+++ /dev/null
-// 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 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 "golang.org/x/crypto/bn256"
-
-import (
- "crypto/rand"
- "io"
- "math/big"
-)
-
-// BUG(agl): this implementation is not constant time.
-// TODO(agl): keep GF(p²) elements in Mongomery form.
-
-// 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) {
- var k *big.Int
- var err error
-
- for {
- k, err = rand.Int(r, Order)
- if err != nil {
- return nil, nil, err
- }
- if k.Sign() > 0 {
- break
- }
- }
-
- 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 = newCurvePoint(nil)
- }
- e.p.Mul(curveGen, k, new(bnPool))
- 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 = newCurvePoint(nil)
- }
- e.p.Mul(a.p, k, new(bnPool))
- return e
-}
-
-// Add sets e to a+b and then returns e.
-// BUG(agl): this function is not complete: a==b fails.
-func (e *G1) Add(a, b *G1) *G1 {
- if e.p == nil {
- e.p = newCurvePoint(nil)
- }
- e.p.Add(a.p, b.p, new(bnPool))
- return e
-}
-
-// Neg sets e to -a and then returns e.
-func (e *G1) Neg(a *G1) *G1 {
- if e.p == nil {
- e.p = newCurvePoint(nil)
- }
- e.p.Negative(a.p)
- return e
-}
-
-// Marshal converts n to a byte slice.
-func (n *G1) Marshal() []byte {
- n.p.MakeAffine(nil)
-
- xBytes := new(big.Int).Mod(n.p.x, p).Bytes()
- yBytes := new(big.Int).Mod(n.p.y, p).Bytes()
-
- // Each value is a 256-bit number.
- const numBytes = 256 / 8
-
- ret := make([]byte, numBytes*2)
- copy(ret[1*numBytes-len(xBytes):], xBytes)
- copy(ret[2*numBytes-len(yBytes):], yBytes)
-
- 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) (*G1, bool) {
- // Each value is a 256-bit number.
- const numBytes = 256 / 8
-
- if len(m) != 2*numBytes {
- return nil, false
- }
-
- if e.p == nil {
- e.p = newCurvePoint(nil)
- }
-
- e.p.x.SetBytes(m[0*numBytes : 1*numBytes])
- e.p.y.SetBytes(m[1*numBytes : 2*numBytes])
-
- if e.p.x.Sign() == 0 && e.p.y.Sign() == 0 {
- // This is the point at infinity.
- e.p.y.SetInt64(1)
- e.p.z.SetInt64(0)
- e.p.t.SetInt64(0)
- } else {
- e.p.z.SetInt64(1)
- e.p.t.SetInt64(1)
-
- if !e.p.IsOnCurve() {
- return nil, false
- }
- }
-
- return e, true
-}
-
-// 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
-}
-
-// RandomG1 returns x and g₂ˣ where x is a random, non-zero number read from r.
-func RandomG2(r io.Reader) (*big.Int, *G2, error) {
- var k *big.Int
- var err error
-
- for {
- k, err = rand.Int(r, Order)
- if err != nil {
- return nil, nil, err
- }
- if k.Sign() > 0 {
- break
- }
- }
-
- return k, new(G2).ScalarBaseMult(k), nil
-}
-
-func (g *G2) String() string {
- return "bn256.G2" + g.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 = newTwistPoint(nil)
- }
- e.p.Mul(twistGen, k, new(bnPool))
- 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 = newTwistPoint(nil)
- }
- e.p.Mul(a.p, k, new(bnPool))
- return e
-}
-
-// Add sets e to a+b and then returns e.
-// BUG(agl): this function is not complete: a==b fails.
-func (e *G2) Add(a, b *G2) *G2 {
- if e.p == nil {
- e.p = newTwistPoint(nil)
- }
- e.p.Add(a.p, b.p, new(bnPool))
- return e
-}
-
-// Marshal converts n into a byte slice.
-func (n *G2) Marshal() []byte {
- n.p.MakeAffine(nil)
-
- xxBytes := new(big.Int).Mod(n.p.x.x, p).Bytes()
- xyBytes := new(big.Int).Mod(n.p.x.y, p).Bytes()
- yxBytes := new(big.Int).Mod(n.p.y.x, p).Bytes()
- yyBytes := new(big.Int).Mod(n.p.y.y, p).Bytes()
-
- // Each value is a 256-bit number.
- const numBytes = 256 / 8
-
- ret := make([]byte, numBytes*4)
- copy(ret[1*numBytes-len(xxBytes):], xxBytes)
- copy(ret[2*numBytes-len(xyBytes):], xyBytes)
- copy(ret[3*numBytes-len(yxBytes):], yxBytes)
- copy(ret[4*numBytes-len(yyBytes):], yyBytes)
-
- 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) (*G2, bool) {
- // Each value is a 256-bit number.
