diff --git a/starky2/src/all_stark.rs b/starky2/src/all_stark.rs
index 7542d3bf..89eff627 100644
--- a/starky2/src/all_stark.rs
+++ b/starky2/src/all_stark.rs
@@ -4,6 +4,7 @@ use plonky2::field::extension_field::{Extendable, FieldExtension};
 use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
 
+use crate::config::StarkConfig;
 use crate::constraint_consumer::{ConstraintConsumer, RecursiveConstraintConsumer};
 use crate::cross_table_lookup::CrossTableLookup;
 use crate::stark::Stark;
@@ -16,6 +17,15 @@ pub struct AllStark<F: RichField + Extendable<D>, const D: usize> {
     pub cross_table_lookups: Vec<CrossTableLookup>,
 }
 
+impl<F: RichField + Extendable<D>, const D: usize> AllStark<F, D> {
+    pub(crate) fn nums_permutation_zs(&self, config: &StarkConfig) -> Vec<usize> {
+        vec![
+            self.cpu_stark.num_permutation_batches(config),
+            self.keccak_stark.num_permutation_batches(config),
+        ]
+    }
+}
+
 #[derive(Copy, Clone)]
 pub struct CpuStark<F, const D: usize> {
     num_rows: usize,
diff --git a/starky2/src/cross_table_lookup.rs b/starky2/src/cross_table_lookup.rs
index fc0e6f33..8072a6c9 100644
--- a/starky2/src/cross_table_lookup.rs
+++ b/starky2/src/cross_table_lookup.rs
@@ -152,11 +152,13 @@ impl<'a, F: RichField + Extendable<D>, const D: usize>
         proofs: &[&StarkProofWithPublicInputs<F, C, D>],
         cross_table_lookups: &'a [CrossTableLookup],
         ctl_challenges: &'a GrandProductChallengeSet<F>,
-        num_permutation_zs: usize,
+        num_permutation_zs: &[usize],
     ) -> Vec<Vec<Self>> {
+        debug_assert_eq!(proofs.len(), num_permutation_zs.len());
         let mut ctl_zs = proofs
             .iter()
-            .map(|p| -> Box<dyn Iterator<Item = _>> {
+            .zip(num_permutation_zs)
+            .map(|(p, &num_permutation)| -> Box<dyn Iterator<Item = _>> {
                 if p.proof.openings.permutation_lookup_zs.is_some() {
                     Box::new(
                         p.proof
@@ -165,7 +167,7 @@ impl<'a, F: RichField + Extendable<D>, const D: usize>
                             .as_ref()
                             .unwrap()
                             .iter()
-                            .skip(num_permutation_zs)
+                            .skip(num_permutation)
                             .zip(
                                 p.proof
                                     .openings
@@ -173,7 +175,7 @@ impl<'a, F: RichField + Extendable<D>, const D: usize>
                                     .as_ref()
                                     .unwrap()
                                     .iter()
-                                    .skip(num_permutation_zs),
+                                    .skip(num_permutation),
                             ),
                     )
                 } else {
diff --git a/starky2/src/verifier.rs b/starky2/src/verifier.rs
index 2c4a7fba..78763fd2 100644
--- a/starky2/src/verifier.rs
+++ b/starky2/src/verifier.rs
@@ -38,6 +38,8 @@ where
         ctl_challenges,
     } = all_proof.get_challenges(&all_stark, config);
 
+    let nums_permutation_zs = all_stark.nums_permutation_zs(config);
+
     let AllStark {
         cpu_stark,
         keccak_stark,
@@ -48,7 +50,7 @@ where
         &all_proof.proofs(),
         &cross_table_lookups,
         &ctl_challenges,
-        0, // TODO: Fix 0
+        &nums_permutation_zs,
     );
 
     verify_stark_proof_with_challenges(
@@ -150,9 +152,10 @@ where
         l_1,
         l_last,
     );
+    let num_permutation_zs = stark.num_permutation_batches(config);
     let permutation_data = stark.uses_permutation_args().then(|| PermutationCheckVars {
-        local_zs: permutation_lookup_zs.as_ref().unwrap().clone(),
-        next_zs: permutation_lookup_zs_right.as_ref().unwrap().clone(),
+        local_zs: permutation_lookup_zs.as_ref().unwrap()[..num_permutation_zs].to_vec(),
+        next_zs: permutation_lookup_zs_right.as_ref().unwrap()[..num_permutation_zs].to_vec(),
         permutation_challenge_sets: challenges.permutation_challenge_sets.unwrap(),
     });
     eval_vanishing_poly::<F, F::Extension, F::Extension, C, S, D, D>(