Official Go implementation of the Ethereum protocol
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go-ethereum/crypto/bls12381/fp2.go

252 lines
4.9 KiB

// 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 fp2Temp struct {
t [4]*fe
}
type fp2 struct {
fp2Temp
}
func newFp2Temp() fp2Temp {
t := [4]*fe{}
for i := 0; i < len(t); i++ {
t[i] = &fe{}
}
return fp2Temp{t}
}
func newFp2() *fp2 {
t := newFp2Temp()
return &fp2{t}
}
func (e *fp2) fromBytes(in []byte) (*fe2, error) {
if len(in) != 96 {
return nil, errors.New("length of input string should be 96 bytes")
}
c1, err := fromBytes(in[:48])
if err != nil {
return nil, err
}
c0, err := fromBytes(in[48:])
if err != nil {
return nil, err
}
return &fe2{*c0, *c1}, nil
}
func (e *fp2) toBytes(a *fe2) []byte {
out := make([]byte, 96)
copy(out[:48], toBytes(&a[1]))
copy(out[48:], toBytes(&a[0]))
return out
}
func (e *fp2) new() *fe2 {
return new(fe2).zero()
}
func (e *fp2) zero() *fe2 {
return new(fe2).zero()
}
func (e *fp2) one() *fe2 {
return new(fe2).one()
}
func (e *fp2) add(c, a, b *fe2) {
add(&c[0], &a[0], &b[0])
add(&c[1], &a[1], &b[1])
}
func (e *fp2) addAssign(a, b *fe2) {
addAssign(&a[0], &b[0])
addAssign(&a[1], &b[1])
}
func (e *fp2) ladd(c, a, b *fe2) {
ladd(&c[0], &a[0], &b[0])
ladd(&c[1], &a[1], &b[1])
}
func (e *fp2) double(c, a *fe2) {
double(&c[0], &a[0])
double(&c[1], &a[1])
}
func (e *fp2) doubleAssign(a *fe2) {
doubleAssign(&a[0])
doubleAssign(&a[1])
}
func (e *fp2) ldouble(c, a *fe2) {
ldouble(&c[0], &a[0])
ldouble(&c[1], &a[1])
}
func (e *fp2) sub(c, a, b *fe2) {
sub(&c[0], &a[0], &b[0])
sub(&c[1], &a[1], &b[1])
}
func (e *fp2) subAssign(c, a *fe2) {
subAssign(&c[0], &a[0])
subAssign(&c[1], &a[1])
}
func (e *fp2) neg(c, a *fe2) {
neg(&c[0], &a[0])
neg(&c[1], &a[1])
}
func (e *fp2) mul(c, a, b *fe2) {
t := e.t
mul(t[1], &a[0], &b[0])
mul(t[2], &a[1], &b[1])
add(t[0], &a[0], &a[1])
add(t[3], &b[0], &b[1])
sub(&c[0], t[1], t[2])
addAssign(t[1], t[2])
mul(t[0], t[0], t[3])
sub(&c[1], t[0], t[1])
}
func (e *fp2) mulAssign(a, b *fe2) {
t := e.t
mul(t[1], &a[0], &b[0])
mul(t[2], &a[1], &b[1])
add(t[0], &a[0], &a[1])
add(t[3], &b[0], &b[1])
sub(&a[0], t[1], t[2])
addAssign(t[1], t[2])
mul(t[0], t[0], t[3])
sub(&a[1], t[0], t[1])
}
func (e *fp2) square(c, a *fe2) {
t := e.t
ladd(t[0], &a[0], &a[1])
sub(t[1], &a[0], &a[1])
ldouble(t[2], &a[0])
mul(&c[0], t[0], t[1])
mul(&c[1], t[2], &a[1])
}
func (e *fp2) squareAssign(a *fe2) {
t := e.t
ladd(t[0], &a[0], &a[1])
sub(t[1], &a[0], &a[1])
ldouble(t[2], &a[0])
mul(&a[0], t[0], t[1])
mul(&a[1], t[2], &a[1])
}
func (e *fp2) mulByNonResidue(c, a *fe2) {
t := e.t
sub(t[0], &a[0], &a[1])
add(&c[1], &a[0], &a[1])
c[0].set(t[0])
}
func (e *fp2) mulByB(c, a *fe2) {
t := e.t
double(t[0], &a[0])
double(t[1], &a[1])
doubleAssign(t[0])
doubleAssign(t[1])
sub(&c[0], t[0], t[1])
add(&c[1], t[0], t[1])
}
func (e *fp2) inverse(c, a *fe2) {
t := e.t
square(t[0], &a[0])
square(t[1], &a[1])
addAssign(t[0], t[1])
inverse(t[0], t[0])
mul(&c[0], &a[0], t[0])
mul(t[0], t[0], &a[1])
neg(&c[1], t[0])
}
func (e *fp2) mulByFq(c, a *fe2, b *fe) {
mul(&c[0], &a[0], b)
mul(&c[1], &a[1], b)
}
func (e *fp2) exp(c, a *fe2, 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 *fp2) frobeniusMap(c, a *fe2, power uint) {
c[0].set(&a[0])
if power%2 == 1 {
neg(&c[1], &a[1])
return
}
c[1].set(&a[1])
}
func (e *fp2) frobeniusMapAssign(a *fe2, power uint) {
if power%2 == 1 {
neg(&a[1], &a[1])
return
}
}
func (e *fp2) sqrt(c, a *fe2) bool {
u, x0, a1, alpha := &fe2{}, &fe2{}, &fe2{}, &fe2{}
u.set(a)
e.exp(a1, a, pMinus3Over4)
e.square(alpha, a1)
e.mul(alpha, alpha, a)
e.mul(x0, a1, a)
if alpha.equal(negativeOne2) {
neg(&c[0], &x0[1])
c[1].set(&x0[0])
return true
}
e.add(alpha, alpha, e.one())
e.exp(alpha, alpha, pMinus1Over2)
e.mul(c, alpha, x0)
e.square(alpha, c)
return alpha.equal(u)
}
func (e *fp2) isQuadraticNonResidue(a *fe2) bool {
// https://github.com/leovt/constructible/wiki/Taking-Square-Roots-in-quadratic-extension-Fields
c0, c1 := new(fe), new(fe)
square(c0, &a[0])
square(c1, &a[1])
add(c1, c1, c0)
return isQuadraticNonResidue(c1)
}