You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
 
 
 

417 lines
11 KiB

package bn128
import (
"errors"
"math/big"
"github.com/arnaucube/go-snark/fields"
)
type Bn128 struct {
Q *big.Int
R *big.Int
Gg1 [2]*big.Int
Gg2 [2][2]*big.Int
NonResidueFq2 *big.Int
NonResidueFq6 [2]*big.Int
Fq1 fields.Fq
Fq2 fields.Fq2
Fq6 fields.Fq6
Fq12 fields.Fq12
G1 G1
G2 G2
LoopCount *big.Int
LoopCountNeg bool
TwoInv *big.Int
CoefB *big.Int
TwistCoefB [2]*big.Int
Twist [2]*big.Int
FrobeniusCoeffsC11 *big.Int
TwistMulByQX [2]*big.Int
TwistMulByQY [2]*big.Int
FinalExp *big.Int
}
func NewBn128() (Bn128, error) {
var b Bn128
q, ok := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10)
if !ok {
return b, errors.New("err with q")
}
b.Q = q
r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
if !ok {
return b, errors.New("err with r")
}
b.R = r
b.Gg1 = [2]*big.Int{
big.NewInt(int64(1)),
big.NewInt(int64(2)),
}
g2_00, ok := new(big.Int).SetString("10857046999023057135944570762232829481370756359578518086990519993285655852781", 10)
if !ok {
return b, errors.New("err with g2_00")
}
g2_01, ok := new(big.Int).SetString("11559732032986387107991004021392285783925812861821192530917403151452391805634", 10)
if !ok {
return b, errors.New("err with g2_00")
}
g2_10, ok := new(big.Int).SetString("8495653923123431417604973247489272438418190587263600148770280649306958101930", 10)
if !ok {
return b, errors.New("err with g2_00")
}
g2_11, ok := new(big.Int).SetString("4082367875863433681332203403145435568316851327593401208105741076214120093531", 10)
if !ok {
return b, errors.New("err with g2_00")
}
b.Gg2 = [2][2]*big.Int{
[2]*big.Int{
g2_00,
g2_01,
},
[2]*big.Int{
g2_10,
g2_11,
},
}
b.Fq1 = fields.NewFq(q)
b.NonResidueFq2, ok = new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208582", 10) // i
if !ok {
return b, errors.New("err with nonResidueFq2")
}
b.NonResidueFq6 = [2]*big.Int{
big.NewInt(int64(9)),
big.NewInt(int64(1)),
}
b.Fq2 = fields.NewFq2(b.Fq1, b.NonResidueFq2)
b.Fq6 = fields.NewFq6(b.Fq2, b.NonResidueFq6)
b.Fq12 = fields.NewFq12(b.Fq6, b.Fq2, b.NonResidueFq6)
b.G1 = NewG1(b.Fq1, b.Gg1)
b.G2 = NewG2(b.Fq2, b.Gg2)
err := b.preparePairing()
if err != nil {
return b, err
}
return b, nil
}
func NewFqR() (fields.Fq, error) {
r, ok := new(big.Int).SetString("21888242871839275222246405745257275088548364400416034343698204186575808495617", 10)
if !ok {
return fields.Fq{}, errors.New("err parsing R")
}
fqR := fields.NewFq(r)
return fqR, nil
}
func (bn128 *Bn128) preparePairing() error {
var ok bool
bn128.LoopCount, ok = new(big.Int).SetString("29793968203157093288", 10)
if !ok {
return errors.New("err with LoopCount from string")
}
bn128.LoopCountNeg = false
bn128.TwoInv = bn128.Fq1.Inverse(big.NewInt(int64(2)))
bn128.CoefB = big.NewInt(int64(3))
bn128.Twist = [2]*big.Int{
big.NewInt(int64(9)),
big.NewInt(int64(1)),
}
bn128.TwistCoefB = bn128.Fq2.MulScalar(bn128.Fq2.Inverse(bn128.Twist), bn128.CoefB)
bn128.FrobeniusCoeffsC11, ok = new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208582", 10)
if !ok {
return errors.New("error parsing frobeniusCoeffsC11")
}
a, ok := new(big.Int).SetString("21575463638280843010398324269430826099269044274347216827212613867836435027261", 10)
if !ok {
return errors.New("error parsing a")
}
b, ok := new(big.Int).SetString("10307601595873709700152284273816112264069230130616436755625194854815875713954", 10)
