456 lines
11 KiB
Go
456 lines
11 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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"errors"
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"math"
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"math/big"
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)
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// PointG2 is type for point in G2.
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// PointG2 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 PointG2 [3]fe2
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// Set copies valeus of one point to another.
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func (p *PointG2) Set(p2 *PointG2) *PointG2 {
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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 G2 point in point at infinity representation
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func (p *PointG2) Zero() *PointG2 {
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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 tempG2 struct {
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t [9]*fe2
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}
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// G2 is struct for G2 group.
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type G2 struct {
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f *fp2
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tempG2
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}
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// NewG2 constructs a new G2 instance.
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func NewG2() *G2 {
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return newG2(nil)
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}
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func newG2(f *fp2) *G2 {
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if f == nil {
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f = newFp2()
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}
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t := newTempG2()
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return &G2{f, t}
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}
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func newTempG2() tempG2 {
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t := [9]*fe2{}
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for i := 0; i < 9; i++ {
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t[i] = &fe2{}
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}
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return tempG2{t}
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}
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// Q returns group order in big.Int.
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func (g *G2) Q() *big.Int {
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return new(big.Int).Set(q)
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}
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func (g *G2) fromBytesUnchecked(in []byte) (*PointG2, error) {
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p0, err := g.f.fromBytes(in[:96])
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if err != nil {
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return nil, err
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}
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p1, err := g.f.fromBytes(in[96:])
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if err != nil {
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return nil, err
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}
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p2 := new(fe2).one()
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return &PointG2{*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 192 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 *G2) FromBytes(in []byte) (*PointG2, error) {
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if len(in) != 192 {
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return nil, errors.New("input string should be equal or larger than 192")
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}
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p0, err := g.f.fromBytes(in[:96])
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if err != nil {
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return nil, err
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}
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p1, err := g.f.fromBytes(in[96:])
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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(fe2).one()
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p := &PointG2{*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 256 bytes returns a valid G1 Point.
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func (g *G2) DecodePoint(in []byte) (*PointG2, error) {
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if len(in) != 256 {
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return nil, errors.New("invalid g2 point length")
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}
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pointBytes := make([]byte, 192)
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x0Bytes, 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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x1Bytes, err := decodeFieldElement(in[64:128])
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if err != nil {
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return nil, err
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}
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y0Bytes, err := decodeFieldElement(in[128:192])
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if err != nil {
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return nil, err
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}
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y1Bytes, err := decodeFieldElement(in[192:])
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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], x1Bytes)
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copy(pointBytes[48:96], x0Bytes)
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copy(pointBytes[96:144], y1Bytes)
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copy(pointBytes[144:192], y0Bytes)
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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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// does not take zcash flags into account,
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// returns (0, 0) if point is infinity.
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func (g *G2) ToBytes(p *PointG2) []byte {
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out := make([]byte, 192)
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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[:96], g.f.toBytes(&p[0]))
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copy(out[96:], g.f.toBytes(&p[1]))
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return out
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}
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// EncodePoint encodes a point into 256 bytes.
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func (g *G2) EncodePoint(p *PointG2) []byte {
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// outRaw is 96 bytes
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outRaw := g.ToBytes(p)
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out := make([]byte, 256)
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// encode x
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copy(out[16:16+48], outRaw[48:96])
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copy(out[80:80+48], outRaw[:48])
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// encode y
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copy(out[144:144+48], outRaw[144:])
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copy(out[208:208+48], outRaw[96:144])
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return out
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}
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// New creates a new G2 Point which is equal to zero in other words point at infinity.
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func (g *G2) New() *PointG2 {
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return new(PointG2).Zero()
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}
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// Zero returns a new G2 Point which is equal to point at infinity.
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func (g *G2) Zero() *PointG2 {
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return new(PointG2).Zero()
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}
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// One returns a new G2 Point which is equal to generator point.
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func (g *G2) One() *PointG2 {
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p := &PointG2{}
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return p.Set(&g2One)
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}
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// IsZero returns true if given point is equal to zero.
