Initial Shplonk prover/verifier implementation (#301)

* feat: Initial Shplonk prover/verifier as EvaluationEngine

* feat: More optimal pairing check

* feat: Avoid including C_P to the proof/transcript

* feat: Check R / evals correlation on verification

* feat: Verify correctness of P_i polynomials computing

* chore: Add TODOs about avoiding operations with constant polynomial

* chore: Fix clippy issues

* chore: Review iteration fixes

* feat: Include Shplonk PCS into the benchmark

benches/pcs.rs

@@ -1,7 +1,7 @@
 use arecibo::provider::{
   hyperkzg::EvaluationEngine as MLEvaluationEngine,
-  ipa_pc::EvaluationEngine as IPAEvaluationEngine, non_hiding_zeromorph::ZMPCS, Bn256Engine,
-  Bn256EngineKZG, Bn256EngineZM,
+  ipa_pc::EvaluationEngine as IPAEvaluationEngine, non_hiding_zeromorph::ZMPCS,
+  shplonk::EvaluationEngine as Shplonk, Bn256Engine, Bn256EngineKZG, Bn256EngineZM,
 };
 use arecibo::spartan::polys::multilinear::MultilinearPolynomial;
 use arecibo::traits::{
@@ -41,7 +41,7 @@ criterion_main!(pcs);
 
 const NUM_VARS_TEST_VECTOR: [usize; 6] = [10, 12, 14, 16, 18, 20];
 
-struct BenchAssests<E: Engine, EE: EvaluationEngineTrait<E>> {
+struct BenchAssets<E: Engine, EE: EvaluationEngineTrait<E>> {
   poly: MultilinearPolynomial<<E as Engine>::Scalar>,
   point: Vec<<E as Engine>::Scalar>,
   eval: <E as Engine>::Scalar,
@@ -73,7 +73,7 @@ pub fn random_poly_with_eval<E: Engine, R: RngCore + CryptoRng>(
   (poly, point, eval)
 }
 
-impl<E: Engine, EE: EvaluationEngineTrait<E>> BenchAssests<E, EE> {
+impl<E: Engine, EE: EvaluationEngineTrait<E>> BenchAssets<E, EE> {
   pub(crate) fn from_num_vars<R: CryptoRng + RngCore>(num_vars: usize, rng: &mut R) -> Self {
     let (poly, point, eval) = random_poly_with_eval::<E, R>(num_vars, rng);
 
@@ -117,7 +117,7 @@ macro_rules! benchmark_all_engines {
             let mut rng = rand::rngs::StdRng::seed_from_u64(*num_vars as u64);
 
             $(
-                let $assets: BenchAssests<_, $eval_engine> = BenchAssests::from_num_vars::<StdRng>(*num_vars, &mut rng);
+                let $assets: BenchAssets<_, $eval_engine> = BenchAssets::from_num_vars::<StdRng>(*num_vars, &mut rng);
             )*
 
             // Proving group
@@ -159,13 +159,14 @@ fn bench_pcs(c: &mut Criterion) {
     bench_pcs_verifying_internal,
     (ipa_assets, IPAEvaluationEngine<Bn256Engine>),
     (hyperkzg_assets, MLEvaluationEngine<Bn256, Bn256EngineKZG>),
-    (zm_assets, ZMPCS<Bn256, Bn256EngineZM>)
+    (zm_assets, ZMPCS<Bn256, Bn256EngineZM>),
+    (shplonk_assets, Shplonk<Bn256, Bn256EngineKZG>)
   );
 }
 
 fn bench_pcs_proving_internal<E: Engine, EE: EvaluationEngineTrait<E>>(
   b: &mut Bencher<'_>,
-  bench_assets: &BenchAssests<E, EE>,
+  bench_assets: &BenchAssets<E, EE>,
 ) {
   // Bench generate proof.
   b.iter(|| {
@@ -184,7 +185,7 @@ fn bench_pcs_proving_internal<E: Engine, EE: EvaluationEngineTrait<E>>(
 
 fn bench_pcs_verifying_internal<E: Engine, EE: EvaluationEngineTrait<E>>(
   b: &mut Bencher<'_>,
-  bench_assets: &BenchAssests<E, EE>,
+  bench_assets: &BenchAssets<E, EE>,
 ) {
   // Bench verify proof.
   b.iter(|| {

src/provider/hyperkzg.rs

@@ -61,18 +61,20 @@ where
   E::Fr: TranscriptReprTrait<E::G1>,
   E::G1Affine: TranscriptReprTrait<E::G1>, // TODO: this bound on DlogGroup is really unusable!
 {
-  fn compute_challenge(
+  /// TODO: write doc
+  pub fn compute_challenge(
     com: &[E::G1Affine],
     transcript: &mut impl TranscriptEngineTrait<NE>,
   ) -> E::Fr {
-    transcript.absorb(b"c", &com.to_vec().as_slice());
+    transcript.absorb(b"c", &com);
     transcript.squeeze(b"c").unwrap()
   }
 
