1 files changed, 428 insertions, 0 deletions
diff --git a/crypto/bn256/bn256.go b/crypto/bn256/bn256.go
new file mode 100644
index 000000000..92418369b
--- /dev/null
+++ b/crypto/bn256/bn256.go
@@ -0,0 +1,428 @@
+// 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 (
+	"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()
+}
+
+// CurvePoints returns p's curve points in big integer
+func (e *G1) CurvePoints() (*big.Int, *big.Int, *big.Int, *big.Int) {
+	return e.p.x, e.p.y, e.p.z, e.p.t
+}
+
+// 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()
+}
+
+// CurvePoints returns the curve points of p which includes the real
+// and imaginary parts of the curve point.
+func (e *G2) CurvePoints() (*gfP2, *gfP2, *gfP2, *gfP2) {
+	return e.p.x, e.p.y, e.p.z, e.p.t
+}
+
+// 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 &GT{optimalAte(g2.p, g1.p, new(bnPool))}
+}
+
+func PairingCheck(a []*G1, b []*G2) bool {
+	pool := new(bnPool)
+	e := newGFp12(pool)
+	e.SetOne()
+	for i := 0; i < len(a); i++ {
+		new_e := miller(b[i].p, a[i].p, pool)
+		e.Mul(e, new_e, pool)
+	}
+	ret := finalExponentiation(e, pool)
+	e.Put(pool)
+	return ret.IsOne()
+}
+
+// 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
+}