435 lines
10 KiB
Go
435 lines
10 KiB
Go
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// 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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"errors"
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"math"
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"math/big"
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)
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// PointG1 is type for point in G1.
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// PointG1 is both used for Affine and Jacobian point representation.
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// If z is equal to one the point is considered as in affine form.
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type PointG1 [3]fe
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func (p *PointG1) Set(p2 *PointG1) *PointG1 {
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p[0].set(&p2[0])
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p[1].set(&p2[1])
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p[2].set(&p2[2])
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return p
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}
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// Zero returns G1 point in point at infinity representation
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func (p *PointG1) Zero() *PointG1 {
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p[0].zero()
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p[1].one()
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p[2].zero()
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return p
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}
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type tempG1 struct {
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t [9]*fe
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}
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// G1 is struct for G1 group.
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type G1 struct {
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tempG1
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}
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// NewG1 constructs a new G1 instance.
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func NewG1() *G1 {
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t := newTempG1()
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return &G1{t}
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}
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func newTempG1() tempG1 {
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t := [9]*fe{}
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for i := 0; i < 9; i++ {
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t[i] = &fe{}
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}
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return tempG1{t}
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}
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// Q returns group order in big.Int.
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func (g *G1) Q() *big.Int {
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return new(big.Int).Set(q)
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}
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func (g *G1) fromBytesUnchecked(in []byte) (*PointG1, error) {
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p0, err := fromBytes(in[:48])
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if err != nil {
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return nil, err
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}
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p1, err := fromBytes(in[48:])
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if err != nil {
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return nil, err
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}
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p2 := new(fe).one()
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return &PointG1{*p0, *p1, *p2}, nil
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}
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// FromBytes constructs a new point given uncompressed byte input.
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// FromBytes does not take zcash flags into account.
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// Byte input expected to be larger than 96 bytes.
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// First 96 bytes should be concatenation of x and y values.
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// Point (0, 0) is considered as infinity.
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func (g *G1) FromBytes(in []byte) (*PointG1, error) {
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if len(in) != 96 {
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return nil, errors.New("input string should be equal or larger than 96")
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}
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p0, err := fromBytes(in[:48])
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if err != nil {
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return nil, err
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}
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p1, err := fromBytes(in[48:])
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if err != nil {
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return nil, err
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}
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// check if given input points to infinity
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if p0.isZero() && p1.isZero() {
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return g.Zero(), nil
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}
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p2 := new(fe).one()
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p := &PointG1{*p0, *p1, *p2}
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if !g.IsOnCurve(p) {
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return nil, errors.New("point is not on curve")
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}
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return p, nil
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}
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// DecodePoint given encoded (x, y) coordinates in 128 bytes returns a valid G1 Point.
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func (g *G1) DecodePoint(in []byte) (*PointG1, error) {
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if len(in) != 128 {
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return nil, errors.New("invalid g1 point length")
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}
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pointBytes := make([]byte, 96)
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// decode x
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xBytes, err := decodeFieldElement(in[:64])
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if err != nil {
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return nil, err
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}
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// decode y
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yBytes, err := decodeFieldElement(in[64:])
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if err != nil {
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return nil, err
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}
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copy(pointBytes[:48], xBytes)
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copy(pointBytes[48:], yBytes)
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return g.FromBytes(pointBytes)
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}
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// ToBytes serializes a point into bytes in uncompressed form.
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// ToBytes does not take zcash flags into account.
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// ToBytes returns (0, 0) if point is infinity.
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func (g *G1) ToBytes(p *PointG1) []byte {
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out := make([]byte, 96)
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if g.IsZero(p) {
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return out
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}
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g.Affine(p)
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copy(out[:48], toBytes(&p[0]))
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copy(out[48:], toBytes(&p[1]))
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return out
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}
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// EncodePoint encodes a point into 128 bytes.
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func (g *G1) EncodePoint(p *PointG1) []byte {
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outRaw := g.ToBytes(p)
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out := make([]byte, 128)
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// encode x
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copy(out[16:], outRaw[:48])
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// encode y
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copy(out[64+16:], outRaw[48:])
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return out
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}
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// New creates a new G1 Point which is equal to zero in other words point at infinity.
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func (g *G1) New() *PointG1 {
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return g.Zero()
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}
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// Zero returns a new G1 Point which is equal to point at infinity.
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func (g *G1) Zero() *PointG1 {
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return new(PointG1).Zero()
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}
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// One returns a new G1 Point which is equal to generator point.
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func (g *G1) One() *PointG1 {
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p := &PointG1{}
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return p.Set(&g1One)
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}
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// IsZero returns true if given point is equal to zero.
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func (g *G1) IsZero(p *PointG1) bool {
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return p[2].isZero()
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}
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// Equal checks if given two G1 point is equal in their affine form.
