mirror of https://github.com/ethereum/go-ethereum
pull/16256/head
commit
13b566e06e
@ -0,0 +1,17 @@ |
||||
# Number of days of inactivity before an issue becomes stale |
||||
daysUntilStale: 366 |
||||
# Number of days of inactivity before a stale issue is closed |
||||
daysUntilClose: 42 |
||||
# Issues with these labels will never be considered stale |
||||
exemptLabels: |
||||
- pinned |
||||
- security |
||||
# Label to use when marking an issue as stale |
||||
staleLabel: stale |
||||
# Comment to post when marking an issue as stale. Set to `false` to disable |
||||
markComment: > |
||||
This issue has been automatically marked as stale because it has not had |
||||
recent activity. It will be closed if no further activity occurs. Thank you |
||||
for your contributions. |
||||
# Comment to post when closing a stale issue. Set to `false` to disable |
||||
closeComment: false |
@ -1,47 +0,0 @@ |
||||
// Copyright 2017 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/>.
|
||||
|
||||
// +build !go1.8
|
||||
|
||||
package ethash |
||||
|
||||
// cacheSize calculates and returns the size of the ethash verification cache that
|
||||
// belongs to a certain block number. The cache size grows linearly, however, we
|
||||
// always take the highest prime below the linearly growing threshold in order to
|
||||
// reduce the risk of accidental regularities leading to cyclic behavior.
|
||||
func cacheSize(block uint64) uint64 { |
||||
// If we have a pre-generated value, use that
|
||||
epoch := int(block / epochLength) |
||||
if epoch < maxEpoch { |
||||
return cacheSizes[epoch] |
||||
} |
||||
// We don't have a way to verify primes fast before Go 1.8
|
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panic("fast prime testing unsupported in Go < 1.8") |
||||
} |
||||
|
||||
// datasetSize calculates and returns the size of the ethash mining dataset that
|
||||
// belongs to a certain block number. The dataset size grows linearly, however, we
|
||||
// always take the highest prime below the linearly growing threshold in order to
|
||||
// reduce the risk of accidental regularities leading to cyclic behavior.
|
||||
func datasetSize(block uint64) uint64 { |
||||
// If we have a pre-generated value, use that
|
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epoch := int(block / epochLength) |
||||
if epoch < maxEpoch { |
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return datasetSizes[epoch] |
||||
} |
||||
// We don't have a way to verify primes fast before Go 1.8
|
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panic("fast prime testing unsupported in Go < 1.8") |
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} |
@ -1,63 +0,0 @@ |
||||
// Copyright 2017 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/>.
|
||||
|
||||
// +build go1.8
|
||||
|
||||
package ethash |
||||
|
||||
import "math/big" |
||||
|
||||
// cacheSize returns the size of the ethash verification cache that belongs to a certain
|
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// block number.
|
||||
func cacheSize(block uint64) uint64 { |
||||
epoch := int(block / epochLength) |
||||
if epoch < maxEpoch { |
||||
return cacheSizes[epoch] |
||||
} |
||||
return calcCacheSize(epoch) |
||||
} |
||||
|
||||
// calcCacheSize calculates the cache size for epoch. The cache size grows linearly,
|
||||
// however, we always take the highest prime below the linearly growing threshold in order
|
||||
// to reduce the risk of accidental regularities leading to cyclic behavior.
|
||||
func calcCacheSize(epoch int) uint64 { |
||||
size := cacheInitBytes + cacheGrowthBytes*uint64(epoch) - hashBytes |
||||
for !new(big.Int).SetUint64(size / hashBytes).ProbablyPrime(1) { // Always accurate for n < 2^64
|
||||
size -= 2 * hashBytes |
||||
} |
||||
return size |
||||
} |
||||
|
||||
// datasetSize returns the size of the ethash mining dataset that belongs to a certain
|
||||
// block number.
|
||||
func datasetSize(block uint64) uint64 { |
||||
epoch := int(block / epochLength) |
||||
if epoch < maxEpoch { |
||||
return datasetSizes[epoch] |
||||
} |
||||
return calcDatasetSize(epoch) |
||||
} |
||||
|
||||
// calcDatasetSize calculates the dataset size for epoch. The dataset size grows linearly,
|
||||
// however, we always take the highest prime below the linearly growing threshold in order
|
||||
// to reduce the risk of accidental regularities leading to cyclic behavior.
|
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func calcDatasetSize(epoch int) uint64 { |
||||
size := datasetInitBytes + datasetGrowthBytes*uint64(epoch) - mixBytes |
||||
for !new(big.Int).SetUint64(size / mixBytes).ProbablyPrime(1) { // Always accurate for n < 2^64
|
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size -= 2 * mixBytes |
||||
} |
||||
return size |
||||
} |
@ -1,37 +0,0 @@ |
||||
// Copyright 2017 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/>.
|
||||
|
||||
// +build go1.8
|
||||
|
||||
package ethash |
||||
|
||||
import "testing" |
||||
|
||||
// Tests whether the dataset size calculator works correctly by cross checking the
|
||||
// hard coded lookup table with the value generated by it.
|
||||
func TestSizeCalculations(t *testing.T) { |
||||
// Verify all the cache and dataset sizes from the lookup table.
|
||||
for epoch, want := range cacheSizes { |
||||
if size := calcCacheSize(epoch); size != want { |
||||
t.Errorf("cache %d: cache size mismatch: have %d, want %d", epoch, size, want) |
||||
} |
||||
} |
||||
for epoch, want := range datasetSizes { |
||||
if size := calcDatasetSize(epoch); size != want { |
||||
t.Errorf("dataset %d: dataset size mismatch: have %d, want %d", epoch, size, want) |
||||
} |
||||
} |
||||
} |
@ -1,23 +0,0 @@ |
||||
// Copyright 2014 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 core |
||||
|
||||
import ( |
||||
"math/big" |
||||
) |
||||
|
||||
var BlockReward = big.NewInt(5e+18) |
@ -0,0 +1,63 @@ |
||||
// Copyright 2018 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/>.
|
||||
|
||||
// +build amd64,!appengine,!gccgo
|
||||
|
||||
// Package bn256 implements the Optimal Ate pairing over a 256-bit Barreto-Naehrig curve.
|
||||
package bn256 |
||||
|
||||
import ( |
||||
"math/big" |
||||
|
||||
"github.com/ethereum/go-ethereum/crypto/bn256/cloudflare" |
||||
) |
||||
|
||||
// G1 is an abstract cyclic group. The zero value is suitable for use as the
|
||||
// output of an operation, but cannot be used as an input.
|
||||
type G1 struct { |
||||
bn256.G1 |
||||
} |
||||
|
||||
// Add sets e to a+b and then returns e.
|
||||
func (e *G1) Add(a, b *G1) *G1 { |
||||
e.G1.Add(&a.G1, &b.G1) |
||||
return e |
||||
} |
||||
|
||||
// ScalarMult sets e to a*k and then returns e.
|
||||
func (e *G1) ScalarMult(a *G1, k *big.Int) *G1 { |
||||
e.G1.ScalarMult(&a.G1, k) |
||||
return e |
||||
} |
||||
|
||||
// G2 is an abstract cyclic group. The zero value is suitable for use as the
|
||||
// output of an operation, but cannot be used as an input.
|
||||
type G2 struct { |
||||
bn256.G2 |
||||
} |
||||
|
||||
// PairingCheck calculates the Optimal Ate pairing for a set of points.
|
||||
func PairingCheck(a []*G1, b []*G2) bool { |
||||
as := make([]*bn256.G1, len(a)) |
||||
for i, p := range a { |
||||
as[i] = &p.G1 |
||||
} |
||||
bs := make([]*bn256.G2, len(b)) |
||||
for i, p := range b { |
||||
bs[i] = &p.G2 |
||||
} |
||||
return bn256.PairingCheck(as, bs) |
||||
} |
@ -0,0 +1,63 @@ |
||||
// Copyright 2018 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/>.
|
||||
|
||||
// +build !amd64 appengine gccgo
|
||||
|
||||
// Package bn256 implements the Optimal Ate pairing over a 256-bit Barreto-Naehrig curve.
|
||||
package bn256 |
||||
|
||||
import ( |
||||
"math/big" |
||||
|
||||
"github.com/ethereum/go-ethereum/crypto/bn256/google" |
||||
) |
||||
|
||||
// G1 is an abstract cyclic group. The zero value is suitable for use as the
|
||||
// output of an operation, but cannot be used as an input.
|
||||
type G1 struct { |
||||
bn256.G1 |
||||
} |
||||
|
||||
// Add sets e to a+b and then returns e.
|
||||
func (e *G1) Add(a, b *G1) *G1 { |
||||
e.G1.Add(&a.G1, &b.G1) |
||||
return e |
||||
} |
||||
|
||||
// ScalarMult sets e to a*k and then returns e.
|
||||
func (e *G1) ScalarMult(a *G1, k *big.Int) *G1 { |
||||
e.G1.ScalarMult(&a.G1, k) |
||||
return e |
||||
} |
||||
|
||||
// G2 is an abstract cyclic group. The zero value is suitable for use as the
|
||||
// output of an operation, but cannot be used as an input.
|
||||
type G2 struct { |
||||
bn256.G2 |
||||
} |
||||
|
||||
// PairingCheck calculates the Optimal Ate pairing for a set of points.
|
||||
func PairingCheck(a []*G1, b []*G2) bool { |
||||
as := make([]*bn256.G1, len(a)) |
||||
for i, p := range a { |
||||
as[i] = &p.G1 |
||||
} |
||||
bs := make([]*bn256.G2, len(b)) |
||||
for i, p := range b { |
||||
bs[i] = &p.G2 |
||||
} |
||||
return bn256.PairingCheck(as, bs) |
||||
} |
@ -0,0 +1,481 @@ |
||||
// Package bn256 implements a particular bilinear group at the 128-bit security
|
||||
// level.
|
||||
//
|
||||
// Bilinear groups are the basis of many of the new cryptographic protocols that
|
||||
// have been proposed over the past decade. They consist of a triplet of groups
|
||||
// (G₁, G₂ and GT) such that there exists a function e(g₁ˣ,g₂ʸ)=gTˣʸ (where gₓ
|
||||
// is a generator of the respective group). That function is called a pairing
|
||||
// function.
|
||||
//
|
||||
// This package specifically implements the Optimal Ate pairing over a 256-bit
|
||||
// Barreto-Naehrig curve as described in
|
||||
// http://cryptojedi.org/papers/dclxvi-20100714.pdf. Its output is compatible
|
||||
// with the implementation described in that paper.
|
||||
package bn256 |
||||
|
||||
import ( |
||||
"crypto/rand" |
||||
"errors" |
||||
"io" |
||||
"math/big" |
||||
) |
||||
|
||||
func randomK(r io.Reader) (k *big.Int, err error) { |
||||
for { |
||||
k, err = rand.Int(r, Order) |
||||
if k.Sign() > 0 || err != nil { |
||||
return |
||||
} |
||||
} |
||||
} |
||||
|
||||
// G1 is an abstract cyclic group. The zero value is suitable for use as the
|
||||
// output of an operation, but cannot be used as an input.
|
||||
type G1 struct { |
||||
p *curvePoint |
||||
} |
||||
|
||||
// RandomG1 returns x and g₁ˣ where x is a random, non-zero number read from r.
|
||||
func RandomG1(r io.Reader) (*big.Int, *G1, error) { |
||||
k, err := randomK(r) |
||||
if err != nil { |
||||
return nil, nil, err |
||||
} |
||||
|
||||
return k, new(G1).ScalarBaseMult(k), nil |
||||
} |
||||
|
||||
func (g *G1) String() string { |
||||
return "bn256.G1" + g.p.String() |
||||
} |
||||
|
||||
// ScalarBaseMult sets e to g*k where g is the generator of the group and then
|
||||
// returns e.
|
||||
func (e *G1) ScalarBaseMult(k *big.Int) *G1 { |
||||
if e.p == nil { |
||||
e.p = &curvePoint{} |
||||
} |
||||
e.p.Mul(curveGen, k) |
||||
return e |
||||
} |
||||
|
||||
// ScalarMult sets e to a*k and then returns e.
|
||||
func (e *G1) ScalarMult(a *G1, k *big.Int) *G1 { |
||||
if e.p == nil { |
||||
e.p = &curvePoint{} |
||||
} |
||||
e.p.Mul(a.p, k) |
||||
return e |
||||
} |
||||
|
||||
// Add sets e to a+b and then returns e.
|
||||
func (e *G1) Add(a, b *G1) *G1 { |
||||
if e.p == nil { |
||||
e.p = &curvePoint{} |
||||
} |
||||
e.p.Add(a.p, b.p) |
||||
return e |
||||
} |
||||
|
||||
// Neg sets e to -a and then returns e.
|
||||
func (e *G1) Neg(a *G1) *G1 { |
||||
if e.p == nil { |
||||
e.p = &curvePoint{} |
||||
} |
||||
e.p.Neg(a.p) |
||||
return e |
||||
} |
||||
|
||||
// Set sets e to a and then returns e.
|
||||
func (e *G1) Set(a *G1) *G1 { |
||||
if e.p == nil { |
||||
e.p = &curvePoint{} |
||||
} |
||||
e.p.Set(a.p) |
||||
return e |
||||
} |
||||
|
||||
// Marshal converts e to a byte slice.
|
||||
func (e *G1) Marshal() []byte { |
||||
// Each value is a 256-bit number.
