ := new(fe2).rand(rand.Reader)
b2 := new(fe2).set(a2)
if !a2.equal(b2) {
t.Fatal("bad copy, 2")
t.Fatal("copy failed")
}
a6, _ := new(fe6).rand(rand.Reader)
b6 := new(fe6).set(a6)
if !a6.equal(b6) {
t.Fatal("bad copy, 6")
t.Fatal("copy failed")
}
a12, _ := new(fe12).rand(rand.Reader)
b12 := new(fe12).set(a12)
if !a12.equal(b12) {
t.Fatal("bad copy, 12")
t.Fatal("copy failed2")
}
}

255
crypto/bls12381/fp.go
View file

@ -1,19 +1,3 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
import (
@ -23,8 +7,8 @@ import (
func fromBytes(in []byte) (*fe, error) {
fe := &fe{}
if len(in) != 48 {
return nil, errors.New("input string should be equal 48 bytes")
if len(in) != fpByteSize {
return nil, errors.New("input string must be equal 48 bytes")
}
fe.setBytes(in)
if !fe.isValid() {
@ -34,6 +18,37 @@ func fromBytes(in []byte) (*fe, error) {
return fe, nil
}
func from64Bytes(in []byte) (*fe, error) {
if len(in) != 32*2 {
return nil, errors.New("input string must be equal 64 bytes")
}
a0 := make([]byte, fpByteSize)
copy(a0[fpByteSize-32:fpByteSize], in[:32])
a1 := make([]byte, fpByteSize)
copy(a1[fpByteSize-32:fpByteSize], in[32:])
e0, err := fromBytes(a0)
if err != nil {
return nil, err
}
e1, err := fromBytes(a1)
if err != nil {
return nil, err
}
// F = 2 ^ 256 * R
F := fe{
0x75b3cd7c5ce820f,
0x3ec6ba621c3edb0b,
0x168a13d82bff6bce,
0x87663c4bf8c449d2,
0x15f34c83ddc8d830,
0xf9628b49caa2e85,
}
mul(e0, e0, &F)
add(e1, e1, e0)
return e1, nil
}
func fromBig(in *big.Int) (*fe, error) {
fe := new(fe).setBig(in)
if !fe.isValid() {
@ -81,6 +96,28 @@ func fromMont(c, a *fe) {
mul(c, a, &fe{1})
}
func wfp2MulGeneric(c *wfe2, a, b *fe2) {
wt0, wt1 := new(wfe), new(wfe)
t0, t1 := new(fe), new(fe)
wmul(wt0, &a[0], &b[0])
wmul(wt1, &a[1], &b[1])
wsub(&c[0], wt0, wt1)
lwaddAssign(wt0, wt1)
ladd(t0, &a[0], &a[1])
ladd(t1, &b[0], &b[1])
wmul(wt1, t0, t1)
lwsub(&c[1], wt1, wt0)
}
func wfp2SquareGeneric(c *wfe2, a *fe2) {
t0, t1, t2 := new(fe), new(fe), new(fe)
ladd(t0, &a[0], &a[1])
sub(t1, &a[0], &a[1])
ldouble(t2, &a[0])
wmul(&c[0], t1, t0)
wmul(&c[1], t2, &a[1])
}
func exp(c, a *fe, e *big.Int) {
z := new(fe).set(r1)
for i := e.BitLen(); i >= 0; i-- {
@ -105,7 +142,7 @@ func inverse(inv, e *fe) {
var z uint64
var found = false
// Phase 1
for i := 0; i < 768; i++ {
for i := 0; i < sixWordBitSize*2; i++ {
if v.isZero() {
found = true
break
@ -135,7 +172,7 @@ func inverse(inv, e *fe) {
return
}
if k < 381 || k > 381+384 {
if k < fpBitSize || k > fpBitSize+sixWordBitSize {
inv.zero()
return
}
@ -147,21 +184,189 @@ func inverse(inv, e *fe) {
lsubAssign(u, r)
// Phase 2
for i := k; i < 384*2; i++ {
for i := k; i < 2*sixWordBitSize; i++ {
double(u, u)
}
inv.set(u)
}
func inverseBatch(in []fe) {
n, N, setFirst := 0, len(in), false
for i := 0; i < len(in); i++ {
if !in[i].isZero() {
n++
}
}
if n == 0 {
return
}
tA := make([]fe, n)
tB := make([]fe, n)
for i, j := 0, 0; i < N; i++ {
if !in[i].isZero() {
if !setFirst {
setFirst = true
tA[j].set(&in[i])
} else {
mul(&tA[j], &in[i], &tA[j-1])
}
j = j + 1
}
}
inverse(&tB[n-1], &tA[n-1])
for i, j := N-1, n-1; j != 0; i-- {
if !in[i].isZero() {
mul(&tB[j-1], &tB[j], &in[i])
j = j - 1
}
}
for i, j := 0, 0; i < N; i++ {
if !in[i].isZero() {
if setFirst {
setFirst = false
in[i].set(&tB[j])
} else {
mul(&in[i], &tA[j-1], &tB[j])
}
j = j + 1
}
}
}
func rsqrt(c, a *fe) bool {
t0, t1 := new(fe), new(fe)
sqrtAddchain(t0, a)
mul(t1, t0, a)
square(t1, t1)
ret := t1.equal(a)
c.set(t0)
return ret
}
func sqrt(c, a *fe) bool {
u, v := new(fe).set(a), new(fe)
// a ^ (p - 3) / 4
sqrtAddchain(c, a)
// a ^ (p + 1) / 4
mul(c, c, u)
square(v, c)
return u.equal(v)
}
func _sqrt(c, a *fe) bool {
u, v := new(fe).set(a), new(fe)
exp(c, a, pPlus1Over4)
square(v, c)
return u.equal(v)
}
func isQuadraticNonResidue(elem *fe) bool {
result := new(fe)
exp(result, elem, pMinus1Over2)
return !result.isOne()
func sqrtAddchain(c, a *fe) {
chain := func(c *fe, n int, a *fe) {
for i := 0; i < n; i++ {
square(c, c)
}
mul(c, c, a)
}
t := make([]fe, 16)
t[13].set(a)
square(&t[0], &t[13])
mul(&t[8], &t[0], &t[13])
square(&t[4], &t[0])
mul(&t[1], &t[8], &t[0])
mul(&t[6], &t[4], &t[8])
mul(&t[9], &t[1], &t[4])
mul(&t[12], &t[6], &t[4])
mul(&t[3], &t[9], &t[4])
mul(&t[7], &t[12], &t[4])
mul(&t[15], &t[3], &t[4])
mul(&t[10], &t[7], &t[4])
mul(&t[2], &t[15], &t[4])
mul(&t[11], &t[10], &t[4])
square(&t[0], &t[3])
mul(&t[14], &t[11], &t[4])
mul(&t[5], &t[0], &t[8])
mul(&t[4], &t[0], &t[1])
chain(&t[0], 12, &t[15])
chain(&t[0], 7, &t[7])
chain(&t[0], 4, &t[1])
chain(&t[0], 6, &t[6])
chain(&t[0], 7, &t[11])
chain(&t[0], 5, &t[4])
chain(&t[0], 2, &t[8])
chain(&t[0], 6, &t[3])
chain(&t[0], 6, &t[3])
chain(&t[0], 6, &t[9])
chain(&t[0], 3, &t[8])
chain(&t[0], 7, &t[3])
chain(&t[0], 4, &t[3])
chain(&t[0], 6, &t[7])
chain(&t[0], 6, &t[14])
chain(&t[0], 3, &t[13])
chain(&t[0], 8, &t[3])
chain(&t[0], 7, &t[11])
chain(&t[0], 5, &t[12])
chain(&t[0], 6, &t[3])
chain(&t[0], 6, &t[5])
chain(&t[0], 4, &t[9])
chain(&t[0], 8, &t[5])
chain(&t[0], 4, &t[3])
chain(&t[0], 7, &t[11])
chain(&t[0], 9, &t[10])
chain(&t[0], 2, &t[8])
chain(&t[0], 5, &t[6])
chain(&t[0], 7, &t[1])
chain(&t[0], 7, &t[9])
chain(&t[0], 6, &t[11])
chain(&t[0], 5, &t[5])
chain(&t[0], 5, &t[10])
chain(&t[0], 5, &t[10])
chain(&t[0], 8, &t[3])
chain(&t[0], 7, &t[2])
chain(&t[0], 9, &t[7])
chain(&t[0], 5, &t[3])
chain(&t[0], 3, &t[8])
chain(&t[0], 8, &t[7])
chain(&t[0], 3, &t[8])
chain(&t[0], 7, &t[9])
chain(&t[0], 9, &t[7])
chain(&t[0], 6, &t[2])
chain(&t[0], 6, &t[4])
chain(&t[0], 5, &t[4])
chain(&t[0], 5, &t[4])
chain(&t[0], 4, &t[3])
chain(&t[0], 3, &t[8])
chain(&t[0], 8, &t[2])
chain(&t[0], 7, &t[4])
chain(&t[0], 5, &t[4])
chain(&t[0], 5, &t[4])
chain(&t[0], 4, &t[7])
chain(&t[0], 4, &t[6])
chain(&t[0], 7, &t[4])
chain(&t[0], 5, &t[5])
chain(&t[0], 5, &t[4])
chain(&t[0], 5, &t[4])
chain(&t[0], 5, &t[4])
chain(&t[0], 5, &t[4])
chain(&t[0], 5, &t[4])
chain(&t[0], 5, &t[4])
chain(&t[0], 4, &t[3])
chain(&t[0], 6, &t[2])
chain(&t[0], 4, &t[1])
square(c, &t[0])
}
func isQuadraticNonResidue(a *fe) bool {
if a.isZero() {
return true
}
return !sqrt(new(fe), a)
}

354
crypto/bls12381/fp12.go
View file

@ -1,19 +1,3 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
import (
@ -27,21 +11,30 @@ type fp12 struct {
}
type fp12temp struct {
t2 [9]*fe2
t6 [5]*fe6
t12 *fe12
t2 [7]*fe2
t6 [4]*fe6
wt2 [3]*wfe2
wt6 [3]*wfe6
}
func newFp12Temp() fp12temp {
t2 := [9]*fe2{}
t6 := [5]*fe6{}
t2 := [7]*fe2{}
t6 := [4]*fe6{}
for i := 0; i < len(t2); i++ {
t2[i] = &fe2{}
}
for i := 0; i < len(t6); i++ {
t6[i] = &fe6{}
}
return fp12temp{t2, t6, &fe12{}}
wt2 := [3]*wfe2{}
for i := 0; i < len(wt2); i++ {
wt2[i] = &wfe2{}
}
wt6 := [3]*wfe6{}
for i := 0; i < len(wt6); i++ {
wt6[i] = &wfe6{}
}
return fp12temp{t2, t6, wt2, wt6}
}
func newFp12(fp6 *fp6) *fp12 {
@ -58,14 +51,14 @@ func (e *fp12) fp2() *fp2 {
func (e *fp12) fromBytes(in []byte) (*fe12, error) {
if len(in) != 576 {
return nil, errors.New("input string should be larger than 96 bytes")
return nil, errors.New("input string length must be equal to 576 bytes")
}
fp6 := e.fp6
c1, err := fp6.fromBytes(in[:288])
c1, err := fp6.fromBytes(in[:6*fpByteSize])
if err != nil {
return nil, err
}
c0, err := fp6.fromBytes(in[288:])
c0, err := fp6.fromBytes(in[6*fpByteSize:])
if err != nil {
return nil, err
}
@ -74,9 +67,9 @@ func (e *fp12) fromBytes(in []byte) (*fe12, error) {
func (e *fp12) toBytes(a *fe12) []byte {
fp6 := e.fp6
out := make([]byte, 576)
copy(out[:288], fp6.toBytes(&a[1]))
copy(out[288:], fp6.toBytes(&a[0]))
out := make([]byte, 12*fpByteSize)
copy(out[:6*fpByteSize], fp6.toBytes(&a[1]))
copy(out[6*fpByteSize:], fp6.toBytes(&a[0]))
return out
}
@ -92,138 +85,125 @@ func (e *fp12) one() *fe12 {
return new(fe12).one()
}
func (e *fp12) add(c, a, b *fe12) {
fp6 := e.fp6
fp6.add(&c[0], &a[0], &b[0])
fp6.add(&c[1], &a[1], &b[1])
func fp12Add(c, a, b *fe12) {
fp6Add(&c[0], &a[0], &b[0])
fp6Add(&c[1], &a[1], &b[1])
}
func (e *fp12) double(c, a *fe12) {
fp6 := e.fp6
fp6.double(&c[0], &a[0])
fp6.double(&c[1], &a[1])
func fp12Double(c, a *fe12) {
fp6Double(&c[0], &a[0])
fp6Double(&c[1], &a[1])
}
func (e *fp12) sub(c, a, b *fe12) {
fp6 := e.fp6
fp6.sub(&c[0], &a[0], &b[0])
fp6.sub(&c[1], &a[1], &b[1])
func fp12Sub(c, a, b *fe12) {
fp6Sub(&c[0], &a[0], &b[0])
fp6Sub(&c[1], &a[1], &b[1])
}
func (e *fp12) neg(c, a *fe12) {
fp6 := e.fp6
fp6.neg(&c[0], &a[0])
fp6.neg(&c[1], &a[1])
func fp12Neg(c, a *fe12) {
fp6Neg(&c[0], &a[0])
fp6Neg(&c[1], &a[1])
}
func (e *fp12) conjugate(c, a *fe12) {
fp6 := e.fp6
func fp12Conjugate(c, a *fe12) {
c[0].set(&a[0])
fp6.neg(&c[1], &a[1])
}
func (e *fp12) square(c, a *fe12) {
fp6, t := e.fp6, e.t6
fp6.add(t[0], &a[0], &a[1])
fp6.mul(t[2], &a[0], &a[1])
fp6.mulByNonResidue(t[1], &a[1])
fp6.addAssign(t[1], &a[0])
fp6.mulByNonResidue(t[3], t[2])
fp6.mulAssign(t[0], t[1])
fp6.subAssign(t[0], t[2])
fp6.sub(&c[0], t[0], t[3])
fp6.double(&c[1], t[2])
}
func (e *fp12) cyclotomicSquare(c, a *fe12) {
t, fp2 := e.t2, e.fp2()
e.fp4Square(t[3], t[4], &a[0][0], &a[1][1])
fp2.sub(t[2], t[3], &a[0][0])
fp2.doubleAssign(t[2])
fp2.add(&c[0][0], t[2], t[3])
fp2.add(t[2], t[4], &a[1][1])
fp2.doubleAssign(t[2])
fp2.add(&c[1][1], t[2], t[4])
e.fp4Square(t[3], t[4], &a[1][0], &a[0][2])
e.fp4Square(t[5], t[6], &a[0][1], &a[1][2])
fp2.sub(t[2], t[3], &a[0][1])
fp2.doubleAssign(t[2])
fp2.add(&c[0][1], t[2], t[3])
fp2.add(t[2], t[4], &a[1][2])
fp2.doubleAssign(t[2])
fp2.add(&c[1][2], t[2], t[4])
fp2.mulByNonResidue(t[3], t[6])
fp2.add(t[2], t[3], &a[1][0])
fp2.doubleAssign(t[2])
fp2.add(&c[1][0], t[2], t[3])
fp2.sub(t[2], t[5], &a[0][2])
fp2.doubleAssign(t[2])
fp2.add(&c[0][2], t[2], t[5])
fp6Neg(&c[1], &a[1])
}
func (e *fp12) mul(c, a, b *fe12) {
t, fp6 := e.t6, e.fp6
fp6.mul(t[1], &a[0], &b[0])
fp6.mul(t[2], &a[1], &b[1])
fp6.add(t[0], t[1], t[2])
fp6.mulByNonResidue(t[2], t[2])
fp6.add(t[3], t[1], t[2])
fp6.add(t[1], &a[0], &a[1])
fp6.add(t[2], &b[0], &b[1])
fp6.mulAssign(t[1], t[2])
c[0].set(t[3])
fp6.sub(&c[1], t[1], t[0])
wt, t := e.wt6, e.t6
e.fp6.wmul(wt[1], &a[0], &b[0])
e.fp6.wmul(wt[2], &a[1], &b[1])
fp6Add(t[0], &a[0], &a[1])
fp6Add(t[3], &b[0], &b[1])
e.fp6.wmul(wt[0], t[0], t[3])
wfp6SubAssign(wt[0], wt[1])
wfp6SubAssign(wt[0], wt[2])
c[1].fromWide(wt[0])
e.fp6.wmulByNonResidueAssign(wt[2])
wfp6AddAssign(wt[1], wt[2])
c[0].fromWide(wt[1])
}
func (e *fp12) mulAssign(a, b *fe12) {
t, fp6 := e.t6, e.fp6
fp6.mul(t[1], &a[0], &b[0])
fp6.mul(t[2], &a[1], &b[1])
fp6.add(t[0], t[1], t[2])
fp6.mulByNonResidue(t[2], t[2])
fp6.add(t[3], t[1], t[2])
fp6.add(t[1], &a[0], &a[1])
fp6.add(t[2], &b[0], &b[1])
fp6.mulAssign(t[1], t[2])
a[0].set(t[3])
fp6.sub(&a[1], t[1], t[0])
wt, t := e.wt6, e.t6
e.fp6.wmul(wt[1], &a[0], &b[0])
e.fp6.wmul(wt[2], &a[1], &b[1])
fp6Add(t[0], &a[0], &a[1])
fp6Add(t[3], &b[0], &b[1])
e.fp6.wmul(wt[0], t[0], t[3])
wfp6SubAssign(wt[0], wt[1])
wfp6SubAssign(wt[0], wt[2])
a[1].fromWide(wt[0])
e.fp6.wmulByNonResidueAssign(wt[2])
wfp6AddAssign(wt[1], wt[2])
a[0].fromWide(wt[1])
}
func (e *fp12) fp4Square(c0, c1, a0, a1 *fe2) {
t, fp2 := e.t2, e.fp2()
fp2.square(t[0], a0)
fp2.square(t[1], a1)
fp2.mulByNonResidue(t[2], t[1])
fp2.add(c0, t[2], t[0])
fp2.add(t[2], a0, a1)
fp2.squareAssign(t[2])
fp2.subAssign(t[2], t[0])
fp2.sub(c1, t[2], t[1])
func (e *fp12) mul014(a *fe12, b0, b1, b4 *fe2) {
wt, t := e.wt6, e.t6
e.fp6.wmul01(wt[0], &a[0], b0, b1)
e.fp6.wmul1(wt[1], &a[1], b4)
fp2LaddAssign(b1, b4)
fp6Ladd(t[2], &a[1], &a[0])
e.fp6.wmul01(wt[2], t[2], b0, b1)
wfp6SubAssign(wt[2], wt[0])
wfp6SubAssign(wt[2], wt[1])
a[1].fromWide(wt[2])
e.fp6.wmulByNonResidueAssign(wt[1])
wfp6AddAssign(wt[0], wt[1])
a[0].fromWide(wt[0])
}
func (e *fp12) square(c, a *fe12) {
t := e.t6
// Multiplication and Squaring on Pairing-Friendly Fields
// Complex squaring algorithm
// https://eprint.iacr.org/2006/471
fp6Add(t[0], &a[0], &a[1])
e.fp6.mul(t[2], &a[0], &a[1])
e.fp6.mulByNonResidue(t[1], &a[1])
fp6AddAssign(t[1], &a[0])
e.fp6.mulByNonResidue(t[3], t[2])
e.fp6.mul(t[0], t[0], t[1])
fp6SubAssign(t[0], t[2])
fp6Sub(&c[0], t[0], t[3])
fp6Double(&c[1], t[2])
}
func (e *fp12) squareAssign(a *fe12) {
t := e.t6
// Multiplication and Squaring on Pairing-Friendly Fields
// Complex squaring algorithm
// https://eprint.iacr.org/2006/471
fp6Add(t[0], &a[0], &a[1])
e.fp6.mul(t[2], &a[0], &a[1])
e.fp6.mulByNonResidue(t[1], &a[1])
fp6AddAssign(t[1], &a[0])
e.fp6.mulByNonResidue(t[3], t[2])
e.fp6.mul(t[0], t[0], t[1])
fp6SubAssign(t[0], t[2])
fp6Sub(&a[0], t[0], t[3])
fp6Double(&a[1], t[2])
}
func (e *fp12) inverse(c, a *fe12) {
fp6, t := e.fp6, e.t6
fp6.square(t[0], &a[0])
fp6.square(t[1], &a[1])
fp6.mulByNonResidue(t[1], t[1])
fp6.sub(t[1], t[0], t[1])
fp6.inverse(t[0], t[1])
fp6.mul(&c[0], &a[0], t[0])
fp6.mulAssign(t[0], &a[1])
fp6.neg(&c[1], t[0])
}
// Guide to Pairing Based Cryptography
// Algorithm 5.16
func (e *fp12) mulBy014Assign(a *fe12, c0, c1, c4 *fe2) {
fp2, fp6, t, t2 := e.fp2(), e.fp6, e.t6, e.t2[0]
fp6.mulBy01(t[0], &a[0], c0, c1)
fp6.mulBy1(t[1], &a[1], c4)
fp2.add(t2, c1, c4)
fp6.add(t[2], &a[1], &a[0])
fp6.mulBy01Assign(t[2], c0, t2)
fp6.subAssign(t[2], t[0])
fp6.sub(&a[1], t[2], t[1])
fp6.mulByNonResidue(t[1], t[1])
fp6.add(&a[0], t[1], t[0])
t := e.t6
e.fp6.square(t[0], &a[0]) // a0^2
e.fp6.square(t[1], &a[1]) // a1^2
e.fp6.mulByNonResidue(t[1], t[1]) // βa1^2
fp6SubAssign(t[0], t[1]) // v = (a0^2 - a1^2)
e.fp6.inverse(t[1], t[0]) // v = v^-1
e.fp6.mul(&c[0], &a[0], t[1]) // c0 = a0v
e.fp6.mulAssign(t[1], &a[1]) //
fp6Neg(&c[1], t[1]) // c1 = -a1v
}
func (e *fp12) exp(c, a *fe12, s *big.Int) {
@ -240,7 +220,7 @@ func (e *fp12) exp(c, a *fe12, s *big.Int) {
func (e *fp12) cyclotomicExp(c, a *fe12, s *big.Int) {
z := e.one()
for i := s.BitLen() - 1; i >= 0; i-- {
e.cyclotomicSquare(z, z)
e.cyclotomicSquare(z)
if s.Bit(i) == 1 {
e.mul(z, z, a)
}
@ -248,30 +228,76 @@ func (e *fp12) cyclotomicExp(c, a *fe12, s *big.Int) {
c.set(z)
}
func (e *fp12) frobeniusMap(c, a *fe12, power uint) {
fp6 := e.fp6
fp6.frobeniusMap(&c[0], &a[0], power)
fp6.frobeniusMap(&c[1], &a[1], power)
switch power {
case 0:
return
case 6:
fp6.neg(&c[1], &c[1])
default:
fp6.mulByBaseField(&c[1], &c[1], &frobeniusCoeffs12[power])
}
func (e *fp12) cyclotomicSquare(a *fe12) {
t := e.t2
// Guide to Pairing Based Cryptography
// 5.5.4 Airthmetic in Cyclotomic Groups
e.fp4Square(t[3], t[4], &a[0][0], &a[1][1])
fp2Sub(t[2], t[3], &a[0][0])
fp2DoubleAssign(t[2])
fp2Add(&a[0][0], t[2], t[3])
fp2Add(t[2], t[4], &a[1][1])
fp2DoubleAssign(t[2])
fp2Add(&a[1][1], t[2], t[4])
e.fp4Square(t[3], t[4], &a[1][0], &a[0][2])
e.fp4Square(t[5], t[6], &a[0][1], &a[1][2])
fp2Sub(t[2], t[3], &a[0][1])
fp2DoubleAssign(t[2])
fp2Add(&a[0][1], t[2], t[3])
fp2Add(t[2], t[4], &a[1][2])
fp2DoubleAssign(t[2])
fp2Add(&a[1][2], t[2], t[4])
mulByNonResidue(t[3], t[6])
fp2Add(t[2], t[3], &a[1][0])
fp2DoubleAssign(t[2])
fp2Add(&a[1][0], t[2], t[3])
fp2Sub(t[2], t[5], &a[0][2])
fp2DoubleAssign(t[2])
fp2Add(&a[0][2], t[2], t[5])
}
func (e *fp12) frobeniusMapAssign(a *fe12, power uint) {
fp6 := e.fp6
fp6.frobeniusMapAssign(&a[0], power)
fp6.frobeniusMapAssign(&a[1], power)
switch power {
case 0:
return
case 6:
fp6.neg(&a[1], &a[1])
default:
fp6.mulByBaseField(&a[1], &a[1], &frobeniusCoeffs12[power])
}
func (e *fp12) fp4Square(c0, c1, a0, a1 *fe2) {
wt, t := e.wt2, e.t2
// Multiplication and Squaring on Pairing-Friendly Fields
// Karatsuba squaring algorithm
// https://eprint.iacr.org/2006/471
wfp2Square(wt[0], a0)
wfp2Square(wt[1], a1)
wfp2MulByNonResidue(wt[2], wt[1])
wfp2AddAssign(wt[2], wt[0])
c0.fromWide(wt[2])
fp2Add(t[0], a0, a1)
wfp2Square(wt[2], t[0])
wfp2SubAssign(wt[2], wt[0])
wfp2SubAssign(wt[2], wt[1])
c1.fromWide(wt[2])
}
func (e *fp12) frobeniusMap1(a *fe12) {
fp6, fp2 := e.fp6, e.fp6.fp2
fp6.frobeniusMap1(&a[0])
fp6.frobeniusMap1(&a[1])
fp2.mulAssign(&a[1][0], &frobeniusCoeffs12[1])
fp2.mulAssign(&a[1][1], &frobeniusCoeffs12[1])
fp2.mulAssign(&a[1][2], &frobeniusCoeffs12[1])
}
func (e *fp12) frobeniusMap2(a *fe12) {
fp6, fp2 := e.fp6, e.fp6.fp2
fp6.frobeniusMap2(&a[0])
fp6.frobeniusMap2(&a[1])
fp2.mulAssign(&a[1][0], &frobeniusCoeffs12[2])
fp2.mulAssign(&a[1][1], &frobeniusCoeffs12[2])
fp2.mulAssign(&a[1][2], &frobeniusCoeffs12[2])
}
func (e *fp12) frobeniusMap3(a *fe12) {
fp6, fp2 := e.fp6, e.fp6.fp2
fp6.frobeniusMap3(&a[0])
fp6.frobeniusMap3(&a[1])
fp2.mulAssign(&a[1][0], &frobeniusCoeffs12[3])
fp2.mulAssign(&a[1][1], &frobeniusCoeffs12[3])
fp2.mulAssign(&a[1][2], &frobeniusCoeffs12[3])
}

292
crypto/bls12381/fp2.go
View file

@ -1,19 +1,3 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
import (
@ -22,7 +6,8 @@ import (
)
type fp2Temp struct {
t [4]*fe
t [3]*fe
w *wfe2
}
type fp2 struct {
@ -30,11 +15,11 @@ type fp2 struct {
}
func newFp2Temp() fp2Temp {
t := [4]*fe{}
t := [3]*fe{}
for i := 0; i < len(t); i++ {
t[i] = &fe{}
}
return fp2Temp{t}
return fp2Temp{t, &wfe2{}}
}
func newFp2() *fp2 {
@ -43,14 +28,14 @@ func newFp2() *fp2 {
}
func (e *fp2) fromBytes(in []byte) (*fe2, error) {
if len(in) != 96 {
return nil, errors.New("length of input string should be 96 bytes")
if len(in) != 2*fpByteSize {
return nil, errors.New("input string must be equal to 96 bytes")
}
c1, err := fromBytes(in[:48])
c1, err := fromBytes(in[:fpByteSize])
if err != nil {
return nil, err
}
c0, err := fromBytes(in[48:])
c0, err := fromBytes(in[fpByteSize:])
if err != nil {
return nil, err
}
@ -58,9 +43,9 @@ func (e *fp2) fromBytes(in []byte) (*fe2, error) {
}
func (e *fp2) toBytes(a *fe2) []byte {
out := make([]byte, 96)
copy(out[:48], toBytes(&a[1]))
copy(out[48:], toBytes(&a[0]))
out := make([]byte, 2*fpByteSize)
copy(out[:fpByteSize], toBytes(&a[1]))
copy(out[fpByteSize:], toBytes(&a[0]))
return out
}
@ -76,82 +61,36 @@ func (e *fp2) one() *fe2 {
return new(fe2).one()
}
func (e *fp2) add(c, a, b *fe2) {
add(&c[0], &a[0], &b[0])
add(&c[1], &a[1], &b[1])
}
func (e *fp2) addAssign(a, b *fe2) {
addAssign(&a[0], &b[0])
addAssign(&a[1], &b[1])
}
func (e *fp2) ladd(c, a, b *fe2) {
ladd(&c[0], &a[0], &b[0])
ladd(&c[1], &a[1], &b[1])
}
func (e *fp2) double(c, a *fe2) {
double(&c[0], &a[0])
double(&c[1], &a[1])
}
func (e *fp2) doubleAssign(a *fe2) {
doubleAssign(&a[0])
doubleAssign(&a[1])
}
func (e *fp2) ldouble(c, a *fe2) {
ldouble(&c[0], &a[0])
ldouble(&c[1], &a[1])
}
func (e *fp2) sub(c, a, b *fe2) {
sub(&c[0], &a[0], &b[0])
sub(&c[1], &a[1], &b[1])
}
func (e *fp2) subAssign(c, a *fe2) {
subAssign(&c[0], &a[0])
subAssign(&c[1], &a[1])
}
func (e *fp2) neg(c, a *fe2) {
func fp2Neg(c, a *fe2) {
neg(&c[0], &a[0])
neg(&c[1], &a[1])
}
func fp2Conjugate(c, a *fe2) {
c[0].set(&a[0])
neg(&c[1], &a[1])
}
func (e *fp2) mul(c, a, b *fe2) {
t := e.t
mul(t[1], &a[0], &b[0])
mul(t[2], &a[1], &b[1])
add(t[0], &a[0], &a[1])
add(t[3], &b[0], &b[1])
sub(&c[0], t[1], t[2])
addAssign(t[1], t[2])
mul(t[0], t[0], t[3])
sub(&c[1], t[0], t[1])
wfp2Mul(e.w, b, a)
c.fromWide(e.w)
}
func (e *fp2) mulAssign(a, b *fe2) {
t := e.t
mul(t[1], &a[0], &b[0])
mul(t[2], &a[1], &b[1])
add(t[0], &a[0], &a[1])
add(t[3], &b[0], &b[1])
sub(&a[0], t[1], t[2])
addAssign(t[1], t[2])
mul(t[0], t[0], t[3])
sub(&a[1], t[0], t[1])
wfp2Mul(e.w, b, a)
a.fromWide(e.w)
}
func (e *fp2) square(c, a *fe2) {
t := e.t
ladd(t[0], &a[0], &a[1])
sub(t[1], &a[0], &a[1])
ldouble(t[2], &a[0])
mul(&c[0], t[0], t[1])
mul(&c[1], t[2], &a[1])
// Guide to Pairing Based Cryptography
// Algorithm 5.16
ladd(t[0], &a[0], &a[1]) // (a0 + a1)
sub(t[1], &a[0], &a[1]) // (a0 - a1)
ldouble(t[2], &a[0]) // 2a0
mul(&c[0], t[0], t[1]) // c0 = (a0 + a1)(a0 - a1)
mul(&c[1], t[2], &a[1]) // c1 = 2a0a1
}
func (e *fp2) squareAssign(a *fe2) {
@ -163,18 +102,23 @@ func (e *fp2) squareAssign(a *fe2) {
mul(&a[1], t[2], &a[1])
}
func (e *fp2) mulByNonResidue(c, a *fe2) {
t := e.t
sub(t[0], &a[0], &a[1])
add(&c[1], &a[0], &a[1])
c[0].set(t[0])
func (e *fp2) mul0(c, a *fe2, b *fe) {
mul(&c[0], &a[0], b)
mul(&c[1], &a[1], b)
}
func (e *fp2) mul0Assign(a *fe2, b *fe) {
mul(&a[0], &a[0], b)
mul(&a[1], &a[1], b)
}
func (e *fp2) mulByB(c, a *fe2) {
t := e.t
// c0 = 4a0 - 4a1
// c1 = 4a0 + 4a1
double(t[0], &a[0])
double(t[1], &a[1])
doubleAssign(t[0])
double(t[1], &a[1])
doubleAssign(t[1])
sub(&c[0], t[0], t[1])
add(&c[1], t[0], t[1])
@ -182,18 +126,70 @@ func (e *fp2) mulByB(c, a *fe2) {
func (e *fp2) inverse(c, a *fe2) {
t := e.t
square(t[0], &a[0])
square(t[1], &a[1])
addAssign(t[0], t[1])
inverse(t[0], t[0])
mul(&c[0], &a[0], t[0])
mul(t[0], t[0], &a[1])
neg(&c[1], t[0])
// Guide to Pairing Based Cryptography
// Algorithm 5.16
square(t[0], &a[0]) // a0^2
square(t[1], &a[1]) // a1^2
addAssign(t[0], t[1]) // a0^2 + a1^2
inverse(t[0], t[0]) // (a0^2 + a1^2)^-1
mul(&c[0], &a[0], t[0]) // c0 = a0(a0^2 + a1^2)^-1
mul(t[0], t[0], &a[1]) // a1(a0^2 + a1^2)^-1
neg(&c[1], t[0]) // c1 = a1(a0^2 + a1^2)^-1
}
func (e *fp2) mulByFq(c, a *fe2, b *fe) {
mul(&c[0], &a[0], b)
mul(&c[1], &a[1], b)
func (e *fp2) inverseBatch(in []fe2) {
n, N, setFirst := 0, len(in), false
for i := 0; i < len(in); i++ {
if !in[i].isZero() {
n++
}
}
if n == 0 {
return
}
tA := make([]fe2, n)
tB := make([]fe2, n)
// a, ab, abc, abcd, ...
for i, j := 0, 0; i < N; i++ {
if !in[i].isZero() {
if !setFirst {
setFirst = true
tA[j].set(&in[i])
} else {
e.mul(&tA[j], &in[i], &tA[j-1])
}
j = j + 1
}
}
// (abcd...)^-1
e.inverse(&tB[n-1], &tA[n-1])
// a^-1, ab^-1, abc^-1, abcd^-1, ...
for i, j := N-1, n-1; j != 0; i-- {
if !in[i].isZero() {
e.mul(&tB[j-1], &tB[j], &in[i])
j = j - 1
}
}
// a^-1, b^-1, c^-1, d^-1
for i, j := 0, 0; i < N; i++ {
if !in[i].isZero() {
if setFirst {
setFirst = false
in[i].set(&tB[j])
} else {
e.mul(&in[i], &tA[j-1], &tB[j])
}
j = j + 1
}
}
}
func (e *fp2) exp(c, a *fe2, s *big.Int) {
@ -207,19 +203,13 @@ func (e *fp2) exp(c, a *fe2, s *big.Int) {
c.set(z)
}
func (e *fp2) frobeniusMap(c, a *fe2, power uint) {
c[0].set(&a[0])
if power%2 == 1 {
neg(&c[1], &a[1])
return
}
c[1].set(&a[1])
func (e *fp2) frobeniusMap1(a *fe2) {
fp2Conjugate(a, a)
}
func (e *fp2) frobeniusMapAssign(a *fe2, power uint) {
if power%2 == 1 {
neg(&a[1], &a[1])
return
func (e *fp2) frobeniusMap(a *fe2, power int) {
if power&1 == 1 {
fp2Conjugate(a, a)
}
}
@ -235,7 +225,7 @@ func (e *fp2) sqrt(c, a *fe2) bool {
c[1].set(&x0[0])
return true
}
e.add(alpha, alpha, e.one())
fp2Add(alpha, alpha, e.one())
e.exp(alpha, alpha, pMinus1Over2)
e.mul(c, alpha, x0)
e.square(alpha, c)
@ -243,10 +233,74 @@ func (e *fp2) sqrt(c, a *fe2) bool {
}
func (e *fp2) isQuadraticNonResidue(a *fe2) bool {
// https://github.com/leovt/constructible/wiki/Taking-Square-Roots-in-quadratic-extension-Fields
c0, c1 := new(fe), new(fe)
square(c0, &a[0])
square(c1, &a[1])
add(c1, c1, c0)
return isQuadraticNonResidue(c1)
}
// faster square root algorith is adapted from blst library
// https://github.com/supranational/blst/blob/master/src/sqrt.c
func (e *fp2) sqrtBLST(out, inp *fe2) bool {
aa, bb := new(fe), new(fe)
ret := new(fe2)
square(aa, &inp[0])
square(bb, &inp[1])
add(aa, aa, bb)
sqrt(aa, aa)
sub(bb, &inp[0], aa)
add(aa, &inp[0], aa)
if aa.isZero() {
aa.set(bb)
}
mul(aa, aa, twoInv)
rsqrt(&ret[0], aa)
ret[1].set(&inp[1])
mul(&ret[1], &ret[1], twoInv)
mul(&ret[1], &ret[1], &ret[0])
mul(&ret[0], &ret[0], aa)
return e.sqrtAlignBLST(out, ret, ret, inp)
}
func (e *fp2) sqrtAlignBLST(out, ret, sqrt, inp *fe2) bool {
t0, t1 := new(fe2), new(fe2)
coeff := e.one()
e.square(t0, sqrt)
//
fp2Sub(t1, t0, inp)
isSqrt := t1.isZero()
//
fp2Add(t1, t0, inp)
flag := t1.isZero()
if flag {
coeff.set(sqrtMinus1)
}
isSqrt = flag || isSqrt
//
sub(&t1[0], &t0[0], &inp[1])
add(&t1[1], &t0[1], &inp[0])
flag = t1.isZero()
if flag {
coeff.set(sqrtSqrtMinus1)
}
isSqrt = flag || isSqrt
//
add(&t1[0], &t0[0], &inp[1])
sub(&t1[1], &t0[1], &inp[0])
flag = t1.isZero()
if flag {
coeff.set(sqrtMinusSqrtMinus1)
}
isSqrt = flag || isSqrt
e.mul(out, coeff, ret)
return isSqrt
}

