diff --git a/starky2/src/all_stark.rs b/starky2/src/all_stark.rs
index c8b7fa76..67445856 100644
--- a/starky2/src/all_stark.rs
+++ b/starky2/src/all_stark.rs
@@ -5,12 +5,14 @@ use plonky2::field::packed_field::PackedField;
 use plonky2::hash::hash_types::RichField;
 
 use crate::constraint_consumer::{ConstraintConsumer, RecursiveConstraintConsumer};
+use crate::cross_table_lookup::CrossTableLookup;
 use crate::stark::Stark;
 use crate::vars::{StarkEvaluationTargets, StarkEvaluationVars};
 
 pub struct AllStark<F: RichField + Extendable<D>, const D: usize> {
-    pub cpu: CpuStark<F, D>,
-    pub keccak: KeccakStark<F, D>,
+    pub cpu_stark: CpuStark<F, D>,
+    pub keccak_stark: KeccakStark<F, D>,
+    pub cross_table_lookups: Vec<CrossTableLookup>,
 }
 
 pub struct CpuStark<F, const D: usize> {
diff --git a/starky2/src/cross_table_lookup.rs b/starky2/src/cross_table_lookup.rs
index 3d689b50..9e485d07 100644
--- a/starky2/src/cross_table_lookup.rs
+++ b/starky2/src/cross_table_lookup.rs
@@ -42,31 +42,30 @@ impl CrossTableLookup {
 /// Lookup data for one table.
 #[derive(Clone)]
 pub struct LookupData<F: Field> {
-    pub zs_beta_gammas: Vec<(PolynomialValues<F>, F, F, Vec<usize>)>,
-}
-
-impl<F: Field> Default for LookupData<F> {
-    fn default() -> Self {
-        Self {
-            zs_beta_gammas: Vec::new(),
-        }
-    }
+    pub beta: F,
+    pub gamma: F,
+    pub zs_columns: Vec<(PolynomialValues<F>, Vec<usize>)>,
 }
 
 impl<F: Field> LookupData<F> {
+    pub fn new(beta: F, gamma: F) -> Self {
+        Self {
+            beta,
+            gamma,
+            zs_columns: vec![],
+        }
+    }
+
     pub fn len(&self) -> usize {
-        self.zs_beta_gammas.len()
+        self.zs_columns.len()
     }
 
     pub fn is_empty(&self) -> bool {
-        self.zs_beta_gammas.is_empty()
+        self.zs_columns.is_empty()
     }
 
     pub fn z_polys(&self) -> Vec<PolynomialValues<F>> {
-        self.zs_beta_gammas
-            .iter()
-            .map(|(p, _, _, _)| p.clone())
-            .collect()
+        self.zs_columns.iter().map(|(p, _)| p.clone()).collect()
     }
 }
 
@@ -76,20 +75,19 @@ pub fn cross_table_lookup_zs<F: RichField, C: GenericConfig<D, F = F>, const D:
     cross_table_lookups: &[CrossTableLookup],
     challenger: &mut Challenger<F, C::Hasher>,
 ) -> Vec<LookupData<F>> {
+    let beta = challenger.get_challenge();
+    let gamma = challenger.get_challenge();
     cross_table_lookups.iter().fold(
-        vec![LookupData::default(); trace_poly_values.len()],
+        vec![LookupData::new(beta, gamma); trace_poly_values.len()],
         |mut acc, cross_table_lookup| {
             let CrossTableLookup {
                 looking_table,
                 looking_columns,
                 looked_table,
                 looked_columns,
-                ..
             } = cross_table_lookup;
 
             for _ in 0..config.num_challenges {
-                let beta = challenger.get_challenge();
-                let gamma = challenger.get_challenge();
                 let z_looking = partial_products(
                     &trace_poly_values[*looking_table as usize],
                     looking_columns,
@@ -103,18 +101,12 @@ pub fn cross_table_lookup_zs<F: RichField, C: GenericConfig<D, F = F>, const D:
                     gamma,
                 );
 
-                acc[*looking_table as usize].zs_beta_gammas.push((
-                    z_looking,
-                    beta,
-                    gamma,
-                    looking_columns.clone(),
-                ));
-                acc[*looked_table as usize].zs_beta_gammas.push((
-                    z_looked,
-                    beta,
-                    gamma,
-                    looked_columns.clone(),
-                ));
+                acc[*looking_table as usize]
+                    .zs_columns
+                    .push((z_looking, looking_columns.clone()));
+                acc[*looked_table as usize]
+                    .zs_columns
+                    .push((z_looked, looked_columns.clone()));
             }
             acc
         },
diff --git a/starky2/src/get_challenges.rs b/starky2/src/get_challenges.rs
index ceafa297..dc69d857 100644
--- a/starky2/src/get_challenges.rs
+++ b/starky2/src/get_challenges.rs
@@ -9,14 +9,16 @@ use plonky2::iop::target::Target;
 use plonky2::plonk::circuit_builder::CircuitBuilder;
 use plonky2::plonk::config::{AlgebraicHasher, GenericConfig};
 