|
||||
const numBytes = 256 / 8 |
||||
|
||||
e.p.MakeAffine() |
||||
ret := make([]byte, numBytes*2) |
||||
if e.p.IsInfinity() { |
||||
return ret |
||||
} |
||||
temp := &gfP{} |
||||
|
||||
montDecode(temp, &e.p.x) |
||||
temp.Marshal(ret) |
||||
montDecode(temp, &e.p.y) |
||||
temp.Marshal(ret[numBytes:]) |
||||
|
||||
return ret |
||||
} |
||||
|
||||
// Unmarshal sets e to the result of converting the output of Marshal back into
|
||||
// a group element and then returns e.
|
||||
func (e *G1) Unmarshal(m []byte) ([]byte, error) { |
||||
// Each value is a 256-bit number.
|
||||
const numBytes = 256 / 8 |
||||
if len(m) < 2*numBytes { |
||||
return nil, errors.New("bn256: not enough data") |
||||
} |
||||
// Unmarshal the points and check their caps
|
||||
if e.p == nil { |
||||
e.p = &curvePoint{} |
||||
} else { |
||||
e.p.x, e.p.y = gfP{0}, gfP{0} |
||||
} |
||||
var err error |
||||
if err = e.p.x.Unmarshal(m); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.y.Unmarshal(m[numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
// Encode into Montgomery form and ensure it's on the curve
|
||||
montEncode(&e.p.x, &e.p.x) |
||||
montEncode(&e.p.y, &e.p.y) |
||||
|
||||
zero := gfP{0} |
||||
if e.p.x == zero && e.p.y == zero { |
||||
// This is the point at infinity.
|
||||
e.p.y = *newGFp(1) |
||||
e.p.z = gfP{0} |
||||
e.p.t = gfP{0} |
||||
} else { |
||||
e.p.z = *newGFp(1) |
||||
e.p.t = *newGFp(1) |
||||
|
||||
if !e.p.IsOnCurve() { |
||||
return nil, errors.New("bn256: malformed point") |
||||
} |
||||
} |
||||
return m[2*numBytes:], nil |
||||
} |
||||
|
||||
// G2 is an abstract cyclic group. The zero value is suitable for use as the
|
||||
// output of an operation, but cannot be used as an input.
|
||||
type G2 struct { |
||||
p *twistPoint |
||||
} |
||||
|
||||
// RandomG2 returns x and g₂ˣ where x is a random, non-zero number read from r.
|
||||
func RandomG2(r io.Reader) (*big.Int, *G2, error) { |
||||
k, err := randomK(r) |
||||
if err != nil { |
||||
return nil, nil, err |
||||
} |
||||
|
||||
return k, new(G2).ScalarBaseMult(k), nil |
||||
} |
||||
|
||||
func (e *G2) String() string { |
||||
return "bn256.G2" + e.p.String() |
||||
} |
||||
|
||||
// ScalarBaseMult sets e to g*k where g is the generator of the group and then
|
||||
// returns out.
|
||||
func (e *G2) ScalarBaseMult(k *big.Int) *G2 { |
||||
if e.p == nil { |
||||
e.p = &twistPoint{} |
||||
} |
||||
e.p.Mul(twistGen, k) |
||||
return e |
||||
} |
||||
|
||||
// ScalarMult sets e to a*k and then returns e.
|
||||
func (e *G2) ScalarMult(a *G2, k *big.Int) *G2 { |
||||
if e.p == nil { |
||||
e.p = &twistPoint{} |
||||
} |
||||
e.p.Mul(a.p, k) |
||||
return e |
||||
} |
||||
|
||||
// Add sets e to a+b and then returns e.
|
||||
func (e *G2) Add(a, b *G2) *G2 { |
||||
if e.p == nil { |
||||
e.p = &twistPoint{} |
||||
} |
||||
e.p.Add(a.p, b.p) |
||||
return e |
||||
} |
||||
|
||||
// Neg sets e to -a and then returns e.
|
||||
func (e *G2) Neg(a *G2) *G2 { |
||||
if e.p == nil { |
||||
e.p = &twistPoint{} |
||||
} |
||||
e.p.Neg(a.p) |
||||
return e |
||||
} |
||||
|
||||
// Set sets e to a and then returns e.
|
||||
func (e *G2) Set(a *G2) *G2 { |
||||
if e.p == nil { |
||||
e.p = &twistPoint{} |
||||
} |
||||
e.p.Set(a.p) |
||||
return e |
||||
} |
||||
|
||||
// Marshal converts e into a byte slice.
|
||||
func (e *G2) Marshal() []byte { |
||||
// Each value is a 256-bit number.
|
||||
const numBytes = 256 / 8 |
||||
|
||||
if e.p == nil { |
||||
e.p = &twistPoint{} |
||||
} |
||||
|
||||
e.p.MakeAffine() |
||||
ret := make([]byte, numBytes*4) |
||||
if e.p.IsInfinity() { |
||||
return ret |
||||
} |
||||
temp := &gfP{} |
||||
|
||||
montDecode(temp, &e.p.x.x) |
||||
temp.Marshal(ret) |
||||
montDecode(temp, &e.p.x.y) |
||||
temp.Marshal(ret[numBytes:]) |
||||
montDecode(temp, &e.p.y.x) |
||||
temp.Marshal(ret[2*numBytes:]) |
||||
montDecode(temp, &e.p.y.y) |
||||
temp.Marshal(ret[3*numBytes:]) |
||||
|
||||
return ret |
||||
} |
||||
|
||||
// Unmarshal sets e to the result of converting the output of Marshal back into
|
||||
// a group element and then returns e.
|
||||
func (e *G2) Unmarshal(m []byte) ([]byte, error) { |
||||
// Each value is a 256-bit number.
|
||||
const numBytes = 256 / 8 |
||||
if len(m) < 4*numBytes { |
||||
return nil, errors.New("bn256: not enough data") |
||||
} |
||||
// Unmarshal the points and check their caps
|
||||
if e.p == nil { |
||||
e.p = &twistPoint{} |
||||
} |
||||
var err error |
||||
if err = e.p.x.x.Unmarshal(m); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.x.y.Unmarshal(m[numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.y.x.Unmarshal(m[2*numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.y.y.Unmarshal(m[3*numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
// Encode into Montgomery form and ensure it's on the curve
|
||||
montEncode(&e.p.x.x, &e.p.x.x) |
||||
montEncode(&e.p.x.y, &e.p.x.y) |
||||
montEncode(&e.p.y.x, &e.p.y.x) |
||||
montEncode(&e.p.y.y, &e.p.y.y) |
||||
|
||||
if e.p.x.IsZero() && e.p.y.IsZero() { |
||||
// This is the point at infinity.
|
||||
e.p.y.SetOne() |
||||
e.p.z.SetZero() |
||||
e.p.t.SetZero() |
||||
} else { |
||||
e.p.z.SetOne() |
||||
e.p.t.SetOne() |
||||
|
||||
if !e.p.IsOnCurve() { |
||||
return nil, errors.New("bn256: malformed point") |
||||
} |
||||
} |
||||
return m[4*numBytes:], nil |
||||
} |
||||
|
||||
// GT is an abstract cyclic group. The zero value is suitable for use as the
|
||||
// output of an operation, but cannot be used as an input.
|
||||
type GT struct { |
||||
p *gfP12 |
||||
} |
||||
|
||||
// Pair calculates an Optimal Ate pairing.
|
||||
func Pair(g1 *G1, g2 *G2) *GT { |
||||
return >{optimalAte(g2.p, g1.p)} |
||||
} |
||||
|
||||
// PairingCheck calculates the Optimal Ate pairing for a set of points.
|
||||
func PairingCheck(a []*G1, b []*G2) bool { |
||||
acc := new(gfP12) |
||||
acc.SetOne() |
||||
|
||||
for i := 0; i < len(a); i++ { |
||||
if a[i].p.IsInfinity() || b[i].p.IsInfinity() { |
||||
continue |
||||
} |
||||
acc.Mul(acc, miller(b[i].p, a[i].p)) |
||||
} |
||||
return finalExponentiation(acc).IsOne() |
||||
} |
||||
|
||||
// Miller applies Miller's algorithm, which is a bilinear function from the
|
||||
// source groups to F_p^12. Miller(g1, g2).Finalize() is equivalent to Pair(g1,
|
||||
// g2).
|
||||
func Miller(g1 *G1, g2 *G2) *GT { |
||||
return >{miller(g2.p, g1.p)} |
||||
} |
||||
|
||||
func (g *GT) String() string { |
||||
return "bn256.GT" + g.p.String() |
||||
} |
||||
|
||||
// ScalarMult sets e to a*k and then returns e.
|
||||
func (e *GT) ScalarMult(a *GT, k *big.Int) *GT { |
||||
if e.p == nil { |
||||
e.p = &gfP12{} |
||||
} |
||||
e.p.Exp(a.p, k) |
||||
return e |
||||
} |
||||
|
||||
// Add sets e to a+b and then returns e.
|
||||
func (e *GT) Add(a, b *GT) *GT { |
||||
if e.p == nil { |
||||
e.p = &gfP12{} |
||||
} |
||||
e.p.Mul(a.p, b.p) |
||||
return e |
||||
} |
||||
|
||||
// Neg sets e to -a and then returns e.
|
||||
func (e *GT) Neg(a *GT) *GT { |
||||
if e.p == nil { |
||||
e.p = &gfP12{} |
||||
} |
||||
e.p.Conjugate(a.p) |
||||
return e |
||||
} |
||||
|
||||
// Set sets e to a and then returns e.
|
||||
func (e *GT) Set(a *GT) *GT { |
||||
if e.p == nil { |
||||
e.p = &gfP12{} |
||||
} |
||||
e.p.Set(a.p) |
||||
return e |
||||
} |
||||
|
||||
// Finalize is a linear function from F_p^12 to GT.
|
||||
func (e *GT) Finalize() *GT { |
||||
ret := finalExponentiation(e.p) |
||||
e.p.Set(ret) |
||||
return e |
||||
} |
||||
|
||||
// Marshal converts e into a byte slice.
|
||||
func (e *GT) Marshal() []byte { |
||||
// Each value is a 256-bit number.
|
||||
const numBytes = 256 / 8 |
||||
|
||||
ret := make([]byte, numBytes*12) |
||||
temp := &gfP{} |
||||
|
||||
montDecode(temp, &e.p.x.x.x) |
||||
temp.Marshal(ret) |
||||
montDecode(temp, &e.p.x.x.y) |
||||
temp.Marshal(ret[numBytes:]) |
||||
montDecode(temp, &e.p.x.y.x) |
||||
temp.Marshal(ret[2*numBytes:]) |
||||
montDecode(temp, &e.p.x.y.y) |
||||
temp.Marshal(ret[3*numBytes:]) |
||||
montDecode(temp, &e.p.x.z.x) |
||||
temp.Marshal(ret[4*numBytes:]) |
||||
montDecode(temp, &e.p.x.z.y) |
||||
temp.Marshal(ret[5*numBytes:]) |
||||
montDecode(temp, &e.p.y.x.x) |
||||
temp.Marshal(ret[6*numBytes:]) |
||||
montDecode(temp, &e.p.y.x.y) |
||||
temp.Marshal(ret[7*numBytes:]) |
||||
montDecode(temp, &e.p.y.y.x) |
||||
temp.Marshal(ret[8*numBytes:]) |
||||
montDecode(temp, &e.p.y.y.y) |
||||
temp.Marshal(ret[9*numBytes:]) |
||||
montDecode(temp, &e.p.y.z.x) |
||||
temp.Marshal(ret[10*numBytes:]) |
||||
montDecode(temp, &e.p.y.z.y) |
||||
temp.Marshal(ret[11*numBytes:]) |
||||
|
||||
return ret |
||||
} |
||||
|
||||
// Unmarshal sets e to the result of converting the output of Marshal back into
|
||||
// a group element and then returns e.
|
||||
func (e *GT) Unmarshal(m []byte) ([]byte, error) { |
||||
// Each value is a 256-bit number.
