mirror of https://github.com/ouqiang/gocron
201 lines
3.6 KiB
Go
201 lines
3.6 KiB
Go
|
// 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
|
||
|
}
|