fix: snark prove and verify check product to be 1

hyperplonk/src/snark.rs

@@ -520,6 +520,13 @@ where
             ));
         }
 
+        // check product check subclaim
+        if prod_evals[3] != perm_check_sub_claim.product_check_sub_claim.final_query.1 {
+            return Err(HyperPlonkErrors::InvalidVerifier(
+                "product of product check is not one".to_string(),
+            ));
+        }
+
         end_timer!(step);
         // =======================================================================
         // 3. Verify the opening against the commitment
@@ -734,17 +741,27 @@ mod tests {
         >>::verify(&bad_vk, &pi.0, &proof,)?);
 
         // bad path 2: wrong witness
-        let mut w1_bad = w1;
+        let mut w1_bad = w1.clone();
         w1_bad.0[0] = E::ScalarField::one();
         assert!(
             <PolyIOP<E::ScalarField> as HyperPlonkSNARK<E, MultilinearKzgPCS<E>>>::prove(
                 &pk,
                 &pi.0,
-                &[w1_bad, w2],
+                &[w1_bad, w2.clone()],
             )
             .is_err()
         );
 
+        // bad path 3: permutation and witness mismatch
+        let permutation = random_permutation(nv, num_witnesses, &mut rng);
+        assert!(
+            <PolyIOP<E::ScalarField> as HyperPlonkSNARK<E, MultilinearKzgPCS<E>>>::prove(
+                &pk,
+                &permutation,
+                &[w1, w2],
+            ).is_err()
+        );
+
         Ok(())
     }
 }

subroutines/src/poly_iop/perm_check/mod.rs

@@ -12,6 +12,7 @@ use crate::{
     poly_iop::{errors::PolyIOPErrors, prelude::ProductCheck, PolyIOP},
 };
 use ark_ec::pairing::Pairing;
+use ark_ff::One;
 use ark_poly::DenseMultilinearExtension;
 use ark_std::{end_timer, start_timer};
 use std::sync::Arc;
@@ -161,6 +162,12 @@ where
             transcript,
         )?;
 
+        if prod_poly.evaluations[(1 << num_vars) - 2] != E::ScalarField::one() {
+            return Err(PolyIOPErrors::InvalidProof(
+                "Product should be one".to_string(),
+            ));
+        }
+
         end_timer!(start);
         Ok((proof, prod_poly, frac_poly))
     }