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Perf: optimize BLS24-317 final exp #356

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Merged
yelhousni merged 1 commit into from
Mar 14, 2023
Merged

Perf: optimize BLS24-317 final exp #356

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20 changes: 14 additions & 6 deletions ecc/bls24-317/internal/fptower/e24_pairing.go
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Original file line number Diff line number Diff line change
Expand Up @@ -12,9 +12,9 @@ func (z *E24) nSquareCompressed(n int) {
}
}

// Expt set z to x^t in E24 and return z (t is the seed of the curve)
// t = 3640754176
func (z *E24) Expt(x *E24) *E24 {
// ExptHalf set z to x^(t/2) in E24 and return z (t is the seed of the curve)
// t/2 = 1820377088
func (z *E24) ExptHalf(x *E24) *E24 {
// Expt computation is derived from the addition chain:
//
// _10 = 2*1
Expand All @@ -23,9 +23,9 @@ func (z *E24) Expt(x *E24) *E24 {
// _11000000 = _11000 << 3
// _11011000 = _11000 + _11000000
// _11011001 = 1 + _11011000
// return (_11011001 << 9 + _11) << 15
// return (_11011001 << 9 + _11) << 14
//
// Operations: 31 squares 4 multiplies
// Operations: 30 squares 4 multiplies
//
// Generated by github.com/mmcloughlin/addchain v0.4.0.

Expand Down Expand Up @@ -60,14 +60,22 @@ func (z *E24) Expt(x *E24) *E24 {
result.Mul(&result, &t0)

// Step 35: result = x^0xd9018000
result.nSquareCompressed(15)
result.nSquareCompressed(14)
result.DecompressKarabina(&result)

z.Set(&result)

return z
}

// Expt set z to x^t in E24 and return z (t is the seed of the curve)
// t = 3640754176
func (z *E24) Expt(x *E24) *E24 {
var result E24
result.ExptHalf(x)
return z.CyclotomicSquare(&result)
}

// MulBy014 multiplication by sparse element (c0, c1, 0, 0, c4, 0)
func (z *E24) MulBy014(c0, c1, c4 *E4) *E24 {

Expand Down
14 changes: 9 additions & 5 deletions ecc/bls24-317/pairing.go
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Original file line number Diff line number Diff line change
Expand Up @@ -84,7 +84,7 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
// https://eprint.iacr.org/2020/875.pdf
// 3(p⁸ - p⁴ +1)/r = (x₀-1)² * (x₀+p) * (x₀²+p²) * (x₀⁴+p⁴-1) + 3
t[0].CyclotomicSquare(&result)
t[1].Expt(&result)
t[1].ExptHalf(&t[0])
t[2].InverseUnitary(&result)
t[1].Mul(&t[1], &t[2])
t[2].Expt(&t[1])
Expand All @@ -98,10 +98,14 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
t[2].Expt(&t[0])
t[0].FrobeniusSquare(&t[1])
t[2].Mul(&t[0], &t[2])
t[1].Expt(&t[2])
t[1].Expt(&t[1])
t[1].Expt(&t[1])
t[1].Expt(&t[1])
t[1].ExptHalf(&t[2])
t[1].ExptHalf(&t[1])
t[1].ExptHalf(&t[1])
t[1].ExptHalf(&t[1])
for s := 0; s < 4; s++ {
t[1].CyclotomicSquareCompressed(&t[1])
}
t[1].DecompressKarabina(&t[1])
t[0].FrobeniusQuad(&t[2])
t[0].Mul(&t[0], &t[1])
t[2].InverseUnitary(&t[2])
Expand Down
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