diff options
Diffstat (limited to 'vendor/golang.org/x/crypto/bn256/bn256.go')
| -rw-r--r-- | vendor/golang.org/x/crypto/bn256/bn256.go | 404 |
1 files changed, 404 insertions, 0 deletions
diff --git a/vendor/golang.org/x/crypto/bn256/bn256.go b/vendor/golang.org/x/crypto/bn256/bn256.go new file mode 100644 index 0000000..014f8b3 --- /dev/null +++ b/vendor/golang.org/x/crypto/bn256/bn256.go @@ -0,0 +1,404 @@ +// 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 +} |