|
||||
const numBytes = 256 / 8 |
||||
|
||||
if len(m) < 12*numBytes { |
||||
return nil, errors.New("bn256: not enough data") |
||||
} |
||||
|
||||
if e.p == nil { |
||||
e.p = &gfP12{} |
||||
} |
||||
|
||||
var err error |
||||
if err = e.p.x.x.x.Unmarshal(m); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.x.x.y.Unmarshal(m[numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.x.y.x.Unmarshal(m[2*numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.x.y.y.Unmarshal(m[3*numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.x.z.x.Unmarshal(m[4*numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.x.z.y.Unmarshal(m[5*numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.y.x.x.Unmarshal(m[6*numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.y.x.y.Unmarshal(m[7*numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.y.y.x.Unmarshal(m[8*numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.y.y.y.Unmarshal(m[9*numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.y.z.x.Unmarshal(m[10*numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
if err = e.p.y.z.y.Unmarshal(m[11*numBytes:]); err != nil { |
||||
return nil, err |
||||
} |
||||
montEncode(&e.p.x.x.x, &e.p.x.x.x) |
||||
montEncode(&e.p.x.x.y, &e.p.x.x.y) |
||||
montEncode(&e.p.x.y.x, &e.p.x.y.x) |
||||
montEncode(&e.p.x.y.y, &e.p.x.y.y) |
||||
montEncode(&e.p.x.z.x, &e.p.x.z.x) |
||||
montEncode(&e.p.x.z.y, &e.p.x.z.y) |
||||
montEncode(&e.p.y.x.x, &e.p.y.x.x) |
||||
montEncode(&e.p.y.x.y, &e.p.y.x.y) |
||||
montEncode(&e.p.y.y.x, &e.p.y.y.x) |
||||
montEncode(&e.p.y.y.y, &e.p.y.y.y) |
||||
montEncode(&e.p.y.z.x, &e.p.y.z.x) |
||||
montEncode(&e.p.y.z.y, &e.p.y.z.y) |
||||
|
||||
return m[12*numBytes:], nil |
||||
} |
@ -0,0 +1,118 @@ |
||||
// +build amd64,!appengine,!gccgo
|
||||
|
||||
package bn256 |
||||
|
||||
import ( |
||||
"bytes" |
||||
"crypto/rand" |
||||
"testing" |
||||
) |
||||
|
||||
func TestG1Marshal(t *testing.T) { |
||||
_, Ga, err := RandomG1(rand.Reader) |
||||
if err != nil { |
||||
t.Fatal(err) |
||||
} |
||||
ma := Ga.Marshal() |
||||
|
||||
Gb := new(G1) |
||||
_, err = Gb.Unmarshal(ma) |
||||
if err != nil { |
||||
t.Fatal(err) |
||||
} |
||||
mb := Gb.Marshal() |
||||
|
||||
if !bytes.Equal(ma, mb) { |
||||
t.Fatal("bytes are different") |
||||
} |
||||
} |
||||
|
||||
func TestG2Marshal(t *testing.T) { |
||||
_, Ga, err := RandomG2(rand.Reader) |
||||
if err != nil { |
||||
t.Fatal(err) |
||||
} |
||||
ma := Ga.Marshal() |
||||
|
||||
Gb := new(G2) |
||||
_, err = Gb.Unmarshal(ma) |
||||
if err != nil { |
||||
t.Fatal(err) |
||||
} |
||||
mb := Gb.Marshal() |
||||
|
||||
if !bytes.Equal(ma, mb) { |
||||
t.Fatal("bytes are different") |
||||
} |
||||
} |
||||
|
||||
func TestBilinearity(t *testing.T) { |
||||
for i := 0; i < 2; i++ { |
||||
a, p1, _ := RandomG1(rand.Reader) |
||||
b, p2, _ := RandomG2(rand.Reader) |
||||
e1 := Pair(p1, p2) |
||||
|
||||
e2 := Pair(&G1{curveGen}, &G2{twistGen}) |
||||
e2.ScalarMult(e2, a) |
||||
e2.ScalarMult(e2, b) |
||||
|
||||
if *e1.p != *e2.p { |
||||
t.Fatalf("bad pairing result: %s", e1) |
||||
} |
||||
} |
||||
} |
||||
|
||||
func TestTripartiteDiffieHellman(t *testing.T) { |
||||
a, _ := rand.Int(rand.Reader, Order) |
||||
b, _ := rand.Int(rand.Reader, Order) |
||||
c, _ := rand.Int(rand.Reader, Order) |
||||
|
||||
pa, pb, pc := new(G1), new(G1), new(G1) |
||||
qa, qb, qc := new(G2), new(G2), new(G2) |
||||
|
||||
pa.Unmarshal(new(G1).ScalarBaseMult(a).Marshal()) |
||||
qa.Unmarshal(new(G2).ScalarBaseMult(a).Marshal()) |
||||
pb.Unmarshal(new(G1).ScalarBaseMult(b).Marshal()) |
||||
qb.Unmarshal(new(G2).ScalarBaseMult(b).Marshal()) |
||||
pc.Unmarshal(new(G1).ScalarBaseMult(c).Marshal()) |
||||
qc.Unmarshal(new(G2).ScalarBaseMult(c).Marshal()) |
||||
|
||||
k1 := Pair(pb, qc) |
||||
k1.ScalarMult(k1, a) |
||||
k1Bytes := k1.Marshal() |
||||
|
||||
k2 := Pair(pc, qa) |
||||
k2.ScalarMult(k2, b) |
||||
k2Bytes := k2.Marshal() |
||||
|
||||
k3 := Pair(pa, qb) |
||||
k3.ScalarMult(k3, c) |
||||
k3Bytes := k3.Marshal() |
||||
|
||||
if !bytes.Equal(k1Bytes, k2Bytes) || !bytes.Equal(k2Bytes, k3Bytes) { |
||||
t.Errorf("keys didn't agree") |
||||
} |
||||
} |
||||
|
||||
func BenchmarkG1(b *testing.B) { |
||||
x, _ := rand.Int(rand.Reader, Order) |
||||
b.ResetTimer() |
||||
|
||||
for i := 0; i < b.N; i++ { |
||||
new(G1).ScalarBaseMult(x) |
||||
} |
||||
} |
||||
|
||||
func BenchmarkG2(b *testing.B) { |
||||
x, _ := rand.Int(rand.Reader, Order) |
||||
b.ResetTimer() |
||||
|
||||
for i := 0; i < b.N; i++ { |
||||
new(G2).ScalarBaseMult(x) |
||||
} |
||||
} |
||||
func BenchmarkPairing(b *testing.B) { |
||||
for i := 0; i < b.N; i++ { |
||||
Pair(&G1{curveGen}, &G2{twistGen}) |
||||
} |
||||
} |
@ -0,0 +1,59 @@ |
||||
// Copyright 2012 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package bn256 |
||||
|
||||
import ( |
||||
"math/big" |
||||
) |
||||
|
||||
func bigFromBase10(s string) *big.Int { |
||||
n, _ := new(big.Int).SetString(s, 10) |
||||
return n |
||||
} |
||||
|
||||
// u is the BN parameter that determines the prime: 1868033³.
|
||||
var u = bigFromBase10("4965661367192848881") |
||||
|
||||
// Order is the number of elements in both G₁ and G₂: 36u⁴+36u³+18u²+6u+1.
|
||||
var Order = bigFromBase10("21888242871839275222246405745257275088548364400416034343698204186575808495617") |
||||
|
||||
// P is a prime over which we form a basic field: 36u⁴+36u³+24u²+6u+1.
|
||||
var P = bigFromBase10("21888242871839275222246405745257275088696311157297823662689037894645226208583") |
||||
|
||||
// p2 is p, represented as little-endian 64-bit words.
|
||||
var p2 = [4]uint64{0x3c208c16d87cfd47, 0x97816a916871ca8d, 0xb85045b68181585d, 0x30644e72e131a029} |
||||
|
||||
// np is the negative inverse of p, mod 2^256.
|
||||
var np = [4]uint64{0x87d20782e4866389, 0x9ede7d651eca6ac9, 0xd8afcbd01833da80, 0xf57a22b791888c6b} |
||||
|
||||
// rN1 is R^-1 where R = 2^256 mod p.
|
||||
var rN1 = &gfP{0xed84884a014afa37, 0xeb2022850278edf8, 0xcf63e9cfb74492d9, 0x2e67157159e5c639} |
||||
|
||||
// r2 is R^2 where R = 2^256 mod p.
|
||||
var r2 = &gfP{0xf32cfc5b538afa89, 0xb5e71911d44501fb, 0x47ab1eff0a417ff6, 0x06d89f71cab8351f} |
||||
|
||||
// r3 is R^3 where R = 2^256 mod p.
|
||||
var r3 = &gfP{0xb1cd6dafda1530df, 0x62f210e6a7283db6, 0xef7f0b0c0ada0afb, 0x20fd6e902d592544} |
||||
|
||||
// xiToPMinus1Over6 is ξ^((p-1)/6) where ξ = i+9.
|
||||
var xiToPMinus1Over6 = &gfP2{gfP{0xa222ae234c492d72, 0xd00f02a4565de15b, 0xdc2ff3a253dfc926, 0x10a75716b3899551}, gfP{0xaf9ba69633144907, 0xca6b1d7387afb78a, 0x11bded5ef08a2087, 0x02f34d751a1f3a7c}} |
||||
|
||||
// xiToPMinus1Over3 is ξ^((p-1)/3) where ξ = i+9.
|
||||
var xiToPMinus1Over3 = &gfP2{gfP{0x6e849f1ea0aa4757, 0xaa1c7b6d89f89141, 0xb6e713cdfae0ca3a, 0x26694fbb4e82ebc3}, gfP{0xb5773b104563ab30, 0x347f91c8a9aa6454, 0x7a007127242e0991, 0x1956bcd8118214ec}} |
||||
|
||||
// xiToPMinus1Over2 is ξ^((p-1)/2) where ξ = i+9.
|
||||
var xiToPMinus1Over2 = &gfP2{gfP{0xa1d77ce45ffe77c7, 0x07affd117826d1db, 0x6d16bd27bb7edc6b, 0x2c87200285defecc}, gfP{0xe4bbdd0c2936b629, 0xbb30f162e133bacb, 0x31a9d1b6f9645366, 0x253570bea500f8dd}} |
||||
|
||||
// xiToPSquaredMinus1Over3 is ξ^((p²-1)/3) where ξ = i+9.
|
||||
var xiToPSquaredMinus1Over3 = &gfP{0x3350c88e13e80b9c, 0x7dce557cdb5e56b9, 0x6001b4b8b615564a, 0x2682e617020217e0} |
||||
|
||||
// xiTo2PSquaredMinus2Over3 is ξ^((2p²-2)/3) where ξ = i+9 (a cubic root of unity, mod p).
|
||||
var xiTo2PSquaredMinus2Over3 = &gfP{0x71930c11d782e155, 0xa6bb947cffbe3323, 0xaa303344d4741444, 0x2c3b3f0d26594943} |
||||
|
||||
// xiToPSquaredMinus1Over6 is ξ^((1p²-1)/6) where ξ = i+9 (a cubic root of -1, mod p).
|
||||
var xiToPSquaredMinus1Over6 = &gfP{0xca8d800500fa1bf2, 0xf0c5d61468b39769, 0x0e201271ad0d4418, 0x04290f65bad856e6} |
||||
|
||||
// xiTo2PMinus2Over3 is ξ^((2p-2)/3) where ξ = i+9.
|
||||
var xiTo2PMinus2Over3 = &gfP2{gfP{0x5dddfd154bd8c949, 0x62cb29a5a4445b60, 0x37bc870a0c7dd2b9, 0x24830a9d3171f0fd}, gfP{0x7361d77f843abe92, 0xa5bb2bd3273411fb, 0x9c941f314b3e2399, 0x15df9cddbb9fd3ec}} |
@ -0,0 +1,229 @@ |
||||
package bn256 |
||||
|
||||
import ( |
||||
"math/big" |
||||
) |
||||
|
||||
// curvePoint implements the elliptic curve y²=x³+3. Points are kept in Jacobian
|
||||
// form and t=z² when valid. G₁ is the set of points of this curve on GF(p).
|
||||
type curvePoint struct { |
||||
x, y, z, t gfP |
||||
} |
||||
|
||||
var curveB = newGFp(3) |
||||
|
||||
// curveGen is the generator of G₁.
|
||||
var curveGen = &curvePoint{ |
||||
x: *newGFp(1), |
||||
y: *newGFp(2), |
||||
z: *newGFp(1), |
||||
t: *newGFp(1), |
||||
} |
||||
|
||||
func (c *curvePoint) String() string { |
||||
c.MakeAffine() |
||||
x, y := &gfP{}, &gfP{} |
||||
montDecode(x, &c.x) |
||||
montDecode(y, &c.y) |
||||
return "(" + x.String() + ", " + y.String() + ")" |
||||
} |
||||
|
||||
func (c *curvePoint) Set(a *curvePoint) { |
||||
c.x.Set(&a.x) |
||||
c.y.Set(&a.y) |
||||
c.z.Set(&a.z) |
||||
c.t.Set(&a.t) |
||||
} |
||||
|
||||
// IsOnCurve returns true iff c is on the curve.
|
||||
func (c *curvePoint) IsOnCurve() bool { |
||||
c.MakeAffine() |
||||
if c.IsInfinity() { |
||||
return true |
||||
} |
||||
|
||||
y2, x3 := &gfP{}, &gfP{} |
||||
gfpMul(y2, &c.y, &c.y) |
||||
gfpMul(x3, &c.x, &c.x) |
||||
gfpMul(x3, x3, &c.x) |
||||
gfpAdd(x3, x3, curveB) |
||||
|
||||
return *y2 == *x3 |
||||
} |
||||
|
||||
func (c *curvePoint) SetInfinity() { |
||||
c.x = gfP{0} |
||||
c.y = *newGFp(1) |
||||
c.z = gfP{0} |
||||
c.t = gfP{0} |
||||
} |
||||
|
||||
func (c *curvePoint) IsInfinity() bool { |
||||
return c.z == gfP{0} |
||||
} |
||||
|
||||
func (c *curvePoint) Add(a, b *curvePoint) { |
||||
if a.IsInfinity() { |
||||
c.Set(b) |
||||
return |
||||
} |
||||
if b.IsInfinity() { |
||||
c.Set(a) |
||||
return |
||||
} |
||||
|
||||
// See http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/addition/add-2007-bl.op3
|
||||
|
||||
// Normalize the points by replacing a = [x1:y1:z1] and b = [x2:y2:z2]
|
||||
// by [u1:s1:z1·z2] and [u2:s2:z1·z2]
|
||||
// where u1 = x1·z2², s1 = y1·z2³ and u1 = x2·z1², s2 = y2·z1³
|
||||
z12, z22 := &gfP{}, &gfP{} |
||||
gfpMul(z12, &a.z, &a.z) |
||||
gfpMul(z22, &b.z, &b.z) |
||||
|
||||
u1, u2 := &gfP{}, &gfP{} |
||||
gfpMul(u1, &a.x, z22) |
||||
gfpMul(u2, &b.x, z12) |
||||
|
||||
t, s1 := &gfP{}, &gfP{} |
||||
gfpMul(t, &b.z, z22) |
||||
gfpMul(s1, &a.y, t) |
||||
|
||||
s2 := &gfP{} |
||||
gfpMul(t, &a.z, z12) |
||||
gfpMul(s2, &b.y, t) |
||||
|
||||
// Compute x = (2h)²(s²-u1-u2)
|
||||
// where s = (s2-s1)/(u2-u1) is the slope of the line through
|
||||
// (u1,s1) and (u2,s2). The extra factor 2h = 2(u2-u1) comes from the value of z below.