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func (g *G2) IsZero(p *PointG2) bool {
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return p[2].isZero()
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}
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// Equal checks if given two G2 point is equal in their affine form.
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func (g *G2) Equal(p1, p2 *PointG2) 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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g.f.square(t[0], &p1[2])
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g.f.square(t[1], &p2[2])
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g.f.mul(t[2], t[0], &p2[0])
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g.f.mul(t[3], t[1], &p1[0])
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g.f.mul(t[0], t[0], &p1[2])
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g.f.mul(t[1], t[1], &p2[2])
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g.f.mul(t[1], t[1], &p1[1])
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g.f.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 *G2) InCorrectSubgroup(p *PointG2) bool {
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tmp := &PointG2{}
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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 G2 point is on curve.
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func (g *G2) IsOnCurve(p *PointG2) 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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g.f.square(t[0], &p[1])
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g.f.square(t[1], &p[0])
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g.f.mul(t[1], t[1], &p[0])
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g.f.square(t[2], &p[2])
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g.f.square(t[3], t[2])
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g.f.mul(t[2], t[2], t[3])
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g.f.mul(t[2], b2, t[2])
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g.f.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 G2 point whether it is in affine form.
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func (g *G2) IsAffine(p *PointG2) bool {
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return p[2].isOne()
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}
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// Affine calculates affine form of given G2 point.
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func (g *G2) Affine(p *PointG2) *PointG2 {
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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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g.f.inverse(t[0], &p[2])
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g.f.square(t[1], t[0])
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g.f.mul(&p[0], &p[0], t[1])
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g.f.mul(t[0], t[0], t[1])
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g.f.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 G2 points p1, p2 and assigns the result to point at first argument.
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func (g *G2) Add(r, p1, p2 *PointG2) *PointG2 {
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// http://www.hyperelliptic.org/EFD/g1p/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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g.f.square(t[7], &p1[2])
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g.f.mul(t[1], &p2[0], t[7])
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g.f.mul(t[2], &p1[2], t[7])
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g.f.mul(t[0], &p2[1], t[2])
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g.f.square(t[8], &p2[2])
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g.f.mul(t[3], &p1[0], t[8])
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g.f.mul(t[4], &p2[2], t[8])
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g.f.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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g.f.sub(t[1], t[1], t[3])
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g.f.double(t[4], t[1])
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g.f.square(t[4], t[4])
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g.f.mul(t[5], t[1], t[4])
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g.f.sub(t[0], t[0], t[2])
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g.f.double(t[0], t[0])
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g.f.square(t[6], t[0])
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g.f.sub(t[6], t[6], t[5])
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g.f.mul(t[3], t[3], t[4])
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g.f.double(t[4], t[3])
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g.f.sub(&r[0], t[6], t[4])
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g.f.sub(t[4], t[3], &r[0])
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g.f.mul(t[6], t[2], t[5])
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g.f.double(t[6], t[6])
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g.f.mul(t[0], t[0], t[4])
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g.f.sub(&r[1], t[0], t[6])
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g.f.add(t[0], &p1[2], &p2[2])
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g.f.square(t[0], t[0])
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g.f.sub(t[0], t[0], t[7])
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g.f.sub(t[0], t[0], t[8])
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g.f.mul(&r[2], t[0], t[1])
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return r
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}
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// Double doubles a G2 point p and assigns the result to the point at first argument.
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func (g *G2) Double(r, p *PointG2) *PointG2 {
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// http://www.hyperelliptic.org/EFD/g1p/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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g.f.square(t[0], &p[0])
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g.f.square(t[1], &p[1])
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g.f.square(t[2], t[1])
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g.f.add(t[1], &p[0], t[1])
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g.f.square(t[1], t[1])
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g.f.sub(t[1], t[1], t[0])
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g.f.sub(t[1], t[1], t[2])
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g.f.double(t[1], t[1])
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g.f.double(t[3], t[0])
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g.f.add(t[0], t[3], t[0])
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g.f.square(t[4], t[0])
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g.f.double(t[3], t[1])
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g.f.sub(&r[0], t[4], t[3])
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g.f.sub(t[1], t[1], &r[0])
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g.f.double(t[2], t[2])
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g.f.double(t[2], t[2])
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g.f.double(t[2], t[2])
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g.f.mul(t[0], t[0], t[1])
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g.f.sub(t[1], t[0], t[2])
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g.f.mul(t[0], &p[1], &p[2])
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r[1].set(t[1])
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g.f.double(&r[2], t[0])
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return r
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}
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// Neg negates a G2 point p and assigns the result to the point at first argument.
