diff --git a/crates/prover/src/core/air/mod.rs b/crates/prover/src/core/air/mod.rs
index 8cf8c725e..b559780df 100644
--- a/crates/prover/src/core/air/mod.rs
+++ b/crates/prover/src/core/air/mod.rs
@@ -7,7 +7,7 @@ use super::fields::qm31::SecureField;
 use super::pcs::TreeVec;
 use super::poly::circle::{CircleEvaluation, CirclePoly};
 use super::poly::BitReversedOrder;
-use super::{ColumnVec, ComponentVec, InteractionElements};
+use super::{ColumnVec, InteractionElements};
 
 pub mod accumulation;
 mod air_ext;
@@ -34,7 +34,7 @@ pub trait AirTraceWriter<B: Backend>: AirTraceVerifier {
         &self,
         trace: &ColumnVec<CircleEvaluation<B, BaseField, BitReversedOrder>>,
         elements: &InteractionElements,
-    ) -> ComponentVec<CircleEvaluation<B, BaseField, BitReversedOrder>>;
+    ) -> Vec<CircleEvaluation<B, BaseField, BitReversedOrder>>;
 
     fn to_air_prover(&self) -> &impl AirProver<B>;
 }
diff --git a/crates/prover/src/core/mod.rs b/crates/prover/src/core/mod.rs
index 3278e60cd..499738c18 100644
--- a/crates/prover/src/core/mod.rs
+++ b/crates/prover/src/core/mod.rs
@@ -1,7 +1,7 @@
 use std::collections::BTreeMap;
 use std::ops::{Deref, DerefMut, Index};
 
-use self::fields::m31::BaseField;
+use self::fields::qm31::SecureField;
 
 pub mod air;
 pub mod backend;
@@ -62,10 +62,10 @@ impl<T> DerefMut for ComponentVec<T> {
 }
 
 #[derive(Default)]
-pub struct InteractionElements(BTreeMap<String, BaseField>);
+pub struct InteractionElements(BTreeMap<String, SecureField>);
 
 impl InteractionElements {
-    pub fn new(elements: BTreeMap<String, BaseField>) -> Self {
+    pub fn new(elements: BTreeMap<String, SecureField>) -> Self {
         Self(elements)
     }
 
@@ -75,7 +75,7 @@ impl InteractionElements {
 }
 
 impl Index<&str> for InteractionElements {
-    type Output = BaseField;
+    type Output = SecureField;
 
     fn index(&self, index: &str) -> &Self::Output {
         // TODO(AlonH): Return an error if the key is not found.
diff --git a/crates/prover/src/core/poly/circle/secure_poly.rs b/crates/prover/src/core/poly/circle/secure_poly.rs
index f9ff38107..931e283e8 100644
--- a/crates/prover/src/core/poly/circle/secure_poly.rs
+++ b/crates/prover/src/core/poly/circle/secure_poly.rs
@@ -35,6 +35,7 @@ impl<B: PolyOps> SecureCirclePoly<B> {
 
     /// Evaluates the polynomial at a point, given evaluations of its composing base field
     /// polynomials at that point.
+    // TODO(AlonH): Move to SecureField and rename.
     pub fn eval_from_partial_evals(evals: [SecureField; SECURE_EXTENSION_DEGREE]) -> SecureField {
         let mut res = evals[0];
         res += evals[1] * SecureField::from_u32_unchecked(0, 1, 0, 0);
diff --git a/crates/prover/src/core/prover/mod.rs b/crates/prover/src/core/prover/mod.rs
index f297ae505..41cb83146 100644
--- a/crates/prover/src/core/prover/mod.rs
+++ b/crates/prover/src/core/prover/mod.rs
@@ -61,7 +61,7 @@ pub fn evaluate_and_commit_on_trace<B: Backend + MerkleOps<MerkleHasher>>(
     let trace_polys = trace
         .clone()
         .into_iter()
-        .map(|poly| poly.interpolate_with_twiddles(twiddles))
+        .map(|eval| eval.interpolate_with_twiddles(twiddles))
         .collect();
     span.exit();
 