|
||||
// This is also:
|
||||
// 4(s2-s1)² - 4h²(u1+u2) = 4(s2-s1)² - 4h³ - 4h²(2u1)
|
||||
// = r² - j - 2v
|
||||
// with the notations below.
|
||||
h := &gfP{} |
||||
gfpSub(h, u2, u1) |
||||
xEqual := *h == gfP{0} |
||||
|
||||
gfpAdd(t, h, h) |
||||
// i = 4h²
|
||||
i := &gfP{} |
||||
gfpMul(i, t, t) |
||||
// j = 4h³
|
||||
j := &gfP{} |
||||
gfpMul(j, h, i) |
||||
|
||||
gfpSub(t, s2, s1) |
||||
yEqual := *t == gfP{0} |
||||
if xEqual && yEqual { |
||||
c.Double(a) |
||||
return |
||||
} |
||||
r := &gfP{} |
||||
gfpAdd(r, t, t) |
||||
|
||||
v := &gfP{} |
||||
gfpMul(v, u1, i) |
||||
|
||||
// t4 = 4(s2-s1)²
|
||||
t4, t6 := &gfP{}, &gfP{} |
||||
gfpMul(t4, r, r) |
||||
gfpAdd(t, v, v) |
||||
gfpSub(t6, t4, j) |
||||
|
||||
gfpSub(&c.x, t6, t) |
||||
|
||||
// Set y = -(2h)³(s1 + s*(x/4h²-u1))
|
||||
// This is also
|
||||
// y = - 2·s1·j - (s2-s1)(2x - 2i·u1) = r(v-x) - 2·s1·j
|
||||
gfpSub(t, v, &c.x) // t7
|
||||
gfpMul(t4, s1, j) // t8
|
||||
gfpAdd(t6, t4, t4) // t9
|
||||
gfpMul(t4, r, t) // t10
|
||||
gfpSub(&c.y, t4, t6) |
||||
|
||||
// Set z = 2(u2-u1)·z1·z2 = 2h·z1·z2
|
||||
gfpAdd(t, &a.z, &b.z) // t11
|
||||
gfpMul(t4, t, t) // t12
|
||||
gfpSub(t, t4, z12) // t13
|
||||
gfpSub(t4, t, z22) // t14
|
||||
gfpMul(&c.z, t4, h) |
||||
} |
||||
|
||||
func (c *curvePoint) Double(a *curvePoint) { |
||||
// See http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/doubling/dbl-2009-l.op3
|
||||
A, B, C := &gfP{}, &gfP{}, &gfP{} |
||||
gfpMul(A, &a.x, &a.x) |
||||
gfpMul(B, &a.y, &a.y) |
||||
gfpMul(C, B, B) |
||||
|
||||
t, t2 := &gfP{}, &gfP{} |
||||
gfpAdd(t, &a.x, B) |
||||
gfpMul(t2, t, t) |
||||
gfpSub(t, t2, A) |
||||
gfpSub(t2, t, C) |
||||
|
||||
d, e, f := &gfP{}, &gfP{}, &gfP{} |
||||
gfpAdd(d, t2, t2) |
||||
gfpAdd(t, A, A) |
||||
gfpAdd(e, t, A) |
||||
gfpMul(f, e, e) |
||||
|
||||
gfpAdd(t, d, d) |
||||
gfpSub(&c.x, f, t) |
||||
|
||||
gfpAdd(t, C, C) |
||||
gfpAdd(t2, t, t) |
||||
gfpAdd(t, t2, t2) |
||||
gfpSub(&c.y, d, &c.x) |
||||
gfpMul(t2, e, &c.y) |
||||
gfpSub(&c.y, t2, t) |
||||
|
||||
gfpMul(t, &a.y, &a.z) |
||||
gfpAdd(&c.z, t, t) |
||||
} |
||||
|
||||
func (c *curvePoint) Mul(a *curvePoint, scalar *big.Int) { |
||||
sum, t := &curvePoint{}, &curvePoint{} |
||||
sum.SetInfinity() |
||||
|
||||
for i := scalar.BitLen(); i >= 0; i-- { |
||||
t.Double(sum) |
||||
if scalar.Bit(i) != 0 { |
||||
sum.Add(t, a) |
||||
} else { |
||||
sum.Set(t) |
||||
} |
||||
} |
||||
c.Set(sum) |
||||
} |
||||
|
||||
func (c *curvePoint) MakeAffine() { |
||||
if c.z == *newGFp(1) { |
||||
return |
||||
} else if c.z == *newGFp(0) { |
||||
c.x = gfP{0} |
||||
c.y = *newGFp(1) |
||||
c.t = gfP{0} |
||||
return |
||||
} |
||||
|
||||
zInv := &gfP{} |
||||
zInv.Invert(&c.z) |
||||
|
||||
t, zInv2 := &gfP{}, &gfP{} |
||||
gfpMul(t, &c.y, zInv) |
||||
gfpMul(zInv2, zInv, zInv) |
||||
|
||||
gfpMul(&c.x, &c.x, zInv2) |
||||
gfpMul(&c.y, t, zInv2) |
||||
|
||||
c.z = *newGFp(1) |
||||
c.t = *newGFp(1) |
||||
} |
||||
|
||||
func (c *curvePoint) Neg(a *curvePoint) { |
||||
c.x.Set(&a.x) |
||||
gfpNeg(&c.y, &a.y) |
||||
c.z.Set(&a.z) |
||||
c.t = gfP{0} |
||||
} |
@ -0,0 +1,45 @@ |
||||
// Copyright 2012 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build amd64,!appengine,!gccgo
|
||||
|
||||
package bn256 |
||||
|
||||
import ( |
||||
"crypto/rand" |
||||
) |
||||
|
||||
func ExamplePair() { |
||||
// This implements the tripartite Diffie-Hellman algorithm from "A One
|
||||
// Round Protocol for Tripartite Diffie-Hellman", A. Joux.
|
||||
// http://www.springerlink.com/content/cddc57yyva0hburb/fulltext.pdf
|
||||
|
||||
// Each of three parties, a, b and c, generate a private value.
|
||||
a, _ := rand.Int(rand.Reader, Order) |
||||
b, _ := rand.Int(rand.Reader, Order) |
||||
c, _ := rand.Int(rand.Reader, Order) |
||||
|
||||
// Then each party calculates g₁ and g₂ times their private value.
|
||||
pa := new(G1).ScalarBaseMult(a) |
||||
qa := new(G2).ScalarBaseMult(a) |
||||
|
||||
pb := new(G1).ScalarBaseMult(b) |
||||
qb := new(G2).ScalarBaseMult(b) |
||||
|
||||
pc := new(G1).ScalarBaseMult(c) |
||||
qc := new(G2).ScalarBaseMult(c) |
||||
|
||||
// Now each party exchanges its public values with the other two and
|
||||
// all parties can calculate the shared key.
|
||||
k1 := Pair(pb, qc) |
||||
k1.ScalarMult(k1, a) |
||||
|
||||
k2 := Pair(pc, qa) |
||||
k2.ScalarMult(k2, b) |
||||
|
||||
k3 := Pair(pa, qb) |
||||
k3.ScalarMult(k3, c) |
||||
|
||||
// k1, k2 and k3 will all be equal.
|
||||
} |
@ -0,0 +1,81 @@ |
||||
package bn256 |
||||
|
||||
import ( |
||||
"errors" |
||||
"fmt" |
||||
) |
||||
|
||||
type gfP [4]uint64 |
||||
|
||||
func newGFp(x int64) (out *gfP) { |
||||
if x >= 0 { |
||||
out = &gfP{uint64(x)} |
||||
} else { |
||||
out = &gfP{uint64(-x)} |
||||
gfpNeg(out, out) |
||||
} |
||||
|
||||
montEncode(out, out) |
||||
return out |
||||
} |
||||
|
||||
func (e *gfP) String() string { |
||||
return fmt.Sprintf("%16.16x%16.16x%16.16x%16.16x", e[3], e[2], e[1], e[0]) |
||||
} |
||||
|
||||
func (e *gfP) Set(f *gfP) { |
||||
e[0] = f[0] |
||||
e[1] = f[1] |
||||
e[2] = f[2] |
||||
e[3] = f[3] |
||||
} |
||||
|
||||
func (e *gfP) Invert(f *gfP) { |
||||
bits := [4]uint64{0x3c208c16d87cfd45, 0x97816a916871ca8d, 0xb85045b68181585d, 0x30644e72e131a029} |
||||
|
||||
sum, power := &gfP{}, &gfP{} |
||||
sum.Set(rN1) |
||||
power.Set(f) |
||||
|
||||
for word := 0; word < 4; word++ { |
||||
for bit := uint(0); bit < 64; bit++ { |
||||
if (bits[word]>>bit)&1 == 1 { |
||||
gfpMul(sum, sum, power) |
||||
} |
||||
gfpMul(power, power, power) |
||||
} |
||||
} |
||||
|
||||
gfpMul(sum, sum, r3) |
||||
e.Set(sum) |
||||
} |
||||
|
||||
func (e *gfP) Marshal(out []byte) { |
||||
for w := uint(0); w < 4; w++ { |
||||
for b := uint(0); b < 8; b++ { |
||||
out[8*w+b] = byte(e[3-w] >> (56 - 8*b)) |
||||
} |
||||
} |
||||
} |
||||
|
||||
func (e *gfP) Unmarshal(in []byte) error { |
||||
// Unmarshal the bytes into little endian form
|
||||
for w := uint(0); w < 4; w++ { |
||||
for b := uint(0); b < 8; b++ { |
||||
e[3-w] += uint64(in[8*w+b]) << (56 - 8*b) |
||||
} |
||||
} |
||||
// Ensure the point respects the curve modulus
|
||||
for i := 3; i >= 0; i-- { |
||||
if e[i] < p2[i] { |
||||
return nil |
||||
} |
||||
if e[i] > p2[i] { |
||||
return errors.New("bn256: coordinate exceeds modulus") |
||||
} |
||||
} |
||||
return errors.New("bn256: coordinate equals modulus") |
||||
} |
||||
|
||||
func montEncode(c, a *gfP) { gfpMul(c, a, r2) } |
||||
func montDecode(c, a *gfP) { gfpMul(c, a, &gfP{1}) } |
@ -0,0 +1,32 @@ |
||||
#define storeBlock(a0,a1,a2,a3, r) \ |
||||
MOVQ a0, 0+r \
|
||||
MOVQ a1, 8+r \
|
||||
MOVQ a2, 16+r \
|
||||
MOVQ a3, 24+r |
||||
|
||||
#define loadBlock(r, a0,a1,a2,a3) \ |
||||
MOVQ 0+r, a0 \
|
||||
MOVQ 8+r, a1 \
|
||||
MOVQ 16+r, a2 \
|
||||
MOVQ 24+r, a3 |
||||
|
||||
#define gfpCarry(a0,a1,a2,a3,a4, b0,b1,b2,b3,b4) \ |
||||
\ // b = a-p
|
||||
MOVQ a0, b0 \
|
||||
MOVQ a1, b1 \
|
||||
MOVQ a2, b2 \
|
||||
MOVQ a3, b3 \
|
||||
MOVQ a4, b4 \
|
||||
\
|
||||
SUBQ ·p2+0(SB), b0 \
|
||||
SBBQ ·p2+8(SB), b1 \
|
||||
SBBQ ·p2+16(SB), b2 \
|
||||
SBBQ ·p2+24(SB), b3 \
|
||||
SBBQ $0, b4 \
|
||||
\
|
||||
\ // if b is negative then return a
|
||||
\ // else return b
|
||||
CMOVQCC b0, a0 \
|
||||
CMOVQCC b1, a1 \
|
||||
CMOVQCC b2, a2 \
|
||||
CMOVQCC b3, a3 |
@ -0,0 +1,160 @@ |
||||
package bn256 |
||||
|
||||
// For details of the algorithms used, see "Multiplication and Squaring on
|
||||
// Pairing-Friendly Fields, Devegili et al.
|
||||
// http://eprint.iacr.org/2006/471.pdf.
|
||||
|
||||
import ( |
||||
"math/big" |
||||
) |
||||
|
||||
// gfP12 implements the field of size p¹² as a quadratic extension of gfP6
|
||||
// where ω²=τ.
