Feat/switch groth16 key

[lucasmenendez]

Description

This PR implements SwitchVerificationKey for groth16 recursion. By including two verification keys for similar circuits, it allows recursive verification of multiple proofs for both circuits, seamlessly switching between their corresponding verification keys as needed.

Type of change

• 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?

There are three similar tests that verify that two proofs from two different circuits are in the third circuit. Each test uses different curves for the inner and outer circuits:

• Test TestMultipleBN254InBN254
• Test TestMultipleBLS12InBW6
• Test TestMultipleBW6InBN254

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

[ivokub]

I'm a bit behind on reviews and will get to it soon

[ivokub]

I'm a bit behind on reviews and will get to it soon

I rebased on top of master and fixed conflicting changes. I'll still have a look at the Groth16 test and add tests for MuxG2/MuxGt. And I'd like to write documentation example. But in general looks good.

[lucasmenendez]

Super nice!!

I'm a bit behind on reviews and will get to it soon

I rebased on top of master and fixed conflicting changes. I'll still have a look at the Groth16 test and add tests for MuxG2/MuxGt. And I'd like to write documentation example. But in general looks good.

[Copilot]

Pull Request Overview

This PR implements key switching for Groth16 recursion by adding a new function SwitchVerificationKey that selects among multiple verification keys based on a runtime selector. Additionally, it provides new helper methods (MuxG2 and MuxGt) along with comprehensive tests across several pairing and verifier packages to support recursive verification for multiple circuits.

Reviewed Changes

Copilot reviewed 14 out of 14 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
std/algebra/native/sw_bls24315/pairing2_test.go	Added helper functions and tests for MuxG2/MuxGt in the context of Groth16 key switching.
std/algebra/emulated/sw_bw6761/pairing.go	Implemented MuxG2 and MuxGt functions and integrated them into the pairing API.
std/algebra/emulated/sw_bn254/pairing_test.go	Updated tests to exercise pairing mux functions for BN254 curves.
std/algebra/native/sw_bls12377/pairing2_test.go	Updated tests and circuit definitions to validate Groth16 key switching for BLS12-377 proofs.
std/recursion/groth16/verifier.go	Introduced the SwitchVerificationKey functionality and updated references to commitment verification.
std/algebra/interfaces.go & std/recursion/plonk/verifier.go	Minor interface updates to support the new MuxG2 and MuxGt methods.

[ivokub]

Thanks! It is super useful. It also revealed a bug we had before.