mirror of
https://github.com/ethereum/go-ethereum.git
synced 2026-08-20 02:42:27 +00:00
846 lines
22 KiB
Go
846 lines
22 KiB
Go
package bls12381
|
||
|
||
import (
|
||
"errors"
|
||
"math"
|
||
"math/big"
|
||
)
|
||
|
||
// PointG1 is type for point in G1 and used for both Affine and Jacobian point representation.
|
||
// A point is accounted as in affine form if z is equal to one.
|
||
type PointG1 [3]fe
|
||
|
||
var wnafMulWindowG1 uint = 5
|
||
|
||
func (p *PointG1) Set(p2 *PointG1) *PointG1 {
|
||
p[0].set(&p2[0])
|
||
p[1].set(&p2[1])
|
||
p[2].set(&p2[2])
|
||
return p
|
||
}
|
||
|
||
func (p *PointG1) Zero() *PointG1 {
|
||
p[0].zero()
|
||
p[1].one()
|
||
p[2].zero()
|
||
return p
|
||
}
|
||
|
||
// IsAffine checks a G1 point whether it is in affine form.
|
||
func (p *PointG1) IsAffine() bool {
|
||
return p[2].isOne()
|
||
}
|
||
|
||
type tempG1 struct {
|
||
t [9]*fe
|
||
}
|
||
|
||
// G1 is struct for G1 group.
|
||
type G1 struct {
|
||
tempG1
|
||
}
|
||
|
||
// NewG1 constructs a new G1 instance.
|
||
func NewG1() *G1 {
|
||
t := newTempG1()
|
||
return &G1{t}
|
||
}
|
||
|
||
func newTempG1() tempG1 {
|
||
t := [9]*fe{}
|
||
for i := 0; i < 9; i++ {
|
||
t[i] = &fe{}
|
||
}
|
||
return tempG1{t}
|
||
}
|
||
|
||
// Q returns group order in big.Int.
|
||
func (g *G1) Q() *big.Int {
|
||
return new(big.Int).Set(qBig)
|
||
}
|
||
|
||
// FromUncompressed expects byte slice at least 96 bytes and given bytes returns a new point in G1.
|
||
// Serialization rules are in line with zcash library. See below for details.
|
||
// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
|
||
// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
|
||
func (g *G1) FromUncompressed(uncompressed []byte) (*PointG1, error) {
|
||
if len(uncompressed) != 2*fpByteSize {
|
||
return nil, errors.New("input string length must be equal to 96 bytes")
|
||
}
|
||
var in [2 * fpByteSize]byte
|
||
copy(in[:], uncompressed[:2*fpByteSize])
|
||
if in[0]&(1<<7) != 0 {
|
||
return nil, errors.New("compression flag must be zero")
|
||
}
|
||
if in[0]&(1<<5) != 0 {
|
||
return nil, errors.New("sort flag must be zero")
|
||
}
|
||
if in[0]&(1<<6) != 0 {
|
||
for i, v := range in {
|
||
if (i == 0 && v != 0x40) || (i != 0 && v != 0x00) {
|
||
return nil, errors.New("input string must be zero when infinity flag is set")
|
||
}
|
||
}
|
||
return g.Zero(), nil
|
||
}
|
||
in[0] &= 0x1f
|
||
x, err := fromBytes(in[:fpByteSize])
|
||
if err != nil {
|
||
return nil, err
|
||
}
|
||
y, err := fromBytes(in[fpByteSize:])
|
||
if err != nil {
|
||
return nil, err
|
||
}
|
||
z := new(fe).one()
|
||
p := &PointG1{*x, *y, *z}
|
||
if !g.IsOnCurve(p) {
|
||
return nil, errors.New("point is not on curve")
|
||
}
|
||
if !g.InCorrectSubgroup(p) {
|
||
return nil, errors.New("point is not on correct subgroup")
|
||
}
|
||
return p, nil
|
||
}
|
||
|
||
// ToUncompressed given a G1 point returns bytes in uncompressed (x, y) form of the point.
|
||
// Serialization rules are in line with zcash library. See below for details.
|
||
// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
|
||
// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
|
||
func (g *G1) ToUncompressed(p *PointG1) []byte {
|
||
out := make([]byte, 2*fpByteSize)
|
||
if g.IsZero(p) {
|
||
out[0] |= 1 << 6
|
||
return out
|
||
}
|
||
g.Affine(p)
|
||
copy(out[:fpByteSize], toBytes(&p[0]))
|
||
copy(out[fpByteSize:], toBytes(&p[1]))
|
||
return out
|
||
}
|
||
|
||
// FromCompressed expects byte slice at least 48 bytes and given bytes returns a new point in G1.