+  /// TODO: write doc
   // Compute challenge q = Hash(vk, C0, ..., C_{k-1}, u0, ...., u_{t-1},
   // (f_i(u_j))_{i=0..k-1,j=0..t-1})
   // It is assumed that both 'C' and 'u' are already absorbed by the transcript
-  fn get_batch_challenge(
+  pub fn get_batch_challenge(
     v: &[Vec<E::Fr>],
     transcript: &mut impl TranscriptEngineTrait<NE>,
   ) -> E::Fr {
@@ -88,14 +90,15 @@ where
     transcript.squeeze(b"r").unwrap()
   }
 
-  fn batch_challenge_powers(q: E::Fr, k: usize) -> Vec<E::Fr> {
-    // Compute powers of q : (1, q, q^2, ..., q^(k-1))
+  /// Compute powers of q : (1, q, q^2, ..., q^(k-1))
+  pub fn batch_challenge_powers(q: E::Fr, k: usize) -> Vec<E::Fr> {
     std::iter::successors(Some(E::Fr::ONE), |&x| Some(x * q))
       .take(k)
       .collect()
   }
 
-  fn verifier_second_challenge(
+  /// TODO: write doc
+  pub fn verifier_second_challenge(
     W: &[E::G1Affine],
     transcript: &mut impl TranscriptEngineTrait<NE>,
   ) -> E::Fr {

src/provider/mod.rs

@@ -4,6 +4,7 @@
 pub mod hyperkzg;
 pub mod ipa_pc;
 pub mod non_hiding_zeromorph;
+pub mod shplonk;
 
 // crate-public modules, made crate-public mostly for tests
 pub(crate) mod bn256_grumpkin;

src/provider/non_hiding_kzg.rs

@@ -226,7 +226,7 @@ pub struct UVKZGProof<E: Engine> {
 }
 
 /// Polynomial and its associated types
-pub type UVKZGPoly<F> = crate::spartan::polys::univariate::UniPoly<F>;
+type UVKZGPoly<F> = crate::spartan::polys::univariate::UniPoly<F>;
 
 #[derive(Debug, Eq, PartialEq, Default)]
 /// KZG Polynomial Commitment Scheme on univariate polynomial.

src/provider/non_hiding_zeromorph.rs

@@ -7,7 +7,7 @@ use crate::{
   errors::{NovaError, PCSError},
   provider::{
     non_hiding_kzg::{
-      KZGProverKey, KZGVerifierKey, UVKZGCommitment, UVKZGEvaluation, UVKZGPoly, UVKZGProof,
+      KZGProverKey, KZGVerifierKey, UVKZGCommitment, UVKZGEvaluation, UVKZGProof,
       UniversalKZGParam, UVKZGPCS,
     },
     traits::DlogGroup,
@@ -33,6 +33,7 @@ use std::sync::Arc;
 use std::{borrow::Borrow, iter, marker::PhantomData};
 
 use crate::provider::kzg_commitment::KZGCommitmentEngine;
+use crate::spartan::polys::univariate::UniPoly;
 
 /// `ZMProverKey` is used to generate a proof
 #[derive(Clone, Debug, Eq, PartialEq)]
@@ -156,7 +157,7 @@ where
     if pp.commit_pp.powers_of_g().len() < poly.Z.len() {
       return Err(PCSError::LengthError.into());
     }
-    UVKZGPCS::commit(&pp.commit_pp, UVKZGPoly::ref_cast(&poly.Z)).map(|c| c.into())
+    UVKZGPCS::commit(&pp.commit_pp, UniPoly::ref_cast(&poly.Z)).map(|c| c.into())
   }
 
   /// On input a polynomial `poly` and a point `point`, outputs a proof for the
@@ -184,10 +185,7 @@ where
     debug_assert_eq!(remainder, eval.0);
 
     // Compute the multilinear quotients q_k = q_k(X_0, ..., X_{k-1})
-    let quotients_polys = quotients
-      .into_iter()
-      .map(UVKZGPoly::new)
-      .collect::<Vec<_>>();
+    let quotients_polys = quotients.into_iter().map(UniPoly::new).collect::<Vec<_>>();
 
     // Compute and absorb commitments C_{q_k} = [q_k], k = 0,...,d-1
     let q_comms = quotients_polys
@@ -215,7 +213,7 @@ where
     let (eval_scalar, (degree_check_q_scalars, zmpoly_q_scalars)) =
       eval_and_quotient_scalars(y, x, z, point);
     // f = z * poly.Z + q_hat + (-z * Φ_n(x) * e) + ∑_k (q_scalars_k * q_k)
-    let mut f = UVKZGPoly::new(poly.Z.clone());
+    let mut f = UniPoly::new(poly.Z.clone());
     f *= &z;
     f += &q_hat;
     f[0] += eval_scalar * eval.0;
@@ -360,8 +358,8 @@ fn quotients<F: PrimeField>(poly: &MultilinearPolynomial<F>, point: &[F]) -> (Ve
 // Compute the batched, lifted-degree quotient `\hat{q}`
 fn batched_lifted_degree_quotient<F: PrimeField>(
   y: F,
-  quotients_polys: &[UVKZGPoly<F>],
-) -> (UVKZGPoly<F>, usize) {
+  quotients_polys: &[UniPoly<F>],
+) -> (UniPoly<F>, usize) {
   let num_vars = quotients_polys.len();
 
   let powers_of_y = (0..num_vars)
@@ -390,7 +388,7 @@ fn batched_lifted_degree_quotient<F: PrimeField>(
       },
     );
 
