Feat: 4-dimensional fake GLV

[yelhousni]

Description

https://ethresear.ch/t/fake-glv-you-dont-need-an-efficient-endomorphism-to-implement-glv-like-scalar-multiplication-in-snark-circuits/20394/7

Type of change

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

How has this been tested?

Correctness tests are implemented in emulated/sw_emulated/point_test.go and native/sw_bls12377/g1_test.go.

How has this been benchmarked?

All benchmarks are in plonkish constraints (scs):

• Scalar muls (EMULATED)

  • Secp256k1:

    • old: 385,461
    • new: 285,176

  • BN254:

    • old: 381,467
    • new: 282,215

  • BW6-761:

    • old: 1,367,067
    • new: 1,017,381

• Scalar muls (NATIVE)

  • BLS12-377:
    • Old: 3,587
    • New (+10): 3,615
    • New (+9): 3,567
    • New (+6): 3,423

• Precompiles:

  • ECRECOVER:
    • Old: 459,065
    • New: 459,058
  • ECMUL:
    • Old: 384,782
    • New: 283,076

• Recursion:

  • Emulated:
    • Old: 28,206,642
    • New: 27,157,691
  • Native:
    • Old: 300,262
    • New: 300,022

Checklist:

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