diff --git a/halo2_proofs/src/arithmetic.rs b/halo2_proofs/src/arithmetic.rs
index 700b37ad58..6f78dcd5c1 100644
--- a/halo2_proofs/src/arithmetic.rs
+++ b/halo2_proofs/src/arithmetic.rs
@@ -402,26 +402,8 @@ pub fn lagrange_interpolate<F: FieldExt>(points: &[F], evals: &[F]) -> Vec<F> {
     }
 }
 
-/// Given roots [a_0, a_1, ... a_n] returns vanishing polynomials
-/// (x - a_0) * (x - a_1) * ... * (x - a_n)
-pub fn vanishing_polynomial<F: FieldExt>(roots: &[F]) -> Vec<F> {
-    fn mul_with<F: FieldExt>(coeffs: Vec<F>, root: &F) -> Vec<F> {
-        let mut ret = vec![F::zero(); coeffs.len() + 1];
-
-        for (i, coeff) in coeffs.iter().enumerate() {
-            ret[i] -= *coeff * root;
-            ret[i + 1] += coeff;
-        }
-
-        ret
-    }
-
-    let mut coeffs = vec![F::one()];
-    for root in roots {
-        coeffs = mul_with(coeffs, root);
-    }
-
-    coeffs
+pub(crate) fn evaluate_vanishing_polynomial<F: FieldExt>(roots: &[F], z: F) -> F {
+    roots.iter().fold(F::one(), |acc, point| (z - point) * acc)
 }
 
 #[cfg(test)]
diff --git a/halo2_proofs/src/poly/multiopen/shplonk/prover.rs b/halo2_proofs/src/poly/multiopen/shplonk/prover.rs
index ebdddd87d7..2398df09ce 100644
--- a/halo2_proofs/src/poly/multiopen/shplonk/prover.rs
+++ b/halo2_proofs/src/poly/multiopen/shplonk/prover.rs
@@ -2,8 +2,8 @@ use super::{
     construct_intermediate_sets, ChallengeU, ChallengeV, ChallengeY, Commitment, Query, RotationSet,
 };
 use crate::arithmetic::{
-    eval_polynomial, kate_division, lagrange_interpolate, vanishing_polynomial, CurveAffine,
-    FieldExt,
+    eval_polynomial, evaluate_vanishing_polynomial, kate_division, lagrange_interpolate,
+    CurveAffine, FieldExt,
 };
 use crate::poly::multiopen::ProverQuery;
 use crate::poly::{commitment::Params, Coeff, Error, Polynomial};
@@ -156,14 +156,13 @@ where
     transcript.write_point(h)?;
     let u: ChallengeU<_> = transcript.squeeze_challenge_scalar();
 
-    let zt_x = vanishing_polynomial(&super_point_set[..]);
-    let zt_eval = eval_polynomial(&zt_x[..], *u);
+    let zt_eval = evaluate_vanishing_polynomial(&super_point_set[..], *u);
 
     let linearisation_contribution =
         |rotation_set: RotationSetExtension<C>| -> Polynomial<C::Scalar, Coeff> {
             // calculate difference vanishing polynomial evaluation
-            let z_diff = vanishing_polynomial(&rotation_set.diffs[..]);
-            let z_i = eval_polynomial(&z_diff[..], *u);
+
+            let z_i = evaluate_vanishing_polynomial(&rotation_set.diffs[..], *u);
 
             // inner linearisation contibutions are
             // [P_i_0(X) - r_i_0, P_i_1(X) - r_i_1, ... ] where
diff --git a/halo2_proofs/src/poly/multiopen/shplonk/verifier.rs b/halo2_proofs/src/poly/multiopen/shplonk/verifier.rs
index 7bbcba96f6..5c3ef5c56a 100644
--- a/halo2_proofs/src/poly/multiopen/shplonk/verifier.rs
+++ b/halo2_proofs/src/poly/multiopen/shplonk/verifier.rs
@@ -1,7 +1,7 @@
 use super::{construct_intermediate_sets, ChallengeU, ChallengeV, ChallengeY};
 use crate::arithmetic::{
-    eval_polynomial, lagrange_interpolate, vanishing_polynomial, CurveAffine, Engine, FieldExt,
-    MillerLoopResult, MultiMillerLoop,
+    eval_polynomial, evaluate_vanishing_polynomial, lagrange_interpolate, CurveAffine, Engine,
+    FieldExt, MillerLoopResult, MultiMillerLoop,
 };
 use crate::poly::{
     commitment::{Params, ParamsVerifier},
@@ -47,14 +47,12 @@ where
     let u: ChallengeU<_> = transcript.squeeze_challenge_scalar();
     let h2 = transcript.read_point().map_err(|_| Error::SamplingError)?;
 
-    let zt_x = vanishing_polynomial(&super_point_set[..]);
-    let zt_eval = eval_polynomial(&zt_x[..], *u);
+    let zt_eval = evaluate_vanishing_polynomial(&super_point_set[..], *u);
 
     let mut outer_msm: PreMSM<C> = PreMSM::new();
 
     for rotation_set in rotation_sets.iter() {
-        let z_diff = vanishing_polynomial(&rotation_set.diffs[..]);
-        let z_i = eval_polynomial(&z_diff[..], *u);
+        let z_i = evaluate_vanishing_polynomial(&rotation_set.diffs[..], *u);
 
         let mut inner_msm: ProjectiveMSM<C> = ProjectiveMSM::new();
         for commitment_data in rotation_set.commitments.iter() {