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func (g *G1) Equal(p1, p2 *PointG1) bool {
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if g.IsZero(p1) {
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return g.IsZero(p2)
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}
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if g.IsZero(p2) {
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return g.IsZero(p1)
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}
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t := g.t
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square(t[0], &p1[2])
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square(t[1], &p2[2])
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mul(t[2], t[0], &p2[0])
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mul(t[3], t[1], &p1[0])
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mul(t[0], t[0], &p1[2])
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mul(t[1], t[1], &p2[2])
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mul(t[1], t[1], &p1[1])
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mul(t[0], t[0], &p2[1])
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return t[0].equal(t[1]) && t[2].equal(t[3])
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}
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// InCorrectSubgroup checks whether given point is in correct subgroup.
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func (g *G1) InCorrectSubgroup(p *PointG1) bool {
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tmp := &PointG1{}
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g.MulScalar(tmp, p, q)
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return g.IsZero(tmp)
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}
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// IsOnCurve checks a G1 point is on curve.
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func (g *G1) IsOnCurve(p *PointG1) bool {
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if g.IsZero(p) {
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return true
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}
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t := g.t
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square(t[0], &p[1])
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square(t[1], &p[0])
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mul(t[1], t[1], &p[0])
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square(t[2], &p[2])
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square(t[3], t[2])
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mul(t[2], t[2], t[3])
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mul(t[2], b, t[2])
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add(t[1], t[1], t[2])
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return t[0].equal(t[1])
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}
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// IsAffine checks a G1 point whether it is in affine form.
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func (g *G1) IsAffine(p *PointG1) bool {
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return p[2].isOne()
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}
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// Add adds two G1 points p1, p2 and assigns the result to point at first argument.
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func (g *G1) Affine(p *PointG1) *PointG1 {
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if g.IsZero(p) {
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return p
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}
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if !g.IsAffine(p) {
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t := g.t
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inverse(t[0], &p[2])
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square(t[1], t[0])
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mul(&p[0], &p[0], t[1])
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mul(t[0], t[0], t[1])
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mul(&p[1], &p[1], t[0])
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p[2].one()
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}
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return p
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}
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// Add adds two G1 points p1, p2 and assigns the result to point at first argument.
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func (g *G1) Add(r, p1, p2 *PointG1) *PointG1 {
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// http://www.hyperelliptic.org/EFD/gp/auto-shortw-jacobian-0.html#addition-add-2007-bl
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if g.IsZero(p1) {
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return r.Set(p2)
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}
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if g.IsZero(p2) {
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return r.Set(p1)
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}
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t := g.t
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square(t[7], &p1[2])
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mul(t[1], &p2[0], t[7])
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mul(t[2], &p1[2], t[7])
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mul(t[0], &p2[1], t[2])
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square(t[8], &p2[2])
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mul(t[3], &p1[0], t[8])
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mul(t[4], &p2[2], t[8])
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mul(t[2], &p1[1], t[4])
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if t[1].equal(t[3]) {
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if t[0].equal(t[2]) {
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return g.Double(r, p1)
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}
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return r.Zero()
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}
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sub(t[1], t[1], t[3])
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double(t[4], t[1])
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square(t[4], t[4])
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mul(t[5], t[1], t[4])
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sub(t[0], t[0], t[2])
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double(t[0], t[0])
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square(t[6], t[0])
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sub(t[6], t[6], t[5])
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mul(t[3], t[3], t[4])
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double(t[4], t[3])
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sub(&r[0], t[6], t[4])
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sub(t[4], t[3], &r[0])
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mul(t[6], t[2], t[5])
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double(t[6], t[6])
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mul(t[0], t[0], t[4])
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sub(&r[1], t[0], t[6])
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add(t[0], &p1[2], &p2[2])
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square(t[0], t[0])
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sub(t[0], t[0], t[7])
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sub(t[0], t[0], t[8])
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mul(&r[2], t[0], t[1])
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return r
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}
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// Double doubles a G1 point p and assigns the result to the point at first argument.
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func (g *G1) Double(r, p *PointG1) *PointG1 {
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// http://www.hyperelliptic.org/EFD/gp/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
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if g.IsZero(p) {
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return r.Set(p)
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}
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t := g.t
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square(t[0], &p[0])
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square(t[1], &p[1])
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square(t[2], t[1])
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add(t[1], &p[0], t[1])
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square(t[1], t[1])
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sub(t[1], t[1], t[0])
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sub(t[1], t[1], t[2])
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double(t[1], t[1])
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double(t[3], t[0])
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add(t[0], t[3], t[0])
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square(t[4], t[0])
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double(t[3], t[1])
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sub(&r[0], t[4], t[3])
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sub(t[1], t[1], &r[0])
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double(t[2], t[2])
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double(t[2], t[2])
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double(t[2], t[2])
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mul(t[0], t[0], t[1])
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sub(t[1], t[0], t[2])
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mul(t[0], &p[1], &p[2])
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r[1].set(t[1])
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double(&r[2], t[0])
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return r
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}
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// Neg negates a G1 point p and assigns the result to the point at first argument.
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func (g *G1) Neg(r, p *PointG1) *PointG1 {
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r[0].set(&p[0])
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r[2].set(&p[2])
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neg(&r[1], &p[1])
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return r
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}
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// Sub subtracts two G1 points p1, p2 and assigns the result to point at first argument.