-  (UVKZGPoly::new(q_hat), 1 << (num_vars - 1))
+  (UniPoly::new(q_hat), 1 << (num_vars - 1))
 }
 
 /// Computes some key terms necessary for computing the partially evaluated univariate ZM polynomial
@@ -523,12 +521,11 @@ mod test {
 
   use super::quotients;
 
+  use crate::spartan::polys::univariate::UniPoly;
   use crate::{
     errors::PCSError,
     provider::{
-      non_hiding_kzg::{
-        trim, KZGProverKey, UVKZGCommitment, UVKZGPoly, UniversalKZGParam, UVKZGPCS,
-      },
+      non_hiding_kzg::{trim, KZGProverKey, UVKZGCommitment, UniversalKZGParam, UVKZGPCS},
       non_hiding_zeromorph::{batched_lifted_degree_quotient, eval_and_quotient_scalars, ZMPCS},
       traits::DlogGroup,
       util::test_utils::prove_verify_from_num_vars,
@@ -598,9 +595,9 @@ mod test {
     let n = 1 << num_vars; // Assuming N = 2^num_vars
 
     // Define mock q_k with deg(q_k) = 2^k - 1
-    let q_0 = UVKZGPoly::new(vec![Scalar::one()]);
-    let q_1 = UVKZGPoly::new(vec![Scalar::from(2), Scalar::from(3)]);
-    let q_2 = UVKZGPoly::new(vec![
+    let q_0 = UniPoly::new(vec![Scalar::one()]);
+    let q_1 = UniPoly::new(vec![Scalar::from(2), Scalar::from(3)]);
+    let q_2 = UniPoly::new(vec![
       Scalar::from(4),
       Scalar::from(5),
       Scalar::from(6),
@@ -644,10 +641,7 @@ mod test {
       });
 
     // Compare the computed and expected batched quotients
-    assert_eq!(
-      batched_quotient.0,
-      UVKZGPoly::new(batched_quotient_expected)
-    );
+    assert_eq!(batched_quotient.0, UniPoly::new(batched_quotient_expected));
   }
 
   #[test]
@@ -657,9 +651,9 @@ mod test {
     let num_vars = 3;
 
     // Define some mock q_k with deg(q_k) = 2^k - 1
-    let _q_0 = UVKZGPoly::new(vec![Scalar::one()]);
-    let _q_1 = UVKZGPoly::new(vec![Scalar::from(2), Scalar::from(3)]);
-    let _q_2 = UVKZGPoly::new(vec![
+    let _q_0 = UniPoly::new(vec![Scalar::one()]);
+    let _q_1 = UniPoly::new(vec![Scalar::from(2), Scalar::from(3)]);
+    let _q_2 = UniPoly::new(vec![
       Scalar::from(4),
       Scalar::from(5),
       Scalar::from(6),
@@ -713,9 +707,9 @@ mod test {
     let mut rng = ChaCha20Rng::from_seed([0u8; 32]);
 
     // Define some mock q_k with deg(q_k) = 2^k - 1
-    let _q_0 = UVKZGPoly::new(vec![Scalar::one()]);
-    let _q_1 = UVKZGPoly::new(vec![Scalar::from(2), Scalar::from(3)]);
-    let _q_2 = UVKZGPoly::new(vec![
+    let _q_0 = UniPoly::new(vec![Scalar::one()]);
+    let _q_1 = UniPoly::new(vec![Scalar::from(2), Scalar::from(3)]);
+    let _q_2 = UniPoly::new(vec![
       Scalar::from(4),
       Scalar::from(5),
       Scalar::from(6),
@@ -755,7 +749,7 @@ mod test {
 
   fn commit_filtered<E>(
     prover_param: impl Borrow<KZGProverKey<E>>,
-    poly: &UVKZGPoly<E::Fr>,
+    poly: &UniPoly<E::Fr>,
   ) -> Result<UVKZGCommitment<E>, NovaError>
   where
     E: MultiMillerLoop,
@@ -802,10 +796,7 @@ mod test {
     }
 
     let (quotients, _remainder) = quotients(&multilinear_poly, random_points.as_slice());
-    let quotients_polys = quotients
-      .into_iter()
-      .map(UVKZGPoly::new)
-      .collect::<Vec<_>>();
+    let quotients_polys = quotients.into_iter().map(UniPoly::new).collect::<Vec<_>>();
 
     let (q_hat, offset) = batched_lifted_degree_quotient(E::Fr::random(&mut rng), &quotients_polys);