diff --git a/src/aggregation/multiple.rs b/src/aggregation/multiple.rs
index b98200d..82fe136 100644
--- a/src/aggregation/multiple.rs
+++ b/src/aggregation/multiple.rs
@@ -66,7 +66,7 @@ pub fn aggregate_polys<F: PrimeField, CS: PCS<F>, T: Transcript<F, CS>>(
     let q = poly::sum_with_powers(gamma, &qs);
     let t_commit =
         start_timer!(|| ark_std::format!("commitment to a degree-{} polynomial", q.degree()));
-    let qc = CS::commit(ck, &q);
+    let qc = CS::commit(ck, &q).unwrap();
     // "W" in the paper
     end_timer!(t_commit);
     transcript.commit_to_q(&qc);
@@ -236,13 +236,13 @@ mod tests {
         end_timer!(t_aggregate_polys);
 
         let claims = group_by_commitment(&opening.fcs, &opening.xss, &opening.yss);
-        let onec = CS::commit(&vk.clone().into(), &poly::constant(F::one()));
+        let onec = CS::commit(&vk.clone().into(), &poly::constant(F::one())).unwrap();
 
         let t_aggregate_claims = start_timer!(|| format!("Aggregate {} claims", claims.len()));
         let agg_claim = aggregate_claims::<_, CS, _>(claims, &agg_proof, &onec, transcript);
         end_timer!(t_aggregate_claims);
 
-        assert_eq!(CS::commit(&ck, &agg_poly), agg_claim.c);
+        assert_eq!(CS::commit(&ck, &agg_poly).unwrap(), agg_claim.c);
         assert_eq!(zeta, agg_claim.xs[0]);
         assert_eq!(agg_poly.evaluate(&zeta), agg_claim.ys[0]);
         assert!(agg_claim.ys[0].is_zero());
diff --git a/src/aggregation/single.rs b/src/aggregation/single.rs
index 6ecf2cd..e88ec10 100644
--- a/src/aggregation/single.rs
+++ b/src/aggregation/single.rs
@@ -23,7 +23,7 @@ impl<F: PrimeField, C: Commitment<F>> Claim<F, C> {
         CS: PCS<F, C = C>,
     {
         Claim {
-            c: CS::commit(ck, poly),
+            c: CS::commit(ck, poly).unwrap(),
             x: at,
             y: poly.evaluate(&at),
         }
@@ -126,7 +126,7 @@ mod tests {
             .collect::<Vec<_>>();
         let agg_claim = aggregate_claims::<F, CS>(&claims_at_same_x, &rs);
 
-        assert_eq!(CS::commit(&ck, &agg_poly), agg_claim.c);
+        assert_eq!(CS::commit(&ck, &agg_poly).unwrap(), agg_claim.c);
         assert_eq!(same_x, agg_claim.x);
         assert_eq!(agg_poly.evaluate(&same_x), agg_claim.y);
     }
diff --git a/src/lib.rs b/src/lib.rs
index 2f8e43d..db7292e 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -208,7 +208,7 @@ mod tests {
         let (fs, roots, vss) = generate_test_data(rng, d, t, m);
 
         let g = Fflonk::combine(t, &fs);
-        let gc = CS::commit(&params.ck(), &g);
+        let gc = CS::commit(&params.ck(), &g).unwrap();
 
         let proof = FflonkyKzg::<F, CS>::open_single(&params.ck(), &fs, t, &roots, transcript);
         assert!(FflonkyKzg::<F, CS>::verify_single(
@@ -245,7 +245,7 @@ mod tests {
         let gcs: Vec<_> = fss
             .iter()
             .zip(ts)
-            .map(|(fs, t)| CS::commit(&params.ck(), &Fflonk::combine(t, &fs)))
+            .map(|(fs, t)| CS::commit(&params.ck(), &Fflonk::combine(t, &fs)).unwrap())
             .collect();
 
         let proof = FflonkyKzg::<F, CS>::open(&params.ck(), &fss, &ts, &rootss, transcript);
diff --git a/src/pcs/id/mod.rs b/src/pcs/id/mod.rs
index a08a2b2..b2ab83b 100644
--- a/src/pcs/id/mod.rs
+++ b/src/pcs/id/mod.rs
@@ -110,15 +110,15 @@ impl<F: PrimeField> PCS<F> for IdentityCommitment {
         ()
     }
 
-    fn commit(_ck: &(), p: &Poly<F>) -> Self::C {
-        WrappedPolynomial(p.clone())
+    fn commit(_ck: &(), p: &Poly<F>) -> Result<Self::C, ()> {
+        Ok(WrappedPolynomial(p.clone()))
     }
 