+use crate::all_stark::AllStark;
 use crate::config::StarkConfig;
 use crate::permutation::{
-    get_n_permutation_challenge_sets, get_n_permutation_challenge_sets_target,
+    get_n_permutation_challenge_sets, get_n_permutation_challenge_sets_target, PermutationChallenge,
 };
 use crate::proof::*;
 use crate::stark::Stark;
 
 fn get_challenges<F, C, S, const D: usize>(
+    challenger: &mut Challenger<F, C::Hasher>,
     stark: &S,
     trace_cap: &MerkleCap<F, C::Hasher>,
     permutation_zs_cap: Option<&MerkleCap<F, C::Hasher>>,
@@ -35,13 +37,11 @@ where
 {
     let num_challenges = config.num_challenges;
 
-    let mut challenger = Challenger::<F, C::Hasher>::new();
-
     challenger.observe_cap(trace_cap);
 
     let permutation_challenge_sets = permutation_zs_cap.map(|permutation_zs_cap| {
         let tmp = get_n_permutation_challenge_sets(
-            &mut challenger,
+            challenger,
             num_challenges,
             stark.permutation_batch_size(),
         );
@@ -70,6 +70,42 @@ where
     }
 }
 
+impl<F: RichField + Extendable<D>, C: GenericConfig<D, F = F>, const D: usize> AllProof<F, C, D> {
+    /// Computes all Fiat-Shamir challenges used in the STARK proof.
+    pub(crate) fn get_challenges(
+        &self,
+        all_stark: &AllStark<F, D>,
+        config: &StarkConfig,
+    ) -> AllProofChallenges<F, D> {
+        let num_challenges = config.num_challenges;
+
+        let mut challenger = Challenger::<F, C::Hasher>::new();
+
+        for proof in self.proofs() {
+            challenger.observe_cap(&proof.proof.trace_cap);
+        }
+
+        let ctl_challenges = PermutationChallenge {
+            beta: challenger.get_challenge(),
+            gamma: challenger.get_challenge(),
+        };
+
+        AllProofChallenges {
+            cpu_challenges: self.cpu_proof.get_challenges(
+                &mut challenger,
+                &all_stark.cpu_stark,
+                config,
+            ),
+            keccak_challenges: self.keccak_proof.get_challenges(
+                &mut challenger,
+                &all_stark.keccak_stark,
+                config,
+            ),
+            ctl_challenges,
+        }
+    }
+}
+
 impl<F, C, const D: usize> StarkProofWithPublicInputs<F, C, D>
 where
     F: RichField + Extendable<D>,
@@ -81,9 +117,9 @@ where
         &self,
         stark: &S,
         config: &StarkConfig,
-        degree_bits: usize,
     ) -> Vec<usize> {
-        self.get_challenges(stark, config, degree_bits)
+        let mut challenger = Challenger::new();
+        self.get_challenges(&mut challenger, stark, config)
             .fri_challenges
             .fri_query_indices
     }
@@ -91,10 +127,12 @@ where
     /// Computes all Fiat-Shamir challenges used in the STARK proof.
     pub(crate) fn get_challenges<S: Stark<F, D>>(
         &self,
+        challenger: &mut Challenger<F, C::Hasher>,
         stark: &S,
         config: &StarkConfig,
-        degree_bits: usize,
     ) -> StarkProofChallenges<F, D> {
+        let degree_bits = self.proof.recover_degree_bits(config);
+
         let StarkProof {
             trace_cap,
             permutation_zs_cap,
@@ -110,6 +148,7 @@ where
         } = &self.proof;
 
         get_challenges::<F, C, S, D>(
+            challenger,
             stark,
             trace_cap,
             permutation_zs_cap.as_ref(),
diff --git a/starky2/src/proof.rs b/starky2/src/proof.rs
index 3fa51a51..89c116df 100644
--- a/starky2/src/proof.rs
+++ b/starky2/src/proof.rs
@@ -16,7 +16,25 @@ use plonky2::plonk::config::GenericConfig;
 use rayon::prelude::*;
 
 use crate::config::StarkConfig;
-use crate::permutation::PermutationChallengeSet;
+use crate::permutation::{PermutationChallenge, PermutationChallengeSet};
+
+#[derive(Debug, Clone)]
+pub struct AllProof<F: RichField + Extendable<D>, C: GenericConfig<D, F = F>, const D: usize> {
+    pub cpu_proof: StarkProofWithPublicInputs<F, C, D>,
+    pub keccak_proof: StarkProofWithPublicInputs<F, C, D>,
+}
+
+impl<F: RichField + Extendable<D>, C: GenericConfig<D, F = F>, const D: usize> AllProof<F, C, D> {
+    pub fn proofs(&self) -> [&StarkProofWithPublicInputs<F, C, D>; 2] {
+        [&self.cpu_proof, &self.keccak_proof]
+    }
+}
+
+pub(crate) struct AllProofChallenges<F: RichField + Extendable<D>, const D: usize> {
+    pub cpu_challenges: StarkProofChallenges<F, D>,
+    pub keccak_challenges: StarkProofChallenges<F, D>,
+    pub ctl_challenges: PermutationChallenge<F>,
+}
 