4025
crypto/bls12381/fp2_arithmetic_x86.s Normal file
View file

File diff suppressed because it is too large Load diff

625
crypto/bls12381/fp6.go
View file

@ -1,19 +1,3 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
import (
@ -22,7 +6,8 @@ import (
)
type fp6Temp struct {
t [6]*fe2
t [5]*fe2
wt [6]*wfe2
}
type fp6 struct {
@ -31,11 +16,15 @@ type fp6 struct {
}
func newFp6Temp() fp6Temp {
t := [6]*fe2{}
t := [5]*fe2{}
for i := 0; i < len(t); i++ {
t[i] = &fe2{}
}
return fp6Temp{t}
wt := [6]*wfe2{}
for i := 0; i < len(wt); i++ {
wt[i] = &wfe2{}
}
return fp6Temp{t, wt}
}
func newFp6(f *fp2) *fp6 {
@ -47,19 +36,19 @@ func newFp6(f *fp2) *fp6 {
}
func (e *fp6) fromBytes(b []byte) (*fe6, error) {
if len(b) < 288 {
return nil, errors.New("input string should be larger than 288 bytes")
if len(b) != 288 {
return nil, errors.New("input string length must be equal to 288 bytes")
}
fp2 := e.fp2
u2, err := fp2.fromBytes(b[:96])
u2, err := fp2.fromBytes(b[:2*fpByteSize])
if err != nil {
return nil, err
}
u1, err := fp2.fromBytes(b[96:192])
u1, err := fp2.fromBytes(b[2*fpByteSize : 4*fpByteSize])
if err != nil {
return nil, err
}
u0, err := fp2.fromBytes(b[192:])
u0, err := fp2.fromBytes(b[4*fpByteSize:])
if err != nil {
return nil, err
}
@ -68,10 +57,10 @@ func (e *fp6) fromBytes(b []byte) (*fe6, error) {
func (e *fp6) toBytes(a *fe6) []byte {
fp2 := e.fp2
out := make([]byte, 288)
copy(out[:96], fp2.toBytes(&a[2]))
copy(out[96:192], fp2.toBytes(&a[1]))
copy(out[192:], fp2.toBytes(&a[0]))
out := make([]byte, 6*fpByteSize)
copy(out[:2*fpByteSize], fp2.toBytes(&a[2]))
copy(out[2*fpByteSize:4*fpByteSize], fp2.toBytes(&a[1]))
copy(out[4*fpByteSize:], fp2.toBytes(&a[0]))
return out
}
@ -87,188 +76,368 @@ func (e *fp6) one() *fe6 {
return new(fe6).one()
}
func (e *fp6) add(c, a, b *fe6) {
fp2 := e.fp2
fp2.add(&c[0], &a[0], &b[0])
fp2.add(&c[1], &a[1], &b[1])
fp2.add(&c[2], &a[2], &b[2])
func fp6Ladd(c, a, b *fe6) {
fp2Ladd(&c[0], &a[0], &b[0])
fp2Ladd(&c[1], &a[1], &b[1])
fp2Ladd(&c[2], &a[2], &b[2])
}
func (e *fp6) addAssign(a, b *fe6) {
fp2 := e.fp2
fp2.addAssign(&a[0], &b[0])
fp2.addAssign(&a[1], &b[1])
fp2.addAssign(&a[2], &b[2])
func wfp6SubAssign(a, b *wfe6) {
wfp2SubAssign(&a[0], &b[0])
wfp2SubAssign(&a[1], &b[1])
wfp2SubAssign(&a[2], &b[2])
}
func (e *fp6) double(c, a *fe6) {
fp2 := e.fp2
fp2.double(&c[0], &a[0])
fp2.double(&c[1], &a[1])
fp2.double(&c[2], &a[2])
func wfp6AddAssign(a, b *wfe6) {
wfp2AddAssign(&a[0], &b[0])
wfp2AddAssign(&a[1], &b[1])
wfp2AddAssign(&a[2], &b[2])
}
func (e *fp6) doubleAssign(a *fe6) {
fp2 := e.fp2
fp2.doubleAssign(&a[0])
fp2.doubleAssign(&a[1])
fp2.doubleAssign(&a[2])
func fp6Add(c, a, b *fe6) {
fp2Add(&c[0], &a[0], &b[0])
fp2Add(&c[1], &a[1], &b[1])
fp2Add(&c[2], &a[2], &b[2])
}
func (e *fp6) sub(c, a, b *fe6) {
fp2 := e.fp2
fp2.sub(&c[0], &a[0], &b[0])
fp2.sub(&c[1], &a[1], &b[1])
fp2.sub(&c[2], &a[2], &b[2])
func fp6AddAssign(a, b *fe6) {
fp2AddAssign(&a[0], &b[0])
fp2AddAssign(&a[1], &b[1])
fp2AddAssign(&a[2], &b[2])
}
func (e *fp6) subAssign(a, b *fe6) {
fp2 := e.fp2
fp2.subAssign(&a[0], &b[0])
fp2.subAssign(&a[1], &b[1])
fp2.subAssign(&a[2], &b[2])
func fp6Double(c, a *fe6) {
fp2Double(&c[0], &a[0])
fp2Double(&c[1], &a[1])
fp2Double(&c[2], &a[2])
}
func (e *fp6) neg(c, a *fe6) {
fp2 := e.fp2
fp2.neg(&c[0], &a[0])
fp2.neg(&c[1], &a[1])
fp2.neg(&c[2], &a[2])
func fp6DoubleAssign(a *fe6) {
fp2DoubleAssign(&a[0])
fp2DoubleAssign(&a[1])
fp2DoubleAssign(&a[2])
}
func (e *fp6) mul(c, a, b *fe6) {
fp2, t := e.fp2, e.t
fp2.mul(t[0], &a[0], &b[0])
fp2.mul(t[1], &a[1], &b[1])
fp2.mul(t[2], &a[2], &b[2])
fp2.add(t[3], &a[1], &a[2])
fp2.add(t[4], &b[1], &b[2])
fp2.mulAssign(t[3], t[4])
fp2.add(t[4], t[1], t[2])
fp2.subAssign(t[3], t[4])
fp2.mulByNonResidue(t[3], t[3])
fp2.add(t[5], t[0], t[3])
fp2.add(t[3], &a[0], &a[1])
fp2.add(t[4], &b[0], &b[1])
fp2.mulAssign(t[3], t[4])
fp2.add(t[4], t[0], t[1])
fp2.subAssign(t[3], t[4])
fp2.mulByNonResidue(t[4], t[2])
fp2.add(&c[1], t[3], t[4])
fp2.add(t[3], &a[0], &a[2])
fp2.add(t[4], &b[0], &b[2])
fp2.mulAssign(t[3], t[4])
fp2.add(t[4], t[0], t[2])
fp2.subAssign(t[3], t[4])
fp2.add(&c[2], t[1], t[3])
c[0].set(t[5])
func fp6Sub(c, a, b *fe6) {
fp2Sub(&c[0], &a[0], &b[0])
fp2Sub(&c[1], &a[1], &b[1])
fp2Sub(&c[2], &a[2], &b[2])
}
func fp6SubAssign(a, b *fe6) {
fp2SubAssign(&a[0], &b[0])
fp2SubAssign(&a[1], &b[1])
fp2SubAssign(&a[2], &b[2])
}
func fp6Neg(c, a *fe6) {
fp2Neg(&c[0], &a[0])
fp2Neg(&c[1], &a[1])
fp2Neg(&c[2], &a[2])
}
func (e *fp6) wmul01(c *wfe6, a *fe6, b0, b1 *fe2) {
wt, t := e.wt, e.t
wfp2Mul(wt[0], &a[0], b0) // v0 = b0a0
wfp2Mul(wt[1], &a[1], b1) // v1 = a1b1
fp2Ladd(t[2], &a[1], &a[2]) // a1 + a2
wfp2Mul(wt[2], t[2], b1) // b1(a1 + a2)
wfp2SubAssign(wt[2], wt[1]) // b1(a1 + a2) - v1
wfp2MulByNonResidueAssign(wt[2])
fp2Ladd(t[3], &a[0], &a[2]) // a0 + a2
wfp2Mul(wt[3], t[3], b0) // b0(a0 + a2)
wfp2SubAssign(wt[3], wt[0])
wfp2Add(&c[2], wt[3], wt[1])
fp2Ladd(t[0], b0, b1) // (b0 + b1)
fp2Ladd(t[1], &a[0], &a[1]) // (a0 + a1)
wfp2Mul(wt[4], t[0], t[1]) // (a0 + a1)(b0 + b1)
wfp2SubAssign(wt[4], wt[0])
wfp2Sub(&c[1], wt[4], wt[1])
wfp2Add(&c[0], wt[2], wt[0])
}
func (e *fp6) wmul1(c *wfe6, a *fe6, b1 *fe2) {
wt := e.wt
wfp2Mul(wt[0], &a[2], b1)
wfp2Mul(&c[2], &a[1], b1)
wfp2Mul(&c[1], &a[0], b1)
wfp2MulByNonResidue(&c[0], wt[0])
}
func (e *fp6) wmul(c *wfe6, a, b *fe6) {
wt, t := e.wt, e.t
// Faster Explicit Formulas for Computing Pairings over Ordinary Curves
// AKLGL
// https://eprint.iacr.org/2010/526.pdf
// Algorithm 3
// 1. T0 = a0b0,T1 = a1b1, T2 = a2b2
wfp2Mul(wt[0], &a[0], &b[0])
wfp2Mul(wt[1], &a[1], &b[1])
wfp2Mul(wt[2], &a[2], &b[2])
// 2. t0 = a1 + a2, t1 = b1 + b2
fp2Ladd(t[0], &a[1], &a[2])
fp2Ladd(t[1], &b[1], &b[2])
// 3. T3 = t0 * t1
wfp2Mul(wt[3], t[0], t[1])
// 4. T4 = T1 + T2
wfp2Add(wt[4], wt[1], wt[2])
// 5,6. T3 = T3 - T4
wfp2SubMixedAssign(wt[3], wt[4])
// 7. T4 = β * T3
wfp2MulByNonResidue(wt[4], wt[3])
// 8. T5 = T4 + T0
wfp2Add(wt[5], wt[4], wt[0])
// 9. t0 = a0 + a1, t1 = b0 + b1
fp2Ladd(t[0], &a[0], &a[1])
fp2Ladd(t[1], &b[0], &b[1])
// 10. T3 = t0 * t1
wfp2Mul(wt[3], t[0], t[1])
// 11. T4 = T0 + T1
wfp2Add(wt[4], wt[0], wt[1])
// 12,13. T3 = T3 - T4
wfp2SubMixedAssign(wt[3], wt[4])
// 14,15. T4 = β * T2
wfp2MulByNonResidue(wt[4], wt[2])
// 17. t0 = a0 + a2, t1 = b0 + b2
fp2Ladd(t[0], &a[0], &a[2])
fp2Ladd(t[1], &b[0], &b[2])
// 16. T6 = T3 + T4
wfp2Add(&c[1], wt[3], wt[4])
// 18. T3 = t0 * t1
wfp2Mul(wt[3], t[0], t[1])
// 19. T4 = T0 + T2
wfp2Add(wt[4], wt[0], wt[2])
// 20,21. T3 = T3 - T4
wfp2SubMixedAssign(wt[3], wt[4])
// 22,23. T7 = T3 + T1
wfp2AddMixed(&c[2], wt[3], wt[1])
// c = T5, T6, T7
c[0].set(wt[5])
}
func (e *fp6) mul(c *fe6, a, b *fe6) {
wt, t := e.wt, e.t
// 1. T0 = a0b0,T1 = a1b1, T2 = a2b2
wfp2Mul(wt[0], &a[0], &b[0])
wfp2Mul(wt[1], &a[1], &b[1])
wfp2Mul(wt[2], &a[2], &b[2])
// 2. t0 = a1 + a2, t1 = b1 + b2
fp2Ladd(t[0], &a[1], &a[2])
fp2Ladd(t[1], &b[1], &b[2])
// 3. T3 = t0 * t1
wfp2Mul(wt[3], t[0], t[1])
// 4. T4 = T1 + T2
wfp2Add(wt[4], wt[1], wt[2])
// 5,6. T3 = T3 - T4
wfp2SubMixedAssign(wt[3], wt[4])
// 7. T4 = β * T3
wfp2MulByNonResidue(wt[4], wt[3])
// 8. T5 = T4 + T0
wfp2Add(wt[5], wt[4], wt[0])
// 9. t0 = a0 + a1, t1 = b0 + b1
fp2Ladd(t[0], &a[0], &a[1])
fp2Ladd(t[1], &b[0], &b[1])
// 10. T3 = t0 * t1
wfp2Mul(wt[3], t[0], t[1])
// 11. T4 = T0 + T1
wfp2Add(wt[4], wt[0], wt[1])
// 12,13. T3 = T3 - T4
wfp2SubMixed(wt[3], wt[3], wt[4])
// 14,15. T4 = β * T2
wfp2MulByNonResidue(wt[4], wt[2])
// 17. t0 = a0 + a2, t1 = b0 + b2
fp2Ladd(t[0], &a[0], &a[2])
fp2Ladd(t[1], &b[0], &b[2])
// 16. T6 = T3 + T4
wfp2Add(wt[3], wt[3], wt[4])
c[1].fromWide(wt[3])
// 18. T3 = t0 * t1
wfp2Mul(wt[3], t[0], t[1])
// 19. T4 = T0 + T2
wfp2Add(wt[4], wt[0], wt[2])
// 20,21. T3 = T3 - T4
wfp2SubMixed(wt[3], wt[3], wt[4])
// 22,23. T7 = T3 + T1
wfp2AddMixed(wt[3], wt[3], wt[1])
c[2].fromWide(wt[3])
// c = T5, T6, T7
c[0].fromWide(wt[5])
}
func (e *fp6) mulAssign(a, b *fe6) {
fp2, t := e.fp2, e.t
fp2.mul(t[0], &a[0], &b[0])
fp2.mul(t[1], &a[1], &b[1])
fp2.mul(t[2], &a[2], &b[2])
fp2.add(t[3], &a[1], &a[2])
fp2.add(t[4], &b[1], &b[2])
fp2.mulAssign(t[3], t[4])
fp2.add(t[4], t[1], t[2])
fp2.subAssign(t[3], t[4])
fp2.mulByNonResidue(t[3], t[3])
fp2.add(t[5], t[0], t[3])
fp2.add(t[3], &a[0], &a[1])
fp2.add(t[4], &b[0], &b[1])
fp2.mulAssign(t[3], t[4])
fp2.add(t[4], t[0], t[1])
fp2.subAssign(t[3], t[4])
fp2.mulByNonResidue(t[4], t[2])
fp2.add(&a[1], t[3], t[4])
fp2.add(t[3], &a[0], &a[2])
fp2.add(t[4], &b[0], &b[2])
fp2.mulAssign(t[3], t[4])
fp2.add(t[4], t[0], t[2])
fp2.subAssign(t[3], t[4])
fp2.add(&a[2], t[1], t[3])
a[0].set(t[5])
wt, t := e.wt, e.t
// Faster Explicit Formulas for Computing Pairings over Ordinary Curves
// AKLGL
// https://eprint.iacr.org/2010/526.pdf
// Algorithm 3
// 1. T0 = a0b0,T1 = a1b1, T2 = a2b2
wfp2Mul(wt[0], &a[0], &b[0])
wfp2Mul(wt[1], &a[1], &b[1])
wfp2Mul(wt[2], &a[2], &b[2])
// 2. t0 = a1 + a2, t1 = b1 + b2
fp2Ladd(t[0], &a[1], &a[2])
fp2Ladd(t[1], &b[1], &b[2])
// 3. T3 = t0 * t1
wfp2Mul(wt[3], t[0], t[1])
// 4. T4 = T1 + T2
wfp2Add(wt[4], wt[1], wt[2])
// 5,6. T3 = T3 - T4
wfp2SubMixed(wt[3], wt[3], wt[4])
// 7. T4 = β * T3
wfp2MulByNonResidue(wt[4], wt[3])
// 8. T5 = T4 + T0
wfp2Add(wt[5], wt[4], wt[0])
// 9. t0 = a0 + a1, t1 = b0 + b1
fp2Ladd(t[0], &a[0], &a[1])
fp2Ladd(t[1], &b[0], &b[1])
// 10. T3 = t0 * t1
wfp2Mul(wt[3], t[0], t[1])
// 11. T4 = T0 + T1
wfp2Add(wt[4], wt[0], wt[1])
// 12,13. T3 = T3 - T4
wfp2SubMixed(wt[3], wt[3], wt[4])
// 14,15. T4 = β * T2
wfp2MulByNonResidue(wt[4], wt[2])
// 17. t0 = a0 + a2, t1 = b0 + b2
fp2Ladd(t[0], &a[0], &a[2])
fp2Ladd(t[1], &b[0], &b[2])
// 16. T6 = T3 + T4
wfp2Add(wt[3], wt[3], wt[4])
a[1].fromWide(wt[3])
// 18. T3 = t0 * t1
wfp2Mul(wt[3], t[0], t[1])
// 19. T4 = T0 + T2
wfp2Add(wt[4], wt[0], wt[2])
// 20,21. T3 = T3 - T4
wfp2SubMixed(wt[3], wt[3], wt[4])
// 22,23. T7 = T3 + T1
wfp2AddMixed(wt[3], wt[3], wt[1])
a[2].fromWide(wt[3])
// a = T5, T6, T7
a[0].fromWide(wt[5])
}
func (e *fp6) square(c, a *fe6) {
fp2, t := e.fp2, e.t
fp2.square(t[0], &a[0])
fp2.mul(t[1], &a[0], &a[1])
fp2.doubleAssign(t[1])
fp2.sub(t[2], &a[0], &a[1])
fp2.addAssign(t[2], &a[2])
fp2.squareAssign(t[2])
fp2.mul(t[3], &a[1], &a[2])
fp2.doubleAssign(t[3])
fp2.square(t[4], &a[2])
fp2.mulByNonResidue(t[5], t[3])
fp2.add(&c[0], t[0], t[5])
fp2.mulByNonResidue(t[5], t[4])
fp2.add(&c[1], t[1], t[5])
fp2.addAssign(t[1], t[2])
fp2.addAssign(t[1], t[3])
fp2.addAssign(t[0], t[4])
fp2.sub(&c[2], t[1], t[0])
wt, t := e.wt, e.t
wfp2Square(wt[0], &a[0])
wfp2Mul(wt[1], &a[0], &a[1])
wfp2DoubleAssign(wt[1])
fp2Sub(t[2], &a[0], &a[1])
fp2AddAssign(t[2], &a[2])
wfp2Square(wt[2], t[2])
wfp2Mul(wt[3], &a[1], &a[2])
wfp2DoubleAssign(wt[3])
wfp2Square(wt[4], &a[2])
wfp2MulByNonResidue(wt[5], wt[3])
wfp2AddAssign(wt[5], wt[0])
c[0].fromWide(wt[5])
wfp2MulByNonResidue(wt[5], wt[4])
wfp2AddAssign(wt[5], wt[1])
c[1].fromWide(wt[5])
wfp2AddAssign(wt[1], wt[2])
wfp2AddAssign(wt[1], wt[3])
wfp2AddAssign(wt[0], wt[4])
wfp2SubAssign(wt[1], wt[0])
c[2].fromWide(wt[1])
}
func (e *fp6) mulBy01Assign(a *fe6, b0, b1 *fe2) {
fp2, t := e.fp2, e.t
fp2.mul(t[0], &a[0], b0)
fp2.mul(t[1], &a[1], b1)
fp2.add(t[5], &a[1], &a[2])
fp2.mul(t[2], b1, t[5])
fp2.subAssign(t[2], t[1])
fp2.mulByNonResidue(t[2], t[2])
fp2.add(t[5], &a[0], &a[2])
fp2.mul(t[3], b0, t[5])
fp2.subAssign(t[3], t[0])
fp2.add(&a[2], t[3], t[1])
fp2.add(t[4], b0, b1)
fp2.add(t[5], &a[0], &a[1])
fp2.mulAssign(t[4], t[5])
fp2.subAssign(t[4], t[0])
fp2.sub(&a[1], t[4], t[1])
fp2.add(&a[0], t[2], t[0])
}
func (e *fp6) mulBy01(c, a *fe6, b0, b1 *fe2) {
fp2, t := e.fp2, e.t
fp2.mul(t[0], &a[0], b0)
fp2.mul(t[1], &a[1], b1)
fp2.add(t[2], &a[1], &a[2])
fp2.mulAssign(t[2], b1)
fp2.subAssign(t[2], t[1])
fp2.mulByNonResidue(t[2], t[2])
fp2.add(t[3], &a[0], &a[2])
fp2.mulAssign(t[3], b0)
fp2.subAssign(t[3], t[0])
fp2.add(&c[2], t[3], t[1])
fp2.add(t[4], b0, b1)
fp2.add(t[3], &a[0], &a[1])
fp2.mulAssign(t[4], t[3])
fp2.subAssign(t[4], t[0])
fp2.sub(&c[1], t[4], t[1])
fp2.add(&c[0], t[2], t[0])
}
func (e *fp6) mulBy1(c, a *fe6, b1 *fe2) {
fp2, t := e.fp2, e.t
fp2.mul(t[0], &a[2], b1)
fp2.mul(&c[2], &a[1], b1)
fp2.mul(&c[1], &a[0], b1)
fp2.mulByNonResidue(&c[0], t[0])
func (e *fp6) wsquare(c *wfe6, a *fe6) {
wt, t := e.wt, e.t
wfp2Square(wt[0], &a[0])
wfp2Mul(wt[1], &a[0], &a[1])
wfp2DoubleAssign(wt[1])
fp2Sub(t[2], &a[0], &a[1])
fp2AddAssign(t[2], &a[2])
wfp2Square(wt[2], t[2])
wfp2Mul(wt[3], &a[1], &a[2])
wfp2DoubleAssign(wt[3])
wfp2Square(wt[4], &a[2])
wfp2MulByNonResidue(wt[5], wt[3])
wfp2Add(&c[0], wt[5], wt[0])
wfp2MulByNonResidue(wt[5], wt[4])
wfp2Add(&c[1], wt[1], wt[5])
wfp2AddAssign(wt[1], wt[2])
wfp2AddAssign(wt[1], wt[3])
wfp2AddAssign(wt[0], wt[4])
wfp2Sub(&c[2], wt[1], wt[0])
}
func (e *fp6) mulByNonResidue(c, a *fe6) {
fp2, t := e.fp2, e.t
t := e.t
t[0].set(&a[0])
fp2.mulByNonResidue(&c[0], &a[2])
mulByNonResidue(&c[0], &a[2])
c[2].set(&a[1])
c[1].set(t[0])
}
func (e *fp6) wmulByNonResidue(c, a *wfe6) {
t := e.wt
t[0].set(&a[0])
wfp2MulByNonResidue(&c[0], &a[2])
c[2].set(&a[1])
c[1].set(t[0])
}
func (e *fp6) wmulByNonResidueAssign(a *wfe6) {
t := e.wt
t[0].set(&a[0])
wfp2MulByNonResidue(&a[0], &a[2])
a[2].set(&a[1])
a[1].set(t[0])
}
func (e *fp6) mulByBaseField(c, a *fe6, b *fe2) {
fp2 := e.fp2
fp2.mul(&c[0], &a[0], b)
@ -291,61 +460,57 @@ func (e *fp6) inverse(c, a *fe6) {
fp2, t := e.fp2, e.t
fp2.square(t[0], &a[0])
fp2.mul(t[1], &a[1], &a[2])
fp2.mulByNonResidue(t[1], t[1])
fp2.subAssign(t[0], t[1])
fp2.square(t[1], &a[1])
fp2.mul(t[2], &a[0], &a[2])
fp2.subAssign(t[1], t[2])
fp2.square(t[2], &a[2])
fp2.mulByNonResidue(t[2], t[2])
fp2.mul(t[3], &a[0], &a[1])
fp2.subAssign(t[2], t[3])
fp2.mul(t[3], &a[2], t[2])
fp2.mul(t[4], &a[1], t[1])
fp2.addAssign(t[3], t[4])
fp2.mulByNonResidue(t[3], t[3])
fp2.mul(t[4], &a[0], t[0])
fp2.addAssign(t[3], t[4])
fp2.inverse(t[3], t[3])
fp2.mul(&c[0], t[0], t[3])
fp2.mul(&c[1], t[2], t[3])
fp2.mul(&c[2], t[1], t[3])
mulByNonResidueAssign(t[1])
fp2SubAssign(t[0], t[1]) // A = v0 - βv5
fp2.square(t[1], &a[1]) // v1 = a1^2
fp2.mul(t[2], &a[0], &a[2]) // v4 = a0a2
fp2SubAssign(t[1], t[2]) // C = v1 - v4
fp2.square(t[2], &a[2]) // v2 = a2^2
mulByNonResidueAssign(t[2]) // βv2
fp2.mul(t[3], &a[0], &a[1]) // v3 = a0a1
fp2SubAssign(t[2], t[3]) // B = βv2 - v3
fp2.mul(t[3], &a[2], t[2]) // B * a2
fp2.mul(t[4], &a[1], t[1]) // C * a1
fp2AddAssign(t[3], t[4]) // Ca1 + Ba2
mulByNonResidueAssign(t[3]) // β(Ca1 + Ba2)
fp2.mul(t[4], &a[0], t[0]) // Aa0
fp2AddAssign(t[3], t[4]) // v6 = Aa0 + β(Ca1 + Ba2)
fp2.inverse(t[3], t[3]) // F = v6^-1
fp2.mul(&c[0], t[0], t[3]) // c0 = AF
fp2.mul(&c[1], t[2], t[3]) // c1 = BF
fp2.mul(&c[2], t[1], t[3]) // c2 = CF
}
func (e *fp6) frobeniusMap(c, a *fe6, power uint) {
func (e *fp6) frobeniusMap(a *fe6, power int) {
fp2 := e.fp2
fp2.frobeniusMap(&c[0], &a[0], power)
fp2.frobeniusMap(&c[1], &a[1], power)
fp2.frobeniusMap(&c[2], &a[2], power)
switch power % 6 {
case 0:
return
case 3:
neg(&c[0][0], &a[1][1])
c[1][1].set(&a[1][0])
fp2.neg(&a[2], &a[2])
default:
fp2.mul(&c[1], &c[1], &frobeniusCoeffs61[power%6])
fp2.mul(&c[2], &c[2], &frobeniusCoeffs62[power%6])
}
fp2.frobeniusMap(&a[0], power)
fp2.frobeniusMap(&a[1], power)
fp2.frobeniusMap(&a[2], power)
fp2.mulAssign(&a[1], &frobeniusCoeffs61[power%6])
fp2.mulAssign(&a[2], &frobeniusCoeffs62[power%6])
}
func (e *fp6) frobeniusMapAssign(a *fe6, power uint) {
func (e *fp6) frobeniusMap1(a *fe6) {
fp2 := e.fp2
fp2.frobeniusMapAssign(&a[0], power)
fp2.frobeniusMapAssign(&a[1], power)
fp2.frobeniusMapAssign(&a[2], power)
fp2.frobeniusMap1(&a[0])
fp2.frobeniusMap1(&a[1])
fp2.frobeniusMap1(&a[2])
fp2.mulAssign(&a[1], &frobeniusCoeffs61[1])
fp2.mulAssign(&a[2], &frobeniusCoeffs62[1])
}
func (e *fp6) frobeniusMap2(a *fe6) {
e.fp2.mulAssign(&a[1], &frobeniusCoeffs61[2])
e.fp2.mulAssign(&a[2], &frobeniusCoeffs62[2])
}
func (e *fp6) frobeniusMap3(a *fe6) {
t := e.t
switch power % 6 {
case 0:
return
case 3:
neg(&t[0][0], &a[1][1])
a[1][1].set(&a[1][0])
a[1][0].set(&t[0][0])
fp2.neg(&a[2], &a[2])
default:
fp2.mulAssign(&a[1], &frobeniusCoeffs61[power%6])
fp2.mulAssign(&a[2], &frobeniusCoeffs62[power%6])
}
e.fp2.frobeniusMap1(&a[0])
e.fp2.frobeniusMap1(&a[1])
e.fp2.frobeniusMap1(&a[2])
neg(&t[0][0], &a[1][1])
a[1][1].set(&a[1][0])
a[1][0].set(&t[0][0])
fp2Neg(&a[2], &a[2])
}

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package bls12381
import (
"crypto/rand"
"io"
"math/big"
"math/bits"
)
const frByteSize = 32
const frBitSize = 255
const frNumberOfLimbs = 4
const fourWordBitSize = 256
type Fr [4]uint64
type wideFr [8]uint64
func NewFr() *Fr {
return &Fr{}
}
func (e *Fr) Rand(r io.Reader) (*Fr, error) {
bi, err := rand.Int(r, qBig)
if err != nil {
return nil, err
}
_ = e.fromBig(bi)
return e, nil
}
func (e *Fr) Set(e2 *Fr) *Fr {
e[0] = e2[0]
e[1] = e2[1]
e[2] = e2[2]
e[3] = e2[3]
return e
}
func (e *Fr) Zero() *Fr {
e[0] = 0
e[1] = 0
e[2] = 0
e[3] = 0
return e
}
func (e *Fr) One() *Fr {
e.Set(&Fr{1})
return e
}
func (e *Fr) RedOne() *Fr {
e.Set(qr1)
return e
}
func (e *Fr) FromBytes(in []byte) *Fr {
e.fromBytes(in)
return e
}
func (e *Fr) RedFromBytes(in []byte) *Fr {
e.fromBytes(in)
e.toMont()
return e
}
func (e *Fr) fromBytes(in []byte) *Fr {
u := new(big.Int).SetBytes(in)
_ = e.fromBig(u)
return e
}
func (e *Fr) fromBig(in *big.Int) *Fr {
e.Zero()
_in := new(big.Int).Set(in)
zero := new(big.Int)
c0 := _in.Cmp(zero)
c1 := _in.Cmp(qBig)
if c0 == -1 || c1 == 1 {
_in.Mod(_in, qBig)
}
words := _in.Bits() // a little-endian Word slice
if bits.UintSize == 64 { // in the 64-bit architecture
for i := 0; i < len(words); i++ {
e[i] = uint64(words[i])
}
} else { // in the 32-bit architecture
for i := 0; i < len(e); i++ {
j := i * 2
if j+1 < len(words) {
e[i] = uint64(words[j+1])<<32 | uint64(words[j])
} else if j < len(words) {
e[i] = uint64(words[j])
} else {
e[i] = uint64(0)
}
}
}
return e
}
func (e *Fr) setUint64(n uint64) *Fr {
e.Zero()
e[0] = n
return e
}
func (e *Fr) ToBytes() []byte {
return NewFr().Set(e).bytes()
}
func (e *Fr) RedToBytes() []byte {
out := NewFr().Set(e)
out.fromMont()
return out.bytes()
}
func (e *Fr) ToBig() *big.Int {
return new(big.Int).SetBytes(e.ToBytes())
}
func (e *Fr) RedToBig() *big.Int {
return new(big.Int).SetBytes(e.RedToBytes())
}
func (e *Fr) bytes() []byte {
out := make([]byte, frByteSize)
var a int
for i := 0; i < frNumberOfLimbs; i++ {
a = frByteSize - i*8
out[a-1] = byte(e[i])
out[a-2] = byte(e[i] >> 8)
out[a-3] = byte(e[i] >> 16)
out[a-4] = byte(e[i] >> 24)
out[a-5] = byte(e[i] >> 32)
out[a-6] = byte(e[i] >> 40)
out[a-7] = byte(e[i] >> 48)
out[a-8] = byte(e[i] >> 56)
}
return out
}
func (e *Fr) IsZero() bool {
return (e[3] | e[2] | e[1] | e[0]) == 0
}
func (e *Fr) IsOne() bool {
return e.Equal(&Fr{1})
}
func (e *Fr) IsRedOne() bool {
return e.Equal(qr1)
}
func (e *Fr) Equal(e2 *Fr) bool {
return e2[0] == e[0] && e2[1] == e[1] && e2[2] == e[2] && e2[3] == e[3]
}
func (e *Fr) Cmp(e1 *Fr) int {
for i := frNumberOfLimbs - 1; i >= 0; i-- {
if e[i] > e1[i] {
return 1
} else if e[i] < e1[i] {
return -1
}
}
return 0
}
func (e *Fr) sliceUint64(from int) uint64 {
if from < 64 {
return e[0]>>from | e[1]<<(64-from)
} else if from < 128 {
return e[1]>>(from-64) | e[2]<<(128-from)
} else if from < 192 {
return e[2]>>(from-128) | e[3]<<(192-from)
}
return e[3] >> (from - 192)
}
func (e *Fr) div2() {
e[0] = e[0]>>1 | e[1]<<63
e[1] = e[1]>>1 | e[2]<<63
e[2] = e[2]>>1 | e[3]<<63
e[3] = e[3] >> 1
}
func (e *Fr) mul2() uint64 {
c := e[3] >> 63
e[3] = e[3]<<1 | e[2]>>63
e[2] = e[2]<<1 | e[1]>>63
e[1] = e[1]<<1 | e[0]>>63
e[0] = e[0] << 1
return c
}
func (e *Fr) isEven() bool {
var mask uint64 = 1
return e[0]&mask == 0
}
func (e *Fr) Bit(at int) bool {
if at < 64 {
return (e[0]>>at)&1 == 1
} else if at < 128 {
return (e[1]>>(at-64))&1 == 1
} else if at < 192 {
return (e[2]>>(at-128))&1 == 1
} else if at < 256 {
return (e[3]>>(at-192))&1 == 1
}
return false
}
func (e *Fr) toMont() {
e.RedMul(e, qr2)
}
func (e *Fr) fromMont() {
e.RedMul(e, &Fr{1})
}
func (e *Fr) FromRed() {
e.fromMont()
}
func (e *Fr) ToRed() {
e.toMont()
}
func (e *Fr) Add(a, b *Fr) {
addFR(e, a, b)
}
func (e *Fr) Double(a *Fr) {
doubleFR(e, a)
}
func (e *Fr) Sub(a, b *Fr) {
subFR(e, a, b)
}
func (e *Fr) Neg(a *Fr) {
negFR(e, a)
}
func (e *Fr) Mul(a, b *Fr) {
e.RedMul(a, b)
e.toMont()
}
func (e *Fr) RedMul(a, b *Fr) {
mulFR(e, a, b)
}
func (e *Fr) Square(a *Fr) {
e.RedSquare(a)
e.toMont()
}
func (e *Fr) RedSquare(a *Fr) {
squareFR(e, a)
}
func (e *Fr) RedExp(a *Fr, ee *big.Int) {
z := new(Fr).RedOne()
for i := ee.BitLen(); i >= 0; i-- {
z.RedSquare(z)
if ee.Bit(i) == 1 {
z.RedMul(z, a)
}
}
e.Set(z)
}
func (e *Fr) Exp(a *Fr, ee *big.Int) {
e.Set(a).toMont()
e.RedExp(e, ee)
e.fromMont()
}
func RedInverseBatchFr(in []Fr) {
inverseBatchFr(in, func(a, b *Fr) { a.RedInverse(b) })
}
func InverseBatchFr(in []Fr) {
inverseBatchFr(in, func(a, b *Fr) { a.Inverse(b) })
}
func inverseBatchFr(in []Fr, invFn func(out *Fr, in *Fr)) {
n, N, setFirst := 0, len(in), false
for i := 0; i < len(in); i++ {
if !in[i].IsZero() {
n++
}
}
if n == 0 {
return
}
tA := make([]Fr, n)
tB := make([]Fr, n)
for i, j := 0, 0; i < N; i++ {
if !in[i].IsZero() {
if !setFirst {
setFirst = true
tA[j].Set(&in[i])
} else {
tA[j].Mul(&in[i], &tA[j-1])
}
j = j + 1
}
}
invFn(&tB[n-1], &tA[n-1])
for i, j := N-1, n-1; j != 0; i-- {
if !in[i].IsZero() {
tB[j-1].Mul(&tB[j], &in[i])
j = j - 1
}
}
for i, j := 0, 0; i < N; i++ {
if !in[i].IsZero() {
if setFirst {
setFirst = false
in[i].Set(&tB[j])
} else {
in[i].Mul(&tA[j-1], &tB[j])
}
j = j + 1
}
}
}
func (e *Fr) Inverse(a *Fr) {
e.Set(a).toMont()
e.RedInverse(e)
e.fromMont()
}
func (e *Fr) RedInverse(ei *Fr) {
if ei.IsZero() {
e.Zero()
return
}
u := new(Fr).Set(&q)
v := new(Fr).Set(ei)
s := &Fr{1}
r := &Fr{0}
var k int
var z uint64
var found = false
// Phase 1
for i := 0; i < fourWordBitSize*2; i++ {
if v.IsZero() {
found = true
break
}
if u.isEven() {
u.div2()
s.mul2()
} else if v.isEven() {
v.div2()
z += r.mul2()
} else if u.Cmp(v) == 1 {
lsubAssignFR(u, v)
u.div2()
laddAssignFR(r, s)
s.mul2()
} else {
lsubAssignFR(v, u)
v.div2()
laddAssignFR(s, r)
z += r.mul2()
}
k += 1
}
if !found {
e.Zero()
return
}
if k < frBitSize || k > frBitSize+fourWordBitSize {
e.Zero()
return
}
if r.Cmp(&q) != -1 || z > 0 {
lsubAssignFR(r, &q)
}
u.Set(&q)
lsubAssignFR(u, r)
// Phase 2
for i := k; i < 2*fourWordBitSize; i++ {
doubleFR(u, u)
}
e.Set(u)
}
func (ew *wideFr) mul(a, b *Fr) {
wmulFR(ew, a, b)
}
func (ew *wideFr) add(a *wideFr) {
waddFR(ew, a)
}
func (ew *wideFr) round() *Fr {
ew.add(halfR)
return ew.high()
}
func (ew *wideFr) high() *Fr {
e := new(Fr)
e[0] = ew[4]
e[1] = ew[5]
e[2] = ew[6]
e[3] = ew[7]
return e
}
func (ew *wideFr) low() *Fr {
e := new(Fr)
e[0] = ew[0]
e[1] = ew[1]
e[2] = ew[2]
e[3] = ew[3]
return e
}
func (e *wideFr) bytes() []byte {
out := make([]byte, frByteSize*2)
var a int
for i := 0; i < frNumberOfLimbs*2; i++ {
a = frByteSize*2 - i*8
out[a-1] = byte(e[i])
out[a-2] = byte(e[i] >> 8)
out[a-3] = byte(e[i] >> 16)
out[a-4] = byte(e[i] >> 24)
out[a-5] = byte(e[i] >> 32)
out[a-6] = byte(e[i] >> 40)
out[a-7] = byte(e[i] >> 48)
out[a-8] = byte(e[i] >> 56)
}
return out
}