@@ -71,17 +71,14 @@ pub fn evaluate_and_commit_on_trace<B: Backend + MerkleOps<MerkleHasher>>(
     span.exit();
 
     let interaction_elements = air.interaction_elements(channel);
-    let interaction_traces = air.interact(&trace, &interaction_elements);
-    let interaction_trace_polys = interaction_traces
-        .0
-        .into_iter()
-        .flat_map(|trace| {
-            trace
-                .into_iter()
-                .map(|poly| poly.interpolate_with_twiddles(twiddles))
-        })
-        .collect_vec();
-    if !interaction_trace_polys.is_empty() {
+    let interaction_trace = air.interact(&trace, &interaction_elements);
+    if !interaction_trace.is_empty() {
+        let span = span!(Level::INFO, "Interaction trace interpolation").entered();
+        let interaction_trace_polys = interaction_trace
+            .into_iter()
+            .map(|eval| eval.interpolate_with_twiddles(twiddles))
+            .collect();
+        span.exit();
         commitment_scheme.commit(interaction_trace_polys, channel, twiddles);
     }
 
@@ -356,7 +353,7 @@ mod tests {
     use crate::core::poly::BitReversedOrder;
     use crate::core::prover::{prove, ProvingError};
     use crate::core::test_utils::test_channel;
-    use crate::core::{ColumnVec, ComponentVec, InteractionElements};
+    use crate::core::{ColumnVec, InteractionElements};
     use crate::qm31;
 
     struct TestAir<C: ComponentProver<CpuBackend>> {
@@ -380,8 +377,8 @@ mod tests {
             &self,
             _trace: &ColumnVec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>>,
             _elements: &InteractionElements,
-        ) -> ComponentVec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>> {
-            ComponentVec(vec![vec![]])
+        ) -> Vec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>> {
+            vec![]
         }
 
         fn to_air_prover(&self) -> &impl AirProver<CpuBackend> {
diff --git a/crates/prover/src/core/utils.rs b/crates/prover/src/core/utils.rs
index 7b033e6e7..cb6cc222e 100644
--- a/crates/prover/src/core/utils.rs
+++ b/crates/prover/src/core/utils.rs
@@ -1,6 +1,7 @@
 use std::iter::Peekable;
+use std::ops::Add;
 
-use num_traits::One;
+use num_traits::{One, Zero};
 
 use super::fields::m31::BaseField;
 use super::fields::qm31::SecureField;
@@ -92,12 +93,15 @@ pub fn generate_secure_powers(felt: SecureField, n_powers: usize) -> Vec<SecureF
 /// Alpha and z should be secure field elements for soundness.
 pub fn shifted_secure_combination<F: ExtensionOf<BaseField>>(
     values: &[F],
-    alpha: BaseField,
-    z: BaseField,
-) -> F {
+    alpha: SecureField,
+    z: SecureField,
+) -> SecureField
+where
+    SecureField: Add<F, Output = SecureField>,
+{
     let res = values
         .iter()
-        .fold(F::zero(), |acc, &value| acc * alpha + value);
+        .fold(SecureField::zero(), |acc, &value| acc * alpha + value);
     res - z
 }
 
diff --git a/crates/prover/src/examples/fibonacci/air.rs b/crates/prover/src/examples/fibonacci/air.rs
index dbec91ecf..c8c1b8c39 100644
--- a/crates/prover/src/examples/fibonacci/air.rs
+++ b/crates/prover/src/examples/fibonacci/air.rs
@@ -9,7 +9,7 @@ use crate::core::channel::Blake2sChannel;
 use crate::core::fields::m31::BaseField;
 use crate::core::poly::circle::CircleEvaluation;
 use crate::core::poly::BitReversedOrder;
-use crate::core::{ColumnVec, ComponentVec, InteractionElements};
+use crate::core::{ColumnVec, InteractionElements};
 
 pub struct FibonacciAir {
     pub component: FibonacciComponent,
@@ -38,8 +38,8 @@ impl AirTraceWriter<CpuBackend> for FibonacciAir {
         &self,
         _trace: &ColumnVec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>>,
         _elements: &InteractionElements,
-    ) -> ComponentVec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>> {
-        ComponentVec(vec![vec![]])
+    ) -> Vec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>> {
+        vec![]
     }
 
