diff --git a/crates/crypto/src/fiat_shamir/default_transcript.rs b/crates/crypto/src/fiat_shamir/default_transcript.rs
index 766c84447..4784e1de7 100644
--- a/crates/crypto/src/fiat_shamir/default_transcript.rs
+++ b/crates/crypto/src/fiat_shamir/default_transcript.rs
@@ -77,7 +77,13 @@ mod tests {
     use super::*;
 
     use alloc::vec::Vec;
-    use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::default_types::FrField;
+    use lambdaworks_math::{
+        elliptic_curve::short_weierstrass::curves::bls12_381::default_types::FrField,
+        field::fields::fft_friendly::{
+            babybear_u32::Babybear31PrimeField,
+            quartic_babybear_u32::Degree4BabyBearU32ExtensionField,
+        },
+    };
 
     #[test]
     fn basic_challenge() {
@@ -116,4 +122,40 @@ mod tests {
             ]
         );
     }
+
+    type FE = FieldElement<Babybear31PrimeField>;
+    type Fp4E = FieldElement<Degree4BabyBearU32ExtensionField>;
+
+    #[test]
+    fn quartic_baby_bear_transcript_distinguish_different_fe() {
+        let mut transcript_1 = DefaultTranscript::<Degree4BabyBearU32ExtensionField>::default();
+        transcript_1.append_field_element(&Fp4E::new([
+            FE::one(),
+            FE::zero(),
+            FE::zero(),
+            FE::zero(),
+        ]));
+        let sample_1 = transcript_1.sample_field_element();
+
+        let mut transcript_2 = DefaultTranscript::<Degree4BabyBearU32ExtensionField>::default();
+        transcript_2.append_field_element(&Fp4E::new([
+            FE::zero(),
+            FE::zero(),
+            FE::zero(),
+            FE::one(),
+        ]));
+        let sample_2 = transcript_2.sample_field_element();
+
+        let mut transcript_3 = DefaultTranscript::<Degree4BabyBearU32ExtensionField>::default();
+        transcript_3.append_field_element(&Fp4E::new([
+            FE::one(),
+            FE::zero(),
+            FE::zero(),
+            FE::zero(),
+        ]));
+        let sample_3 = transcript_3.sample_field_element();
+
+        assert!(sample_1 != sample_2);
+        assert!(sample_1 == sample_3);
+    }
 }
diff --git a/crates/math/src/field/fields/fft_friendly/quartic_babybear_u32.rs b/crates/math/src/field/fields/fft_friendly/quartic_babybear_u32.rs
index 81640818f..571962ac9 100644
--- a/crates/math/src/field/fields/fft_friendly/quartic_babybear_u32.rs
+++ b/crates/math/src/field/fields/fft_friendly/quartic_babybear_u32.rs
@@ -2,7 +2,7 @@ use crate::field::{
     element::FieldElement,
     errors::FieldError,
     fields::fft_friendly::babybear_u32::Babybear31PrimeField,
-    traits::{IsFFTField, IsField, IsSubFieldOf},
+    traits::{HasDefaultTranscript, IsFFTField, IsField, IsSubFieldOf},
 };
 
 use crate::traits::ByteConversion;
@@ -342,6 +342,39 @@ impl IsFFTField for Degree4BabyBearU32ExtensionField {
     ];
 }
 
+impl HasDefaultTranscript for Degree4BabyBearU32ExtensionField {
+    fn get_random_field_element_from_rng(rng: &mut impl rand::Rng) -> FieldElement<Self> {
+        //Babybear Prime p = 2^31 - 2^27 + 1
+        const MODULUS: u32 = 2013265921;
+
+        //Babybear prime needs 31 bits and is represented with 32 bits.
+        //The mask is used to remove the first bit.
+        const MASK: u32 = 0x7FFF_FFFF;
+
+        let mut sample = [0u8; 4];
+
+        let mut coeffs = [
+            FieldElement::zero(),
+            FieldElement::zero(),
+            FieldElement::zero(),
+            FieldElement::zero(),
+        ];
+
+        for coeff in &mut coeffs {
+            loop {
+                rng.fill(&mut sample);
+                let int_sample = u32::from_be_bytes(sample) & MASK;
+                if int_sample < MODULUS {
+                    *coeff = FieldElement::from(&int_sample);
+                    break;
+                }
+            }
+        }
+
+        FieldElement::<Self>::new(coeffs)
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
diff --git a/crates/provers/stark/src/examples/fibonacci_rap.rs b/crates/provers/stark/src/examples/fibonacci_rap.rs
index 90581232c..78acefdc5 100644
--- a/crates/provers/stark/src/examples/fibonacci_rap.rs
+++ b/crates/provers/stark/src/examples/fibonacci_rap.rs
@@ -305,11 +305,9 @@ pub fn fibonacci_rap_trace<F: IsFFTField>(
     let mut trace_cols = vec![fib_seq, fib_permuted];
     resize_to_next_power_of_two(&mut trace_cols);
 
-    let mut trace = TraceTable::allocate_with_zeros(trace_cols[0].len(), 2, 1, 1);
-    for i in 0..trace.num_rows() {
-        trace.set_main(i, 0, trace_cols[0][i].clone());
-        trace.set_main(i, 1, trace_cols[1][i].clone());
-    }
+    let aux_columns = vec![vec![FieldElement::<F>::zero(); trace_cols[0].len()]];
+
+    let trace: TraceTable<F, F> = TraceTable::from_columns(trace_cols, aux_columns, 1);
 
     trace
 }