1 files changed, 200 insertions, 0 deletions
diff --git a/crypto/bn256/gfp12.go b/crypto/bn256/gfp12.go
new file mode 100644
index 000000000..f084eddf2
--- /dev/null
+++ b/crypto/bn256/gfp12.go
@@ -0,0 +1,200 @@
+// 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"
+)
+
+// gfP12 implements the field of size p¹² as a quadratic extension of gfP6
+// where ω²=τ.
+type gfP12 struct {
+	x, y *gfP6 // value is xω + y
+}
+
+func newGFp12(pool *bnPool) *gfP12 {
+	return &gfP12{newGFp6(pool), newGFp6(pool)}
+}
+
+func (e *gfP12) String() string {
+	return "(" + e.x.String() + "," + e.y.String() + ")"
+}
+
+func (e *gfP12) Put(pool *bnPool) {
+	e.x.Put(pool)
+	e.y.Put(pool)
+}
+
+func (e *gfP12) Set(a *gfP12) *gfP12 {
+	e.x.Set(a.x)
+	e.y.Set(a.y)
+	return e
+}
+
+func (e *gfP12) SetZero() *gfP12 {
+	e.x.SetZero()
+	e.y.SetZero()
+	return e
+}
+
+func (e *gfP12) SetOne() *gfP12 {
+	e.x.SetZero()
+	e.y.SetOne()
+	return e
+}
+
+func (e *gfP12) Minimal() {
+	e.x.Minimal()
+	e.y.Minimal()
+}
+
+func (e *gfP12) IsZero() bool {
+	e.Minimal()
+	return e.x.IsZero() && e.y.IsZero()
+}
+
+func (e *gfP12) IsOne() bool {
+	e.Minimal()
+	return e.x.IsZero() && e.y.IsOne()
+}
+
+func (e *gfP12) Conjugate(a *gfP12) *gfP12 {
+	e.x.Negative(a.x)
+	e.y.Set(a.y)
+	return a
+}
+
+func (e *gfP12) Negative(a *gfP12) *gfP12 {
+	e.x.Negative(a.x)
+	e.y.Negative(a.y)
+	return e
+}
+
+// Frobenius computes (xω+y)^p = x^p ω·ξ^((p-1)/6) + y^p
+func (e *gfP12) Frobenius(a *gfP12, pool *bnPool) *gfP12 {
+	e.x.Frobenius(a.x, pool)
+	e.y.Frobenius(a.y, pool)
+	e.x.MulScalar(e.x, xiToPMinus1Over6, pool)
+	return e
+}
+
+// FrobeniusP2 computes (xω+y)^p² = x^p² ω·ξ^((p²-1)/6) + y^p²
+func (e *gfP12) FrobeniusP2(a *gfP12, pool *bnPool) *gfP12 {
+	e.x.FrobeniusP2(a.x)
+	e.x.MulGFP(e.x, xiToPSquaredMinus1Over6)
+	e.y.FrobeniusP2(a.y)
+	return e
+}
+
+func (e *gfP12) Add(a, b *gfP12) *gfP12 {
+	e.x.Add(a.x, b.x)
+	e.y.Add(a.y, b.y)
+	return e
+}
+
+func (e *gfP12) Sub(a, b *gfP12) *gfP12 {
+	e.x.Sub(a.x, b.x)
+	e.y.Sub(a.y, b.y)
+	return e
+}
+
+func (e *gfP12) Mul(a, b *gfP12, pool *bnPool) *gfP12 {
+	tx := newGFp6(pool)
+	tx.Mul(a.x, b.y, pool)
+	t := newGFp6(pool)
+	t.Mul(b.x, a.y, pool)
+	tx.Add(tx, t)
+
+	ty := newGFp6(pool)
+	ty.Mul(a.y, b.y, pool)
+	t.Mul(a.x, b.x, pool)
+	t.MulTau(t, pool)
+	e.y.Add(ty, t)
+	e.x.Set(tx)
+
+	tx.Put(pool)
+	ty.Put(pool)
+	t.Put(pool)
+	return e
+}
+
+func (e *gfP12) MulScalar(a *gfP12, b *gfP6, pool *bnPool) *gfP12 {
+	e.x.Mul(e.x, b, pool)
+	e.y.Mul(e.y, b, pool)
+	return e
+}
+
+func (c *gfP12) Exp(a *gfP12, power *big.Int, pool *bnPool) *gfP12 {
+	sum := newGFp12(pool)
+	sum.SetOne()
+	t := newGFp12(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
+}
+
+func (e *gfP12) Square(a *gfP12, pool *bnPool) *gfP12 {
+	// Complex squaring algorithm
+	v0 := newGFp6(pool)
+	v0.Mul(a.x, a.y, pool)
+
+	t := newGFp6(pool)
+	t.MulTau(a.x, pool)
+	t.Add(a.y, t)
+	ty := newGFp6(pool)
+	ty.Add(a.x, a.y)
+	ty.Mul(ty, t, pool)
+	ty.Sub(ty, v0)
+	t.MulTau(v0, pool)
+	ty.Sub(ty, t)
+
+	e.y.Set(ty)
+	e.x.Double(v0)
+
+	v0.Put(pool)
+	t.Put(pool)
+	ty.Put(pool)
+
+	return e
+}
+
+func (e *gfP12) Invert(a *gfP12, pool *bnPool) *gfP12 {
+	// See "Implementing cryptographic pairings", M. Scott, section 3.2.
+	// ftp://136.206.11.249/pub/crypto/pairings.pdf
+	t1 := newGFp6(pool)
+	t2 := newGFp6(pool)
+
+	t1.Square(a.x, pool)
+	t2.Square(a.y, pool)
+	t1.MulTau(t1, pool)
+	t1.Sub(t2, t1)
+	t2.Invert(t1, pool)
+
+	e.x.Negative(a.x)
+	e.y.Set(a.y)
+	e.MulScalar(e, t2, pool)
+
+	t1.Put(pool)
+	t2.Put(pool)
+
+	return e
+}