@@ -133,6 +133,16 @@ C: C.to_owned(),
     })
   }
 
+  // Checks regularity conditions on the R1CSShape, required in Spartan-class SNARKs
+  // Panics if num_cons, num_vars, or num_io are not powers of two, or if num_io > num_vars
+  #[inline]
+  pub(crate) fn check_regular_shape(&self) {
+    assert_eq!(self.num_cons.next_power_of_two(), self.num_cons);
+    assert_eq!(self.num_vars.next_power_of_two(), self.num_vars);
+    assert_eq!(self.num_io.next_power_of_two(), self.num_io);
+    assert!(self.num_io < self.num_vars);
+  }
+
   pub fn multiply_vec(
     &self,
     z: &[G::Scalar],

@@ -967,10 +967,7 @@ // a list of polynomial evaluation claims that will be batched
     let mut w_u_vec = Vec::new();
 
     // sanity check that R1CSShape has certain size characteristics
-    assert_eq!(pk.S.num_cons.next_power_of_two(), pk.S.num_cons);
-    assert_eq!(pk.S.num_vars.next_power_of_two(), pk.S.num_vars);
-    assert_eq!(pk.S.num_io.next_power_of_two(), pk.S.num_io);
-    assert!(pk.S.num_io < pk.S.num_vars);
+    pk.S.check_regular_shape();
 
     // append the verifier key (which includes commitment to R1CS matrices) and the RelaxedR1CSInstance to the transcript
     transcript.absorb(b"vk", &pk.vk_digest);

@@ -102,10 +102,7 @@ let W = W.pad(&pk.S); // pad the witness
     let mut transcript = G::TE::new(b"RelaxedR1CSSNARK");
 
     // sanity check that R1CSShape has certain size characteristics
-    assert_eq!(pk.S.num_cons.next_power_of_two(), pk.S.num_cons);
-    assert_eq!(pk.S.num_vars.next_power_of_two(), pk.S.num_vars);
-    assert_eq!(pk.S.num_io.next_power_of_two(), pk.S.num_io);
-    assert!(pk.S.num_io < pk.S.num_vars);
+    pk.S.check_regular_shape();
 
     // append the digest of vk (which includes R1CS matrices) and the RelaxedR1CSInstance to the transcript
     transcript.absorb(b"vk", &pk.vk_digest);

@@ -61,6 +61,34 @@
     Ok((e, r))
   }
 
+  #[inline]
+  fn compute_eval_points<F>(
+    poly_A: &MultilinearPolynomial<G::Scalar>,
+    poly_B: &MultilinearPolynomial<G::Scalar>,
+    comb_func: &F,
+  ) -> (G::Scalar, G::Scalar)
+  where
+    F: Fn(&G::Scalar, &G::Scalar) -> G::Scalar + Sync,
+  {
+    let len = poly_A.len() / 2;
+    (0..len)
+      .into_par_iter()
+      .map(|i| {
+        // eval 0: bound_func is A(low)
+        let eval_point_0 = comb_func(&poly_A[i], &poly_B[i]);
+
+        // eval 2: bound_func is -A(low) + 2*A(high)
+        let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
+        let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
+        let eval_point_2 = comb_func(&poly_A_bound_point, &poly_B_bound_point);
+        (eval_point_0, eval_point_2)
+      })
+      .reduce(
+        || (G::Scalar::ZERO, G::Scalar::ZERO),
+        |a, b| (a.0 + b.0, a.1 + b.1),
+      )
+  }
+
   pub fn prove_quad<F>(
     claim: &G::Scalar,
     num_rounds: usize,
@@ -77,25 +105,7 @@ let mut polys: Vec<CompressedUniPoly<G>> = Vec::new();
     let mut claim_per_round = *claim;
     for _ in 0..num_rounds {
       let poly = {
-        let len = poly_A.len() / 2;
-
-        // Make an iterator returning the contributions to the evaluations
-        let (eval_point_0, eval_point_2) = (0..len)
-          .into_par_iter()
-          .map(|i| {
-            // eval 0: bound_func is A(low)
-            let eval_point_0 = comb_func(&poly_A[i], &poly_B[i]);
-
-            // eval 2: bound_func is -A(low) + 2*A(high)
-            let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
-            let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
-            let eval_point_2 = comb_func(&poly_A_bound_point, &poly_B_bound_point);
-            (eval_point_0, eval_point_2)
-          })
-          .reduce(
-            || (G::Scalar::ZERO, G::Scalar::ZERO),
-            |a, b| (a.0 + b.0, a.1 + b.1),
-          );
+        let (eval_point_0, eval_point_2) = Self::compute_eval_points(poly_A, poly_B, &comb_func);
 
