Feat: Jacobian Triple for j=0 curves

[yelhousni]

Description

This PR introduces Jacobian Triple for j=0 curves, i.e. [3]P in Jacobian coordinates for curves in the form y^2=x^3+b. This works for all curves supported by gnark-crypto (both G1 and G2) except STARK curve. We follow [XuHanTian24]. The cost is 4S+6M instead of 10S+13M (double+add). The PR also uses Triple in several places across the curves packages.

Type of change

• New feature (non-breaking change which adds functionality)

How has this been tested?

Testing [3]P == [2]P+P and all the methods which now use Triple method.

How has this been benchmarked?

e.g. BLS12-381 on my MBA M1:

goos: darwin
goarch: arm64
pkg: github.com/consensys/gnark-crypto/ecc/bls12-381
cpu: Apple M1
BenchmarkG1Triple
BenchmarkG1Triple/method=double-and-add
BenchmarkG1Triple/method=double-and-add-8                1435972               818.2 ns/op
BenchmarkG1Triple/method=triple
BenchmarkG1Triple/method=triple-8                        3346026               358.0 ns/op
BenchmarkG2Triple
BenchmarkG2Triple/method=double-and-add
BenchmarkG2Triple/method=double-and-add-8                 539943              2215 ns/op
BenchmarkG2Triple/method=triple
BenchmarkG2Triple/method=triple-8                        1205182               997.0 ns/op

Checklist:

• I have performed a self-review of my code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• I have added tests that prove my fix is effective or that my feature works
• I did not modify files generated from templates
• golangci-lint does not output errors locally
• New and existing unit tests pass locally with my changes
• Any dependent changes have been merged and published in downstream modules

[Copilot]

Pull Request Overview

This PR introduces a new Triple method for computing [3]P (scalar multiplication by 3) in Jacobian coordinates for j=0 elliptic curves. The implementation follows the XuHanTian24 paper and provides significant performance improvements over the traditional double-and-add approach, reducing costs from 10S+13M to 4S+6M.

• Adds optimized Triple method for all j=0 curves (all supported curves except STARK)
• Integrates Triple into existing scalar multiplication methods and precomputation tables
• Optimizes several curve-specific operations like mulBySeed and ClearCofactor to use Triple

Reviewed Changes

Copilot reviewed 34 out of 34 changed files in this pull request and generated 11 comments.

File	Description
internal/generator/ecc/template/tests/point.go.tmpl	Adds test property verifying [3]P == [2]P+P
internal/generator/ecc/template/point.go.tmpl	Implements Triple method and integrates it into various multiplication routines
Multiple curve files (g1.go, g2.go, g1_test.go, g2_test.go)	Generated implementations of Triple method and optimizations for specific curves