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crypto/bls12381/fr_arithmetic_x86.s Normal file
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crypto/bls12381/fr_fallback.go Normal file
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// +build !amd64 generic
// Copyright 2020 ConsenSys Software Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// Code generated by goff (v0.3.5) DO NOT EDIT
// /!\ WARNING /!\
// this code has not been audited and is provided as-is. In particular,
// there is no security guarantees such as constant time implementation
// or side-channel attack resistance
// /!\ WARNING /!\
package bls12381
import "math/bits"
func addFR(z, x, y *Fr) {
var carry uint64
z[0], carry = bits.Add64(x[0], y[0], 0)
z[1], carry = bits.Add64(x[1], y[1], carry)
z[2], carry = bits.Add64(x[2], y[2], carry)
z[3], _ = bits.Add64(x[3], y[3], carry)
// if z > q --> z -= q
// note: this is NOT constant time
if !(z[3] < 8353516859464449352 || (z[3] == 8353516859464449352 && (z[2] < 3691218898639771653 || (z[2] == 3691218898639771653 && (z[1] < 6034159408538082302 || (z[1] == 6034159408538082302 && (z[0] < 18446744069414584321))))))) {
var b uint64
z[0], b = bits.Sub64(z[0], 18446744069414584321, 0)
z[1], b = bits.Sub64(z[1], 6034159408538082302, b)
z[2], b = bits.Sub64(z[2], 3691218898639771653, b)
z[3], _ = bits.Sub64(z[3], 8353516859464449352, b)
}
}
func laddAssignFR(z, y *Fr) {
var carry uint64
z[0], carry = bits.Add64(z[0], y[0], 0)
z[1], carry = bits.Add64(z[1], y[1], carry)
z[2], carry = bits.Add64(z[2], y[2], carry)
z[3], _ = bits.Add64(z[3], y[3], carry)
}
func doubleFR(z, x *Fr) {
var carry uint64
z[0], carry = bits.Add64(x[0], x[0], 0)
z[1], carry = bits.Add64(x[1], x[1], carry)
z[2], carry = bits.Add64(x[2], x[2], carry)
z[3], _ = bits.Add64(x[3], x[3], carry)
// if z > q --> z -= q
// note: this is NOT constant time
if !(z[3] < 8353516859464449352 || (z[3] == 8353516859464449352 && (z[2] < 3691218898639771653 || (z[2] == 3691218898639771653 && (z[1] < 6034159408538082302 || (z[1] == 6034159408538082302 && (z[0] < 18446744069414584321))))))) {
var b uint64
z[0], b = bits.Sub64(z[0], 18446744069414584321, 0)
z[1], b = bits.Sub64(z[1], 6034159408538082302, b)
z[2], b = bits.Sub64(z[2], 3691218898639771653, b)
z[3], _ = bits.Sub64(z[3], 8353516859464449352, b)
}
}
func subFR(z, x, y *Fr) {
var b uint64
z[0], b = bits.Sub64(x[0], y[0], 0)
z[1], b = bits.Sub64(x[1], y[1], b)
z[2], b = bits.Sub64(x[2], y[2], b)
z[3], b = bits.Sub64(x[3], y[3], b)
if b != 0 {
var c uint64
z[0], c = bits.Add64(z[0], 18446744069414584321, 0)
z[1], c = bits.Add64(z[1], 6034159408538082302, c)
z[2], c = bits.Add64(z[2], 3691218898639771653, c)
z[3], _ = bits.Add64(z[3], 8353516859464449352, c)
}
}
func lsubAssignFR(z, y *Fr) {
var b uint64
z[0], b = bits.Sub64(z[0], y[0], 0)
z[1], b = bits.Sub64(z[1], y[1], b)
z[2], b = bits.Sub64(z[2], y[2], b)
z[3], b = bits.Sub64(z[3], y[3], b)
}
func negFR(z, x *Fr) {
if x.IsZero() {
z.Zero()
return
}
var borrow uint64
z[0], borrow = bits.Sub64(18446744069414584321, x[0], 0)
z[1], borrow = bits.Sub64(6034159408538082302, x[1], borrow)
z[2], borrow = bits.Sub64(3691218898639771653, x[2], borrow)
z[3], _ = bits.Sub64(8353516859464449352, x[3], borrow)
}
func mulFR(z, x, y *Fr) {
var t [4]uint64
var c [3]uint64
{
// round 0
v := x[0]
c[1], c[0] = bits.Mul64(v, y[0])
m := c[0] * 18446744069414584319
c[2] = madd0(m, 18446744069414584321, c[0])
c[1], c[0] = madd1(v, y[1], c[1])
c[2], t[0] = madd2(m, 6034159408538082302, c[2], c[0])
c[1], c[0] = madd1(v, y[2], c[1])
c[2], t[1] = madd2(m, 3691218898639771653, c[2], c[0])
c[1], c[0] = madd1(v, y[3], c[1])
t[3], t[2] = madd3(m, 8353516859464449352, c[0], c[2], c[1])
}
{
// round 1
v := x[1]
c[1], c[0] = madd1(v, y[0], t[0])
m := c[0] * 18446744069414584319
c[2] = madd0(m, 18446744069414584321, c[0])
c[1], c[0] = madd2(v, y[1], c[1], t[1])
c[2], t[0] = madd2(m, 6034159408538082302, c[2], c[0])
c[1], c[0] = madd2(v, y[2], c[1], t[2])
c[2], t[1] = madd2(m, 3691218898639771653, c[2], c[0])
c[1], c[0] = madd2(v, y[3], c[1], t[3])
t[3], t[2] = madd3(m, 8353516859464449352, c[0], c[2], c[1])
}
{
// round 2
v := x[2]
c[1], c[0] = madd1(v, y[0], t[0])
m := c[0] * 18446744069414584319
c[2] = madd0(m, 18446744069414584321, c[0])
c[1], c[0] = madd2(v, y[1], c[1], t[1])
c[2], t[0] = madd2(m, 6034159408538082302, c[2], c[0])
c[1], c[0] = madd2(v, y[2], c[1], t[2])
c[2], t[1] = madd2(m, 3691218898639771653, c[2], c[0])
c[1], c[0] = madd2(v, y[3], c[1], t[3])
t[3], t[2] = madd3(m, 8353516859464449352, c[0], c[2], c[1])
}
{
// round 3
v := x[3]
c[1], c[0] = madd1(v, y[0], t[0])
m := c[0] * 18446744069414584319
c[2] = madd0(m, 18446744069414584321, c[0])
c[1], c[0] = madd2(v, y[1], c[1], t[1])
c[2], z[0] = madd2(m, 6034159408538082302, c[2], c[0])
c[1], c[0] = madd2(v, y[2], c[1], t[2])
c[2], z[1] = madd2(m, 3691218898639771653, c[2], c[0])
c[1], c[0] = madd2(v, y[3], c[1], t[3])
z[3], z[2] = madd3(m, 8353516859464449352, c[0], c[2], c[1])
}
// if z > q --> z -= q
// note: this is NOT constant time
if !(z[3] < 8353516859464449352 || (z[3] == 8353516859464449352 && (z[2] < 3691218898639771653 || (z[2] == 3691218898639771653 && (z[1] < 6034159408538082302 || (z[1] == 6034159408538082302 && (z[0] < 18446744069414584321))))))) {
var b uint64
z[0], b = bits.Sub64(z[0], 18446744069414584321, 0)
z[1], b = bits.Sub64(z[1], 6034159408538082302, b)
z[2], b = bits.Sub64(z[2], 3691218898639771653, b)
z[3], _ = bits.Sub64(z[3], 8353516859464449352, b)
}
}
func squareFR(z, x *Fr) {
var t [4]uint64
var c [3]uint64
{
// round 0
v := x[0]
c[1], c[0] = bits.Mul64(v, x[0])
m := c[0] * 18446744069414584319
c[2] = madd0(m, 18446744069414584321, c[0])
c[1], c[0] = madd1(v, x[1], c[1])
c[2], t[0] = madd2(m, 6034159408538082302, c[2], c[0])
c[1], c[0] = madd1(v, x[2], c[1])
c[2], t[1] = madd2(m, 3691218898639771653, c[2], c[0])
c[1], c[0] = madd1(v, x[3], c[1])
t[3], t[2] = madd3(m, 8353516859464449352, c[0], c[2], c[1])
}
{
// round 1
v := x[1]
c[1], c[0] = madd1(v, x[0], t[0])
m := c[0] * 18446744069414584319
c[2] = madd0(m, 18446744069414584321, c[0])
c[1], c[0] = madd2(v, x[1], c[1], t[1])
c[2], t[0] = madd2(m, 6034159408538082302, c[2], c[0])
c[1], c[0] = madd2(v, x[2], c[1], t[2])
c[2], t[1] = madd2(m, 3691218898639771653, c[2], c[0])
c[1], c[0] = madd2(v, x[3], c[1], t[3])
t[3], t[2] = madd3(m, 8353516859464449352, c[0], c[2], c[1])
}
{
// round 2
v := x[2]
c[1], c[0] = madd1(v, x[0], t[0])
m := c[0] * 18446744069414584319
c[2] = madd0(m, 18446744069414584321, c[0])
c[1], c[0] = madd2(v, x[1], c[1], t[1])
c[2], t[0] = madd2(m, 6034159408538082302, c[2], c[0])
c[1], c[0] = madd2(v, x[2], c[1], t[2])
c[2], t[1] = madd2(m, 3691218898639771653, c[2], c[0])
c[1], c[0] = madd2(v, x[3], c[1], t[3])
t[3], t[2] = madd3(m, 8353516859464449352, c[0], c[2], c[1])
}
{
// round 3
v := x[3]
c[1], c[0] = madd1(v, x[0], t[0])
m := c[0] * 18446744069414584319
c[2] = madd0(m, 18446744069414584321, c[0])
c[1], c[0] = madd2(v, x[1], c[1], t[1])
c[2], z[0] = madd2(m, 6034159408538082302, c[2], c[0])
c[1], c[0] = madd2(v, x[2], c[1], t[2])
c[2], z[1] = madd2(m, 3691218898639771653, c[2], c[0])
c[1], c[0] = madd2(v, x[3], c[1], t[3])
z[3], z[2] = madd3(m, 8353516859464449352, c[0], c[2], c[1])
}
// if z > q --> z -= q
// note: this is NOT constant time
if !(z[3] < 8353516859464449352 || (z[3] == 8353516859464449352 && (z[2] < 3691218898639771653 || (z[2] == 3691218898639771653 && (z[1] < 6034159408538082302 || (z[1] == 6034159408538082302 && (z[0] < 18446744069414584321))))))) {
var b uint64
z[0], b = bits.Sub64(z[0], 18446744069414584321, 0)
z[1], b = bits.Sub64(z[1], 6034159408538082302, b)
z[2], b = bits.Sub64(z[2], 3691218898639771653, b)
z[3], _ = bits.Sub64(z[3], 8353516859464449352, b)
}
}
func waddFR(z, y *wideFr) {
var carry uint64
z[0], carry = bits.Add64(z[0], y[0], 0)
z[1], carry = bits.Add64(z[1], y[1], carry)
z[2], carry = bits.Add64(z[2], y[2], carry)
z[3], carry = bits.Add64(z[3], y[3], carry)
z[4], carry = bits.Add64(z[4], y[4], carry)
z[5], carry = bits.Add64(z[5], y[5], carry)
z[6], carry = bits.Add64(z[6], y[6], carry)
z[7], _ = bits.Add64(z[7], y[7], carry)
}
// We applied custom multiplication since goff does generate multiplication code nested with reduction
func wmulFR(w *wideFr, a, b *Fr) {
// Handbook of Applied Cryptography
// Hankerson, Menezes, Vanstone
// 14.12 Algorithm Multiple-precision multiplication
var w0, w1, w2, w3, w4, w5, w6, w7 uint64
var a0 = a[0]
var a1 = a[1]
var a2 = a[2]
var a3 = a[3]
var b0 = b[0]
var b1 = b[1]
var b2 = b[2]
var b3 = b[3]
var u, v, c, t uint64
// i = 0, j = 0
c, w0 = bits.Mul64(a0, b0)
// i = 0, j = 1
u, v = bits.Mul64(a1, b0)
w1 = v + c
c = u + (v&c|(v|c)&^w1)>>63
// i = 0, j = 2
u, v = bits.Mul64(a2, b0)
w2 = v + c
c = u + (v&c|(v|c)&^w2)>>63
// i = 0, j = 3
u, v = bits.Mul64(a3, b0)
w3 = v + c
w4 = u + (v&c|(v|c)&^w3)>>63
// i = 1, j = 0
c, v = bits.Mul64(a0, b1)
t = v + w1
c += (v&w1 | (v|w1)&^t) >> 63
w1 = t
// i = 1, j = 1
u, v = bits.Mul64(a1, b1)
t = v + w2
u += (v&w2 | (v|w2)&^t) >> 63
w2 = t + c
c = u + (t&c|(t|c)&^w2)>>63
// i = 1, j = 2
u, v = bits.Mul64(a2, b1)
t = v + w3
u += (v&w3 | (v|w3)&^t) >> 63
w3 = t + c
c = u + (t&c|(t|c)&^w3)>>63
// i = 1, j = 3
u, v = bits.Mul64(a3, b1)
t = v + w4
u += (v&w4 | (v|w4)&^t) >> 63
w4 = t + c
w5 = u + (t&c|(t|c)&^w4)>>63
// i = 2, j = 0
c, v = bits.Mul64(a0, b2)
t = v + w2
c += (v&w2 | (v|w2)&^t) >> 63
w2 = t
// i = 2, j = 1
u, v = bits.Mul64(a1, b2)
t = v + w3
u += (v&w3 | (v|w3)&^t) >> 63
w3 = t + c
c = u + (t&c|(t|c)&^w3)>>63
// i = 2, j = 2
u, v = bits.Mul64(a2, b2)
t = v + w4
u += (v&w4 | (v|w4)&^t) >> 63
w4 = t + c
c = u + (t&c|(t|c)&^w4)>>63
// i = 2, j = 3
u, v = bits.Mul64(a3, b2)
t = v + w5
u += (v&w5 | (v|w5)&^t) >> 63
w5 = t + c
w6 = u + (t&c|(t|c)&^w5)>>63
// i = 3, j = 0
c, v = bits.Mul64(a0, b3)
t = v + w3
c += (v&w3 | (v|w3)&^t) >> 63
w3 = t
// i = 3, j = 1
u, v = bits.Mul64(a1, b3)
t = v + w4
u += (v&w4 | (v|w4)&^t) >> 63
w4 = t + c
c = u + (t&c|(t|c)&^w4)>>63
// i = 3, j = 2
u, v = bits.Mul64(a2, b3)
t = v + w5
u += (v&w5 | (v|w5)&^t) >> 63
w5 = t + c
c = u + (t&c|(t|c)&^w5)>>63
// i = 3, j = 3
u, v = bits.Mul64(a3, b3)
t = v + w6
u += (v&w6 | (v|w6)&^t) >> 63
w6 = t + c
w7 = u + (t&c|(t|c)&^w6)>>63
w[0] = w0
w[1] = w1
w[2] = w2
w[3] = w3
w[4] = w4
w[5] = w5
w[6] = w6
w[7] = w7
}

417
crypto/bls12381/fr_test.go Normal file
View file

@ -0,0 +1,417 @@
package bls12381
import (
"bytes"
"crypto/rand"
"math/big"
"testing"
)
func TestScalarField(t *testing.T) {
r := new(Fr).Set(qr1)
r.fromMont()
if r[0] != 1 && r[1] != 0 && r[2] != 0 && r[3] != 0 {
t.Fatal("bad r value")
}
r.Set(qr2)
r.fromMont()
r.fromMont()
if r[0] != 1 && r[1] != 0 && r[2] != 0 && r[3] != 0 {
t.Fatal("bad r2 value")
}
r = &Fr{1}
r.toMont()
if !r.Equal(qr1) {
t.Fatal("mont transformaition failed")
}
}
func TestFrSerialization(t *testing.T) {
in := make([]byte, frByteSize)
e := new(Fr).FromBytes(in)
if !e.IsZero() {
t.Fatal("serialization failed, from bytes zero")
}
if !bytes.Equal(in, e.ToBytes()) {
t.Fatal("serialization failed, to bytes zero")
}
e = new(Fr).RedFromBytes(in)
if !e.IsZero() {
t.Fatal("serialization failed, from bytes zero, reduced")
}
if !bytes.Equal(in, e.RedToBytes()) {
t.Fatal("serialization failed, to bytes zero, reduced")
}
a, err := new(Fr).Rand(rand.Reader)
if err != nil {
t.Fatal(err)
}
b := new(Fr)
b.fromBytes(a.bytes())
if !a.Equal(b) {
t.Fatal("serialization failed, set bytes")
}
b = new(Fr).FromBytes(a.ToBytes())
if !a.Equal(b) {
t.Fatal("serialization failed, from/to bytes")
}
b = new(Fr).RedFromBytes(a.RedToBytes())
if !a.Equal(b) {
t.Fatal("serialization failed, from/to bytes, reduced")
}
}
func TestFrSliceUint(t *testing.T) {
s, err := new(Fr).Rand(rand.Reader)
if err != nil {
t.Fatal(err)
}
sBig := s.ToBig()
for offset := 0; offset < 260; offset++ {
a0 := new(big.Int).Rsh(sBig, uint(offset)).Uint64()
a1 := s.sliceUint64(offset)
if a0 != a1 {
t.Fatal("uint slice failed", offset)
}
}
}
func TestFrBitTest(t *testing.T) {
s, err := new(Fr).Rand(rand.Reader)
if err != nil {
t.Fatal(err)
}
sBig := s.ToBig()
for i := 0; i < 260; i++ {
a0 := sBig.Bit(i) == 1
a1 := s.Bit(i)
if a0 != a1 {
t.Fatal("bit test failed", i)
}
}
}
func TestFrBitShift(t *testing.T) {
a, _ := new(Fr).Rand(rand.Reader)
b := new(Fr).Set(a)
b.mul2()
b.div2()
if !b.Equal(a) {
t.Fatal("mul2 div2 failed")
}
a, _ = new(Fr).Rand(rand.Reader)
a[0] = a[0] & 0xfffffffffffffffe
b.Set(a)
b.div2()
b.mul2()
if !b.Equal(a) {
t.Fatal("mul2 div2 failed")
}
}
func TestFrAdditionCrossAgainstBigInt(t *testing.T) {
for i := 0; i < fuz; i++ {
a, _ := new(Fr).Rand(rand.Reader)
b, _ := new(Fr).Rand(rand.Reader)
c := new(Fr)
bigA := a.ToBig()
bigB := b.ToBig()
bigC := new(big.Int)
c.Add(a, b)
out1 := c.ToBytes()
out2 := padBytes(bigC.Add(bigA, bigB).Mod(bigC, qBig).Bytes(), frByteSize)
if !bytes.Equal(out1, out2) {
t.Fatal("cross test against big.Int is failed, add")
}
c.Double(a)
out1 = c.ToBytes()
out2 = padBytes(bigC.Add(bigA, bigA).Mod(bigC, qBig).Bytes(), frByteSize)
if !bytes.Equal(out1, out2) {
t.Fatal("cross test against big.Int is failed, double")
}
c.Sub(a, b)
out1 = c.ToBytes()
out2 = padBytes(bigC.Sub(bigA, bigB).Mod(bigC, qBig).Bytes(), frByteSize)
if !bytes.Equal(out1, out2) {
t.Fatal("cross test against big.Int is failed, sub")
}
c.Neg(a)
out1 = c.ToBytes()
out2 = padBytes(bigC.Neg(bigA).Mod(bigC, qBig).Bytes(), frByteSize)
if !bytes.Equal(out1, out2) {
t.Fatal("cross test against big.Int is failed, neg")
}
}
}
func TestFrAdditionProperties(t *testing.T) {
for i := 0; i < fuz; i++ {
zero := new(Fr)
a, _ := new(Fr).Rand(rand.Reader)
b, _ := new(Fr).Rand(rand.Reader)
c1, c2 := new(Fr), new(Fr)
c1.Add(a, zero)
if !c1.Equal(a) {
t.Fatal("a + 0 == a")
}
c1.Sub(a, zero)
if !c1.Equal(a) {
t.Fatal("a - 0 == a")
}
c1.Double(zero)
if !c1.Equal(zero) {
t.Fatal("2 * 0 == 0")
}
c1.Neg(zero)
if !c1.Equal(zero) {
t.Fatal("-0 == 0")
}
c1.Sub(zero, a)
c2.Neg(a)
if !c1.Equal(c2) {
t.Fatal("0-a == -a")
}
c1.Double(a)
c2.Add(a, a)
if !c1.Equal(c2) {
t.Fatal("2 * a == a + a")
}
c1.Add(a, b)
c2.Add(b, a)
if !c1.Equal(c2) {
t.Fatal("a + b = b + a")
}
c1.Sub(a, b)
c2.Sub(b, a)
c2.Neg(c2)
if !c1.Equal(c2) {
t.Fatal("a - b = - ( b - a )")
}
c0, _ := new(Fr).Rand(rand.Reader)
c1.Add(a, b)
c1.Add(c1, c0)
c2.Add(a, c0)
c2.Add(c2, b)
if !c1.Equal(c2) {
t.Fatal("(a + b) + c == (a + c ) + b")
}
c1.Sub(a, b)
c1.Sub(c1, c0)
c2.Sub(a, c0)
c2.Sub(c2, b)
if !c1.Equal(c2) {
t.Fatal("(a - b) - c == (a - c ) -b")
}
}
}
func TestFrMultiplicationCrossAgainstBigInt(t *testing.T) {
for i := 0; i < fuz; i++ {
a, _ := new(Fr).Rand(rand.Reader)
b, _ := new(Fr).Rand(rand.Reader)
c := new(Fr)
bigA := a.ToBig()
bigB := b.ToBig()
bigC := new(big.Int)
c.Mul(a, b)
out1 := c.ToBytes()
out2 := padBytes(bigC.Mul(bigA, bigB).Mod(bigC, qBig).Bytes(), frByteSize)
if !bytes.Equal(out1, out2) {
t.Fatal("cross test against big.Int is failed")
}
}
}
func TestFrMultiplicationCrossAgainstBigIntReduced(t *testing.T) {
for i := 0; i < fuz; i++ {
a, _ := new(Fr).Rand(rand.Reader)
b, _ := new(Fr).Rand(rand.Reader)
c := new(Fr)
bigA := a.RedToBig()
bigB := b.RedToBig()
bigC := new(big.Int)
c.RedMul(a, b)
out1 := c.RedToBytes()
out2 := padBytes(bigC.Mul(bigA, bigB).Mod(bigC, qBig).Bytes(), frByteSize)
if !bytes.Equal(out1, out2) {
t.Fatal("cross test against big.Int is failed, reduced")
}
}
}
func TestFrMultiplicationProperties(t *testing.T) {
for i := 0; i < fuz; i++ {
a, _ := new(Fr).Rand(rand.Reader)
b, _ := new(Fr).Rand(rand.Reader)
zero, one := new(Fr).Zero(), new(Fr).One()
c1, c2 := new(Fr), new(Fr)
c1.Mul(a, zero)
if !c1.Equal(zero) {
t.Fatal("a * 0 == 0")
}
c1.Mul(a, one)
if !c1.Equal(a) {
t.Fatal("a * 1 == a")
}
c1.Mul(a, b)
c2.Mul(b, a)
if !c1.Equal(c2) {
t.Fatal("a * b == b * a")
}
c0, _ := new(Fr).Rand(rand.Reader)
c1.Mul(a, b)
c1.Mul(c1, c0)
c2.Mul(c0, b)
c2.Mul(c2, a)
if !c1.Equal(c2) {
t.Fatal("(a * b) * c == (a * c) * b")
}
a.Square(zero)
if !a.Equal(zero) {
t.Fatal("0^2 == 0")
}
a.Square(one)
if !a.Equal(one) {
t.Fatal("1^2 == 1")
}
_, _ = a.Rand(rand.Reader)
c1.Square(a)
c2.Mul(a, a)
if !c1.Equal(c1) {
t.Fatal("a^2 == a*a")
}
}
}
func TestFrMultiplicationPropertiesReduced(t *testing.T) {
for i := 0; i < fuz; i++ {
a, _ := new(Fr).Rand(rand.Reader)
b, _ := new(Fr).Rand(rand.Reader)
zero, one := new(Fr).Zero(), new(Fr).RedOne()
c1, c2 := new(Fr), new(Fr)
c1.RedMul(a, zero)
if !c1.Equal(zero) {
t.Fatal("a * 0 == 0")
}
c1.RedMul(a, one)
if !c1.Equal(a) {
t.Fatal("a * 1 == a")
}
c1.RedMul(a, b)
c2.RedMul(b, a)
if !c1.Equal(c2) {
t.Fatal("a * b == b * a")
}
c0, _ := new(Fr).Rand(rand.Reader)
c1.RedMul(a, b)
c1.RedMul(c1, c0)
c2.RedMul(c0, b)
c2.RedMul(c2, a)
if !c1.Equal(c2) {
t.Fatal("(a * b) * c == (a * c) * b")
}
a.RedSquare(zero)
if !a.Equal(zero) {
t.Fatal("0^2 == 0")
}
a.RedSquare(one)
if !a.Equal(one) {
t.Fatal("1^2 == 1")
}
_, _ = a.Rand(rand.Reader)
c1.RedSquare(a)
c2.RedMul(a, a)
if !c1.Equal(c1) {
t.Fatal("a^2 == a*a")
}
}
}
func TestFrExponentiation(t *testing.T) {
for i := 0; i < fuz; i++ {
a, _ := new(Fr).Rand(rand.Reader)
u := new(Fr)
u.Exp(a, big.NewInt(0))
if !u.IsOne() {
t.Fatal("a^0 == 1")
}
u.Exp(a, big.NewInt(1))
if !u.Equal(a) {
t.Fatal("a^1 == a")
}
v := new(Fr)
u.Mul(a, a)
u.Mul(u, u)
u.Mul(u, u)
v.Exp(a, big.NewInt(8))
if !u.Equal(v) {
t.Fatal("((a^2)^2)^2 == a^8")
}
u.Exp(a, qBig)
if !u.Equal(a) {
t.Fatal("a^p == a")
}
qMinus1 := new(big.Int).Sub(qBig, big.NewInt(1))
u.Exp(a, qMinus1)
if !u.IsOne() {
t.Fatal("a^(p-1) == 1")
}
}
}
func TestFrInversion(t *testing.T) {
for i := 0; i < fuz; i++ {
u := new(Fr)
zero, one := new(Fr).Zero(), new(Fr).One()
u.Inverse(zero)
if !u.Equal(zero) {
t.Fatal("(0^-1) == 0)")
}
u.Inverse(one)
if !u.IsOne() {
t.Fatal("(1^-1) == 1)")
}
a, _ := new(Fr).Rand(rand.Reader)
u.Inverse(a)
u.Mul(u, a)
if !u.IsOne() {
t.Fatal("a * a^-1 == 1")
}
v := new(Fr)
z := new(big.Int)
u.Exp(a, z.Sub(qBig, big.NewInt(2)))
v.Inverse(a)
if !v.Equal(u) {
t.Fatal("a^(p-2) == a^-1")
}
}
}
func TestFnBatchInversion(t *testing.T) {
for i := 0; i < fuz; i++ {
zero, one := new(Fr).Zero(), new(Fr).One()
a, _ := new(Fr).Rand(rand.Reader)
u := new(Fr)
z := new(big.Int)
u.Exp(a, z.Sub(qBig, big.NewInt(2)))
var arr []Fr
arr = append(arr, *zero, *one, *a)
InverseBatchFr(arr)
if !arr[0].Equal(zero) {
t.Fatal("(0^-1) == 0)")
}
if !arr[1].IsOne() {
t.Fatal("(1^-1) == 1)")
}
if !arr[2].Equal(u) {
t.Fatal("a^(p-2) == a^-1")
}
}
}