|
||||
type gfP12 struct { |
||||
x, y gfP6 // value is xω + y
|
||||
} |
||||
|
||||
func (e *gfP12) String() string { |
||||
return "(" + e.x.String() + "," + e.y.String() + ")" |
||||
} |
||||
|
||||
func (e *gfP12) Set(a *gfP12) *gfP12 { |
||||
e.x.Set(&a.x) |
||||
e.y.Set(&a.y) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP12) SetZero() *gfP12 { |
||||
e.x.SetZero() |
||||
e.y.SetZero() |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP12) SetOne() *gfP12 { |
||||
e.x.SetZero() |
||||
e.y.SetOne() |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP12) IsZero() bool { |
||||
return e.x.IsZero() && e.y.IsZero() |
||||
} |
||||
|
||||
func (e *gfP12) IsOne() bool { |
||||
return e.x.IsZero() && e.y.IsOne() |
||||
} |
||||
|
||||
func (e *gfP12) Conjugate(a *gfP12) *gfP12 { |
||||
e.x.Neg(&a.x) |
||||
e.y.Set(&a.y) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP12) Neg(a *gfP12) *gfP12 { |
||||
e.x.Neg(&a.x) |
||||
e.y.Neg(&a.y) |
||||
return e |
||||
} |
||||
|
||||
// Frobenius computes (xω+y)^p = x^p ω·ξ^((p-1)/6) + y^p
|
||||
func (e *gfP12) Frobenius(a *gfP12) *gfP12 { |
||||
e.x.Frobenius(&a.x) |
||||
e.y.Frobenius(&a.y) |
||||
e.x.MulScalar(&e.x, xiToPMinus1Over6) |
||||
return e |
||||
} |
||||
|
||||
// FrobeniusP2 computes (xω+y)^p² = x^p² ω·ξ^((p²-1)/6) + y^p²
|
||||
func (e *gfP12) FrobeniusP2(a *gfP12) *gfP12 { |
||||
e.x.FrobeniusP2(&a.x) |
||||
e.x.MulGFP(&e.x, xiToPSquaredMinus1Over6) |
||||
e.y.FrobeniusP2(&a.y) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP12) FrobeniusP4(a *gfP12) *gfP12 { |
||||
e.x.FrobeniusP4(&a.x) |
||||
e.x.MulGFP(&e.x, xiToPSquaredMinus1Over3) |
||||
e.y.FrobeniusP4(&a.y) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP12) Add(a, b *gfP12) *gfP12 { |
||||
e.x.Add(&a.x, &b.x) |
||||
e.y.Add(&a.y, &b.y) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP12) Sub(a, b *gfP12) *gfP12 { |
||||
e.x.Sub(&a.x, &b.x) |
||||
e.y.Sub(&a.y, &b.y) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP12) Mul(a, b *gfP12) *gfP12 { |
||||
tx := (&gfP6{}).Mul(&a.x, &b.y) |
||||
t := (&gfP6{}).Mul(&b.x, &a.y) |
||||
tx.Add(tx, t) |
||||
|
||||
ty := (&gfP6{}).Mul(&a.y, &b.y) |
||||
t.Mul(&a.x, &b.x).MulTau(t) |
||||
|
||||
e.x.Set(tx) |
||||
e.y.Add(ty, t) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP12) MulScalar(a *gfP12, b *gfP6) *gfP12 { |
||||
e.x.Mul(&e.x, b) |
||||
e.y.Mul(&e.y, b) |
||||
return e |
||||
} |
||||
|
||||
func (c *gfP12) Exp(a *gfP12, power *big.Int) *gfP12 { |
||||
sum := (&gfP12{}).SetOne() |
||||
t := &gfP12{} |
||||
|
||||
for i := power.BitLen() - 1; i >= 0; i-- { |
||||
t.Square(sum) |
||||
if power.Bit(i) != 0 { |
||||
sum.Mul(t, a) |
||||
} else { |
||||
sum.Set(t) |
||||
} |
||||
} |
||||
|
||||
c.Set(sum) |
||||
return c |
||||
} |
||||
|
||||
func (e *gfP12) Square(a *gfP12) *gfP12 { |
||||
// Complex squaring algorithm
|
||||
v0 := (&gfP6{}).Mul(&a.x, &a.y) |
||||
|
||||
t := (&gfP6{}).MulTau(&a.x) |
||||
t.Add(&a.y, t) |
||||
ty := (&gfP6{}).Add(&a.x, &a.y) |
||||
ty.Mul(ty, t).Sub(ty, v0) |
||||
t.MulTau(v0) |
||||
ty.Sub(ty, t) |
||||
|
||||
e.x.Add(v0, v0) |
||||
e.y.Set(ty) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP12) Invert(a *gfP12) *gfP12 { |
||||
// See "Implementing cryptographic pairings", M. Scott, section 3.2.
|
||||
// ftp://136.206.11.249/pub/crypto/pairings.pdf
|
||||
t1, t2 := &gfP6{}, &gfP6{} |
||||
|
||||
t1.Square(&a.x) |
||||
t2.Square(&a.y) |
||||
t1.MulTau(t1).Sub(t2, t1) |
||||
t2.Invert(t1) |
||||
|
||||
e.x.Neg(&a.x) |
||||
e.y.Set(&a.y) |
||||
e.MulScalar(e, t2) |
||||
return e |
||||
} |
@ -0,0 +1,156 @@ |
||||
package bn256 |
||||
|
||||
// For details of the algorithms used, see "Multiplication and Squaring on
|
||||
// Pairing-Friendly Fields, Devegili et al.
|
||||
// http://eprint.iacr.org/2006/471.pdf.
|
||||
|
||||
// gfP2 implements a field of size p² as a quadratic extension of the base field
|
||||
// where i²=-1.
|
||||
type gfP2 struct { |
||||
x, y gfP // value is xi+y.
|
||||
} |
||||
|
||||
func gfP2Decode(in *gfP2) *gfP2 { |
||||
out := &gfP2{} |
||||
montDecode(&out.x, &in.x) |
||||
montDecode(&out.y, &in.y) |
||||
return out |
||||
} |
||||
|
||||
func (e *gfP2) String() string { |
||||
return "(" + e.x.String() + ", " + e.y.String() + ")" |
||||
} |
||||
|
||||
func (e *gfP2) Set(a *gfP2) *gfP2 { |
||||
e.x.Set(&a.x) |
||||
e.y.Set(&a.y) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP2) SetZero() *gfP2 { |
||||
e.x = gfP{0} |
||||
e.y = gfP{0} |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP2) SetOne() *gfP2 { |
||||
e.x = gfP{0} |
||||
e.y = *newGFp(1) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP2) IsZero() bool { |
||||
zero := gfP{0} |
||||
return e.x == zero && e.y == zero |
||||
} |
||||
|
||||
func (e *gfP2) IsOne() bool { |
||||
zero, one := gfP{0}, *newGFp(1) |
||||
return e.x == zero && e.y == one |
||||
} |
||||
|
||||
func (e *gfP2) Conjugate(a *gfP2) *gfP2 { |
||||
e.y.Set(&a.y) |
||||
gfpNeg(&e.x, &a.x) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP2) Neg(a *gfP2) *gfP2 { |
||||
gfpNeg(&e.x, &a.x) |
||||
gfpNeg(&e.y, &a.y) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP2) Add(a, b *gfP2) *gfP2 { |
||||
gfpAdd(&e.x, &a.x, &b.x) |
||||
gfpAdd(&e.y, &a.y, &b.y) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP2) Sub(a, b *gfP2) *gfP2 { |
||||
gfpSub(&e.x, &a.x, &b.x) |
||||
gfpSub(&e.y, &a.y, &b.y) |
||||
return e |
||||
} |
||||
|
||||
// See "Multiplication and Squaring in Pairing-Friendly Fields",
|
||||
// http://eprint.iacr.org/2006/471.pdf
|
||||
func (e *gfP2) Mul(a, b *gfP2) *gfP2 { |
||||
tx, t := &gfP{}, &gfP{} |
||||
gfpMul(tx, &a.x, &b.y) |
||||
gfpMul(t, &b.x, &a.y) |
||||
gfpAdd(tx, tx, t) |
||||
|
||||
ty := &gfP{} |
||||
gfpMul(ty, &a.y, &b.y) |
||||
gfpMul(t, &a.x, &b.x) |
||||
gfpSub(ty, ty, t) |
||||
|
||||
e.x.Set(tx) |
||||
e.y.Set(ty) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP2) MulScalar(a *gfP2, b *gfP) *gfP2 { |
||||
gfpMul(&e.x, &a.x, b) |
||||
gfpMul(&e.y, &a.y, b) |
||||
return e |
||||
} |
||||
|
||||
// MulXi sets e=ξa where ξ=i+9 and then returns e.
|
||||
func (e *gfP2) MulXi(a *gfP2) *gfP2 { |
||||
// (xi+y)(i+9) = (9x+y)i+(9y-x)
|
||||
tx := &gfP{} |
||||
gfpAdd(tx, &a.x, &a.x) |
||||
gfpAdd(tx, tx, tx) |
||||
gfpAdd(tx, tx, tx) |
||||
gfpAdd(tx, tx, &a.x) |
||||
|
||||
gfpAdd(tx, tx, &a.y) |
||||
|
||||
ty := &gfP{} |
||||
gfpAdd(ty, &a.y, &a.y) |
||||
gfpAdd(ty, ty, ty) |
||||
gfpAdd(ty, ty, ty) |
||||
gfpAdd(ty, ty, &a.y) |
||||
|
||||
gfpSub(ty, ty, &a.x) |
||||
|
||||
e.x.Set(tx) |
||||
e.y.Set(ty) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP2) Square(a *gfP2) *gfP2 { |
||||
// Complex squaring algorithm:
|
||||
// (xi+y)² = (x+y)(y-x) + 2*i*x*y
|
||||
tx, ty := &gfP{}, &gfP{} |
||||
gfpSub(tx, &a.y, &a.x) |
||||
gfpAdd(ty, &a.x, &a.y) |
||||
gfpMul(ty, tx, ty) |
||||
|
||||
gfpMul(tx, &a.x, &a.y) |
||||
gfpAdd(tx, tx, tx) |
||||
|
||||
e.x.Set(tx) |
||||
e.y.Set(ty) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP2) Invert(a *gfP2) *gfP2 { |
||||
// See "Implementing cryptographic pairings", M. Scott, section 3.2.
|
||||
// ftp://136.206.11.249/pub/crypto/pairings.pdf
|
||||
t1, t2 := &gfP{}, &gfP{} |
||||
gfpMul(t1, &a.x, &a.x) |
||||
gfpMul(t2, &a.y, &a.y) |
||||
gfpAdd(t1, t1, t2) |
||||
|
||||
inv := &gfP{} |
||||
inv.Invert(t1) |
||||
|
||||
gfpNeg(t1, &a.x) |
||||
|
||||
gfpMul(&e.x, t1, inv) |
||||
gfpMul(&e.y, &a.y, inv) |
||||
return e |
||||
} |
@ -0,0 +1,213 @@ |
||||
package bn256 |
||||
|
||||
// For details of the algorithms used, see "Multiplication and Squaring on
|
||||
// Pairing-Friendly Fields, Devegili et al.
|
||||
// http://eprint.iacr.org/2006/471.pdf.
|
||||
|
||||
// gfP6 implements the field of size p⁶ as a cubic extension of gfP2 where τ³=ξ
|
||||
// and ξ=i+3.
|
||||
type gfP6 struct { |
||||
x, y, z gfP2 // value is xτ² + yτ + z
|
||||
} |
||||
|
||||
func (e *gfP6) String() string { |
||||
return "(" + e.x.String() + ", " + e.y.String() + ", " + e.z.String() + ")" |
||||
} |
||||
|
||||
func (e *gfP6) Set(a *gfP6) *gfP6 { |
||||
e.x.Set(&a.x) |
||||
e.y.Set(&a.y) |
||||
e.z.Set(&a.z) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP6) SetZero() *gfP6 { |
||||
e.x.SetZero() |
||||
e.y.SetZero() |
||||
e.z.SetZero() |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP6) SetOne() *gfP6 { |
||||
e.x.SetZero() |
||||
e.y.SetZero() |
||||
e.z.SetOne() |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP6) IsZero() bool { |
||||
return e.x.IsZero() && e.y.IsZero() && e.z.IsZero() |
||||
} |
||||
|
||||
func (e *gfP6) IsOne() bool { |
||||
return e.x.IsZero() && e.y.IsZero() && e.z.IsOne() |
||||
} |
||||
|
||||
func (e *gfP6) Neg(a *gfP6) *gfP6 { |
||||
e.x.Neg(&a.x) |
||||
e.y.Neg(&a.y) |
||||
e.z.Neg(&a.z) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP6) Frobenius(a *gfP6) *gfP6 { |
||||
e.x.Conjugate(&a.x) |
||||
e.y.Conjugate(&a.y) |
||||
e.z.Conjugate(&a.z) |
||||
|
||||
e.x.Mul(&e.x, xiTo2PMinus2Over3) |
||||
e.y.Mul(&e.y, xiToPMinus1Over3) |
||||
return e |
||||
} |
||||
|
||||
// FrobeniusP2 computes (xτ²+yτ+z)^(p²) = xτ^(2p²) + yτ^(p²) + z
|
||||
func (e *gfP6) FrobeniusP2(a *gfP6) *gfP6 { |
||||
// τ^(2p²) = τ²τ^(2p²-2) = τ²ξ^((2p²-2)/3)
|
||||
e.x.MulScalar(&a.x, xiTo2PSquaredMinus2Over3) |
||||
// τ^(p²) = ττ^(p²-1) = τξ^((p²-1)/3)
|
||||
e.y.MulScalar(&a.y, xiToPSquaredMinus1Over3) |
||||
e.z.Set(&a.z) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP6) FrobeniusP4(a *gfP6) *gfP6 { |
||||
e.x.MulScalar(&a.x, xiToPSquaredMinus1Over3) |
||||
e.y.MulScalar(&a.y, xiTo2PSquaredMinus2Over3) |
||||
e.z.Set(&a.z) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP6) Add(a, b *gfP6) *gfP6 { |
||||
e.x.Add(&a.x, &b.x) |
||||
e.y.Add(&a.y, &b.y) |
||||
e.z.Add(&a.z, &b.z) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP6) Sub(a, b *gfP6) *gfP6 { |
||||
e.x.Sub(&a.x, &b.x) |
||||
e.y.Sub(&a.y, &b.y) |
||||
e.z.Sub(&a.z, &b.z) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP6) Mul(a, b *gfP6) *gfP6 { |
||||
// "Multiplication and Squaring on Pairing-Friendly Fields"
|
||||
// Section 4, Karatsuba method.