|
||
// Serialization rules are in line with zcash library. See below for details.
|
||
// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
|
||
// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
|
||
func (g *G1) FromCompressed(compressed []byte) (*PointG1, error) {
|
||
if len(compressed) != fpByteSize {
|
||
return nil, errors.New("input string length must be equal to 48 bytes")
|
||
}
|
||
var in [fpByteSize]byte
|
||
copy(in[:], compressed[:])
|
||
if in[0]&(1<<7) == 0 {
|
||
return nil, errors.New("compression flag must be set")
|
||
}
|
||
if in[0]&(1<<6) != 0 {
|
||
// in[0] == (1 << 6) + (1 << 7)
|
||
for i, v := range in {
|
||
if (i == 0 && v != 0xc0) || (i != 0 && v != 0x00) {
|
||
return nil, errors.New("input string must be zero when infinity flag is set")
|
||
}
|
||
}
|
||
return g.Zero(), nil
|
||
}
|
||
a := in[0]&(1<<5) != 0
|
||
in[0] &= 0x1f
|
||
x, err := fromBytes(in[:])
|
||
if err != nil {
|
||
return nil, err
|
||
}
|
||
// solve curve equation
|
||
y := &fe{}
|
||
square(y, x)
|
||
mul(y, y, x)
|
||
add(y, y, b)
|
||
if ok := sqrt(y, y); !ok {
|
||
return nil, errors.New("point is not on curve")
|
||
}
|
||
if y.signBE() == a {
|
||
neg(y, y)
|
||
}
|
||
z := new(fe).one()
|
||
p := &PointG1{*x, *y, *z}
|
||
if !g.InCorrectSubgroup(p) {
|
||
return nil, errors.New("point is not on correct subgroup")
|
||
}
|
||
return p, nil
|
||
}
|
||
|
||
// ToCompressed given a G1 point returns bytes in compressed form of the point.
|
||
// Serialization rules are in line with zcash library. See below for details.
|
||
// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
|
||
// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
|
||
func (g *G1) ToCompressed(p *PointG1) []byte {
|
||
out := make([]byte, fpByteSize)
|
||
g.Affine(p)
|
||
if g.IsZero(p) {
|
||
out[0] |= 1 << 6
|
||
} else {
|
||
copy(out[:], toBytes(&p[0]))
|
||
if !p[1].signBE() {
|
||
out[0] |= 1 << 5
|
||
}
|
||
}
|
||
out[0] |= 1 << 7
|
||
return out
|
||
}
|
||
|
||
func (g *G1) fromBytesUnchecked(in []byte) (*PointG1, error) {
|
||
p0, err := fromBytes(in[:fpByteSize])
|
||
if err != nil {
|
||
return nil, err
|
||
}
|
||
p1, err := fromBytes(in[fpByteSize:])
|
||
if err != nil {
|
||
return nil, err
|
||
}
|
||
p2 := new(fe).one()
|
||
return &PointG1{*p0, *p1, *p2}, nil
|
||
}
|
||
|
||
// FromBytes constructs a new point given uncompressed byte input.
|
||
// Input string is expected to be equal to 96 bytes and concatenation of x and y cooridanates.
|
||
// (0, 0) is considered as infinity.
|
||
func (g *G1) FromBytes(in []byte) (*PointG1, error) {
|
||
if len(in) != 2*fpByteSize {
|
||
return nil, errors.New("input string length must be equal to 96 bytes")
|
||
}
|
||
p0, err := fromBytes(in[:fpByteSize])
|
||
if err != nil {
|
||
return nil, err
|
||
}
|
||
p1, err := fromBytes(in[fpByteSize:])
|
||
if err != nil {
|
||
return nil, err
|
||
}
|
||
// check if given input points to infinity
|
||
if p0.isZero() && p1.isZero() {
|
||
return g.Zero(), nil
|
||
}
|
||
p2 := new(fe).one()
|
||
p := &PointG1{*p0, *p1, *p2}
|
||
if !g.IsOnCurve(p) {
|
||
return nil, errors.New("point is not on curve")
|
||
}
|
||
return p, nil
|
||
}
|
||
|
||
// ToBytes serializes a point into bytes in uncompressed form.
|
||
// ToBytes returns (0, 0) if point is infinity.