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func (g *G1) Sub(c, a, b *PointG1) *PointG1 {
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d := &PointG1{}
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g.Neg(d, b)
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g.Add(c, a, d)
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return c
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}
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// MulScalar multiplies a point by given scalar value in big.Int and assigns the result to point at first argument.
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func (g *G1) MulScalar(c, p *PointG1, e *big.Int) *PointG1 {
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q, n := &PointG1{}, &PointG1{}
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n.Set(p)
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l := e.BitLen()
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for i := 0; i < l; i++ {
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if e.Bit(i) == 1 {
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g.Add(q, q, n)
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}
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g.Double(n, n)
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}
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return c.Set(q)
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}
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// ClearCofactor maps given a G1 point to correct subgroup
|
||
|
|
func (g *G1) ClearCofactor(p *PointG1) {
|
||
|
|
g.MulScalar(p, p, cofactorEFFG1)
|
||
|
|
}
|
||
|
|
|
||
|
|
// MultiExp calculates multi exponentiation. Given pairs of G1 point and scalar values
|
||
|
|
// (P_0, e_0), (P_1, e_1), ... (P_n, e_n) calculates r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n
|
||
|
|
// Length of points and scalars are expected to be equal, otherwise an error is returned.
|
||
|
|
// Result is assigned to point at first argument.
|
||
|
|
func (g *G1) MultiExp(r *PointG1, points []*PointG1, powers []*big.Int) (*PointG1, error) {
|
||
|
|
if len(points) != len(powers) {
|
||
|
|
return nil, errors.New("point and scalar vectors should be in same length")
|
||
|
|
}
|
||
|
|
var c uint32 = 3
|
||
|
|
if len(powers) >= 32 {
|
||
|
|
c = uint32(math.Ceil(math.Log10(float64(len(powers)))))
|
||
|
|
}
|
||
|
|
bucketSize, numBits := (1<<c)-1, uint32(g.Q().BitLen())
|
||
|
|
windows := make([]*PointG1, numBits/c+1)
|
||
|
|
bucket := make([]*PointG1, bucketSize)
|
||
|
|
acc, sum := g.New(), g.New()
|
||
|
|
for i := 0; i < bucketSize; i++ {
|
||
|
|
bucket[i] = g.New()
|
||
|
|
}
|
||
|
|
mask := (uint64(1) << c) - 1
|
||
|
|
j := 0
|
||
|
|
var cur uint32
|
||
|
|
for cur <= numBits {
|
||
|
|
acc.Zero()
|
||
|
|
bucket = make([]*PointG1, (1<<c)-1)
|
||
|
|
for i := 0; i < len(bucket); i++ {
|
||
|
|
bucket[i] = g.New()
|
||
|
|
}
|
||
|
|
for i := 0; i < len(powers); i++ {
|
||
|
|
s0 := powers[i].Uint64()
|
||
|
|
index := uint(s0 & mask)
|
||
|
|
if index != 0 {
|
||
|
|
g.Add(bucket[index-1], bucket[index-1], points[i])
|
||
|
|
}
|
||
|
|
powers[i] = new(big.Int).Rsh(powers[i], uint(c))
|
||
|
|
}
|
||
|
|
sum.Zero()
|
||
|
|
for i := len(bucket) - 1; i >= 0; i-- {
|
||
|
|
g.Add(sum, sum, bucket[i])
|
||
|
|
g.Add(acc, acc, sum)
|
||
|
|
}
|
||
|
|
windows[j] = g.New()
|
||
|
|
windows[j].Set(acc)
|
||
|
|
j++
|
||
|
|
cur += c
|
||
|
|
}
|
||
|
|
acc.Zero()
|
||
|
|
for i := len(windows) - 1; i >= 0; i-- {
|
||
|
|
for j := uint32(0); j < c; j++ {
|
||
|
|
g.Double(acc, acc)
|
||
|
|
}
|
||
|
|
g.Add(acc, acc, windows[i])
|
||
|
|
}
|
||
|
|
return r.Set(acc), nil
|
||
|
|
}
|
||
|
|
|
||
|
|
// MapToCurve given a byte slice returns a valid G1 point.
|
||
|
|
// This mapping function implements the Simplified Shallue-van de Woestijne-Ulas method.
|
||
|
|
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06
|
||
|
|
// Input byte slice should be a valid field element, otherwise an error is returned.
|
||
|
|
func (g *G1) MapToCurve(in []byte) (*PointG1, error) {
|
||
|
|
u, err := fromBytes(in)
|
||
|
|
if err != nil {
|
||
|
|
return nil, err
|
||
|
|
}
|
||
|
|
x, y := swuMapG1(u)
|
||
|
|
isogenyMapG1(x, y)
|
||
|
|
one := new(fe).one()
|
||
|
|
p := &PointG1{*x, *y, *one}
|
||
|
|
g.ClearCofactor(p)
|
||
|
|
return g.Affine(p), nil
|
||
|
|
}
|