plugeth/crypto/bls12381/g2.go
2024-02-05 22:16:32 +01:00

456 lines
11 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"
"math/big"
)
// PointG2 is type for point in G2.
// PointG2 is both used for Affine and Jacobian point representation.
// If z is equal to one the point is considered as in affine form.
type PointG2 [3]fe2
// Set copies values of one point to another.
func (p *PointG2) Set(p2 *PointG2) *PointG2 {
p[0].set(&p2[0])
p[1].set(&p2[1])
p[2].set(&p2[2])
return p
}
// Zero returns G2 point in point at infinity representation
func (p *PointG2) Zero() *PointG2 {
p[0].zero()
p[1].one()
p[2].zero()
return p
}
type tempG2 struct {
t [9]*fe2
}
// G2 is struct for G2 group.
type G2 struct {
f *fp2
tempG2
}
// NewG2 constructs a new G2 instance.
func NewG2() *G2 {
return newG2(nil)
}
func newG2(f *fp2) *G2 {
if f == nil {
f = newFp2()
}
t := newTempG2()
return &G2{f, t}
}
func newTempG2() tempG2 {
t := [9]*fe2{}
for i := 0; i < 9; i++ {
t[i] = &fe2{}
}
return tempG2{t}
}
// Q returns group order in big.Int.
func (g *G2) Q() *big.Int {
return new(big.Int).Set(q)
}
func (g *G2) fromBytesUnchecked(in []byte) (*PointG2, error) {
p0, err := g.f.fromBytes(in[:96])
if err != nil {
return nil, err
}
p1, err := g.f.fromBytes(in[96:])
if err != nil {
return nil, err
}
p2 := new(fe2).one()
return &PointG2{*p0, *p1, *p2}, nil
}
// FromBytes constructs a new point given uncompressed byte input.
// FromBytes does not take zcash flags into account.
// Byte input expected to be larger than 96 bytes.
// First 192 bytes should be concatenation of x and y values
// Point (0, 0) is considered as infinity.
func (g *G2) FromBytes(in []byte) (*PointG2, error) {
if len(in) != 192 {
return nil, errors.New("input string should be equal or larger than 192")
}
p0, err := g.f.fromBytes(in[:96])
if err != nil {
return nil, err
}
p1, err := g.f.fromBytes(in[96:])
if err != nil {
return nil, err
}
// check if given input points to infinity
if p0.isZero() && p1.isZero() {
return g.Zero(), nil
}
p2 := new(fe2).one()
p := &PointG2{*p0, *p1, *p2}
if !g.IsOnCurve(p) {
return nil, errors.New("point is not on curve")
}
return p, nil
}
// DecodePoint given encoded (x, y) coordinates in 256 bytes returns a valid G2 Point.
func (g *G2) DecodePoint(in []byte) (*PointG2, error) {
if len(in) != 256 {
return nil, errors.New("invalid g2 point length")
}
pointBytes := make([]byte, 192)
x0Bytes, err := decodeFieldElement(in[:64])
if err != nil {
return nil, err
}
x1Bytes, err := decodeFieldElement(in[64:128])
if err != nil {
return nil, err
}
y0Bytes, err := decodeFieldElement(in[128:192])
if err != nil {
return nil, err
}
y1Bytes, err := decodeFieldElement(in[192:])
if err != nil {
return nil, err
}
copy(pointBytes[:48], x1Bytes)
copy(pointBytes[48:96], x0Bytes)
copy(pointBytes[96:144], y1Bytes)
copy(pointBytes[144:192], y0Bytes)
return g.FromBytes(pointBytes)
}
// ToBytes serializes a point into bytes in uncompressed form,
// does not take zcash flags into account,
// returns (0, 0) if point is infinity.
func (g *G2) ToBytes(p *PointG2) []byte {
out := make([]byte, 192)
if g.IsZero(p) {
return out
}
g.Affine(p)
copy(out[:96], g.f.toBytes(&p[0]))
copy(out[96:], g.f.toBytes(&p[1]))
return out
}
// EncodePoint encodes a point into 256 bytes.