-    fn open(_ck: &(), _p: &Poly<F>, _x: F) -> Self::Proof {
-        ()
+    fn open(_ck: &(), _p: &Poly<F>, _x: F) -> Result<Self::Proof, ()> {
+        Ok(())
     }
 
-    fn verify(_vk: &(), c: Self::C, x: F, z: F, _proof: Self::Proof) -> bool {
-        c.evaluate(&x) == z
+    fn verify(_vk: &(), c: Self::C, x: F, z: F, _proof: Self::Proof) -> Result<(), ()> {
+        (c.evaluate(&x) == z).then(|| ()).ok_or(())
     }
 }
diff --git a/src/pcs/kzg/mod.rs b/src/pcs/kzg/mod.rs
index b286fc5..cbb5d7c 100644
--- a/src/pcs/kzg/mod.rs
+++ b/src/pcs/kzg/mod.rs
@@ -65,7 +65,6 @@ impl<E: Pairing> KZG<E> {
         rs: &[E::ScalarField],
         vk: &KzgVerifierKey<E>,
     ) -> AccumulatedOpening<E> {
-        assert_eq!(openings.len(), rs.len());
         let openings = Self::parse(openings);
         let ((accs, proofs), ys): ((Vec<E::G1>, Vec<E::G1Affine>), Vec<E::ScalarField>) =
             openings.into_iter().unzip();
@@ -117,8 +116,7 @@ impl<E: Pairing> KZG<E> {
     fn _commit(coeffs: &[E::ScalarField], bases: &[E::G1Affine]) -> KzgCommitment<E> {
         // `msm` allows to call into implementation of `VariableBaseMSM` for `Projective.
         // This allows to call into custom implementations of `msm` (`msm_unchecked` not).
-        let len = usize::min(coeffs.len(), bases.len());
-        let proj = <E::G1 as VariableBaseMSM>::msm(&bases[..len], &coeffs[..len]).unwrap();
+        let proj = <E::G1 as VariableBaseMSM>::msm(&bases[..coeffs.len()], &coeffs).unwrap();
         KzgCommitment(proj.into_affine())
     }
 }
@@ -135,35 +133,28 @@ impl<E: Pairing> PCS<E::ScalarField> for KZG<E> {
         URS::<E>::generate(max_degree + 1, 2, rng)
     }
 
-    fn commit(ck: &Self::CK, p: &Poly<E::ScalarField>) -> Self::C {
+    fn commit(ck: &Self::CK, p: &Poly<E::ScalarField>) -> Result<Self::C, ()> {
         let ck = &ck.monomial;
-        assert!(
-            p.degree() <= ck.max_degree(),
-            "Can't commit to degree {} polynomial using {} bases",
-            p.degree(),
-            ck.max_evals()
-        );
-        Self::_commit(&p.coeffs, &ck.powers_in_g1)
+        if p.degree() > ck.max_degree() {
+            return Err(());
+        }
+        Ok(Self::_commit(&p.coeffs, &ck.powers_in_g1))
     }
 
-    fn commit_evals(ck: &Self::CK, evals: &Evaluations<E::ScalarField>) -> Self::C {
+    fn commit_evals(ck: &Self::CK, evals: &Evaluations<E::ScalarField>) -> Result<Self::C, ()> {
         let ck = ck
             .lagrangian
             .as_ref()
             .expect("lagrangian key hadn't been generated");
-        assert_eq!(evals.domain(), ck.domain);
-        assert!(
-            evals.evals.len() <= ck.max_evals(),
-            "Can't commit to {} values using {} bases",
-            evals.evals.len(),
-            ck.max_evals()
-        );
-        Self::_commit(&evals.evals, &ck.lis_in_g)
+        if evals.evals.len() > ck.max_evals() || evals.domain() != ck.domain {
+            return Err(());
+        }
+        Ok(Self::_commit(&evals.evals, &ck.lis_in_g))
     }
 
-    fn open(ck: &Self::CK, p: &Poly<E::ScalarField>, x: E::ScalarField) -> Self::Proof {
+    fn open(ck: &Self::CK, p: &Poly<E::ScalarField>, x: E::ScalarField) -> Result<Self::Proof, ()> {
         let q = Self::compute_quotient(p, x);
-        Self::commit(ck, &q).0
+        Self::commit(ck, &q).map(|c| c.0)
     }
 
     fn verify(
@@ -172,14 +163,14 @@ impl<E: Pairing> PCS<E::ScalarField> for KZG<E> {
         x: E::ScalarField,
         y: E::ScalarField,
         proof: Self::Proof,
-    ) -> bool {
+    ) -> Result<(), ()> {
         let opening = KzgOpening {
             c: c.0,
             x,
             y,
             proof,
         };
-        Self::verify_single(opening, vk)
+        Self::verify_single(opening, vk).then(|| ()).ok_or(())
     }
 
