Update BaseFold number of queries to 200 according to the recent papers.

[yczhangsjtu]

Extracting small PRs from #294

[kunxian-xia]

Can you put some links or comments here to justify the reduction?

[yczhangsjtu]

Sure. I'll copy from the original PR.

[yczhangsjtu]

According to Theorem 1 of paper (https://eprint.iacr.org/2024/1571), the soundness error is bounded by $O(1/|F|) + (\sqrt{\rho}+\epsilon)^s$ where $s$ is the query complexity and $\epsilon$ is a small value that can be ignored. So the number of queries can be estimated by

$$ \frac{2\lambda}{-\log\rho} $$

If we take $\lambda=100$ and $\rho=1/2$, then the number of queries is $200$.

[hero78119]

Thanks for the change, I will try to verify with quick benchmark and report e2e result here

[matthiasgoergens]

@yczhangsjtu Could you make that explanation part of the code base, perhaps as a comment?

[hero78119]

Hi @yczhangsjtu I try run benchmark on 2^20 which involve basefold commit/opening riscv_add
On ceno server, benchmark result shows no significant change before/after.
does it fit the expectation, or do you have any benchmark result for that change?
Just double check in case the change actually not take effect

[kunxian-xia]

We should expect a big reduction of the proof size. @yczhangsjtu Can you give us how many bytes do we save after applying this PR?