 #[derive(Debug, Clone)]
 pub struct StarkProof<F: RichField + Extendable<D>, C: GenericConfig<D, F = F>, const D: usize> {
diff --git a/starky2/src/prover.rs b/starky2/src/prover.rs
index aba1f830..0f5013a4 100644
--- a/starky2/src/prover.rs
+++ b/starky2/src/prover.rs
@@ -28,19 +28,18 @@ use crate::permutation::{
     compute_permutation_z_polys, get_n_permutation_challenge_sets, PermutationChallengeSet,
 };
 use crate::permutation::{PermutationChallenge, PermutationCheckVars};
-use crate::proof::{StarkOpeningSet, StarkProof, StarkProofWithPublicInputs};
+use crate::proof::{AllProof, StarkOpeningSet, StarkProof, StarkProofWithPublicInputs};
 use crate::stark::Stark;
 use crate::vanishing_poly::eval_vanishing_poly;
 use crate::vars::StarkEvaluationVars;
 
 pub fn prove<F, C, S, const D: usize>(
-    all_starks: AllStark<F, D>,
+    all_stark: AllStark<F, D>,
     config: &StarkConfig,
     trace_poly_values: Vec<Vec<PolynomialValues<F>>>,
-    cross_table_lookups: Vec<CrossTableLookup>,
     public_inputs: Vec<Vec<F>>,
     timing: &mut TimingTree,
-) -> Result<Vec<StarkProofWithPublicInputs<F, C, D>>>
+) -> Result<AllProof<F, C, D>>
 where
     F: RichField + Extendable<D>,
     C: GenericConfig<D, F = F>,
@@ -93,12 +92,12 @@ where
     let lookup_zs = cross_table_lookup_zs::<F, C, D>(
         config,
         &trace_poly_values,
-        &cross_table_lookups,
+        &all_stark.cross_table_lookups,
         &mut challenger,
     );
 
     let cpu_proof = prove_single_table(
-        &all_starks.cpu,
+        &all_stark.cpu_stark,
         config,
         &trace_poly_values[Table::Cpu as usize],
         &trace_commitments[Table::Cpu as usize],
@@ -108,7 +107,7 @@ where
         timing,
     )?;
     let keccak_proof = prove_single_table(
-        &all_starks.keccak,
+        &all_stark.keccak_stark,
         config,
         &trace_poly_values[Table::Keccak as usize],
         &trace_commitments[Table::Keccak as usize],
@@ -118,7 +117,10 @@ where
         timing,
     )?;
 
-    Ok(vec![cpu_proof, keccak_proof])
+    Ok(AllProof {
+        cpu_proof,
+        keccak_proof,
+    })
 }
 
 fn prove_single_table<F, C, S, const D: usize>(
@@ -375,26 +377,24 @@ where
                 },
             );
             let lookup_check_data = lookup_data
-                .zs_beta_gammas
+                .zs_columns
                 .iter()
                 .enumerate()
-                .map(
-                    |(i, (_, beta, gamma, columns))| CTLCheckVars::<F, F, P, 1> {
-                        local_z: permutation_zs_commitment_challenges
-                            .unwrap()
-                            .0
-                            .get_lde_values_packed(i_start, step)[num_permutation_zs + i],
-                        next_z: permutation_zs_commitment_challenges
-                            .unwrap()
-                            .0
-                            .get_lde_values_packed(i_next_start, step)[num_permutation_zs + i],
-                        challenges: PermutationChallenge {
-                            beta: *beta,
-                            gamma: *gamma,
-                        },
-                        columns: columns.to_vec(),
+                .map(|(i, (_, columns))| CTLCheckVars::<F, F, P, 1> {
+                    local_z: permutation_zs_commitment_challenges
+                        .unwrap()
+                        .0
+                        .get_lde_values_packed(i_start, step)[num_permutation_zs + i],
+                    next_z: permutation_zs_commitment_challenges
+                        .unwrap()
+                        .0
+                        .get_lde_values_packed(i_next_start, step)[num_permutation_zs + i],
+                    challenges: PermutationChallenge {
+                        beta: lookup_data.beta,
+                        gamma: lookup_data.gamma,
                     },
-                )
+                    columns: columns.to_vec(),
+                })
                 .collect::<Vec<_>>();
             eval_vanishing_poly::<F, F, P, C, S, D, 1>(
                 stark,
diff --git a/starky2/src/verifier.rs b/starky2/src/verifier.rs
index 9375c9f4..b5f144fb 100644
--- a/starky2/src/verifier.rs
+++ b/starky2/src/verifier.rs
@@ -9,35 +9,69 @@ use plonky2::hash::hash_types::RichField;
 use plonky2::plonk::config::{GenericConfig, Hasher};
 use plonky2::plonk::plonk_common::reduce_with_powers;
 