     fn batch_verify<R: Rng>(
@@ -189,9 +180,10 @@ impl<E: Pairing> PCS<E::ScalarField> for KZG<E> {
         y: Vec<E::ScalarField>,
         proof: Vec<Self::Proof>,
         rng: &mut R,
-    ) -> bool {
-        assert_eq!(c.len(), x.len());
-        assert_eq!(c.len(), y.len());
+    ) -> Result<(), ()> {
+        if c.len() != x.len() || c.len() != y.len() {
+            return Err(());
+        }
         let openings = c
             .into_iter()
             .zip(x.into_iter())
@@ -204,7 +196,7 @@ impl<E: Pairing> PCS<E::ScalarField> for KZG<E> {
                 proof,
             })
             .collect();
-        Self::verify_batch(openings, vk, rng)
+        Self::verify_batch(openings, vk, rng).then(|| ()).ok_or(())
     }
 }
 
@@ -247,15 +239,15 @@ mod tests {
             "Committing to a dense degree-{} polynomial",
             ck.max_degree()
         ));
-        let c = KZG::<E>::commit(&ck, &p);
+        let c = KZG::<E>::commit(&ck, &p).unwrap();
         end_timer!(t_commit);
 
         let t_prove = start_timer!(|| "Generating an opening proof for a single point");
-        let proof = KZG::<E>::open(&ck, &p, x);
+        let proof = KZG::<E>::open(&ck, &p, x).unwrap();
         end_timer!(t_prove);
 
         let t_verify = start_timer!(|| "Verification of a single-point opening");
-        assert!(KZG::<E>::verify(&vk, c, x, z, proof));
+        assert!(KZG::<E>::verify(&vk, c, x, z, proof).is_ok());
         end_timer!(t_verify);
     }
 
@@ -273,8 +265,8 @@ mod tests {
                 let f = Poly::<E::ScalarField>::rand(d, rng);
                 let x = xs[i];
                 let y = f.evaluate(&x);
-                let c = KZG::<E>::commit(ck, &f).0;
-                let proof = KZG::<E>::open(ck, &f, x);
+                let c = KZG::<E>::commit(ck, &f).unwrap().0;
+                let proof = KZG::<E>::open(ck, &f, x).unwrap();
                 KzgOpening { c, x, y, proof }
             })
             .collect()
diff --git a/src/pcs/mod.rs b/src/pcs/mod.rs
index 743144d..7a8f576 100644
--- a/src/pcs/mod.rs
+++ b/src/pcs/mod.rs
@@ -82,21 +82,23 @@ pub trait PCS<F: PrimeField> {
     // vk needs to be convertible to a ck that is only required to commit to the p=1 constant polynomial,
     // see https://eprint.iacr.org/archive/2020/1536/1629188090.pdf, section 4.2
     type VK: VerifierKey + Into<Self::CK>;
+
     type Params: PcsParams<CK = Self::CK, VK = Self::VK>;
 
     fn setup<R: Rng>(max_degree: usize, rng: &mut R) -> Self::Params;
 
-    fn commit(ck: &Self::CK, p: &Poly<F>) -> Self::C;
+    fn commit(ck: &Self::CK, p: &Poly<F>) -> Result<Self::C, ()>;
 
-    fn commit_evals(ck: &Self::CK, evals: &Evaluations<F>) -> Self::C {
+    fn commit_evals(ck: &Self::CK, evals: &Evaluations<F>) -> Result<Self::C, ()> {
         let poly = evals.interpolate_by_ref();
         Self::commit(ck, &poly)
     }
 
-    fn open(ck: &Self::CK, p: &Poly<F>, x: F) -> Self::Proof; //TODO: eval?
+    fn open(ck: &Self::CK, p: &Poly<F>, x: F) -> Result<Self::Proof, ()>;
 
-    fn verify(vk: &Self::VK, c: Self::C, x: F, z: F, proof: Self::Proof) -> bool;
+    fn verify(vk: &Self::VK, c: Self::C, x: F, z: F, proof: Self::Proof) -> Result<(), ()>;
 
