feat: Add generic hyrax scheme

[stuarttimwhite]

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Rationale for this change

There is a need for a Hyrax scheme specifically for implementing proof of sql with the sp1 zkvm (docs here).

What changes are included in this PR?

1. A generic Hyrax scheme.

Are these changes tested?

There will be a follow up PR with a specific Sp1 implementation, which will have sp1 specific tests.

[JayWhite2357]

Requesting changes so that this PR is blocked until I approve @Dustin-Ray and @jacobtrombetta can you give an initial review.

[Dustin-Ray]

@stuarttimwhite Its really cool you were able to spin this up so quickly, nice work.

Right off the bat I would ask that we add unit testing for any new functionality being added, particularly in the hyrax_commitment.rs and hyrax_commitment_evaluation_proof.rs modules. Please see this and this in the dory module for examples of tests that we will need in order to be sure this protocol works as expected.

RE your comment about the helper module containing duplicate code from dory, if its not a huge lift you could try to just use the dory code, but if you want to save that for later I think it would be ok.

[jacobtrombetta]

Are there any tests that were used to confirm the Hyrax commitment scheme is working as expected? I don't see any, which makes me nervous. Since these are commitments we should really include tests.

[jacobtrombetta]

Can you add any more to the description about the Hyrax scheme or what sp1 is? For example, I don't know what sp1 is or why it is important. Additional information will also help other people when looking at the code. Here is an example from when the Hyrax multilinear PCS was added to Arkworks: arkworks-rs/poly-commit#130. (The PR also includes tests in the PR, if you were looking to add tests to this PR.)

[Dustin-Ray]

Can you add any more to the description about the Hyrax scheme or what sp1 is? For example, I don't know what sp1 is or why it is important. Additional information will also help other people when looking at the code. Here is an example from when the Hyrax multilinear PCS was added to Arkworks: arkworks-rs/poly-commit#130. (The PR also includes tests in the PR, if you were looking to add tests to this PR.)

This is a nice comment, @stuarttimwhite if you look through the dory code, there are specific references to the paper involved the implementation and the specific sections where certain algorithms appear. But even for a brief description or background, I think referring to the hyrax paper could be a good place to start

[Dustin-Ray]

This comment doesnt make a lot of sense

[stuarttimwhite]

Made a change. Should be more clear now.

[Dustin-Ray]

Im a bit wary of the complexity introduced with the associated types, but I think its ok for now, and they work for the use case here.

What would be interesting to see is if you can please add a test here that shows a round trip usage of hyrax evaluation proof, I think that would put us in a pretty good place

[stuarttimwhite]

Im a bit wary of the complexity introduced with the associated types, but I think its ok for now, and they work for the use case here.

What would be interesting to see is if you can please add a test here that shows a round trip usage of hyrax evaluation proof, I think that would put us in a pretty good place

Unfortunately test code can't be used within integration_tests. I do plan to add a test using the Sp1Configuration in the next PR here, so this would be remedied in relatively short order. And I have run a simple query locally using the test scheme within integration_tests (temporarily unmarking code as test code as needed), and that test passed. Would it be acceptable to wait for the next PR to add the round trip tests?