|
||
func (g *G1) ToBytes(p *PointG1) []byte {
|
||
out := make([]byte, 2*fpByteSize)
|
||
if g.IsZero(p) {
|
||
return out
|
||
}
|
||
g.Affine(p)
|
||
copy(out[:fpByteSize], toBytes(&p[0]))
|
||
copy(out[fpByteSize:], toBytes(&p[1]))
|
||
return out
|
||
}
|
||
|
||
// New creates a new G1 Point which is equal to zero in other words point at infinity.
|
||
func (g *G1) New() *PointG1 {
|
||
return g.Zero()
|
||
}
|
||
|
||
// Zero returns a new G1 Point which is equal to point at infinity.
|
||
func (g *G1) Zero() *PointG1 {
|
||
return new(PointG1).Zero()
|
||
}
|
||
|
||
// One returns a new G1 Point which is equal to generator point.
|
||
func (g *G1) One() *PointG1 {
|
||
p := &PointG1{}
|
||
return p.Set(&g1One)
|
||
}
|
||
|
||
// IsZero returns true if given point is equal to zero.
|
||
func (g *G1) IsZero(p *PointG1) bool {
|
||
return p[2].isZero()
|
||
}
|
||
|
||
// Equal checks if given two G1 point is equal in their affine form.
|
||
func (g *G1) Equal(p1, p2 *PointG1) bool {
|
||
if g.IsZero(p1) {
|
||
return g.IsZero(p2)
|
||
}
|
||
if g.IsZero(p2) {
|
||
return g.IsZero(p1)
|
||
}
|
||
t := g.t
|
||
square(t[0], &p1[2])
|
||
square(t[1], &p2[2])
|
||
mul(t[2], t[0], &p2[0])
|
||
mul(t[3], t[1], &p1[0])
|
||
mul(t[0], t[0], &p1[2])
|
||
mul(t[1], t[1], &p2[2])
|
||
mul(t[1], t[1], &p1[1])
|
||
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 *G1) InCorrectSubgroup(p *PointG1) bool {
|
||
|
||
// Faster Subgroup Checks for BLS12-381
|
||
// S. Bowe
|
||
// https://eprint.iacr.org/2019/814.pdf
|
||
|
||
mulZ := func(p *PointG1) {
|
||
// z = [(x^2 − 1)/3]
|
||
z := &Fr{0x0000000055555555, 0x396c8c005555e156}
|
||
e := z.toWNAF(wnafMulWindowG1)
|
||
g.wnafMul(p, p, e)
|
||
}
|
||
|
||
// [(x^2 − 1)/3](2σ(P) − P − σ^2(P)) − σ^2(P) ?= O
|
||
t0 := g.New().Set(p)
|
||
g.glvEndomorphism(t0, t0)
|
||
t1 := g.New().Set(t0) // σ(P)
|
||
g.glvEndomorphism(t0, t0) // σ^2(P)
|
||
g.Double(t1, t1) // 2σ(P)
|
||
g.Sub(t1, t1, p) // 2σ(P) − P
|
||
g.Sub(t1, t1, t0) // 2σ(P) − P − σ^2(P)
|
||
mulZ(t1) // [(x^2 − 1)/3](2σ(P) − P − σ^2(P))
|
||
g.Sub(t1, t1, t0) // [(x^2 − 1)/3](2σ(P) − P − σ^2(P)) − σ^2(P)
|
||
return g.IsZero(t1)
|
||
}
|
||
|
||
// IsOnCurve checks a G1 point is on curve.
|
||
func (g *G1) IsOnCurve(p *PointG1) bool {
|
||
if g.IsZero(p) {
|
||
return true
|
||
}
|
||
t := g.t
|
||
square(t[0], &p[1]) // y^2
|
||
square(t[1], &p[0]) // x^2
|
||
mul(t[1], t[1], &p[0]) // x^3
|
||
if p.IsAffine() {
|
||
addAssign(t[1], b) // x^2 + b
|
||
return t[0].equal(t[1]) // y^2 ?= x^3 + b
|
||
}
|
||
square(t[2], &p[2]) // z^2
|
||
square(t[3], t[2]) // z^4
|
||
mul(t[2], t[2], t[3]) // z^6
|
||
mul(t[2], b, t[2]) // b * z^6
|
||
add(t[1], t[1], t[2]) // x^3 + b * z^6
|
||
return t[0].equal(t[1]) // y^2 ?= x^3 + b * z^6
|
||
}
|
||
|
||
// IsAffine checks a G1 point whether it is in affine form.