|
||||
// http://eprint.iacr.org/2006/471.pdf
|
||||
v0 := (&gfP2{}).Mul(&a.z, &b.z) |
||||
v1 := (&gfP2{}).Mul(&a.y, &b.y) |
||||
v2 := (&gfP2{}).Mul(&a.x, &b.x) |
||||
|
||||
t0 := (&gfP2{}).Add(&a.x, &a.y) |
||||
t1 := (&gfP2{}).Add(&b.x, &b.y) |
||||
tz := (&gfP2{}).Mul(t0, t1) |
||||
tz.Sub(tz, v1).Sub(tz, v2).MulXi(tz).Add(tz, v0) |
||||
|
||||
t0.Add(&a.y, &a.z) |
||||
t1.Add(&b.y, &b.z) |
||||
ty := (&gfP2{}).Mul(t0, t1) |
||||
t0.MulXi(v2) |
||||
ty.Sub(ty, v0).Sub(ty, v1).Add(ty, t0) |
||||
|
||||
t0.Add(&a.x, &a.z) |
||||
t1.Add(&b.x, &b.z) |
||||
tx := (&gfP2{}).Mul(t0, t1) |
||||
tx.Sub(tx, v0).Add(tx, v1).Sub(tx, v2) |
||||
|
||||
e.x.Set(tx) |
||||
e.y.Set(ty) |
||||
e.z.Set(tz) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP6) MulScalar(a *gfP6, b *gfP2) *gfP6 { |
||||
e.x.Mul(&a.x, b) |
||||
e.y.Mul(&a.y, b) |
||||
e.z.Mul(&a.z, b) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP6) MulGFP(a *gfP6, b *gfP) *gfP6 { |
||||
e.x.MulScalar(&a.x, b) |
||||
e.y.MulScalar(&a.y, b) |
||||
e.z.MulScalar(&a.z, b) |
||||
return e |
||||
} |
||||
|
||||
// MulTau computes τ·(aτ²+bτ+c) = bτ²+cτ+aξ
|
||||
func (e *gfP6) MulTau(a *gfP6) *gfP6 { |
||||
tz := (&gfP2{}).MulXi(&a.x) |
||||
ty := (&gfP2{}).Set(&a.y) |
||||
|
||||
e.y.Set(&a.z) |
||||
e.x.Set(ty) |
||||
e.z.Set(tz) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP6) Square(a *gfP6) *gfP6 { |
||||
v0 := (&gfP2{}).Square(&a.z) |
||||
v1 := (&gfP2{}).Square(&a.y) |
||||
v2 := (&gfP2{}).Square(&a.x) |
||||
|
||||
c0 := (&gfP2{}).Add(&a.x, &a.y) |
||||
c0.Square(c0).Sub(c0, v1).Sub(c0, v2).MulXi(c0).Add(c0, v0) |
||||
|
||||
c1 := (&gfP2{}).Add(&a.y, &a.z) |
||||
c1.Square(c1).Sub(c1, v0).Sub(c1, v1) |
||||
xiV2 := (&gfP2{}).MulXi(v2) |
||||
c1.Add(c1, xiV2) |
||||
|
||||
c2 := (&gfP2{}).Add(&a.x, &a.z) |
||||
c2.Square(c2).Sub(c2, v0).Add(c2, v1).Sub(c2, v2) |
||||
|
||||
e.x.Set(c2) |
||||
e.y.Set(c1) |
||||
e.z.Set(c0) |
||||
return e |
||||
} |
||||
|
||||
func (e *gfP6) Invert(a *gfP6) *gfP6 { |
||||
// See "Implementing cryptographic pairings", M. Scott, section 3.2.
|
||||
// ftp://136.206.11.249/pub/crypto/pairings.pdf
|
||||
|
||||
// Here we can give a short explanation of how it works: let j be a cubic root of
|
||||
// unity in GF(p²) so that 1+j+j²=0.
|
||||
// Then (xτ² + yτ + z)(xj²τ² + yjτ + z)(xjτ² + yj²τ + z)
|
||||
// = (xτ² + yτ + z)(Cτ²+Bτ+A)
|
||||
// = (x³ξ²+y³ξ+z³-3ξxyz) = F is an element of the base field (the norm).
|
||||
//
|
||||
// On the other hand (xj²τ² + yjτ + z)(xjτ² + yj²τ + z)
|
||||
// = τ²(y²-ξxz) + τ(ξx²-yz) + (z²-ξxy)
|
||||
//
|
||||
// So that's why A = (z²-ξxy), B = (ξx²-yz), C = (y²-ξxz)
|
||||
t1 := (&gfP2{}).Mul(&a.x, &a.y) |
||||
t1.MulXi(t1) |
||||
|
||||
A := (&gfP2{}).Square(&a.z) |
||||
A.Sub(A, t1) |
||||
|
||||
B := (&gfP2{}).Square(&a.x) |
||||
B.MulXi(B) |
||||
t1.Mul(&a.y, &a.z) |
||||
B.Sub(B, t1) |
||||
|
||||
C := (&gfP2{}).Square(&a.y) |
||||
t1.Mul(&a.x, &a.z) |
||||
C.Sub(C, t1) |
||||
|
||||
F := (&gfP2{}).Mul(C, &a.y) |
||||
F.MulXi(F) |
||||
t1.Mul(A, &a.z) |
||||
F.Add(F, t1) |
||||
t1.Mul(B, &a.x).MulXi(t1) |
||||
F.Add(F, t1) |
||||
|
||||
F.Invert(F) |
||||
|
||||
e.x.Mul(C, F) |
||||
e.y.Mul(B, F) |
||||
e.z.Mul(A, F) |
||||
return e |
||||
} |
@ -0,0 +1,15 @@ |
||||
// +build amd64,!appengine,!gccgo
|
||||
|
||||
package bn256 |
||||
|
||||
// go:noescape
|
||||
func gfpNeg(c, a *gfP) |
||||
|
||||
//go:noescape
|
||||
func gfpAdd(c, a, b *gfP) |
||||
|
||||
//go:noescape
|
||||
func gfpSub(c, a, b *gfP) |
||||
|
||||
//go:noescape
|
||||
func gfpMul(c, a, b *gfP) |
@ -0,0 +1,97 @@ |
||||
// +build amd64,!appengine,!gccgo |
||||
|
||||
#include "gfp.h" |
||||
#include "mul.h" |
||||
#include "mul_bmi2.h" |
||||
|
||||
TEXT ·gfpNeg(SB),0,$0-16 |
||||
MOVQ ·p2+0(SB), R8 |
||||
MOVQ ·p2+8(SB), R9 |
||||
MOVQ ·p2+16(SB), R10 |
||||
MOVQ ·p2+24(SB), R11 |
||||
|
||||
MOVQ a+8(FP), DI |
||||
SUBQ 0(DI), R8 |
||||
SBBQ 8(DI), R9 |
||||
SBBQ 16(DI), R10 |
||||
SBBQ 24(DI), R11 |
||||
|
||||
MOVQ $0, AX |
||||
gfpCarry(R8,R9,R10,R11,AX, R12,R13,R14,R15,BX) |
||||
|
||||
MOVQ c+0(FP), DI |
||||
storeBlock(R8,R9,R10,R11, 0(DI)) |
||||
RET |
||||
|
||||
TEXT ·gfpAdd(SB),0,$0-24 |
||||
MOVQ a+8(FP), DI |
||||
MOVQ b+16(FP), SI |
||||
|
||||
loadBlock(0(DI), R8,R9,R10,R11) |
||||
MOVQ $0, R12 |
||||
|
||||
ADDQ 0(SI), R8 |
||||
ADCQ 8(SI), R9 |
||||
ADCQ 16(SI), R10 |
||||
ADCQ 24(SI), R11 |
||||
ADCQ $0, R12 |
||||
|
||||
gfpCarry(R8,R9,R10,R11,R12, R13,R14,R15,AX,BX) |
||||
|
||||
MOVQ c+0(FP), DI |
||||
storeBlock(R8,R9,R10,R11, 0(DI)) |
||||
RET |
||||
|
||||
TEXT ·gfpSub(SB),0,$0-24 |
||||
MOVQ a+8(FP), DI |
||||
MOVQ b+16(FP), SI |
||||
|
||||
loadBlock(0(DI), R8,R9,R10,R11) |
||||
|
||||
MOVQ ·p2+0(SB), R12 |
||||
MOVQ ·p2+8(SB), R13 |
||||
MOVQ ·p2+16(SB), R14 |
||||
MOVQ ·p2+24(SB), R15 |
||||
MOVQ $0, AX |
||||
|
||||
SUBQ 0(SI), R8 |
||||
SBBQ 8(SI), R9 |
||||
SBBQ 16(SI), R10 |
||||
SBBQ 24(SI), R11 |
||||
|
||||
CMOVQCC AX, R12 |
||||
CMOVQCC AX, R13 |
||||
CMOVQCC AX, R14 |
||||
CMOVQCC AX, R15 |
||||
|
||||
ADDQ R12, R8 |
||||
ADCQ R13, R9 |
||||
ADCQ R14, R10 |
||||
ADCQ R15, R11 |
||||
|
||||
MOVQ c+0(FP), DI |
||||
storeBlock(R8,R9,R10,R11, 0(DI)) |
||||
RET |
||||
|
||||
TEXT ·gfpMul(SB),0,$160-24 |
||||
MOVQ a+8(FP), DI |
||||
MOVQ b+16(FP), SI |
||||
|
||||
// Jump to a slightly different implementation if MULX isn't supported. |
||||
CMPB runtime·support_bmi2(SB), $0 |
||||
JE nobmi2Mul |
||||
|
||||
mulBMI2(0(DI),8(DI),16(DI),24(DI), 0(SI)) |
||||
storeBlock( R8, R9,R10,R11, 0(SP)) |
||||
storeBlock(R12,R13,R14,R15, 32(SP)) |
||||
gfpReduceBMI2() |
||||
JMP end |
||||
|
||||
nobmi2Mul: |
||||
mul(0(DI),8(DI),16(DI),24(DI), 0(SI), 0(SP)) |
||||
gfpReduce(0(SP)) |
||||
|
||||
end: |
||||
MOVQ c+0(FP), DI |
||||
storeBlock(R12,R13,R14,R15, 0(DI)) |
||||
RET |
@ -0,0 +1,19 @@ |
||||
// +build !amd64 appengine gccgo
|
||||
|
||||
package bn256 |
||||
|
||||
func gfpNeg(c, a *gfP) { |
||||
panic("unsupported architecture") |
||||
} |
||||
|
||||
func gfpAdd(c, a, b *gfP) { |
||||
panic("unsupported architecture") |
||||
} |
||||
|
||||
func gfpSub(c, a, b *gfP) { |
||||
panic("unsupported architecture") |
||||
} |
||||
|
||||
func gfpMul(c, a, b *gfP) { |
||||
panic("unsupported architecture") |
||||
} |
@ -0,0 +1,62 @@ |
||||
// +build amd64,!appengine,!gccgo
|
||||
|
||||
package bn256 |
||||
|
||||
import ( |
||||
"testing" |
||||
) |
||||
|
||||
// Tests that negation works the same way on both assembly-optimized and pure Go
|
||||
// implementation.
|
||||
func TestGFpNeg(t *testing.T) { |
||||
n := &gfP{0x0123456789abcdef, 0xfedcba9876543210, 0xdeadbeefdeadbeef, 0xfeebdaedfeebdaed} |
||||
w := &gfP{0xfedcba9876543211, 0x0123456789abcdef, 0x2152411021524110, 0x0114251201142512} |
||||
h := &gfP{} |
||||
|
||||
gfpNeg(h, n) |
||||
if *h != *w { |
||||
t.Errorf("negation mismatch: have %#x, want %#x", *h, *w) |
||||
} |
||||
} |
||||
|
||||
// Tests that addition works the same way on both assembly-optimized and pure Go
|
||||
// implementation.
|
||||
func TestGFpAdd(t *testing.T) { |
||||
a := &gfP{0x0123456789abcdef, 0xfedcba9876543210, 0xdeadbeefdeadbeef, 0xfeebdaedfeebdaed} |
||||
b := &gfP{0xfedcba9876543210, 0x0123456789abcdef, 0xfeebdaedfeebdaed, 0xdeadbeefdeadbeef} |
||||
w := &gfP{0xc3df73e9278302b8, 0x687e956e978e3572, 0x254954275c18417f, 0xad354b6afc67f9b4} |
||||
h := &gfP{} |
||||
|
||||
gfpAdd(h, a, b) |
||||
if *h != *w { |
||||
t.Errorf("addition mismatch: have %#x, want %#x", *h, *w) |
||||
} |
||||
} |
||||
|
||||
// Tests that subtraction works the same way on both assembly-optimized and pure Go
|
||||
// implementation.
