341 lines
6.5 KiB
Go
341 lines
6.5 KiB
Go
// Copyright 2020 The go-ethereum Authors
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// This file is part of the go-ethereum library.
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//
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// The go-ethereum library is free software: you can redistribute it and/or modify
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// it under the terms of the GNU Lesser General Public License as published by
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// the Free Software Foundation, either version 3 of the License, or
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// (at your option) any later version.
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//
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// The go-ethereum library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU Lesser General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public License
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// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
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package bls12381
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import (
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"crypto/rand"
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"encoding/hex"
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"fmt"
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"io"
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"math/big"
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)
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// fe is base field element representation
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type fe [6]uint64
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// fe2 is element representation of 'fp2' which is quadratic extension of base field 'fp'
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// Representation follows c[0] + c[1] * u encoding order.
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type fe2 [2]fe
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// fe6 is element representation of 'fp6' field which is cubic extension of 'fp2'
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// Representation follows c[0] + c[1] * v + c[2] * v^2 encoding order.
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type fe6 [3]fe2
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// fe12 is element representation of 'fp12' field which is quadratic extension of 'fp6'
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// Representation follows c[0] + c[1] * w encoding order.
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type fe12 [2]fe6
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func (fe *fe) setBytes(in []byte) *fe {
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size := 48
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l := len(in)
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if l >= size {
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l = size
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}
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padded := make([]byte, size)
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copy(padded[size-l:], in[:])
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var a int
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for i := 0; i < 6; i++ {
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a = size - i*8
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fe[i] = uint64(padded[a-1]) | uint64(padded[a-2])<<8 |
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uint64(padded[a-3])<<16 | uint64(padded[a-4])<<24 |
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uint64(padded[a-5])<<32 | uint64(padded[a-6])<<40 |
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uint64(padded[a-7])<<48 | uint64(padded[a-8])<<56
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}
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return fe
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}
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func (fe *fe) setBig(a *big.Int) *fe {
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return fe.setBytes(a.Bytes())
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}
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func (fe *fe) setString(s string) (*fe, error) {
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if s[:2] == "0x" {
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s = s[2:]
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}
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bytes, err := hex.DecodeString(s)
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if err != nil {
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return nil, err
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}
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return fe.setBytes(bytes), nil
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}
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func (fe *fe) set(fe2 *fe) *fe {
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fe[0] = fe2[0]
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fe[1] = fe2[1]
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fe[2] = fe2[2]
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fe[3] = fe2[3]
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fe[4] = fe2[4]
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fe[5] = fe2[5]
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return fe
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}
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func (fe *fe) bytes() []byte {
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out := make([]byte, 48)
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var a int
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for i := 0; i < 6; i++ {
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a = 48 - i*8
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out[a-1] = byte(fe[i])
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out[a-2] = byte(fe[i] >> 8)
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out[a-3] = byte(fe[i] >> 16)
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out[a-4] = byte(fe[i] >> 24)
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out[a-5] = byte(fe[i] >> 32)
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out[a-6] = byte(fe[i] >> 40)
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out[a-7] = byte(fe[i] >> 48)
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out[a-8] = byte(fe[i] >> 56)
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}
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return out
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}
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func (fe *fe) big() *big.Int {
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return new(big.Int).SetBytes(fe.bytes())
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}
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func (fe *fe) string() (s string) {
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for i := 5; i >= 0; i-- {
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s = fmt.Sprintf("%s%16.16x", s, fe[i])
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}
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return "0x" + s
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}
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func (fe *fe) zero() *fe {
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fe[0] = 0
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fe[1] = 0
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fe[2] = 0
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fe[3] = 0
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fe[4] = 0
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fe[5] = 0
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return fe
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}
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func (fe *fe) one() *fe {
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return fe.set(r1)
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}
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func (fe *fe) rand(r io.Reader) (*fe, error) {
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bi, err := rand.Int(r, modulus.big())
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if err != nil {
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return nil, err
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}
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return fe.setBig(bi), nil
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}
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func (fe *fe) isValid() bool {
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return fe.cmp(&modulus) < 0
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}
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func (fe *fe) isOdd() bool {
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var mask uint64 = 1
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return fe[0]&mask != 0
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}
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func (fe *fe) isEven() bool {
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var mask uint64 = 1
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return fe[0]&mask == 0
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}
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func (fe *fe) isZero() bool {
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return (fe[5] | fe[4] | fe[3] | fe[2] | fe[1] | fe[0]) == 0
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}
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func (fe *fe) isOne() bool {
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return fe.equal(r1)
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}
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func (fe *fe) cmp(fe2 *fe) int {
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for i := 5; i >= 0; i-- {
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if fe[i] > fe2[i] {
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return 1
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} else if fe[i] < fe2[i] {
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return -1
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}
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}
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return 0