|
||
func (g *G1) IsAffine(p *PointG1) bool {
|
||
return p[2].isOne()
|
||
}
|
||
|
||
// Affine returns the affine representation of the given point
|
||
func (g *G1) Affine(p *PointG1) *PointG1 {
|
||
return g.affine(p, p)
|
||
}
|
||
|
||
func (g *G1) affine(r, p *PointG1) *PointG1 {
|
||
if g.IsZero(p) {
|
||
return r.Zero()
|
||
}
|
||
if !g.IsAffine(p) {
|
||
t := g.t
|
||
inverse(t[0], &p[2]) // z^-1
|
||
square(t[1], t[0]) // z^-2
|
||
mul(&r[0], &p[0], t[1]) // x = x * z^-2
|
||
mul(t[0], t[0], t[1]) // z^-3
|
||
mul(&r[1], &p[1], t[0]) // y = y * z^-3
|
||
r[2].one() // z = 1
|
||
} else {
|
||
r.Set(p)
|
||
}
|
||
return r
|
||
}
|
||
|
||
// AffineBatch given multiple of points returns affine representations
|
||
func (g *G1) AffineBatch(p []*PointG1) {
|
||
inverses := make([]fe, len(p))
|
||
for i := 0; i < len(p); i++ {
|
||
inverses[i].set(&p[i][2])
|
||
}
|
||
inverseBatch(inverses)
|
||
t := g.t
|
||
for i := 0; i < len(p); i++ {
|
||
if !g.IsAffine(p[i]) && !g.IsZero(p[i]) {
|
||
square(t[1], &inverses[i])
|
||
mul(&p[i][0], &p[i][0], t[1])
|
||
mul(t[0], &inverses[i], t[1])
|
||
mul(&p[i][1], &p[i][1], t[0])
|
||
p[i][2].one()
|
||
}
|
||
}
|
||
}
|
||
|
||
// Add adds two G1 points p1, p2 and assigns the result to point at first argument.
|
||
func (g *G1) Add(r, p1, p2 *PointG1) *PointG1 {
|
||
|
||
// http://www.hyperelliptic.org/EFD/gp/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)
|
||
}
|
||
if g.IsAffine(p2) {
|
||
return g.AddMixed(r, p1, p2)
|
||
}
|
||
t := g.t
|
||
square(t[7], &p1[2]) // z1z1
|
||
mul(t[1], &p2[0], t[7]) // u2 = x2 * z1z1
|
||
mul(t[2], &p1[2], t[7]) // z1z1 * z1
|
||
mul(t[0], &p2[1], t[2]) // s2 = y2 * z1z1 * z1
|
||
square(t[8], &p2[2]) // z2z2
|
||
mul(t[3], &p1[0], t[8]) // u1 = x1 * z2z2
|
||
mul(t[4], &p2[2], t[8]) // z2z2 * z2
|
||
mul(t[2], &p1[1], t[4]) // s1 = y1 * z2z2 * z2
|
||
if t[1].equal(t[3]) {
|
||
if t[0].equal(t[2]) {
|
||
return g.Double(r, p1)
|
||
} else {
|
||
return r.Zero()
|
||
}
|
||
}
|
||
subAssign(t[1], t[3]) // h = u2 - u1
|
||
double(t[4], t[1]) // 2h
|
||
square(t[4], t[4]) // i = 2h^2
|
||
mul(t[5], t[1], t[4]) // j = h*i
|
||
subAssign(t[0], t[2]) // s2 - s1
|
||
doubleAssign(t[0]) // r = 2*(s2 - s1)
|
||
square(t[6], t[0]) // r^2
|
||
subAssign(t[6], t[5]) // r^2 - j
|
||
mul(t[3], t[3], t[4]) // v = u1 * i
|
||
double(t[4], t[3]) // 2*v
|
||
sub(&r[0], t[6], t[4]) // x3 = r^2 - j - 2*v
|
||
sub(t[4], t[3], &r[0]) // v - x3
|
||
mul(t[6], t[2], t[5]) // s1 * j
|
||
doubleAssign(t[6]) // 2 * s1 * j
|
||
mul(t[0], t[0], t[4]) // r * (v - x3)
|
||
sub(&r[1], t[0], t[6]) // y3 = r * (v - x3) - (2 * s1 * j)
|
||
add(t[0], &p1[2], &p2[2]) // z1 + z2
|
||
square(t[0], t[0]) // (z1 + z2)^2
|
||
subAssign(t[0], t[7]) // (z1 + z2)^2 - z1z1
|
||
subAssign(t[0], t[8]) // (z1 + z2)^2 - z1z1 - z2z2
|
||
mul(&r[2], t[0], t[1]) // z3 = ((z1 + z2)^2 - z1z1 - z2z2) * h
|
||
return r
|
||
}
|
||
|
||
// Add adds two G1 points p1, p2 and assigns the result to point at first argument.