810
crypto/bls12381/g1.go
View file

@ -1,19 +1,3 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
import (
@ -22,11 +6,12 @@ import (
"math/big"
)
// PointG1 is type for point in G1.
// PointG1 is both used for Affine and Jacobian point representation.
// If z is equal to one the point is considered as in affine form.
// PointG1 is type for point in G1 and used for both Affine and Jacobian point representation.
// A point is accounted as in affine form if z is equal to one.
type PointG1 [3]fe
var wnafMulWindowG1 uint = 5
func (p *PointG1) Set(p2 *PointG1) *PointG1 {
p[0].set(&p2[0])
p[1].set(&p2[1])
@ -34,7 +19,6 @@ func (p *PointG1) Set(p2 *PointG1) *PointG1 {
return p
}
// Zero returns G1 point in point at infinity representation
func (p *PointG1) Zero() *PointG1 {
p[0].zero()
p[1].one()
@ -42,6 +26,11 @@ func (p *PointG1) Zero() *PointG1 {
return p
}
// IsAffine checks a G1 point whether it is in affine form.
func (p *PointG1) IsAffine() bool {
return p[2].isOne()
}
type tempG1 struct {
t [9]*fe
}
@ -67,15 +56,141 @@ func newTempG1() tempG1 {
// Q returns group order in big.Int.
func (g *G1) Q() *big.Int {
return new(big.Int).Set(q)
return new(big.Int).Set(qBig)
}
func (g *G1) fromBytesUnchecked(in []byte) (*PointG1, error) {
p0, err := fromBytes(in[:48])
// FromUncompressed expects byte slice at least 96 bytes and given bytes returns a new point in G1.
// Serialization rules are in line with zcash library. See below for details.
// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
func (g *G1) FromUncompressed(uncompressed []byte) (*PointG1, error) {
if len(uncompressed) != 2*fpByteSize {
return nil, errors.New("input string length must be equal to 96 bytes")
}
var in [2 * fpByteSize]byte
copy(in[:], uncompressed[:2*fpByteSize])
if in[0]&(1<<7) != 0 {
return nil, errors.New("compression flag must be zero")
}
if in[0]&(1<<5) != 0 {
return nil, errors.New("sort flag must be zero")
}
if in[0]&(1<<6) != 0 {
for i, v := range in {
if (i == 0 && v != 0x40) || (i != 0 && v != 0x00) {
return nil, errors.New("input string must be zero when infinity flag is set")
}
}
return g.Zero(), nil
}
in[0] &= 0x1f
x, err := fromBytes(in[:fpByteSize])
if err != nil {
return nil, err
}
p1, err := fromBytes(in[48:])
y, err := fromBytes(in[fpByteSize:])
if err != nil {
return nil, err
}
z := new(fe).one()
p := &PointG1{*x, *y, *z}
if !g.IsOnCurve(p) {
return nil, errors.New("point is not on curve")
}
if !g.InCorrectSubgroup(p) {
return nil, errors.New("point is not on correct subgroup")
}
return p, nil
}
// ToUncompressed given a G1 point returns bytes in uncompressed (x, y) form of the point.
// Serialization rules are in line with zcash library. See below for details.
// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
func (g *G1) ToUncompressed(p *PointG1) []byte {
out := make([]byte, 2*fpByteSize)
if g.IsZero(p) {
out[0] |= 1 << 6
return out
}
g.Affine(p)
copy(out[:fpByteSize], toBytes(&p[0]))
copy(out[fpByteSize:], toBytes(&p[1]))
return out
}
// FromCompressed expects byte slice at least 48 bytes and given bytes returns a new point in G1.
// Serialization rules are in line with zcash library. See below for details.
// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
func (g *G1) FromCompressed(compressed []byte) (*PointG1, error) {
if len(compressed) != fpByteSize {
return nil, errors.New("input string length must be equal to 48 bytes")
}
var in [fpByteSize]byte
copy(in[:], compressed[:])
if in[0]&(1<<7) == 0 {
return nil, errors.New("compression flag must be set")
}
if in[0]&(1<<6) != 0 {
// in[0] == (1 << 6) + (1 << 7)
for i, v := range in {
if (i == 0 && v != 0xc0) || (i != 0 && v != 0x00) {
return nil, errors.New("input string must be zero when infinity flag is set")
}
}
return g.Zero(), nil
}
a := in[0]&(1<<5) != 0
in[0] &= 0x1f
x, err := fromBytes(in[:])
if err != nil {
return nil, err
}
// solve curve equation
y := &fe{}
square(y, x)
mul(y, y, x)
add(y, y, b)
if ok := sqrt(y, y); !ok {
return nil, errors.New("point is not on curve")
}
if y.signBE() == a {
neg(y, y)
}
z := new(fe).one()
p := &PointG1{*x, *y, *z}
if !g.InCorrectSubgroup(p) {
return nil, errors.New("point is not on correct subgroup")
}
return p, nil
}
// ToCompressed given a G1 point returns bytes in compressed form of the point.
// Serialization rules are in line with zcash library. See below for details.
// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
func (g *G1) ToCompressed(p *PointG1) []byte {
out := make([]byte, fpByteSize)
g.Affine(p)
if g.IsZero(p) {
out[0] |= 1 << 6
} else {
copy(out[:], toBytes(&p[0]))
if !p[1].signBE() {
out[0] |= 1 << 5
}
}
out[0] |= 1 << 7
return out
}
func (g *G1) fromBytesUnchecked(in []byte) (*PointG1, error) {
p0, err := fromBytes(in[:fpByteSize])
if err != nil {
return nil, err
}
p1, err := fromBytes(in[fpByteSize:])
if err != nil {
return nil, err
}
@ -84,19 +199,17 @@ func (g *G1) fromBytesUnchecked(in []byte) (*PointG1, error) {
}
// FromBytes constructs a new point given uncompressed byte input.
// FromBytes does not take zcash flags into account.
// Byte input expected to be larger than 96 bytes.
// First 96 bytes should be concatenation of x and y values.
// Point (0, 0) is considered as infinity.
// Input string is expected to be equal to 96 bytes and concatenation of x and y cooridanates.
// (0, 0) is considered as infinity.
func (g *G1) FromBytes(in []byte) (*PointG1, error) {
if len(in) != 96 {
return nil, errors.New("input string should be equal or larger than 96")
if len(in) != 2*fpByteSize {
return nil, errors.New("input string length must be equal to 96 bytes")
}
p0, err := fromBytes(in[:48])
p0, err := fromBytes(in[:fpByteSize])
if err != nil {
return nil, err
}
p1, err := fromBytes(in[48:])
p1, err := fromBytes(in[fpByteSize:])
if err != nil {
return nil, err
}
@ -112,49 +225,16 @@ func (g *G1) FromBytes(in []byte) (*PointG1, error) {
return p, nil
}
// DecodePoint given encoded (x, y) coordinates in 128 bytes returns a valid G1 Point.
func (g *G1) DecodePoint(in []byte) (*PointG1, error) {
if len(in) != 128 {
return nil, errors.New("invalid g1 point length")
}
pointBytes := make([]byte, 96)
// decode x
xBytes, err := decodeFieldElement(in[:64])
if err != nil {
return nil, err
}
// decode y
yBytes, err := decodeFieldElement(in[64:])
if err != nil {
return nil, err
}
copy(pointBytes[:48], xBytes)
copy(pointBytes[48:], yBytes)
return g.FromBytes(pointBytes)
}
// ToBytes serializes a point into bytes in uncompressed form.
// ToBytes does not take zcash flags into account.
// ToBytes returns (0, 0) if point is infinity.
func (g *G1) ToBytes(p *PointG1) []byte {
out := make([]byte, 96)
out := make([]byte, 2*fpByteSize)
if g.IsZero(p) {
return out
}
g.Affine(p)
copy(out[:48], toBytes(&p[0]))
copy(out[48:], toBytes(&p[1]))
return out
}
// EncodePoint encodes a point into 128 bytes.
func (g *G1) EncodePoint(p *PointG1) []byte {
outRaw := g.ToBytes(p)
out := make([]byte, 128)
// encode x
copy(out[16:], outRaw[:48])
// encode y
copy(out[64+16:], outRaw[48:])
copy(out[:fpByteSize], toBytes(&p[0]))
copy(out[fpByteSize:], toBytes(&p[1]))
return out
}
@ -201,9 +281,29 @@ func (g *G1) Equal(p1, p2 *PointG1) bool {
// InCorrectSubgroup checks whether given point is in correct subgroup.
func (g *G1) InCorrectSubgroup(p *PointG1) bool {
tmp := &PointG1{}
g.MulScalar(tmp, p, q)
return g.IsZero(tmp)
// Faster Subgroup Checks for BLS12-381
// S. Bowe
// https://eprint.iacr.org/2019/814.pdf
mulZ := func(p *PointG1) {
// z = [(x^2 − 1)/3]
z := &Fr{0x0000000055555555, 0x396c8c005555e156}
e := z.toWNAF(wnafMulWindowG1)
g.wnafMul(p, p, e)
}
// [(x^2 − 1)/3](2σ(P) − P − σ^2(P)) − σ^2(P) ?= O
t0 := g.New().Set(p)
g.glvEndomorphism(t0, t0)
t1 := g.New().Set(t0) // σ(P)
g.glvEndomorphism(t0, t0) // σ^2(P)
g.Double(t1, t1) // 2σ(P)
g.Sub(t1, t1, p) // 2σ(P) − P
g.Sub(t1, t1, t0) // 2σ(P) − P − σ^2(P)
mulZ(t1) // [(x^2 − 1)/3](2σ(P) − P − σ^2(P))
g.Sub(t1, t1, t0) // [(x^2 − 1)/3](2σ(P) − P − σ^2(P)) − σ^2(P)
return g.IsZero(t1)
}
// IsOnCurve checks a G1 point is on curve.
@ -212,15 +312,19 @@ func (g *G1) IsOnCurve(p *PointG1) bool {
return true
}
t := g.t
square(t[0], &p[1])
square(t[1], &p[0])
mul(t[1], t[1], &p[0])
square(t[2], &p[2])
square(t[3], t[2])
mul(t[2], t[2], t[3])
mul(t[2], b, t[2])
add(t[1], t[1], t[2])
return t[0].equal(t[1])
square(t[0], &p[1]) // y^2
square(t[1], &p[0]) // x^2
mul(t[1], t[1], &p[0]) // x^3
if p.IsAffine() {
addAssign(t[1], b) // x^2 + b
return t[0].equal(t[1]) // y^2 ?= x^3 + b
}
square(t[2], &p[2]) // z^2
square(t[3], t[2]) // z^4
mul(t[2], t[2], t[3]) // z^6
mul(t[2], b, t[2]) // b * z^6
add(t[1], t[1], t[2]) // x^3 + b * z^6
return t[0].equal(t[1]) // y^2 ?= x^3 + b * z^6
}
// IsAffine checks a G1 point whether it is in affine form.
@ -228,26 +332,105 @@ func (g *G1) IsAffine(p *PointG1) bool {
return p[2].isOne()
}
// Affine calculates affine form of given G1 point.
// Affine returns the affine representation of the given point
func (g *G1) Affine(p *PointG1) *PointG1 {
return g.affine(p, p)
}
func (g *G1) affine(r, p *PointG1) *PointG1 {
if g.IsZero(p) {
return p
return r.Zero()
}
if !g.IsAffine(p) {
t := g.t
inverse(t[0], &p[2])
square(t[1], t[0])
mul(&p[0], &p[0], t[1])
mul(t[0], t[0], t[1])
mul(&p[1], &p[1], t[0])
p[2].one()
inverse(t[0], &p[2]) // z^-1
square(t[1], t[0]) // z^-2
mul(&r[0], &p[0], t[1]) // x = x * z^-2
mul(t[0], t[0], t[1]) // z^-3
mul(&r[1], &p[1], t[0]) // y = y * z^-3
r[2].one() // z = 1
} else {
r.Set(p)
}
return r
}
// AffineBatch given multiple of points returns affine representations
func (g *G1) AffineBatch(p []*PointG1) {
inverses := make([]fe, len(p))
for i := 0; i < len(p); i++ {
inverses[i].set(&p[i][2])
}
inverseBatch(inverses)
t := g.t
for i := 0; i < len(p); i++ {
if !g.IsAffine(p[i]) && !g.IsZero(p[i]) {
square(t[1], &inverses[i])
mul(&p[i][0], &p[i][0], t[1])
mul(t[0], &inverses[i], t[1])
mul(&p[i][1], &p[i][1], t[0])
p[i][2].one()
}
}
return p
}
// Add adds two G1 points p1, p2 and assigns the result to point at first argument.
func (g *G1) Add(r, p1, p2 *PointG1) *PointG1 {
// www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl
// http://www.hyperelliptic.org/EFD/gp/auto-shortw-jacobian-0.html#addition-add-2007-bl
if g.IsZero(p1) {
return r.Set(p2)
}
if g.IsZero(p2) {
return r.Set(p1)
}
if g.IsAffine(p2) {
return g.AddMixed(r, p1, p2)
}
t := g.t
square(t[7], &p1[2]) // z1z1
mul(t[1], &p2[0], t[7]) // u2 = x2 * z1z1
mul(t[2], &p1[2], t[7]) // z1z1 * z1
mul(t[0], &p2[1], t[2]) // s2 = y2 * z1z1 * z1
square(t[8], &p2[2]) // z2z2
mul(t[3], &p1[0], t[8]) // u1 = x1 * z2z2
mul(t[4], &p2[2], t[8]) // z2z2 * z2
mul(t[2], &p1[1], t[4]) // s1 = y1 * z2z2 * z2
if t[1].equal(t[3]) {
if t[0].equal(t[2]) {
return g.Double(r, p1)
} else {
return r.Zero()
}
}
subAssign(t[1], t[3]) // h = u2 - u1
double(t[4], t[1]) // 2h
square(t[4], t[4]) // i = 2h^2
mul(t[5], t[1], t[4]) // j = h*i
subAssign(t[0], t[2]) // s2 - s1
doubleAssign(t[0]) // r = 2*(s2 - s1)
square(t[6], t[0]) // r^2
subAssign(t[6], t[5]) // r^2 - j
mul(t[3], t[3], t[4]) // v = u1 * i
double(t[4], t[3]) // 2*v
sub(&r[0], t[6], t[4]) // x3 = r^2 - j - 2*v
sub(t[4], t[3], &r[0]) // v - x3
mul(t[6], t[2], t[5]) // s1 * j
doubleAssign(t[6]) // 2 * s1 * j
mul(t[0], t[0], t[4]) // r * (v - x3)
sub(&r[1], t[0], t[6]) // y3 = r * (v - x3) - (2 * s1 * j)
add(t[0], &p1[2], &p2[2]) // z1 + z2
square(t[0], t[0]) // (z1 + z2)^2
subAssign(t[0], t[7]) // (z1 + z2)^2 - z1z1
subAssign(t[0], t[8]) // (z1 + z2)^2 - z1z1 - z2z2
mul(&r[2], t[0], t[1]) // z3 = ((z1 + z2)^2 - z1z1 - z2z2) * h
return r
}
// Add adds two G1 points p1, p2 and assigns the result to point at first argument.
// Expects the second point p2 in affine form.
func (g *G1) AddMixed(r, p1, p2 *PointG1) *PointG1 {
// http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-madd-2007-bl
if g.IsZero(p1) {
return r.Set(p2)
}
@ -255,73 +438,68 @@ func (g *G1) Add(r, p1, p2 *PointG1) *PointG1 {
return r.Set(p1)
}
t := g.t
square(t[7], &p1[2])
mul(t[1], &p2[0], t[7])
mul(t[2], &p1[2], t[7])
mul(t[0], &p2[1], t[2])
square(t[8], &p2[2])
mul(t[3], &p1[0], t[8])
mul(t[4], &p2[2], t[8])
mul(t[2], &p1[1], t[4])
if t[1].equal(t[3]) {
if t[0].equal(t[2]) {
return g.Double(r, p1)
}
return r.Zero()
square(t[7], &p1[2]) // z1z1
mul(t[1], &p2[0], t[7]) // u2 = x2 * z1z1
mul(t[2], &p1[2], t[7]) // z1z1 * z1
mul(t[0], &p2[1], t[2]) // s2 = y2 * z1z1 * z1
if p1[0].equal(t[1]) && p1[1].equal(t[0]) {
return g.Double(r, p1)
}
sub(t[1], t[1], t[3])
double(t[4], t[1])
square(t[4], t[4])
mul(t[5], t[1], t[4])
sub(t[0], t[0], t[2])
double(t[0], t[0])
square(t[6], t[0])
sub(t[6], t[6], t[5])
mul(t[3], t[3], t[4])
double(t[4], t[3])
sub(&r[0], t[6], t[4])
sub(t[4], t[3], &r[0])
mul(t[6], t[2], t[5])
double(t[6], t[6])
mul(t[0], t[0], t[4])
sub(&r[1], t[0], t[6])
add(t[0], &p1[2], &p2[2])
square(t[0], t[0])
sub(t[0], t[0], t[7])
sub(t[0], t[0], t[8])
mul(&r[2], t[0], t[1])
sub(t[1], t[1], &p1[0]) // h = u2 - x1
square(t[2], t[1]) // hh
double(t[4], t[2])
doubleAssign(t[4]) // 4hh
mul(t[5], t[1], t[4]) // j = h*i
subAssign(t[0], &p1[1]) // s2 - y1
doubleAssign(t[0]) // r = 2*(s2 - y1)
square(t[6], t[0]) // r^2
subAssign(t[6], t[5]) // r^2 - j
mul(t[3], &p1[0], t[4]) // v = x1 * i
double(t[4], t[3]) // 2*v
sub(&r[0], t[6], t[4]) // x3 = r^2 - j - 2*v
sub(t[4], t[3], &r[0]) // v - x3
mul(t[6], &p1[1], t[5]) // y1 * j
doubleAssign(t[6]) // 2 * y1 * j
mul(t[0], t[0], t[4]) // r * (v - x3)
sub(&r[1], t[0], t[6]) // y3 = r * (v - x3) - (2 * y1 * j)
add(t[0], &p1[2], t[1]) // z1 + h
square(t[0], t[0]) // (z1 + h)^2
subAssign(t[0], t[7]) // (z1 + h)^2 - z1z1
sub(&r[2], t[0], t[2]) // z3 = (z1 + z2)^2 - z1z1 - hh
return r
}
// Double doubles a G1 point p and assigns the result to the point at first argument.
func (g *G1) Double(r, p *PointG1) *PointG1 {
// http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
// http://www.hyperelliptic.org/EFD/gp/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
if g.IsZero(p) {
return r.Set(p)
return r.Zero()
}
t := g.t
square(t[0], &p[0])
square(t[1], &p[1])
square(t[2], t[1])
add(t[1], &p[0], t[1])
square(t[1], t[1])
sub(t[1], t[1], t[0])
sub(t[1], t[1], t[2])
double(t[1], t[1])
double(t[3], t[0])
add(t[0], t[3], t[0])
square(t[4], t[0])
double(t[3], t[1])
sub(&r[0], t[4], t[3])
sub(t[1], t[1], &r[0])
double(t[2], t[2])
double(t[2], t[2])
double(t[2], t[2])
mul(t[0], t[0], t[1])
sub(t[1], t[0], t[2])
mul(t[0], &p[1], &p[2])
r[1].set(t[1])
double(&r[2], t[0])
square(t[0], &p[0]) // a = x^2
square(t[1], &p[1]) // b = y^2
square(t[2], t[1]) // c = b^2
add(t[1], &p[0], t[1]) // b + x1
square(t[1], t[1]) // (b + x1)^2
subAssign(t[1], t[0]) // (b + x1)^2 - a
subAssign(t[1], t[2]) // (b + x1)^2 - a - c
doubleAssign(t[1]) // d = 2((b+x1)^2 - a - c)
double(t[3], t[0]) // 2a
addAssign(t[0], t[3]) // e = 3a
square(t[4], t[0]) // f = e^2
double(t[3], t[1]) // 2d
sub(&r[0], t[4], t[3]) // x3 = f - 2d
subAssign(t[1], &r[0]) // d-x3
doubleAssign(t[2]) //
doubleAssign(t[2]) //
doubleAssign(t[2]) // 8c
mul(t[0], t[0], t[1]) // e * (d - x3)
sub(t[1], t[0], t[2]) // x3 = e * (d - x3) - 8c
mul(t[0], &p[1], &p[2]) // y1 * z1
r[1].set(t[1]) //
double(&r[2], t[0]) // z3 = 2(y1 * z1)
return r
}
@ -341,12 +519,32 @@ func (g *G1) Sub(c, a, b *PointG1) *PointG1 {
return c
}
// MulScalar multiplies a point by given scalar value and assigns the result to point at first argument.
func (g *G1) MulScalar(r, p *PointG1, e *Fr) *PointG1 {
return g.glvMulFr(r, p, e)
}
// MulScalar multiplies a point by given scalar value in big.Int and assigns the result to point at first argument.
func (g *G1) MulScalar(c, p *PointG1, e *big.Int) *PointG1 {
func (g *G1) MulScalarBig(r, p *PointG1, e *big.Int) *PointG1 {
return g.glvMulBig(r, p, e)
}
func (g *G1) mulScalar(c, p *PointG1, e *Fr) *PointG1 {
q, n := &PointG1{}, &PointG1{}
n.Set(p)
l := e.BitLen()
for i := 0; i < l; i++ {
for i := 0; i < frBitSize; i++ {
if e.Bit(i) {
g.Add(q, q, n)
}
g.Double(n, n)
}
return c.Set(q)
}
func (g *G1) mulScalarBig(c, p *PointG1, e *big.Int) *PointG1 {
q, n := &PointG1{}, &PointG1{}
n.Set(p)
for i := 0; i < frBitSize; i++ {
if e.Bit(i) == 1 {
g.Add(q, q, n)
}
@ -355,67 +553,242 @@ func (g *G1) MulScalar(c, p *PointG1, e *big.Int) *PointG1 {
return c.Set(q)
}
// ClearCofactor maps given a G1 point to correct subgroup
func (g *G1) ClearCofactor(p *PointG1) {
g.MulScalar(p, p, cofactorEFFG1)
func (g *G1) wnafMulFr(r, p *PointG1, e *Fr) *PointG1 {
wnaf := e.toWNAF(wnafMulWindowG1)
return g.wnafMul(r, p, wnaf)
}
// MultiExp calculates multi exponentiation. Given pairs of G1 point and scalar values
// (P_0, e_0), (P_1, e_1), ... (P_n, e_n) calculates r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n
// Length of points and scalars are expected to be equal, otherwise an error is returned.
// Result is assigned to point at first argument.
func (g *G1) MultiExp(r *PointG1, points []*PointG1, powers []*big.Int) (*PointG1, error) {
if len(points) != len(powers) {
return nil, errors.New("point and scalar vectors should be in same length")
func (g *G1) wnafMulBig(r, p *PointG1, e *big.Int) *PointG1 {
wnaf := bigToWNAF(e, wnafMulWindowG1)
return g.wnafMul(r, p, wnaf)
}
func (g *G1) wnafMul(c, p *PointG1, wnaf nafNumber) *PointG1 {
l := (1 << (wnafMulWindowG1 - 1))
twoP, acc := g.New(), new(PointG1).Set(p)
g.Double(twoP, p)
g.Affine(twoP)
// table = {p, 3p, 5p, ..., -p, -3p, -5p}
table := make([]*PointG1, l*2)
table[0], table[l] = g.New(), g.New()
table[0].Set(p)
g.Neg(table[l], table[0])
for i := 1; i < l; i++ {
g.AddMixed(acc, acc, twoP)
table[i], table[i+l] = g.New(), g.New()
table[i].Set(acc)
g.Neg(table[i+l], table[i])
}
var c uint32 = 3
if len(powers) >= 32 {
c = uint32(math.Ceil(math.Log10(float64(len(powers)))))
}
bucketSize, numBits := (1<<c)-1, uint32(g.Q().BitLen())
windows := make([]*PointG1, numBits/c+1)
bucket := make([]*PointG1, bucketSize)
acc, sum := g.New(), g.New()
for i := 0; i < bucketSize; i++ {
bucket[i] = g.New()
}
mask := (uint64(1) << c) - 1
j := 0
var cur uint32
for cur <= numBits {
acc.Zero()
bucket = make([]*PointG1, (1<<c)-1)
for i := 0; i < len(bucket); i++ {
bucket[i] = g.New()
q := g.Zero()
for i := len(wnaf) - 1; i >= 0; i-- {
if wnaf[i] > 0 {
g.Add(q, q, table[wnaf[i]>>1])
} else if wnaf[i] < 0 {
g.Add(q, q, table[((-wnaf[i])>>1)+l])
}
for i := 0; i < len(powers); i++ {
s0 := powers[i].Uint64()
index := uint(s0 & mask)
if index != 0 {
g.Add(bucket[index-1], bucket[index-1], points[i])
if i != 0 {
g.Double(q, q)
}
}
return c.Set(q)
}
func (g *G1) glvMulFr(r, p *PointG1, e *Fr) *PointG1 {
return g.glvMul(r, p, new(glvVectorFr).new(e))
}
func (g *G1) glvMulBig(r, p *PointG1, e *big.Int) *PointG1 {
return g.glvMul(r, p, new(glvVectorBig).new(e))
}
func (g *G1) glvMul(r, p0 *PointG1, v glvVector) *PointG1 {
w := glvMulWindowG1
l := 1 << (w - 1)
// prepare tables
// tableK1 = {P, 3P, 5P, ...}
// tableK2 = {λP, 3λP, 5λP, ...}
tableK1, tableK2 := make([]*PointG1, l), make([]*PointG1, l)
double := g.New()
g.Double(double, p0)
g.affine(double, double)
tableK1[0] = new(PointG1)
tableK1[0].Set(p0)
for i := 1; i < l; i++ {
tableK1[i] = new(PointG1)
g.AddMixed(tableK1[i], tableK1[i-1], double)
}
g.AffineBatch(tableK1)
for i := 0; i < l; i++ {
tableK2[i] = new(PointG1)
g.glvEndomorphism(tableK2[i], tableK1[i])
}
// recode small scalars
naf1, naf2 := v.wnaf(w)
lenNAF1, lenNAF2 := len(naf1), len(naf2)
lenNAF := lenNAF1
if lenNAF2 > lenNAF {
lenNAF = lenNAF2
}
acc, p1 := g.New(), g.New()
// function for naf addition
add := func(table []*PointG1, naf int) {
if naf != 0 {
nafAbs := naf
if nafAbs < 0 {
nafAbs = -nafAbs
}
powers[i] = new(big.Int).Rsh(powers[i], uint(c))
p1.Set(table[nafAbs>>1])
if naf < 0 {
g.Neg(p1, p1)
}
g.AddMixed(acc, acc, p1)
}
sum.Zero()
for i := len(bucket) - 1; i >= 0; i-- {
g.Add(sum, sum, bucket[i])
g.Add(acc, acc, sum)
}
windows[j] = g.New()
windows[j].Set(acc)
j++
cur += c
}
acc.Zero()
for i := len(windows) - 1; i >= 0; i-- {
for j := uint32(0); j < c; j++ {
// sliding
for i := lenNAF - 1; i >= 0; i-- {
if i < lenNAF1 {
add(tableK1, naf1[i])
}
if i < lenNAF2 {
add(tableK2, naf2[i])
}
if i != 0 {
g.Double(acc, acc)
}
g.Add(acc, acc, windows[i])
}
return r.Set(acc)
}
// MultiExpBig calculates multi exponentiation. Scalar values are received as big.Int type.
// Given pairs of G1 point and scalar values `(P_0, e_0), (P_1, e_1), ... (P_n, e_n)`,
// calculates `r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n`.
// Length of points and scalars are expected to be equal, otherwise an error is returned.
// Result is assigned to point at first argument.
func (g *G1) MultiExpBig(r *PointG1, points []*PointG1, scalars []*big.Int) (*PointG1, error) {
if len(points) != len(scalars) {
return nil, errors.New("point and scalar vectors should be in same length")
}
c := 3
if len(scalars) >= 32 {
c = int(math.Ceil(math.Log(float64(len(scalars)))))
}
bucketSize := (1 << c) - 1
windows := make([]PointG1, 255/c+1)
bucket := make([]PointG1, bucketSize)
for j := 0; j < len(windows); j++ {
for i := 0; i < bucketSize; i++ {
bucket[i].Zero()
}
for i := 0; i < len(scalars); i++ {
index := bucketSize & int(new(big.Int).Rsh(scalars[i], uint(c*j)).Int64())
if index != 0 {
g.Add(&bucket[index-1], &bucket[index-1], points[i])
}
}
acc, sum := g.New(), g.New()
for i := bucketSize - 1; i >= 0; i-- {
g.Add(sum, sum, &bucket[i])
g.Add(acc, acc, sum)
}
windows[j].Set(acc)
}
acc := g.New()
for i := len(windows) - 1; i >= 0; i-- {
for j := 0; j < c; j++ {
g.Double(acc, acc)
}
g.Add(acc, acc, &windows[i])
}
return r.Set(acc), nil
}
// MultiExp calculates multi exponentiation. Given pairs of G1 point and scalar values `(P_0, e_0), (P_1, e_1), ... (P_n, e_n)`,
// calculates `r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n`. Length of points and scalars are expected to be equal,
// otherwise an error is returned. Result is assigned to point at first argument.
func (g *G1) MultiExp(r *PointG1, points []*PointG1, scalars []*Fr) (*PointG1, error) {
if len(points) != len(scalars) {
return nil, errors.New("point and scalar vectors should be in same length")
}
g.AffineBatch(points)
c := 3
if len(scalars) >= 32 {
c = int(math.Ceil(math.Log(float64(len(scalars)))))
}
bucketSize := (1 << c) - 1
windows := make([]*PointG1, 255/c+1)
bucket := make([]PointG1, bucketSize)
for j := 0; j < len(windows); j++ {
for i := 0; i < bucketSize; i++ {
bucket[i].Zero()
}
for i := 0; i < len(scalars); i++ {
index := bucketSize & int(scalars[i].sliceUint64(c*j))
if index != 0 {
g.AddMixed(&bucket[index-1], &bucket[index-1], points[i])
}
}
acc, sum := g.New(), g.New()
for i := bucketSize - 1; i >= 0; i-- {
g.Add(sum, sum, &bucket[i])
g.Add(acc, acc, sum)
}
windows[j] = g.New().Set(acc)
}
g.AffineBatch(windows)
acc := g.New()
for i := len(windows) - 1; i >= 0; i-- {
for j := 0; j < c; j++ {
g.Double(acc, acc)
}
g.AddMixed(acc, acc, windows[i])
}
return r.Set(acc), nil
}
func (g *G1) ClearCofactor(p *PointG1) *PointG1 {
chain := func(p0 *PointG1, n int, p1 *PointG1) {
for i := 0; i < n; i++ {
g.Double(p0, p0)
}
g.Add(p0, p0, p1)
}
t := g.New().Set(p)
chain(p, 1, t)
chain(p, 2, t)
chain(p, 3, t)
chain(p, 9, t)
chain(p, 32, t)
chain(p, 16, t)
return p
}
// MapToCurve given a byte slice returns a valid G1 point.
// This mapping function implements the Simplified Shallue-van de Woestijne-Ulas method.
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06
@ -432,3 +805,42 @@ func (g *G1) MapToCurve(in []byte) (*PointG1, error) {
g.ClearCofactor(p)
return g.Affine(p), nil
}
// EncodeToCurve given a message and domain seperator tag returns the hash result
// which is a valid curve point.
// Implementation follows BLS12381G1_XMD:SHA-256_SSWU_NU_ suite at
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06
func (g *G1) EncodeToCurve(msg, domain []byte) (*PointG1, error) {
hashRes, err := hashToFpXMDSHA256(msg, domain, 1)
if err != nil {
return nil, err
}
u := hashRes[0]
x, y := swuMapG1(u)
isogenyMapG1(x, y)
one := new(fe).one()
p := &PointG1{*x, *y, *one}
g.ClearCofactor(p)
return g.Affine(p), nil
}
// HashToCurve given a message and domain seperator tag returns the hash result
// which is a valid curve point.
// Implementation follows BLS12381G1_XMD:SHA-256_SSWU_RO_ suite at
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06
func (g *G1) HashToCurve(msg, domain []byte) (*PointG1, error) {
hashRes, err := hashToFpXMDSHA256(msg, domain, 2)
if err != nil {
return nil, err
}
u0, u1 := hashRes[0], hashRes[1]
x0, y0 := swuMapG1(u0)
x1, y1 := swuMapG1(u1)
one := new(fe).one()
p0, p1 := &PointG1{*x0, *y0, *one}, &PointG1{*x1, *y1, *one}
g.Add(p0, p0, p1)
g.Affine(p0)
isogenyMapG1(&p0[0], &p0[1])
g.ClearCofactor(p0)
return g.Affine(p0), nil
}

