diff --git a/crates/prover/src/core/air/air_ext.rs b/crates/prover/src/core/air/air_ext.rs
index 9c49beb58..75cda1ed6 100644
--- a/crates/prover/src/core/air/air_ext.rs
+++ b/crates/prover/src/core/air/air_ext.rs
@@ -1,4 +1,4 @@
-use std::collections::BTreeSet;
+use std::collections::{BTreeMap, BTreeSet};
 use std::iter::zip;
 
 use itertools::{zip_eq, Itertools};
@@ -13,7 +13,7 @@ use crate::core::fields::qm31::SecureField;
 use crate::core::poly::circle::{CanonicCoset, CircleEvaluation, CirclePoly, SecureCirclePoly};
 use crate::core::poly::BitReversedOrder;
 use crate::core::prover::LOG_BLOWUP_FACTOR;
-use crate::core::{ComponentVec, InteractionElements};
+use crate::core::{ColumnVec, ComponentVec, InteractionElements};
 
 pub trait AirExt: Air {
     fn composition_log_degree_bound(&self) -> u32 {
@@ -49,7 +49,7 @@ pub trait AirExt: Air {
             ids.extend(component.interaction_element_ids());
         }
         let elements = channel.draw_felts(ids.len()).into_iter().map(|e| e.0 .0);
-        InteractionElements(zip_eq(ids, elements).collect_vec())
+        InteractionElements(BTreeMap::from_iter(zip_eq(ids, elements)))
     }
 
     fn eval_composition_polynomial_at_point(
@@ -97,6 +97,24 @@ pub trait AirExt: Air {
 impl<A: Air + ?Sized> AirExt for A {}
 
 pub trait AirProverExt<B: Backend>: AirProver<B> {
+    fn interact(
+        &self,
+        trace: &ColumnVec<CircleEvaluation<B, BaseField, BitReversedOrder>>,
+        elements: &InteractionElements,
+    ) -> ComponentVec<CircleEvaluation<B, BaseField, BitReversedOrder>> {
+        let trace_iter = &mut trace.iter();
+        ComponentVec(
+            self.prover_components()
+                .iter()
+                .map(|component| {
+                    let n_columns = component.trace_log_degree_bounds().len();
+                    let trace_columns = trace_iter.take(n_columns).collect_vec();
+                    component.write_interaction_trace(&trace_columns, elements)
+                })
+                .collect(),
+        )
+    }
+
     fn compute_composition_polynomial(
         &self,
         random_coeff: SecureField,
@@ -118,4 +136,5 @@ pub trait AirProverExt<B: Backend>: AirProver<B> {
         accumulator.finalize()
     }
 }
+
 impl<B: Backend, A: AirProver<B>> AirProverExt<B> for A {}
diff --git a/crates/prover/src/core/air/mod.rs b/crates/prover/src/core/air/mod.rs
index 659a40a71..4d26487ec 100644
--- a/crates/prover/src/core/air/mod.rs
+++ b/crates/prover/src/core/air/mod.rs
@@ -5,7 +5,7 @@ use super::fields::m31::BaseField;
 use super::fields::qm31::SecureField;
 use super::poly::circle::{CircleEvaluation, CirclePoly};
 use super::poly::BitReversedOrder;
-use super::ColumnVec;
+use super::{ColumnVec, InteractionElements};
 
 pub mod accumulation;
 mod air_ext;
@@ -53,7 +53,15 @@ pub trait Component {
     );
 }
 
-pub trait ComponentProver<B: Backend>: Component {
+pub trait ComponentTraceWriter<B: Backend> {
+    fn write_interaction_trace(
+        &self,
+        trace: &ColumnVec<&CircleEvaluation<B, BaseField, BitReversedOrder>>,
+        elements: &InteractionElements,
+    ) -> ColumnVec<CircleEvaluation<B, BaseField, BitReversedOrder>>;
+}
+
+pub trait ComponentProver<B: Backend>: Component + ComponentTraceWriter<B> {
     /// Evaluates the constraint quotients of the component on the evaluation domain.
     /// Accumulates quotients in `evaluation_accumulator`.
     fn evaluate_constraint_quotients_on_domain(
diff --git a/crates/prover/src/core/mod.rs b/crates/prover/src/core/mod.rs
index a3314ed9d..899c584f6 100644
--- a/crates/prover/src/core/mod.rs
+++ b/crates/prover/src/core/mod.rs
@@ -1,4 +1,5 @@
-use std::ops::{Deref, DerefMut};
+use std::collections::BTreeMap;
+use std::ops::{Deref, DerefMut, Index};
 
 use self::fields::m31::BaseField;
 