|
||
// Expects the second point p2 in affine form.
|
||
func (g *G1) AddMixed(r, p1, p2 *PointG1) *PointG1 {
|
||
// http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-madd-2007-bl
|
||
if g.IsZero(p1) {
|
||
return r.Set(p2)
|
||
}
|
||
if g.IsZero(p2) {
|
||
return r.Set(p1)
|
||
}
|
||
t := g.t
|
||
square(t[7], &p1[2]) // z1z1
|
||
mul(t[1], &p2[0], t[7]) // u2 = x2 * z1z1
|
||
mul(t[2], &p1[2], t[7]) // z1z1 * z1
|
||
mul(t[0], &p2[1], t[2]) // s2 = y2 * z1z1 * z1
|
||
|
||
if p1[0].equal(t[1]) && p1[1].equal(t[0]) {
|
||
return g.Double(r, p1)
|
||
}
|
||
|
||
sub(t[1], t[1], &p1[0]) // h = u2 - x1
|
||
square(t[2], t[1]) // hh
|
||
double(t[4], t[2])
|
||
doubleAssign(t[4]) // 4hh
|
||
mul(t[5], t[1], t[4]) // j = h*i
|
||
subAssign(t[0], &p1[1]) // s2 - y1
|
||
doubleAssign(t[0]) // r = 2*(s2 - y1)
|
||
square(t[6], t[0]) // r^2
|
||
subAssign(t[6], t[5]) // r^2 - j
|
||
mul(t[3], &p1[0], t[4]) // v = x1 * i
|
||
double(t[4], t[3]) // 2*v
|
||
sub(&r[0], t[6], t[4]) // x3 = r^2 - j - 2*v
|
||
sub(t[4], t[3], &r[0]) // v - x3
|
||
mul(t[6], &p1[1], t[5]) // y1 * j
|
||
doubleAssign(t[6]) // 2 * y1 * j
|
||
mul(t[0], t[0], t[4]) // r * (v - x3)
|
||
sub(&r[1], t[0], t[6]) // y3 = r * (v - x3) - (2 * y1 * j)
|
||
add(t[0], &p1[2], t[1]) // z1 + h
|
||
square(t[0], t[0]) // (z1 + h)^2
|
||
subAssign(t[0], t[7]) // (z1 + h)^2 - z1z1
|
||
sub(&r[2], t[0], t[2]) // z3 = (z1 + z2)^2 - z1z1 - hh
|
||
return r
|
||
}
|
||
|
||
// Double doubles a G1 point p and assigns the result to the point at first argument.
|
||
func (g *G1) Double(r, p *PointG1) *PointG1 {
|
||
// http://www.hyperelliptic.org/EFD/gp/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
|
||
if g.IsZero(p) {
|
||
return r.Zero()
|
||
}
|
||
t := g.t
|
||
square(t[0], &p[0]) // a = x^2
|
||
square(t[1], &p[1]) // b = y^2
|
||
square(t[2], t[1]) // c = b^2
|
||
add(t[1], &p[0], t[1]) // b + x1
|
||
square(t[1], t[1]) // (b + x1)^2
|
||
subAssign(t[1], t[0]) // (b + x1)^2 - a
|
||
subAssign(t[1], t[2]) // (b + x1)^2 - a - c
|
||
doubleAssign(t[1]) // d = 2((b+x1)^2 - a - c)
|
||
double(t[3], t[0]) // 2a
|
||
addAssign(t[0], t[3]) // e = 3a
|
||
square(t[4], t[0]) // f = e^2
|
||
double(t[3], t[1]) // 2d
|
||
sub(&r[0], t[4], t[3]) // x3 = f - 2d
|
||
subAssign(t[1], &r[0]) // d-x3
|
||
doubleAssign(t[2]) //
|
||
doubleAssign(t[2]) //
|
||
doubleAssign(t[2]) // 8c
|
||
mul(t[0], t[0], t[1]) // e * (d - x3)
|
||
sub(t[1], t[0], t[2]) // x3 = e * (d - x3) - 8c
|
||
mul(t[0], &p[1], &p[2]) // y1 * z1
|
||
r[1].set(t[1]) //
|
||
double(&r[2], t[0]) // z3 = 2(y1 * z1)
|
||
return r
|
||
}
|
||
|
||
// Neg negates a G1 point p and assigns the result to the point at first argument.