func (g *G2) EncodePoint(p *PointG2) []byte {
// outRaw is 96 bytes
outRaw := g.ToBytes(p)
out := make([]byte, 256)
// encode x
copy(out[16:16+48], outRaw[48:96])
copy(out[80:80+48], outRaw[:48])
// encode y
copy(out[144:144+48], outRaw[144:])
copy(out[208:208+48], outRaw[96:144])
return out
}
// New creates a new G2 Point which is equal to zero in other words point at infinity.
func (g *G2) New() *PointG2 {
return new(PointG2).Zero()
}
// Zero returns a new G2 Point which is equal to point at infinity.
func (g *G2) Zero() *PointG2 {
return new(PointG2).Zero()
}
// One returns a new G2 Point which is equal to generator point.
func (g *G2) One() *PointG2 {
p := &PointG2{}
return p.Set(&g2One)
}
// IsZero returns true if given point is equal to zero.
func (g *G2) IsZero(p *PointG2) bool {
return p[2].isZero()
}
// Equal checks if given two G2 point is equal in their affine form.
func (g *G2) Equal(p1, p2 *PointG2) bool {
if g.IsZero(p1) {
return g.IsZero(p2)
}
if g.IsZero(p2) {
return g.IsZero(p1)
}
t := g.t
g.f.square(t[0], &p1[2])
g.f.square(t[1], &p2[2])
g.f.mul(t[2], t[0], &p2[0])
g.f.mul(t[3], t[1], &p1[0])
g.f.mul(t[0], t[0], &p1[2])
g.f.mul(t[1], t[1], &p2[2])
g.f.mul(t[1], t[1], &p1[1])
g.f.mul(t[0], t[0], &p2[1])
return t[0].equal(t[1]) && t[2].equal(t[3])
}
// InCorrectSubgroup checks whether given point is in correct subgroup.
func (g *G2) InCorrectSubgroup(p *PointG2) bool {
tmp := &PointG2{}
g.MulScalar(tmp, p, q)
return g.IsZero(tmp)
}
// IsOnCurve checks a G2 point is on curve.
func (g *G2) IsOnCurve(p *PointG2) bool {
if g.IsZero(p) {
return true
}
t := g.t
g.f.square(t[0], &p[1])
g.f.square(t[1], &p[0])
g.f.mul(t[1], t[1], &p[0])
g.f.square(t[2], &p[2])
g.f.square(t[3], t[2])
g.f.mul(t[2], t[2], t[3])
g.f.mul(t[2], b2, t[2])
g.f.add(t[1], t[1], t[2])
return t[0].equal(t[1])
}
// IsAffine checks a G2 point whether it is in affine form.
func (g *G2) IsAffine(p *PointG2) bool {
return p[2].isOne()
}
// Affine calculates affine form of given G2 point.
func (g *G2) Affine(p *PointG2) *PointG2 {
if g.IsZero(p) {
return p
}
if !g.IsAffine(p) {
t := g.t
g.f.inverse(t[0], &p[2])
g.f.square(t[1], t[0])
g.f.mul(&p[0], &p[0], t[1])
g.f.mul(t[0], t[0], t[1])
g.f.mul(&p[1], &p[1], t[0])
p[2].one()
}
return p
}
// Add adds two G2 points p1, p2 and assigns the result to point at first argument.
