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path: root/crypto/bn256/gfp2.go
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-rw-r--r--crypto/bn256/gfp2.go227
1 files changed, 227 insertions, 0 deletions
diff --git a/crypto/bn256/gfp2.go b/crypto/bn256/gfp2.go
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+++ b/crypto/bn256/gfp2.go
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+// 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
+}