594
crypto/bls12381/g1_test.go
View file

@ -3,52 +3,117 @@ package bls12381
import (
"bytes"
"crypto/rand"
"fmt"
"io/ioutil"
"math/big"
"testing"
"github.com/ethereum/go-ethereum/common"
)
func (g *G1) one() *PointG1 {
one, _ := g.fromBytesUnchecked(
common.FromHex("" +
"17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb" +
"08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1",
),
)
return one
return g.New().Set(&g1One)
}
func (g *G1) rand() *PointG1 {
k, err := rand.Int(rand.Reader, q)
if err != nil {
panic(err)
p := &PointG1{}
z, _ := new(fe).rand(rand.Reader)
z6, bz6 := new(fe), new(fe)
square(z6, z)
square(z6, z6)
mul(z6, z6, z)
mul(z6, z6, z)
mul(bz6, z6, b)
for {
x, _ := new(fe).rand(rand.Reader)
y := new(fe)
square(y, x)
mul(y, y, x)
add(y, y, bz6)
if sqrt(y, y) {
p.Set(&PointG1{*x, *y, *z})
break
}
}
return g.MulScalar(&PointG1{}, g.one(), k)
if !g.IsOnCurve(p) {
panic("rand point must be on curve")
}
if g.InCorrectSubgroup(p) {
panic("rand point must be out of correct subgroup")
}
return p
}
func (g *G1) randCorrect() *PointG1 {
p := g.ClearCofactor(g.rand())
if !g.InCorrectSubgroup(p) {
panic("must be in correct subgroup")
}
return p
}
func (g *G1) randAffine() *PointG1 {
return g.Affine(g.randCorrect())
}
func (g *G1) new() *PointG1 {
return g.Zero()
}
func TestG1Serialization(t *testing.T) {
g1 := NewG1()
var err error
g := NewG1()
zero := g.Zero()
b0 := g.ToUncompressed(zero)
p0, err := g.FromUncompressed(b0)
if err != nil {
t.Fatal(err)
}
if !g.IsZero(p0) {
t.Fatal("infinity serialization failed")
}
b0 = g.ToCompressed(zero)
p0, err = g.FromCompressed(b0)
if err != nil {
t.Fatal(err)
}
if !g.IsZero(p0) {
t.Fatal("infinity serialization failed")
}
b0 = g.ToBytes(zero)
p0, err = g.FromBytes(b0)
if err != nil {
t.Fatal(err)
}
if !g.IsZero(p0) {
t.Fatal("infinity serialization failed")
}
for i := 0; i < fuz; i++ {
a := g1.rand()
buf := g1.ToBytes(a)
b, err := g1.FromBytes(buf)
a := g.randAffine()
uncompressed := g.ToUncompressed(a)
b, err := g.FromUncompressed(uncompressed)
if err != nil {
t.Fatal(err)
}
if !g1.Equal(a, b) {
t.Fatal("bad serialization from/to")
if !g.Equal(a, b) {
t.Fatal("serialization failed")
}
compressed := g.ToCompressed(b)
a, err = g.FromCompressed(compressed)
if err != nil {
t.Fatal(err)
}
if !g.Equal(a, b) {
t.Fatal("serialization failed")
}
}
for i := 0; i < fuz; i++ {
a := g1.rand()
encoded := g1.EncodePoint(a)
b, err := g1.DecodePoint(encoded)
a := g.randAffine()
uncompressed := g.ToBytes(a)
b, err := g.FromBytes(uncompressed)
if err != nil {
t.Fatal(err)
}
if !g1.Equal(a, b) {
t.Fatal("bad serialization encode/decode")
if !g.Equal(a, b) {
t.Fatal("serialization failed")
}
}
}
@ -66,6 +131,26 @@ func TestG1IsOnCurve(t *testing.T) {
}
}
func TestG1BatchAffine(t *testing.T) {
n := 20
g := NewG1()
points0 := make([]*PointG1, n)
points1 := make([]*PointG1, n)
for i := 0; i < n; i++ {
points0[i] = g.rand()
points1[i] = g.New().Set(points0[i])
if g.IsAffine(points0[i]) {
t.Fatal("expect non affine point")
}
}
g.AffineBatch(points0)
for i := 0; i < n; i++ {
if !g.Equal(points0[i], points1[i]) {
t.Fatal("batch affine failed")
}
}
}
func TestG1AdditiveProperties(t *testing.T) {
g := NewG1()
t0, t1 := g.New(), g.New()
@ -135,14 +220,71 @@ func TestG1AdditiveProperties(t *testing.T) {
}
}
func TestG1MixedAdd(t *testing.T) {
g := NewG1()
for i := 0; i < fuz; i++ {
a, b := g.rand(), g.rand()
if g.IsAffine(a) || g.IsAffine(b) {
t.Fatal("expect non affine points")
}
bAffine := g.New().Set(b)
g.Affine(bAffine)
r0, r1 := g.New(), g.New()
g.Add(r0, a, b)
g.AddMixed(r1, a, bAffine)
if !g.Equal(r0, r1) {
t.Fatal("mixed addition failed")
}
aAffine := g.New().Set(a)
g.Affine(aAffine)
g.AddMixed(r0, a, aAffine)
g.Double(r1, a)
if !g.Equal(r0, r1) {
t.Fatal("mixed addition must double where points are equal")
}
}
}
func TestG1MultiplicationCross(t *testing.T) {
g := NewG1()
for i := 0; i < fuz; i++ {
a := g.randCorrect()
s, _ := new(Fr).Rand(rand.Reader)
sBig := s.ToBig()
res0, res1, res2, res3, res4 := g.New(), g.New(), g.New(), g.New(), g.New()
g.mulScalar(res0, a, s)
g.glvMulFr(res1, a, s)
g.glvMulBig(res2, a, sBig)
g.wnafMulFr(res3, a, s)
g.wnafMulBig(res4, a, sBig)
if !g.Equal(res0, res1) {
t.Fatal("cross multiplication failed (glv, fr)", i)
}
if !g.Equal(res0, res2) {
t.Fatal("cross multiplication failed (glv, big)", i)
}
if !g.Equal(res0, res3) {
t.Fatal("cross multiplication failed (wnaf, fr)", i)
}
if !g.Equal(res0, res4) {
t.Fatal("cross multiplication failed (wnaf, big)", i)
}
}
}
func TestG1MultiplicativeProperties(t *testing.T) {
g := NewG1()
t0, t1 := g.New(), g.New()
zero := g.Zero()
for i := 0; i < fuz; i++ {
a := g.rand()
s1, s2, s3 := randScalar(q), randScalar(q), randScalar(q)
sone := big.NewInt(1)
a := g.randCorrect()
s1, _ := new(Fr).Rand(rand.Reader)
s2, _ := new(Fr).Rand(rand.Reader)
s3, _ := new(Fr).Rand(rand.Reader)
sone := &Fr{1}
g.MulScalar(t0, zero, s1)
if !g.Equal(t0, zero) {
t.Fatal(" 0 ^ s == 0")
@ -160,7 +302,7 @@ func TestG1MultiplicativeProperties(t *testing.T) {
s3.Mul(s1, s2)
g.MulScalar(t1, a, s3)
if !g.Equal(t0, t1) {
t.Errorf(" (a ^ s1) ^ s2 == a ^ (s1 * s2)")
t.Fatal(" (a ^ s1) ^ s2 == a ^ (s1 * s2)")
}
g.MulScalar(t0, a, s1)
g.MulScalar(t1, a, s2)
@ -168,12 +310,71 @@ func TestG1MultiplicativeProperties(t *testing.T) {
s3.Add(s1, s2)
g.MulScalar(t1, a, s3)
if !g.Equal(t0, t1) {
t.Errorf(" (a ^ s1) + (a ^ s2) == a ^ (s1 + s2)")
t.Fatal(" (a ^ s1) + (a ^ s2) == a ^ (s1 + s2)")
}
}
}
func TestZKCryptoVectorsG1UncompressedValid(t *testing.T) {
data, err := ioutil.ReadFile("tests/g1_uncompressed_valid_test_vectors.dat")
if err != nil {
panic(err)
}
g := NewG1()
p1 := g.Zero()
for i := 0; i < 1000; i++ {
vector := data[i*2*fpByteSize : (i+1)*2*fpByteSize]
p2, err := g.FromUncompressed(vector)
if err != nil {
t.Fatal("decoing fails", err, i)
}
uncompressed := g.ToUncompressed(p2)
if !bytes.Equal(vector, uncompressed) || !g.Equal(p1, p2) {
t.Fatal("serialization failed")
}
g.Add(p1, p1, &g1One)
}
}
func TestZKCryptoVectorsG1CompressedValid(t *testing.T) {
data, err := ioutil.ReadFile("tests/g1_compressed_valid_test_vectors.dat")
if err != nil {
panic(err)
}
g := NewG1()
p1 := g.Zero()
for i := 0; i < 1000; i++ {
vector := data[i*fpByteSize : (i+1)*fpByteSize]
p2, err := g.FromCompressed(vector)
if err != nil {
t.Fatal("decoing fails", err, i)
}
compressed := g.ToCompressed(p2)
if !bytes.Equal(vector, compressed) || !g.Equal(p1, p2) {
t.Fatal("serialization failed")
}
g.Add(p1, p1, &g1One)
}
}
func TestG1MultiExpExpected(t *testing.T) {
g := NewG1()
one := g.one()
var scalars [2]*Fr
var bases [2]*PointG1
scalars[0] = &Fr{2}
scalars[1] = &Fr{3}
bases[0], bases[1] = new(PointG1).Set(one), new(PointG1).Set(one)
expected, result := g.New(), g.New()
g.mulScalar(expected, one, &Fr{5})
_, _ = g.MultiExp(result, bases[:], scalars[:])
if !g.Equal(expected, result) {
t.Fatal("multi-exponentiation failed")
}
}
func TestG1MultiExpBigExpected(t *testing.T) {
g := NewG1()
one := g.one()
var scalars [2]*big.Int
@ -182,36 +383,76 @@ func TestG1MultiExpExpected(t *testing.T) {
scalars[1] = big.NewInt(3)
bases[0], bases[1] = new(PointG1).Set(one), new(PointG1).Set(one)
expected, result := g.New(), g.New()
g.MulScalar(expected, one, big.NewInt(5))
_, _ = g.MultiExp(result, bases[:], scalars[:])
g.mulScalarBig(expected, one, big.NewInt(5))
_, _ = g.MultiExpBig(result, bases[:], scalars[:])
if !g.Equal(expected, result) {
t.Fatal("bad multi-exponentiation")
t.Fatal("multi-exponentiation failed")
}
}
func TestG1MultiExpBatch(t *testing.T) {
func TestG1MultiExpBig(t *testing.T) {
g := NewG1()
one := g.one()
n := 1000
bases := make([]*PointG1, n)
scalars := make([]*big.Int, n)
// scalars: [s0,s1 ... s(n-1)]
// bases: [P0,P1,..P(n-1)] = [s(n-1)*G, s(n-2)*G ... s0*G]
for i, j := 0, n-1; i < n; i, j = i+1, j-1 {
scalars[j], _ = rand.Int(rand.Reader, big.NewInt(100000))
bases[i] = g.New()
g.MulScalar(bases[i], one, scalars[j])
for n := 1; n < 1024+1; n = n * 2 {
bases := make([]*PointG1, n)
scalars := make([]*big.Int, n)
var err error
for i := 0; i < n; i++ {
scalars[i], err = rand.Int(rand.Reader, qBig)
if err != nil {
t.Fatal(err)
}
bases[i] = g.randAffine()
}
expected, tmp := g.New(), g.New()
for i := 0; i < n; i++ {
g.mulScalarBig(tmp, bases[i], scalars[i])
g.Add(expected, expected, tmp)
}
result := g.New()
_, _ = g.MultiExpBig(result, bases, scalars)
if !g.Equal(expected, result) {
t.Fatal("multi-exponentiation failed")
}
}
// expected: s(n-1)*P0 + s(n-2)*P1 + s0*P(n-1)
expected, tmp := g.New(), g.New()
for i := 0; i < n; i++ {
g.MulScalar(tmp, bases[i], scalars[i])
g.Add(expected, expected, tmp)
}
func TestG1MultiExp(t *testing.T) {
g := NewG1()
for n := 1; n < 1024+1; n = n * 2 {
bases := make([]*PointG1, n)
scalars := make([]*Fr, n)
var err error
for i := 0; i < n; i++ {
scalars[i], err = new(Fr).Rand(rand.Reader)
if err != nil {
t.Fatal(err)
}
bases[i] = g.randAffine()
}
expected, tmp := g.New(), g.New()
for i := 0; i < n; i++ {
g.mulScalar(tmp, bases[i], scalars[i])
g.Add(expected, expected, tmp)
}
result := g.New()
_, _ = g.MultiExp(result, bases, scalars)
if !g.Equal(expected, result) {
t.Fatal("multi-exponentiation failed")
}
}
result := g.New()
_, _ = g.MultiExp(result, bases, scalars)
if !g.Equal(expected, result) {
t.Fatal("bad multi-exponentiation")
}
func TestG1ClearCofactor(t *testing.T) {
g := NewG1()
for i := 0; i < fuz; i++ {
p0 := g.rand()
if g.InCorrectSubgroup(p0) {
t.Fatal("rand point should be out of correct subgroup")
}
g.ClearCofactor(p0)
if !g.InCorrectSubgroup(p0) {
t.Fatal("cofactor clearing is failed")
}
}
}
@ -221,24 +462,39 @@ func TestG1MapToCurve(t *testing.T) {
expected []byte
}{
{
u: make([]byte, 48),
expected: common.FromHex("11a9a0372b8f332d5c30de9ad14e50372a73fa4c45d5f2fa5097f2d6fb93bcac592f2e1711ac43db0519870c7d0ea415" + "092c0f994164a0719f51c24ba3788de240ff926b55f58c445116e8bc6a47cd63392fd4e8e22bdf9feaa96ee773222133"),
u: make([]byte, fpByteSize),
expected: fromHex(-1,
"11a9a0372b8f332d5c30de9ad14e50372a73fa4c45d5f2fa5097f2d6fb93bcac592f2e1711ac43db0519870c7d0ea415",
"092c0f994164a0719f51c24ba3788de240ff926b55f58c445116e8bc6a47cd63392fd4e8e22bdf9feaa96ee773222133",
),
},
{
u: common.FromHex("07fdf49ea58e96015d61f6b5c9d1c8f277146a533ae7fbca2a8ef4c41055cd961fbc6e26979b5554e4b4f22330c0e16d"),
expected: common.FromHex("1223effdbb2d38152495a864d78eee14cb0992d89a241707abb03819a91a6d2fd65854ab9a69e9aacb0cbebfd490732c" + "0f925d61e0b235ecd945cbf0309291878df0d06e5d80d6b84aa4ff3e00633b26f9a7cb3523ef737d90e6d71e8b98b2d5"),
u: fromHex(-1, "07fdf49ea58e96015d61f6b5c9d1c8f277146a533ae7fbca2a8ef4c41055cd961fbc6e26979b5554e4b4f22330c0e16d"),
expected: fromHex(-1,
"1223effdbb2d38152495a864d78eee14cb0992d89a241707abb03819a91a6d2fd65854ab9a69e9aacb0cbebfd490732c",
"0f925d61e0b235ecd945cbf0309291878df0d06e5d80d6b84aa4ff3e00633b26f9a7cb3523ef737d90e6d71e8b98b2d5",
),
},
{
u: common.FromHex("1275ab3adbf824a169ed4b1fd669b49cf406d822f7fe90d6b2f8c601b5348436f89761bb1ad89a6fb1137cd91810e5d2"),
expected: common.FromHex("179d3fd0b4fb1da43aad06cea1fb3f828806ddb1b1fa9424b1e3944dfdbab6e763c42636404017da03099af0dcca0fd6" + "0d037cb1c6d495c0f5f22b061d23f1be3d7fe64d3c6820cfcd99b6b36fa69f7b4c1f4addba2ae7aa46fb25901ab483e4"),
u: fromHex(-1, "1275ab3adbf824a169ed4b1fd669b49cf406d822f7fe90d6b2f8c601b5348436f89761bb1ad89a6fb1137cd91810e5d2"),
expected: fromHex(-1,
"179d3fd0b4fb1da43aad06cea1fb3f828806ddb1b1fa9424b1e3944dfdbab6e763c42636404017da03099af0dcca0fd6",
"0d037cb1c6d495c0f5f22b061d23f1be3d7fe64d3c6820cfcd99b6b36fa69f7b4c1f4addba2ae7aa46fb25901ab483e4",
),
},
{
u: common.FromHex("0e93d11d30de6d84b8578827856f5c05feef36083eef0b7b263e35ecb9b56e86299614a042e57d467fa20948e8564909"),
expected: common.FromHex("15aa66c77eded1209db694e8b1ba49daf8b686733afaa7b68c683d0b01788dfb0617a2e2d04c0856db4981921d3004af" + "0952bb2f61739dd1d201dd0a79d74cda3285403d47655ee886afe860593a8a4e51c5b77a22d2133e3a4280eaaaa8b788"),
u: fromHex(-1, "0e93d11d30de6d84b8578827856f5c05feef36083eef0b7b263e35ecb9b56e86299614a042e57d467fa20948e8564909"),
expected: fromHex(-1,
"15aa66c77eded1209db694e8b1ba49daf8b686733afaa7b68c683d0b01788dfb0617a2e2d04c0856db4981921d3004af",
"0952bb2f61739dd1d201dd0a79d74cda3285403d47655ee886afe860593a8a4e51c5b77a22d2133e3a4280eaaaa8b788",
),
},
{
u: common.FromHex("015a41481155d17074d20be6d8ec4d46632a51521cd9c916e265bd9b47343b3689979b50708c8546cbc2916b86cb1a3a"),
expected: common.FromHex("06328ce5106e837935e8da84bd9af473422e62492930aa5f460369baad9545defa468d9399854c23a75495d2a80487ee" + "094bfdfe3e552447433b5a00967498a3f1314b86ce7a7164c8a8f4131f99333b30a574607e301d5f774172c627fd0bca"),
u: fromHex(-1, "015a41481155d17074d20be6d8ec4d46632a51521cd9c916e265bd9b47343b3689979b50708c8546cbc2916b86cb1a3a"),
expected: fromHex(-1,
"06328ce5106e837935e8da84bd9af473422e62492930aa5f460369baad9545defa468d9399854c23a75495d2a80487ee",
"094bfdfe3e552447433b5a00967498a3f1314b86ce7a7164c8a8f4131f99333b30a574607e301d5f774172c627fd0bca",
),
},
} {
g := NewG1()
@ -252,31 +508,217 @@ func TestG1MapToCurve(t *testing.T) {
}
}
func BenchmarkG1Add(t *testing.B) {
g1 := NewG1()
a, b, c := g1.rand(), g1.rand(), PointG1{}
t.ResetTimer()
for i := 0; i < t.N; i++ {
g1.Add(&c, a, b)
func TestG1EncodeToCurve(t *testing.T) {
domain := []byte("BLS12381G1_XMD:SHA-256_SSWU_NU_TESTGEN")
for i, v := range []struct {
msg []byte
expected []byte
}{
{
msg: []byte(""),
expected: fromHex(-1,
"1223effdbb2d38152495a864d78eee14cb0992d89a241707abb03819a91a6d2fd65854ab9a69e9aacb0cbebfd490732c",
"0f925d61e0b235ecd945cbf0309291878df0d06e5d80d6b84aa4ff3e00633b26f9a7cb3523ef737d90e6d71e8b98b2d5",
),
},
{
msg: []byte("abc"),
expected: fromHex(-1,
"179d3fd0b4fb1da43aad06cea1fb3f828806ddb1b1fa9424b1e3944dfdbab6e763c42636404017da03099af0dcca0fd6",
"0d037cb1c6d495c0f5f22b061d23f1be3d7fe64d3c6820cfcd99b6b36fa69f7b4c1f4addba2ae7aa46fb25901ab483e4",
),
},
{
msg: []byte("abcdef0123456789"),
expected: fromHex(-1,
"15aa66c77eded1209db694e8b1ba49daf8b686733afaa7b68c683d0b01788dfb0617a2e2d04c0856db4981921d3004af",
"0952bb2f61739dd1d201dd0a79d74cda3285403d47655ee886afe860593a8a4e51c5b77a22d2133e3a4280eaaaa8b788",
),
},
{
msg: []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"),
expected: fromHex(-1,
"06328ce5106e837935e8da84bd9af473422e62492930aa5f460369baad9545defa468d9399854c23a75495d2a80487ee",
"094bfdfe3e552447433b5a00967498a3f1314b86ce7a7164c8a8f4131f99333b30a574607e301d5f774172c627fd0bca",
),
},
} {
g := NewG1()
p0, err := g.EncodeToCurve(v.msg, domain)
if err != nil {
t.Fatal("encode to point fails", i, err)
}
if !bytes.Equal(g.ToBytes(p0), v.expected) {
t.Fatal("encode to point fails", i)
}
}
}
func BenchmarkG1Mul(t *testing.B) {
worstCaseScalar, _ := new(big.Int).SetString("ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", 16)
g1 := NewG1()
a, e, c := g1.rand(), worstCaseScalar, PointG1{}
func TestG1HashToCurve(t *testing.T) {
domain := []byte("BLS12381G1_XMD:SHA-256_SSWU_RO_TESTGEN")
for i, v := range []struct {
msg []byte
expected []byte
}{
{
msg: []byte(""),
expected: fromHex(-1,
"0576730ab036cbac1d95b38dca905586f28d0a59048db4e8778782d89bff856ddef89277ead5a21e2975c4a6e3d8c79e",
"1273e568bebf1864393c517f999b87c1eaa1b8432f95aea8160cd981b5b05d8cd4a7cf00103b6ef87f728e4b547dd7ae",
),
},
{
msg: []byte("abc"),
expected: fromHex(-1,
"061daf0cc00d8912dac1d4cf5a7c32fca97f8b3bf3f805121888e5eb89f77f9a9f406569027ac6d0e61b1229f42c43d6",
"0de1601e5ba02cb637c1d35266f5700acee9850796dc88e860d022d7b9e7e3dce5950952e97861e5bb16d215c87f030d",
),
},
{
msg: []byte("abcdef0123456789"),
expected: fromHex(-1,
"0fb3455436843e76079c7cf3dfef75e5a104dfe257a29a850c145568d500ad31ccfe79be9ae0ea31a722548070cf98cd",
"177989f7e2c751658df1b26943ee829d3ebcf131d8f805571712f3a7527ee5334ecff8a97fc2a50cea86f5e6212e9a57",
),
},
{
msg: []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"),
expected: fromHex(-1,
"0514af2137c1ae1d78d5cb97ee606ea142824c199f0f25ac463a0c78200de57640d34686521d3e9cf6b3721834f8a038",
"047a85d6898416a0899e26219bca7c4f0fa682717199de196b02b95eaf9fb55456ac3b810e78571a1b7f5692b7c58ab6",
),
},
} {
g := NewG1()
p0, err := g.HashToCurve(v.msg, domain)
if err != nil {
t.Fatal("hash to point fails", i, err)
}
if !bytes.Equal(g.ToBytes(p0), v.expected) {
t.Fatal("hash to point fails", i)
}
}
}
func BenchmarkG1Add(t *testing.B) {
g := NewG1()
a, b, c := g.rand(), g.rand(), PointG1{}
t.ResetTimer()
for i := 0; i < t.N; i++ {
g1.MulScalar(&c, a, e)
g.Add(&c, a, b)
}
}
func BenchmarkG1MulWNAF(t *testing.B) {
g := NewG1()
p := new(PointG1).Set(&g1One)
s, _ := new(Fr).Rand(rand.Reader)
sBig := s.ToBig()
res := new(PointG1)
t.Run("Naive", func(t *testing.B) {
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.mulScalar(res, p, s)
}
})
for i := 1; i < 8; i++ {
wnafMulWindowG1 = uint(i)
t.Run(fmt.Sprintf("Fr, window: %d", i), func(t *testing.B) {
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.wnafMulFr(res, p, s)
}
})
t.Run(fmt.Sprintf("Big, window: %d", i), func(t *testing.B) {
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.wnafMulBig(res, p, sBig)
}
})
}
}
func BenchmarkG1MulGLV(t *testing.B) {
g := NewG1()
p := new(PointG1).Set(&g1One)
s, _ := new(Fr).Rand(rand.Reader)
sBig := s.ToBig()
res := new(PointG1)
t.Run("Naive", func(t *testing.B) {
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.mulScalar(res, p, s)
}
})
for i := 1; i < 8; i++ {
glvMulWindowG1 = uint(i)
t.Run(fmt.Sprintf("Fr, window: %d", i), func(t *testing.B) {
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.glvMulFr(res, p, s)
}
})
t.Run(fmt.Sprintf("Big, window: %d", i), func(t *testing.B) {
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.glvMulBig(res, p, sBig)
}
})
}
}
func BenchmarkG1MultiExp(t *testing.B) {
g := NewG1()
v := func(n int) ([]*PointG1, []*Fr) {
bases := make([]*PointG1, n)
scalars := make([]*Fr, n)
var err error
for i := 0; i < n; i++ {
scalars[i], err = new(Fr).Rand(rand.Reader)
if err != nil {
t.Fatal(err)
}
bases[i] = g.randAffine()
}
return bases, scalars
}
for _, i := range []int{2, 10, 100, 1000} {
t.Run(fmt.Sprint(i), func(t *testing.B) {
bases, scalars := v(i)
result := g.New()
t.ResetTimer()
for i := 0; i < t.N; i++ {
_, _ = g.MultiExp(result, bases, scalars)
}
})
}
}
func BenchmarkG1ClearCofactor(t *testing.B) {
g := NewG1()
a := g.rand()
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.ClearCofactor(a)
}
}
func BenchmarkG1SubgroupCheck(t *testing.B) {
g := NewG1()
a := g.rand()
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.InCorrectSubgroup(a)
}
}
func BenchmarkG1MapToCurve(t *testing.B) {
a := make([]byte, 48)
g1 := NewG1()
a := fromHex(fpByteSize, "0x1234")
g := NewG1()
t.ResetTimer()
for i := 0; i < t.N; i++ {
_, err := g1.MapToCurve(a)
_, err := g.MapToCurve(a)
if err != nil {
t.Fatal(err)
}

862
crypto/bls12381/g2.go
View file

@ -1,19 +1,3 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
import (
@ -22,9 +6,8 @@ import (
"math/big"
)
// PointG2 is type for point in G2.
// PointG2 is both used for Affine and Jacobian point representation.
// If z is equal to one the point is considered as in affine form.
// PointG2 is type for point in G2 and used for both affine and Jacobian representation.
// A point is accounted as in affine form if z is equal to one.
type PointG2 [3]fe2
// Set copies values of one point to another.
@ -35,7 +18,6 @@ func (p *PointG2) Set(p2 *PointG2) *PointG2 {
return p
}
// Zero returns G2 point in point at infinity representation
func (p *PointG2) Zero() *PointG2 {
p[0].zero()
p[1].one()
@ -43,6 +25,11 @@ func (p *PointG2) Zero() *PointG2 {
return p
}
// IsAffine checks a G1 point whether it is in affine form.
func (p *PointG2) IsAffine() bool {
return p[2].isOne()
}
type tempG2 struct {
t [9]*fe2
}
@ -76,15 +63,141 @@ func newTempG2() tempG2 {
// Q returns group order in big.Int.
func (g *G2) Q() *big.Int {
return new(big.Int).Set(q)
return new(big.Int).Set(qBig)
}
func (g *G2) fromBytesUnchecked(in []byte) (*PointG2, error) {
p0, err := g.f.fromBytes(in[:96])
// FromUncompressed expects byte slice at least 192 bytes and given bytes returns a new point in G2.
// Serialization rules are in line with zcash library. See below for details.
// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
func (g *G2) FromUncompressed(uncompressed []byte) (*PointG2, error) {
if len(uncompressed) != 4*fpByteSize {
return nil, errors.New("input string length must be equal to 192 bytes")
}
var in [4 * fpByteSize]byte
copy(in[:], uncompressed[:4*fpByteSize])
if in[0]&(1<<7) != 0 {
return nil, errors.New("compression flag must be zero")
}
if in[0]&(1<<5) != 0 {
return nil, errors.New("sort flag must be zero")
}
if in[0]&(1<<6) != 0 {
for i, v := range in {
if (i == 0 && v != 0x40) || (i != 0 && v != 0x00) {
return nil, errors.New("input string must be zero when infinity flag is set")
}
}
return g.Zero(), nil
}
in[0] &= 0x1f
x, err := g.f.fromBytes(in[:2*fpByteSize])
if err != nil {
return nil, err
}
p1, err := g.f.fromBytes(in[96:])
y, err := g.f.fromBytes(in[2*fpByteSize:])
if err != nil {
return nil, err
}
z := new(fe2).one()
p := &PointG2{*x, *y, *z}
if !g.IsOnCurve(p) {
return nil, errors.New("point is not on curve")
}
if !g.InCorrectSubgroup(p) {
return nil, errors.New("point is not on correct subgroup")
}
return p, nil
}
// ToUncompressed given a G2 point returns bytes in uncompressed (x, y) form of the point.
// Serialization rules are in line with zcash library. See below for details.
// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
func (g *G2) ToUncompressed(p *PointG2) []byte {
out := make([]byte, 4*fpByteSize)
g.Affine(p)
if g.IsZero(p) {
out[0] |= 1 << 6
return out
}
copy(out[:2*fpByteSize], g.f.toBytes(&p[0]))
copy(out[2*fpByteSize:], g.f.toBytes(&p[1]))
return out
}
// FromCompressed expects byte slice at least 96 bytes and given bytes returns a new point in G2.
// Serialization rules are in line with zcash library. See below for details.
// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
func (g *G2) FromCompressed(compressed []byte) (*PointG2, error) {
if len(compressed) != 2*fpByteSize {
return nil, errors.New("input string length must be equal to 96 bytes")
}
var in [2 * fpByteSize]byte
copy(in[:], compressed[:])
if in[0]&(1<<7) == 0 {
return nil, errors.New("compression flag must be set")
}
if in[0]&(1<<6) != 0 {
// in[0] == (1 << 6) + (1 << 7)
for i, v := range in {
if (i == 0 && v != 0xc0) || (i != 0 && v != 0x00) {
return nil, errors.New("input string must be zero when infinity flag is set")
}
}
return g.Zero(), nil
}
a := in[0]&(1<<5) != 0
in[0] &= 0x1f
x, err := g.f.fromBytes(in[:])
if err != nil {
return nil, err
}
// solve curve equation
y := &fe2{}
g.f.square(y, x)
g.f.mul(y, y, x)
fp2Add(y, y, b2)
if ok := g.f.sqrt(y, y); !ok {
return nil, errors.New("point is not on curve")
}
if y.signBE() == a {
fp2Neg(y, y)
}
z := new(fe2).one()
p := &PointG2{*x, *y, *z}
if !g.InCorrectSubgroup(p) {
return nil, errors.New("point is not on correct subgroup")
}
return p, nil
}
// ToCompressed given a G2 point returns bytes in compressed form of the point.
// Serialization rules are in line with zcash library. See below for details.
// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
func (g *G2) ToCompressed(p *PointG2) []byte {
out := make([]byte, 2*fpByteSize)
g.Affine(p)
if g.IsZero(p) {
out[0] |= 1 << 6
} else {
copy(out[:], g.f.toBytes(&p[0]))
if !p[1].signBE() {
out[0] |= 1 << 5
}
}
out[0] |= 1 << 7
return out
}
func (g *G2) fromBytesUnchecked(in []byte) (*PointG2, error) {
p0, err := g.f.fromBytes(in[:2*fpByteSize])
if err != nil {
return nil, err
}
p1, err := g.f.fromBytes(in[2*fpByteSize:])
if err != nil {
return nil, err
}
@ -93,19 +206,17 @@ func (g *G2) fromBytesUnchecked(in []byte) (*PointG2, error) {
}
// FromBytes constructs a new point given uncompressed byte input.
// FromBytes does not take zcash flags into account.
// Byte input expected to be larger than 96 bytes.
// First 192 bytes should be concatenation of x and y values
// Input string expected to be 192 bytes and concatenation of x and y values
// Point (0, 0) is considered as infinity.
func (g *G2) FromBytes(in []byte) (*PointG2, error) {
if len(in) != 192 {
return nil, errors.New("input string should be equal or larger than 192")
if len(in) != 4*fpByteSize {
return nil, errors.New("input string length must be equal to 192 bytes")
}
p0, err := g.f.fromBytes(in[:96])
p0, err := g.f.fromBytes(in[:2*fpByteSize])
if err != nil {
return nil, err
}
p1, err := g.f.fromBytes(in[96:])
p1, err := g.f.fromBytes(in[2*fpByteSize:])
if err != nil {
return nil, err
}
@ -121,60 +232,16 @@ func (g *G2) FromBytes(in []byte) (*PointG2, error) {
return p, nil
}
// DecodePoint given encoded (x, y) coordinates in 256 bytes returns a valid G2 Point.
func (g *G2) DecodePoint(in []byte) (*PointG2, error) {
if len(in) != 256 {
return nil, errors.New("invalid g2 point length")
}
pointBytes := make([]byte, 192)
x0Bytes, err := decodeFieldElement(in[:64])
if err != nil {
return nil, err
}
x1Bytes, err := decodeFieldElement(in[64:128])
if err != nil {
return nil, err
}
y0Bytes, err := decodeFieldElement(in[128:192])
if err != nil {
return nil, err
}
y1Bytes, err := decodeFieldElement(in[192:])
if err != nil {
return nil, err
}
copy(pointBytes[:48], x1Bytes)
copy(pointBytes[48:96], x0Bytes)
copy(pointBytes[96:144], y1Bytes)
copy(pointBytes[144:192], y0Bytes)
return g.FromBytes(pointBytes)
}
// ToBytes serializes a point into bytes in uncompressed form,
// does not take zcash flags into account,
// returns (0, 0) if point is infinity.
func (g *G2) ToBytes(p *PointG2) []byte {
out := make([]byte, 192)
out := make([]byte, 4*fpByteSize)
if g.IsZero(p) {
return out
}
g.Affine(p)
copy(out[:96], g.f.toBytes(&p[0]))
copy(out[96:], g.f.toBytes(&p[1]))
return out
}
// EncodePoint encodes a point into 256 bytes.
func (g *G2) EncodePoint(p *PointG2) []byte {
// outRaw is 96 bytes
outRaw := g.ToBytes(p)
out := make([]byte, 256)
// encode x
copy(out[16:16+48], outRaw[48:96])
copy(out[80:80+48], outRaw[:48])
// encode y
copy(out[144:144+48], outRaw[144:])
copy(out[208:208+48], outRaw[96:144])
copy(out[:2*fpByteSize], g.f.toBytes(&p[0]))
copy(out[2*fpByteSize:], g.f.toBytes(&p[1]))
return out
}
@ -212,35 +279,32 @@ func (g *G2) Equal(p1, p2 *PointG2) bool {
g.f.square(t[1], &p2[2])
g.f.mul(t[2], t[0], &p2[0])
g.f.mul(t[3], t[1], &p1[0])
g.f.mul(t[0], t[0], &p1[2])
g.f.mul(t[1], t[1], &p2[2])
g.f.mul(t[1], t[1], &p1[1])
g.f.mul(t[0], t[0], &p2[1])
g.f.mulAssign(t[0], &p1[2])
g.f.mulAssign(t[1], &p2[2])
g.f.mulAssign(t[1], &p1[1])
g.f.mulAssign(t[0], &p2[1])
return t[0].equal(t[1]) && t[2].equal(t[3])
}
// InCorrectSubgroup checks whether given point is in correct subgroup.
func (g *G2) InCorrectSubgroup(p *PointG2) bool {
tmp := &PointG2{}
g.MulScalar(tmp, p, q)
return g.IsZero(tmp)
}
// IsOnCurve checks a G2 point is on curve.
func (g *G2) IsOnCurve(p *PointG2) bool {
if g.IsZero(p) {
return true
}
t := g.t
g.f.square(t[0], &p[1])
g.f.square(t[1], &p[0])
g.f.mul(t[1], t[1], &p[0])
g.f.square(t[2], &p[2])
g.f.square(t[3], t[2])
g.f.mul(t[2], t[2], t[3])
g.f.mul(t[2], b2, t[2])
g.f.add(t[1], t[1], t[2])
return t[0].equal(t[1])
g.f.square(t[0], &p[1]) // y^2
g.f.square(t[1], &p[0]) // x^2
g.f.mul(t[1], t[1], &p[0]) // x^3
if p.IsAffine() {
fp2Add(t[1], t[1], b2) // x^2 + b
return t[0].equal(t[1]) // y^2 ?= x^3 + b
}
g.f.square(t[2], &p[2]) // z^2
g.f.square(t[3], t[2]) // z^4
g.f.mulAssign(t[2], t[3]) // z^6
g.f.mulAssign(t[2], b2) // b*z^6
fp2AddAssign(t[1], t[2]) // x^3 + b * z^6
return t[0].equal(t[1]) // y^2 ?= x^3 + b * z^6
}
// IsAffine checks a G2 point whether it is in affine form.
@ -250,24 +314,102 @@ func (g *G2) IsAffine(p *PointG2) bool {
// Affine calculates affine form of given G2 point.
func (g *G2) Affine(p *PointG2) *PointG2 {
return g.affine(p, p)
}
func (g *G2) affine(r, p *PointG2) *PointG2 {
if g.IsZero(p) {
return p
return r.Zero()
}
if !g.IsAffine(p) {
t := g.t
g.f.inverse(t[0], &p[2])
g.f.square(t[1], t[0])
g.f.mul(&p[0], &p[0], t[1])
g.f.mul(t[0], t[0], t[1])
g.f.mul(&p[1], &p[1], t[0])
p[2].one()
g.f.inverse(t[0], &p[2]) // z^-1
g.f.square(t[1], t[0]) // z^-2
g.f.mulAssign(&r[0], t[1]) // x = x * z^-2
g.f.mulAssign(t[0], t[1]) // z^-3
g.f.mulAssign(&r[1], t[0]) // y = y * z^-3
r[2].one() // z = 1
} else {
r.Set(p)
}
return r
}
// AffineBatch given multiple of points returns affine representations
func (g *G2) AffineBatch(p []*PointG2) {
inverses := make([]fe2, len(p))
for i := 0; i < len(p); i++ {
inverses[i].set(&p[i][2])
}
g.f.inverseBatch(inverses)
t := g.t
for i := 0; i < len(p); i++ {
if !g.IsAffine(p[i]) && !g.IsZero(p[i]) {
g.f.square(t[1], &inverses[i])
g.f.mulAssign(&p[i][0], t[1])
g.f.mul(t[0], &inverses[i], t[1])
g.f.mulAssign(&p[i][1], t[0])
p[i][2].one()
}
}
return p
}
// Add adds two G2 points p1, p2 and assigns the result to point at first argument.
func (g *G2) Add(r, p1, p2 *PointG2) *PointG2 {
// http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl
// http://www.hyperelliptic.org/EFD/gp/auto-shortw-jacobian-0.html#addition-add-2007-bl
if g.IsZero(p1) {
return r.Set(p2)
}
if g.IsZero(p2) {
return r.Set(p1)
}
if g.IsAffine(p2) {
return g.AddMixed(r, p1, p2)
}
t := g.t
g.f.square(t[7], &p1[2]) // z1z1
g.f.mul(t[1], &p2[0], t[7]) // u2 = x2 * z1z1
g.f.mul(t[2], &p1[2], t[7]) // z1z1 * z1
g.f.mul(t[0], &p2[1], t[2]) // s2 = y2 * z1z1 * z1
g.f.square(t[8], &p2[2]) // z2z2
g.f.mul(t[3], &p1[0], t[8]) // u1 = x1 * z2z2
g.f.mul(t[4], &p2[2], t[8]) // z2z2 * z2
g.f.mul(t[2], &p1[1], t[4]) // s1 = y1 * z2z2 * z2
if t[1].equal(t[3]) {
if t[0].equal(t[2]) {
return g.Double(r, p1)
} else {
return r.Zero()
}
}
fp2SubAssign(t[1], t[3]) // h = u2 - u1
fp2Double(t[4], t[1]) // 2h
g.f.squareAssign(t[4]) // i = 2h^2
g.f.mul(t[5], t[1], t[4]) // j = h*i
fp2SubAssign(t[0], t[2]) // s2 - s1
fp2DoubleAssign(t[0]) // r = 2*(s2 - s1)
g.f.square(t[6], t[0]) // r^2
fp2SubAssign(t[6], t[5]) // r^2 - j
g.f.mulAssign(t[3], t[4]) // v = u1 * i
fp2Double(t[4], t[3]) // 2*v
fp2Sub(&r[0], t[6], t[4]) // x3 = r^2 - j - 2*v
fp2Sub(t[4], t[3], &r[0]) // v - x3
g.f.mul(t[6], t[2], t[5]) // s1 * j
fp2DoubleAssign(t[6]) // 2 * s1 * j
g.f.mulAssign(t[0], t[4]) // r * (v - x3)
fp2Sub(&r[1], t[0], t[6]) // y3 = r * (v - x3) - (2 * s1 * j)
fp2Add(t[0], &p1[2], &p2[2]) // z1 + z2
g.f.squareAssign(t[0]) // (z1 + z2)^2
fp2SubAssign(t[0], t[7]) // (z1 + z2)^2 - z1z1
fp2SubAssign(t[0], t[8]) // (z1 + z2)^2 - z1z1 - z2z2
g.f.mul(&r[2], t[0], t[1]) // z3 = ((z1 + z2)^2 - z1z1 - z2z2) * h
return r
}
// Add adds two G1 points p1, p2 and assigns the result to point at first argument.
// Expects the second point p2 in affine form.
func (g *G2) AddMixed(r, p1, p2 *PointG2) *PointG2 {
// http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-madd-2007-bl
if g.IsZero(p1) {
return r.Set(p2)
}
@ -275,80 +417,75 @@ func (g *G2) Add(r, p1, p2 *PointG2) *PointG2 {
return r.Set(p1)
}
t := g.t
g.f.square(t[7], &p1[2])
g.f.mul(t[1], &p2[0], t[7])
g.f.mul(t[2], &p1[2], t[7])
g.f.mul(t[0], &p2[1], t[2])
g.f.square(t[8], &p2[2])
g.f.mul(t[3], &p1[0], t[8])
g.f.mul(t[4], &p2[2], t[8])
g.f.mul(t[2], &p1[1], t[4])
if t[1].equal(t[3]) {
if t[0].equal(t[2]) {
return g.Double(r, p1)
}
return r.Zero()
g.f.square(t[7], &p1[2]) // z1z1
g.f.mul(t[1], &p2[0], t[7]) // u2 = x2 * z1z1
g.f.mul(t[2], &p1[2], t[7]) // z1z1 * z1
g.f.mul(t[0], &p2[1], t[2]) // s2 = y2 * z1z1 * z1
if p1[0].equal(t[1]) && p1[1].equal(t[0]) {
return g.Double(r, p1)
}
g.f.sub(t[1], t[1], t[3])
g.f.double(t[4], t[1])
g.f.square(t[4], t[4])
g.f.mul(t[5], t[1], t[4])
g.f.sub(t[0], t[0], t[2])
g.f.double(t[0], t[0])
g.f.square(t[6], t[0])
g.f.sub(t[6], t[6], t[5])
g.f.mul(t[3], t[3], t[4])
g.f.double(t[4], t[3])
g.f.sub(&r[0], t[6], t[4])
g.f.sub(t[4], t[3], &r[0])
g.f.mul(t[6], t[2], t[5])
g.f.double(t[6], t[6])
g.f.mul(t[0], t[0], t[4])
g.f.sub(&r[1], t[0], t[6])
g.f.add(t[0], &p1[2], &p2[2])
g.f.square(t[0], t[0])
g.f.sub(t[0], t[0], t[7])
g.f.sub(t[0], t[0], t[8])
g.f.mul(&r[2], t[0], t[1])
fp2SubAssign(t[1], &p1[0]) // h = u2 - x1
g.f.square(t[2], t[1]) // hh
fp2Double(t[4], t[2])
fp2DoubleAssign(t[4]) // 4hh
g.f.mul(t[5], t[1], t[4]) // j = h*i
fp2SubAssign(t[0], &p1[1]) // s2 - y1
fp2DoubleAssign(t[0]) // r = 2*(s2 - y1)
g.f.square(t[6], t[0]) // r^2
fp2SubAssign(t[6], t[5]) // r^2 - j
g.f.mul(t[3], &p1[0], t[4]) // v = x1 * i
fp2Double(t[4], t[3]) // 2*v
fp2Sub(&r[0], t[6], t[4]) // x3 = r^2 - j - 2*v
fp2Sub(t[4], t[3], &r[0]) // v - x3
g.f.mul(t[6], &p1[1], t[5]) // y1 * j
fp2DoubleAssign(t[6]) // 2 * y1 * j
g.f.mulAssign(t[0], t[4]) // r * (v - x3)
fp2Sub(&r[1], t[0], t[6]) // y3 = r * (v - x3) - (2 * y1 * j)
fp2Add(t[0], &p1[2], t[1]) // z1 + h
g.f.squareAssign(t[0]) // (z1 + h)^2
fp2SubAssign(t[0], t[7]) // (z1 + h)^2 - z1z1
fp2Sub(&r[2], t[0], t[2]) // z3 = (z1 + z2)^2 - z1z1 - hh
return r
}
// Double doubles a G2 point p and assigns the result to the point at first argument.
func (g *G2) Double(r, p *PointG2) *PointG2 {
// http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
// http://www.hyperelliptic.org/EFD/gp/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
if g.IsZero(p) {
return r.Set(p)
}
t := g.t
g.f.square(t[0], &p[0])
g.f.square(t[1], &p[1])
g.f.square(t[2], t[1])
g.f.add(t[1], &p[0], t[1])
g.f.square(t[1], t[1])
g.f.sub(t[1], t[1], t[0])
g.f.sub(t[1], t[1], t[2])
g.f.double(t[1], t[1])
g.f.double(t[3], t[0])
g.f.add(t[0], t[3], t[0])
g.f.square(t[4], t[0])
g.f.double(t[3], t[1])
g.f.sub(&r[0], t[4], t[3])
g.f.sub(t[1], t[1], &r[0])
g.f.double(t[2], t[2])
g.f.double(t[2], t[2])
g.f.double(t[2], t[2])
g.f.mul(t[0], t[0], t[1])
g.f.sub(t[1], t[0], t[2])
g.f.mul(t[0], &p[1], &p[2])
r[1].set(t[1])
g.f.double(&r[2], t[0])
g.f.square(t[0], &p[0]) // a = x^2
g.f.square(t[1], &p[1]) // b = y^2
g.f.square(t[2], t[1]) // c = b^2
fp2AddAssign(t[1], &p[0]) // b + x1
g.f.squareAssign(t[1]) // (b + x1)^2
fp2SubAssign(t[1], t[0]) // (b + x1)^2 - a
fp2SubAssign(t[1], t[2]) // (b + x1)^2 - a - c
fp2DoubleAssign(t[1]) // d = 2((b+x1)^2 - a - c)
fp2Double(t[3], t[0]) // 2a
fp2AddAssign(t[0], t[3]) // e = 3a
g.f.square(t[4], t[0]) // f = e^2
fp2Double(t[3], t[1]) // 2d
fp2Sub(&r[0], t[4], t[3]) // x3 = f - 2d
fp2SubAssign(t[1], &r[0]) // d-x3
fp2DoubleAssign(t[2]) //
fp2DoubleAssign(t[2]) //
fp2DoubleAssign(t[2]) // 8c
g.f.mulAssign(t[0], t[1]) // e * (d - x3)
fp2Sub(t[1], t[0], t[2]) // x3 = e * (d - x3) - 8c
g.f.mul(t[0], &p[1], &p[2]) // y1 * z1
r[1].set(t[1]) //
fp2Double(&r[2], t[0]) // z3 = 2(y1 * z1)
return r
}
// Neg negates a G2 point p and assigns the result to the point at first argument.
func (g *G2) Neg(r, p *PointG2) *PointG2 {
r[0].set(&p[0])
g.f.neg(&r[1], &p[1])
fp2Neg(&r[1], &p[1])
r[2].set(&p[2])
return r
}
@ -361,8 +498,29 @@ func (g *G2) Sub(c, a, b *PointG2) *PointG2 {
return c
}
// MulScalar multiplies a point by given scalar value in big.Int and assigns the result to point at first argument.
func (g *G2) MulScalar(c, p *PointG2, e *big.Int) *PointG2 {
// MulScalar multiplies a point by given scalar value and assigns the result to point at first argument.
func (g *G2) MulScalar(r, p *PointG2, e *Fr) *PointG2 {
return g.glvMulFr(r, p, e)
}
// MulScalarBig multiplies a point by given scalar value in big.Int and assigns the result to point at first argument.
func (g *G2) MulScalarBig(r, p *PointG2, e *big.Int) *PointG2 {
return g.glvMulBig(r, p, e)
}
func (g *G2) mulScalar(c, p *PointG2, e *Fr) *PointG2 {
q, n := &PointG2{}, &PointG2{}
n.Set(p)
for i := 0; i < frBitSize; i++ {
if e.Bit(i) {
g.Add(q, q, n)
}
g.Double(n, n)
}
return c.Set(q)
}
func (g *G2) mulScalarBig(c, p *PointG2, e *big.Int) *PointG2 {
q, n := &PointG2{}, &PointG2{}
n.Set(p)
l := e.BitLen()
@ -375,67 +533,299 @@ func (g *G2) MulScalar(c, p *PointG2, e *big.Int) *PointG2 {
return c.Set(q)
}
// ClearCofactor maps given a G2 point to correct subgroup
func (g *G2) ClearCofactor(p *PointG2) {
g.MulScalar(p, p, cofactorEFFG2)
func (g *G2) wnafMulFr(r, p *PointG2, e *Fr) *PointG2 {
wnaf := e.toWNAF(wnafMulWindowG2)
return g.wnafMul(r, p, wnaf)
}
// MultiExp calculates multi exponentiation. Given pairs of G2 point and scalar values
// (P_0, e_0), (P_1, e_1), ... (P_n, e_n) calculates r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n
// Length of points and scalars are expected to be equal, otherwise an error is returned.
// Result is assigned to point at first argument.
func (g *G2) MultiExp(r *PointG2, points []*PointG2, powers []*big.Int) (*PointG2, error) {
if len(points) != len(powers) {
return nil, errors.New("point and scalar vectors should be in same length")
func (g *G2) wnafMulBig(r, p *PointG2, e *big.Int) *PointG2 {
wnaf := bigToWNAF(e, wnafMulWindowG2)
return g.wnafMul(r, p, wnaf)
}
func (g *G2) wnafMul(c, p *PointG2, wnaf nafNumber) *PointG2 {
l := (1 << (wnafMulWindowG2 - 1))
twoP, acc := g.New(), new(PointG2).Set(p)
g.Double(twoP, p)
g.Affine(twoP)
// table = {p, 3p, 5p, ..., -p, -3p, -5p}
table := make([]*PointG2, l*2)
table[0], table[l] = g.New(), g.New()
table[0].Set(p)
g.Neg(table[l], table[0])
for i := 1; i < l; i++ {
g.AddMixed(acc, acc, twoP)
table[i], table[i+l] = g.New(), g.New()
table[i].Set(acc)
g.Neg(table[i+l], table[i])
}
var c uint32 = 3
if len(powers) >= 32 {
c = uint32(math.Ceil(math.Log10(float64(len(powers)))))
}
bucketSize, numBits := (1<<c)-1, uint32(g.Q().BitLen())
windows := make([]*PointG2, numBits/c+1)
bucket := make([]*PointG2, bucketSize)
acc, sum := g.New(), g.New()
for i := 0; i < bucketSize; i++ {
bucket[i] = g.New()
}
mask := (uint64(1) << c) - 1
j := 0
var cur uint32
for cur <= numBits {
acc.Zero()
bucket = make([]*PointG2, (1<<c)-1)
for i := 0; i < len(bucket); i++ {
bucket[i] = g.New()
q := g.Zero()
for i := len(wnaf) - 1; i >= 0; i-- {
if wnaf[i] > 0 {
g.Add(q, q, table[wnaf[i]>>1])
} else if wnaf[i] < 0 {
g.Add(q, q, table[((-wnaf[i])>>1)+l])
}
for i := 0; i < len(powers); i++ {
s0 := powers[i].Uint64()
index := uint(s0 & mask)
if index != 0 {
g.Add(bucket[index-1], bucket[index-1], points[i])
if i != 0 {
g.Double(q, q)
}
}
return c.Set(q)
}
func (g *G2) glvMulFr(r, p *PointG2, e *Fr) *PointG2 {
return g.glvMul(r, p, new(glvVectorFr).new(e))
}
func (g *G2) glvMulBig(r, p *PointG2, e *big.Int) *PointG2 {
return g.glvMul(r, p, new(glvVectorBig).new(e))
}
func (g *G2) glvMul(r, p0 *PointG2, v glvVector) *PointG2 {
w := glvMulWindowG2
l := 1 << (w - 1)
// prepare tables
// tableK1 = {P, 3P, 5P, ...}
// tableK2 = {λP, 3λP, 5λP, ...}
tableK1, tableK2 := make([]*PointG2, l), make([]*PointG2, l)
double := g.New()
g.Double(double, p0)
g.affine(double, double)
tableK1[0] = new(PointG2)
tableK1[0].Set(p0)
for i := 1; i < l; i++ {
tableK1[i] = new(PointG2)
g.AddMixed(tableK1[i], tableK1[i-1], double)
}
g.AffineBatch(tableK1)
for i := 0; i < l; i++ {
tableK2[i] = new(PointG2)
g.glvEndomorphism(tableK2[i], tableK1[i])
}
// recode small scalars
naf1, naf2 := v.wnaf(w)
lenNAF1, lenNAF2 := len(naf1), len(naf2)
lenNAF := lenNAF1
if lenNAF2 > lenNAF {
lenNAF = lenNAF2
}
acc, p1 := g.New(), g.New()
// function for naf addition
add := func(table []*PointG2, naf int) {
if naf != 0 {
nafAbs := naf
if nafAbs < 0 {
nafAbs = -nafAbs
}
powers[i] = new(big.Int).Rsh(powers[i], uint(c))
p1.Set(table[nafAbs>>1])
if naf < 0 {
g.Neg(p1, p1)
}
g.AddMixed(acc, acc, p1)
}
sum.Zero()
for i := len(bucket) - 1; i >= 0; i-- {
g.Add(sum, sum, bucket[i])
g.Add(acc, acc, sum)
}
windows[j] = g.New()
windows[j].Set(acc)
j++
cur += c
}
acc.Zero()
for i := len(windows) - 1; i >= 0; i-- {
for j := uint32(0); j < c; j++ {
// sliding
for i := lenNAF - 1; i >= 0; i-- {
if i < lenNAF1 {
add(tableK1, naf1[i])
}
if i < lenNAF2 {
add(tableK2, naf2[i])
}
if i != 0 {
g.Double(acc, acc)
}
g.Add(acc, acc, windows[i])
}
return r.Set(acc)
}
// MultiExpBig calculates multi exponentiation. Scalar values are received as big.Int type.
// Given pairs of G2 point and scalar values `(P_0, e_0), (P_1, e_1), ... (P_n, e_n)`,
// calculates `r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n`.
// Length of points and scalars are expected to be equal, otherwise an error is returned.
// Result is assigned to point at first argument.
func (g *G2) MultiExpBig(r *PointG2, points []*PointG2, scalars []*big.Int) (*PointG2, error) {
if len(points) != len(scalars) {
return nil, errors.New("point and scalar vectors should be in same length")
}
c := 3
if len(scalars) >= 32 {
c = int(math.Ceil(math.Log(float64(len(scalars)))))
}
bucketSize := (1 << c) - 1
windows := make([]PointG2, 255/c+1)
bucket := make([]PointG2, bucketSize)
for j := 0; j < len(windows); j++ {
for i := 0; i < bucketSize; i++ {
bucket[i].Zero()
}
for i := 0; i < len(scalars); i++ {
index := bucketSize & int(new(big.Int).Rsh(scalars[i], uint(c*j)).Int64())
if index != 0 {
g.Add(&bucket[index-1], &bucket[index-1], points[i])
}
}
acc, sum := g.New(), g.New()
for i := bucketSize - 1; i >= 0; i-- {
g.Add(sum, sum, &bucket[i])
g.Add(acc, acc, sum)
}
windows[j].Set(acc)
}
acc := g.New()
for i := len(windows) - 1; i >= 0; i-- {
for j := 0; j < c; j++ {
g.Double(acc, acc)
}
g.Add(acc, acc, &windows[i])
}
return r.Set(acc), nil
}
// MultiExp calculates multi exponentiation. Given pairs of G2 point and scalar values `(P_0, e_0), (P_1, e_1), ... (P_n, e_n)`,
// calculates `r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n`. Length of points and scalars are expected to be equal,
// otherwise an error is returned. Result is assigned to point at first argument.
func (g *G2) MultiExp(r *PointG2, points []*PointG2, scalars []*Fr) (*PointG2, error) {
if len(points) != len(scalars) {
return nil, errors.New("point and scalar vectors should be in same length")
}
g.AffineBatch(points)
c := 3
if len(scalars) >= 32 {
c = int(math.Ceil(math.Log(float64(len(scalars)))))
}
bucketSize := (1 << c) - 1
windows := make([]*PointG2, 255/c+1)
bucket := make([]PointG2, bucketSize)
for j := 0; j < len(windows); j++ {
for i := 0; i < bucketSize; i++ {
bucket[i].Zero()
}
for i := 0; i < len(scalars); i++ {
index := bucketSize & int(scalars[i].sliceUint64(c*j))
if index != 0 {
g.AddMixed(&bucket[index-1], &bucket[index-1], points[i])
}
}
acc, sum := g.New(), g.New()
for i := bucketSize - 1; i >= 0; i-- {
g.Add(sum, sum, &bucket[i])
g.Add(acc, acc, sum)
}
windows[j] = g.New().Set(acc)
}
g.AffineBatch(windows)
acc := g.New()
for i := len(windows) - 1; i >= 0; i-- {
for j := 0; j < c; j++ {
g.Double(acc, acc)
}
g.AddMixed(acc, acc, windows[i])
}
return r.Set(acc), nil
}
// InCorrectSubgroup checks whether given point is in correct subgroup.
func (g *G2) InCorrectSubgroup(p *PointG2) bool {
// Faster Subgroup Checks for BLS12-381
// S. Bowe
// https://eprint.iacr.org/2019/814.pdf
// [z]ψ^3(P) − ψ^2(P) + P = O
t0, t1 := g.New().Set(p), g.New()
g.psi(t0)
g.psi(t0)
g.Neg(t1, t0) // - ψ^2(P)
g.psi(t0) // ψ^3(P)
g.mulX(t0) // - x ψ^3(P)
g.Neg(t0, t0)
g.Add(t0, t0, t1)
g.Add(t0, t0, p)
return g.IsZero(t0)
}
// ClearCofactor maps given a G2 point to correct subgroup
func (g *G2) ClearCofactor(p *PointG2) *PointG2 {
// Efficient hash maps to G2 on BLS curves
// A. Budroni, F. Pintore
// https://eprint.iacr.org/2017/419.pdf
// [h(ψ)]P = [x^2 − x − 1]P + [x − 1]ψ(P) + ψ^2(2P)
t0, t1, t2, t3 := g.New().Set(p), g.New().Set(p), g.New().Set(p), g.New()
g.Double(t0, t0)
g.psi(t0)
g.psi(t0) // P2 = ψ^2(2P)
g.psi(t2) // P1 = ψ(P)
g.mulX(t1) // -xP0
g.Sub(t3, t1, t2) // -xP0 - P1
g.mulX(t3) // (x^2)P0 + xP1
g.Sub(t1, t1, p) // (-x-1)P0
g.Add(t3, t3, t1) // (x^2-x-1)P0 + xP1
g.Sub(t3, t3, t2) // (x^2-x-1)P0 + (x-1)P1
g.Add(t3, t3, t0) // (x^2-x-1)P0 + (x-1)P1 + P2
return p.Set(t3)
}
func (g *G2) psi(p *PointG2) {
fp2Conjugate(&p[0], &p[0])
fp2Conjugate(&p[1], &p[1])
fp2Conjugate(&p[2], &p[2])
g.f.mul(&p[0], &p[0], &psix)
g.f.mul(&p[1], &p[1], &psiy)
}
func (g *G2) mulX(p *PointG2) {
chain := func(p0 *PointG2, n int, p1 *PointG2) {
g.Add(p0, p0, p1)
for i := 0; i < n; i++ {
g.Double(p0, p0)
}
}
t := g.New().Set(p)
g.Double(p, t)
chain(p, 2, t)
chain(p, 3, t)
chain(p, 9, t)
chain(p, 32, t)
chain(p, 16, t)
}
// MapToCurve given a byte slice returns a valid G2 point.
// This mapping function implements the Simplified Shallue-van de Woestijne-Ulas method.
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-05#section-6.6.2
@ -453,3 +843,45 @@ func (g *G2) MapToCurve(in []byte) (*PointG2, error) {
g.ClearCofactor(q)
return g.Affine(q), nil
}
// EncodeToCurve given a message and domain seperator tag returns the hash result
// which is a valid curve point.
// Implementation follows BLS12381G1_XMD:SHA-256_SSWU_NU_ suite at
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06
func (g *G2) EncodeToCurve(msg, domain []byte) (*PointG2, error) {
hashRes, err := hashToFpXMDSHA256(msg, domain, 2)
if err != nil {
return nil, err
}
fp2 := g.f
u := &fe2{*hashRes[0], *hashRes[1]}
x, y := swuMapG2(fp2, u)
isogenyMapG2(fp2, x, y)
z := new(fe2).one()
q := &PointG2{*x, *y, *z}
g.ClearCofactor(q)
return g.Affine(q), nil
}
// HashToCurve given a message and domain seperator tag returns the hash result
// which is a valid curve point.
// Implementation follows BLS12381G1_XMD:SHA-256_SSWU_RO_ suite at
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06
func (g *G2) HashToCurve(msg, domain []byte) (*PointG2, error) {
hashRes, err := hashToFpXMDSHA256(msg, domain, 4)
if err != nil {
return nil, err
}
fp2 := g.f
u0, u1 := &fe2{*hashRes[0], *hashRes[1]}, &fe2{*hashRes[2], *hashRes[3]}
x0, y0 := swuMapG2(fp2, u0)
x1, y1 := swuMapG2(fp2, u1)
z0 := new(fe2).one()
z1 := new(fe2).one()
p0, p1 := &PointG2{*x0, *y0, *z0}, &PointG2{*x1, *y1, *z1}
g.Add(p0, p0, p1)
g.Affine(p0)
isogenyMapG2(fp2, &p0[0], &p0[1])
g.ClearCofactor(p0)
return g.Affine(p0), nil
}