+    // TODO: is the default implementation useful?
     fn batch_verify<R: Rng>(
         vk: &Self::VK,
         c: Vec<Self::C>,
@@ -104,13 +106,15 @@ pub trait PCS<F: PrimeField> {
         y: Vec<F>,
         proof: Vec<Self::Proof>,
         _rng: &mut R,
-    ) -> bool {
+    ) -> Result<(), ()> {
         assert_eq!(c.len(), x.len());
         assert_eq!(c.len(), y.len());
         c.into_iter()
             .zip(x.into_iter())
             .zip(y.into_iter())
             .zip(proof.into_iter())
-            .all(|(((c, x), y), proof)| Self::verify(vk, c, x, y, proof))
+            .all(|(((c, x), y), proof)| Self::verify(vk, c, x, y, proof).is_ok())
+            .then(|| ())
+            .ok_or(())
     }
 }
diff --git a/src/shplonk.rs b/src/shplonk.rs
index 1078e39..278aaa6 100644
--- a/src/shplonk.rs
+++ b/src/shplonk.rs
@@ -31,7 +31,7 @@ impl<F: PrimeField, CS: PCS<F>> Shplonk<F, CS> {
     ) -> AggregateProof<F, CS> {
         let (agg_poly, zeta, agg_proof) = aggregate_polys::<F, CS, T>(ck, fs, xss, transcript);
         assert!(agg_poly.evaluate(&zeta).is_zero());
-        let opening_proof = CS::open(ck, &agg_poly, zeta);
+        let opening_proof = CS::open(ck, &agg_poly, zeta).unwrap();
         AggregateProof {
             agg_proof,
             opening_proof,
@@ -53,7 +53,8 @@ impl<F: PrimeField, CS: PCS<F>> Shplonk<F, CS> {
         let onec = CS::commit(
             &vk.clone().into(),
             &Poly::from_coefficients_slice(&[F::one()]),
-        );
+        )
+        .unwrap();
         let claims = group_by_commitment(fcs, xss, yss);
         let agg_claim = aggregate_claims::<F, CS, T>(claims, &agg_proof, &onec, transcript);
         CS::verify(
@@ -63,6 +64,7 @@ impl<F: PrimeField, CS: PCS<F>> Shplonk<F, CS> {
             agg_claim.ys[0],
             opening_proof,
         )
+        .is_ok()
     }
 }
 
@@ -115,7 +117,7 @@ pub(crate) mod tests {
         // polynomials
         let fs: Vec<_> = (0..t).map(|_| Poly::<F>::rand(d, rng)).collect();
         // commitments
-        let fcs: Vec<_> = fs.iter().map(|fi| CS::commit(&ck, fi)).collect();
+        let fcs: Vec<_> = fs.iter().map(|fi| CS::commit(&ck, fi).unwrap()).collect();
 
         // evaluations per polynomial
         let yss: Vec<_> = fs
diff --git a/tests/plonk/batchy.rs b/tests/plonk/batchy.rs
index c39aeb8..52eccd3 100644
--- a/tests/plonk/batchy.rs
+++ b/tests/plonk/batchy.rs
@@ -99,7 +99,7 @@ impl<F: PrimeField, CS: PCS<F>> PlonkBatchKzgTest<F, CS> {
     fn commit_polynomial(&self, ck: &CS::CK, poly: &Poly<F>) -> CS::C {
         let t_commitment =
             start_timer!(|| format!("Committing to degree {} polynomials", poly.degree()));
-        let commitment = CS::commit(ck, poly);
+        let commitment = CS::commit(ck, poly).unwrap();
         end_timer!(t_commitment);
         commitment
     }
@@ -182,9 +182,9 @@ impl<F: PrimeField, CS: PCS<F>> DecoyPlonk<F, CS> for PlonkBatchKzgTest<F, CS> {
         let agg_poly_at_zeta =
             poly::sum_with_coeffs(self.challenges.nus.clone(), &polys_to_open_at_zeta);
 
-        let proof_at_zeta = CS::open(ck, &agg_poly_at_zeta, zeta);
+        let proof_at_zeta = CS::open(ck, &agg_poly_at_zeta, zeta).unwrap();
         let proof_at_zeta_omega =
-            CS::open(ck, &self.polys.poly_to_open_at_zeta_omega_5(), zeta_omega);
+            CS::open(ck, &self.polys.poly_to_open_at_zeta_omega_5(), zeta_omega).unwrap();
 
         // TODO: compute
         let t_extra = start_timer!(|| "Extra: commiting to the linearization polynomial");
@@ -262,6 +262,6 @@ impl<F: PrimeField, CS: PCS<F>> DecoyPlonk<F, CS> for PlonkBatchKzgTest<F, CS> {
         );
         end_timer!(t_kzg_batch_opening);
         end_timer!(t_kzg);
-        valid
+        valid.is_ok()
     }
 }
diff --git a/tests/plonk/fflonky.rs b/tests/plonk/fflonky.rs
index f602474..2d23164 100644
--- a/tests/plonk/fflonky.rs
+++ b/tests/plonk/fflonky.rs
@@ -117,7 +117,7 @@ impl<F: PrimeField, CS: PCS<F>> PlonkWithFflonkTest<F, CS> {
             "committing to the combined polynomial: degree = {}",
             poly.degree()
         ));
-        let commitment = CS::commit(ck, &poly);
+        let commitment = CS::commit(ck, &poly).unwrap();
         end_timer!(t_commit_combined);
 
         end_timer!(t_commit);