diff --git a/src/core/air/evaluation.rs b/src/core/air/evaluation.rs
index fc7bdac5e..9e7f8d36c 100644
--- a/src/core/air/evaluation.rs
+++ b/src/core/air/evaluation.rs
@@ -3,10 +3,10 @@
 //! Given a random alpha, the combined polynomial is defined as
 //!   f(p) = sum_i alpha^{N-1-i} u_i (P).
 use crate::core::backend::cpu::CPUCircleEvaluation;
-use crate::core::backend::{Backend, CPUBackend};
+use crate::core::backend::{Backend, CPUBackend, Col, Column};
 use crate::core::fields::m31::BaseField;
 use crate::core::fields::qm31::SecureField;
-use crate::core::fields::{Col, Column, ExtensionOf, FieldExpOps};
+use crate::core::fields::{ExtensionOf, FieldExpOps};
 use crate::core::poly::circle::{CircleDomain, CirclePoly, SecureCirclePoly};
 use crate::core::poly::BitReversedOrder;
 use crate::core::utils::IteratorMutExt;
diff --git a/src/core/backend/avx512/bit_reverse.rs b/src/core/backend/avx512/bit_reverse.rs
index 42a939564..83a68d01e 100644
--- a/src/core/backend/avx512/bit_reverse.rs
+++ b/src/core/backend/avx512/bit_reverse.rs
@@ -141,8 +141,8 @@ mod tests {
     use super::bit_reverse16;
     use crate::core::backend::avx512::bit_reverse::bit_reverse_m31;
     use crate::core::backend::avx512::BaseFieldVec;
+    use crate::core::backend::Column;
     use crate::core::fields::m31::BaseField;
-    use crate::core::fields::Column;
     use crate::core::utils::bit_reverse;
 
     #[test]
diff --git a/src/core/backend/avx512/circle.rs b/src/core/backend/avx512/circle.rs
index c491571c1..c8e085ff9 100644
--- a/src/core/backend/avx512/circle.rs
+++ b/src/core/backend/avx512/circle.rs
@@ -5,10 +5,10 @@ use super::m31::PackedBaseField;
 use super::{as_cpu_vec, AVX512Backend, VECS_LOG_SIZE};
 use crate::core::backend::avx512::fft::rfft;
 use crate::core::backend::avx512::BaseFieldVec;
-use crate::core::backend::CPUBackend;
+use crate::core::backend::{CPUBackend, Col};
 use crate::core::circle::{CirclePoint, Coset};
 use crate::core::fields::m31::BaseField;
-use crate::core::fields::{Col, ExtensionOf, FieldExpOps};
+use crate::core::fields::{ExtensionOf, FieldExpOps};
 use crate::core::poly::circle::{
     CanonicCoset, CircleDomain, CircleEvaluation, CirclePoly, PolyOps,
 };
@@ -178,8 +178,8 @@ impl PolyOps for AVX512Backend {
 mod tests {
     use crate::core::backend::avx512::fft::{CACHED_FFT_LOG_SIZE, MIN_FFT_LOG_SIZE};
     use crate::core::backend::avx512::AVX512Backend;
+    use crate::core::backend::Column;
     use crate::core::fields::m31::BaseField;
-    use crate::core::fields::Column;
     use crate::core::poly::circle::{CanonicCoset, CircleDomain, CircleEvaluation, CirclePoly};
     use crate::core::poly::{BitReversedOrder, NaturalOrder};
 
diff --git a/src/core/backend/avx512/fft/ifft.rs b/src/core/backend/avx512/fft/ifft.rs
index ed1823c66..814812122 100644
--- a/src/core/backend/avx512/fft/ifft.rs
+++ b/src/core/backend/avx512/fft/ifft.rs
@@ -522,9 +522,9 @@ mod tests {
     use crate::core::backend::avx512::m31::PackedBaseField;
     use crate::core::backend::avx512::BaseFieldVec;
     use crate::core::backend::cpu::CPUCircleEvaluation;
+    use crate::core::backend::Column;
     use crate::core::fft::ibutterfly;
     use crate::core::fields::m31::BaseField;
-    use crate::core::fields::Column;
     use crate::core::poly::circle::{CanonicCoset, CircleDomain};
 
