feat: add optimal ate pairing variant to bw6-761

[yelhousni]

Description

This PR implements an optimal ate variant of the Miller loop for the BW6-761 curve. This corresponds to equation (4') in https://hackmd.io/@gnark/BW6-761-changes. This is needed for testing purposes in Consensys/gnark#846.

Type of change

Please delete options that are not relevant.

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

How has this been tested?

Added a test for bilinearity in pairing_test.go.

How has this been benchmarked?

Benchmarks are not important for this PR as the new method is only used to test the gnark circuit implementation. However, this blog post is a good resource for benchamrks https://hackmd.io/@gnark/BW6-761-changes.

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

[github-actions]

Summary

✅ Passed: 5903
❌ Failed: 0
🚧 Skipped: 5

🚧 Skipped

• TestReference (github.com/consensys/gnark-crypto/ecc/bn254/fr/sis)
• TestLimbDecomposition (github.com/consensys/gnark-crypto/ecc/bn254/fr/sis)
• TestAppend (github.com/consensys/gnark-crypto/ecc/bn254/fr/tensor-commitment)
• TestAppendSis (github.com/consensys/gnark-crypto/ecc/bn254/fr/tensor-commitment)
• TestCommitmentSis (github.com/consensys/gnark-crypto/ecc/bn254/fr/tensor-commitment)

[yelhousni]

Closing this PR as it seems optimal Tate (the current gnark-crypto master Miller loop version) in-circuit yields better performance.