607
crypto/bls12381/g2_test.go
View file

@ -3,54 +3,117 @@ package bls12381
import (
"bytes"
"crypto/rand"
"fmt"
"io/ioutil"
"math/big"
"testing"
"github.com/ethereum/go-ethereum/common"
)
func (g *G2) one() *PointG2 {
one, _ := g.fromBytesUnchecked(
common.FromHex("" +
"13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e" +
"024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8" +
"0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be" +
"0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801",
),
)
return one
return g.New().Set(&g2One)
}
func (g *G2) rand() *PointG2 {
k, err := rand.Int(rand.Reader, q)
if err != nil {
panic(err)
p := &PointG2{}
z, _ := new(fe2).rand(rand.Reader)
z6, bz6 := new(fe2), new(fe2)
g.f.square(z6, z)
g.f.square(z6, z6)
g.f.mul(z6, z6, z)
g.f.mul(z6, z6, z)
g.f.mul(bz6, z6, b2)
for {
x, _ := new(fe2).rand(rand.Reader)
y := new(fe2)
g.f.square(y, x)
g.f.mul(y, y, x)
fp2Add(y, y, bz6)
if g.f.sqrt(y, y) {
p.Set(&PointG2{*x, *y, *z})
break
}
}
return g.MulScalar(&PointG2{}, g.one(), k)
if !g.IsOnCurve(p) {
panic("rand point must be on curve")
}
if g.InCorrectSubgroup(p) {
panic("rand point must be out of correct subgroup")
}
return p
}
func (g *G2) randCorrect() *PointG2 {
p := g.ClearCofactor(g.rand())
if !g.InCorrectSubgroup(p) {
panic("must be in correct subgroup")
}
return p
}
func (g *G2) randAffine() *PointG2 {
return g.Affine(g.randCorrect())
}
func (g *G2) new() *PointG2 {
return g.Zero()
}
func TestG2Serialization(t *testing.T) {
var err error
g2 := NewG2()
zero := g2.Zero()
b0 := g2.ToUncompressed(zero)
p0, err := g2.FromUncompressed(b0)
if err != nil {
t.Fatal(err)
}
if !g2.IsZero(p0) {
t.Fatal("infinity serialization failed")
}
b0 = g2.ToCompressed(zero)
p0, err = g2.FromCompressed(b0)
if err != nil {
t.Fatal(err)
}
if !g2.IsZero(p0) {
t.Fatal("infinity serialization failed")
}
b0 = g2.ToBytes(zero)
p0, err = g2.FromBytes(b0)
if err != nil {
t.Fatal(err)
}
if !g2.IsZero(p0) {
t.Fatal("infinity serialization failed")
}
for i := 0; i < fuz; i++ {
a := g2.rand()
buf := g2.ToBytes(a)
b, err := g2.FromBytes(buf)
a := g2.randAffine()
uncompressed := g2.ToUncompressed(a)
b, err := g2.FromUncompressed(uncompressed)
if err != nil {
t.Fatal(err)
}
if !g2.Equal(a, b) {
t.Fatal("bad serialization from/to")
t.Fatal("serialization failed")
}
compressed := g2.ToCompressed(b)
a, err = g2.FromCompressed(compressed)
if err != nil {
t.Fatal(err)
}
if !g2.Equal(a, b) {
t.Fatal("serialization failed")
}
}
for i := 0; i < fuz; i++ {
a := g2.rand()
encoded := g2.EncodePoint(a)
b, err := g2.DecodePoint(encoded)
uncompressed := g2.ToBytes(a)
b, err := g2.FromBytes(uncompressed)
if err != nil {
t.Fatal(err)
}
if !g2.Equal(a, b) {
t.Fatal("bad serialization encode/decode")
t.Fatal("serialization failed")
}
}
}
@ -68,6 +131,26 @@ func TestG2IsOnCurve(t *testing.T) {
}
}
func TestG2BatchAffine(t *testing.T) {
n := 20
g := NewG2()
points0 := make([]*PointG2, n)
points1 := make([]*PointG2, n)
for i := 0; i < n; i++ {
points0[i] = g.rand()
points1[i] = g.New().Set(points0[i])
if g.IsAffine(points0[i]) {
t.Fatal("expect non affine point")
}
}
g.AffineBatch(points0)
for i := 0; i < n; i++ {
if !g.Equal(points0[i], points1[i]) {
t.Fatal("batch affine failed")
}
}
}
func TestG2AdditiveProperties(t *testing.T) {
g := NewG2()
t0, t1 := g.New(), g.New()
@ -138,14 +221,71 @@ func TestG2AdditiveProperties(t *testing.T) {
}
}
func TestG2MixedAdd(t *testing.T) {
g := NewG2()
for i := 0; i < fuz; i++ {
a, b := g.rand(), g.rand()
if g.IsAffine(a) || g.IsAffine(b) {
t.Fatal("expect non affine points")
}
bAffine := g.New().Set(b)
g.Affine(bAffine)
r0, r1 := g.New(), g.New()
g.Add(r0, a, b)
g.AddMixed(r1, a, bAffine)
if !g.Equal(r0, r1) {
t.Fatal("mixed addition failed")
}
aAffine := g.New().Set(a)
g.Affine(aAffine)
g.AddMixed(r0, a, aAffine)
g.Double(r1, a)
if !g.Equal(r0, r1) {
t.Fatal("mixed addition must double where points are equal")
}
}
}
func TestG2MultiplicationCross(t *testing.T) {
g := NewG2()
for i := 0; i < fuz; i++ {
a := g.randCorrect()
s, _ := new(Fr).Rand(rand.Reader)
sBig := s.ToBig()
res0, res1, res2, res3, res4 := g.New(), g.New(), g.New(), g.New(), g.New()
g.mulScalar(res0, a, s)
g.glvMulFr(res1, a, s)
g.glvMulBig(res2, a, sBig)
g.wnafMulFr(res3, a, s)
g.wnafMulBig(res4, a, sBig)
if !g.Equal(res0, res1) {
t.Fatal("cross multiplication failed (glv, fr)", i)
}
if !g.Equal(res0, res2) {
t.Fatal("cross multiplication failed (glv, big)", i)
}
if !g.Equal(res0, res3) {
t.Fatal("cross multiplication failed (wnaf, fr)", i)
}
if !g.Equal(res0, res4) {
t.Fatal("cross multiplication failed (wnaf, big)", i)
}
}
}
func TestG2MultiplicativeProperties(t *testing.T) {
g := NewG2()
t0, t1 := g.New(), g.New()
zero := g.Zero()
for i := 0; i < fuz; i++ {
a := g.rand()
s1, s2, s3 := randScalar(q), randScalar(q), randScalar(q)
sone := big.NewInt(1)
a := g.randCorrect()
s1, _ := new(Fr).Rand(rand.Reader)
s2, _ := new(Fr).Rand(rand.Reader)
s3, _ := new(Fr).Rand(rand.Reader)
sone := &Fr{1}
g.MulScalar(t0, zero, s1)
if !g.Equal(t0, zero) {
t.Fatal(" 0 ^ s == 0")
@ -163,7 +303,7 @@ func TestG2MultiplicativeProperties(t *testing.T) {
s3.Mul(s1, s2)
g.MulScalar(t1, a, s3)
if !g.Equal(t0, t1) {
t.Errorf(" (a ^ s1) ^ s2 == a ^ (s1 * s2)")
t.Fatal(" (a ^ s1) ^ s2 == a ^ (s1 * s2)")
}
g.MulScalar(t0, a, s1)
g.MulScalar(t1, a, s2)
@ -171,12 +311,71 @@ func TestG2MultiplicativeProperties(t *testing.T) {
s3.Add(s1, s2)
g.MulScalar(t1, a, s3)
if !g.Equal(t0, t1) {
t.Errorf(" (a ^ s1) + (a ^ s2) == a ^ (s1 + s2)")
t.Fatal(" (a ^ s1) + (a ^ s2) == a ^ (s1 + s2)")
}
}
}
func TestZKCryptoVectorsG2UncompressedValid(t *testing.T) {
data, err := ioutil.ReadFile("tests/g2_uncompressed_valid_test_vectors.dat")
if err != nil {
panic(err)
}
g := NewG2()
p1 := g.Zero()
for i := 0; i < 1000; i++ {
vector := data[i*192 : (i+1)*192]
p2, err := g.FromUncompressed(vector)
if err != nil {
t.Fatal("decoing fails", err, i)
}
uncompressed := g.ToUncompressed(p2)
if !bytes.Equal(vector, uncompressed) || !g.Equal(p1, p2) {
t.Fatal("serialization failed")
}
g.Add(p1, p1, &g2One)
}
}
func TestZKCryptoVectorsG2CompressedValid(t *testing.T) {
data, err := ioutil.ReadFile("tests/g2_compressed_valid_test_vectors.dat")
if err != nil {
panic(err)
}
g := NewG2()
p1 := g.Zero()
for i := 0; i < 1000; i++ {
vector := data[i*2*fpByteSize : (i+1)*2*fpByteSize]
p2, err := g.FromCompressed(vector)
if err != nil {
t.Fatal("decoing fails", err, i)
}
compressed := g.ToCompressed(p2)
if !bytes.Equal(vector, compressed) || !g.Equal(p1, p2) {
t.Fatal("serialization failed")
}
g.Add(p1, p1, &g2One)
}
}
func TestG2MultiExpExpected(t *testing.T) {
g := NewG2()
one := g.one()
var scalars [2]*Fr
var bases [2]*PointG2
scalars[0] = &Fr{2}
scalars[1] = &Fr{3}
bases[0], bases[1] = new(PointG2).Set(one), new(PointG2).Set(one)
expected, result := g.New(), g.New()
g.mulScalar(expected, one, &Fr{5})
_, _ = g.MultiExp(result, bases[:], scalars[:])
if !g.Equal(expected, result) {
t.Fatal("multi-exponentiation failed")
}
}
func TestG2MultiExpBigExpected(t *testing.T) {
g := NewG2()
one := g.one()
var scalars [2]*big.Int
@ -185,36 +384,76 @@ func TestG2MultiExpExpected(t *testing.T) {
scalars[1] = big.NewInt(3)
bases[0], bases[1] = new(PointG2).Set(one), new(PointG2).Set(one)
expected, result := g.New(), g.New()
g.MulScalar(expected, one, big.NewInt(5))
_, _ = g.MultiExp(result, bases[:], scalars[:])
g.mulScalarBig(expected, one, big.NewInt(5))
_, _ = g.MultiExpBig(result, bases[:], scalars[:])
if !g.Equal(expected, result) {
t.Fatal("bad multi-exponentiation")
t.Fatal("multi-exponentiation failed")
}
}
func TestG2MultiExpBatch(t *testing.T) {
func TestG2MultiExp(t *testing.T) {
g := NewG2()
one := g.one()
n := 1000
bases := make([]*PointG2, n)
scalars := make([]*big.Int, n)
// scalars: [s0,s1 ... s(n-1)]
// bases: [P0,P1,..P(n-1)] = [s(n-1)*G, s(n-2)*G ... s0*G]
for i, j := 0, n-1; i < n; i, j = i+1, j-1 {
scalars[j], _ = rand.Int(rand.Reader, big.NewInt(100000))
bases[i] = g.New()
g.MulScalar(bases[i], one, scalars[j])
for n := 1; n < 1024+1; n = n * 2 {
bases := make([]*PointG2, n)
scalars := make([]*Fr, n)
var err error
for i := 0; i < n; i++ {
scalars[i], err = new(Fr).Rand(rand.Reader)
if err != nil {
t.Fatal(err)
}
bases[i] = g.rand()
}
expected, tmp := g.New(), g.New()
for i := 0; i < n; i++ {
g.mulScalar(tmp, bases[i], scalars[i])
g.Add(expected, expected, tmp)
}
result := g.New()
_, _ = g.MultiExp(result, bases, scalars)
if !g.Equal(expected, result) {
t.Fatal("multi-exponentiation failed")
}
}
// expected: s(n-1)*P0 + s(n-2)*P1 + s0*P(n-1)
expected, tmp := g.New(), g.New()
for i := 0; i < n; i++ {
g.MulScalar(tmp, bases[i], scalars[i])
g.Add(expected, expected, tmp)
}
func TestG2MultiExpBig(t *testing.T) {
g := NewG2()
for n := 1; n < 1024+1; n = n * 2 {
bases := make([]*PointG2, n)
scalars := make([]*big.Int, n)
var err error
for i := 0; i < n; i++ {
scalars[i], err = rand.Int(rand.Reader, qBig)
if err != nil {
t.Fatal(err)
}
bases[i] = g.rand()
}
expected, tmp := g.New(), g.New()
for i := 0; i < n; i++ {
g.mulScalarBig(tmp, bases[i], scalars[i])
g.Add(expected, expected, tmp)
}
result := g.New()
_, _ = g.MultiExpBig(result, bases, scalars)
if !g.Equal(expected, result) {
t.Fatal("multi-exponentiation failed")
}
}
result := g.New()
_, _ = g.MultiExp(result, bases, scalars)
if !g.Equal(expected, result) {
t.Fatal("bad multi-exponentiation")
}
func TestG2ClearCofactor(t *testing.T) {
g := NewG2()
for i := 0; i < fuz; i++ {
p0 := g.rand()
if g.InCorrectSubgroup(p0) {
t.Fatal("rand point should be out of correct subgroup")
}
g.ClearCofactor(p0)
if !g.InCorrectSubgroup(p0) {
t.Fatal("cofactor clearing is failed")
}
}
}
@ -224,24 +463,60 @@ func TestG2MapToCurve(t *testing.T) {
expected []byte
}{
{
u: make([]byte, 96),
expected: common.FromHex("0a67d12118b5a35bb02d2e86b3ebfa7e23410db93de39fb06d7025fa95e96ffa428a7a27c3ae4dd4b40bd251ac658892" + "018320896ec9eef9d5e619848dc29ce266f413d02dd31d9b9d44ec0c79cd61f18b075ddba6d7bd20b7ff27a4b324bfce" + "04c69777a43f0bda07679d5805e63f18cf4e0e7c6112ac7f70266d199b4f76ae27c6269a3ceebdae30806e9a76aadf5c" + "0260e03644d1a2c321256b3246bad2b895cad13890cbe6f85df55106a0d334604fb143c7a042d878006271865bc35941"),
u: make([]byte, 2*fpByteSize),
expected: fromHex(-1, "0a67d12118b5a35bb02d2e86b3ebfa7e23410db93de39fb06d7025fa95e96ffa428a7a27c3ae4dd4b40bd251ac658892",
"018320896ec9eef9d5e619848dc29ce266f413d02dd31d9b9d44ec0c79cd61f18b075ddba6d7bd20b7ff27a4b324bfce",
"04c69777a43f0bda07679d5805e63f18cf4e0e7c6112ac7f70266d199b4f76ae27c6269a3ceebdae30806e9a76aadf5c",
"0260e03644d1a2c321256b3246bad2b895cad13890cbe6f85df55106a0d334604fb143c7a042d878006271865bc35941",
),
},
{
u: common.FromHex("025fbc07711ba267b7e70c82caa70a16fbb1d470ae24ceef307f5e2000751677820b7013ad4e25492dcf30052d3e5eca" + "0e775d7827adf385b83e20e4445bd3fab21d7b4498426daf3c1d608b9d41e9edb5eda0df022e753b8bb4bc3bb7db4914"),
expected: common.FromHex("0d4333b77becbf9f9dfa3ca928002233d1ecc854b1447e5a71f751c9042d000f42db91c1d6649a5e0ad22bd7bf7398b8" + "027e4bfada0b47f9f07e04aec463c7371e68f2fd0c738cd517932ea3801a35acf09db018deda57387b0f270f7a219e4d" + "0cc76dc777ea0d447e02a41004f37a0a7b1fafb6746884e8d9fc276716ccf47e4e0899548a2ec71c2bdf1a2a50e876db" + "053674cba9ef516ddc218fedb37324e6c47de27f88ab7ef123b006127d738293c0277187f7e2f80a299a24d84ed03da7"),
u: fromHex(-1,
"025fbc07711ba267b7e70c82caa70a16fbb1d470ae24ceef307f5e2000751677820b7013ad4e25492dcf30052d3e5eca",
"0e775d7827adf385b83e20e4445bd3fab21d7b4498426daf3c1d608b9d41e9edb5eda0df022e753b8bb4bc3bb7db4914",
),
expected: fromHex(-1,
"0d4333b77becbf9f9dfa3ca928002233d1ecc854b1447e5a71f751c9042d000f42db91c1d6649a5e0ad22bd7bf7398b8",
"027e4bfada0b47f9f07e04aec463c7371e68f2fd0c738cd517932ea3801a35acf09db018deda57387b0f270f7a219e4d",
"0cc76dc777ea0d447e02a41004f37a0a7b1fafb6746884e8d9fc276716ccf47e4e0899548a2ec71c2bdf1a2a50e876db",
"053674cba9ef516ddc218fedb37324e6c47de27f88ab7ef123b006127d738293c0277187f7e2f80a299a24d84ed03da7",
),
},
{
u: common.FromHex("1870a7dbfd2a1deb74015a3546b20f598041bf5d5202997956a94a368d30d3f70f18cdaa1d33ce970a4e16af961cbdcb" + "045ab31ce4b5a8ba7c4b2851b64f063a66cd1223d3c85005b78e1beee65e33c90ceef0244e45fc45a5e1d6eab6644fdb"),
expected: common.FromHex("18f0f87b40af67c056915dbaf48534c592524e82c1c2b50c3734d02c0172c80df780a60b5683759298a3303c5d942778" + "09349f1cb5b2e55489dcd45a38545343451cc30a1681c57acd4fb0a6db125f8352c09f4a67eb7d1d8242cb7d3405f97b" + "10a2ba341bc689ab947b7941ce6ef39be17acaab067bd32bd652b471ab0792c53a2bd03bdac47f96aaafe96e441f63c0" + "02f2d9deb2c7742512f5b8230bf0fd83ea42279d7d39779543c1a43b61c885982b611f6a7a24b514995e8a098496b811"),
u: fromHex(-1,
"1870a7dbfd2a1deb74015a3546b20f598041bf5d5202997956a94a368d30d3f70f18cdaa1d33ce970a4e16af961cbdcb",
"045ab31ce4b5a8ba7c4b2851b64f063a66cd1223d3c85005b78e1beee65e33c90ceef0244e45fc45a5e1d6eab6644fdb",
),
expected: fromHex(-1,
"18f0f87b40af67c056915dbaf48534c592524e82c1c2b50c3734d02c0172c80df780a60b5683759298a3303c5d942778",
"09349f1cb5b2e55489dcd45a38545343451cc30a1681c57acd4fb0a6db125f8352c09f4a67eb7d1d8242cb7d3405f97b",
"10a2ba341bc689ab947b7941ce6ef39be17acaab067bd32bd652b471ab0792c53a2bd03bdac47f96aaafe96e441f63c0",
"02f2d9deb2c7742512f5b8230bf0fd83ea42279d7d39779543c1a43b61c885982b611f6a7a24b514995e8a098496b811",
),
},
{
u: common.FromHex("088fe329b054db8a6474f21a7fbfdf17b4c18044db299d9007af582c3d5f17d00e56d99921d4b5640fce44b05219b5de" + "0b6e6135a4cd31ba980ddbd115ac48abef7ec60e226f264d7befe002c165f3a496f36f76dd524efd75d17422558d10b4"),
expected: common.FromHex("19808ec5930a53c7cf5912ccce1cc33f1b3dcff24a53ce1cc4cba41fd6996dbed4843ccdd2eaf6a0cd801e562718d163" + "149fe43777d34f0d25430dea463889bd9393bdfb4932946db23671727081c629ebb98a89604f3433fba1c67d356a4af7" + "04783e391c30c83f805ca271e353582fdf19d159f6a4c39b73acbb637a9b8ac820cfbe2738d683368a7c07ad020e3e33" + "04c0d6793a766233b2982087b5f4a254f261003ccb3262ea7c50903eecef3e871d1502c293f9e063d7d293f6384f4551"),
u: fromHex(-1,
"088fe329b054db8a6474f21a7fbfdf17b4c18044db299d9007af582c3d5f17d00e56d99921d4b5640fce44b05219b5de",
"0b6e6135a4cd31ba980ddbd115ac48abef7ec60e226f264d7befe002c165f3a496f36f76dd524efd75d17422558d10b4",
),
expected: fromHex(-1,
"19808ec5930a53c7cf5912ccce1cc33f1b3dcff24a53ce1cc4cba41fd6996dbed4843ccdd2eaf6a0cd801e562718d163",
"149fe43777d34f0d25430dea463889bd9393bdfb4932946db23671727081c629ebb98a89604f3433fba1c67d356a4af7",
"04783e391c30c83f805ca271e353582fdf19d159f6a4c39b73acbb637a9b8ac820cfbe2738d683368a7c07ad020e3e33",
"04c0d6793a766233b2982087b5f4a254f261003ccb3262ea7c50903eecef3e871d1502c293f9e063d7d293f6384f4551",
),
},
{
u: common.FromHex("03df16a66a05e4c1188c234788f43896e0565bfb64ac49b9639e6b284cc47dad73c47bb4ea7e677db8d496beb907fbb6" + "0f45b50647d67485295aa9eb2d91a877b44813677c67c8d35b2173ff3ba95f7bd0806f9ca8a1436b8b9d14ee81da4d7e"),
expected: common.FromHex("0b8e0094c886487870372eb6264613a6a087c7eb9804fab789be4e47a57b29eb19b1983a51165a1b5eb025865e9fc63a" + "0804152cbf8474669ad7d1796ab92d7ca21f32d8bed70898a748ed4e4e0ec557069003732fc86866d938538a2ae95552" + "14c80f068ece15a3936bb00c3c883966f75b4e8d9ddde809c11f781ab92d23a2d1d103ad48f6f3bb158bf3e3a4063449" + "09e5c8242dd7281ad32c03fe4af3f19167770016255fb25ad9b67ec51d62fade31a1af101e8f6172ec2ee8857662be3a"),
u: fromHex(-1,
"03df16a66a05e4c1188c234788f43896e0565bfb64ac49b9639e6b284cc47dad73c47bb4ea7e677db8d496beb907fbb6",
"0f45b50647d67485295aa9eb2d91a877b44813677c67c8d35b2173ff3ba95f7bd0806f9ca8a1436b8b9d14ee81da4d7e",
),
expected: fromHex(-1,
"0b8e0094c886487870372eb6264613a6a087c7eb9804fab789be4e47a57b29eb19b1983a51165a1b5eb025865e9fc63a",
"0804152cbf8474669ad7d1796ab92d7ca21f32d8bed70898a748ed4e4e0ec557069003732fc86866d938538a2ae95552",
"14c80f068ece15a3936bb00c3c883966f75b4e8d9ddde809c11f781ab92d23a2d1d103ad48f6f3bb158bf3e3a4063449",
"09e5c8242dd7281ad32c03fe4af3f19167770016255fb25ad9b67ec51d62fade31a1af101e8f6172ec2ee8857662be3a",
),
},
} {
g := NewG2()
@ -255,6 +530,114 @@ func TestG2MapToCurve(t *testing.T) {
}
}
func TestG2EncodeToCurve(t *testing.T) {
domain := []byte("BLS12381G2_XMD:SHA-256_SSWU_NU_TESTGEN")
for i, v := range []struct {
msg []byte
expected []byte
}{
{
msg: []byte(""),
expected: fromHex(-1,
"0d4333b77becbf9f9dfa3ca928002233d1ecc854b1447e5a71f751c9042d000f42db91c1d6649a5e0ad22bd7bf7398b8",
"027e4bfada0b47f9f07e04aec463c7371e68f2fd0c738cd517932ea3801a35acf09db018deda57387b0f270f7a219e4d",
"0cc76dc777ea0d447e02a41004f37a0a7b1fafb6746884e8d9fc276716ccf47e4e0899548a2ec71c2bdf1a2a50e876db",
"053674cba9ef516ddc218fedb37324e6c47de27f88ab7ef123b006127d738293c0277187f7e2f80a299a24d84ed03da7",
),
},
{
msg: []byte("abc"),
expected: fromHex(-1,
"18f0f87b40af67c056915dbaf48534c592524e82c1c2b50c3734d02c0172c80df780a60b5683759298a3303c5d942778",
"09349f1cb5b2e55489dcd45a38545343451cc30a1681c57acd4fb0a6db125f8352c09f4a67eb7d1d8242cb7d3405f97b",
"10a2ba341bc689ab947b7941ce6ef39be17acaab067bd32bd652b471ab0792c53a2bd03bdac47f96aaafe96e441f63c0",
"02f2d9deb2c7742512f5b8230bf0fd83ea42279d7d39779543c1a43b61c885982b611f6a7a24b514995e8a098496b811",
),
},
{
msg: []byte("abcdef0123456789"),
expected: fromHex(-1,
"19808ec5930a53c7cf5912ccce1cc33f1b3dcff24a53ce1cc4cba41fd6996dbed4843ccdd2eaf6a0cd801e562718d163",
"149fe43777d34f0d25430dea463889bd9393bdfb4932946db23671727081c629ebb98a89604f3433fba1c67d356a4af7",
"04783e391c30c83f805ca271e353582fdf19d159f6a4c39b73acbb637a9b8ac820cfbe2738d683368a7c07ad020e3e33",
"04c0d6793a766233b2982087b5f4a254f261003ccb3262ea7c50903eecef3e871d1502c293f9e063d7d293f6384f4551",
),
},
{
msg: []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"),
expected: fromHex(-1,
"0b8e0094c886487870372eb6264613a6a087c7eb9804fab789be4e47a57b29eb19b1983a51165a1b5eb025865e9fc63a",
"0804152cbf8474669ad7d1796ab92d7ca21f32d8bed70898a748ed4e4e0ec557069003732fc86866d938538a2ae95552",
"14c80f068ece15a3936bb00c3c883966f75b4e8d9ddde809c11f781ab92d23a2d1d103ad48f6f3bb158bf3e3a4063449",
"09e5c8242dd7281ad32c03fe4af3f19167770016255fb25ad9b67ec51d62fade31a1af101e8f6172ec2ee8857662be3a",
),
},
} {
g := NewG2()
p0, err := g.EncodeToCurve(v.msg, domain)
if err != nil {
t.Fatal("encode to point fails", i, err)
}
if !bytes.Equal(g.ToBytes(p0), v.expected) {
t.Fatal("encode to point fails x", i)
}
}
}
func TestG2HashToCurve(t *testing.T) {
domain := []byte("BLS12381G2_XMD:SHA-256_SSWU_RO_TESTGEN")
for i, v := range []struct {
msg []byte
expected []byte
}{
{
msg: []byte(""),
expected: fromHex(-1,
"0fbdae26f9f9586a46d4b0b70390d09064ef2afe5c99348438a3c7d9756471e015cb534204c1b6824617a85024c772dc",
"0a650bd36ae7455cb3fe5d8bb1310594551456f5c6593aec9ee0c03d2f6cb693bd2c5e99d4e23cbaec767609314f51d3",
"02e5cf8f9b7348428cc9e66b9a9b36fe45ba0b0a146290c3a68d92895b1af0e1f2d9f889fb412670ae8478d8abd4c5aa",
"0d8d49e7737d8f9fc5cef7c4b8817633103faf2613016cb86a1f3fc29968fe2413e232d9208d2d74a89bf7a48ac36f83",
),
},
{
msg: []byte("abc"),
expected: fromHex(-1,
"03578447618463deb106b60e609c6f7cc446dc6035f84a72801ba17c94cd800583b493b948eff0033f09086fdd7f6175",
"1953ce6d4267939c7360756d9cca8eb34aac4633ef35369a7dc249445069888e7d1b3f9d2e75fbd468fbcbba7110ea02",
"0184d26779ae9d4670aca9b267dbd4d3b30443ad05b8546d36a195686e1ccc3a59194aea05ed5bce7c3144a29ec047c4",
"0882ab045b8fe4d7d557ebb59a63a35ac9f3d312581b509af0f8eaa2960cbc5e1e36bb969b6e22980b5cbdd0787fcf4e",
),
},
{
msg: []byte("abcdef0123456789"),
expected: fromHex(-1,
"195fad48982e186ce3c5c82133aefc9b26d55979b6f530992a8849d4263ec5d57f7a181553c8799bcc83da44847bdc8d",
"17b461fc3b96a30c2408958cbfa5f5927b6063a8ad199d5ebf2d7cdeffa9c20c85487204804fab53f950b2f87db365aa",
"005cdf3d984e3391e7e969276fb4bc02323c5924a4449af167030d855acc2600cf3d4fab025432c6d868c79571a95bef",
"174a3473a3af2d0302b9065e895ca4adba4ece6ce0b41148ba597001abb152f852dd9a96fb45c9de0a43d944746f833e",
),
},
{
msg: []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"),
expected: fromHex(-1,
"123b6bd9feeba26dd4ad00f8bfda2718c9700dc093ea5287d7711844644eb981848316d3f3f57d5d3a652c6cdc816aca",
"0a162306f3b0f2bb326f0c4fb0e1fea020019c3af796dcd1d7264f50ddae94cacf3cade74603834d44b9ab3d5d0a6c98",
"05483f3b96d9252dd4fc0868344dfaf3c9d145e3387db23fa8e449304fab6a7b6ec9c15f05c0a1ea66ff0efcc03e001a",
"15c1d4f1a685bb63ee67ca1fd96155e3d091e852a684b78d085fd34f6091e5249ddddbdcf2e7ec82ce6c04c63647eeb7",
),
},
} {
g := NewG2()
p0, err := g.HashToCurve(v.msg, domain)
if err != nil {
t.Fatal("encode to point fails", i, err)
}
if !bytes.Equal(g.ToBytes(p0), v.expected) {
t.Fatal("encode to point fails x", i)
}
}
}
func BenchmarkG2Add(t *testing.B) {
g2 := NewG2()
a, b, c := g2.rand(), g2.rand(), PointG2{}
@ -264,18 +647,112 @@ func BenchmarkG2Add(t *testing.B) {
}
}
func BenchmarkG2Mul(t *testing.B) {
worstCaseScalar, _ := new(big.Int).SetString("ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", 16)
func BenchmarkG2MulWNAF(t *testing.B) {
g := NewG2()
p := new(PointG2).Set(&g2One)
s, _ := new(Fr).Rand(rand.Reader)
sBig := s.ToBig()
res := new(PointG2)
t.Run("Naive", func(t *testing.B) {
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.mulScalar(res, p, s)
}
})
for i := 1; i < 8; i++ {
wnafMulWindowG2 = uint(i)
t.Run(fmt.Sprintf("Fr, window: %d", i), func(t *testing.B) {
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.wnafMulFr(res, p, s)
}
})
t.Run(fmt.Sprintf("Big, window: %d", i), func(t *testing.B) {
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.wnafMulBig(res, p, sBig)
}
})
}
}
func BenchmarkG2MulGLV(t *testing.B) {
g := NewG2()
p := new(PointG2).Set(&g2One)
s, _ := new(Fr).Rand(rand.Reader)
sBig := s.ToBig()
res := new(PointG2)
t.Run("Naive", func(t *testing.B) {
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.mulScalar(res, p, s)
}
})
for i := 1; i < 8; i++ {
glvMulWindowG2 = uint(i)
t.Run(fmt.Sprintf("Fr, window: %d", i), func(t *testing.B) {
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.glvMulFr(res, p, s)
}
})
t.Run(fmt.Sprintf("Big, window: %d", i), func(t *testing.B) {
t.ResetTimer()
for i := 0; i < t.N; i++ {
g.glvMulBig(res, p, sBig)
}
})
}
}
func BenchmarkG2MultiExp(t *testing.B) {
g := NewG2()
v := func(n int) ([]*PointG2, []*Fr) {
bases := make([]*PointG2, n)
scalars := make([]*Fr, n)
var err error
for i := 0; i < n; i++ {
scalars[i], err = new(Fr).Rand(rand.Reader)
if err != nil {
t.Fatal(err)
}
bases[i] = g.randAffine()
}
return bases, scalars
}
for _, i := range []int{2, 10, 100, 1000} {
t.Run(fmt.Sprint(i), func(t *testing.B) {
bases, scalars := v(i)
result := g.New()
t.ResetTimer()
for i := 0; i < t.N; i++ {
_, _ = g.MultiExp(result, bases, scalars)
}
})
}
}
func BenchmarkG2ClearCofactor(t *testing.B) {
g2 := NewG2()
a, e, c := g2.rand(), worstCaseScalar, PointG2{}
a := g2.rand()
t.ResetTimer()
for i := 0; i < t.N; i++ {
g2.MulScalar(&c, a, e)
g2.ClearCofactor(a)
}
}
func BenchmarkG2SubgroupCheck(t *testing.B) {
g2 := NewG2()
a := g2.rand()
t.ResetTimer()
for i := 0; i < t.N; i++ {
g2.InCorrectSubgroup(a)
}
}
func BenchmarkG2SWUMap(t *testing.B) {
a := make([]byte, 96)
a := fromHex(2*fpByteSize, "0x1234")
g2 := NewG2()
t.ResetTimer()
for i := 0; i < t.N; i++ {