     #[test]
diff --git a/src/core/backend/avx512/fft/rfft.rs b/src/core/backend/avx512/fft/rfft.rs
index 33d57c6da..75a2730a4 100644
--- a/src/core/backend/avx512/fft/rfft.rs
+++ b/src/core/backend/avx512/fft/rfft.rs
@@ -494,9 +494,9 @@ mod tests {
     use super::*;
     use crate::core::backend::avx512::{BaseFieldVec, PackedBaseField};
     use crate::core::backend::cpu::CPUCirclePoly;
+    use crate::core::backend::Column;
     use crate::core::fft::butterfly;
     use crate::core::fields::m31::BaseField;
-    use crate::core::fields::Column;
     use crate::core::poly::circle::{CanonicCoset, CircleDomain};
 
     #[test]
diff --git a/src/core/backend/avx512/mod.rs b/src/core/backend/avx512/mod.rs
index 766ece4a5..e84a2c02d 100644
--- a/src/core/backend/avx512/mod.rs
+++ b/src/core/backend/avx512/mod.rs
@@ -10,8 +10,9 @@ use num_traits::Zero;
 
 use self::bit_reverse::bit_reverse_m31;
 pub use self::m31::{PackedBaseField, K_BLOCK_SIZE};
+use super::{Column, ColumnOps};
 use crate::core::fields::m31::BaseField;
-use crate::core::fields::{Column, FieldExpOps, FieldOps};
+use crate::core::fields::{FieldExpOps, FieldOps};
 use crate::core::utils;
 
 const VECS_LOG_SIZE: usize = 4;
@@ -46,7 +47,7 @@ impl BaseFieldVec {
     }
 }
 
-impl FieldOps<BaseField> for AVX512Backend {
+impl ColumnOps<BaseField> for AVX512Backend {
     type Column = BaseFieldVec;
 
     fn bit_reverse_column(column: &mut Self::Column) {
@@ -57,7 +58,9 @@ impl FieldOps<BaseField> for AVX512Backend {
         }
         bit_reverse_m31(&mut column.data);
     }
+}
 
+impl FieldOps<BaseField> for AVX512Backend {
     fn batch_inverse(column: &Self::Column, dst: &mut Self::Column) {
         PackedBaseField::batch_inverse(&column.data, &mut dst.data);
     }
@@ -130,8 +133,8 @@ mod tests {
     use rand::{Rng, SeedableRng};
 
     use super::*;
+    use crate::core::backend::{Col, Column};
     use crate::core::fields::m31::P;
-    use crate::core::fields::{Col, Column};
 
     type B = AVX512Backend;
 
diff --git a/src/core/backend/cpu/circle.rs b/src/core/backend/cpu/circle.rs
index be2b9abf2..9d6f9360d 100644
--- a/src/core/backend/cpu/circle.rs
+++ b/src/core/backend/cpu/circle.rs
@@ -1,10 +1,11 @@
 use num_traits::Zero;
 
 use super::CPUBackend;
+use crate::core::backend::{Col, ColumnOps};
 use crate::core::circle::{CirclePoint, Coset};
 use crate::core::fft::{butterfly, ibutterfly};
 use crate::core::fields::m31::BaseField;
-use crate::core::fields::{Col, ExtensionOf, FieldExpOps, FieldOps};
+use crate::core::fields::{ExtensionOf, FieldExpOps};
 use crate::core::poly::circle::{
     CanonicCoset, CircleDomain, CircleEvaluation, CirclePoly, PolyOps,
 };
diff --git a/src/core/backend/cpu/mod.rs b/src/core/backend/cpu/mod.rs
index 997d0ae3d..9d32bbfbc 100644
--- a/src/core/backend/cpu/mod.rs
+++ b/src/core/backend/cpu/mod.rs
@@ -3,8 +3,8 @@ mod fri;
 
 use std::fmt::Debug;
 
-use super::{Backend, FieldOps};
-use crate::core::fields::{Column, Field};
+use super::{Backend, Column, ColumnOps, FieldOps};
+use crate::core::fields::Field;
 use crate::core::poly::circle::{CircleEvaluation, CirclePoly};
 use crate::core::poly::line::LineEvaluation;
 use crate::core::utils::bit_reverse;
@@ -14,13 +14,15 @@ pub struct CPUBackend;
 
 impl Backend for CPUBackend {}
 
-impl<F: Field> FieldOps<F> for CPUBackend {
-    type Column = Vec<F>;
+impl<T: Debug + Clone + Default> ColumnOps<T> for CPUBackend {
+    type Column = Vec<T>;
 
     fn bit_reverse_column(column: &mut Self::Column) {
         bit_reverse(column)
     }
+}
 
