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pairing.go
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/
pairing.go
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package bls
type BLSPairingEngine struct {
G1 *G1
G2 *G2
fp12 *fp12
fp2 *fp2
fp *fp
t2 [10]*fe2
t12 [9]fe12
t12x [9]*fe12
}
func NewBLSPairingEngine() *BLSPairingEngine {
fp := newFp()
fp2 := newFp2(fp)
fp6 := newFp6(fp2)
fp12 := newFp12(fp6)
g1 := NewG1(fp)
g2 := NewG2(fp2)
t2 := [10]*fe2{}
t12x := [9]*fe12{}
for i := 0; i < len(t2); i++ {
t2[i] = &fe2{}
}
for i := 0; i < len(t12x); i++ {
t12x[i] = &fe12{}
}
t12 := [9]fe12{}
return &BLSPairingEngine{
fp: fp,
fp2: fp2,
fp12: fp12,
t2: t2,
t12: t12,
t12x: t12x,
G1: g1,
G2: g2,
}
}
func (e *BLSPairingEngine) doublingStep(coeff *[3]fe2, r *PointG2) {
fp2 := e.fp2
t := e.t2
fp2.mul(t[0], &r[0], &r[1])
fp2.mulByFq(t[0], t[0], twoInv)
fp2.square(t[1], &r[1])
fp2.square(t[2], &r[2])
fp2.double(t[7], t[2])
fp2.add(t[7], t[7], t[2])
fp2.mulByB(t[3], t[7])
fp2.double(t[4], t[3])
fp2.add(t[4], t[4], t[3])
fp2.add(t[5], t[1], t[4])
fp2.mulByFq(t[5], t[5], twoInv)
fp2.add(t[6], &r[1], &r[2])
fp2.square(t[6], t[6])
fp2.add(t[7], t[2], t[1])
fp2.sub(t[6], t[6], t[7])
fp2.sub(&coeff[0], t[3], t[1])
fp2.square(t[7], &r[0])
fp2.sub(t[4], t[1], t[4])
fp2.mul(&r[0], t[4], t[0])
fp2.square(t[2], t[3])
fp2.double(t[3], t[2])
fp2.add(t[3], t[3], t[2])
fp2.square(t[5], t[5])
fp2.sub(&r[1], t[5], t[3])
fp2.mul(&r[2], t[1], t[6])
fp2.double(t[0], t[7])
fp2.add(&coeff[1], t[0], t[7])
fp2.neg(&coeff[2], t[6])
}
func (e *BLSPairingEngine) additionStep(coeff *[3]fe2, r, q *PointG2) {
fp2 := e.fp2
t := e.t2
fp2.mul(t[0], &q[1], &r[2])
fp2.neg(t[0], t[0])
fp2.add(t[0], t[0], &r[1])
fp2.mul(t[1], &q[0], &r[2])
fp2.neg(t[1], t[1])
fp2.add(t[1], t[1], &r[0])
fp2.square(t[2], t[0])
fp2.square(t[3], t[1])
fp2.mul(t[4], t[1], t[3])
fp2.mul(t[2], &r[2], t[2])
fp2.mul(t[3], &r[0], t[3])
fp2.double(t[5], t[3])
fp2.sub(t[5], t[4], t[5])
fp2.add(t[5], t[5], t[2])
fp2.mul(&r[0], t[1], t[5])
fp2.sub(t[2], t[3], t[5])
fp2.mul(t[2], t[2], t[0])
fp2.mul(t[3], &r[1], t[4])
fp2.sub(&r[1], t[2], t[3])
fp2.mul(&r[2], &r[2], t[4])
fp2.mul(t[2], t[1], &q[1])
fp2.mul(t[3], t[0], &q[0])
fp2.sub(&coeff[0], t[3], t[2])
fp2.neg(&coeff[1], t[0])
fp2.copy(&coeff[2], t[1])
}
func (e *BLSPairingEngine) prepare(ellCoeffs *[70][3]fe2, twistPoint *PointG2) {
if e.G2.IsZero(twistPoint) {
return
}
r := &PointG2{}
e.G2.Copy(r, twistPoint)
j := 0
for i := int(x.BitLen() - 2); i >= 0; i-- {
e.doublingStep(&ellCoeffs[j], r)
if x.Bit(i) != 0 {
j++
ellCoeffs[j] = fe6{}
e.additionStep(&ellCoeffs[j], r, twistPoint)
}
j++
}
}
// notice that this function expects: len(points) == len(twistPoints)