@@ -60,4 +61,13 @@ impl<T> DerefMut for ComponentVec<T> {
     }
 }
 
-pub struct InteractionElements(Vec<(String, BaseField)>);
+pub struct InteractionElements(BTreeMap<String, BaseField>);
+
+impl Index<&str> for InteractionElements {
+    type Output = BaseField;
+
+    fn index(&self, index: &str) -> &Self::Output {
+        // TODO(AlonH): Return an error if the key is not found.
+        &self.0[index]
+    }
+}
diff --git a/crates/prover/src/core/prover/mod.rs b/crates/prover/src/core/prover/mod.rs
index ba4b34fb1..dc4739aca 100644
--- a/crates/prover/src/core/prover/mod.rs
+++ b/crates/prover/src/core/prover/mod.rs
@@ -269,15 +269,21 @@ mod tests {
     use num_traits::Zero;
 
     use crate::core::air::accumulation::{DomainEvaluationAccumulator, PointEvaluationAccumulator};
-    use crate::core::air::{Air, AirProver, Component, ComponentProver, ComponentTrace};
+    use crate::core::air::{
+        Air, AirProver, Component, ComponentProver, ComponentTrace, ComponentTraceWriter,
+    };
     use crate::core::backend::cpu::CpuCircleEvaluation;
     use crate::core::backend::CpuBackend;
     use crate::core::circle::{CirclePoint, CirclePointIndex, Coset};
     use crate::core::fields::m31::BaseField;
     use crate::core::fields::qm31::SecureField;
-    use crate::core::poly::circle::{CanonicCoset, CircleDomain, MAX_CIRCLE_DOMAIN_LOG_SIZE};
+    use crate::core::poly::circle::{
+        CanonicCoset, CircleDomain, CircleEvaluation, MAX_CIRCLE_DOMAIN_LOG_SIZE,
+    };
+    use crate::core::poly::BitReversedOrder;
     use crate::core::prover::{prove, ProvingError};
     use crate::core::test_utils::test_channel;
+    use crate::core::{ColumnVec, InteractionElements};
     use crate::qm31;
 
     struct TestAir<C: ComponentProver<CpuBackend>> {
@@ -335,6 +341,16 @@ mod tests {
         }
     }
 
+    impl ComponentTraceWriter<CpuBackend> for TestComponent {
+        fn write_interaction_trace(
+            &self,
+            _trace: &ColumnVec<&CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>>,
+            _elements: &InteractionElements,
+        ) -> ColumnVec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>> {
+            vec![]
+        }
+    }
+
     impl ComponentProver<CpuBackend> for TestComponent {
         fn evaluate_constraint_quotients_on_domain(
             &self,
diff --git a/crates/prover/src/examples/fibonacci/component.rs b/crates/prover/src/examples/fibonacci/component.rs
index c1e1f71d4..b61bcfc4e 100644
--- a/crates/prover/src/examples/fibonacci/component.rs
+++ b/crates/prover/src/examples/fibonacci/component.rs
@@ -4,16 +4,17 @@ use num_traits::One;
 
 use crate::core::air::accumulation::{DomainEvaluationAccumulator, PointEvaluationAccumulator};
 use crate::core::air::mask::shifted_mask_points;
-use crate::core::air::{Component, ComponentProver, ComponentTrace};
+use crate::core::air::{Component, ComponentProver, ComponentTrace, ComponentTraceWriter};
 use crate::core::backend::CpuBackend;
 use crate::core::circle::{CirclePoint, Coset};
 use crate::core::constraints::{coset_vanishing, pair_vanishing};
 use crate::core::fields::m31::BaseField;
 use crate::core::fields::qm31::SecureField;
 use crate::core::fields::{ExtensionOf, FieldExpOps};
-use crate::core::poly::circle::CanonicCoset;
+use crate::core::poly::circle::{CanonicCoset, CircleEvaluation};
+use crate::core::poly::BitReversedOrder;
 use crate::core::utils::bit_reverse_index;
-use crate::core::ColumnVec;
+use crate::core::{ColumnVec, InteractionElements};
 
 pub struct FibonacciComponent {
     pub log_size: u32,
@@ -116,6 +117,16 @@ impl Component for FibonacciComponent {
     }
 }
 