+impl<F: Field> FieldOps<F> for CPUBackend {
     /// Batch inversion using the Montgomery's trick.
     // TODO(Ohad): Benchmark this function.
     fn batch_inverse(column: &Self::Column, dst: &mut Self::Column) {
@@ -28,18 +30,18 @@ impl<F: Field> FieldOps<F> for CPUBackend {
     }
 }
 
-impl<F: Field> Column<F> for Vec<F> {
+impl<T: Debug + Clone + Default> Column<T> for Vec<T> {
     fn zeros(len: usize) -> Self {
-        vec![F::zero(); len]
+        vec![T::default(); len]
     }
-    fn to_vec(&self) -> Vec<F> {
+    fn to_vec(&self) -> Vec<T> {
         self.clone()
     }
     fn len(&self) -> usize {
         self.len()
     }
-    fn at(&self, index: usize) -> F {
-        self[index]
+    fn at(&self, index: usize) -> T {
+        self[index].clone()
     }
 }
 
@@ -54,9 +56,9 @@ mod tests {
     use rand::prelude::*;
     use rand::rngs::SmallRng;
 
-    use crate::core::backend::{CPUBackend, FieldOps};
+    use crate::core::backend::{CPUBackend, Column, FieldOps};
     use crate::core::fields::qm31::QM31;
-    use crate::core::fields::{Column, FieldExpOps};
+    use crate::core::fields::FieldExpOps;
 
     #[test]
     fn batch_inverse_test() {
diff --git a/src/core/backend/mod.rs b/src/core/backend/mod.rs
index 6e74f9bf2..026fbacc4 100644
--- a/src/core/backend/mod.rs
+++ b/src/core/backend/mod.rs
@@ -14,3 +14,26 @@ pub trait Backend:
     Copy + Clone + Debug + FieldOps<BaseField> + FieldOps<SecureField> + PolyOps
 {
 }
+
+pub trait ColumnOps<T> {
+    type Column: Column<T>;
+    fn bit_reverse_column(column: &mut Self::Column);
+}
+
+pub type Col<B, T> = <B as ColumnOps<T>>::Column;
+
+// TODO(spapini): Consider removing the generic parameter and only support BaseField.
+pub trait Column<T>: Clone + Debug + FromIterator<T> {
+    /// Creates a new column of zeros with the given length.
+    fn zeros(len: usize) -> Self;
+    /// Returns a cpu vector of the column.
+    fn to_vec(&self) -> Vec<T>;
+    /// Returns the length of the column.
+    fn len(&self) -> usize;
+    /// Returns true if the column is empty.
+    fn is_empty(&self) -> bool {
+        self.len() == 0
+    }
+    /// Retrieves the element at the given index.
+    fn at(&self, index: usize) -> T;
+}
diff --git a/src/core/fields/mod.rs b/src/core/fields/mod.rs
index 44a7c1cca..72693b5fa 100644
--- a/src/core/fields/mod.rs
+++ b/src/core/fields/mod.rs
@@ -3,15 +3,14 @@ use std::ops::{Mul, MulAssign, Neg};
 
 use num_traits::{NumAssign, NumAssignOps, NumOps, One};
 
+use super::backend::ColumnOps;
+
 #[cfg(target_arch = "x86_64")]
 pub mod cm31;
 pub mod m31;
 pub mod qm31;
 
-pub trait FieldOps<F: Field> {
-    type Column: Column<F>;
-    fn bit_reverse_column(column: &mut Self::Column);
-
+pub trait FieldOps<F: Field>: ColumnOps<F> {
     // TODO(Ohad): change to use a mutable slice.
     fn batch_inverse(column: &Self::Column, dst: &mut Self::Column);
 }
@@ -95,29 +94,12 @@ fn batch_inverse_classic<T: FieldExpOps>(column: &[T], dst: &mut [T]) {
     dst[0] = curr_inverse;
 }
 
