Remove toxic waste from setup parameters

Refactorings

ZeroMorph skeleton

Drafts a non-hiding variant of the KZG PCS on univariate Dense polynomial representations

Details:
- Changed access levels and ordering for various modules and functions like `sumcheck`, `cpu_best_multiexp`, and `mod kzg;`.
- Upgraded `halo2curves` version and added new dependencies like `pairing`, `anyhow`, `rand`, and `group`.
- Leveraged the UniPoly in sumcheck.rs
- Created `non_hiding_kzg.rs` file, introducing new structures and functionalities like `UVUniversalKZGParam`, `UVKZGProverKey`, `UVKZGPoly`, and `UVKZGPCS` along with their implementation and tests.
- Modified the import of `Engine` in `kzg.rs` from `halo2curves::pairing::Engine` to `pairing::Engine` (reflecting the new version of halo2curves).

feat: add batch commit / open / prove

Minor adjustments

refactor: Remove kzg and zeromorph provider modules

- Added new data structures and their related functions including the `ZMProverKey`, `ZMVerifierKey`, `ZMCommitment`, `ZMEvaluation`, `ZMProof` and `ZMPCS` in `non_hiding_zeromorph.rs`
- Implemented new functionalities in `non_hiding_zeromorph.rs` and `spartan/polynomial.rs` to provide better handling of polynomials, including fetching commitments for a polynomial, computing the quotient polynomials of an existing polynomial.
- Enhanced the `UniPoly` struct in `spartan/sumcheck.rs` with `Index` and `IndexMut` for better coefficient access, and `AddAssign` and `MulAssign` for scalar and self types.
- Removed and replaced certain elements in `UVUniversalKZGParam` struct in `non_hiding_kzg.rs` for improved flexibility, and included import and implementation of `TranscriptReprTrait`.

draft ZM verify

set up test structure

defer test_quo

- Temporarily disabled some assertions in both `non_hiding_zeromorph.rs` and `polynomial.rs` for debugging purposes.
- Introduced `evaluate_opt`, `fix_variables`, and `fix_one_variable_helper` functions in `polynomial.rs` to support multilinear polynomial evaluation and partial evaluation.

fix: add domain separators

- Integrated additional functionality into the ZMPCS implementation in `non_hiding_zeromorph.rs` by adding a protocol name function.
- Improved security in `non_hiding_zeromorph.rs` by integrating domain separators into transcript's `open` and `verify` functions.

refactor: Refactor code and test performance for NHZM

- Implement `AsRef` trait for `UniPoly` structure in `src/spartan/sumcheck.rs` to facilitate direct access to its coefficients.
- Refactor code in `src/provider/non_hiding_zeromorph.rs` to directly use `into_iter` in map function when creating `quotients_polys`, avoiding a large clone
- Enhance test performance in `src/provider/non_hiding_zeromorph.rs` by pre-generating a `universal_setup` for tests, introducing a `max_vars` variable and RNG in the `commit_open_verify_with` test function, and adjusting the range of num_vars used for testing.

fix: adjust APIs & Serialize impls for the Nova traits

wip

fix: ignore panicking test

fix: add doctest for evaluate_opt

fix: remove obsolete comments

chore: move UniPoly methods where they should be

test: make clear current zeromorph operates in monomial basis

- Added an additional test `test_dense_evaliations()` to provide more comprehensive testing for the `evaluate()` and `evaluate_opt()` functions in `MultilinearPolynomial`.

refactor TranscriptReprTrait impl for compat with Commitments

- Added serialization, deserialization, and Abomonation traits to UVUniversalKZGParam struct in `non_hiding_kzg.rs` file along with implementing comparison and length evaluation traits.
- Created a new file `kzg_commitment.rs` which implements KZG Commitment Engine and setup, commit functions.
- Integrated `kzg_commitment` in module `provider` and set up conversions between Commitment and UVKZGCommitment.
- Enhanced assertion in `minroot_serde.rs` file from clone comparison to dereferenced comparison in MinRoot delay case.

feat: Improve `prove` and `verify` methods in `ZMPCS` struct

- Updated `prove` and `verify` methods in `ZMPCS<E>` struct within `non_hiding_zeromorph.rs` with actual logic for commitment, evaluation, and verification.
- Adjusted the construction of `ZMCommitment` and `ZMEvaluation` within `prove` and `verify` methods.
- Commented on portions of the code in `non_hiding_zeromorph.rs` that need further modification and refinement.
- Modified test value for `test_pp_digest_with` in the `test_supernova_pp_digest` test case to match the new expected output.

fix: remove superfluous eval functions

fix: remove endianness shenanigans

test: add evaluation unit test

… computation

- Introduced a new module `util` within the `provider` module, implementing fixed-base MSM,
- New trait constraint has been imposed for `E::Fr: PrimeFieldBits` within the `non_hiding_zeromorph.rs` file, and usages have been adjusted in the `test` module.
- Adding the `PrimeFieldBits` import from the `ff` crate and importing `provider::util` from the local crate.

refactor: Refactor utility functions for elliptic curve operations

- Renamed and moved `util.rs` to `fb_msm.rs` under the `provider` directory.
- documented the FB MSM

Co-authored-by: Adrian Hamelink <[email protected]>

- Enhanced the clarity and accuracy of code comments and documentation in `non_hiding_zeromorph.rs`, specifically within the `ZMPCS` struct's methods.
- Enriched the `quotients` function's documentation, detailing its mathematical underpinnings
- Implemented a new rigorous test, `test_quotients`, to ensure the `quotients` function's output satisfies the polynomial identity.

* fix: remove a TODO using RefCast

* fix: remove unsightly clone

* doc: comment intermediate ZM steps

* refactor: Refactor `open` function in zeromorph provider

Extracted the computation of `q_hat` in the `open` function into a new function `batched_lifted_degree_quotient` for more modular code.

* test: test batched_lifted_degree_quotient

Addition of a new test `test_batched_lifted_degree_quotient` to validate batched degree quotient lifting for polynomials.

* refactor: Refine computations in non_hiding_zeromorph.rs

- Overhauled the 'eval_and_quotient_scalars' function with a revised return type with pair of vectors rather than scalar and a vector,
- correspondingly split scalars `degree_check_q_scalars` and `zmpoly_q_scalars` within the `open` method of `non_hiding_zeromorph.rs`.
- Adjusted the 'verify' method to accommodate the modified 'eval_and_quotient_scalars' function output changes.

* test: test partially evaluated quotient \zeta_x

- Introduced a new test case `test_partially_evaluated_quotient_zeta` to validate `zeta_x` construction.
- correct an off-by-one error in the y_k terms

* test: test partially evaluated quotient

- Created a new function `phi` for evaluating using an inefficient formula in `non_hiding_zeromorph.rs`
- Implemented a new test function `test_partially_evaluated_quotient_z` for validation of `Z_x` computation method in `non_hiding_zeromorph.rs`

* fix: refine q_hat comment

- Updated and enhanced clarity and consistency of mathematical notation in comments across `non_hiding_kzg.rs` and `non_hiding_zeromorph.rs` files.
- Implemented error handling in the `ZMPCS::verify` function within the `non_hiding_zeromorph.rs` file.