perf: twisted Edwards affine arithmetic

[yelhousni]

Description

• Affine arithmetic in twisted Edwards to use extended coordinates with Z1=Z2=1.
• Affine scalar multiplication to use mixed addition.

Type of change

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

How has this been tested?

Current tests in twistededwards/ and eddsa/ pass.

How has this been benchmarked?

• e.g. baby-jubjub:

benchmark                 old ns/op     new ns/op     delta
BenchmarkAdd/Affine-8     4191          2277          -45.67%

benchmark             old ns/op     new ns/op     delta
BenchmarkDouble/Affine-8     2186          1198          -45.20%

benchmark                      old ns/op     new ns/op     delta
BenchmarkScalarMulAffine-8     50688         49545         -2.25%

• Saves 2-3% in EdDSA verify across different curves.

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 refactors the twisted Edwards affine arithmetic to use extended coordinates with Z1=Z2=1 for performance improvements. The change replaces the existing point addition and doubling formulas with optimized implementations based on extended coordinates.

• Implements new extended coordinate formulas for Add and Double operations
• Reduces the number of field inversions from 2 to 1 per operation
• Uses optimized variable naming conventions (A, B, C, D, E, F, G, H) following standard extended coordinate algorithms

Reviewed Changes

Copilot reviewed 9 out of 9 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
internal/generator/edwards/template/point.go.tmpl	Template file with new extended coordinate arithmetic implementations
ecc/bw6-761/twistededwards/point.go	Generated code with optimized Add/Double methods
ecc/bw6-633/twistededwards/point.go	Generated code with optimized Add/Double methods
ecc/bn254/twistededwards/point.go	Generated code with optimized Add/Double methods
ecc/bls24-317/twistededwards/point.go	Generated code with optimized Add/Double methods
ecc/bls24-315/twistededwards/point.go	Generated code with optimized Add/Double methods
ecc/bls12-381/twistededwards/point.go	Generated code with optimized Add/Double methods
ecc/bls12-381/bandersnatch/point.go	Generated code with optimized Add/Double methods
ecc/bls12-377/twistededwards/point.go	Generated code with optimized Add/Double methods

---

_{Tip: Customize your code reviews with copilot-instructions.md. Create the file or learn how to get started.}

[Copilot]

Pull Request Overview

Copilot reviewed 9 out of 9 changed files in this pull request and generated 1 comment.

---

_{Tip: Customize your code reviews with copilot-instructions.md. Create the file or learn how to get started.}

[YaoJGalteland]

LGTM. The rearrangement is correct, and the optimization reduces two DIV operations to one inverse operation.