-pub type Col<B, F> = <B as FieldOps<F>>::Column;
-
-// TODO(spapini): Consider removing the generic parameter and only support BaseField.
-pub trait Column<F: Field>: Clone + Debug + FromIterator<F> {
-    /// Creates a new column of zeros with the given length.
-    fn zeros(len: usize) -> Self;
-    /// Returns a cpu vector of the column.
-    fn to_vec(&self) -> Vec<F>;
-    /// Returns the length of the column.
-    fn len(&self) -> usize;
-    /// Returns true if the column is empty.
-    fn is_empty(&self) -> bool {
-        self.len() == 0
-    }
-    /// Retrieves the element at the given index.
-    fn at(&self, index: usize) -> F;
-}
-
 pub trait Field:
     NumAssign
     + Neg<Output = Self>
     + ComplexConjugate
     + Copy
+    + Default
     + Debug
     + Display
     + PartialOrd
diff --git a/src/core/fri.rs b/src/core/fri.rs
index da8dc588d..b7f8971f4 100644
--- a/src/core/fri.rs
+++ b/src/core/fri.rs
@@ -22,8 +22,8 @@ use super::queries::{Queries, SparseSubCircleDomain};
 use crate::commitment_scheme::hasher::Hasher;
 use crate::commitment_scheme::merkle_decommitment::MerkleDecommitment;
 use crate::commitment_scheme::merkle_tree::MerkleTree;
+use crate::core::backend::Column;
 use crate::core::circle::Coset;
-use crate::core::fields::Column;
 use crate::core::poly::line::LineDomain;
 use crate::core::utils::bit_reverse_index;
 
diff --git a/src/core/poly/circle/evaluation.rs b/src/core/poly/circle/evaluation.rs
index f40b07aa5..5c52f953d 100644
--- a/src/core/poly/circle/evaluation.rs
+++ b/src/core/poly/circle/evaluation.rs
@@ -3,9 +3,10 @@ use std::ops::{Deref, Index};
 
 use super::{CanonicCoset, CircleDomain, CirclePoly, PolyOps};
 use crate::core::backend::cpu::CPUCircleEvaluation;
+use crate::core::backend::{Col, Column};
 use crate::core::circle::{CirclePointIndex, Coset};
 use crate::core::fields::m31::BaseField;
-use crate::core::fields::{Col, Column, ExtensionOf, FieldOps};
+use crate::core::fields::{ExtensionOf, FieldOps};
 use crate::core::poly::twiddles::TwiddleTree;
 use crate::core::poly::{BitReversedOrder, NaturalOrder};
 use crate::core::utils::bit_reverse_index;
diff --git a/src/core/poly/circle/ops.rs b/src/core/poly/circle/ops.rs
index ac49eb5cf..1e9479f10 100644
--- a/src/core/poly/circle/ops.rs
+++ b/src/core/poly/circle/ops.rs
@@ -1,7 +1,8 @@
 use super::{CanonicCoset, CircleDomain, CircleEvaluation, CirclePoly};
+use crate::core::backend::Col;
 use crate::core::circle::{CirclePoint, Coset};
 use crate::core::fields::m31::BaseField;
-use crate::core::fields::{Col, ExtensionOf, FieldOps};
+use crate::core::fields::{ExtensionOf, FieldOps};
 use crate::core::poly::twiddles::TwiddleTree;
 use crate::core::poly::BitReversedOrder;
 
diff --git a/src/core/poly/circle/poly.rs b/src/core/poly/circle/poly.rs
index e48f3cbba..906f8a0a8 100644
--- a/src/core/poly/circle/poly.rs
+++ b/src/core/poly/circle/poly.rs
@@ -1,7 +1,8 @@
 use super::{CircleDomain, CircleEvaluation, PolyOps};
+use crate::core::backend::{Col, Column};
 use crate::core::circle::CirclePoint;
 use crate::core::fields::m31::BaseField;
-use crate::core::fields::{Col, Column, ExtensionOf, FieldOps};
+use crate::core::fields::{ExtensionOf, FieldOps};
 use crate::core::poly::twiddles::TwiddleTree;
 use crate::core::poly::BitReversedOrder;
 
diff --git a/src/core/poly/line.rs b/src/core/poly/line.rs
index b9029d03f..e369401a0 100644
--- a/src/core/poly/line.rs
+++ b/src/core/poly/line.rs
@@ -9,10 +9,11 @@ use num_traits::Zero;
 use super::utils::fold;
 use super::{BitReversedOrder, NaturalOrder};
 use crate::core::backend::cpu::CPULineEvaluation;
+use crate::core::backend::{Col, Column};
 use crate::core::circle::{CirclePoint, Coset, CosetIterator};
 use crate::core::fft::{butterfly, ibutterfly};
 use crate::core::fields::m31::BaseField;
-use crate::core::fields::{Col, Column, ExtensionOf, Field, FieldExpOps, FieldOps};
+use crate::core::fields::{ExtensionOf, Field, FieldExpOps, FieldOps};
 use crate::core::poly::utils::repeat_value;
 use crate::core::utils::bit_reverse;