         let evals = vec![eval_point_0, claim_per_round - eval_point_0, eval_point_2];
         UniPoly::from_evals(&evals)
@@ -136,7 +146,7 @@ comb_func: F,
     transcript: &mut G::TE,
   ) -> Result<(Self, Vec<G::Scalar>, (Vec<G::Scalar>, Vec<G::Scalar>)), NovaError>
   where
-    F: Fn(&G::Scalar, &G::Scalar) -> G::Scalar,
+    F: Fn(&G::Scalar, &G::Scalar) -> G::Scalar + Sync,
   {
     let mut e = *claim;
     let mut r: Vec<G::Scalar> = Vec::new();
@@ -146,20 +156,7 @@ for _j in 0..num_rounds {
       let mut evals: Vec<(G::Scalar, G::Scalar)> = Vec::new();
 
       for (poly_A, poly_B) in poly_A_vec.iter().zip(poly_B_vec.iter()) {
-        let mut eval_point_0 = G::Scalar::ZERO;
-        let mut eval_point_2 = G::Scalar::ZERO;
-
-        let len = poly_A.len() / 2;
-        for i in 0..len {
-          // eval 0: bound_func is A(low)
-          eval_point_0 += comb_func(&poly_A[i], &poly_B[i]);
-
-          // eval 2: bound_func is -A(low) + 2*A(high)
-          let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
-          let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
-          eval_point_2 += comb_func(&poly_A_bound_point, &poly_B_bound_point);
-        }
-
+        let (eval_point_0, eval_point_2) = Self::compute_eval_points(poly_A, poly_B, &comb_func);
         evals.push((eval_point_0, eval_point_2));
       }
 

@@ -6,9 +6,11 @@ traits::{AbsorbInROTrait, Group, TranscriptReprTrait},
 };
 use core::{
   fmt::Debug,
-  ops::{Add, AddAssign, Mul, MulAssign},
+  ops::{Add, AddAssign},
 };
 use serde::{Deserialize, Serialize};
+
+use super::ScalarMul;
 
 /// Defines basic operations on commitments
 pub trait CommitmentOps<Rhs = Self, Output = Self>:
@@ -30,12 +32,6 @@ impl<T, Rhs, Output> CommitmentOpsOwned<Rhs, Output> for T where
   T: for<'r> CommitmentOps<&'r Rhs, Output>
 {
 }
-
-/// A helper trait for types implementing a multiplication of a commitment with a scalar
-pub trait ScalarMul<Rhs, Output = Self>: Mul<Rhs, Output = Output> + MulAssign<Rhs> {}
-
-impl<T, Rhs, Output> ScalarMul<Rhs, Output> for T where T: Mul<Rhs, Output = Output> + MulAssign<Rhs>
-{}
 
 /// This trait defines the behavior of the commitment
 pub trait CommitmentTrait<G: Group>:

@@ -236,11 +236,9 @@ }
 
 impl<G: Group, T: TranscriptReprTrait<G>> TranscriptReprTrait<G> for &[T] {
   fn to_transcript_bytes(&self) -> Vec<u8> {
-    (0..self.len())
-      .map(|i| self[i].to_transcript_bytes())
-      .collect::<Vec<_>>()
-      .into_iter()
-      .flatten()
+    self
+      .iter()
+      .flat_map(|t| t.to_transcript_bytes())
       .collect::<Vec<u8>>()
   }
 }