mirror of
https://github.com/Luzifer/ansible-role-version.git
synced 2024-12-23 11:01:20 +00:00
408 lines
9.6 KiB
Go
408 lines
9.6 KiB
Go
// 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.
|
|
//
|
|
// 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.
|
|
//
|
|
// (This package previously claimed to operate at a 128-bit security level.
|
|
// However, recent improvements in attacks mean that is no longer true. See
|
|
// https://moderncrypto.org/mail-archive/curves/2016/000740.html.)
|
|
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 (e *G1) String() string {
|
|
return "bn256.G1" + e.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 (e *G1) Marshal() []byte {
|
|
e.p.MakeAffine(nil)
|
|
|
|
xBytes := new(big.Int).Mod(e.p.x, p).Bytes()
|
|
yBytes := new(big.Int).Mod(e.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 (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 = 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
|
|
}
|