if !ok {
return errors.New("error parsing b")
}
bn128.TwistMulByQX = [2]*big.Int{
a,
b,
}
a, ok = new(big.Int).SetString("2821565182194536844548159561693502659359617185244120367078079554186484126554", 10)
if !ok {
return errors.New("error parsing a")
}
b, ok = new(big.Int).SetString("3505843767911556378687030309984248845540243509899259641013678093033130930403", 10)
if !ok {
return errors.New("error parsing b")
}
bn128.TwistMulByQY = [2]*big.Int{
a,
b,
}
bn128.FinalExp, ok = new(big.Int).SetString("552484233613224096312617126783173147097382103762957654188882734314196910839907541213974502761540629817009608548654680343627701153829446747810907373256841551006201639677726139946029199968412598804882391702273019083653272047566316584365559776493027495458238373902875937659943504873220554161550525926302303331747463515644711876653177129578303191095900909191624817826566688241804408081892785725967931714097716709526092261278071952560171111444072049229123565057483750161460024353346284167282452756217662335528813519139808291170539072125381230815729071544861602750936964829313608137325426383735122175229541155376346436093930287402089517426973178917569713384748081827255472576937471496195752727188261435633271238710131736096299798168852925540549342330775279877006784354801422249722573783561685179618816480037695005515426162362431072245638324744480", 10)
if !ok {
return errors.New("error parsing finalExp")
}
return nil
}
func (bn128 Bn128) Pairing(p1 [3]*big.Int, p2 [3][2]*big.Int) [2][3][2]*big.Int {
pre1 := bn128.PreComputeG1(p1)
pre2 := bn128.PreComputeG2(p2)
r1 := bn128.MillerLoop(pre1, pre2)
res := bn128.FinalExponentiation(r1)
return res
}
type AteG1Precomp struct {
Px *big.Int
Py *big.Int
}
func (bn128 Bn128) PreComputeG1(p [3]*big.Int) AteG1Precomp {
pCopy := bn128.G1.Affine(p)
res := AteG1Precomp{
Px: pCopy[0],
Py: pCopy[1],
}
return res
}
type EllCoeffs struct {
Ell0 [2]*big.Int
EllVW [2]*big.Int
EllVV [2]*big.Int
}
type AteG2Precomp struct {
Qx [2]*big.Int
Qy [2]*big.Int
Coeffs []EllCoeffs
}
func (bn128 Bn128) PreComputeG2(p [3][2]*big.Int) AteG2Precomp {
qCopy := bn128.G2.Affine(p)
res := AteG2Precomp{
qCopy[0],
qCopy[1],
[]EllCoeffs{},
}
r := [3][2]*big.Int{
bn128.Fq2.Copy(qCopy[0]),
bn128.Fq2.Copy(qCopy[1]),
bn128.Fq2.One(),
}
var c EllCoeffs
for i := bn128.LoopCount.BitLen() - 2; i >= 0; i-- {
bit := bn128.LoopCount.Bit(i)
c, r = bn128.DoublingStep(r)
res.Coeffs = append(res.Coeffs, c)
if bit == 1 {
c, r = bn128.MixedAdditionStep(qCopy, r)
res.Coeffs = append(res.Coeffs, c)
}
}
q1 := bn128.G2.Affine(bn128.G2MulByQ(qCopy))
if !bn128.Fq2.Equal(q1[2], bn128.Fq2.One()) {
// return res, errors.New("q1[2] != Fq2.One")
panic(errors.New("q1[2] != Fq2.One()"))
}
q2 := bn128.G2.Affine(bn128.G2MulByQ(q1))
if !bn128.Fq2.Equal(q2[2], bn128.Fq2.One()) {
// return res, errors.New("q2[2] != Fq2.One")
panic(errors.New("q2[2] != Fq2.One()"))
}
if bn128.LoopCountNeg {
r[1] = bn128.Fq2.Neg(r[1])
}
q2[1] = bn128.Fq2.Neg(q2[1])
c, r = bn128.MixedAdditionStep(q1, r)
res.Coeffs = append(res.Coeffs, c)
c, r = bn128.MixedAdditionStep(q2, r)
res.Coeffs = append(res.Coeffs, c)
return res
}
func (bn128 Bn128) DoublingStep(current [3][2]*big.Int) (EllCoeffs, [3][2]*big.Int) {
x := current[0]
y := current[1]
z := current[2]
a := bn128.Fq2.MulScalar(bn128.Fq2.Mul(x, y), bn128.TwoInv)
