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- // 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 fp12 struct {
- fp12temp
- fp6 *fp6
- }
- type fp12temp struct {
- t2 [9]*fe2
- t6 [5]*fe6
- t12 *fe12
- }
- func newFp12Temp() fp12temp {
- t2 := [9]*fe2{}
- t6 := [5]*fe6{}
- for i := 0; i < len(t2); i++ {
- t2[i] = &fe2{}
- }
- for i := 0; i < len(t6); i++ {
- t6[i] = &fe6{}
- }
- return fp12temp{t2, t6, &fe12{}}
- }
- func newFp12(fp6 *fp6) *fp12 {
- t := newFp12Temp()
- if fp6 == nil {
- return &fp12{t, newFp6(nil)}
- }
- return &fp12{t, fp6}
- }
- func (e *fp12) fp2() *fp2 {
- return e.fp6.fp2
- }
- func (e *fp12) fromBytes(in []byte) (*fe12, error) {
- if len(in) != 576 {
- return nil, errors.New("input string should be larger than 96 bytes")
- }
- fp6 := e.fp6
- c1, err := fp6.fromBytes(in[:288])
- if err != nil {
- return nil, err
- }
- c0, err := fp6.fromBytes(in[288:])
- if err != nil {
- return nil, err
- }
- return &fe12{*c0, *c1}, nil
- }
- func (e *fp12) toBytes(a *fe12) []byte {
- fp6 := e.fp6
- out := make([]byte, 576)
- copy(out[:288], fp6.toBytes(&a[1]))
- copy(out[288:], fp6.toBytes(&a[0]))
- return out
- }
- func (e *fp12) new() *fe12 {
- return new(fe12)
- }
- func (e *fp12) zero() *fe12 {
- return new(fe12)
- }
- func (e *fp12) one() *fe12 {
- return new(fe12).one()
- }
- func (e *fp12) add(c, a, b *fe12) {
- fp6 := e.fp6
- fp6.add(&c[0], &a[0], &b[0])
- fp6.add(&c[1], &a[1], &b[1])
- }
- func (e *fp12) double(c, a *fe12) {
- fp6 := e.fp6
- fp6.double(&c[0], &a[0])
- fp6.double(&c[1], &a[1])
- }
- func (e *fp12) sub(c, a, b *fe12) {
- fp6 := e.fp6
- fp6.sub(&c[0], &a[0], &b[0])
- fp6.sub(&c[1], &a[1], &b[1])
- }
- func (e *fp12) neg(c, a *fe12) {
- fp6 := e.fp6
- fp6.neg(&c[0], &a[0])
- fp6.neg(&c[1], &a[1])
- }
- func (e *fp12) conjugate(c, a *fe12) {
- fp6 := e.fp6
- c[0].set(&a[0])
- fp6.neg(&c[1], &a[1])
- }
- func (e *fp12) square(c, a *fe12) {
- fp6, t := e.fp6, e.t6
- fp6.add(t[0], &a[0], &a[1])
- fp6.mul(t[2], &a[0], &a[1])
- fp6.mulByNonResidue(t[1], &a[1])
- fp6.addAssign(t[1], &a[0])
- fp6.mulByNonResidue(t[3], t[2])
- fp6.mulAssign(t[0], t[1])
- fp6.subAssign(t[0], t[2])
- fp6.sub(&c[0], t[0], t[3])
- fp6.double(&c[1], t[2])
- }
- func (e *fp12) cyclotomicSquare(c, a *fe12) {
- t, fp2 := e.t2, e.fp2()
- e.fp4Square(t[3], t[4], &a[0][0], &a[1][1])
- fp2.sub(t[2], t[3], &a[0][0])
- fp2.doubleAssign(t[2])
- fp2.add(&c[0][0], t[2], t[3])
- fp2.add(t[2], t[4], &a[1][1])
- fp2.doubleAssign(t[2])
- fp2.add(&c[1][1], t[2], t[4])
- e.fp4Square(t[3], t[4], &a[1][0], &a[0][2])
- e.fp4Square(t[5], t[6], &a[0][1], &a[1][2])
- fp2.sub(t[2], t[3], &a[0][1])
- fp2.doubleAssign(t[2])
- fp2.add(&c[0][1], t[2], t[3])
- fp2.add(t[2], t[4], &a[1][2])
- fp2.doubleAssign(t[2])
- fp2.add(&c[1][2], t[2], t[4])
- fp2.mulByNonResidue(t[3], t[6])