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}
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func (fe *fe) equal(fe2 *fe) bool {
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return fe2[0] == fe[0] && fe2[1] == fe[1] && fe2[2] == fe[2] && fe2[3] == fe[3] && fe2[4] == fe[4] && fe2[5] == fe[5]
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}
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func (e *fe) sign() bool {
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r := new(fe)
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fromMont(r, e)
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return r[0]&1 == 0
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}
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func (fe *fe) div2(e uint64) {
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fe[0] = fe[0]>>1 | fe[1]<<63
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fe[1] = fe[1]>>1 | fe[2]<<63
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fe[2] = fe[2]>>1 | fe[3]<<63
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fe[3] = fe[3]>>1 | fe[4]<<63
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fe[4] = fe[4]>>1 | fe[5]<<63
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fe[5] = fe[5]>>1 | e<<63
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}
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func (fe *fe) mul2() uint64 {
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e := fe[5] >> 63
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fe[5] = fe[5]<<1 | fe[4]>>63
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fe[4] = fe[4]<<1 | fe[3]>>63
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fe[3] = fe[3]<<1 | fe[2]>>63
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fe[2] = fe[2]<<1 | fe[1]>>63
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fe[1] = fe[1]<<1 | fe[0]>>63
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fe[0] = fe[0] << 1
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return e
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}
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func (e *fe2) zero() *fe2 {
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e[0].zero()
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e[1].zero()
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return e
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}
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func (e *fe2) one() *fe2 {
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e[0].one()
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e[1].zero()
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return e
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}
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func (e *fe2) set(e2 *fe2) *fe2 {
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e[0].set(&e2[0])
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e[1].set(&e2[1])
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return e
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}
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func (e *fe2) rand(r io.Reader) (*fe2, error) {
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a0, err := new(fe).rand(r)
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if err != nil {
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return nil, err
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}
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a1, err := new(fe).rand(r)
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if err != nil {
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return nil, err
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}
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return &fe2{*a0, *a1}, nil
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}
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func (e *fe2) isOne() bool {
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return e[0].isOne() && e[1].isZero()
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}
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func (e *fe2) isZero() bool {
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return e[0].isZero() && e[1].isZero()
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}
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func (e *fe2) equal(e2 *fe2) bool {
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return e[0].equal(&e2[0]) && e[1].equal(&e2[1])
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}
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func (e *fe2) sign() bool {
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r := new(fe)
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if !e[0].isZero() {
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fromMont(r, &e[0])
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return r[0]&1 == 0
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}
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fromMont(r, &e[1])
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return r[0]&1 == 0
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}
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func (e *fe6) zero() *fe6 {
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e[0].zero()
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e[1].zero()
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e[2].zero()
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return e
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}
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func (e *fe6) one() *fe6 {
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e[0].one()
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e[1].zero()
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e[2].zero()
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return e
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}
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func (e *fe6) set(e2 *fe6) *fe6 {
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e[0].set(&e2[0])
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e[1].set(&e2[1])
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e[2].set(&e2[2])
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return e
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}
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func (e *fe6) rand(r io.Reader) (*fe6, error) {
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a0, err := new(fe2).rand(r)
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if err != nil {
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return nil, err
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}
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a1, err := new(fe2).rand(r)
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if err != nil {
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return nil, err
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}
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a2, err := new(fe2).rand(r)
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if err != nil {
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return nil, err
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}
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return &fe6{*a0, *a1, *a2}, nil
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}
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func (e *fe6) isOne() bool {
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return e[0].isOne() && e[1].isZero() && e[2].isZero()
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}
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func (e *fe6) isZero() bool {
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return e[0].isZero() && e[1].isZero() && e[2].isZero()
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}
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func (e *fe6) equal(e2 *fe6) bool {
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return e[0].equal(&e2[0]) && e[1].equal(&e2[1]) && e[2].equal(&e2[2])
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}
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func (e *fe12) zero() *fe12 {
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e[0].zero()
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e[1].zero()
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return e
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}
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func (e *fe12) one() *fe12 {
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e[0].one()
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e[1].zero()
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return e
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}
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func (e *fe12) set(e2 *fe12) *fe12 {
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e[0].set(&e2[0])
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e[1].set(&e2[1])
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return e
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}
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func (e *fe12) rand(r io.Reader) (*fe12, error) {
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a0, err := new(fe6).rand(r)
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if err != nil {
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return nil, err
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}
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a1, err := new(fe6).rand(r)
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if err != nil {
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return nil, err
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}
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return &fe12{*a0, *a1}, nil
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}
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func (e *fe12) isOne() bool {
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return e[0].isOne() && e[1].isZero()
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}
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func (e *fe12) isZero() bool {
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return e[0].isZero() && e[1].isZero()
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}
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func (e *fe12) equal(e2 *fe12) bool {
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return e[0].equal(&e2[0]) && e[1].equal(&e2[1])
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}
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