refactor: Refactor testing setup and remove dependencies in provider …

…module

- Removal of the redundant `src/provider/util/fb_msm.rs` file which included functions for scalar multiplication
- Update of `kzg_commitment.rs` with the removal of `ff::PrimeFieldBits` dependency, transitional update of requirements, and improved method setups.

benches/pcs.rs

@@ -156,7 +156,7 @@ fn bench_pcs(c: &mut Criterion) {
     bench_pcs_proving_internal,
     bench_pcs_verifying_internal,
     (ipa_assets, IPAEvaluationEngine<Bn256Engine>),
-    (mlkzg_assets, MLEvaluationEngine<Bn256, Bn256EngineKZG>),
+    (hyperkzg_assets, MLEvaluationEngine<Bn256, Bn256EngineKZG>),
     (zm_assets, ZMPCS<Bn256, Bn256EngineZM>)
   );
 }

src/provider/hyperkzg.rs

@@ -1,4 +1,10 @@
-//! This module implements Nova's evaluation engine using multilinear KZG
+//! This module implements Nova's evaluation engine using `HyperKZG`, a KZG-based polynomial commitment for multilinear polynomials
+//! HyperKZG is based on the transformation from univariate PCS to multilinear PCS in the Gemini paper (section 2.4.2 in https://eprint.iacr.org/2022/420.pdf).
+//! However, there are some key differences:
+//! (1) HyperKZG works with multilinear polynomials represented in evaluation form (rather than in coefficient form in Gemini's transformation).
+//! This means that Spartan's polynomial IOP can use commit to its polynomials as-is without incurring any interpolations or FFTs.
+//! (2) HyperKZG is specialized to use KZG as the univariate commitment scheme, so it includes several optimizations (both during the transformation of multilinear-to-univariate claims
+//! and within the KZG commitment scheme implementation itself).
 #![allow(non_snake_case)]
 use crate::{
   errors::NovaError,
@@ -17,7 +23,7 @@ use crate::{
   zip_with,
 };
 use core::marker::PhantomData;
-use ff::{Field, PrimeFieldBits};
+use ff::Field;
 use group::{Curve, Group as _};
 use halo2curves::pairing::{Engine, MillerLoopResult, MultiMillerLoop};
 use itertools::Itertools as _;
@@ -51,7 +57,7 @@ where
   NE: NovaEngine<GE = E::G1, Scalar = E::Fr>,
   E::G1: DlogGroup<PreprocessedGroupElement = E::G1Affine, Scalar = E::Fr>,
   E::Fr: TranscriptReprTrait<E::G1>,
-  E::G1Affine: TranscriptReprTrait<E::G1>, // TODO: this bound on DlogGroup is really unusable!
+  E::G1Affine: TranscriptReprTrait<E::G1>,
 {
   fn compute_challenge(
     com: &[E::G1Affine],
@@ -106,7 +112,6 @@ where
   E::G2Affine: Serialize + DeserializeOwned,
   E::G1: DlogGroup<PreprocessedGroupElement = E::G1Affine, Scalar = E::Fr>,
   <E::G1 as Group>::Base: TranscriptReprTrait<E::G1>, // Note: due to the move of the bound TranscriptReprTrait<G> on G::Base from Group to Engine
-  E::Fr: PrimeFieldBits, // TODO due to use of gen_srs_for_testing, make optional
   E::Fr: TranscriptReprTrait<E::G1>,
   E::G1Affine: TranscriptReprTrait<E::G1>,
 {
@@ -296,7 +301,7 @@ where
       assert!(t == 3);
       assert!(W.len() == 3);
       // We write a special case for t=3, since this what is required for
-      // mlkzg. Following the paper directly, we must compute:
+      // hyperkzg. Following the paper directly, we must compute:
       // let L0 = C_B - vk.G * B_u[0] + W[0] * u[0];
       // let L1 = C_B - vk.G * B_u[1] + W[1] * u[1];
       // let L2 = C_B - vk.G * B_u[2] + W[2] * u[2];
@@ -418,7 +423,7 @@ where
 #[cfg(test)]
 mod tests {
   use super::*;
-  use crate::provider::util::test_utils::prove_verify_from_num_vars;
+  use crate::provider::test_utils::prove_verify_from_num_vars;
   use crate::{
     provider::keccak::Keccak256Transcript, traits::commitment::CommitmentTrait, CommitmentKey,
   };
@@ -429,7 +434,7 @@ mod tests {
   type Fr = <NE as NovaEngine>::Scalar;
 
