diff --git a/src/core/backend/cpu/mod.rs b/src/core/backend/cpu/mod.rs
index 9d32bbfbc..5927165d0 100644
--- a/src/core/backend/cpu/mod.rs
+++ b/src/core/backend/cpu/mod.rs
@@ -1,5 +1,6 @@
 mod circle;
 mod fri;
+pub mod quotients;
 
 use std::fmt::Debug;
 
diff --git a/src/core/backend/cpu/quotients.rs b/src/core/backend/cpu/quotients.rs
new file mode 100644
index 000000000..3b90ff41c
--- /dev/null
+++ b/src/core/backend/cpu/quotients.rs
@@ -0,0 +1,45 @@
+use num_traits::Zero;
+
+use super::CPUBackend;
+use crate::core::air::accumulation::ColumnAccumulator;
+use crate::core::backend::Col;
+use crate::core::commitment_scheme::quotients::{BatchedColumnOpenings, QuotientOps};
+use crate::core::constraints::pair_vanishing;
+use crate::core::fields::m31::BaseField;
+use crate::core::fields::qm31::SecureField;
+use crate::core::fields::{ComplexConjugate, FieldExpOps};
+use crate::core::poly::circle::CircleDomain;
+use crate::core::utils::bit_reverse_index;
+
+impl QuotientOps for CPUBackend {
+    fn accumulate_quotients(
+        domain: CircleDomain,
+        mut accum: ColumnAccumulator<'_, Self>,
+        columns: &[Col<Self, BaseField>],
+        random_coeff: SecureField,
+        openings: &[BatchedColumnOpenings],
+    ) {
+        for row in 0..domain.size() {
+            let domain_point = domain.at(bit_reverse_index(row, domain.log_size()));
+            let mut row_accumlator = SecureField::zero();
+            for opening in openings {
+                let mut numerator = SecureField::zero();
+                for (column_index, open_value) in &opening.column_indices_and_values {
+                    let column = &columns[*column_index];
+                    let value = column[row];
+                    numerator = numerator * random_coeff + (value - *open_value);
+                }
+
+                let denominator = pair_vanishing(
+                    opening.point,
+                    opening.point.complex_conjugate(),
+                    domain_point.into_ef(),
+                );
+
+                row_accumlator *= random_coeff.pow(opening.column_indices_and_values.len() as u128)
+                    + numerator / denominator;
+            }
+            accum.accumulate(row, row_accumlator);
+        }
+    }
+}
diff --git a/src/core/commitment_scheme/mod.rs b/src/core/commitment_scheme/mod.rs
index 7131d1b9d..ae61d794e 100644
--- a/src/core/commitment_scheme/mod.rs
+++ b/src/core/commitment_scheme/mod.rs
@@ -5,6 +5,7 @@
 //! the unique decoding regime. This is enough for a STARK proof though, where we onyl want to imply
 //! the existence of such polynomials, and re ok with having a small decoding list.
 
+pub mod quotients;
 mod utils;
 
 use std::iter::zip;
diff --git a/src/core/commitment_scheme/quotients.rs b/src/core/commitment_scheme/quotients.rs
new file mode 100644
index 000000000..f1707b091
--- /dev/null
+++ b/src/core/commitment_scheme/quotients.rs
@@ -0,0 +1,21 @@
+use crate::core::air::accumulation::ColumnAccumulator;
+use crate::core::backend::{Backend, Col};
+use crate::core::circle::CirclePoint;
+use crate::core::fields::m31::BaseField;
+use crate::core::fields::qm31::SecureField;
+use crate::core::poly::circle::CircleDomain;
+
+pub trait QuotientOps: Backend {
+    fn accumulate_quotients(
+        domain: CircleDomain,
+        accum: ColumnAccumulator<'_, Self>,
+        columns: &[Col<Self, BaseField>],
+        random_coeff: SecureField,
+        openings: &[BatchedColumnOpenings],
+    );
+}
+
+pub struct BatchedColumnOpenings {
+    pub point: CirclePoint<SecureField>,
+    pub column_indices_and_values: Vec<(usize, SecureField)>,
+}