|
||||
func TestGFpSub(t *testing.T) { |
||||
a := &gfP{0x0123456789abcdef, 0xfedcba9876543210, 0xdeadbeefdeadbeef, 0xfeebdaedfeebdaed} |
||||
b := &gfP{0xfedcba9876543210, 0x0123456789abcdef, 0xfeebdaedfeebdaed, 0xdeadbeefdeadbeef} |
||||
w := &gfP{0x02468acf13579bdf, 0xfdb97530eca86420, 0xdfc1e401dfc1e402, 0x203e1bfe203e1bfd} |
||||
h := &gfP{} |
||||
|
||||
gfpSub(h, a, b) |
||||
if *h != *w { |
||||
t.Errorf("subtraction mismatch: have %#x, want %#x", *h, *w) |
||||
} |
||||
} |
||||
|
||||
// Tests that multiplication works the same way on both assembly-optimized and pure Go
|
||||
// implementation.
|
||||
func TestGFpMul(t *testing.T) { |
||||
a := &gfP{0x0123456789abcdef, 0xfedcba9876543210, 0xdeadbeefdeadbeef, 0xfeebdaedfeebdaed} |
||||
b := &gfP{0xfedcba9876543210, 0x0123456789abcdef, 0xfeebdaedfeebdaed, 0xdeadbeefdeadbeef} |
||||
w := &gfP{0xcbcbd377f7ad22d3, 0x3b89ba5d849379bf, 0x87b61627bd38b6d2, 0xc44052a2a0e654b2} |
||||
h := &gfP{} |
||||
|
||||
gfpMul(h, a, b) |
||||
if *h != *w { |
||||
t.Errorf("multiplication mismatch: have %#x, want %#x", *h, *w) |
||||
} |
||||
} |
@ -0,0 +1,73 @@ |
||||
// +build amd64,!appengine,!gccgo
|
||||
|
||||
package bn256 |
||||
|
||||
import ( |
||||
"testing" |
||||
|
||||
"crypto/rand" |
||||
) |
||||
|
||||
func TestRandomG2Marshal(t *testing.T) { |
||||
for i := 0; i < 10; i++ { |
||||
n, g2, err := RandomG2(rand.Reader) |
||||
if err != nil { |
||||
t.Error(err) |
||||
continue |
||||
} |
||||
t.Logf("%d: %x\n", n, g2.Marshal()) |
||||
} |
||||
} |
||||
|
||||
func TestPairings(t *testing.T) { |
||||
a1 := new(G1).ScalarBaseMult(bigFromBase10("1")) |
||||
a2 := new(G1).ScalarBaseMult(bigFromBase10("2")) |
||||
a37 := new(G1).ScalarBaseMult(bigFromBase10("37")) |
||||
an1 := new(G1).ScalarBaseMult(bigFromBase10("21888242871839275222246405745257275088548364400416034343698204186575808495616")) |
||||
|
||||
b0 := new(G2).ScalarBaseMult(bigFromBase10("0")) |
||||
b1 := new(G2).ScalarBaseMult(bigFromBase10("1")) |
||||
b2 := new(G2).ScalarBaseMult(bigFromBase10("2")) |
||||
b27 := new(G2).ScalarBaseMult(bigFromBase10("27")) |
||||
b999 := new(G2).ScalarBaseMult(bigFromBase10("999")) |
||||
bn1 := new(G2).ScalarBaseMult(bigFromBase10("21888242871839275222246405745257275088548364400416034343698204186575808495616")) |
||||
|
||||
p1 := Pair(a1, b1) |
||||
pn1 := Pair(a1, bn1) |
||||
np1 := Pair(an1, b1) |
||||
if pn1.String() != np1.String() { |
||||
t.Error("Pairing mismatch: e(a, -b) != e(-a, b)") |
||||
} |
||||
if !PairingCheck([]*G1{a1, an1}, []*G2{b1, b1}) { |
||||
t.Error("MultiAte check gave false negative!") |
||||
} |
||||
p0 := new(GT).Add(p1, pn1) |
||||
p0_2 := Pair(a1, b0) |
||||
if p0.String() != p0_2.String() { |
||||
t.Error("Pairing mismatch: e(a, b) * e(a, -b) != 1") |
||||
} |
||||
p0_3 := new(GT).ScalarMult(p1, bigFromBase10("21888242871839275222246405745257275088548364400416034343698204186575808495617")) |
||||
if p0.String() != p0_3.String() { |
||||
t.Error("Pairing mismatch: e(a, b) has wrong order") |
||||
} |
||||
p2 := Pair(a2, b1) |
||||
p2_2 := Pair(a1, b2) |
||||
p2_3 := new(GT).ScalarMult(p1, bigFromBase10("2")) |
||||
if p2.String() != p2_2.String() { |
||||
t.Error("Pairing mismatch: e(a, b * 2) != e(a * 2, b)") |
||||
} |
||||
if p2.String() != p2_3.String() { |
||||
t.Error("Pairing mismatch: e(a, b * 2) != e(a, b) ** 2") |
||||
} |
||||
if p2.String() == p1.String() { |
||||
t.Error("Pairing is degenerate!") |
||||
} |
||||
if PairingCheck([]*G1{a1, a1}, []*G2{b1, b1}) { |
||||
t.Error("MultiAte check gave false positive!") |
||||
} |
||||
p999 := Pair(a37, b27) |
||||
p999_2 := Pair(a1, b999) |
||||
if p999.String() != p999_2.String() { |
||||
t.Error("Pairing mismatch: e(a * 37, b * 27) != e(a, b * 999)") |
||||
} |
||||
} |
@ -0,0 +1,181 @@ |
||||
#define mul(a0,a1,a2,a3, rb, stack) \ |
||||
MOVQ a0, AX \
|
||||
MULQ 0+rb \
|
||||
MOVQ AX, R8 \
|
||||
MOVQ DX, R9 \
|
||||
MOVQ a0, AX \
|
||||
MULQ 8+rb \
|
||||
ADDQ AX, R9 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R10 \
|
||||
MOVQ a0, AX \
|
||||
MULQ 16+rb \
|
||||
ADDQ AX, R10 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R11 \
|
||||
MOVQ a0, AX \
|
||||
MULQ 24+rb \
|
||||
ADDQ AX, R11 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R12 \
|
||||
\
|
||||
storeBlock(R8,R9,R10,R11, 0+stack) \
|
||||
MOVQ R12, 32+stack \
|
||||
\
|
||||
MOVQ a1, AX \
|
||||
MULQ 0+rb \
|
||||
MOVQ AX, R8 \
|
||||
MOVQ DX, R9 \
|
||||
MOVQ a1, AX \
|
||||
MULQ 8+rb \
|
||||
ADDQ AX, R9 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R10 \
|
||||
MOVQ a1, AX \
|
||||
MULQ 16+rb \
|
||||
ADDQ AX, R10 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R11 \
|
||||
MOVQ a1, AX \
|
||||
MULQ 24+rb \
|
||||
ADDQ AX, R11 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R12 \
|
||||
\
|
||||
ADDQ 8+stack, R8 \
|
||||
ADCQ 16+stack, R9 \
|
||||
ADCQ 24+stack, R10 \
|
||||
ADCQ 32+stack, R11 \
|
||||
ADCQ $0, R12 \
|
||||
storeBlock(R8,R9,R10,R11, 8+stack) \
|
||||
MOVQ R12, 40+stack \
|
||||
\
|
||||
MOVQ a2, AX \
|
||||
MULQ 0+rb \
|
||||
MOVQ AX, R8 \
|
||||
MOVQ DX, R9 \
|
||||
MOVQ a2, AX \
|
||||
MULQ 8+rb \
|
||||
ADDQ AX, R9 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R10 \
|
||||
MOVQ a2, AX \
|
||||
MULQ 16+rb \
|
||||
ADDQ AX, R10 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R11 \
|
||||
MOVQ a2, AX \
|
||||
MULQ 24+rb \
|
||||
ADDQ AX, R11 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R12 \
|
||||
\
|
||||
ADDQ 16+stack, R8 \
|
||||
ADCQ 24+stack, R9 \
|
||||
ADCQ 32+stack, R10 \
|
||||
ADCQ 40+stack, R11 \
|
||||
ADCQ $0, R12 \
|
||||
storeBlock(R8,R9,R10,R11, 16+stack) \
|
||||
MOVQ R12, 48+stack \
|
||||
\
|
||||
MOVQ a3, AX \
|
||||
MULQ 0+rb \
|
||||
MOVQ AX, R8 \
|
||||
MOVQ DX, R9 \
|
||||
MOVQ a3, AX \
|
||||
MULQ 8+rb \
|
||||
ADDQ AX, R9 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R10 \
|
||||
MOVQ a3, AX \
|
||||
MULQ 16+rb \
|
||||
ADDQ AX, R10 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R11 \
|
||||
MOVQ a3, AX \
|
||||
MULQ 24+rb \
|
||||
ADDQ AX, R11 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R12 \
|
||||
\
|
||||
ADDQ 24+stack, R8 \
|
||||
ADCQ 32+stack, R9 \
|
||||
ADCQ 40+stack, R10 \
|
||||
ADCQ 48+stack, R11 \
|
||||
ADCQ $0, R12 \
|
||||
storeBlock(R8,R9,R10,R11, 24+stack) \
|
||||
MOVQ R12, 56+stack |
||||
|
||||
#define gfpReduce(stack) \ |
||||
\ // m = (T * N') mod R, store m in R8:R9:R10:R11
|
||||
MOVQ ·np+0(SB), AX \
|
||||
MULQ 0+stack \
|
||||
MOVQ AX, R8 \
|
||||
MOVQ DX, R9 \
|
||||
MOVQ ·np+0(SB), AX \
|
||||
MULQ 8+stack \
|
||||
ADDQ AX, R9 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R10 \
|
||||
MOVQ ·np+0(SB), AX \
|
||||
MULQ 16+stack \
|
||||
ADDQ AX, R10 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R11 \
|
||||
MOVQ ·np+0(SB), AX \
|
||||
MULQ 24+stack \
|
||||
ADDQ AX, R11 \
|
||||
\
|
||||
MOVQ ·np+8(SB), AX \
|
||||
MULQ 0+stack \
|
||||
MOVQ AX, R12 \
|
||||
MOVQ DX, R13 \
|
||||
MOVQ ·np+8(SB), AX \
|
||||
MULQ 8+stack \
|
||||
ADDQ AX, R13 \
|
||||
ADCQ $0, DX \
|
||||
MOVQ DX, R14 \
|
||||
MOVQ ·np+8(SB), AX \
|
||||
MULQ 16+stack \
|
||||
ADDQ AX, R14 \
|
||||
\
|
||||
ADDQ R12, R9 \
|
||||
ADCQ R13, R10 \
|
||||
ADCQ R14, R11 \
|
||||
\
|
||||
MOVQ ·np+16(SB), AX \
|
||||
MULQ 0+stack \
|
||||
MOVQ AX, R12 \
|
||||
MOVQ DX, R13 \
|
||||
MOVQ ·np+16(SB), AX \
|
||||
MULQ 8+stack \
|
||||
ADDQ AX, R13 \
|
||||
\
|
||||
ADDQ R12, R10 \
|
||||
ADCQ R13, R11 \
|
||||
\
|
||||
MOVQ ·np+24(SB), AX \
|
||||
MULQ 0+stack \
|
||||
ADDQ AX, R11 \
|
||||
\
|
||||
storeBlock(R8,R9,R10,R11, 64+stack) \
|
||||
\
|
||||
\ // m * N
|
||||
mul(·p2+0(SB),·p2+8(SB),·p2+16(SB),·p2+24(SB), 64+stack, 96+stack) \
|
||||
\
|
||||
\ // Add the 512-bit intermediate to m*N
|
||||
loadBlock(96+stack, R8,R9,R10,R11) \
|
||||
loadBlock(128+stack, R12,R13,R14,R15) \
|
||||
\
|
||||
MOVQ $0, AX \
|
||||
ADDQ 0+stack, R8 \
|
||||
ADCQ 8+stack, R9 \
|
||||
ADCQ 16+stack, R10 \
|
||||
ADCQ 24+stack, R11 \
|
||||
ADCQ 32+stack, R12 \
|
||||
ADCQ 40+stack, R13 \
|
||||
ADCQ 48+stack, R14 \
|
||||
ADCQ 56+stack, R15 \
|
||||
ADCQ $0, AX \
|
||||
\
|
||||
gfpCarry(R12,R13,R14,R15,AX, R8,R9,R10,R11,BX) |