func (e *BLSPairingEngine) millerLoop(f *fe12, points []PointG1, twistPoints []PointG2) {
for i := 0; i <= len(points)-1; i++ {
e.G1.Affine(&points[i])
e.G2.Affine(&twistPoints[i])
}
ellCoeffs := make([][70][3]fe2, len(points))
for i := 0; i < len(points); i++ {
if !e.G1.IsZero(&points[i]) && !e.G2.IsZero(&twistPoints[i]) {
e.prepare(&ellCoeffs[i], &twistPoints[i])
}
}
fp12 := e.fp12
fp2 := e.fp2
t := e.t2
fp12.copy(f, &fp12One)
// first iteration
// x.BitLen() - 2
// w/o squaring f
for i := 0; i <= len(points)-1; i++ {
fp2.mulByFq(t[0], &ellCoeffs[i][0][2], &points[i][1])
fp2.mulByFq(t[1], &ellCoeffs[i][0][1], &points[i][0])
fp12.mulBy014Assign(f, &ellCoeffs[i][0][0], t[1], t[0])
}
for i := 0; i <= len(points)-1; i++ {
fp2.mulByFq(t[0], &ellCoeffs[i][1][2], &points[i][1])
fp2.mulByFq(t[1], &ellCoeffs[i][1][1], &points[i][0])
fp12.mulBy014Assign(f, &ellCoeffs[i][1][0], t[1], t[0])
}
j := 2
for i := int(x.BitLen() - 3); i >= 0; i-- {
fp12.square(f, f)
for i := 0; i <= len(points)-1; i++ {
fp2.mulByFq(t[0], &ellCoeffs[i][j][2], &points[i][1])
fp2.mulByFq(t[1], &ellCoeffs[i][j][1], &points[i][0])
fp12.mulBy014Assign(f, &ellCoeffs[i][j][0], t[1], t[0])
}
if x.Bit(i) != 0 {
j++
for i := 0; i <= len(points)-1; i++ {
fp2.mulByFq(t[0], &ellCoeffs[i][j][2], &points[i][1])
fp2.mulByFq(t[1], &ellCoeffs[i][j][1], &points[i][0])
fp12.mulBy014Assign(f, &ellCoeffs[i][j][0], t[1], t[0])
}
}
j++
}
fp12.conjugate(f, f)
}
func (e *BLSPairingEngine) exp(c, a *fe12) {
fp12 := e.fp12
fp12.cyclotomicExp(c, a, x)
fp12.conjugate(c, c)
}
func (e *BLSPairingEngine) finalExp(f *fe12) {
fp12 := e.fp12
t := e.t12
fp12.frobeniusMap(&t[0], f, 6)
fp12.inverse(&t[1], f)
fp12.mul(&t[2], &t[0], &t[1])
fp12.copy(&t[1], &t[2])
fp12.frobeniusMapAssign(&t[2], 2)
fp12.mulAssign(&t[2], &t[1])
fp12.cyclotomicSquare(&t[1], &t[2])
fp12.conjugate(&t[1], &t[1])
e.exp(&t[3], &t[2])
fp12.cyclotomicSquare(&t[4], &t[3])
fp12.mul(&t[5], &t[1], &t[3])
e.exp(&t[1], &t[5])
e.exp(&t[0], &t[1])
e.exp(&t[6], &t[0])
fp12.mulAssign(&t[6], &t[4])
e.exp(&t[4], &t[6])
fp12.conjugate(&t[5], &t[5])
fp12.mulAssign(&t[4], &t[5])
fp12.mulAssign(&t[4], &t[2])
fp12.conjugate(&t[5], &t[2])
fp12.mulAssign(&t[1], &t[2])
fp12.frobeniusMapAssign(&t[1], 3)
fp12.mulAssign(&t[6], &t[5])
fp12.frobeniusMapAssign(&t[6], 1)
fp12.mulAssign(&t[3], &t[0])
fp12.frobeniusMapAssign(&t[3], 2)
fp12.mulAssign(&t[3], &t[1])
fp12.mulAssign(&t[3], &t[6])
fp12.mul(f, &t[3], &t[4])
}
func (e *BLSPairingEngine) pair(f *fe12, points []PointG1, twistPoints []PointG2) {
e.millerLoop(f, points, twistPoints)
e.finalExp(f)
}
func (e *BLSPairingEngine) PairingCheck(points []PointG1, twistPoints []PointG2) bool {
f := &fe12{}
e.millerLoop(f, points, twistPoints)
e.finalExp(f)
return e.fp12.equal(&fp12One, f)
}