|
||
func (g *G1) Neg(r, p *PointG1) *PointG1 {
|
||
r[0].set(&p[0])
|
||
r[2].set(&p[2])
|
||
neg(&r[1], &p[1])
|
||
return r
|
||
}
|
||
|
||
// Sub subtracts two G1 points p1, p2 and assigns the result to point at first argument.
|
||
func (g *G1) Sub(c, a, b *PointG1) *PointG1 {
|
||
d := &PointG1{}
|
||
g.Neg(d, b)
|
||
g.Add(c, a, d)
|
||
return c
|
||
}
|
||
|
||
// MulScalar multiplies a point by given scalar value and assigns the result to point at first argument.
|
||
func (g *G1) MulScalar(r, p *PointG1, e *Fr) *PointG1 {
|
||
return g.glvMulFr(r, p, e)
|
||
}
|
||
|
||
// MulScalar multiplies a point by given scalar value in big.Int and assigns the result to point at first argument.
|
||
func (g *G1) MulScalarBig(r, p *PointG1, e *big.Int) *PointG1 {
|
||
return g.glvMulBig(r, p, e)
|
||
}
|
||
|
||
func (g *G1) mulScalar(c, p *PointG1, e *Fr) *PointG1 {
|
||
q, n := &PointG1{}, &PointG1{}
|
||
n.Set(p)
|
||
for i := 0; i < frBitSize; i++ {
|
||
if e.Bit(i) {
|
||
g.Add(q, q, n)
|
||
}
|
||
g.Double(n, n)
|
||
}
|
||
return c.Set(q)
|
||
}
|
||
|
||
func (g *G1) mulScalarBig(c, p *PointG1, e *big.Int) *PointG1 {
|
||
q, n := &PointG1{}, &PointG1{}
|
||
n.Set(p)
|
||
for i := 0; i < frBitSize; i++ {
|
||
if e.Bit(i) == 1 {
|
||
g.Add(q, q, n)
|
||
}
|
||
g.Double(n, n)
|
||
}
|
||
return c.Set(q)
|
||
}
|
||
|
||
func (g *G1) wnafMulFr(r, p *PointG1, e *Fr) *PointG1 {
|
||
wnaf := e.toWNAF(wnafMulWindowG1)
|
||
return g.wnafMul(r, p, wnaf)
|
||
}
|
||
|
||
func (g *G1) wnafMulBig(r, p *PointG1, e *big.Int) *PointG1 {
|
||
wnaf := bigToWNAF(e, wnafMulWindowG1)
|
||
return g.wnafMul(r, p, wnaf)
|
||
}
|
||
|
||
func (g *G1) wnafMul(c, p *PointG1, wnaf nafNumber) *PointG1 {
|
||
|
||
l := (1 << (wnafMulWindowG1 - 1))
|
||
|
||
twoP, acc := g.New(), new(PointG1).Set(p)
|
||
g.Double(twoP, p)
|
||
g.Affine(twoP)
|
||
|
||
// table = {p, 3p, 5p, ..., -p, -3p, -5p}
|
||
table := make([]*PointG1, l*2)
|
||
table[0], table[l] = g.New(), g.New()
|
||
table[0].Set(p)
|
||
g.Neg(table[l], table[0])
|
||
|
||
for i := 1; i < l; i++ {
|
||
g.AddMixed(acc, acc, twoP)
|
||
table[i], table[i+l] = g.New(), g.New()
|
||
table[i].Set(acc)
|
||
g.Neg(table[i+l], table[i])
|
||
}
|
||
|
||
q := g.Zero()
|
||
for i := len(wnaf) - 1; i >= 0; i-- {
|
||
if wnaf[i] > 0 {
|
||
g.Add(q, q, table[wnaf[i]>>1])
|
||
} else if wnaf[i] < 0 {
|
||
g.Add(q, q, table[((-wnaf[i])>>1)+l])
|
||
}
|
||
if i != 0 {
|
||
g.Double(q, q)
|
||
}
|
||
}
|
||
return c.Set(q)
|
||
}
|
||
|
||
func (g *G1) glvMulFr(r, p *PointG1, e *Fr) *PointG1 {
|
||
return g.glvMul(r, p, new(glvVectorFr).new(e))
|
||
}
|
||
|
||
func (g *G1) glvMulBig(r, p *PointG1, e *big.Int) *PointG1 {
|
||
return g.glvMul(r, p, new(glvVectorBig).new(e))
|
||
}
|
||
|
||
func (g *G1) glvMul(r, p0 *PointG1, v glvVector) *PointG1 {
|
||
|
||
w := glvMulWindowG1
|
||
l := 1 << (w - 1)
|
||