     fn to_air_prover(&self) -> &impl AirProver<CpuBackend> {
@@ -87,8 +87,8 @@ impl AirTraceWriter<CpuBackend> for MultiFibonacciAir {
         &self,
         _trace: &ColumnVec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>>,
         _elements: &InteractionElements,
-    ) -> ComponentVec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>> {
-        ComponentVec(vec![vec![]])
+    ) -> Vec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>> {
+        vec![]
     }
 
     fn to_air_prover(&self) -> &impl AirProver<CpuBackend> {
diff --git a/crates/prover/src/examples/wide_fibonacci/component.rs b/crates/prover/src/examples/wide_fibonacci/component.rs
index 758559abd..6a0c0e685 100644
--- a/crates/prover/src/examples/wide_fibonacci/component.rs
+++ b/crates/prover/src/examples/wide_fibonacci/component.rs
@@ -8,9 +8,10 @@ use crate::core::circle::CirclePoint;
 use crate::core::constraints::{coset_vanishing, point_vanishing};
 use crate::core::fields::m31::BaseField;
 use crate::core::fields::qm31::SecureField;
+use crate::core::fields::secure_column::{SecureColumn, SECURE_EXTENSION_DEGREE};
 use crate::core::fields::FieldExpOps;
 use crate::core::pcs::TreeVec;
-use crate::core::poly::circle::{CanonicCoset, CircleEvaluation};
+use crate::core::poly::circle::{CanonicCoset, CircleEvaluation, SecureCirclePoly};
 use crate::core::poly::BitReversedOrder;
 use crate::core::utils::shifted_secure_combination;
 use crate::core::{ColumnVec, InteractionElements};
@@ -73,7 +74,7 @@ impl Component for WideFibComponent {
     fn trace_log_degree_bounds(&self) -> TreeVec<ColumnVec<u32>> {
         TreeVec::new(vec![
             vec![self.log_column_size(); self.n_columns()],
-            vec![self.log_column_size(); 1],
+            vec![self.log_column_size(); SECURE_EXTENSION_DEGREE],
         ])
     }
 
@@ -83,7 +84,7 @@ impl Component for WideFibComponent {
     ) -> TreeVec<ColumnVec<Vec<CirclePoint<SecureField>>>> {
         TreeVec::new(vec![
             fixed_mask_points(&vec![vec![0_usize]; self.n_columns()], point),
-            vec![vec![point]],
+            vec![vec![point]; SECURE_EXTENSION_DEGREE],
         ])
     }
 
@@ -100,7 +101,11 @@ impl Component for WideFibComponent {
     ) {
         let constraint_zero_domain = CanonicCoset::new(self.log_column_size()).coset;
         let (alpha, z) = (interaction_elements[ALPHA_ID], interaction_elements[Z_ID]);
-        let lookup_numerator = (mask[self.n_columns()][0]
+        let lookup_value =
+            SecureCirclePoly::<CpuBackend>::eval_from_partial_evals(std::array::from_fn(|i| {
+                mask[self.n_columns() + i][0]
+            }));
+        let lookup_numerator = (lookup_value
             * shifted_secure_combination(
                 &[mask[self.n_columns() - 2][0], mask[self.n_columns() - 1][0]],
                 alpha,
@@ -125,12 +130,21 @@ impl ComponentTraceWriter<CpuBackend> for WideFibComponent {
         trace: &ColumnVec<&CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>>,
         elements: &InteractionElements,
     ) -> ColumnVec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>> {
-        let interaction_trace_domain = trace[0].domain;
         let trace_values = trace.iter().map(|eval| &eval.values[..]).collect_vec();
         let (alpha, z) = (elements[ALPHA_ID], elements[Z_ID]);
+        // TODO(AlonH): Return a secure column directly.
         let values = write_lookup_column(&trace_values, alpha, z);
-        let eval = CircleEvaluation::new(interaction_trace_domain, values);
-        vec![eval]
+        let secure_column: SecureColumn<CpuBackend> = values.into_iter().collect();
+        secure_column
+            .columns
+            .into_iter()
+            .map(|eval| {
+                CircleEvaluation::<CpuBackend, BaseField, BitReversedOrder>::new(
+                    trace[0].domain,
+                    eval,
+                )
+            })
+            .collect_vec()
     }
 }
 
