352 lines
7.9 KiB
Go
352 lines
7.9 KiB
Go
// Copyright 2020 The go-ethereum Authors
|
|
// This file is part of the go-ethereum library.
|
|
//
|
|
// The go-ethereum library is free software: you can redistribute it and/or modify
|
|
// it under the terms of the GNU Lesser General Public License as published by
|
|
// the Free Software Foundation, either version 3 of the License, or
|
|
// (at your option) any later version.
|
|
//
|
|
// The go-ethereum library is distributed in the hope that it will be useful,
|
|
// but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
// GNU Lesser General Public License for more details.
|
|
//
|
|
// You should have received a copy of the GNU Lesser General Public License
|
|
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
|
|
|
|
package bls12381
|
|
|
|
import (
|
|
"errors"
|
|
"math/big"
|
|
)
|
|
|
|
type fp6Temp struct {
|
|
t [6]*fe2
|
|
}
|
|
|
|
type fp6 struct {
|
|
fp2 *fp2
|
|
fp6Temp
|
|
}
|
|
|
|
func newFp6Temp() fp6Temp {
|
|
t := [6]*fe2{}
|
|
for i := 0; i < len(t); i++ {
|
|
t[i] = &fe2{}
|
|
}
|
|
return fp6Temp{t}
|
|
}
|
|
|
|
func newFp6(f *fp2) *fp6 {
|
|
t := newFp6Temp()
|
|
if f == nil {
|
|
return &fp6{newFp2(), t}
|
|
}
|
|
return &fp6{f, t}
|
|
}
|
|
|
|
func (e *fp6) fromBytes(b []byte) (*fe6, error) {
|
|
if len(b) < 288 {
|
|
return nil, errors.New("input string should be larger than 288 bytes")
|
|
}
|
|
fp2 := e.fp2
|
|
u2, err := fp2.fromBytes(b[:96])
|
|
if err != nil {
|
|
return nil, err
|
|
}
|
|
u1, err := fp2.fromBytes(b[96:192])
|
|
if err != nil {
|
|
return nil, err
|
|
}
|
|
u0, err := fp2.fromBytes(b[192:])
|
|
if err != nil {
|
|
return nil, err
|
|
}
|
|
return &fe6{*u0, *u1, *u2}, nil
|
|
}
|
|
|
|
func (e *fp6) toBytes(a *fe6) []byte {
|
|
fp2 := e.fp2
|
|
out := make([]byte, 288)
|
|
copy(out[:96], fp2.toBytes(&a[2]))
|
|
copy(out[96:192], fp2.toBytes(&a[1]))
|
|
copy(out[192:], fp2.toBytes(&a[0]))
|
|
return out
|
|
}
|
|
|
|
func (e *fp6) new() *fe6 {
|
|
return new(fe6)
|
|
}
|
|
|
|
func (e *fp6) zero() *fe6 {
|
|
return new(fe6)
|
|
}
|
|
|
|
func (e *fp6) one() *fe6 {
|
|
return new(fe6).one()
|
|
}
|
|
|
|
func (e *fp6) add(c, a, b *fe6) {
|
|
fp2 := e.fp2
|
|
fp2.add(&c[0], &a[0], &b[0])
|
|
fp2.add(&c[1], &a[1], &b[1])
|
|
