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sm9: change finalExponentiation implementation

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Sun Yimin 2022-06-20 13:34:53 +08:00 committed by GitHub
parent 974ba65845
commit 195f6f73ba
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1 changed files with 46 additions and 41 deletions
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87
sm9/bn256/bn_pair.go
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@ -1,9 +1,5 @@
package bn256
import (
"math/big"
)
func lineFunctionAdd(r, p *twistPoint, q *curvePoint, r2 *gfP2) (a, b, c, d *gfP2, rOut *twistPoint) {
// See the mixed addition algorithm from "Faster Computation of the
// Tate Pairing", http://arxiv.org/pdf/0904.0854v3.pdf
@ -195,48 +191,57 @@ func miller(q *twistPoint, p *curvePoint) *gfP12 {
return ret
}
func finalExponentiationHardPart(in *gfP12) *gfP12 {
a, b, t0, t1 := &gfP12{}, &gfP12{}, &gfP12{}, &gfP12{}
a.Exp(in, sixUPlus5)
a.Invert(a)
b.Frobenius(a)
b.Mul(a, b) // b = ab
a.Mul(a, b)
t0.Frobenius(in)
t1.Mul(t0, in) // t1 = in ^(p+1)
t1.Exp(t1, big.NewInt(9))
a.Mul(a, t1)
t1.Square(in)
t1.Square(t1)
a.Mul(a, t1)
t0.Square(t0) // (in^p)^2
t0.Mul(t0, b) // b*(in^p)^2
b.FrobeniusP2(in)
t0.Mul(b, t0) // b*(in^p)^2 * in^(p^2)
t0.Exp(t0, sixU2Plus1)
a.Mul(a, t0)
b.FrobeniusP3(in)
b.Mul(a, b)
return b
}
// finalExponentiation computes the (p¹²-1)/Order-th power of an element of
// GF(p¹²) to obtain an element of GT. https://eprint.iacr.org/2007/390.pdf
// http://cryptojedi.org/papers/dclxvi-20100714.pdf
func finalExponentiation(in *gfP12) *gfP12 {
t0, t1 := &gfP12{}, &gfP12{}
t1 := &gfP12{}
t0.FrobeniusP6(in)
t1.Invert(in)
t0.Mul(t0, t1)
t1.FrobeniusP2(t0)
t0.Mul(t0, t1)
// This is the p^6-Frobenius
t1.FrobeniusP6(in)
return finalExponentiationHardPart(t0)
inv := &gfP12{}
inv.Invert(in)
t1.Mul(t1, inv)
t2 := (&gfP12{}).FrobeniusP2(t1)
t1.Mul(t1, t2)
fp := (&gfP12{}).Frobenius(t1)
fp2 := (&gfP12{}).FrobeniusP2(t1)
fp3 := (&gfP12{}).Frobenius(fp2)
fu := (&gfP12{}).Exp(t1, u)
fu2 := (&gfP12{}).Exp(fu, u)
fu3 := (&gfP12{}).Exp(fu2, u)
y3 := (&gfP12{}).Frobenius(fu)
fu2p := (&gfP12{}).Frobenius(fu2)
fu3p := (&gfP12{}).Frobenius(fu3)
y2 := (&gfP12{}).FrobeniusP2(fu2)
y0 := &gfP12{}
y0.Mul(fp, fp2).Mul(y0, fp3)
y1 := (&gfP12{}).Conjugate(t1)
y5 := (&gfP12{}).Conjugate(fu2)
y3.Conjugate(y3)
y4 := (&gfP12{}).Mul(fu, fu2p)
y4.Conjugate(y4)
y6 := (&gfP12{}).Mul(fu3, fu3p)
y6.Conjugate(y6)
t0 := (&gfP12{}).Square(y6)
t0.Mul(t0, y4).Mul(t0, y5)
t1.Mul(y3, y5).Mul(t1, t0)
t0.Mul(t0, y2)
t1.Square(t1).Mul(t1, t0).Square(t1)
t0.Mul(t1, y1)
t1.Mul(t1, y0)
t0.Square(t0).Mul(t0, t1)
return t0
}
func pairing(a *twistPoint, b *curvePoint) *gfP12 {