diff --git a/evm/src/lookup.rs b/evm/src/lookup.rs
index 1c25700b..b886e736 100644
--- a/evm/src/lookup.rs
+++ b/evm/src/lookup.rs
@@ -1,4 +1,5 @@
 use itertools::Itertools;
+use num_bigint::BigUint;
 use plonky2::field::batch_util::batch_add_inplace;
 use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::packed::PackedField;
@@ -49,6 +50,10 @@ pub(crate) fn lookup_helper_columns<F: Field>(
         constraint_degree, 3,
         "TODO: Allow other constraint degrees."
     );
+
+    let num_total_logup_entries = trace_poly_values[0].values.len() * lookup.columns.len();
+    assert!(BigUint::from(num_total_logup_entries) < F::characteristic());
+
     let num_helper_columns = lookup.num_helper_columns(constraint_degree);
     let mut helper_columns: Vec<PolynomialValues<F>> = Vec::with_capacity(num_helper_columns);
 
@@ -123,7 +128,7 @@ where
 }
 
 /// Constraints for the logUp lookup argument.
-pub(crate) fn eval_lookups_checks<F, FE, P, S, const D: usize, const D2: usize>(
+pub(crate) fn eval_packed_lookups_generic<F, FE, P, S, const D: usize, const D2: usize>(
     stark: &S,
     lookups: &[Lookup],
     vars: StarkEvaluationVars<FE, P, { S::COLUMNS }>,
@@ -180,7 +185,7 @@ pub struct LookupCheckVarsTarget<const D: usize> {
     pub(crate) challenges: Vec<Target>,
 }
 
-pub(crate) fn eval_lookups_checks_circuit<
+pub(crate) fn eval_ext_lookups_circuit<
     F: RichField + Extendable<D>,
     S: Stark<F, D>,
     const D: usize,
diff --git a/evm/src/recursive_verifier.rs b/evm/src/recursive_verifier.rs
index 6abd61e7..3539f35b 100644
--- a/evm/src/recursive_verifier.rs
+++ b/evm/src/recursive_verifier.rs
@@ -352,6 +352,7 @@ where
         &proof_target,
         &challenges,
         &ctl_vars,
+        &ctl_challenges_target,
         inner_config,
     );
 
@@ -395,6 +396,7 @@ fn verify_stark_proof_with_challenges_circuit<
     proof: &StarkProofTarget<D>,
     challenges: &StarkProofChallengesTarget<D>,
     ctl_vars: &[CtlCheckVarsTarget<F, D>],
+    ctl_challenges: &GrandProductChallengeSet<Target>,
     inner_config: &StarkConfig,
 ) where
     C::Hasher: AlgebraicHasher<F>,
@@ -435,9 +437,10 @@ fn verify_stark_proof_with_challenges_circuit<
 
     let num_lookup_columns = stark.num_lookup_helper_columns(inner_config);
     let lookup_challenges = (num_lookup_columns > 0).then(|| {
-        ctl_vars
+        ctl_challenges
+            .challenges
             .iter()
-            .map(|ch| ch.challenges.beta)
+            .map(|ch| ch.beta)
             .collect::<Vec<_>>()
     });
 
diff --git a/evm/src/vanishing_poly.rs b/evm/src/vanishing_poly.rs
index 21d36167..a3951120 100644
--- a/evm/src/vanishing_poly.rs
+++ b/evm/src/vanishing_poly.rs
@@ -9,7 +9,7 @@ use crate::cross_table_lookup::{
     CtlCheckVarsTarget,
 };
 use crate::lookup::{
-    eval_lookups_checks, eval_lookups_checks_circuit, Lookup, LookupCheckVars,
+    eval_ext_lookups_circuit, eval_packed_lookups_generic, Lookup, LookupCheckVars,
     LookupCheckVarsTarget,
 };
 use crate::stark::Stark;
@@ -30,7 +30,13 @@ pub(crate) fn eval_vanishing_poly<F, FE, P, S, const D: usize, const D2: usize>(
 {
     stark.eval_packed_generic(vars, consumer);
     if let Some(lookup_vars) = lookup_vars {
-        eval_lookups_checks::<F, FE, P, S, D, D2>(stark, lookups, vars, lookup_vars, consumer);
+        eval_packed_lookups_generic::<F, FE, P, S, D, D2>(
+            stark,
+            lookups,
+            vars,
+            lookup_vars,
+            consumer,
+        );
     }
     eval_cross_table_lookup_checks::<F, FE, P, S, D, D2>(vars, ctl_vars, consumer);
 }
@@ -49,7 +55,7 @@ pub(crate) fn eval_vanishing_poly_circuit<F, S, const D: usize>(
 {
     stark.eval_ext_circuit(builder, vars, consumer);
     if let Some(lookup_vars) = lookup_vars {
-        eval_lookups_checks_circuit::<F, S, D>(builder, stark, vars, lookup_vars, consumer);
+        eval_ext_lookups_circuit::<F, S, D>(builder, stark, vars, lookup_vars, consumer);
     }
     eval_cross_table_lookup_checks_circuit::<S, F, D>(builder, vars, ctl_vars, consumer);
 }