- fp2.add(t[2], t[3], &a[1][0])
- fp2.doubleAssign(t[2])
- fp2.add(&c[1][0], t[2], t[3])
- fp2.sub(t[2], t[5], &a[0][2])
- fp2.doubleAssign(t[2])
- fp2.add(&c[0][2], t[2], t[5])
- }
- func (e *fp12) mul(c, a, b *fe12) {
- t, fp6 := e.t6, e.fp6
- fp6.mul(t[1], &a[0], &b[0])
- fp6.mul(t[2], &a[1], &b[1])
- fp6.add(t[0], t[1], t[2])
- fp6.mulByNonResidue(t[2], t[2])
- fp6.add(t[3], t[1], t[2])
- fp6.add(t[1], &a[0], &a[1])
- fp6.add(t[2], &b[0], &b[1])
- fp6.mulAssign(t[1], t[2])
- c[0].set(t[3])
- fp6.sub(&c[1], t[1], t[0])
- }
- func (e *fp12) mulAssign(a, b *fe12) {
- t, fp6 := e.t6, e.fp6
- fp6.mul(t[1], &a[0], &b[0])
- fp6.mul(t[2], &a[1], &b[1])
- fp6.add(t[0], t[1], t[2])
- fp6.mulByNonResidue(t[2], t[2])
- fp6.add(t[3], t[1], t[2])
- fp6.add(t[1], &a[0], &a[1])
- fp6.add(t[2], &b[0], &b[1])
- fp6.mulAssign(t[1], t[2])
- a[0].set(t[3])
- fp6.sub(&a[1], t[1], t[0])
- }
- func (e *fp12) fp4Square(c0, c1, a0, a1 *fe2) {
- t, fp2 := e.t2, e.fp2()
- fp2.square(t[0], a0)
- fp2.square(t[1], a1)
- fp2.mulByNonResidue(t[2], t[1])
- fp2.add(c0, t[2], t[0])
- fp2.add(t[2], a0, a1)
- fp2.squareAssign(t[2])
- fp2.subAssign(t[2], t[0])
- fp2.sub(c1, t[2], t[1])
- }
- func (e *fp12) inverse(c, a *fe12) {
- fp6, t := e.fp6, e.t6
- fp6.square(t[0], &a[0])
- fp6.square(t[1], &a[1])
- fp6.mulByNonResidue(t[1], t[1])
- fp6.sub(t[1], t[0], t[1])
- fp6.inverse(t[0], t[1])
- fp6.mul(&c[0], &a[0], t[0])
- fp6.mulAssign(t[0], &a[1])
- fp6.neg(&c[1], t[0])
- }
- func (e *fp12) mulBy014Assign(a *fe12, c0, c1, c4 *fe2) {
- fp2, fp6, t, t2 := e.fp2(), e.fp6, e.t6, e.t2[0]
- fp6.mulBy01(t[0], &a[0], c0, c1)
- fp6.mulBy1(t[1], &a[1], c4)
- fp2.add(t2, c1, c4)
- fp6.add(t[2], &a[1], &a[0])
- fp6.mulBy01Assign(t[2], c0, t2)
- fp6.subAssign(t[2], t[0])
- fp6.sub(&a[1], t[2], t[1])
- fp6.mulByNonResidue(t[1], t[1])
- fp6.add(&a[0], t[1], t[0])
- }
- func (e *fp12) exp(c, a *fe12, 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 *fp12) cyclotomicExp(c, a *fe12, s *big.Int) {
- z := e.one()
- for i := s.BitLen() - 1; i >= 0; i-- {
- e.cyclotomicSquare(z, z)
- if s.Bit(i) == 1 {
- e.mul(z, z, a)
- }
- }
- c.set(z)
- }
- func (e *fp12) frobeniusMap(c, a *fe12, power uint) {
- fp6 := e.fp6
- fp6.frobeniusMap(&c[0], &a[0], power)
- fp6.frobeniusMap(&c[1], &a[1], power)
- switch power {
- case 0:
- return
- case 6:
- fp6.neg(&c[1], &c[1])
- default:
- fp6.mulByBaseField(&c[1], &c[1], &frobeniusCoeffs12[power])
- }
- }
- func (e *fp12) frobeniusMapAssign(a *fe12, power uint) {
- fp6 := e.fp6
- fp6.frobeniusMapAssign(&a[0], power)
- fp6.frobeniusMapAssign(&a[1], power)
- switch power {
- case 0:
- return
- case 6:
- fp6.neg(&a[1], &a[1])
- default:
- fp6.mulByBaseField(&a[1], &a[1], &frobeniusCoeffs12[power])
- }
- }
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