|
||
// prepare tables
|
||
// tableK1 = {P, 3P, 5P, ...}
|
||
// tableK2 = {λP, 3λP, 5λP, ...}
|
||
tableK1, tableK2 := make([]*PointG1, l), make([]*PointG1, l)
|
||
double := g.New()
|
||
g.Double(double, p0)
|
||
g.affine(double, double)
|
||
tableK1[0] = new(PointG1)
|
||
tableK1[0].Set(p0)
|
||
for i := 1; i < l; i++ {
|
||
tableK1[i] = new(PointG1)
|
||
g.AddMixed(tableK1[i], tableK1[i-1], double)
|
||
}
|
||
g.AffineBatch(tableK1)
|
||
for i := 0; i < l; i++ {
|
||
tableK2[i] = new(PointG1)
|
||
g.glvEndomorphism(tableK2[i], tableK1[i])
|
||
}
|
||
|
||
// recode small scalars
|
||
naf1, naf2 := v.wnaf(w)
|
||
lenNAF1, lenNAF2 := len(naf1), len(naf2)
|
||
lenNAF := lenNAF1
|
||
if lenNAF2 > lenNAF {
|
||
lenNAF = lenNAF2
|
||
}
|
||
|
||
acc, p1 := g.New(), g.New()
|
||
|
||
// function for naf addition
|
||
add := func(table []*PointG1, naf int) {
|
||
if naf != 0 {
|
||
nafAbs := naf
|
||
if nafAbs < 0 {
|
||
nafAbs = -nafAbs
|
||
}
|
||
p1.Set(table[nafAbs>>1])
|
||
if naf < 0 {
|
||
g.Neg(p1, p1)
|
||
}
|
||
g.AddMixed(acc, acc, p1)
|
||
}
|
||
}
|
||
|
||
// sliding
|
||
for i := lenNAF - 1; i >= 0; i-- {
|
||
if i < lenNAF1 {
|
||
add(tableK1, naf1[i])
|
||
}
|
||
if i < lenNAF2 {
|
||
add(tableK2, naf2[i])
|
||
}
|
||
if i != 0 {
|
||
g.Double(acc, acc)
|
||
}
|
||
}
|
||
return r.Set(acc)
|
||
}
|
||
|
||
// MultiExpBig calculates multi exponentiation. Scalar values are received as big.Int type.
|
||
// 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) MultiExpBig(r *PointG1, points []*PointG1, scalars []*big.Int) (*PointG1, error) {
|
||
if len(points) != len(scalars) {
|
||
return nil, errors.New("point and scalar vectors should be in same length")
|
||
}
|
||
|
||
c := 3
|
||
if len(scalars) >= 32 {
|
||
c = int(math.Ceil(math.Log(float64(len(scalars)))))
|
||
}
|
||
|
||
bucketSize := (1 << c) - 1
|
||
windows := make([]PointG1, 255/c+1)
|
||
bucket := make([]PointG1, bucketSize)
|
||
|
||
for j := 0; j < len(windows); j++ {
|
||
|
||
for i := 0; i < bucketSize; i++ {
|
||
bucket[i].Zero()
|
||
}
|
||
|
||
for i := 0; i < len(scalars); i++ {
|
||
index := bucketSize & int(new(big.Int).Rsh(scalars[i], uint(c*j)).Int64())
|
||
if index != 0 {
|
||
g.Add(&bucket[index-1], &bucket[index-1], points[i])
|
||
}
|
||
}
|
||
|
||
acc, sum := g.New(), g.New()
|
||
for i := bucketSize - 1; i >= 0; i-- {
|
||
g.Add(sum, sum, &bucket[i])
|
||
g.Add(acc, acc, sum)
|
||
}
|
||
windows[j].Set(acc)
|
||
}
|
||
|
||
acc := g.New()
|
||
for i := len(windows) - 1; i >= 0; i-- {
|
||
for j := 0; j < c; j++ {
|
||
g.Double(acc, acc)
|
||
}
|
||
g.Add(acc, acc, &windows[i])
|
||
}
|
||
return r.Set(acc), nil
|
||
}
|
||
|
||
// 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, scalars []*Fr) (*PointG1, error) {
|
||
if len(points) != len(scalars) {
|
||
return nil, errors.New("point and scalar vectors should be in same length")
