feat: commitment equivalence gadget

[mrain]

Closes: #8

Known problem:

• Very inefficient, deserializing the SRS takes almost forever.
• cc @ggutoski: is it possible to verify a namespace proof without constructing a VidScheme? Current APIs doesn't feel ergonomic to me.
• Merkle tree proof verification is not ergonomic, either.

This PR:

• takes a namespace payload and compute a hash for rollup
• checks the namespace proof of this payload against vid commitment

This PR does not:

Key places to review:

[ggutoski]

• cc @ggutoski: is it possible to verify a namespace proof without constructing a VidScheme? Current APIs doesn't feel ergonomic to me.

I agree the need for a VidScheme is not ergonomic. I tried to eliminate it when I originally wrote the code. But verification uses many things from a VidScheme. So if we remove the VidScheme then we would need to add most VidScheme fields to the arglist for payload_verify, which is even worse.

https://github.com/EspressoSystems/jellyfish/blob/89b9345dc018d9bdb3d385aefd2036d5e42e9f17/vid/src/advz/payload_prover.rs#L238-L242

payload_verify needs the following things from VidScheme:

• recovery_threshold, multiplicity just integers, no big deal.
• ck: KzgProverParam the SRS (ugh) to re-compute a KZG commitment.
• eval_domain: Radix2EvaluationDomain for FFT (ugh). This is temporary; needed only because we don't yet have KZG in eval form.

[mrain]

Now I highly doubt that we can make any further meaningful improvement on the efficiency.

As tested here: https://github.com/mrain/sp1-project-template/blob/main/program/src/main.rs
Ark implemented msm (with 1 point/scalar) compiles to over 6m instructions in sp1 env. Even one single scalar multiplication costs over 4m instructions.

cc @ggutoski @alxiong @philippecamacho @akonring

[alxiong]

we can make any further meaningful improvement on the efficiency.

we should open an issue upstream to request Succinct to include a MSM precompile. I guess that's only reasonable way out?

[mrain]

we can make any further meaningful improvement on the efficiency.

we should open an issue upstream to request Succinct to include a MSM precompile. I guess that's only reasonable way out?

There're precompiles: https://docs.succinct.xyz/writing-programs/precompiles.html and #21
I'll look into it later.