200
crypto/bls12381/glv.go Normal file
View file

@ -0,0 +1,200 @@
package bls12381
import (
"math/big"
)
// Guide to Pairing Based Cryptography
// 6.3.2. Decompositions for the k = 12 BLS Family
// glvQ1 = x^2 * R / q
var glvQ1 = &Fr{0x63f6e522f6cfee30, 0x7c6becf1e01faadd, 0x1, 0}
var glvQ1Big = bigFromHex("0x017c6becf1e01faadd63f6e522f6cfee30")
// glvQ2 = R / q = 2
var glvQ2 = &Fr{0x02, 0, 0, 0}
var glvQ2Big = bigFromHex("0x02")
// glvB1 = x^2 - 1 = 0xac45a4010001a40200000000ffffffff
var glvB1 = &Fr{0x00000000ffffffff, 0xac45a4010001a402, 0, 0}
var glvB1Big = bigFromHex("0xac45a4010001a40200000000ffffffff")
// glvB2 = x^2 = 0xac45a4010001a4020000000100000000
var glvB2 = &Fr{0x0000000100000000, 0xac45a4010001a402, 0, 0}
var glvB2Big = bigFromHex("0xac45a4010001a4020000000100000000")
// glvLambdaA = x^2 - 1
var glvLambda = &Fr{0x00000000ffffffff, 0xac45a4010001a402, 0, 0}
var glvLambdaBig = bigFromHex("0xac45a4010001a40200000000ffffffff")
// halfR = 2**256 / 2
var halfR = &wideFr{0, 0, 0, 0x8000000000000000, 0, 0, 0}
var halfRBig = bigFromHex("0x8000000000000000000000000000000000000000000000000000000000000000")
// r128 = 2**128 - 1
var r128 = &Fr{0xffffffffffffffff, 0xffffffffffffffff, 0, 0}
// glvPhi1 ^ 3 = 1
var glvPhi1 = &fe{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741}
// glvPhi2 ^ 3 = 1
var glvPhi2 = &fe{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160}
var glvMulWindowG1 uint = 4
var glvMulWindowG2 uint = 4
type glvVector interface {
wnaf(w uint) (nafNumber, nafNumber)
}
type glvVectorFr struct {
k1 *Fr
k2 *Fr
neg1 bool
neg2 bool
}
type glvVectorBig struct {
k1 *big.Int
k2 *big.Int
}
func (v *glvVectorFr) wnaf(w uint) (nafNumber, nafNumber) {
naf1 := v.k1.toWNAF(w)
naf2 := v.k2.toWNAF(w)
if v.neg1 {
naf1.neg()
}
if !v.neg2 {
naf2.neg()
}
return naf1, naf2
}
func (v *glvVectorBig) wnaf(w uint) (nafNumber, nafNumber) {
naf1, naf2 := bigToWNAF(v.k1, w), bigToWNAF(v.k2, w)
zero := new(big.Int)
if v.k1.Cmp(zero) < 0 {
naf1.neg()
}
if v.k2.Cmp(zero) > 0 {
naf2.neg()
}
return naf1, naf2
}
func (v *glvVectorFr) new(m *Fr) *glvVectorFr {
// Guide to Pairing Based Cryptography
// 6.3.2. Decompositions for the k = 12 BLS Family
// alpha1 = round(x^2 * m / r)
alpha1 := alpha1(m)
// alpha2 = round(m / r)
alpha2 := alpha2(m)
z1, z2 := new(Fr), new(Fr)
// z1 = (x^2 - 1) * round(x^2 * m / r)
z1.Mul(alpha1, glvB1)
// z2 = x^2 * round(m / r)
z2.Mul(alpha2, glvB2)
k1, k2 := new(Fr), new(Fr)
// k1 = m - z1 - alpha2
k1.Sub(m, z1)
k1.Sub(k1, alpha2)
// k2 = z2 - alpha1
k2.Sub(z2, alpha1)
if k1.Cmp(r128) == 1 {
k1.Neg(k1)
v.neg1 = true
}
v.k1 = new(Fr).Set(k1)
if k2.Cmp(r128) == 1 {
k2.Neg(k2)
v.neg2 = true
}
v.k2 = new(Fr).Set(k2)
return v
}
func (v *glvVectorBig) new(m *big.Int) *glvVectorBig {
// Guide to Pairing Based Cryptography
// 6.3.2. Decompositions for the k = 12 BLS Family
// alpha1 = round(x^2 * m / r)
alpha1 := new(big.Int).Mul(m, glvQ1Big)
alpha1.Add(alpha1, halfRBig)
alpha1.Rsh(alpha1, fourWordBitSize)
// alpha2 = round(m / r)
alpha2 := new(big.Int).Mul(m, glvQ2Big)
alpha2.Add(alpha2, halfRBig)
alpha2.Rsh(alpha2, fourWordBitSize)
z1, z2 := new(big.Int), new(big.Int)
// z1 = (x^2 - 1) * round(x^2 * m / r)
z1.Mul(alpha1, glvB1Big).Mod(z1, qBig)
// z2 = x^2 * round(m / r)
z2.Mul(alpha2, glvB2Big).Mod(z2, qBig)
k1, k2 := new(big.Int), new(big.Int)
// k1 = m - z1 - alpha2
k1.Sub(m, z1)
k1.Sub(k1, alpha2)
// k2 = z2 - alpha1
k2.Sub(z2, alpha1)
v.k1 = new(big.Int).Set(k1)
v.k2 = new(big.Int).Set(k2)
return v
}
// round(x^2 * m / q)
func alpha1(m *Fr) *Fr {
a := new(wideFr)
a.mul(m, glvQ1)
return a.round()
}
// round(m / q)
func alpha2(m *Fr) *Fr {
a := new(wideFr)
a.mul(m, glvQ2)
return a.round()
}
func phi(a, b *fe) {
mul(a, b, glvPhi1)
}
func (e *fp2) phi(a, b *fe2) {
mul(&a[0], &b[0], glvPhi2)
mul(&a[1], &b[1], glvPhi2)
}
func (g *G1) glvEndomorphism(r, p *PointG1) {
t := g.Affine(p)
if g.IsZero(p) {
r.Zero()
return
}
r[1].set(&t[1])
phi(&r[0], &t[0])
r[2].one()
}
func (g *G2) glvEndomorphism(r, p *PointG2) {
t := g.Affine(p)
if g.IsZero(p) {
r.Zero()
return
}
r[1].set(&t[1])
g.f.phi(&r[0], &t[0])
r[2].one()
}

134
crypto/bls12381/glv_test.go Normal file
View file

@ -0,0 +1,134 @@
package bls12381
import (
"crypto/rand"
"math/big"
"testing"
)
func TestGLVConstruction(t *testing.T) {
t.Run("Parameters", func(t *testing.T) {
t0, t1 := new(Fr), new(Fr)
one := new(Fr).setUint64(1)
t0.Square(glvLambda)
t0.Add(t0, glvLambda)
t1.Sub(&q, one)
if !t0.Equal(t1) {
t.Fatal("lambda1^2 + lambda1 + 1 = 0")
}
c0 := new(fe)
square(c0, glvPhi1)
mul(c0, c0, glvPhi1)
if !c0.isOne() {
t.Fatal("phi1^3 = 1")
}
square(c0, glvPhi2)
mul(c0, c0, glvPhi2)
if !c0.isOne() {
t.Fatal("phi2^3 = 1")
}
})
t.Run("Endomorphism G1", func(t *testing.T) {
g := NewG1()
{
p0, p1 := g.randAffine(), g.New()
g.MulScalar(p1, p0, glvLambda)
g.Affine(p1)
r := g.New()
g.glvEndomorphism(r, p0)
if !g.Equal(r, p1) {
t.Fatal("f(x, y) = (phi * x, y)")
}
}
})
t.Run("Endomorphism G2", func(t *testing.T) {
g := NewG2()
{
p0, p1 := g.randAffine(), g.New()
g.MulScalar(p1, p0, glvLambda)
g.Affine(p1)
r := g.New()
g.glvEndomorphism(r, p0)
if !g.Equal(r, p1) {
t.Fatal("f(x, y) = (phi * x, y)")
}
}
})
t.Run("Scalar Decomposition", func(t *testing.T) {
for i := 0; i < fuz; i++ {
m, err := new(Fr).Rand(rand.Reader)
if err != nil {
t.Fatal(err)
}
mBig := m.ToBig()
var vFr *glvVectorFr
var vBig *glvVectorBig
{
vFr = new(glvVectorFr).new(m)
v := vFr
if v.k1.Cmp(r128) >= 0 {
t.Fatal("bad scalar component, k1")
}
if v.k2.Cmp(r128) >= 0 {
t.Fatal("bad scalar component, k2")
}
k := new(Fr)
if v.neg1 && v.neg2 {
k.Mul(glvLambda, v.k2)
k.Sub(k, v.k1)
} else if v.neg1 {
k.Mul(glvLambda, v.k2)
k.Add(k, v.k1)
k.Neg(k)
} else if v.neg2 {
k.Mul(glvLambda, v.k2)
k.Add(v.k1, k)
} else {
k.Mul(glvLambda, v.k2)
k.Sub(v.k1, k)
}
if !k.Equal(m) {
t.Fatal("scalar decomposing failed")
}
}
r128Big := r128.ToBig()
{
vBig = new(glvVectorBig).new(mBig)
if new(big.Int).Abs(vBig.k1).Cmp(r128Big) >= 0 {
t.Fatal("bad scalar component, big k1")
}
if new(big.Int).Abs(vBig.k2).Cmp(r128Big) >= 0 {
t.Fatal("bad scalar component, big k2")
}
k := new(big.Int)
k.Mul(glvLambdaBig, vBig.k2)
k.Sub(vBig.k1, k).Mod(k, qBig)
if k.Cmp(mBig) != 0 {
t.Fatal("scalar decomposing with big.Int failed", i)
}
}
zeroBig := new(big.Int)
k1Abs, k2Abs := new(big.Int).Abs(vBig.k1), new(big.Int).Abs(vBig.k2)
if vFr.neg1 != (vBig.k1.Cmp(zeroBig) == -1) {
t.Fatal("cross: scalar decomposing with failed neg1")
}
if vFr.neg2 != (vBig.k2.Cmp(zeroBig) == -1) {
t.Fatal("cross: scalar decomposing with failed neg2")
}
if k1Abs.Cmp(vFr.k1.ToBig()) != 0 {
t.Fatal("cross: scalar decomposing with failed k1", i)
}
if k2Abs.Cmp(vFr.k2.ToBig()) != 0 {
t.Fatal("cross: scalar decomposing with failed k2", i)
}
}
})
}

28
crypto/bls12381/gt.go
View file

@ -1,19 +1,3 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
import (
@ -29,6 +13,7 @@ type GT struct {
fp12 *fp12
}
// Set copies given value into the destination
func (e *E) Set(e2 *E) *E {
return e.set(e2)
}
@ -57,7 +42,7 @@ func NewGT() *GT {
// Q returns group order in big.Int.
func (g *GT) Q() *big.Int {
return new(big.Int).Set(q)
return new(big.Int).Set(qBig)
}
// FromBytes expects 576 byte input and returns target group element
@ -81,7 +66,7 @@ func (g *GT) ToBytes(e *E) []byte {
// IsValid checks whether given target group element is in correct subgroup.
func (g *GT) IsValid(e *E) bool {
r := g.New()
g.fp12.exp(r, e, q)
g.fp12.exp(r, e, qBig)
return r.isOne()
}
@ -92,12 +77,12 @@ func (g *GT) New() *E {
// Add adds two field element `a` and `b` and assigns the result to the element in first argument.
func (g *GT) Add(c, a, b *E) {
g.fp12.add(c, a, b)
fp12Add(c, a, b)
}
// Sub subtracts two field element `a` and `b`, and assigns the result to the element in first argument.
func (g *GT) Sub(c, a, b *E) {
g.fp12.sub(c, a, b)
fp12Sub(c, a, b)
}
// Mul multiplies two field element `a` and `b` and assigns the result to the element in first argument.
@ -107,7 +92,8 @@ func (g *GT) Mul(c, a, b *E) {
// Square squares an element `a` and assigns the result to the element in first argument.
func (g *GT) Square(c, a *E) {
g.fp12.cyclotomicSquare(c, a)
c.set(a)
g.fp12.cyclotomicSquare(c)
}
// Exp exponents an element `a` by a scalar `s` and assigns the result to the element in first argument.

70
crypto/bls12381/hash_to_field.go Normal file
View file

@ -0,0 +1,70 @@
package bls12381
import (
"crypto/sha256"
"errors"
)
func hashToFpXMDSHA256(msg []byte, domain []byte, count int) ([]*fe, error) {
randBytes, err := expandMsgSHA256XMD(msg, domain, count*64)
if err != nil {
return nil, err
}
els := make([]*fe, count)
for i := 0; i < count; i++ {
els[i], err = from64Bytes(randBytes[i*64 : (i+1)*64])
if err != nil {
return nil, err
}
}
return els, nil
}
func expandMsgSHA256XMD(msg []byte, domain []byte, outLen int) ([]byte, error) {
h := sha256.New()
domainLen := uint8(len(domain))
if domainLen > 255 {
return nil, errors.New("invalid domain length")
}
// DST_prime = DST || I2OSP(len(DST), 1)
// b_0 = H(Z_pad || msg || l_i_b_str || I2OSP(0, 1) || DST_prime)
_, _ = h.Write(make([]byte, h.BlockSize()))
_, _ = h.Write(msg)
_, _ = h.Write([]byte{uint8(outLen >> 8), uint8(outLen)})
_, _ = h.Write([]byte{0})
_, _ = h.Write(domain)
_, _ = h.Write([]byte{domainLen})
b0 := h.Sum(nil)
// b_1 = H(b_0 || I2OSP(1, 1) || DST_prime)
h.Reset()
_, _ = h.Write(b0)
_, _ = h.Write([]byte{1})
_, _ = h.Write(domain)
_, _ = h.Write([]byte{domainLen})
b1 := h.Sum(nil)
// b_i = H(strxor(b_0, b_(i - 1)) || I2OSP(i, 1) || DST_prime)
ell := (outLen + h.Size() - 1) / h.Size()
bi := b1
out := make([]byte, outLen)
for i := 1; i < ell; i++ {
h.Reset()
// b_i = H(strxor(b_0, b_(i - 1)) || I2OSP(i, 1) || DST_prime)
tmp := make([]byte, h.Size())
for j := 0; j < h.Size(); j++ {
tmp[j] = b0[j] ^ bi[j]
}
_, _ = h.Write(tmp)
_, _ = h.Write([]byte{1 + uint8(i)})
_, _ = h.Write(domain)
_, _ = h.Write([]byte{domainLen})
// b_1 || ... || b_(ell - 1)
copy(out[(i-1)*h.Size():i*h.Size()], bi[:])
bi = h.Sum(nil)
}
// b_ell
copy(out[(ell-1)*h.Size():], bi[:])
return out[:outLen], nil
}

164
crypto/bls12381/isogeny.go
View file

@ -1,82 +1,70 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
// isogenyMapG1 applies 11-isogeny map for BLS12-381 G1 defined at draft-irtf-cfrg-hash-to-curve-06.
func isogenyMapG1(x, y *fe) {
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#appendix-C.2
params := isogenyConstantsG1
degree := 15
xNum, xDen, yNum, yDen := new(fe), new(fe), new(fe), new(fe)
xNum.set(params[0][degree])
xDen.set(params[1][degree])
yNum.set(params[2][degree])
yDen.set(params[3][degree])
for i := degree - 1; i >= 0; i-- {
xNum.set(isogenyConstansG1[0][15])
xDen.set(isogenyConstansG1[1][15])
yNum.set(isogenyConstansG1[2][15])
yDen.set(isogenyConstansG1[3][15])
for i := 14; i > -1; i-- {
mul(xNum, xNum, x)
mul(xDen, xDen, x)
mul(yNum, yNum, x)
mul(yDen, yDen, x)
add(xNum, xNum, params[0][i])
add(xDen, xDen, params[1][i])
add(yNum, yNum, params[2][i])
add(yDen, yDen, params[3][i])
addAssign(xNum, isogenyConstansG1[0][i])
addAssign(xDen, isogenyConstansG1[1][i])
addAssign(yNum, isogenyConstansG1[2][i])
addAssign(yDen, isogenyConstansG1[3][i])
}
inverse(xDen, xDen)
inverse(yDen, yDen)
mul(xNum, xNum, xDen)
mul(x, xNum, xDen)
mul(yNum, yNum, yDen)
mul(yNum, yNum, y)
x.set(xNum)
y.set(yNum)
mul(y, y, yNum)
}
// isogenyMapG2 applies 11-isogeny map for BLS12-381 G1 defined at draft-irtf-cfrg-hash-to-curve-06.
// isogenyMapG2 applies 3-isogeny map for BLS12-381 G2 defined at draft-irtf-cfrg-hash-to-curve-06.
func isogenyMapG2(e *fp2, x, y *fe2) {
if e == nil {
e = newFp2()
}
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#appendix-C.2
params := isogenyConstantsG2
degree := 3
xNum := new(fe2).set(params[0][degree])
xDen := new(fe2).set(params[1][degree])
yNum := new(fe2).set(params[2][degree])
yDen := new(fe2).set(params[3][degree])
for i := degree - 1; i >= 0; i-- {
e.mul(xNum, xNum, x)
e.mul(xDen, xDen, x)
e.mul(yNum, yNum, x)
e.mul(yDen, yDen, x)
e.add(xNum, xNum, params[0][i])
e.add(xDen, xDen, params[1][i])
e.add(yNum, yNum, params[2][i])
e.add(yDen, yDen, params[3][i])
}
xNum := new(fe2).set(isogenyConstantsG2[0][3])
xDen := new(fe2).set(x)
yNum := new(fe2).set(isogenyConstantsG2[2][3])
yDen := new(fe2).set(x)
e.mulAssign(xNum, x)
e.mulAssign(yNum, x)
fp2AddAssign(xNum, isogenyConstantsG2[0][2])
fp2AddAssign(yNum, isogenyConstantsG2[2][2])
fp2AddAssign(yDen, isogenyConstantsG2[3][2])
e.mulAssign(xNum, x)
e.mulAssign(yNum, x)
e.mulAssign(yDen, x)
fp2AddAssign(xNum, isogenyConstantsG2[0][1])
fp2AddAssign(xDen, isogenyConstantsG2[1][1])
fp2AddAssign(yNum, isogenyConstantsG2[2][1])
fp2AddAssign(yDen, isogenyConstantsG2[3][1])
e.mulAssign(xNum, x)
e.mulAssign(xDen, x)
e.mulAssign(yNum, x)
e.mulAssign(yDen, x)
fp2AddAssign(xNum, isogenyConstantsG2[0][0])
fp2AddAssign(xDen, isogenyConstantsG2[1][0])
fp2AddAssign(yNum, isogenyConstantsG2[2][0])
fp2AddAssign(yDen, isogenyConstantsG2[3][0])
e.inverse(xDen, xDen)
e.inverse(yDen, yDen)
e.mul(xNum, xNum, xDen)
e.mul(yNum, yNum, yDen)
e.mul(yNum, yNum, y)
x.set(xNum)
y.set(yNum)
e.mul(x, xNum, xDen)
e.mulAssign(yNum, yDen)
e.mulAssign(y, yNum)
}
var isogenyConstantsG1 = [4][16]*fe{
var isogenyConstansG1 = [4][16]*fe{
{
{0x4d18b6f3af00131c, 0x19fa219793fee28c, 0x3f2885f1467f19ae, 0x23dcea34f2ffb304, 0xd15b58d2ffc00054, 0x0913be200a20bef4},
{0x898985385cdbbd8b, 0x3c79e43cc7d966aa, 0x1597e193f4cd233a, 0x8637ef1e4d6623ad, 0x11b22deed20d827b, 0x07097bc5998784ad},
@ -154,74 +142,74 @@ var isogenyConstantsG1 = [4][16]*fe{
var isogenyConstantsG2 = [4][4]*fe2{
{
{
fe{0x47f671c71ce05e62, 0x06dd57071206393e, 0x7c80cd2af3fd71a2, 0x048103ea9e6cd062, 0xc54516acc8d037f6, 0x13808f550920ea41},
fe{0x47f671c71ce05e62, 0x06dd57071206393e, 0x7c80cd2af3fd71a2, 0x048103ea9e6cd062, 0xc54516acc8d037f6, 0x13808f550920ea41},
{0x47f671c71ce05e62, 0x06dd57071206393e, 0x7c80cd2af3fd71a2, 0x048103ea9e6cd062, 0xc54516acc8d037f6, 0x13808f550920ea41},
{0x47f671c71ce05e62, 0x06dd57071206393e, 0x7c80cd2af3fd71a2, 0x048103ea9e6cd062, 0xc54516acc8d037f6, 0x13808f550920ea41},
},
{
fe{0, 0, 0, 0, 0, 0},
fe{0x5fe55555554c71d0, 0x873fffdd236aaaa3, 0x6a6b4619b26ef918, 0x21c2888408874945, 0x2836cda7028cabc5, 0x0ac73310a7fd5abd},
{0, 0, 0, 0, 0, 0},
{0x5fe55555554c71d0, 0x873fffdd236aaaa3, 0x6a6b4619b26ef918, 0x21c2888408874945, 0x2836cda7028cabc5, 0x0ac73310a7fd5abd},
},
{
fe{0x0a0c5555555971c3, 0xdb0c00101f9eaaae, 0xb1fb2f941d797997, 0xd3960742ef416e1c, 0xb70040e2c20556f4, 0x149d7861e581393b},
fe{0xaff2aaaaaaa638e8, 0x439fffee91b55551, 0xb535a30cd9377c8c, 0x90e144420443a4a2, 0x941b66d3814655e2, 0x0563998853fead5e},
{0x0a0c5555555971c3, 0xdb0c00101f9eaaae, 0xb1fb2f941d797997, 0xd3960742ef416e1c, 0xb70040e2c20556f4, 0x149d7861e581393b},
{0xaff2aaaaaaa638e8, 0x439fffee91b55551, 0xb535a30cd9377c8c, 0x90e144420443a4a2, 0x941b66d3814655e2, 0x0563998853fead5e},
},
{
fe{0x40aac71c71c725ed, 0x190955557a84e38e, 0xd817050a8f41abc3, 0xd86485d4c87f6fb1, 0x696eb479f885d059, 0x198e1a74328002d2},
fe{0, 0, 0, 0, 0, 0},
{0x40aac71c71c725ed, 0x190955557a84e38e, 0xd817050a8f41abc3, 0xd86485d4c87f6fb1, 0x696eb479f885d059, 0x198e1a74328002d2},
{0, 0, 0, 0, 0, 0},
},
},
{
{
fe{0, 0, 0, 0, 0, 0},
fe{0x1f3affffff13ab97, 0xf25bfc611da3ff3e, 0xca3757cb3819b208, 0x3e6427366f8cec18, 0x03977bc86095b089, 0x04f69db13f39a952},
{0, 0, 0, 0, 0, 0},
{0x1f3affffff13ab97, 0xf25bfc611da3ff3e, 0xca3757cb3819b208, 0x3e6427366f8cec18, 0x03977bc86095b089, 0x04f69db13f39a952},
},
{
fe{0x447600000027552e, 0xdcb8009a43480020, 0x6f7ee9ce4a6e8b59, 0xb10330b7c0a95bc6, 0x6140b1fcfb1e54b7, 0x0381be097f0bb4e1},
fe{0x7588ffffffd8557d, 0x41f3ff646e0bffdf, 0xf7b1e8d2ac426aca, 0xb3741acd32dbb6f8, 0xe9daf5b9482d581f, 0x167f53e0ba7431b8},
{0x447600000027552e, 0xdcb8009a43480020, 0x6f7ee9ce4a6e8b59, 0xb10330b7c0a95bc6, 0x6140b1fcfb1e54b7, 0x0381be097f0bb4e1},
{0x7588ffffffd8557d, 0x41f3ff646e0bffdf, 0xf7b1e8d2ac426aca, 0xb3741acd32dbb6f8, 0xe9daf5b9482d581f, 0x167f53e0ba7431b8},
},
{
fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
fe{0, 0, 0, 0, 0, 0},
{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
{0, 0, 0, 0, 0, 0},
},
{
fe{0, 0, 0, 0, 0, 0},
fe{0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0},
},
},
{
{
fe{0x96d8f684bdfc77be, 0xb530e4f43b66d0e2, 0x184a88ff379652fd, 0x57cb23ecfae804e1, 0x0fd2e39eada3eba9, 0x08c8055e31c5d5c3},
fe{0x96d8f684bdfc77be, 0xb530e4f43b66d0e2, 0x184a88ff379652fd, 0x57cb23ecfae804e1, 0x0fd2e39eada3eba9, 0x08c8055e31c5d5c3},
{0x96d8f684bdfc77be, 0xb530e4f43b66d0e2, 0x184a88ff379652fd, 0x57cb23ecfae804e1, 0x0fd2e39eada3eba9, 0x08c8055e31c5d5c3},
{0x96d8f684bdfc77be, 0xb530e4f43b66d0e2, 0x184a88ff379652fd, 0x57cb23ecfae804e1, 0x0fd2e39eada3eba9, 0x08c8055e31c5d5c3},
},
{
fe{0, 0, 0, 0, 0, 0},
fe{0xbf0a71c71c91b406, 0x4d6d55d28b7638fd, 0x9d82f98e5f205aee, 0xa27aa27b1d1a18d5, 0x02c3b2b2d2938e86, 0x0c7d13420b09807f},
{0, 0, 0, 0, 0, 0},
{0xbf0a71c71c91b406, 0x4d6d55d28b7638fd, 0x9d82f98e5f205aee, 0xa27aa27b1d1a18d5, 0x02c3b2b2d2938e86, 0x0c7d13420b09807f},
},
{
fe{0xd7f9555555531c74, 0x21cffff748daaaa8, 0x5a9ad1866c9bbe46, 0x4870a2210221d251, 0x4a0db369c0a32af1, 0x02b1ccc429ff56af},
fe{0xe205aaaaaaac8e37, 0xfcdc000768795556, 0x0c96011a8a1537dd, 0x1c06a963f163406e, 0x010df44c82a881e6, 0x174f45260f808feb},
{0xd7f9555555531c74, 0x21cffff748daaaa8, 0x5a9ad1866c9bbe46, 0x4870a2210221d251, 0x4a0db369c0a32af1, 0x02b1ccc429ff56af},
{0xe205aaaaaaac8e37, 0xfcdc000768795556, 0x0c96011a8a1537dd, 0x1c06a963f163406e, 0x010df44c82a881e6, 0x174f45260f808feb},
},
{
fe{0xa470bda12f67f35c, 0xc0fe38e23327b425, 0xc9d3d0f2c6f0678d, 0x1c55c9935b5a982e, 0x27f6c0e2f0746764, 0x117c5e6e28aa9054},
fe{0, 0, 0, 0, 0, 0},
{0xa470bda12f67f35c, 0xc0fe38e23327b425, 0xc9d3d0f2c6f0678d, 0x1c55c9935b5a982e, 0x27f6c0e2f0746764, 0x117c5e6e28aa9054},
{0, 0, 0, 0, 0, 0},
},
},
{
{
fe{0x0162fffffa765adf, 0x8f7bea480083fb75, 0x561b3c2259e93611, 0x11e19fc1a9c875d5, 0xca713efc00367660, 0x03c6a03d41da1151},
fe{0x0162fffffa765adf, 0x8f7bea480083fb75, 0x561b3c2259e93611, 0x11e19fc1a9c875d5, 0xca713efc00367660, 0x03c6a03d41da1151},
{0x0162fffffa765adf, 0x8f7bea480083fb75, 0x561b3c2259e93611, 0x11e19fc1a9c875d5, 0xca713efc00367660, 0x03c6a03d41da1151},
{0x0162fffffa765adf, 0x8f7bea480083fb75, 0x561b3c2259e93611, 0x11e19fc1a9c875d5, 0xca713efc00367660, 0x03c6a03d41da1151},
},
{
fe{0, 0, 0, 0, 0, 0},
fe{0x5db0fffffd3b02c5, 0xd713f52358ebfdba, 0x5ea60761a84d161a, 0xbb2c75a34ea6c44a, 0x0ac6735921c1119b, 0x0ee3d913bdacfbf6},
{0, 0, 0, 0, 0, 0},
{0x5db0fffffd3b02c5, 0xd713f52358ebfdba, 0x5ea60761a84d161a, 0xbb2c75a34ea6c44a, 0x0ac6735921c1119b, 0x0ee3d913bdacfbf6},
},
{
fe{0x66b10000003affc5, 0xcb1400e764ec0030, 0xa73e5eb56fa5d106, 0x8984c913a0fe09a9, 0x11e10afb78ad7f13, 0x05429d0e3e918f52},
fe{0x534dffffffc4aae6, 0x5397ff174c67ffcf, 0xbff273eb870b251d, 0xdaf2827152870915, 0x393a9cbaca9e2dc3, 0x14be74dbfaee5748},
{0x66b10000003affc5, 0xcb1400e764ec0030, 0xa73e5eb56fa5d106, 0x8984c913a0fe09a9, 0x11e10afb78ad7f13, 0x05429d0e3e918f52},
{0x534dffffffc4aae6, 0x5397ff174c67ffcf, 0xbff273eb870b251d, 0xdaf2827152870915, 0x393a9cbaca9e2dc3, 0x14be74dbfaee5748},
},
{
fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
fe{0, 0, 0, 0, 0, 0},
{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
{0, 0, 0, 0, 0, 0},
},
},
}