func (g *G2) Add(r, p1, p2 *PointG2) *PointG2 {
// http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl
if g.IsZero(p1) {
return r.Set(p2)
}
if g.IsZero(p2) {
return r.Set(p1)
}
t := g.t
g.f.square(t[7], &p1[2])
g.f.mul(t[1], &p2[0], t[7])
g.f.mul(t[2], &p1[2], t[7])
g.f.mul(t[0], &p2[1], t[2])
g.f.square(t[8], &p2[2])
g.f.mul(t[3], &p1[0], t[8])
g.f.mul(t[4], &p2[2], t[8])
g.f.mul(t[2], &p1[1], t[4])
if t[1].equal(t[3]) {
if t[0].equal(t[2]) {
return g.Double(r, p1)
}
return r.Zero()
}
g.f.sub(t[1], t[1], t[3])
g.f.double(t[4], t[1])
g.f.square(t[4], t[4])
g.f.mul(t[5], t[1], t[4])
g.f.sub(t[0], t[0], t[2])
g.f.double(t[0], t[0])
g.f.square(t[6], t[0])
g.f.sub(t[6], t[6], t[5])
g.f.mul(t[3], t[3], t[4])
g.f.double(t[4], t[3])
g.f.sub(&r[0], t[6], t[4])
g.f.sub(t[4], t[3], &r[0])
g.f.mul(t[6], t[2], t[5])
g.f.double(t[6], t[6])
g.f.mul(t[0], t[0], t[4])
g.f.sub(&r[1], t[0], t[6])
g.f.add(t[0], &p1[2], &p2[2])
g.f.square(t[0], t[0])
g.f.sub(t[0], t[0], t[7])
g.f.sub(t[0], t[0], t[8])
g.f.mul(&r[2], t[0], t[1])
return r
}
// Double doubles a G2 point p and assigns the result to the point at first argument.
func (g *G2) Double(r, p *PointG2) *PointG2 {
// http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
if g.IsZero(p) {
return r.Set(p)
}
t := g.t
g.f.square(t[0], &p[0])
g.f.square(t[1], &p[1])
g.f.square(t[2], t[1])
g.f.add(t[1], &p[0], t[1])
g.f.square(t[1], t[1])
g.f.sub(t[1], t[1], t[0])
g.f.sub(t[1], t[1], t[2])
g.f.double(t[1], t[1])
g.f.double(t[3], t[0])
g.f.add(t[0], t[3], t[0])
g.f.square(t[4], t[0])
g.f.double(t[3], t[1])
g.f.sub(&r[0], t[4], t[3])
g.f.sub(t[1], t[1], &r[0])
g.f.double(t[2], t[2])
g.f.double(t[2], t[2])
g.f.double(t[2], t[2])
g.f.mul(t[0], t[0], t[1])
g.f.sub(t[1], t[0], t[2])
g.f.mul(t[0], &p[1], &p[2])
r[1].set(t[1])
g.f.double(&r[2], t[0])
return r
}
// Neg negates a G2 point p and assigns the result to the point at first argument.
func (g *G2) Neg(r, p *PointG2) *PointG2 {
r[0].set(&p[0])
g.f.neg(&r[1], &p[1])
r[2].set(&p[2])
return r
}
// Sub subtracts two G2 points p1, p2 and assigns the result to point at first argument.
func (g *G2) Sub(c, a, b *PointG2) *PointG2 {
d := &PointG2{}
g.Neg(d, b)
g.Add(c, a, d)
return c
}
// MulScalar multiplies a point by given scalar value in big.Int and assigns the result to point at first argument.
func (g *G2) MulScalar(c, p *PointG2, e *big.Int) *PointG2 {
q, n := &PointG2{}, &PointG2{}
n.Set(p)
l := e.BitLen()
for i := 0; i < l; i++ {
if e.Bit(i) == 1 {
g.Add(q, q, n)
}
g.Double(n, n)
}
return c.Set(q)
}
// ClearCofactor maps given a G2 point to correct subgroup
func (g *G2) ClearCofactor(p *PointG2) {
g.MulScalar(p, p, cofactorEFFG2)
}
// MultiExp calculates multi exponentiation. Given pairs of G2 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 *G2) MultiExp(r *PointG2, points []*PointG2, powers []*big.Int) (*PointG2, 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([]*PointG2, numBits/c+1)
bucket := make([]*PointG2, 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([]*PointG2, (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 G2 point.
// This mapping function implements the Simplified Shallue-van de Woestijne-Ulas method.
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-05#section-6.6.2
// Input byte slice should be a valid field element, otherwise an error is returned.
func (g *G2) MapToCurve(in []byte) (*PointG2, error) {
fp2 := g.f
u, err := fp2.fromBytes(in)
if err != nil {
return nil, err
}
x, y := swuMapG2(fp2, u)
isogenyMapG2(fp2, x, y)
z := new(fe2).one()
q := &PointG2{*x, *y, *z}
g.ClearCofactor(q)
return g.Affine(q), nil
}