+impl ComponentTraceWriter<CpuBackend> for FibonacciComponent {
+    fn write_interaction_trace(
+        &self,
+        _trace: &ColumnVec<&CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>>,
+        _elements: &InteractionElements,
+    ) -> ColumnVec<CircleEvaluation<CpuBackend, BaseField, BitReversedOrder>> {
+        vec![]
+    }
+}
+
 impl ComponentProver<CpuBackend> for FibonacciComponent {
     fn evaluate_constraint_quotients_on_domain(
         &self,
diff --git a/crates/prover/src/examples/wide_fibonacci/component.rs b/crates/prover/src/examples/wide_fibonacci/component.rs
index b8c9b97c5..2c19edbee 100644
--- a/crates/prover/src/examples/wide_fibonacci/component.rs
+++ b/crates/prover/src/examples/wide_fibonacci/component.rs
@@ -1,17 +1,25 @@
+use itertools::Itertools;
+
 use crate::core::air::accumulation::PointEvaluationAccumulator;
 use crate::core::air::mask::fixed_mask_points;
-use crate::core::air::{Air, Component};
+use crate::core::air::{Air, Component, ComponentTraceWriter};
+use crate::core::backend::CpuBackend;
 use crate::core::circle::CirclePoint;
 use crate::core::constraints::coset_vanishing;
 use crate::core::fields::m31::BaseField;
 use crate::core::fields::qm31::SecureField;
 use crate::core::fields::FieldExpOps;
-use crate::core::poly::circle::CanonicCoset;
-use crate::core::ColumnVec;
+use crate::core::poly::circle::{CanonicCoset, CircleEvaluation};
+use crate::core::poly::BitReversedOrder;
+use crate::core::{ColumnVec, InteractionElements};
+use crate::examples::wide_fibonacci::trace_gen::write_lookup_column;
 
 pub const LOG_N_COLUMNS: usize = 8;
 pub const N_COLUMNS: usize = 1 << LOG_N_COLUMNS;
 
+const ALPHA_ID: &str = "wide_fibonacci_alpha";
+const Z_ID: &str = "wide_fibonacci_z";
+
 /// Component that computes 2^`self.log_n_instances` instances of fibonacci sequences of size
 /// 2^`self.log_fibonacci_size`. The numbers are computes over [N_COLUMNS] trace columns. The
 /// number of rows (i.e the size of the columns) is determined by the parameters above (see
@@ -68,10 +76,7 @@ impl Component for WideFibComponent {
     }
 
     fn interaction_element_ids(&self) -> Vec<String> {
-        vec![
-            "wide_fibonacci_alpha".to_string(),
-            "wide_fibonacci_z".to_string(),
-        ]
+        vec![ALPHA_ID.to_string(), Z_ID.to_string()]
     }
 
     fn evaluate_constraint_quotients_at_point(
@@ -90,6 +95,21 @@ impl Component for WideFibComponent {
     }
 }
 
+impl ComponentTraceWriter<CpuBackend> for WideFibComponent {
+    fn write_interaction_trace(
+        &self,
+        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]);
+        let values = write_lookup_column(&trace_values, alpha, z);
+        let eval = CircleEvaluation::new(interaction_trace_domain, values);
+        vec![eval]
+    }
+}
+
 // Input for the fibonacci claim.
 #[derive(Debug, Clone, Copy)]
 pub struct Input {
diff --git a/crates/prover/src/examples/wide_fibonacci/mod.rs b/crates/prover/src/examples/wide_fibonacci/mod.rs
index cded94425..59486b9ac 100644
--- a/crates/prover/src/examples/wide_fibonacci/mod.rs
+++ b/crates/prover/src/examples/wide_fibonacci/mod.rs
@@ -110,7 +110,8 @@ mod tests {
         let alpha = m31!(7);
         let z = m31!(11);
         let trace = gen_trace(&wide_fib, vec![input]);
-        let lookup_column = write_lookup_column(&trace, alpha, z);
+        let input_trace = trace.iter().map(|values| &values[..]).collect_vec();
+        let lookup_column = write_lookup_column(&input_trace, alpha, z);
 