fp2.add(&c[2], &a[2], &b[2])
|
|
}
|
|
|
|
func (e *fp6) addAssign(a, b *fe6) {
|
|
fp2 := e.fp2
|
|
fp2.addAssign(&a[0], &b[0])
|
|
fp2.addAssign(&a[1], &b[1])
|
|
fp2.addAssign(&a[2], &b[2])
|
|
}
|
|
|
|
func (e *fp6) double(c, a *fe6) {
|
|
fp2 := e.fp2
|
|
fp2.double(&c[0], &a[0])
|
|
fp2.double(&c[1], &a[1])
|
|
fp2.double(&c[2], &a[2])
|
|
}
|
|
|
|
func (e *fp6) doubleAssign(a *fe6) {
|
|
fp2 := e.fp2
|
|
fp2.doubleAssign(&a[0])
|
|
fp2.doubleAssign(&a[1])
|
|
fp2.doubleAssign(&a[2])
|
|
}
|
|
|
|
func (e *fp6) sub(c, a, b *fe6) {
|
|
fp2 := e.fp2
|
|
fp2.sub(&c[0], &a[0], &b[0])
|
|
fp2.sub(&c[1], &a[1], &b[1])
|
|
fp2.sub(&c[2], &a[2], &b[2])
|
|
}
|
|
|
|
func (e *fp6) subAssign(a, b *fe6) {
|
|
fp2 := e.fp2
|
|
fp2.subAssign(&a[0], &b[0])
|
|
fp2.subAssign(&a[1], &b[1])
|
|
fp2.subAssign(&a[2], &b[2])
|
|
}
|
|
|
|
func (e *fp6) neg(c, a *fe6) {
|
|
fp2 := e.fp2
|
|
fp2.neg(&c[0], &a[0])
|
|
fp2.neg(&c[1], &a[1])
|
|
fp2.neg(&c[2], &a[2])
|
|
}
|
|
|
|
func (e *fp6) mul(c, a, b *fe6) {
|
|
fp2, t := e.fp2, e.t
|
|
fp2.mul(t[0], &a[0], &b[0])
|
|
fp2.mul(t[1], &a[1], &b[1])
|
|
fp2.mul(t[2], &a[2], &b[2])
|
|
fp2.add(t[3], &a[1], &a[2])
|
|
fp2.add(t[4], &b[1], &b[2])
|
|
fp2.mulAssign(t[3], t[4])
|
|
fp2.add(t[4], t[1], t[2])
|
|
fp2.subAssign(t[3], t[4])
|
|
fp2.mulByNonResidue(t[3], t[3])
|
|
fp2.add(t[5], t[0], t[3])
|
|
fp2.add(t[3], &a[0], &a[1])
|
|
fp2.add(t[4], &b[0], &b[1])
|
|
fp2.mulAssign(t[3], t[4])
|
|
fp2.add(t[4], t[0], t[1])
|
|
fp2.subAssign(t[3], t[4])
|
|
fp2.mulByNonResidue(t[4], t[2])
|
|
fp2.add(&c[1], t[3], t[4])
|
|
fp2.add(t[3], &a[0], &a[2])
|
|
fp2.add(t[4], &b[0], &b[2])
|
|
fp2.mulAssign(t[3], t[4])
|
|
fp2.add(t[4], t[0], t[2])
|
|
fp2.subAssign(t[3], t[4])
|
|
fp2.add(&c[2], t[1], t[3])
|
|
c[0].set(t[5])
|
|
}
|
|
|
|
func (e *fp6) mulAssign(a, b *fe6) {
|
|
fp2, t := e.fp2, e.t
|
|
fp2.mul(t[0], &a[0], &b[0])
|
|
fp2.mul(t[1], &a[1], &b[1])
|
|
fp2.mul(t[2], &a[2], &b[2])
|
|
fp2.add(t[3], &a[1], &a[2])
|
|
fp2.add(t[4], &b[1], &b[2])
|
|
fp2.mulAssign(t[3], t[4])
|
|
fp2.add(t[4], t[1], t[2])
|
|
fp2.subAssign(t[3], t[4])
|
|
fp2.mulByNonResidue(t[3], t[3])
|
|
fp2.add(t[5], t[0], t[3])
|
|
fp2.add(t[3], &a[0], &a[1])
|
|
fp2.add(t[4], &b[0], &b[1])
|
|
fp2.mulAssign(t[3], t[4])
|
|