diff --git a/crates/prover/src/examples/wide_fibonacci/constraint_eval.rs b/crates/prover/src/examples/wide_fibonacci/constraint_eval.rs
index 9f309d844..841fe90f1 100644
--- a/crates/prover/src/examples/wide_fibonacci/constraint_eval.rs
+++ b/crates/prover/src/examples/wide_fibonacci/constraint_eval.rs
@@ -16,10 +16,10 @@ use crate::core::constraints::{coset_vanishing, point_vanishing};
 use crate::core::fields::m31::BaseField;
 use crate::core::fields::qm31::SecureField;
 use crate::core::fields::FieldExpOps;
-use crate::core::poly::circle::{CanonicCoset, CircleEvaluation};
+use crate::core::poly::circle::{CanonicCoset, CircleEvaluation, SecureCirclePoly};
 use crate::core::poly::BitReversedOrder;
 use crate::core::utils::{bit_reverse, shifted_secure_combination};
-use crate::core::{ColumnVec, ComponentVec, InteractionElements};
+use crate::core::{ColumnVec, InteractionElements};
 use crate::examples::wide_fibonacci::component::LOG_N_COLUMNS;
 
 // TODO(AlonH): Rename file to `cpu.rs`.
@@ -27,7 +27,7 @@ use crate::examples::wide_fibonacci::component::LOG_N_COLUMNS;
 impl AirTraceVerifier for WideFibAir {
     fn interaction_elements(&self, channel: &mut Blake2sChannel) -> InteractionElements {
         let ids = self.component.interaction_element_ids();
-        let elements = channel.draw_felts(ids.len()).into_iter().map(|e| e.0 .0);
+        let elements = channel.draw_felts(ids.len());
         InteractionElements::new(BTreeMap::from_iter(zip_eq(ids, elements)))
     }
 }
@@ -37,10 +37,9 @@ impl AirTraceWriter<CpuBackend> for WideFibAir {
         &self,
         trace: &ColumnVec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>>,
         elements: &InteractionElements,
-    ) -> ComponentVec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>> {
-        ComponentVec(vec![self
-            .component
-            .write_interaction_trace(&trace.iter().collect(), elements)])
+    ) -> Vec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>> {
+        self.component
+            .write_interaction_trace(&trace.iter().collect(), elements)
     }
 
     fn to_air_prover(&self) -> &impl AirProver<CpuBackend> {
@@ -92,8 +91,12 @@ impl ComponentProver<CpuBackend> for WideFibComponent {
             }
 
             // Lookup constraints.
+            let lookup_value =
+                SecureCirclePoly::<CpuBackend>::eval_from_partial_evals(std::array::from_fn(|j| {
+                    trace_evals[1][j][i].into()
+                }));
             lookup_numerators[i] = accum.random_coeff_powers[self.n_columns() - 2]
-                * ((trace_evals[1][0][i]
+                * ((lookup_value
                     * shifted_secure_combination(
                         &[
                             trace_evals[0][self.n_columns() - 2][i],
diff --git a/crates/prover/src/examples/wide_fibonacci/mod.rs b/crates/prover/src/examples/wide_fibonacci/mod.rs
index 809a35616..678e6ca22 100644
--- a/crates/prover/src/examples/wide_fibonacci/mod.rs
+++ b/crates/prover/src/examples/wide_fibonacci/mod.rs
@@ -18,6 +18,7 @@ mod tests {
     use crate::core::backend::CpuBackend;
     use crate::core::channel::{Blake2sChannel, Channel};
     use crate::core::fields::m31::BaseField;
+    use crate::core::fields::qm31::SecureField;
     use crate::core::fields::IntoSlice;
     use crate::core::pcs::TreeVec;
     use crate::core::poly::circle::CanonicCoset;
@@ -40,15 +41,15 @@ mod tests {
     }
 
     pub fn assert_constraints_on_lookup_column(
-        column: &[BaseField],
+        column: &[SecureField],
         input_trace: &[Vec<BaseField>],
-        alpha: BaseField,
-        z: BaseField,
+        alpha: SecureField,
+        z: SecureField,
     ) {
         let n_columns = input_trace.len();
         let column_length = column.len();
         assert_eq!(column_length, input_trace[0].len());
-        let mut prev_value = BaseField::one();
+        let mut prev_value = SecureField::one();
         for (i, cell) in column.iter().enumerate() {
             assert_eq!(
                 *cell
@@ -110,8 +111,8 @@ mod tests {
             b: m31!(1),
         };
 