         assert_constraints_on_lookup_column(&lookup_column, &trace, alpha, z)
     }
diff --git a/crates/prover/src/examples/wide_fibonacci/simd.rs b/crates/prover/src/examples/wide_fibonacci/simd.rs
index 1308d54e3..246e37372 100644
--- a/crates/prover/src/examples/wide_fibonacci/simd.rs
+++ b/crates/prover/src/examples/wide_fibonacci/simd.rs
@@ -4,7 +4,9 @@ use tracing::{span, Level};
 
 use super::component::{WideFibAir, WideFibComponent};
 use crate::core::air::accumulation::DomainEvaluationAccumulator;
-use crate::core::air::{AirProver, Component, ComponentProver, ComponentTrace};
+use crate::core::air::{
+    AirProver, Component, ComponentProver, ComponentTrace, ComponentTraceWriter,
+};
 use crate::core::backend::simd::column::BaseFieldVec;
 use crate::core::backend::simd::m31::{PackedBaseField, LOG_N_LANES};
 use crate::core::backend::simd::qm31::PackedSecureField;
@@ -15,7 +17,7 @@ use crate::core::fields::m31::BaseField;
 use crate::core::fields::{FieldExpOps, FieldOps};
 use crate::core::poly::circle::{CanonicCoset, CircleEvaluation};
 use crate::core::poly::BitReversedOrder;
-use crate::core::ColumnVec;
+use crate::core::{ColumnVec, InteractionElements};
 use crate::examples::wide_fibonacci::component::N_COLUMNS;
 
 impl AirProver<SimdBackend> for WideFibAir {
@@ -50,6 +52,16 @@ pub fn gen_trace(
         .collect_vec()
 }
 
+impl ComponentTraceWriter<SimdBackend> for WideFibComponent {
+    fn write_interaction_trace(
+        &self,
+        _trace: &ColumnVec<&CircleEvaluation<SimdBackend, BaseField, BitReversedOrder>>,
+        _elements: &InteractionElements,
+    ) -> ColumnVec<CircleEvaluation<SimdBackend, BaseField, BitReversedOrder>> {
+        vec![]
+    }
+}
+
 impl ComponentProver<SimdBackend> for WideFibComponent {
     fn evaluate_constraint_quotients_on_domain(
         &self,
diff --git a/crates/prover/src/examples/wide_fibonacci/trace_gen.rs b/crates/prover/src/examples/wide_fibonacci/trace_gen.rs
index c6180b536..2d5ecd148 100644
--- a/crates/prover/src/examples/wide_fibonacci/trace_gen.rs
+++ b/crates/prover/src/examples/wide_fibonacci/trace_gen.rs
@@ -5,7 +5,7 @@ use crate::core::fields::m31::BaseField;
 use crate::core::fields::FieldExpOps;
 use crate::core::utils::shifted_secure_combination;
 
-/// Given a private input, write the trace row for the wide Fibonacci example to dst. Returns the
+/// Writes the trace row for the wide Fibonacci example to dst, given a private input. Returns the
 /// last two elements of the row in case the sequence is continued.
 pub fn write_trace_row(
     dst: &mut [Vec<BaseField>],
@@ -22,8 +22,11 @@ pub fn write_trace_row(
     (dst[n_columns - 2][row_index], dst[n_columns - 1][row_index])
 }
 
+/// Writes and returns the lookup column for the wide Fibonacci example, which is the partial
+/// product of the shifted secure combination of the first two elements in each row divided by the
+/// the shifted secure combination of the last two elements in each row.
 pub fn write_lookup_column(
-    input_trace: &[Vec<BaseField>],
+    input_trace: &[&[BaseField]],
     // TODO(AlonH): Change alpha and z to SecureField.
     alpha: BaseField,
     z: BaseField,