@@ -12,4 +12,6 @@ random_permutation, random_permutation_mles, random_zero_mle_list, DenseMultilinearExtension,
 };
 pub use univariate_polynomial::{build_l, get_uni_domain};
 pub use util::{bit_decompose, gen_eval_point, get_batched_nv, get_index};
-pub use virtual_polynomial::{build_eq_x_r, build_eq_x_r_vec, VPAuxInfo, VirtualPolynomial};
+pub use virtual_polynomial::{
+    build_eq_x_r, build_eq_x_r_vec, eq_eval, VPAuxInfo, VirtualPolynomial,
+};

@@ -325,6 +325,23 @@ println!()
     }
 }
 
+/// Evaluate eq polynomial.
+pub fn eq_eval<F: PrimeField>(x: &[F], y: &[F]) -> Result<F, ArithErrors> {
+    if x.len() != y.len() {
+        return Err(ArithErrors::InvalidParameters(
+            "x and y have different length".to_string(),
+        ));
+    }
+    let start = start_timer!(|| "eq_eval");
+    let mut res = F::one();
+    for (&xi, &yi) in x.iter().zip(y.iter()) {
+        let xi_yi = xi * yi;
+        res *= xi_yi + xi_yi - xi - yi + F::one();
+    }
+    end_timer!(start);
+    Ok(res)
+}
+
 /// This function build the eq(x, r) polynomial for any given r.
 ///
 /// Evaluate

@@ -24,7 +24,6 @@ rayon = { version = "1.5.2", default-features = false, optional = true }
 
 [dev-dependencies]
 ark-bls12-381 = { version = "0.3.0", default-features = false, features = [ "curve" ] }
-
 # Benchmarks
 [[bench]]
 name = "hyperplonk-benches"

@@ -10,6 +10,7 @@ witness::WitnessColumn,
 };
 
 pub struct MockCircuit<F: PrimeField> {
+    pub public_inputs: Vec<F>,
     pub witnesses: Vec<WitnessColumn<F>>,
     pub index: HyperPlonkIndex<F>,
 }
@@ -85,10 +86,12 @@ for i in 0..num_witnesses {
                 witnesses[i].append(cur_witness[i]);
             }
         }
+        let pub_input_len = ark_std::cmp::min(4, num_constraints);
+        let public_inputs = witnesses[0].0[0..pub_input_len].to_vec();
 
         let params = HyperPlonkParams {
             num_constraints,
-            num_pub_input: num_constraints,
+            num_pub_input: public_inputs.len(),
             gate_func: gate.clone(),
         };
 
@@ -99,7 +102,11 @@ permutation,
             selectors,
         };
 
-        Self { witnesses, index }
+        Self {
+            public_inputs,
+            witnesses,
+            index,
+        }
     }
 
     pub fn is_satisfied(&self) -> bool {
@@ -177,7 +184,6 @@ let circuit = MockCircuit::<Fr>::new(1 << nv, gate);
         assert!(circuit.is_satisfied());
 
         let index = circuit.index;
-
         // generate pk and vks
         let (pk, vk) =
             <PolyIOP<Fr> as HyperPlonkSNARK<Bls12_381, MultilinearKzgPCS<Bls12_381>>>::preprocess(
@@ -187,14 +193,14 @@ // generate a proof and verify
         let proof =
             <PolyIOP<Fr> as HyperPlonkSNARK<Bls12_381, MultilinearKzgPCS<Bls12_381>>>::prove(
                 &pk,
-                &circuit.witnesses[0].0,
+                &circuit.public_inputs,
                 &circuit.witnesses,
             )?;
 
         let verify =
             <PolyIOP<Fr> as HyperPlonkSNARK<Bls12_381, MultilinearKzgPCS<Bls12_381>>>::verify(
                 &vk,
-                &circuit.witnesses[0].0,
+                &circuit.public_inputs,
                 &proof,
             )?;
         assert!(verify);

@@ -324,8 +324,11 @@
         // - 4.4. public input consistency checks
         //   - pi_poly(r_pi) where r_pi is sampled from transcript
         let r_pi = transcript.get_and_append_challenge_vectors(b"r_pi", ell)?;
-        let tmp_point = [vec![E::Fr::zero(); num_vars - ell], r_pi].concat();
-        pcs_acc.insert_poly_and_points(&witness_polys[0], &witness_commits[0], &tmp_point);
+        // padded with zeros
+        let r_pi_padded = [r_pi, vec![E::Fr::zero(); num_vars - ell]].concat();
+        // Evaluate witness_poly[0] at r_pi||0s which is equal to public_input evaluated
+        // at r_pi. Assumes that public_input is a power of 2
+        pcs_acc.insert_poly_and_points(&witness_polys[0], &witness_commits[0], &r_pi_padded);
         end_timer!(step);
 