-        let alpha = m31!(7);
-        let z = m31!(11);
+        let alpha = qm31!(7, 1, 3, 4);
+        let z = qm31!(11, 1, 2, 3);
         let trace = gen_trace(&wide_fib, vec![input]);
         let input_trace = trace.iter().map(|values| &values[..]).collect_vec();
         let lookup_column = write_lookup_column(&input_trace, alpha, z);
@@ -163,15 +164,14 @@ mod tests {
                 .iter()
                 .cloned()
                 .enumerate()
-                .map(|(i, id)| (id, m31!(43 + i as u32))),
+                .map(|(i, id)| (id, qm31!(43 + i as u32, 1, 2, 3))),
         ));
-        let interaction_trace =
-            wide_fib.write_interaction_trace(&trace.iter().collect(), &interaction_elements);
-
-        let interaction_poly = interaction_trace
-            .iter()
-            .map(|trace| trace.clone().interpolate())
+        let interaction_poly = wide_fib
+            .write_interaction_trace(&trace.iter().collect(), &interaction_elements)
+            .into_iter()
+            .map(|eval| eval.interpolate())
             .collect_vec();
+
         let interaction_trace = interaction_poly
             .iter()
             .map(|poly| poly.evaluate(eval_domain))
diff --git a/crates/prover/src/examples/wide_fibonacci/simd.rs b/crates/prover/src/examples/wide_fibonacci/simd.rs
index cd7698f3e..877b03ba8 100644
--- a/crates/prover/src/examples/wide_fibonacci/simd.rs
+++ b/crates/prover/src/examples/wide_fibonacci/simd.rs
@@ -23,7 +23,7 @@ use crate::core::fields::{FieldExpOps, FieldOps};
 use crate::core::pcs::TreeVec;
 use crate::core::poly::circle::{CanonicCoset, CircleEvaluation};
 use crate::core::poly::BitReversedOrder;
-use crate::core::{ColumnVec, ComponentVec, InteractionElements};
+use crate::core::{ColumnVec, InteractionElements};
 use crate::examples::wide_fibonacci::component::{ALPHA_ID, N_COLUMNS, Z_ID};
 
 // TODO(AlonH): Remove this once the Cpu and Simd implementations are aligned.
@@ -70,8 +70,8 @@ impl AirTraceWriter<SimdBackend> for SimdWideFibAir {
         &self,
         _trace: &ColumnVec<CircleEvaluation<SimdBackend, BaseField, BitReversedOrder>>,
         _elements: &InteractionElements,
-    ) -> ComponentVec<CircleEvaluation<SimdBackend, BaseField, BitReversedOrder>> {
-        ComponentVec(vec![vec![]])
+    ) -> Vec<CircleEvaluation<SimdBackend, BaseField, BitReversedOrder>> {
+        vec![]
     }
 
     fn to_air_prover(&self) -> &impl AirProver<SimdBackend> {
diff --git a/crates/prover/src/examples/wide_fibonacci/trace_gen.rs b/crates/prover/src/examples/wide_fibonacci/trace_gen.rs
index 2d5ecd148..9f6e9e50b 100644
--- a/crates/prover/src/examples/wide_fibonacci/trace_gen.rs
+++ b/crates/prover/src/examples/wide_fibonacci/trace_gen.rs
@@ -2,6 +2,7 @@ use num_traits::One;
 
 use super::component::Input;
 use crate::core::fields::m31::BaseField;
+use crate::core::fields::qm31::SecureField;
 use crate::core::fields::FieldExpOps;
 use crate::core::utils::shifted_secure_combination;
 
@@ -27,13 +28,12 @@ pub fn write_trace_row(
 /// the shifted secure combination of the last two elements in each row.
 pub fn write_lookup_column(
     input_trace: &[&[BaseField]],
-    // TODO(AlonH): Change alpha and z to SecureField.
-    alpha: BaseField,
-    z: BaseField,
-) -> Vec<BaseField> {
+    alpha: SecureField,
+    z: SecureField,
+) -> Vec<SecureField> {
     let n_rows = input_trace[0].len();
     let n_columns = input_trace.len();
-    let mut prev_value = BaseField::one();
+    let mut prev_value = SecureField::one();
     (0..n_rows)
         .map(|i| {
             let numerator =