   #[test]
-  fn test_mlkzg_eval() {
+  fn test_hyperkzg_eval() {
     // Test with poly(X1, X2) = 1 + X1 + X2 + X1*X2
     let n = 4;
     let ck: CommitmentKey<NE> =
@@ -466,7 +471,7 @@ mod tests {
   }
 
   #[test]
-  fn test_mlkzg_alternative() {
+  fn test_hyperkzg_alternative() {
     fn test_inner(n: usize, poly: &[Fr], point: &[Fr], eval: Fr) -> Result<(), NovaError> {
       let ck: CommitmentKey<NE> =
         <KZGCommitmentEngine<E> as CommitmentEngineTrait<NE>>::setup(b"test", n);
@@ -514,7 +519,7 @@ mod tests {
   }
 
   #[test]
-  fn test_mlkzg() {
+  fn test_hyperkzg() {
     let n = 4;
 
     // poly = [1, 2, 1, 4]
@@ -583,8 +588,8 @@ mod tests {
   }
 
   #[test]
-  fn test_mlkzg_more() {
-    // test the mlkzg prover and verifier with random instances (derived from a seed)
+  fn test_hyperkzg_more() {
+    // test the hyperkzg prover and verifier with random instances (derived from a seed)
     for num_vars in [4, 5, 6] {
       prove_verify_from_num_vars::<_, EvaluationEngine<E, NE>>(num_vars);
     }

src/provider/ipa_pc.rs

@@ -411,7 +411,7 @@ where
 #[cfg(test)]
 mod test {
   use crate::provider::ipa_pc::EvaluationEngine;
-  use crate::provider::util::test_utils::prove_verify_from_num_vars;
+  use crate::provider::test_utils::prove_verify_from_num_vars;
   use crate::provider::GrumpkinEngine;
 
   #[test]

src/provider/kzg_commitment.rs

@@ -3,7 +3,6 @@
 
 use std::marker::PhantomData;
 
-use ff::PrimeFieldBits;
 use group::{prime::PrimeCurveAffine, Curve};
 use halo2curves::pairing::Engine;
 use rand::rngs::StdRng;
@@ -33,7 +32,6 @@ where
   E::G1: DlogGroup<PreprocessedGroupElement = E::G1Affine, Scalar = E::Fr>,
   E::G1Affine: Serialize + for<'de> Deserialize<'de>,
   E::G2Affine: Serialize + for<'de> Deserialize<'de>,
-  E::Fr: PrimeFieldBits, // TODO due to use of gen_srs_for_testing, make optional
 {
   type CommitmentKey = UniversalKZGParam<E>;
   type Commitment = Commitment<NE>;

src/provider/mod.rs

@@ -15,7 +15,8 @@ pub(crate) mod traits;
 // a non-hiding variant of {kzg, zeromorph}
 pub(crate) mod kzg_commitment;
 pub(crate) mod non_hiding_kzg;
-pub(crate) mod util;
+#[cfg(test)]
+pub(crate) mod test_utils;
 
 // crate-private modules
 mod keccak;

src/provider/non_hiding_kzg.rs

@@ -1,5 +1,5 @@
 //! Non-hiding variant of KZG10 scheme for univariate polynomials.
-use ff::{Field, PrimeField, PrimeFieldBits};
+use ff::Field;
 use group::{prime::PrimeCurveAffine, Curve, Group as _};
 use halo2curves::pairing::{Engine, MillerLoopResult, MultiMillerLoop};
 use rand_core::{CryptoRng, RngCore};
@@ -9,7 +9,6 @@ use std::{borrow::Borrow, marker::PhantomData, ops::Mul};
 use crate::{
   errors::{NovaError, PCSError},
   provider::traits::DlogGroup,
-  provider::util::fb_msm,
   traits::{commitment::Len, Group, TranscriptReprTrait},
 };
 
