Small fix of zk rows for chunking

[querolita]

This is part of the investigation of the chunking bug in Pickles and o1js (RFCs here and here).

This branch is based on this branch by @Trivo25.

Explain your changes:

• Discussions taking place in the o1js RFC PR suggest that the number of zero knowledge rows was not being correctly propagated to o1js. I started inspecting where the zk rows parameter was coming from and found a few places were it was not being correctly used.
• in kimchi_bindings/wasm/src/plonk_verifier_index.rs there were two places where a hardcoded 3 was still being used to initialize w and the permutation polynomial. Instead, the updated zk_rows should be used:
  • res.set(zk_w(domain, index.zk_rows)).unwrap();
  • res.set(permutation_vanishing_polynomial(domain, index.zk_rows)).unwrap();
• in src/lib/pickles/compile.ml and src/lib/pickles/step_branch_data.ml, the number of rows was not computed correctly.
  • I modified the calculation to become ((2 * (permuts + 1) * num_chunks) - 2 + permuts) / permuts instead.
  • According to the chunking RFC and Kimchi,

   zk_rows = (16 * (domain_size / max_poly_size) + 5) / 7

Explain how you tested your changes:

• Before these changes were performed, the chunk4.ml used to fail with the error (Pickles.verify dlog_check).
  • The fix in the verifier index solves that error.
  • Nonetheless, the o1js tests still complain that there are not enough random rows to achieve zero-knowledge (expected: 4, got: 3). This suggests some miscalculation in the bindings that I still haven't found.
• The second fix does not have an impact in all scenarios, but only in somewhat specific situations where the old formula and the new one return different values. An example is when num_chunks = 11, but this si not a power of 2. Another one is when num_chunks = 4 (basically anytime (16*c+6)/7 gives an integer number). There, the old computation gives 10 rows whereas this one gives 9. Having more rows is not a problem for zero knowledge-ness itself (it would be the other way round though). But this mismatch between the Kimchi side and the Pickles side can be a source of problems. Thus, it is better if we use the same formula on both sides. This, prevents us from getting another (Pickles.verify dlog_check) error.

TODO:

• Find further places in the codebase where a hardcoded 3 might be used to instantiate variables instead of a proper variable default_zk_rows or similar.
• Look into o1js-bindings and learn about the dependencies between libraries across our stack.

Partially addresses o1-labs/o1js#1806

Checklist:

• Dependency versions are unchanged
  • Notify Velocity team if dependencies must change in CI
• Modified the current draft of release notes with details on what is completed or incomplete within this project
• Document code purpose, how to use it
  • Mention expected invariants, implicit constraints
• Tests were added for the new behavior
  • Document test purpose, significance of failures
  • Test names should reflect their purpose
• All tests pass (CI will check this if you didn't)
• Serialized types are in stable-versioned modules
• Does this close issues? List them

• Closes #0000

[dannywillems]

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[querolita]

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[querolita]

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[querolita]

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