+use crate::all_stark::{AllStark, KeccakStark};
 use crate::config::StarkConfig;
 use crate::constraint_consumer::ConstraintConsumer;
 use crate::permutation::PermutationCheckVars;
-use crate::proof::{StarkOpeningSet, StarkProofChallenges, StarkProofWithPublicInputs};
+use crate::proof::{
+    AllProof, AllProofChallenges, StarkOpeningSet, StarkProofChallenges, StarkProofWithPublicInputs,
+};
 use crate::stark::Stark;
 use crate::vanishing_poly::eval_vanishing_poly;
 use crate::vars::StarkEvaluationVars;
 
-pub fn verify_stark_proof<
-    F: RichField + Extendable<D>,
-    C: GenericConfig<D, F = F>,
-    S: Stark<F, D>,
-    const D: usize,
->(
-    stark: S,
-    proof_with_pis: StarkProofWithPublicInputs<F, C, D>,
+pub fn verify_proof<F: RichField + Extendable<D>, C: GenericConfig<D, F = F>, const D: usize>(
+    all_stark: AllStark<F, D>,
+    all_proof: AllProof<F, C, D>,
     config: &StarkConfig,
 ) -> Result<()>
 where
-    [(); S::COLUMNS]:,
-    [(); S::PUBLIC_INPUTS]:,
+    [(); KeccakStark::<F, D>::COLUMNS]:,
     [(); C::Hasher::HASH_SIZE]:,
 {
-    ensure!(proof_with_pis.public_inputs.len() == S::PUBLIC_INPUTS);
-    let degree_bits = proof_with_pis.proof.recover_degree_bits(config);
-    let challenges = proof_with_pis.get_challenges(&stark, config, degree_bits);
-    verify_stark_proof_with_challenges(stark, proof_with_pis, challenges, degree_bits, config)
+    let AllProofChallenges {
+        cpu_challenges,
+        keccak_challenges,
+        ctl_challenges,
+    } = all_proof.get_challenges(&all_stark, config);
+
+    // Verify CTL
+
+    verify_stark_proof_with_challenges(
+        all_stark.cpu_stark,
+        all_proof.cpu_proof,
+        cpu_challenges,
+        config,
+    )?;
+    verify_stark_proof_with_challenges(
+        all_stark.keccak_stark,
+        all_proof.keccak_proof,
+        keccak_challenges,
+        config,
+    )
 }
 
+// pub fn verify_stark_proof<
+//     F: RichField + Extendable<D>,
+//     C: GenericConfig<D, F = F>,
+//     S: Stark<F, D>,
+//     const D: usize,
+// >(
+//     stark: S,
+//     proof_with_pis: StarkProofWithPublicInputs<F, C, D>,
+//     config: &StarkConfig,
+// ) -> Result<()>
+// where
+//     [(); S::COLUMNS]:,
+//     [(); S::PUBLIC_INPUTS]:,
+//     [(); C::Hasher::HASH_SIZE]:,
+// {
+//     ensure!(proof_with_pis.public_inputs.len() == S::PUBLIC_INPUTS);
+//     let degree_bits = proof_with_pis.proof.recover_degree_bits(config);
+//     let challenges = proof_with_pis.get_challenges(&stark, config, degree_bits);
+//     verify_stark_proof_with_challenges(stark, proof_with_pis, challenges, degree_bits, config)
+// }
+
 pub(crate) fn verify_stark_proof_with_challenges<
     F: RichField + Extendable<D>,
     C: GenericConfig<D, F = F>,
@@ -47,7 +81,6 @@ pub(crate) fn verify_stark_proof_with_challenges<
     stark: S,
     proof_with_pis: StarkProofWithPublicInputs<F, C, D>,
     challenges: StarkProofChallenges<F, D>,
-    degree_bits: usize,
     config: &StarkConfig,
 ) -> Result<()>
 where
@@ -77,6 +110,7 @@ where
             .collect::<Vec<_>>(),
     };
 
+    let degree_bits = proof.recover_degree_bits(config);
     let (l_1, l_last) = eval_l_1_and_l_last(degree_bits, challenges.stark_zeta);
     let last = F::primitive_root_of_unity(degree_bits).inverse();
     let z_last = challenges.stark_zeta - last.into();