@@ -119,10 +118,7 @@ impl<E: Engine> UniversalKZGParam<E> {
   }
 }
 
-impl<E: Engine> UniversalKZGParam<E>
-where
-  E::Fr: PrimeFieldBits,
-{
+impl<E: Engine> UniversalKZGParam<E> {
   /// Build SRS for testing.
   /// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
   /// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
@@ -131,25 +127,24 @@ where
     let g = E::G1::random(&mut rng);
     let h = E::G2::random(rng);
 
-    let nz_powers_of_beta = (0..=max_degree)
-      .scan(beta, |acc, _| {
-        let val = *acc;
-        *acc *= beta;
-        Some(val)
-      })
-      .collect::<Vec<E::Fr>>();
-
-    let window_size = fb_msm::get_mul_window_size(max_degree);
-    let scalar_bits = E::Fr::NUM_BITS as usize;
-
     let (powers_of_g_projective, powers_of_h_projective) = rayon::join(
       || {
-        let g_table = fb_msm::get_window_table(scalar_bits, window_size, g);
-        fb_msm::multi_scalar_mul::<E::G1>(scalar_bits, window_size, &g_table, &nz_powers_of_beta)
+        (0..=max_degree)
+          .scan(g, |acc, _| {
+            let val = *acc;
+            *acc *= beta;
+            Some(val)
+          })
+          .collect::<Vec<E::G1>>()
       },
       || {
-        let h_table = fb_msm::get_window_table(scalar_bits, window_size, h);
-        fb_msm::multi_scalar_mul::<E::G2>(scalar_bits, window_size, &h_table, &nz_powers_of_beta)
+        (0..=max_degree)
+          .scan(h, |acc, _| {
+            let val = *acc;
+            *acc *= beta;
+            Some(val)
+          })
+          .collect::<Vec<E::G2>>()
       },
     );
 
@@ -306,6 +301,7 @@ where
 mod tests {
   use super::*;
   use crate::spartan::polys::univariate::UniPoly;
+  use ff::PrimeField;
   use rand::{thread_rng, Rng};
   use rand_core::{CryptoRng, RngCore};
 
@@ -318,7 +314,6 @@ mod tests {
   where
     E: MultiMillerLoop,
     E::G1: DlogGroup<PreprocessedGroupElement = E::G1Affine, Scalar = E::Fr>,
-    E::Fr: PrimeFieldBits,
   {
     for _ in 0..100 {
       let mut rng = &mut thread_rng();

src/provider/non_hiding_zeromorph.rs

@@ -18,7 +18,7 @@ use crate::{
   },
   Commitment,
 };
-use ff::{BatchInvert, Field, PrimeField, PrimeFieldBits};
+use ff::{BatchInvert, Field, PrimeField};
 use group::{Curve, Group as _};
 use halo2curves::pairing::{Engine, MillerLoopResult, MultiMillerLoop};
 use itertools::Itertools as _;
@@ -463,7 +463,6 @@ where
   E::G1Affine: Serialize + DeserializeOwned,
   E::G2Affine: Serialize + DeserializeOwned,
   <E::G1 as Group>::Base: TranscriptReprTrait<E::G1>, // Note: due to the move of the bound TranscriptReprTrait<G> on G::Base from Group to Engine
-  E::Fr: PrimeFieldBits, // TODO due to use of gen_srs_for_testing, make optional
 {
   type ProverKey = ZMProverKey<E>;
   type VerifierKey = ZMVerifierKey<E>;
@@ -529,8 +528,8 @@ mod test {
       non_hiding_zeromorph::{
         batched_lifted_degree_quotient, eval_and_quotient_scalars, trim, ZMEvaluation, ZMPCS,
       },
+      test_utils::prove_verify_from_num_vars,
       traits::DlogGroup,
-      util::test_utils::prove_verify_from_num_vars,
       Bn256Engine, Bn256EngineZM,
     },
     spartan::polys::multilinear::MultilinearPolynomial,