diff --git a/crates/brainfuck_prover/src/brainfuck_air/mod.rs b/crates/brainfuck_prover/src/brainfuck_air/mod.rs
index df61c64..12160fa 100644
--- a/crates/brainfuck_prover/src/brainfuck_air/mod.rs
+++ b/crates/brainfuck_prover/src/brainfuck_air/mod.rs
@@ -1,4 +1,5 @@
 use crate::components::{
+    instruction::table::InstructionElements,
     io::table::IoElements,
     memory::{
         self,
@@ -66,6 +67,7 @@ pub struct BrainfuckInteractionElements {
     pub input_lookup_elements: IoElements,
     pub output_lookup_elements: IoElements,
     pub memory_lookup_elements: MemoryElements,
+    pub instruction_lookup_elements: InstructionElements,
 }
 
 impl BrainfuckInteractionElements {
@@ -76,6 +78,7 @@ impl BrainfuckInteractionElements {
             input_lookup_elements: IoElements::draw(channel),
             output_lookup_elements: IoElements::draw(channel),
             memory_lookup_elements: MemoryElements::draw(channel),
+            instruction_lookup_elements: InstructionElements::draw(channel),
         }
     }
 }
diff --git a/crates/brainfuck_prover/src/components/instruction/table.rs b/crates/brainfuck_prover/src/components/instruction/table.rs
index 0c483fd..c1c6df2 100644
--- a/crates/brainfuck_prover/src/components/instruction/table.rs
+++ b/crates/brainfuck_prover/src/components/instruction/table.rs
@@ -3,13 +3,17 @@ use brainfuck_vm::{
     instruction::VALID_INSTRUCTIONS_BF, machine::ProgramMemory, registers::Registers,
 };
 use num_traits::Zero;
-use stwo_prover::core::{
-    backend::{
-        simd::{column::BaseColumn, m31::LOG_N_LANES},
-        Column,
+use stwo_prover::{
+    constraint_framework::{logup::LookupElements, Relation, RelationEFTraitBound},
+    core::{
+        backend::{
+            simd::{column::BaseColumn, m31::LOG_N_LANES},
+            Column,
+        },
+        channel::Channel,
+        fields::m31::BaseField,
+        poly::circle::{CanonicCoset, CircleEvaluation},
     },
-    fields::m31::BaseField,
-    poly::circle::{CanonicCoset, CircleEvaluation},
 };
 
 /// Represents the Instruction Table, which holds the required registers
@@ -349,6 +353,59 @@ impl TraceColumn for InstructionColumn {
     }
 }
 
+/// The number of random elements necessary for the Instruction lookup argument.
+const INSTRUCTION_LOOKUP_ELEMENTS: usize = 3;
+
+/// The interaction elements are drawn for the extension column of the Memory component.
+///
+/// The logUp protocol uses these elements to combine the values of the different
+/// registers of the main trace to create a random linear combination
+/// of them, and use it in the denominator of the fractions in the logUp protocol.
+///
+/// There are 3 lookup elements in the Memory component, as only the 'real' registers
+/// are used: `clk`, `mp` and `mv`. `d` is used to eventually nullify the numerator.
+#[derive(Clone, Debug, Eq, PartialEq)]
+pub struct InstructionElements(LookupElements<INSTRUCTION_LOOKUP_ELEMENTS>);
+
+impl InstructionElements {
+    /// Provides dummy lookup elements.
+    pub fn dummy() -> Self {
+        Self(LookupElements::dummy())
+    }
+
+    /// Draw random elements from the Fiat-Shamir [`Channel`].
+    ///
+    /// These elements are randomly secured, and will be use
+    /// to generate the interaction trace with the logUp protocol.
+    pub fn draw(channel: &mut impl Channel) -> Self {
+        Self(LookupElements::draw(channel))
+    }
+}
+
+impl<F: Clone, EF: RelationEFTraitBound<F>> Relation<F, EF> for InstructionElements {
+    /// Combine multiple values from a basefield (e.g. [`BaseField`])
+    /// and combine them to a value from an extension field (e.g. [`PackedSecureField`])
+    ///
+    /// This is used when computing the interaction values from the main trace values.
+    fn combine(&self, values: &[F]) -> EF {
+        values
+            .iter()
+            .zip(self.0.alpha_powers)
+            .fold(EF::zero(), |acc, (value, power)| acc + EF::from(power) * value.clone()) -
+            self.0.z.into()
+    }
+
+    /// Returns the name of the struct.
+    fn get_name(&self) -> &str {
+        stringify!(InstructionElements)
+    }
+
+    /// Returns the number interaction elements.
+    fn get_size(&self) -> usize {
+        INSTRUCTION_LOOKUP_ELEMENTS
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;