diff --git a/halo2_proofs/src/plonk.rs b/halo2_proofs/src/plonk.rs
index aa33c1a6f..10ed84f85 100644
--- a/halo2_proofs/src/plonk.rs
+++ b/halo2_proofs/src/plonk.rs
@@ -410,7 +410,7 @@ impl<C: CurveAffine> VerifyingKey<C> {
 /// Generalizes various behaviors of how proofs are generated by the PLONK prover and consumed by
 /// the PLONK verifier.
 pub trait ProofGenerator<C: CurveAffine, E: EncodedChallenge<C>> {
-    /// How the prover commits tp it's polynomial evualuations
+    /// How the prover commits to its polynomial evaluations
     type EvalComm: EvaluationCommitment<C, E>;
     /// How fixed polynomials should be evaluated by the prover
     type FixedEval: FixedPolyEvaluator<C, E, Self::EvalComm>;
diff --git a/halo2_proofs/src/plonk/permutation/prover.rs b/halo2_proofs/src/plonk/permutation/prover.rs
index f31c6ed19..51d4b3374 100644
--- a/halo2_proofs/src/plonk/permutation/prover.rs
+++ b/halo2_proofs/src/plonk/permutation/prover.rs
@@ -10,7 +10,7 @@ use super::super::{circuit::Any, ChallengeBeta, ChallengeGamma, ChallengeX};
 use super::{Argument, ProvingKey};
 use crate::{
     arithmetic::{eval_polynomial, parallelize, CurveAffine},
-    plonk::{self, Error},
+    plonk::{self, Error, FixedPolyEvaluator, ProofGenerator},
     poly::{
         self,
         commitment::{Blind, Params},
@@ -219,17 +219,22 @@ impl<C: CurveAffine> super::ProvingKey<C> {
         })
     }
 
-    pub(in crate::plonk) fn evaluate<E: EncodedChallenge<C>, T: TranscriptWrite<C, E>>(
+    pub(in crate::plonk) fn evaluate<
+        E: EncodedChallenge<C>,
+        T: TranscriptWrite<C, E>,
+        Gen: ProofGenerator<C, E>,
+    >(
         &self,
         x: ChallengeX<C>,
         transcript: &mut T,
     ) -> Result<(), Error> {
         // Hash permutation evals
-        for eval in self.polys.iter().map(|poly| eval_polynomial(poly, *x)) {
-            transcript.write_scalar(eval)?;
-        }
-
-        Ok(())
+        Gen::FixedEval::eval_to_transcript(
+            &self.polys,
+            std::iter::repeat(*x).take(self.polys.len()),
+            transcript,
+        )
+        .map_err(Error::from)
     }
 }
 
diff --git a/halo2_proofs/src/plonk/prover.rs b/halo2_proofs/src/plonk/prover.rs
index c677f4065..1beaabbd5 100644
--- a/halo2_proofs/src/plonk/prover.rs
+++ b/halo2_proofs/src/plonk/prover.rs
@@ -574,7 +574,7 @@ where
     let vanishing = vanishing.evaluate(x, xn, domain, transcript)?;
 
     // Evaluate common permutation data
-    pk.permutation.evaluate(x, transcript)?;
+    pk.permutation.evaluate::<_, _, Gen>(x, transcript)?;
 
     // Evaluate the permutations, if any, at omega^i x.
     let permutations: Vec<permutation::prover::Evaluated<Scheme::Curve>> = permutations