feat: verify commitments in groth16 recursion verifier

[ahmetyalp]

Description

This PR adds commitment verification to groth16 recursion AssertProof method. This implementation only supports at most one commitment.

TODO:

• Depends on refactor: make pedersen vk fields public gnark-crypto#488. Need to update go.mod after that PR merged

Type of change

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

How has this been tested?

• Added test case TestBN254InBN254Commitment to test inner circuit with commitment

How has this been benchmarked?

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]

Thanks for the contribution! I started reviewing the PR, but it takes a bit time. I'm proposing some refactors related to this PR and some which I wanted to include as part of a cleanup of Groth16 verifier (simpler init of groth16 verifier instance for example).

I'll have a longer response with specific items/suggestions soon.

[ivokub]

Thanks for the contribution! I refactored to be more aligned with PLONK verifier and allow for independent Pedersen commitment verification.

Could you have a look that I hadn't missed something and the refactored version works for you. If you give a go-ahead, then I'll merge.

[ivokub]

I'd not add the test property. The command assert.CheckCircuit is usually meant for end-to-end testing in CI and its internal behaviour is toggled with build tags:

// default options;
// go test -short 					--> testEngineOnly
// go test 							--> constraintOnlyProfile
// go test -tags=prover_checks 		--> proverOnlyProfile
// go test -tags=release_checks 	--> releaseProfile

Now, if we define and use WithProverCheck option, then when running tests with -short tag or without any tags, we would still be running the prover (which may be really slow).

Better option for testing prover is to use tags=provers_checks tag like

go test -timeout 10m -tags debug,prover_checks -run ^TestBN254InBN254Commitment$ github.com/consensys/gnark/std/recursion/groth16 -v -count=1

[ahmetyalp]

I run our tests with the refactored version. Everything seems fine. I left a comment about subgroupCheck, everything else LGTM. Thanks for the review and refactoring @ivokub