         // =======================================================================
@@ -515,7 +518,7 @@ end_timer!(step);
         // =======================================================================
         // 3. Verify the opening against the commitment
         // =======================================================================
-        let step = start_timer!(|| "verify commitments");
+        let step = start_timer!(|| "assemble commitments");
 
         // generate evaluation points and commitments
         let mut comms = vec![];
@@ -535,7 +538,6 @@ points.push(perm_check_point.clone());
         points.push(perm_check_point_0.clone());
         points.push(perm_check_point_1.clone());
         points.push(prod_final_query_point);
-
         // frac(x)'s points
         comms.push(proof.perm_check_proof.frac_comm);
         comms.push(proof.perm_check_proof.frac_comm);
@@ -575,21 +577,24 @@
         // - 4.4. public input consistency checks
         //   - pi_poly(r_pi) where r_pi is sampled from transcript
         let r_pi = transcript.get_and_append_challenge_vectors(b"r_pi", ell)?;
-        let tmp_point = [vec![E::Fr::zero(); num_vars - ell], r_pi].concat();
+
         // check public evaluation
         let pi_poly = DenseMultilinearExtension::from_evaluations_slice(ell as usize, pub_input);
-        let expect_pi_eval = evaluate_opt(&pi_poly, &tmp_point[..]);
+        let expect_pi_eval = evaluate_opt(&pi_poly, &r_pi[..]);
         if expect_pi_eval != *pi_eval {
             return Err(HyperPlonkErrors::InvalidProver(format!(
                 "Public input eval mismatch: got {}, expect {}",
                 pi_eval, expect_pi_eval,
             )));
         }
+        let r_pi_padded = [r_pi, vec![E::Fr::zero(); num_vars - ell]].concat();
+
         comms.push(proof.witness_commits[0]);
-        points.push(tmp_point);
-
+        points.push(r_pi_padded);
         assert_eq!(comms.len(), proof.batch_openings.f_i_eval_at_point_i.len());
 
+        end_timer!(step);
+        let step = start_timer!(|| "PCS batch verify");
         // check proof
         let res = PCS::batch_verify(
             &vk.pcs_param,

@@ -137,6 +137,13 @@ pub_input.len(),
             params.num_pub_input
         )));
     }
+    if !pub_input.len().is_power_of_two() {
+        return Err(HyperPlonkErrors::InvalidProver(format!(
+            "Public input length is not power of two: got {}",
+            pub_input.len(),
+        )));
+    }
+
     // witnesses length
     for (i, w) in witnesses.iter().enumerate() {
         if w.0.len() != params.num_constraints {

@@ -178,6 +178,8 @@ ///
 /// This implementation is linear in number of inputs in terms of field
 /// operations. It also has a quadratic term in primitive operations which is
 /// negligible compared to field operations.
+/// TODO: The quadratic term can be removed by precomputing the lagrange
+/// coefficients.
 fn interpolate_uni_poly<F: PrimeField>(p_i: &[F], eval_at: F) -> Result<F, PolyIOPErrors> {
     let start = start_timer!(|| "sum check interpolate uni poly opt");
 

@@ -3,9 +3,8 @@
 use std::fmt::Debug;
 
 use crate::poly_iop::{errors::PolyIOPErrors, sum_check::SumCheck, PolyIOP};
-use arithmetic::build_eq_x_r;
+use arithmetic::eq_eval;
 use ark_ff::PrimeField;
-use ark_poly::MultilinearExtension;
 use ark_std::{end_timer, start_timer};
 use transcript::IOPTranscript;
 
@@ -103,11 +102,8 @@ <Self as SumCheck<F>>::verify(F::zero(), proof, &hat_fx_aux_info, transcript)?;
 
         // expected_eval = sumcheck.expect_eval/eq(v, r)
         // where v = sum_check_sub_claim.point
-        let eq_x_r = build_eq_x_r(&r)?;
-        let expected_evaluation = sum_subclaim.expected_evaluation
-            / eq_x_r.evaluate(&sum_subclaim.point).ok_or_else(|| {
-                PolyIOPErrors::InvalidParameters("evaluation dimension does not match".to_string())
-            })?;
+        let eq_x_r_eval = eq_eval(&sum_subclaim.point, &r)?;
+        let expected_evaluation = sum_subclaim.expected_evaluation / eq_x_r_eval;
 
         end_timer!(start);
         Ok(ZeroCheckSubClaim {