b := bn128.Fq2.Square(y)
c := bn128.Fq2.Square(z)
d := bn128.Fq2.Add(c, bn128.Fq2.Add(c, c))
e := bn128.Fq2.Mul(bn128.TwistCoefB, d)
f := bn128.Fq2.Add(e, bn128.Fq2.Add(e, e))
g := bn128.Fq2.MulScalar(bn128.Fq2.Add(b, f), bn128.TwoInv)
h := bn128.Fq2.Sub(
bn128.Fq2.Square(bn128.Fq2.Add(y, z)),
bn128.Fq2.Add(b, c))
i := bn128.Fq2.Sub(e, b)
j := bn128.Fq2.Square(x)
eSqr := bn128.Fq2.Square(e)
current[0] = bn128.Fq2.Mul(a, bn128.Fq2.Sub(b, f))
current[1] = bn128.Fq2.Sub(bn128.Fq2.Sub(bn128.Fq2.Square(g), eSqr),
bn128.Fq2.Add(eSqr, eSqr))
current[2] = bn128.Fq2.Mul(b, h)
res := EllCoeffs{
Ell0: bn128.Fq2.Mul(i, bn128.Twist),
EllVW: bn128.Fq2.Neg(h),
EllVV: bn128.Fq2.Add(j, bn128.Fq2.Add(j, j)),
}
return res, current
}
func (bn128 Bn128) MixedAdditionStep(base, current [3][2]*big.Int) (EllCoeffs, [3][2]*big.Int) {
x1 := current[0]
y1 := current[1]
z1 := current[2]
x2 := base[0]
y2 := base[1]
d := bn128.Fq2.Sub(x1, bn128.Fq2.Mul(x2, z1))
e := bn128.Fq2.Sub(y1, bn128.Fq2.Mul(y2, z1))
f := bn128.Fq2.Square(d)
g := bn128.Fq2.Square(e)
h := bn128.Fq2.Mul(d, f)
i := bn128.Fq2.Mul(x1, f)
j := bn128.Fq2.Sub(
bn128.Fq2.Add(h, bn128.Fq2.Mul(z1, g)),
bn128.Fq2.Add(i, i))
current[0] = bn128.Fq2.Mul(d, j)
current[1] = bn128.Fq2.Sub(
bn128.Fq2.Mul(e, bn128.Fq2.Sub(i, j)),
bn128.Fq2.Mul(h, y1))
current[2] = bn128.Fq2.Mul(z1, h)
coef := EllCoeffs{
Ell0: bn128.Fq2.Mul(
bn128.Twist,
bn128.Fq2.Sub(
bn128.Fq2.Mul(e, x2),
bn128.Fq2.Mul(d, y2))),
EllVW: d,
EllVV: bn128.Fq2.Neg(e),
}
return coef, current
}
func (bn128 Bn128) G2MulByQ(p [3][2]*big.Int) [3][2]*big.Int {
fmx := [2]*big.Int{
p[0][0],
bn128.Fq1.Mul(p[0][1], bn128.Fq1.Copy(bn128.FrobeniusCoeffsC11)),
}
fmy := [2]*big.Int{
p[1][0],
bn128.Fq1.Mul(p[1][1], bn128.Fq1.Copy(bn128.FrobeniusCoeffsC11)),
}
fmz := [2]*big.Int{
p[2][0],
bn128.Fq1.Mul(p[2][1], bn128.Fq1.Copy(bn128.FrobeniusCoeffsC11)),
}
return [3][2]*big.Int{
bn128.Fq2.Mul(bn128.TwistMulByQX, fmx),
bn128.Fq2.Mul(bn128.TwistMulByQY, fmy),
fmz,
}
}
func (bn128 Bn128) MillerLoop(pre1 AteG1Precomp, pre2 AteG2Precomp) [2][3][2]*big.Int {
// https://cryptojedi.org/papers/dclxvi-20100714.pdf
// https://eprint.iacr.org/2008/096.pdf
idx := 0
var c EllCoeffs
f := bn128.Fq12.One()
for i := bn128.LoopCount.BitLen() - 2; i >= 0; i-- {
bit := bn128.LoopCount.Bit(i)
c = pre2.Coeffs[idx]
idx++
f = bn128.Fq12.Square(f)
f = bn128.MulBy024(f,
c.Ell0,
bn128.Fq2.MulScalar(c.EllVW, pre1.Py),
bn128.Fq2.MulScalar(c.EllVV, pre1.Px))
if bit == 1 {
c = pre2.Coeffs[idx]
idx++
f = bn128.MulBy024(
f,
c.Ell0,
bn128.Fq2.MulScalar(c.EllVW, pre1.Py),
bn128.Fq2.MulScalar(c.EllVV, pre1.Px))
}
}
if bn128.LoopCountNeg {
f = bn128.Fq12.Inverse(f)
}
c = pre2.Coeffs[idx]
idx++
f = bn128.MulBy024(
f,
c.Ell0,
bn128.Fq2.MulScalar(c.EllVW, pre1.Py),
bn128.Fq2.MulScalar(c.EllVV, pre1.Px))
c = pre2.Coeffs[idx]
idx++
f = bn128.MulBy024(
f,
c.Ell0,
bn128.Fq2.MulScalar(c.EllVW, pre1.Py),
bn128.Fq2.MulScalar(c.EllVV, pre1.Px))
return f
}
func (bn128 Bn128) MulBy024(a [2][3][2]*big.Int, ell0, ellVW, ellVV [2]*big.Int) [2][3][2]*big.Int {
b := [2][3][2]*big.Int{
[3][2]*big.Int{
ell0,
bn128.Fq2.Zero(),
ellVV,
},
[3][2]*big.Int{
bn128.Fq2.Zero(),
ellVW,
bn128.Fq2.Zero(),
},
}
return bn128.Fq12.Mul(a, b)
}
func (bn128 Bn128) FinalExponentiation(r [2][3][2]*big.Int) [2][3][2]*big.Int {
res := bn128.Fq12.Exp(r, bn128.FinalExp)
return res
}