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func (g *G2) Neg(r, p *PointG2) *PointG2 {
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r[0].set(&p[0])
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g.f.neg(&r[1], &p[1])
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r[2].set(&p[2])
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return r
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}
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// Sub subtracts two G2 points p1, p2 and assigns the result to point at first argument.
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func (g *G2) Sub(c, a, b *PointG2) *PointG2 {
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d := &PointG2{}
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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 *G2) MulScalar(c, p *PointG2, e *big.Int) *PointG2 {
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q, n := &PointG2{}, &PointG2{}
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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 G2 point to correct subgroup
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func (g *G2) ClearCofactor(p *PointG2) {
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g.MulScalar(p, p, cofactorEFFG2)
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}
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// MultiExp calculates multi exponentiation. Given pairs of G2 point and scalar values
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// (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
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// Length of points and scalars are expected to be equal, otherwise an error is returned.
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// Result is assigned to point at first argument.
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func (g *G2) MultiExp(r *PointG2, points []*PointG2, powers []*big.Int) (*PointG2, error) {
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if len(points) != len(powers) {
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return nil, errors.New("point and scalar vectors should be in same length")
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}
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var c uint32 = 3
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if len(powers) >= 32 {
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c = uint32(math.Ceil(math.Log10(float64(len(powers)))))
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}
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bucketSize, numBits := (1<<c)-1, uint32(g.Q().BitLen())
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windows := make([]*PointG2, numBits/c+1)
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bucket := make([]*PointG2, bucketSize)
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acc, sum := g.New(), g.New()
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for i := 0; i < bucketSize; i++ {
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bucket[i] = g.New()
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}
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mask := (uint64(1) << c) - 1
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j := 0
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var cur uint32
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for cur <= numBits {
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acc.Zero()
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bucket = make([]*PointG2, (1<<c)-1)
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for i := 0; i < len(bucket); i++ {
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bucket[i] = g.New()
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}
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for i := 0; i < len(powers); i++ {
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s0 := powers[i].Uint64()
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index := uint(s0 & mask)
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if index != 0 {
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g.Add(bucket[index-1], bucket[index-1], points[i])
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}
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powers[i] = new(big.Int).Rsh(powers[i], uint(c))
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}
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sum.Zero()
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for i := len(bucket) - 1; i >= 0; i-- {
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g.Add(sum, sum, bucket[i])
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g.Add(acc, acc, sum)
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}
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windows[j] = g.New()
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windows[j].Set(acc)
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j++
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cur += c
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}
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acc.Zero()
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for i := len(windows) - 1; i >= 0; i-- {
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for j := uint32(0); j < c; j++ {
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g.Double(acc, acc)
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}
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g.Add(acc, acc, windows[i])
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}
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return r.Set(acc), nil
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}
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// MapToCurve given a byte slice returns a valid G2 point.
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// This mapping function implements the Simplified Shallue-van de Woestijne-Ulas method.
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// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-05#section-6.6.2
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// Input byte slice should be a valid field element, otherwise an error is returned.
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func (g *G2) MapToCurve(in []byte) (*PointG2, error) {
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fp2 := g.f
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u, err := fp2.fromBytes(in)
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if err != nil {
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return nil, err
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}
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x, y := swuMapG2(fp2, u)
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isogenyMapG2(fp2, x, y)
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z := new(fe2).one()
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q := &PointG2{*x, *y, *z}
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g.ClearCofactor(q)
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return g.Affine(q), nil
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}
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