|
||
}
|
||
|
||
g.AffineBatch(points)
|
||
|
||
c := 3
|
||
if len(scalars) >= 32 {
|
||
c = int(math.Ceil(math.Log(float64(len(scalars)))))
|
||
}
|
||
|
||
bucketSize := (1 << c) - 1
|
||
windows := make([]*PointG1, 255/c+1)
|
||
bucket := make([]PointG1, bucketSize)
|
||
|
||
for j := 0; j < len(windows); j++ {
|
||
|
||
for i := 0; i < bucketSize; i++ {
|
||
bucket[i].Zero()
|
||
}
|
||
|
||
for i := 0; i < len(scalars); i++ {
|
||
index := bucketSize & int(scalars[i].sliceUint64(c*j))
|
||
if index != 0 {
|
||
g.AddMixed(&bucket[index-1], &bucket[index-1], points[i])
|
||
}
|
||
}
|
||
|
||
acc, sum := g.New(), g.New()
|
||
for i := bucketSize - 1; i >= 0; i-- {
|
||
g.Add(sum, sum, &bucket[i])
|
||
g.Add(acc, acc, sum)
|
||
}
|
||
windows[j] = g.New().Set(acc)
|
||
}
|
||
|
||
g.AffineBatch(windows)
|
||
|
||
acc := g.New()
|
||
for i := len(windows) - 1; i >= 0; i-- {
|
||
for j := 0; j < c; j++ {
|
||
g.Double(acc, acc)
|
||
}
|
||
g.AddMixed(acc, acc, windows[i])
|
||
}
|
||
return r.Set(acc), nil
|
||
}
|
||
|
||
func (g *G1) ClearCofactor(p *PointG1) *PointG1 {
|
||
chain := func(p0 *PointG1, n int, p1 *PointG1) {
|
||
for i := 0; i < n; i++ {
|
||
g.Double(p0, p0)
|
||
}
|
||
g.Add(p0, p0, p1)
|
||
}
|
||
t := g.New().Set(p)
|
||
chain(p, 1, t)
|
||
chain(p, 2, t)
|
||
chain(p, 3, t)
|
||
chain(p, 9, t)
|
||
chain(p, 32, t)
|
||
chain(p, 16, t)
|
||
return p
|
||
}
|
||
|
||
// 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
|
||
}
|
||
|
||
// EncodeToCurve given a message and domain seperator tag returns the hash result
|
||
// which is a valid curve point.
|
||
// Implementation follows BLS12381G1_XMD:SHA-256_SSWU_NU_ suite at
|
||
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06
|
||
func (g *G1) EncodeToCurve(msg, domain []byte) (*PointG1, error) {
|
||
hashRes, err := hashToFpXMDSHA256(msg, domain, 1)
|
||
if err != nil {
|
||
return nil, err
|
||
}
|
||
u := hashRes[0]
|
||
x, y := swuMapG1(u)
|
||
isogenyMapG1(x, y)
|
||
one := new(fe).one()
|
||
p := &PointG1{*x, *y, *one}
|
||
g.ClearCofactor(p)
|
||
return g.Affine(p), nil
|
||
}
|
||
|
||
// HashToCurve given a message and domain seperator tag returns the hash result
|
||
// which is a valid curve point.
|
||
// Implementation follows BLS12381G1_XMD:SHA-256_SSWU_RO_ suite at
|
||
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06
|
||
func (g *G1) HashToCurve(msg, domain []byte) (*PointG1, error) {
|
||
hashRes, err := hashToFpXMDSHA256(msg, domain, 2)
|
||
if err != nil {
|
||
return nil, err
|
||
}
|
||
u0, u1 := hashRes[0], hashRes[1]
|
||
x0, y0 := swuMapG1(u0)
|
||
x1, y1 := swuMapG1(u1)
|
||
one := new(fe).one()
|
||
p0, p1 := &PointG1{*x0, *y0, *one}, &PointG1{*x1, *y1, *one}
|
||
g.Add(p0, p0, p1)
|
||
g.Affine(p0)
|
||
isogenyMapG1(&p0[0], &p0[1])
|
||
g.ClearCofactor(p0)
|
||
return g.Affine(p0), nil
|
||
}
|