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sm9: pairing 避免除数处理

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emmansun 2023-05-02 11:39:16 +08:00
parent bf17ff1a4d
commit de6e4c2464
1 changed files with 12 additions and 32 deletions
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44
sm9/bn256/bn_pair.go
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@ -1,14 +1,12 @@
// Package bn256 defines/implements ShangMi(SM) sm9's curves and pairing.
package bn256
func lineFunctionAdd(r, p *twistPoint, q *curvePoint, r2 *gfP2) (a, b, c, d *gfP2, rOut *twistPoint) {
func lineFunctionAdd(r, p *twistPoint, q *curvePoint, r2 *gfP2) (a, b, c *gfP2, rOut *twistPoint) {
// See the mixed addition algorithm from "Faster Computation of the
// Tate Pairing", http://arxiv.org/pdf/0904.0854v3.pdf
B := (&gfP2{}).Mul(&p.x, &r.t) // B = Xp * Zr^2
d = (&gfP2{}).Mul(B, &r.z) // d = Xp * Zr^3
D := (&gfP2{}).Mul(&r.z, &r.x)
d.Sub(D, d) // d = Xr*Zr - Xp * Zr^3
D = (&gfP2{}).Add(&p.y, &r.z) // D = Yp + Zr
D.Square(D).Sub(D, r2).Sub(D, &r.t).Mul(D, &r.t) // D = ((Yp + Zr)^2 - Zr^2 - Yp^2)*Zr^2 = 2Yp*Zr^3
@ -54,7 +52,7 @@ func lineFunctionAdd(r, p *twistPoint, q *curvePoint, r2 *gfP2) (a, b, c, d *gfP
return
}
func lineFunctionDouble(r *twistPoint, q *curvePoint) (a, b, c, d *gfP2, rOut *twistPoint) {
func lineFunctionDouble(r *twistPoint, q *curvePoint) (a, b, c *gfP2, rOut *twistPoint) {
// See the doubling algorithm for a=0 from "Faster Computation of the
// Tate Pairing", http://arxiv.org/pdf/0904.0854v3.pdf
A := (&gfP2{}).Square(&r.x)
@ -81,8 +79,6 @@ func lineFunctionDouble(r *twistPoint, q *curvePoint) (a, b, c, d *gfP2, rOut *t
rOut.t.Square(&rOut.z)
d = (&gfP2{}).Mul(&rOut.z, &rOut.t) // d = 2Yr*Zr^3
t.Mul(E, &r.t).Add(t, t)
b = (&gfP2{}).Neg(t)
b.MulScalar(b, &q.x)
@ -98,7 +94,7 @@ func lineFunctionDouble(r *twistPoint, q *curvePoint) (a, b, c, d *gfP2, rOut *t
return
}
func mulLine(ret *gfP12, retDen *gfP4, a, b, c, d *gfP2) {
func mulLine(ret *gfP12, a, b, c *gfP2) {
tx, ty, tz, t, bx, bz := &gfP4{}, &gfP4{}, &gfP4{}, &gfP4{}, &gfP4{}, &gfP4{}
bx.x.SetZero()
bx.y.Set(b)
@ -118,11 +114,6 @@ func mulLine(ret *gfP12, retDen *gfP4, a, b, c, d *gfP2) {
ret.x.Add(tx, t)
ret.z.Set(tz)
txD := &gfP2{}
txD.Mul(&retDen.y, d)
retDen.y.MulU(&retDen.x, d)
retDen.x.Set(txD)
}
//
@ -134,7 +125,6 @@ func mulLine(ret *gfP12, retDen *gfP4, a, b, c, d *gfP2) {
//
func miller(q *twistPoint, p *curvePoint) *gfP12 {
ret := (&gfP12{}).SetOne()
retDen := (&gfP4{}).SetOne() // denominator
aAffine := &twistPoint{}
aAffine.Set(q)
@ -153,23 +143,22 @@ func miller(q *twistPoint, p *curvePoint) *gfP12 {
r2 := (&gfP2{}).Square(&aAffine.y)
for i := len(sixUPlus2NAF) - 1; i > 0; i-- {
a, b, c, d, newR := lineFunctionDouble(r, bAffine)
a, b, c, newR := lineFunctionDouble(r, bAffine)
if i != len(sixUPlus2NAF)-1 {
ret.Square(ret)
retDen.Square(retDen)
}
mulLine(ret, retDen, a, b, c, d)
mulLine(ret, a, b, c)
r = newR
switch sixUPlus2NAF[i-1] {
case 1:
a, b, c, d, newR = lineFunctionAdd(r, aAffine, bAffine, r2)
a, b, c, newR = lineFunctionAdd(r, aAffine, bAffine, r2)
case -1:
a, b, c, d, newR = lineFunctionAdd(r, minusA, bAffine, r2)
a, b, c, newR = lineFunctionAdd(r, minusA, bAffine, r2)
default:
continue
}
mulLine(ret, retDen, a, b, c, d)
mulLine(ret, a, b, c)
r = newR
}
@ -201,22 +190,13 @@ func miller(q *twistPoint, p *curvePoint) *gfP12 {
minusQ2.t.SetOne()
r2.Square(&q1.y)
a, b, c, d, newR := lineFunctionAdd(r, q1, bAffine, r2)
mulLine(ret, retDen, a, b, c, d)
a, b, c, newR := lineFunctionAdd(r, q1, bAffine, r2)
mulLine(ret, a, b, c)
r = newR
r2.Square(&minusQ2.y)
a, b, c, d, _ = lineFunctionAdd(r, minusQ2, bAffine, r2)
mulLine(ret, retDen, a, b, c, d)
//retDen.Invert(retDen)
t2, t3 := &gfP2{}, &gfP2{}
t3.SquareU(&retDen.x)
t3.Invert(t3)
t2.Mul(&retDen.x, t3)
retDen.x.Set(t2)
ret.MulScalar(ret, retDen)
a, b, c, _ = lineFunctionAdd(r, minusQ2, bAffine, r2)
mulLine(ret, a, b, c)
return ret
}