Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Perf: optimize BLS24-317 final exp #356

Merged
merged 1 commit into from
Mar 14, 2023
+23 −11
Merged

Perf: optimize BLS24-317 final exp #356

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
20 changes: 14 additions & 6 deletions ecc/bls24-317/internal/fptower/e24_pairing.go
View file
Open in desktop
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
View file
Open in desktop
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