- const numBytes = 256 / 8
-
- if len(m) != 4*numBytes {
- return nil, false
- }
-
- if e.p == nil {
- e.p = newTwistPoint(nil)
- }
-
- e.p.x.x.SetBytes(m[0*numBytes : 1*numBytes])
- e.p.x.y.SetBytes(m[1*numBytes : 2*numBytes])
- e.p.y.x.SetBytes(m[2*numBytes : 3*numBytes])
- e.p.y.y.SetBytes(m[3*numBytes : 4*numBytes])
-
- if e.p.x.x.Sign() == 0 &&
- e.p.x.y.Sign() == 0 &&
- e.p.y.x.Sign() == 0 &&
- e.p.y.y.Sign() == 0 {
- // 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, false
- }
- }
-
- return e, true
-}
-
-// 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
-}
-
-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 = newGFp12(nil)
- }
- e.p.Exp(a.p, k, new(bnPool))
- 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 = newGFp12(nil)
- }
- e.p.Mul(a.p, b.p, new(bnPool))
- return e
-}
-
-// Neg sets e to -a and then returns e.
-func (e *GT) Neg(a *GT) *GT {
- if e.p == nil {
- e.p = newGFp12(nil)
- }
- e.p.Invert(a.p, new(bnPool))
- return e
-}
-
-// Marshal converts n into a byte slice.
-func (n *GT) Marshal() []byte {
- n.p.Minimal()
-
- xxxBytes := n.p.x.x.x.Bytes()
- xxyBytes := n.p.x.x.y.Bytes()
- xyxBytes := n.p.x.y.x.Bytes()
- xyyBytes := n.p.x.y.y.Bytes()
- xzxBytes := n.p.x.z.x.Bytes()
- xzyBytes := n.p.x.z.y.Bytes()
- yxxBytes := n.p.y.x.x.Bytes()
- yxyBytes := n.p.y.x.y.Bytes()
- yyxBytes := n.p.y.y.x.Bytes()
- yyyBytes := n.p.y.y.y.Bytes()
- yzxBytes := n.p.y.z.x.Bytes()
- yzyBytes := n.p.y.z.y.Bytes()
-
- // Each value is a 256-bit number.
- const numBytes = 256 / 8
-
- ret := make([]byte, numBytes*12)
- copy(ret[1*numBytes-len(xxxBytes):], xxxBytes)
- copy(ret[2*numBytes-len(xxyBytes):], xxyBytes)
- copy(ret[3*numBytes-len(xyxBytes):], xyxBytes)
- copy(ret[4*numBytes-len(xyyBytes):], xyyBytes)
- copy(ret[5*numBytes-len(xzxBytes):], xzxBytes)
- copy(ret[6*numBytes-len(xzyBytes):], xzyBytes)
- copy(ret[7*numBytes-len(yxxBytes):], yxxBytes)
- copy(ret[8*numBytes-len(yxyBytes):], yxyBytes)
- copy(ret[9*numBytes-len(yyxBytes):], yyxBytes)
- copy(ret[10*numBytes-len(yyyBytes):], yyyBytes)
- copy(ret[11*numBytes-len(yzxBytes):], yzxBytes)
- copy(ret[12*numBytes-len(yzyBytes):], yzyBytes)
-
- 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) (*GT, bool) {
- // Each value is a 256-bit number.
- const numBytes = 256 / 8
-
- if len(m) != 12*numBytes {
- return nil, false
- }
-
- if e.p == nil {
- e.p = newGFp12(nil)
- }
-
- e.p.x.x.x.SetBytes(m[0*numBytes : 1*numBytes])
- e.p.x.x.y.SetBytes(m[1*numBytes : 2*numBytes])
- e.p.x.y.x.SetBytes(m[2*numBytes : 3*numBytes])
- e.p.x.y.y.SetBytes(m[3*numBytes : 4*numBytes])
- e.p.x.z.x.SetBytes(m[4*numBytes : 5*numBytes])
- e.p.x.z.y.SetBytes(m[5*numBytes : 6*numBytes])
- e.p.y.x.x.SetBytes(m[6*numBytes : 7*numBytes])
- e.p.y.x.y.SetBytes(m[7*numBytes : 8*numBytes])
- e.p.y.y.x.SetBytes(m[8*numBytes : 9*numBytes])
- e.p.y.y.y.SetBytes(m[9*numBytes : 10*numBytes])
- e.p.y.z.x.SetBytes(m[10*numBytes : 11*numBytes])
- e.p.y.z.y.SetBytes(m[11*numBytes : 12*numBytes])
-
- return e, true
-}
-
-// Pair calculates an Optimal Ate pairing.
-func Pair(g1 *G1, g2 *G2) *GT {
- return >{optimalAte(g2.p, g1.p, new(bnPool))}
-}
-
-// bnPool implements a tiny cache of *big.Int objects that's used to reduce the
-// number of allocations made during processing.
-type bnPool struct {
- bns []*big.Int
- count int
-}
-
-func (pool *bnPool) Get() *big.Int {
- if pool == nil {
- return new(big.Int)
- }
-
- pool.count++
- l := len(pool.bns)
- if l == 0 {
- return new(big.Int)
- }
-
- bn := pool.bns[l-1]
- pool.bns = pool.bns[:l-1]
- return bn
-}
-
-func (pool *bnPool) Put(bn *big.Int) {
- if pool == nil {
- return
- }
- pool.bns = append(pool.bns, bn)
- pool.count--
-}
-
-func (pool *bnPool) Count() int {
- return pool.count
-}
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