fp2.add(t[4], t[0], t[1])
|
|
fp2.subAssign(t[3], t[4])
|
|
fp2.mulByNonResidue(t[4], t[2])
|
|
fp2.add(&a[1], t[3], t[4])
|
|
fp2.add(t[3], &a[0], &a[2])
|
|
fp2.add(t[4], &b[0], &b[2])
|
|
fp2.mulAssign(t[3], t[4])
|
|
fp2.add(t[4], t[0], t[2])
|
|
fp2.subAssign(t[3], t[4])
|
|
fp2.add(&a[2], t[1], t[3])
|
|
a[0].set(t[5])
|
|
}
|
|
|
|
func (e *fp6) square(c, a *fe6) {
|
|
fp2, t := e.fp2, e.t
|
|
fp2.square(t[0], &a[0])
|
|
fp2.mul(t[1], &a[0], &a[1])
|
|
fp2.doubleAssign(t[1])
|
|
fp2.sub(t[2], &a[0], &a[1])
|
|
fp2.addAssign(t[2], &a[2])
|
|
fp2.squareAssign(t[2])
|
|
fp2.mul(t[3], &a[1], &a[2])
|
|
fp2.doubleAssign(t[3])
|
|
fp2.square(t[4], &a[2])
|
|
fp2.mulByNonResidue(t[5], t[3])
|
|
fp2.add(&c[0], t[0], t[5])
|
|
fp2.mulByNonResidue(t[5], t[4])
|
|
fp2.add(&c[1], t[1], t[5])
|
|
fp2.addAssign(t[1], t[2])
|
|
fp2.addAssign(t[1], t[3])
|
|
fp2.addAssign(t[0], t[4])
|
|
fp2.sub(&c[2], t[1], t[0])
|
|
}
|
|
|
|
func (e *fp6) mulBy01Assign(a *fe6, b0, b1 *fe2) {
|
|
fp2, t := e.fp2, e.t
|
|
fp2.mul(t[0], &a[0], b0)
|
|
fp2.mul(t[1], &a[1], b1)
|
|
fp2.add(t[5], &a[1], &a[2])
|
|
fp2.mul(t[2], b1, t[5])
|
|
fp2.subAssign(t[2], t[1])
|
|
fp2.mulByNonResidue(t[2], t[2])
|
|
fp2.add(t[5], &a[0], &a[2])
|
|
fp2.mul(t[3], b0, t[5])
|
|
fp2.subAssign(t[3], t[0])
|
|
fp2.add(&a[2], t[3], t[1])
|
|
fp2.add(t[4], b0, b1)
|
|
fp2.add(t[5], &a[0], &a[1])
|
|
fp2.mulAssign(t[4], t[5])
|
|
fp2.subAssign(t[4], t[0])
|
|
fp2.sub(&a[1], t[4], t[1])
|
|
fp2.add(&a[0], t[2], t[0])
|
|
}
|
|
|
|
func (e *fp6) mulBy01(c, a *fe6, b0, b1 *fe2) {
|
|
fp2, t := e.fp2, e.t
|
|
fp2.mul(t[0], &a[0], b0)
|
|
fp2.mul(t[1], &a[1], b1)
|
|
fp2.add(t[2], &a[1], &a[2])
|
|
fp2.mulAssign(t[2], b1)
|
|
fp2.subAssign(t[2], t[1])
|
|
fp2.mulByNonResidue(t[2], t[2])
|
|
fp2.add(t[3], &a[0], &a[2])
|
|
fp2.mulAssign(t[3], b0)
|
|
fp2.subAssign(t[3], t[0])
|
|
fp2.add(&c[2], t[3], t[1])
|
|
fp2.add(t[4], b0, b1)
|
|
fp2.add(t[3], &a[0], &a[1])
|
|
fp2.mulAssign(t[4], t[3])
|
|
fp2.subAssign(t[4], t[0])
|
|
fp2.sub(&c[1], t[4], t[1])
|
|
fp2.add(&c[0], t[2], t[0])
|
|
}
|
|
|
|
func (e *fp6) mulBy1(c, a *fe6, b1 *fe2) {
|
|
fp2, t := e.fp2, e.t
|
|
fp2.mul(t[0], &a[2], b1)
|
|
fp2.mul(&c[2], &a[1], b1)
|
|
fp2.mul(&c[1], &a[0], b1)
|
|
fp2.mulByNonResidue(&c[0], t[0])