374
crypto/bls12381/pairing.go
View file

@ -1,19 +1,3 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
type pair struct {
@ -35,8 +19,8 @@ type Engine struct {
pairs []pair
}
// NewPairingEngine creates new pairing engine instance.
func NewPairingEngine() *Engine {
// NewEngine creates new pairing engine insteace.
func NewEngine() *Engine {
fp2 := newFp2()
fp6 := newFp6(fp2)
fp12 := newFp12(fp6)
@ -52,24 +36,25 @@ func NewPairingEngine() *Engine {
}
type pairingEngineTemp struct {
t2 [10]*fe2
t12 [9]fe12
t2 [9]*fe2
t12 [3]fe12
}
func newEngineTemp() pairingEngineTemp {
t2 := [10]*fe2{}
for i := 0; i < 10; i++ {
t2 := [9]*fe2{}
for i := 0; i < len(t2); i++ {
t2[i] = &fe2{}
}
t12 := [9]fe12{}
t12 := [3]fe12{}
return pairingEngineTemp{t2, t12}
}
// AddPair adds a g1, g2 point pair to pairing engine
func (e *Engine) AddPair(g1 *PointG1, g2 *PointG2) *Engine {
p := newPair(g1, g2)
if !e.isZero(p) {
e.affine(p)
if !(e.G1.IsZero(p.g1) || e.G2.IsZero(p.g2)) {
e.G1.Affine(p.g1)
e.G2.Affine(p.g2)
e.pairs = append(e.pairs, p)
}
return e
@ -77,8 +62,9 @@ func (e *Engine) AddPair(g1 *PointG1, g2 *PointG2) *Engine {
// AddPairInv adds a G1, G2 point pair to pairing engine. G1 point is negated.
func (e *Engine) AddPairInv(g1 *PointG1, g2 *PointG2) *Engine {
e.G1.Neg(g1, g1)
e.AddPair(g1, g2)
ng1 := e.G1.New().Set(g1)
e.G1.Neg(ng1, g1)
e.AddPair(ng1, g2)
return e
}
@ -88,170 +74,246 @@ func (e *Engine) Reset() *Engine {
return e
}
func (e *Engine) isZero(p pair) bool {
return e.G1.IsZero(p.g1) || e.G2.IsZero(p.g2)
}
func (e *Engine) double(f *fe12, r *PointG2, k int) {
fp2, t := e.fp2, e.t2
func (e *Engine) affine(p pair) {
e.G1.Affine(p.g1)
e.G2.Affine(p.g2)
}
func (e *Engine) doublingStep(coeff *[3]fe2, r *PointG2) {
// Adaptation of Formula 3 in https://eprint.iacr.org/2010/526.pdf
fp2 := e.fp2
t := e.t2
fp2.mul(t[0], &r[0], &r[1])
fp2.mulByFq(t[0], t[0], twoInv)
fp2.mul0(t[0], t[0], twoInv)
fp2.square(t[1], &r[1])
fp2.square(t[2], &r[2])
fp2.double(t[7], t[2])
fp2.add(t[7], t[7], t[2])
fp2Double(t[7], t[2])
fp2AddAssign(t[7], t[2])
fp2.mulByB(t[3], t[7])
fp2.double(t[4], t[3])
fp2.add(t[4], t[4], t[3])
fp2.add(t[5], t[1], t[4])
fp2.mulByFq(t[5], t[5], twoInv)
fp2.add(t[6], &r[1], &r[2])
fp2.square(t[6], t[6])
fp2.add(t[7], t[2], t[1])
fp2.sub(t[6], t[6], t[7])
fp2.sub(&coeff[0], t[3], t[1])
fp2Double(t[4], t[3])
fp2AddAssign(t[4], t[3])
fp2Add(t[5], t[1], t[4])
fp2.mul0(t[5], t[5], twoInv)
fp2Add(t[6], &r[1], &r[2])
fp2.squareAssign(t[6])
fp2Add(t[7], t[2], t[1])
fp2SubAssign(t[6], t[7])
fp2Sub(t[8], t[3], t[1])
fp2.square(t[7], &r[0])
fp2.sub(t[4], t[1], t[4])
fp2Sub(t[4], t[1], t[4])
fp2.mul(&r[0], t[4], t[0])
fp2.square(t[2], t[3])
fp2.double(t[3], t[2])
fp2.add(t[3], t[3], t[2])
fp2.square(t[5], t[5])
fp2.sub(&r[1], t[5], t[3])
fp2Double(t[3], t[2])
fp2AddAssign(t[3], t[2])
fp2.squareAssign(t[5])
fp2Sub(&r[1], t[5], t[3])
fp2.mul(&r[2], t[1], t[6])
fp2.double(t[0], t[7])
fp2.add(&coeff[1], t[0], t[7])
fp2.neg(&coeff[2], t[6])
fp2Double(t[0], t[7])
fp2AddAssign(t[0], t[7])
fp2Neg(t[6], t[6])
// line eval
e.fp2.mul0Assign(t[6], &e.pairs[k].g1[1])
e.fp2.mul0Assign(t[0], &e.pairs[k].g1[0])
e.fp12.mul014(f, t[8], t[0], t[6])
}
func (e *Engine) additionStep(coeff *[3]fe2, r, q *PointG2) {
// Algorithm 12 in https://eprint.iacr.org/2010/526.pdf
fp2 := e.fp2
t := e.t2
fp2.mul(t[0], &q[1], &r[2])
fp2.neg(t[0], t[0])
fp2.add(t[0], t[0], &r[1])
fp2.mul(t[1], &q[0], &r[2])
fp2.neg(t[1], t[1])
fp2.add(t[1], t[1], &r[0])
func (e *Engine) add(f *fe12, r *PointG2, k int) {
fp2, t := e.fp2, e.t2
fp2.mul(t[0], &e.pairs[k].g2[1], &r[2])
fp2Neg(t[0], t[0])
fp2AddAssign(t[0], &r[1])
fp2.mul(t[1], &e.pairs[k].g2[0], &r[2])
fp2Neg(t[1], t[1])
fp2AddAssign(t[1], &r[0])
fp2.square(t[2], t[0])
fp2.square(t[3], t[1])
fp2.mul(t[4], t[1], t[3])
fp2.mul(t[2], &r[2], t[2])
fp2.mul(t[3], &r[0], t[3])
fp2.double(t[5], t[3])
fp2.sub(t[5], t[4], t[5])
fp2.add(t[5], t[5], t[2])
fp2.mulAssign(t[3], &r[0])
fp2Double(t[5], t[3])
fp2Sub(t[5], t[4], t[5])
fp2AddAssign(t[5], t[2])
fp2.mul(&r[0], t[1], t[5])
fp2.sub(t[2], t[3], t[5])
fp2.mul(t[2], t[2], t[0])
fp2.mul(t[3], &r[1], t[4])
fp2.sub(&r[1], t[2], t[3])
fp2.mul(&r[2], &r[2], t[4])
fp2.mul(t[2], t[1], &q[1])
fp2.mul(t[3], t[0], &q[0])
fp2.sub(&coeff[0], t[3], t[2])
fp2.neg(&coeff[1], t[0])
coeff[2].set(t[1])
fp2SubAssign(t[3], t[5])
fp2.mulAssign(t[3], t[0])
fp2.mul(t[2], &r[1], t[4])
fp2Sub(&r[1], t[3], t[2])
fp2.mulAssign(&r[2], t[4])
fp2.mul(t[2], t[1], &e.pairs[k].g2[1])
fp2.mul(t[3], t[0], &e.pairs[k].g2[0])
fp2SubAssign(t[3], t[2])
fp2Neg(t[0], t[0])
// line eval
e.fp2.mul0Assign(t[1], &e.pairs[k].g1[1])
e.fp2.mul0Assign(t[0], &e.pairs[k].g1[0])
e.fp12.mul014(f, t[3], t[0], t[1])
}
func (e *Engine) preCompute(ellCoeffs *[68][3]fe2, twistPoint *PointG2) {
// Algorithm 5 in https://eprint.iacr.org/2019/077.pdf
if e.G2.IsZero(twistPoint) {
return
}
r := new(PointG2).Set(twistPoint)
j := 0
for i := x.BitLen() - 2; i >= 0; i-- {
e.doublingStep(&ellCoeffs[j], r)
if x.Bit(i) != 0 {
j++
ellCoeffs[j] = fe6{}
e.additionStep(&ellCoeffs[j], r, twistPoint)
func (e *Engine) nDoubleAdd(f *fe12, r []PointG2, n int) {
for i := 0; i < n; i++ {
e.fp12.squareAssign(f)
for j := 0; j < len(e.pairs); j++ {
e.double(f, &r[j], j)
}
}
for j := 0; j < len(e.pairs); j++ {
e.add(f, &r[j], j)
}
}
func (e *Engine) nDouble(f *fe12, r []PointG2, n int) {
for i := 0; i < n; i++ {
e.fp12.squareAssign(f)
for j := 0; j < len(e.pairs); j++ {
e.double(f, &r[j], j)
}
j++
}
}
func (e *Engine) millerLoop(f *fe12) {
pairs := e.pairs
ellCoeffs := make([][68][3]fe2, len(pairs))
for i := 0; i < len(pairs); i++ {
e.preCompute(&ellCoeffs[i], pairs[i].g2)
}
fp12, fp2 := e.fp12, e.fp2
t := e.t2
f.one()
j := 0
for i := 62; /* x.BitLen() - 2 */ i >= 0; i-- {
if i != 62 {
fp12.square(f, f)
}
for i := 0; i <= len(pairs)-1; i++ {
fp2.mulByFq(t[0], &ellCoeffs[i][j][2], &pairs[i].g1[1])
fp2.mulByFq(t[1], &ellCoeffs[i][j][1], &pairs[i].g1[0])
fp12.mulBy014Assign(f, &ellCoeffs[i][j][0], t[1], t[0])
}
if x.Bit(i) != 0 {
j++
for i := 0; i <= len(pairs)-1; i++ {
fp2.mulByFq(t[0], &ellCoeffs[i][j][2], &pairs[i].g1[1])
fp2.mulByFq(t[1], &ellCoeffs[i][j][1], &pairs[i].g1[0])
fp12.mulBy014Assign(f, &ellCoeffs[i][j][0], t[1], t[0])
}
}
j++
r := make([]PointG2, len(e.pairs))
for i := 0; i < len(e.pairs); i++ {
r[i].Set(e.pairs[i].g2)
}
fp12.conjugate(f, f)
for j := 0; j < len(e.pairs); j++ {
e.double(f, &r[j], j)
}
for j := 0; j < len(e.pairs); j++ {
e.add(f, &r[j], j)
}
e.nDoubleAdd(f, r, 2)
e.nDoubleAdd(f, r, 3)
e.nDoubleAdd(f, r, 9)
e.nDoubleAdd(f, r, 32)
e.nDouble(f, r, 16)
fp12Conjugate(f, f)
}
// exp raises element by x = -15132376222941642752
func (e *Engine) exp(c, a *fe12) {
fp12 := e.fp12
fp12.cyclotomicExp(c, a, x)
fp12.conjugate(c, c)
c.set(a)
e.fp12.cyclotomicSquare(c) // (a ^ 2)
// (a ^ (2 + 1)) ^ (2 ^ 2) = a ^ 12
e.fp12.mulAssign(c, a)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
// (a ^ (12 + 1)) ^ (2 ^ 3) = a ^ 104
e.fp12.mulAssign(c, a)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
// (a ^ (104 + 1)) ^ (2 ^ 9) = a ^ 53760
e.fp12.mulAssign(c, a)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
// (a ^ (53760 + 1)) ^ (2 ^ 32) = a ^ 230901736800256
e.fp12.mulAssign(c, a)
for i := 0; i < 32; i++ {
e.fp12.cyclotomicSquare(c)
}
// (a ^ (230901736800256 + 1)) ^ (2 ^ 16) = a ^ 15132376222941642752
e.fp12.mulAssign(c, a)
for i := 0; i < 16; i++ {
e.fp12.cyclotomicSquare(c)
}
// invert chain result since x is negative
fp12Conjugate(c, c)
}
// expDrop raises element by x = -15132376222941642752 / 2
func (e *Engine) expDrop(c, a *fe12) {
c.set(a)
e.fp12.cyclotomicSquare(c) // (a ^ 2)
// (a ^ (2 + 1)) ^ (2 ^ 2) = a ^ 12
e.fp12.mulAssign(c, a)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
// (a ^ (12 + 1)) ^ (2 ^ 3) = a ^ 104
e.fp12.mulAssign(c, a)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
// (a ^ (104 + 1)) ^ (2 ^ 9) = a ^ 53760
e.fp12.mulAssign(c, a)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
e.fp12.cyclotomicSquare(c)
// (a ^ (53760 + 1)) ^ (2 ^ 32) = a ^ 230901736800256
e.fp12.mulAssign(c, a)
for i := 0; i < 32; i++ {
e.fp12.cyclotomicSquare(c)
}
// (a ^ (230901736800256 + 1)) ^ (2 ^ 16) = a ^ 15132376222941642752
e.fp12.mulAssign(c, a)
for i := 0; i < 15; i++ {
e.fp12.cyclotomicSquare(c)
}
// invert chain result since x is negative
fp12Conjugate(c, c)
}
func (e *Engine) finalExp(f *fe12) {
fp12 := e.fp12
t := e.t12
// Efficient Final Exponentiation via Cyclotomic Structure for Pairings over Families of Elliptic Curves
// https: //eprint.iacr.org/2020/875.pdf
// easy part
fp12.frobeniusMap(&t[0], f, 6)
fp12.inverse(&t[1], f)
fp12.mul(&t[2], &t[0], &t[1])
t[1].set(&t[2])
fp12.frobeniusMapAssign(&t[2], 2)
fp12.mulAssign(&t[2], &t[1])
fp12.cyclotomicSquare(&t[1], &t[2])
fp12.conjugate(&t[1], &t[1])
fp12Conjugate(&t[0], f)
e.fp12.inverse(f, f)
e.fp12.mulAssign(&t[0], f)
f.set(&t[0])
e.fp12.frobeniusMap2(f)
e.fp12.mulAssign(f, &t[0])
// hard part
e.exp(&t[3], &t[2])
fp12.cyclotomicSquare(&t[4], &t[3])
fp12.mul(&t[5], &t[1], &t[3])
e.exp(&t[1], &t[5])
t[0].set(f)
e.fp12.cyclotomicSquare(&t[0])
e.expDrop(&t[1], &t[0])
fp12Conjugate(&t[2], f)
e.fp12.mulAssign(&t[1], &t[2])
e.exp(&t[2], &t[1])
fp12Conjugate(&t[1], &t[1])
e.fp12.mulAssign(&t[1], &t[2])
e.exp(&t[2], &t[1])
e.fp12.frobeniusMap1(&t[1])
e.fp12.mulAssign(&t[1], &t[2])
e.fp12.mulAssign(f, &t[0])
e.exp(&t[0], &t[1])
e.exp(&t[6], &t[0])
fp12.mulAssign(&t[6], &t[4])
e.exp(&t[4], &t[6])
fp12.conjugate(&t[5], &t[5])
fp12.mulAssign(&t[4], &t[5])
fp12.mulAssign(&t[4], &t[2])
fp12.conjugate(&t[5], &t[2])
fp12.mulAssign(&t[1], &t[2])
fp12.frobeniusMapAssign(&t[1], 3)
fp12.mulAssign(&t[6], &t[5])
fp12.frobeniusMapAssign(&t[6], 1)
fp12.mulAssign(&t[3], &t[0])
fp12.frobeniusMapAssign(&t[3], 2)
fp12.mulAssign(&t[3], &t[1])
fp12.mulAssign(&t[3], &t[6])
fp12.mul(f, &t[3], &t[4])
e.exp(&t[2], &t[0])
t[0].set(&t[1])
e.fp12.frobeniusMap2(&t[0])
fp12Conjugate(&t[1], &t[1])
e.fp12.mulAssign(&t[1], &t[2])
e.fp12.mulAssign(&t[1], &t[0])
e.fp12.mulAssign(f, &t[1])
}
func (e *Engine) calculate() *fe12 {

128
crypto/bls12381/pairing_test.go
View file

@ -3,28 +3,27 @@ package bls12381
import (
"math/big"
"testing"
"github.com/ethereum/go-ethereum/common"
)
func TestPairingExpected(t *testing.T) {
bls := NewPairingEngine()
bls := NewEngine()
G1, G2 := bls.G1, bls.G2
GT := bls.GT()
expected, err := GT.FromBytes(
common.FromHex("" +
"0f41e58663bf08cf068672cbd01a7ec73baca4d72ca93544deff686bfd6df543d48eaa24afe47e1efde449383b676631" +
"04c581234d086a9902249b64728ffd21a189e87935a954051c7cdba7b3872629a4fafc05066245cb9108f0242d0fe3ef" +
"03350f55a7aefcd3c31b4fcb6ce5771cc6a0e9786ab5973320c806ad360829107ba810c5a09ffdd9be2291a0c25a99a2" +
"11b8b424cd48bf38fcef68083b0b0ec5c81a93b330ee1a677d0d15ff7b984e8978ef48881e32fac91b93b47333e2ba57" +
"06fba23eb7c5af0d9f80940ca771b6ffd5857baaf222eb95a7d2809d61bfe02e1bfd1b68ff02f0b8102ae1c2d5d5ab1a" +
"19f26337d205fb469cd6bd15c3d5a04dc88784fbb3d0b2dbdea54d43b2b73f2cbb12d58386a8703e0f948226e47ee89d" +
"018107154f25a764bd3c79937a45b84546da634b8f6be14a8061e55cceba478b23f7dacaa35c8ca78beae9624045b4b6" +
"01b2f522473d171391125ba84dc4007cfbf2f8da752f7c74185203fcca589ac719c34dffbbaad8431dad1c1fb597aaa5" +
"193502b86edb8857c273fa075a50512937e0794e1e65a7617c90d8bd66065b1fffe51d7a579973b1315021ec3c19934f" +
"1368bb445c7c2d209703f239689ce34c0378a68e72a6b3b216da0e22a5031b54ddff57309396b38c881c4c849ec23e87" +
"089a1c5b46e5110b86750ec6a532348868a84045483c92b7af5af689452eafabf1a8943e50439f1d59882a98eaa0170f" +
"1250ebd871fc0a92a7b2d83168d0d727272d441befa15c503dd8e90ce98db3e7b6d194f60839c508a84305aaca1789b6",
fromHex(
fpByteSize,
"0x0f41e58663bf08cf068672cbd01a7ec73baca4d72ca93544deff686bfd6df543d48eaa24afe47e1efde449383b676631",
"0x04c581234d086a9902249b64728ffd21a189e87935a954051c7cdba7b3872629a4fafc05066245cb9108f0242d0fe3ef",
"0x03350f55a7aefcd3c31b4fcb6ce5771cc6a0e9786ab5973320c806ad360829107ba810c5a09ffdd9be2291a0c25a99a2",
"0x11b8b424cd48bf38fcef68083b0b0ec5c81a93b330ee1a677d0d15ff7b984e8978ef48881e32fac91b93b47333e2ba57",
"0x06fba23eb7c5af0d9f80940ca771b6ffd5857baaf222eb95a7d2809d61bfe02e1bfd1b68ff02f0b8102ae1c2d5d5ab1a",
"0x19f26337d205fb469cd6bd15c3d5a04dc88784fbb3d0b2dbdea54d43b2b73f2cbb12d58386a8703e0f948226e47ee89d",
"0x018107154f25a764bd3c79937a45b84546da634b8f6be14a8061e55cceba478b23f7dacaa35c8ca78beae9624045b4b6",
"0x01b2f522473d171391125ba84dc4007cfbf2f8da752f7c74185203fcca589ac719c34dffbbaad8431dad1c1fb597aaa5",
"0x193502b86edb8857c273fa075a50512937e0794e1e65a7617c90d8bd66065b1fffe51d7a579973b1315021ec3c19934f",
"0x1368bb445c7c2d209703f239689ce34c0378a68e72a6b3b216da0e22a5031b54ddff57309396b38c881c4c849ec23e87",
"0x089a1c5b46e5110b86750ec6a532348868a84045483c92b7af5af689452eafabf1a8943e50439f1d59882a98eaa0170f",
"0x1250ebd871fc0a92a7b2d83168d0d727272d441befa15c503dd8e90ce98db3e7b6d194f60839c508a84305aaca1789b6",
),
)
if err != nil {
@ -32,7 +31,7 @@ func TestPairingExpected(t *testing.T) {
}
r := bls.AddPair(G1.One(), G2.One()).Result()
if !r.Equal(expected) {
t.Fatal("bad pairing")
t.Fatal("expected pairing failed")
}
if !GT.IsValid(r) {
t.Fatal("element is not in correct subgroup")
@ -40,7 +39,7 @@ func TestPairingExpected(t *testing.T) {
}
func TestPairingNonDegeneracy(t *testing.T) {
bls := NewPairingEngine()
bls := NewEngine()
G1, G2 := bls.G1, bls.G2
g1Zero, g2Zero, g1One, g2One := G1.Zero(), G2.Zero(), G1.One(), G2.One()
GT := bls.GT()
@ -89,19 +88,20 @@ func TestPairingNonDegeneracy(t *testing.T) {
bls.Reset()
{
expected, err := GT.FromBytes(
common.FromHex("" +
"0f41e58663bf08cf068672cbd01a7ec73baca4d72ca93544deff686bfd6df543d48eaa24afe47e1efde449383b676631" +
"04c581234d086a9902249b64728ffd21a189e87935a954051c7cdba7b3872629a4fafc05066245cb9108f0242d0fe3ef" +
"03350f55a7aefcd3c31b4fcb6ce5771cc6a0e9786ab5973320c806ad360829107ba810c5a09ffdd9be2291a0c25a99a2" +
"11b8b424cd48bf38fcef68083b0b0ec5c81a93b330ee1a677d0d15ff7b984e8978ef48881e32fac91b93b47333e2ba57" +
"06fba23eb7c5af0d9f80940ca771b6ffd5857baaf222eb95a7d2809d61bfe02e1bfd1b68ff02f0b8102ae1c2d5d5ab1a" +
"19f26337d205fb469cd6bd15c3d5a04dc88784fbb3d0b2dbdea54d43b2b73f2cbb12d58386a8703e0f948226e47ee89d" +
"018107154f25a764bd3c79937a45b84546da634b8f6be14a8061e55cceba478b23f7dacaa35c8ca78beae9624045b4b6" +
"01b2f522473d171391125ba84dc4007cfbf2f8da752f7c74185203fcca589ac719c34dffbbaad8431dad1c1fb597aaa5" +
"193502b86edb8857c273fa075a50512937e0794e1e65a7617c90d8bd66065b1fffe51d7a579973b1315021ec3c19934f" +
"1368bb445c7c2d209703f239689ce34c0378a68e72a6b3b216da0e22a5031b54ddff57309396b38c881c4c849ec23e87" +
"089a1c5b46e5110b86750ec6a532348868a84045483c92b7af5af689452eafabf1a8943e50439f1d59882a98eaa0170f" +
"1250ebd871fc0a92a7b2d83168d0d727272d441befa15c503dd8e90ce98db3e7b6d194f60839c508a84305aaca1789b6",
fromHex(
fpByteSize,
"0x0f41e58663bf08cf068672cbd01a7ec73baca4d72ca93544deff686bfd6df543d48eaa24afe47e1efde449383b676631",
"0x04c581234d086a9902249b64728ffd21a189e87935a954051c7cdba7b3872629a4fafc05066245cb9108f0242d0fe3ef",
"0x03350f55a7aefcd3c31b4fcb6ce5771cc6a0e9786ab5973320c806ad360829107ba810c5a09ffdd9be2291a0c25a99a2",
"0x11b8b424cd48bf38fcef68083b0b0ec5c81a93b330ee1a677d0d15ff7b984e8978ef48881e32fac91b93b47333e2ba57",
"0x06fba23eb7c5af0d9f80940ca771b6ffd5857baaf222eb95a7d2809d61bfe02e1bfd1b68ff02f0b8102ae1c2d5d5ab1a",
"0x19f26337d205fb469cd6bd15c3d5a04dc88784fbb3d0b2dbdea54d43b2b73f2cbb12d58386a8703e0f948226e47ee89d",
"0x018107154f25a764bd3c79937a45b84546da634b8f6be14a8061e55cceba478b23f7dacaa35c8ca78beae9624045b4b6",
"0x01b2f522473d171391125ba84dc4007cfbf2f8da752f7c74185203fcca589ac719c34dffbbaad8431dad1c1fb597aaa5",
"0x193502b86edb8857c273fa075a50512937e0794e1e65a7617c90d8bd66065b1fffe51d7a579973b1315021ec3c19934f",
"0x1368bb445c7c2d209703f239689ce34c0378a68e72a6b3b216da0e22a5031b54ddff57309396b38c881c4c849ec23e87",
"0x089a1c5b46e5110b86750ec6a532348868a84045483c92b7af5af689452eafabf1a8943e50439f1d59882a98eaa0170f",
"0x1250ebd871fc0a92a7b2d83168d0d727272d441befa15c503dd8e90ce98db3e7b6d194f60839c508a84305aaca1789b6",
),
)
if err != nil {
@ -113,13 +113,13 @@ func TestPairingNonDegeneracy(t *testing.T) {
bls.AddPair(g1One, g2One)
e := bls.Result()
if !e.Equal(expected) {
t.Fatal("bad pairing")
t.Fatal("pairing failed")
}
}
}
func TestPairingBilinearity(t *testing.T) {
bls := NewPairingEngine()
bls := NewEngine()
g1, g2 := bls.G1, bls.G2
gt := bls.GT()
// e(a*G1, b*G2) = e(G1, G2)^c
@ -129,50 +129,50 @@ func TestPairingBilinearity(t *testing.T) {
G1, G2 := g1.One(), g2.One()
e0 := bls.AddPair(G1, G2).Result()
P1, P2 := g1.New(), g2.New()
g1.MulScalar(P1, G1, a)
g2.MulScalar(P2, G2, b)
g1.MulScalarBig(P1, G1, a)
g2.MulScalarBig(P2, G2, b)
e1 := bls.AddPair(P1, P2).Result()
gt.Exp(e0, e0, c)
if !e0.Equal(e1) {
t.Fatal("bad pairing, 1")
t.Fatal("pairing failed")
}
}
// e(a * G1, b * G2) = e((a + b) * G1, G2)
// e(a * G1, b * G2) = e((a * b) * G1, G2)
{
// scalars
a, b := big.NewInt(17), big.NewInt(117)
c := new(big.Int).Mul(a, b)
// LHS
G1, G2 := g1.One(), g2.One()
g1.MulScalar(G1, G1, c)
g1.MulScalarBig(G1, G1, c)
bls.AddPair(G1, G2)
// RHS
P1, P2 := g1.One(), g2.One()
g1.MulScalar(P1, P1, a)
g2.MulScalar(P2, P2, b)
g1.MulScalarBig(P1, P1, a)
g2.MulScalarBig(P2, P2, b)
bls.AddPairInv(P1, P2)
// should be one
if !bls.Check() {
t.Fatal("bad pairing, 2")
t.Fatal("pairing failed")
}
}
// e(a * G1, b * G2) = e((a + b) * G1, G2)
// e(a * G1, b * G2) = e(G1, (a * b) * G2)
{
// scalars
a, b := big.NewInt(17), big.NewInt(117)
c := new(big.Int).Mul(a, b)
// LHS
G1, G2 := g1.One(), g2.One()
g2.MulScalar(G2, G2, c)
g2.MulScalarBig(G2, G2, c)
bls.AddPair(G1, G2)
// RHS
H1, H2 := g1.One(), g2.One()
g1.MulScalar(H1, H1, a)
g2.MulScalar(H2, H2, b)
g1.MulScalarBig(H1, H1, a)
g2.MulScalarBig(H2, H2, b)
bls.AddPairInv(H1, H2)
// should be one
if !bls.Check() {
t.Fatal("bad pairing, 3")
t.Fatal("pairing failed")
}
}
}
@ -180,17 +180,17 @@ func TestPairingBilinearity(t *testing.T) {
func TestPairingMulti(t *testing.T) {
// e(G1, G2) ^ t == e(a01 * G1, a02 * G2) * e(a11 * G1, a12 * G2) * ... * e(an1 * G1, an2 * G2)
// where t = sum(ai1 * ai2)
bls := NewPairingEngine()
bls := NewEngine()
g1, g2 := bls.G1, bls.G2
numOfPair := 100
targetExp := new(big.Int)
// RHS
for i := 0; i < numOfPair; i++ {
// (ai1 * G1, ai2 * G2)
a1, a2 := randScalar(q), randScalar(q)
a1, a2 := randScalar(qBig), randScalar(qBig)
P1, P2 := g1.One(), g2.One()
g1.MulScalar(P1, P1, a1)
g2.MulScalar(P2, P2, a2)
g1.MulScalarBig(P1, P1, a1)
g2.MulScalarBig(P2, P2, a2)
bls.AddPair(P1, P2)
// accumulate targetExp
// t += (ai1 * ai2)
@ -200,7 +200,7 @@ func TestPairingMulti(t *testing.T) {
// LHS
// e(t * G1, G2)
T1, T2 := g1.One(), g2.One()
g1.MulScalar(T1, T1, targetExp)
g1.MulScalarBig(T1, T1, targetExp)
bls.AddPairInv(T1, T2)
if !bls.Check() {
t.Fatal("fail multi pairing")
@ -208,7 +208,7 @@ func TestPairingMulti(t *testing.T) {
}
func TestPairingEmpty(t *testing.T) {
bls := NewPairingEngine()
bls := NewEngine()
if !bls.Check() {
t.Fatal("empty check should be accepted")
}
@ -218,7 +218,7 @@ func TestPairingEmpty(t *testing.T) {
}
func BenchmarkPairing(t *testing.B) {
bls := NewPairingEngine()
bls := NewEngine()
g1, g2, gt := bls.G1, bls.G2, bls.GT()
bls.AddPair(g1.One(), g2.One())
e := gt.New()
@ -228,3 +228,25 @@ func BenchmarkPairing(t *testing.B) {
}
_ = e
}
func BenchmarkMillerLoop(t *testing.B) {
bls := NewEngine()
g1, g2, gt := bls.G1, bls.G2, bls.GT()
bls.AddPair(g1.One(), g2.One())
f := gt.New().one()
t.ResetTimer()
for i := 0; i < t.N; i++ {
bls.millerLoop(f)
}
}
func BenchmarkFinalExp(t *testing.B) {
bls := NewEngine()
g1, g2, gt := bls.G1, bls.G2, bls.GT()
bls.AddPair(g1.One(), g2.One())
f := gt.New().one()
t.ResetTimer()
for i := 0; i < t.N; i++ {
bls.finalExp(f)
}
}

30
crypto/bls12381/swu.go
View file

@ -1,23 +1,7 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
// swuMapG1 is implementation of Simplified Shallue-van de Woestijne-Ulas Method
// follows the implementation at draft-irtf-cfrg-hash-to-curve-06.
// follows the implmentation at draft-irtf-cfrg-hash-to-curve-06.
func swuMapG1(u *fe) (*fe, *fe) {
var params = swuParamsForG1
var tv [4]*fe
@ -79,19 +63,19 @@ func swuMapG2(e *fp2, u *fe2) (*fe2, *fe2) {
e.mul(tv[0], tv[0], params.z)
e.square(tv[1], tv[0])
x1 := e.new()
e.add(x1, tv[0], tv[1])
fp2Add(x1, tv[0], tv[1])
e.inverse(x1, x1)
e1 := x1.isZero()
e.add(x1, x1, e.one())
fp2Add(x1, x1, e.one())
if e1 {
x1.set(params.zInv)
}
e.mul(x1, x1, params.minusBOverA)
gx1 := e.new()
e.square(gx1, x1)
e.add(gx1, gx1, params.a)
fp2Add(gx1, gx1, params.a)
e.mul(gx1, gx1, x1)
e.add(gx1, gx1, params.b)
fp2Add(gx1, gx1, params.b)
x2 := e.new()
e.mul(x2, tv[0], x1)
e.mul(tv[1], tv[0], tv[1])
@ -107,9 +91,9 @@ func swuMapG2(e *fp2, u *fe2) (*fe2, *fe2) {
y2.set(gx2)
}
y := e.new()
e.sqrt(y, y2)
e.sqrtBLST(y, y2)
if y.sign() != u.sign() {
e.neg(y, y)
fp2Neg(y, y)
}
return x, y
}

40
crypto/bls12381/utils.go
View file

@ -1,45 +1,13 @@
// Copyright 2020 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package bls12381
import (
"errors"
"math/big"
"github.com/ethereum/go-ethereum/common"
)
func bigFromHex(hex string) *big.Int {
return new(big.Int).SetBytes(common.FromHex(hex))
}
// decodeFieldElement expects 64 byte input with zero top 16 bytes,
// returns lower 48 bytes.
func decodeFieldElement(in []byte) ([]byte, error) {
if len(in) != 64 {
return nil, errors.New("invalid field element length")
if len(hex) > 1 && hex[:2] == "0x" {
hex = hex[2:]
}
// check top bytes
for i := 0; i < 16; i++ {
if in[i] != byte(0x00) {
return nil, errors.New("invalid field element top bytes")
}
}
out := make([]byte, 48)
copy(out[:], in[16:])
return out, nil
n, _ := new(big.Int).SetString(hex, 16)
return n
}

110
crypto/bls12381/wnaf.go Normal file
View file

@ -0,0 +1,110 @@
package bls12381
import (
"math/big"
)
type nafNumber []int
func (n nafNumber) neg() {
for i := 0; i < len(n); i++ {
n[i] = -n[i]
}
}
var bigZero = big.NewInt(0)
var bigOne = big.NewInt(1)
func (e *Fr) toWNAF(w uint) nafNumber {
naf := nafNumber{}
if w == 0 {
return naf
}
windowSize, halfSize, mask := 1<<(w+1), 1<<w, (1<<(w+1))-1
ee := new(Fr).Set(e)
z := new(Fr)
for !ee.IsZero() {
if !ee.isEven() {
nafSign := int(ee[0]) & mask
if nafSign >= halfSize {
nafSign = nafSign - windowSize
}
naf = append(naf, int(nafSign))
if nafSign < 0 {
laddAssignFR(ee, z.setUint64(uint64(-nafSign)))
} else {
lsubAssignFR(ee, z.setUint64(uint64(nafSign)))
}
} else {
naf = append(naf, 0)
}
ee.div2()
}
return naf
}
func (e *Fr) fromWNAF(naf nafNumber, w uint) *Fr {
if w == 0 {
return e
}
l := (1 << (w - 1))
table := make([]*Fr, l)
table[0] = new(Fr).One()
two := new(Fr).setUint64(2)
for i := 1; i < l; i++ {
table[i] = new(Fr)
table[i].Add(table[i-1], two)
}
acc := new(Fr).Zero()
for i := len(naf) - 1; i >= 0; i-- {
if naf[i] < 0 {
acc.Sub(acc, table[-naf[i]>>1])
} else if naf[i] > 0 {
acc.Add(acc, table[naf[i]>>1])
}
if i != 0 {
acc.Double(acc)
}
}
return e.Set(acc)
}
// caution: does not cover negative case
func bigToWNAF(e *big.Int, w uint) nafNumber {
naf := nafNumber{}
if w == 0 {
return naf
}
windowSize := new(big.Int).Lsh(bigOne, uint(w+1))
halfSize := new(big.Int).Rsh(windowSize, 1)
ee := new(big.Int).Abs(e)
for ee.Cmp(bigZero) != 0 {
if ee.Bit(0) == 1 {
nafSign := new(big.Int)
nafSign.Mod(ee, windowSize)
if nafSign.Cmp(halfSize) >= 0 {
nafSign.Sub(nafSign, windowSize)
}
naf = append(naf, int(nafSign.Int64()))
ee.Sub(ee, nafSign)
} else {
naf = append(naf, 0)
}
ee.Rsh(ee, 1)
}
return naf
}
func bigFromWNAF(naf nafNumber) *big.Int {
acc := new(big.Int)
k := new(big.Int).Set(bigOne)
for i := 0; i < len(naf); i++ {
if naf[i] != 0 {
z := new(big.Int).Mul(k, big.NewInt(int64(naf[i])))
acc.Add(acc, z)
}
k.Lsh(k, 1)
}
return acc
}

67
crypto/bls12381/wnaf_test.go Normal file
View file

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package bls12381
import (
"crypto/rand"
"math/big"
"testing"
)
var maxWindowSize uint = 9
func TestWNAFBig(t *testing.T) {
var w uint
for w = 1; w <= maxWindowSize; w++ {
for i := 0; i < fuz; i++ {
e0, err := rand.Int(rand.Reader, new(big.Int).SetUint64(100))
if err != nil {
t.Fatal(err)
}
n0 := bigToWNAF(e0, w)
e1 := bigFromWNAF(n0)
if e0.Cmp(e1) != 0 {
t.Fatal("wnaf conversion failed")
}
}
}
}
func TestFrWNAF(t *testing.T) {
var w uint
for w = 1; w <= maxWindowSize; w++ {
for i := 0; i < fuz; i++ {
a0, _ := new(Fr).Rand(rand.Reader)
naf := a0.toWNAF(w)
a1 := new(Fr).fromWNAF(naf, w)
if !a0.Equal(a1) {
t.Fatal("wnaf conversion failed")
}
naf.neg()
a1.fromWNAF(naf, w)
a0.Neg(a0)
if !a0.Equal(a1) {
t.Fatal("negated wnaf conversion failed")
}
}
}
}
func TestFrWNAFCrossAgainstBig(t *testing.T) {
var maxWindowSize uint = 20
var w uint
for w = 1; w <= maxWindowSize; w++ {
for i := 0; i < fuz; i++ {
a, _ := new(Fr).Rand(rand.Reader)
aBig := a.ToBig()
naf1 := a.toWNAF(w)
naf2 := bigToWNAF(aBig, w)
if len(naf1) != len(naf2) {
t.Fatal("naf conversion failed", len(naf1), len(naf2))
}
for i := 0; i < len(naf1); i++ {
if naf1[i] != naf2[i] {
t.Fatal("naf conversion failed", i)
}
}
}
}
}