@ -0,0 +1,112 @@ |
||||
#define mulBMI2(a0,a1,a2,a3, rb) \ |
||||
MOVQ a0, DX \
|
||||
MOVQ $0, R13 \
|
||||
MULXQ 0+rb, R8, R9 \
|
||||
MULXQ 8+rb, AX, R10 \
|
||||
ADDQ AX, R9 \
|
||||
MULXQ 16+rb, AX, R11 \
|
||||
ADCQ AX, R10 \
|
||||
MULXQ 24+rb, AX, R12 \
|
||||
ADCQ AX, R11 \
|
||||
ADCQ $0, R12 \
|
||||
ADCQ $0, R13 \
|
||||
\
|
||||
MOVQ a1, DX \
|
||||
MOVQ $0, R14 \
|
||||
MULXQ 0+rb, AX, BX \
|
||||
ADDQ AX, R9 \
|
||||
ADCQ BX, R10 \
|
||||
MULXQ 16+rb, AX, BX \
|
||||
ADCQ AX, R11 \
|
||||
ADCQ BX, R12 \
|
||||
ADCQ $0, R13 \
|
||||
MULXQ 8+rb, AX, BX \
|
||||
ADDQ AX, R10 \
|
||||
ADCQ BX, R11 \
|
||||
MULXQ 24+rb, AX, BX \
|
||||
ADCQ AX, R12 \
|
||||
ADCQ BX, R13 \
|
||||
ADCQ $0, R14 \
|
||||
\
|
||||
MOVQ a2, DX \
|
||||
MOVQ $0, R15 \
|
||||
MULXQ 0+rb, AX, BX \
|
||||
ADDQ AX, R10 \
|
||||
ADCQ BX, R11 \
|
||||
MULXQ 16+rb, AX, BX \
|
||||
ADCQ AX, R12 \
|
||||
ADCQ BX, R13 \
|
||||
ADCQ $0, R14 \
|
||||
MULXQ 8+rb, AX, BX \
|
||||
ADDQ AX, R11 \
|
||||
ADCQ BX, R12 \
|
||||
MULXQ 24+rb, AX, BX \
|
||||
ADCQ AX, R13 \
|
||||
ADCQ BX, R14 \
|
||||
ADCQ $0, R15 \
|
||||
\
|
||||
MOVQ a3, DX \
|
||||
MULXQ 0+rb, AX, BX \
|
||||
ADDQ AX, R11 \
|
||||
ADCQ BX, R12 \
|
||||
MULXQ 16+rb, AX, BX \
|
||||
ADCQ AX, R13 \
|
||||
ADCQ BX, R14 \
|
||||
ADCQ $0, R15 \
|
||||
MULXQ 8+rb, AX, BX \
|
||||
ADDQ AX, R12 \
|
||||
ADCQ BX, R13 \
|
||||
MULXQ 24+rb, AX, BX \
|
||||
ADCQ AX, R14 \
|
||||
ADCQ BX, R15 |
||||
|
||||
#define gfpReduceBMI2() \ |
||||
\ // m = (T * N') mod R, store m in R8:R9:R10:R11
|
||||
MOVQ ·np+0(SB), DX \
|
||||
MULXQ 0(SP), R8, R9 \
|
||||
MULXQ 8(SP), AX, R10 \
|
||||
ADDQ AX, R9 \
|
||||
MULXQ 16(SP), AX, R11 \
|
||||
ADCQ AX, R10 \
|
||||
MULXQ 24(SP), AX, BX \
|
||||
ADCQ AX, R11 \
|
||||
\
|
||||
MOVQ ·np+8(SB), DX \
|
||||
MULXQ 0(SP), AX, BX \
|
||||
ADDQ AX, R9 \
|
||||
ADCQ BX, R10 \
|
||||
MULXQ 16(SP), AX, BX \
|
||||
ADCQ AX, R11 \
|
||||
MULXQ 8(SP), AX, BX \
|
||||
ADDQ AX, R10 \
|
||||
ADCQ BX, R11 \
|
||||
\
|
||||
MOVQ ·np+16(SB), DX \
|
||||
MULXQ 0(SP), AX, BX \
|
||||
ADDQ AX, R10 \
|
||||
ADCQ BX, R11 \
|
||||
MULXQ 8(SP), AX, BX \
|
||||
ADDQ AX, R11 \
|
||||
\
|
||||
MOVQ ·np+24(SB), DX \
|
||||
MULXQ 0(SP), AX, BX \
|
||||
ADDQ AX, R11 \
|
||||
\
|
||||
storeBlock(R8,R9,R10,R11, 64(SP)) \
|
||||
\
|
||||
\ // m * N
|
||||
mulBMI2(·p2+0(SB),·p2+8(SB),·p2+16(SB),·p2+24(SB), 64(SP)) \
|
||||
\
|
||||
\ // Add the 512-bit intermediate to m*N
|
||||
MOVQ $0, AX \
|
||||
ADDQ 0(SP), R8 \
|
||||
ADCQ 8(SP), R9 \
|
||||
ADCQ 16(SP), R10 \
|
||||
ADCQ 24(SP), R11 \
|
||||
ADCQ 32(SP), R12 \
|
||||
ADCQ 40(SP), R13 \
|
||||
ADCQ 48(SP), R14 \
|
||||
ADCQ 56(SP), R15 \
|
||||
ADCQ $0, AX \
|
||||
\
|
||||
gfpCarry(R12,R13,R14,R15,AX, R8,R9,R10,R11,BX) |
@ -0,0 +1,204 @@ |
||||
package bn256 |
||||
|
||||
import ( |
||||
"math/big" |
||||
) |
||||
|
||||
// twistPoint implements the elliptic curve y²=x³+3/ξ over GF(p²). Points are
|
||||
// kept in Jacobian form and t=z² when valid. The group G₂ is the set of
|
||||
// n-torsion points of this curve over GF(p²) (where n = Order)
|
||||
type twistPoint struct { |
||||
x, y, z, t gfP2 |
||||
} |
||||
|
||||
var twistB = &gfP2{ |
||||
gfP{0x38e7ecccd1dcff67, 0x65f0b37d93ce0d3e, 0xd749d0dd22ac00aa, 0x0141b9ce4a688d4d}, |
||||
gfP{0x3bf938e377b802a8, 0x020b1b273633535d, 0x26b7edf049755260, 0x2514c6324384a86d}, |
||||
} |
||||
|
||||
// twistGen is the generator of group G₂.
|
||||
var twistGen = &twistPoint{ |
||||
gfP2{ |
||||
gfP{0xafb4737da84c6140, 0x6043dd5a5802d8c4, 0x09e950fc52a02f86, 0x14fef0833aea7b6b}, |
||||
gfP{0x8e83b5d102bc2026, 0xdceb1935497b0172, 0xfbb8264797811adf, 0x19573841af96503b}, |
||||
}, |
||||
gfP2{ |
||||
gfP{0x64095b56c71856ee, 0xdc57f922327d3cbb, 0x55f935be33351076, 0x0da4a0e693fd6482}, |
||||
gfP{0x619dfa9d886be9f6, 0xfe7fd297f59e9b78, 0xff9e1a62231b7dfe, 0x28fd7eebae9e4206}, |
||||
}, |
||||
gfP2{*newGFp(0), *newGFp(1)}, |
||||
gfP2{*newGFp(0), *newGFp(1)}, |
||||
} |
||||
|
||||
func (c *twistPoint) String() string { |
||||
c.MakeAffine() |
||||
x, y := gfP2Decode(&c.x), gfP2Decode(&c.y) |
||||
return "(" + x.String() + ", " + y.String() + ")" |
||||
} |
||||
|
||||
func (c *twistPoint) Set(a *twistPoint) { |
||||
c.x.Set(&a.x) |
||||
c.y.Set(&a.y) |
||||
c.z.Set(&a.z) |
||||
c.t.Set(&a.t) |
||||
} |
||||
|
||||
// IsOnCurve returns true iff c is on the curve.
|
||||
func (c *twistPoint) IsOnCurve() bool { |
||||
c.MakeAffine() |
||||
if c.IsInfinity() { |
||||
return true |
||||
} |
||||
|
||||
y2, x3 := &gfP2{}, &gfP2{} |
||||
y2.Square(&c.y) |
||||
x3.Square(&c.x).Mul(x3, &c.x).Add(x3, twistB) |
||||
|
||||
if *y2 != *x3 { |
||||
return false |
||||
} |
||||
cneg := &twistPoint{} |
||||
cneg.Mul(c, Order) |
||||
return cneg.z.IsZero() |
||||
} |
||||
|
||||
func (c *twistPoint) SetInfinity() { |
||||
c.x.SetZero() |
||||
c.y.SetOne() |
||||
c.z.SetZero() |
||||
c.t.SetZero() |
||||
} |
||||
|
||||
func (c *twistPoint) IsInfinity() bool { |
||||
return c.z.IsZero() |
||||
} |
||||
|
||||
func (c *twistPoint) Add(a, b *twistPoint) { |
||||
// For additional comments, see the same function in curve.go.
|
||||
|
||||
if a.IsInfinity() { |
||||
c.Set(b) |
||||
return |
||||
} |
||||
if b.IsInfinity() { |
||||
c.Set(a) |
||||
return |
||||
} |
||||
|
||||
// See http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/addition/add-2007-bl.op3
|
||||
z12 := (&gfP2{}).Square(&a.z) |
||||
z22 := (&gfP2{}).Square(&b.z) |
||||
u1 := (&gfP2{}).Mul(&a.x, z22) |
||||
u2 := (&gfP2{}).Mul(&b.x, z12) |
||||
|
||||
t := (&gfP2{}).Mul(&b.z, z22) |
||||
s1 := (&gfP2{}).Mul(&a.y, t) |
||||
|
||||
t.Mul(&a.z, z12) |
||||
s2 := (&gfP2{}).Mul(&b.y, t) |
||||
|
||||
h := (&gfP2{}).Sub(u2, u1) |
||||
xEqual := h.IsZero() |
||||
|
||||
t.Add(h, h) |
||||
i := (&gfP2{}).Square(t) |
||||
j := (&gfP2{}).Mul(h, i) |
||||
|
||||
t.Sub(s2, s1) |
||||
yEqual := t.IsZero() |
||||
if xEqual && yEqual { |
||||
c.Double(a) |
||||
return |
||||
} |
||||
r := (&gfP2{}).Add(t, t) |
||||
|
||||
v := (&gfP2{}).Mul(u1, i) |
||||
|
||||
t4 := (&gfP2{}).Square(r) |
||||
t.Add(v, v) |
||||
t6 := (&gfP2{}).Sub(t4, j) |
||||
c.x.Sub(t6, t) |
||||
|
||||
t.Sub(v, &c.x) // t7
|
||||
t4.Mul(s1, j) // t8
|
||||
t6.Add(t4, t4) // t9
|
||||
t4.Mul(r, t) // t10
|
||||
c.y.Sub(t4, t6) |
||||
|
||||
t.Add(&a.z, &b.z) // t11
|
||||
t4.Square(t) // t12
|
||||
t.Sub(t4, z12) // t13
|
||||
t4.Sub(t, z22) // t14
|
||||
c.z.Mul(t4, h) |
||||
} |
||||
|
||||
func (c *twistPoint) Double(a *twistPoint) { |
||||
// See http://hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian-0/doubling/dbl-2009-l.op3
|
||||
A := (&gfP2{}).Square(&a.x) |
||||
B := (&gfP2{}).Square(&a.y) |
||||
C := (&gfP2{}).Square(B) |
||||
|
||||
t := (&gfP2{}).Add(&a.x, B) |
||||
t2 := (&gfP2{}).Square(t) |
||||
t.Sub(t2, A) |
||||
t2.Sub(t, C) |
||||
d := (&gfP2{}).Add(t2, t2) |
||||
t.Add(A, A) |
||||
e := (&gfP2{}).Add(t, A) |
||||
f := (&gfP2{}).Square(e) |
||||
|
||||
t.Add(d, d) |
||||
c.x.Sub(f, t) |
||||
|
||||
t.Add(C, C) |
||||
t2.Add(t, t) |
||||
t.Add(t2, t2) |
||||
c.y.Sub(d, &c.x) |
||||
t2.Mul(e, &c.y) |
||||
c.y.Sub(t2, t) |
||||
|
||||
t.Mul(&a.y, &a.z) |
||||
c.z.Add(t, t) |
||||
} |
||||
|
||||
func (c *twistPoint) Mul(a *twistPoint, scalar *big.Int) { |
||||
sum, t := &twistPoint{}, &twistPoint{} |
||||
|
||||
for i := scalar.BitLen(); i >= 0; i-- { |
||||
t.Double(sum) |
||||
if scalar.Bit(i) != 0 { |
||||
sum.Add(t, a) |
||||
} else { |
||||
sum.Set(t) |
||||
} |
||||
} |
||||
|
||||
c.Set(sum) |
||||
} |
||||
|
||||
func (c *twistPoint) MakeAffine() { |
||||
if c.z.IsOne() { |
||||
return |
||||
} else if c.z.IsZero() { |
||||
c.x.SetZero() |
||||
c.y.SetOne() |
||||
c.t.SetZero() |
||||
return |
||||
} |
||||
|
||||
zInv := (&gfP2{}).Invert(&c.z) |
||||
t := (&gfP2{}).Mul(&c.y, zInv) |
||||
zInv2 := (&gfP2{}).Square(zInv) |
||||
c.y.Mul(t, zInv2) |
||||
t.Mul(&c.x, zInv2) |
||||
c.x.Set(t) |
||||
c.z.SetOne() |
||||
c.t.SetOne() |
||||
} |
||||
|
||||
func (c *twistPoint) Neg(a *twistPoint) { |
||||
c.x.Set(&a.x) |
||||
c.y.Neg(&a.y) |
||||
c.z.Set(&a.z) |
||||
c.t.SetZero() |
||||
} |
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Reference in new issue