mirror of
https://github.com/emmansun/gmsm.git
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67 lines
1.5 KiB
Go
67 lines
1.5 KiB
Go
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package bn256
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func pairingB6(a *twistPoint, b *curvePoint) *gfP12 {
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e := miller(a, b)
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eb6 := (&gfP12b6{}).SetGfP12(e)
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ret := finalExponentiationB6(eb6)
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if a.IsInfinity() || b.IsInfinity() {
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ret.SetOne()
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}
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return ret.ToGfP12()
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}
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// finalExponentiation computes the (p¹²-1)/Order-th power of an element of
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// GF(p¹²) to obtain an element of GT. https://eprint.iacr.org/2007/390.pdf
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// http://cryptojedi.org/papers/dclxvi-20100714.pdf
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func finalExponentiationB6(in *gfP12b6) *gfP12b6 {
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t1 := &gfP12b6{}
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// This is the p^6-Frobenius
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t1.x.Neg(&in.x)
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t1.y.Set(&in.y)
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inv := &gfP12b6{}
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inv.Invert(in)
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t1.Mul(t1, inv)
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t2 := (&gfP12b6{}).FrobeniusP2(t1)
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t1.Mul(t1, t2)
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fp := (&gfP12b6{}).Frobenius(t1)
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fp2 := (&gfP12b6{}).FrobeniusP2(t1)
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fp3 := (&gfP12b6{}).Frobenius(fp2)
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fu := (&gfP12b6{}).Exp(t1, u)
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fu2 := (&gfP12b6{}).Exp(fu, u)
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fu3 := (&gfP12b6{}).Exp(fu2, u)
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y3 := (&gfP12b6{}).Frobenius(fu)
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fu2p := (&gfP12b6{}).Frobenius(fu2)
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fu3p := (&gfP12b6{}).Frobenius(fu3)
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y2 := (&gfP12b6{}).FrobeniusP2(fu2)
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y0 := &gfP12b6{}
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y0.Mul(fp, fp2).Mul(y0, fp3)
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y1 := (&gfP12b6{}).Conjugate(t1)
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y5 := (&gfP12b6{}).Conjugate(fu2)
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y3.Conjugate(y3)
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y4 := (&gfP12b6{}).Mul(fu, fu2p)
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y4.Conjugate(y4)
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y6 := (&gfP12b6{}).Mul(fu3, fu3p)
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y6.Conjugate(y6)
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t0 := (&gfP12b6{}).Square(y6)
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t0.Mul(t0, y4).Mul(t0, y5)
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t1.Mul(y3, y5).Mul(t1, t0)
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t0.Mul(t0, y2)
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t1.Square(t1).Mul(t1, t0).Square(t1)
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t0.Mul(t1, y1)
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t1.Mul(t1, y0)
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t0.Square(t0).Mul(t0, t1)
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return t0
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}
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