|
|
}
|
|
|
|
func (e *fp6) mulByNonResidue(c, a *fe6) {
|
|
fp2, t := e.fp2, e.t
|
|
t[0].set(&a[0])
|
|
fp2.mulByNonResidue(&c[0], &a[2])
|
|
c[2].set(&a[1])
|
|
c[1].set(t[0])
|
|
}
|
|
|
|
func (e *fp6) mulByBaseField(c, a *fe6, b *fe2) {
|
|
fp2 := e.fp2
|
|
fp2.mul(&c[0], &a[0], b)
|
|
fp2.mul(&c[1], &a[1], b)
|
|
fp2.mul(&c[2], &a[2], b)
|
|
}
|
|
|
|
func (e *fp6) exp(c, a *fe6, s *big.Int) {
|
|
z := e.one()
|
|
for i := s.BitLen() - 1; i >= 0; i-- {
|
|
e.square(z, z)
|
|
if s.Bit(i) == 1 {
|
|
e.mul(z, z, a)
|
|
}
|
|
}
|
|
c.set(z)
|
|
}
|
|
|
|
func (e *fp6) inverse(c, a *fe6) {
|
|
fp2, t := e.fp2, e.t
|
|
fp2.square(t[0], &a[0])
|
|
fp2.mul(t[1], &a[1], &a[2])
|
|
fp2.mulByNonResidue(t[1], t[1])
|
|
fp2.subAssign(t[0], t[1])
|
|
fp2.square(t[1], &a[1])
|
|
fp2.mul(t[2], &a[0], &a[2])
|
|
fp2.subAssign(t[1], t[2])
|
|
fp2.square(t[2], &a[2])
|
|
fp2.mulByNonResidue(t[2], t[2])
|
|
fp2.mul(t[3], &a[0], &a[1])
|
|
fp2.subAssign(t[2], t[3])
|
|
fp2.mul(t[3], &a[2], t[2])
|
|
fp2.mul(t[4], &a[1], t[1])
|
|
fp2.addAssign(t[3], t[4])
|
|
fp2.mulByNonResidue(t[3], t[3])
|
|
fp2.mul(t[4], &a[0], t[0])
|
|
fp2.addAssign(t[3], t[4])
|
|
fp2.inverse(t[3], t[3])
|
|
fp2.mul(&c[0], t[0], t[3])
|
|
fp2.mul(&c[1], t[2], t[3])
|
|
fp2.mul(&c[2], t[1], t[3])
|
|
}
|
|
|
|
func (e *fp6) frobeniusMap(c, a *fe6, power uint) {
|
|
fp2 := e.fp2
|
|
fp2.frobeniusMap(&c[0], &a[0], power)
|
|
fp2.frobeniusMap(&c[1], &a[1], power)
|
|
fp2.frobeniusMap(&c[2], &a[2], power)
|
|
switch power % 6 {
|
|
case 0:
|
|
return
|
|
case 3:
|
|
neg(&c[0][0], &a[1][1])
|
|
c[1][1].set(&a[1][0])
|
|
fp2.neg(&a[2], &a[2])
|
|
default:
|
|
fp2.mul(&c[1], &c[1], &frobeniusCoeffs61[power%6])
|
|
fp2.mul(&c[2], &c[2], &frobeniusCoeffs62[power%6])
|
|
}
|
|
}
|
|
|
|
func (e *fp6) frobeniusMapAssign(a *fe6, power uint) {
|
|
fp2 := e.fp2
|
|
fp2.frobeniusMapAssign(&a[0], power)
|
|
fp2.frobeniusMapAssign(&a[1], power)
|
|
fp2.frobeniusMapAssign(&a[2], power)
|
|
t := e.t
|
|
switch power % 6 {
|
|
case 0:
|
|
return
|
|
case 3:
|
|
neg(&t[0][0], &a[1][1])
|
|
a[1][1].set(&a[1][0])
|
|
a[1][0].set(&t[0][0])
|
|
fp2.neg(&a[2], &a[2])
|
|
default:
|
|
fp2.mulAssign(&a[1], &frobeniusCoeffs61[power%6])
|
|
fp2.mulAssign(&a[2], &frobeniusCoeffs62[power%6])
|
|
}
|
|
}
|