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[perf] Faster G2 subgroup membership on BN254 #251

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Merged
yelhousni merged 2 commits into from
Oct 28, 2022
Merged

[perf] Faster G2 subgroup membership on BN254 #251

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a980428
perf(bn254): faster subgroup membership
yelhousni Oct 25, 2022
ad842f5
refactor(bn254): remove unused variable (fixedCoeff)
yelhousni Oct 25, 2022
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3 changes: 2 additions & 1 deletion ecc/bls12-377/g2.go
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3 changes: 2 additions & 1 deletion ecc/bls12-378/g2.go
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3 changes: 2 additions & 1 deletion ecc/bls12-381/g2.go
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3 changes: 2 additions & 1 deletion ecc/bls24-315/g2.go
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3 changes: 2 additions & 1 deletion ecc/bls24-317/g2.go
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6 changes: 0 additions & 6 deletions ecc/bn254/bn254.go
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Original file line number Diff line number Diff line change
Expand Up @@ -99,9 +99,6 @@ var endo struct {
// seed x₀ of the curve
var xGen big.Int

// trace - 1 = 6x₀²
var fixedCoeff big.Int

func init() {

bCurveCoeff.SetUint64(3)
Expand Down Expand Up @@ -147,9 +144,6 @@ func init() {

xGen.SetString("4965661367192848881", 10)

// 6x₀²
fixedCoeff.SetString("147946756881789318990833708069417712966", 10)

}

// Generators return the generators of the r-torsion group, resp. in ker(pi-id), ker(Tr)
Expand Down
19 changes: 13 additions & 6 deletions ecc/bn254/g2.go
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30 changes: 20 additions & 10 deletions internal/generator/ecc/template/point.go.tmpl
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Original file line number Diff line number Diff line change
Expand Up @@ -416,15 +416,22 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
}
{{else if eq .PointName "g2"}}
// IsInSubGroup returns true if p is on the r-torsion, false otherwise.
// [r]P == 0 <==> Frob(P) == [6x²]P
// https://eprint.iacr.org/2022/348.pdf, sec. 3 and 5.1
// [r]P == 0 <==> [x₀+1]P + ψ([x₀]P) + ψ²([x₀]P) = ψ³([2x₀]P)
func (p *{{ $TJacobian }}) IsInSubGroup() bool {
var a, res G2Jac
a.psi(p)
res.ScalarMultiplication(p, &fixedCoeff).
SubAssign(&a)

return res.IsOnCurve() && res.Z.IsZero()
var a, b, c, res G2Jac
a.ScalarMultiplication(p, &xGen)
b.psi(&a)
a.AddAssign(p)
res.psi(&b)
c.Set(&res).
AddAssign(&b).
AddAssign(&a)
res.psi(&res).
Double(&res).
SubAssign(&c)

return res.IsOnCurve() && res.Z.IsZero()
}
{{- end}}
{{else if or (eq .Name "bw6-761") (eq .Name "bw6-756")}}
Expand Down Expand Up @@ -491,7 +498,8 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
{{else if eq .PointName "g2"}}
// IsInSubGroup returns true if p is on the r-torsion, false otherwise.
// https://eprint.iacr.org/2021/1130.pdf, sec.4
// ψ(p) = x₀ P
// and https://eprint.iacr.org/2022/352.pdf, sec. 4.2
// ψ(p) = [x₀]P
func (p *{{ $TJacobian }}) IsInSubGroup() bool {
var res, tmp {{ $TJacobian }}
tmp.psi(p)
Expand Down Expand Up @@ -529,7 +537,8 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
{{if eq .Name "bls12-381"}}
// IsInSubGroup returns true if p is on the r-torsion, false otherwise.
// https://eprint.iacr.org/2021/1130.pdf, sec.4
// ψ(p) = x₀ P
// and https://eprint.iacr.org/2022/352.pdf, sec. 4.2
// ψ(p) = [x₀]P
func (p *{{ $TJacobian }}) IsInSubGroup() bool {
var res, tmp {{ $TJacobian }}
tmp.psi(p)
Expand All @@ -540,7 +549,8 @@ func (p *{{ $TJacobian }}) IsOnCurve() bool {
}
{{else if or (eq .Name "bls12-377") (eq .Name "bls12-378")}}
// https://eprint.iacr.org/2021/1130.pdf, sec.4
// ψ(p) = x₀ P
// and https://eprint.iacr.org/2022/352.pdf, sec. 4.2
// ψ(p) = [x₀]P
func (p *{{ $TJacobian }}) IsInSubGroup() bool {
var res, tmp {{ $TJacobian }}
tmp.psi(p)
Expand Down
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