1 files changed, 227 insertions, 0 deletions
diff --git a/crypto/bn256/gfp2.go b/crypto/bn256/gfp2.go
new file mode 100644
index 000000000..3981f6cb4
--- /dev/null
+++ b/crypto/bn256/gfp2.go
@@ -0,0 +1,227 @@
+// 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
+
+// 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"
+)
+
+// gfP2 implements a field of size p² as a quadratic extension of the base
+// field where i²=-1.
+type gfP2 struct {
+	x, y *big.Int // value is xi+y.
+}
+
+func newGFp2(pool *bnPool) *gfP2 {
+	return &gfP2{pool.Get(), pool.Get()}
+}
+
+func (e *gfP2) String() string {
+	x := new(big.Int).Mod(e.x, P)
+	y := new(big.Int).Mod(e.y, P)
+	return "(" + x.String() + "," + y.String() + ")"
+}
+
+func (e *gfP2) Put(pool *bnPool) {
+	pool.Put(e.x)
+	pool.Put(e.y)
+}
+
+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.SetInt64(0)
+	e.y.SetInt64(0)
+	return e
+}
+
+func (e *gfP2) SetOne() *gfP2 {
+	e.x.SetInt64(0)
+	e.y.SetInt64(1)
+	return e
+}
+
+func (e *gfP2) Minimal() {
+	if e.x.Sign() < 0 || e.x.Cmp(P) >= 0 {
+		e.x.Mod(e.x, P)
+	}
+	if e.y.Sign() < 0 || e.y.Cmp(P) >= 0 {
+		e.y.Mod(e.y, P)
+	}
+}
+
+func (e *gfP2) IsZero() bool {
+	return e.x.Sign() == 0 && e.y.Sign() == 0
+}
+
+func (e *gfP2) IsOne() bool {
+	if e.x.Sign() != 0 {
+		return false
+	}
+	words := e.y.Bits()
+	return len(words) == 1 && words[0] == 1
+}
+
+func (e *gfP2) Conjugate(a *gfP2) *gfP2 {
+	e.y.Set(a.y)
+	e.x.Neg(a.x)
+	return e
+}
+
+func (e *gfP2) Negative(a *gfP2) *gfP2 {
+	e.x.Neg(a.x)
+	e.y.Neg(a.y)
+	return e
+}
+
+func (e *gfP2) Add(a, b *gfP2) *gfP2 {
+	e.x.Add(a.x, b.x)
+	e.y.Add(a.y, b.y)
+	return e
+}
+
+func (e *gfP2) Sub(a, b *gfP2) *gfP2 {
+	e.x.Sub(a.x, b.x)
+	e.y.Sub(a.y, b.y)
+	return e
+}
+
+func (e *gfP2) Double(a *gfP2) *gfP2 {
+	e.x.Lsh(a.x, 1)
+	e.y.Lsh(a.y, 1)
+	return e
+}
+
+func (c *gfP2) Exp(a *gfP2, power *big.Int, pool *bnPool) *gfP2 {
+	sum := newGFp2(pool)
+	sum.SetOne()
+	t := newGFp2(pool)
+
+	for i := power.BitLen() - 1; i >= 0; i-- {
+		t.Square(sum, pool)
+		if power.Bit(i) != 0 {
+			sum.Mul(t, a, pool)
+		} else {
+			sum.Set(t)
+		}
+	}
+
+	c.Set(sum)
+
+	sum.Put(pool)
+	t.Put(pool)
+
+	return c
+}
+
+// See "Multiplication and Squaring in Pairing-Friendly Fields",
+// http://eprint.iacr.org/2006/471.pdf
+func (e *gfP2) Mul(a, b *gfP2, pool *bnPool) *gfP2 {
+	tx := pool.Get().Mul(a.x, b.y)
+	t := pool.Get().Mul(b.x, a.y)
+	tx.Add(tx, t)
+	tx.Mod(tx, P)
+
+	ty := pool.Get().Mul(a.y, b.y)
+	t.Mul(a.x, b.x)
+	ty.Sub(ty, t)
+	e.y.Mod(ty, P)
+	e.x.Set(tx)
+
+	pool.Put(tx)
+	pool.Put(ty)
+	pool.Put(t)
+
+	return e
+}
+
+func (e *gfP2) MulScalar(a *gfP2, b *big.Int) *gfP2 {
+	e.x.Mul(a.x, b)
+	e.y.Mul(a.y, b)
+	return e
+}
+
+// MulXi sets e=ξa where ξ=i+9 and then returns e.
+func (e *gfP2) MulXi(a *gfP2, pool *bnPool) *gfP2 {
+	// (xi+y)(i+3) = (9x+y)i+(9y-x)
+	tx := pool.Get().Lsh(a.x, 3)
+	tx.Add(tx, a.x)
+	tx.Add(tx, a.y)
+
+	ty := pool.Get().Lsh(a.y, 3)
+	ty.Add(ty, a.y)
+	ty.Sub(ty, a.x)
+
+	e.x.Set(tx)
+	e.y.Set(ty)
+
+	pool.Put(tx)
+	pool.Put(ty)
+
+	return e
+}
+
+func (e *gfP2) Square(a *gfP2, pool *bnPool) *gfP2 {
+	// Complex squaring algorithm:
+	// (xi+b)² = (x+y)(y-x) + 2*i*x*y
+	t1 := pool.Get().Sub(a.y, a.x)
+	t2 := pool.Get().Add(a.x, a.y)
+	ty := pool.Get().Mul(t1, t2)
+	ty.Mod(ty, P)
+
+	t1.Mul(a.x, a.y)
+	t1.Lsh(t1, 1)
+
+	e.x.Mod(t1, P)
+	e.y.Set(ty)
+
+	pool.Put(t1)
+	pool.Put(t2)
+	pool.Put(ty)
+
+	return e
+}
+
+func (e *gfP2) Invert(a *gfP2, pool *bnPool) *gfP2 {
+	// See "Implementing cryptographic pairings", M. Scott, section 3.2.
+	// ftp://136.206.11.249/pub/crypto/pairings.pdf
+	t := pool.Get()
+	t.Mul(a.y, a.y)
+	t2 := pool.Get()
+	t2.Mul(a.x, a.x)
+	t.Add(t, t2)
+
+	inv := pool.Get()
+	inv.ModInverse(t, P)
+
+	e.x.Neg(a.x)
+	e.x.Mul(e.x, inv)
+	e.x.Mod(e.x, P)
+
+	e.y.Mul(a.y, inv)
+	e.y.Mod(e.y, P)
+
+	pool.Put(t)
+	pool.Put(t2)
+	pool.Put(inv)
+
+	return e
+}
+
+func (e *gfP2) Real() *big.Int {
+	return e.x
+}
+
+func (e *gfP2) Imag() *big.Int {
+	return e.y
+}