diff --git a/backends/tfhe-cuda-backend/cuda/include/ciphertext.h b/backends/tfhe-cuda-backend/cuda/include/ciphertext.h
index b3978834a9..a5aa671628 100644
--- a/backends/tfhe-cuda-backend/cuda/include/ciphertext.h
+++ b/backends/tfhe-cuda-backend/cuda/include/ciphertext.h
@@ -18,7 +18,7 @@ void cuda_convert_lwe_ciphertext_vector_to_cpu_64(void *stream,
 void cuda_glwe_sample_extract_64(void *stream, uint32_t gpu_index,
                                  void *lwe_array_out, void const *glwe_array_in,
                                  uint32_t const *nth_array, uint32_t num_nths,
-                                 uint32_t glwe_dimension,
+                                 uint32_t lwe_per_glwe, uint32_t glwe_dimension,
                                  uint32_t polynomial_size);
 }
 #endif
diff --git a/backends/tfhe-cuda-backend/cuda/src/crypto/ciphertext.cu b/backends/tfhe-cuda-backend/cuda/src/crypto/ciphertext.cu
index 90d1ca35f3..202df829a4 100644
--- a/backends/tfhe-cuda-backend/cuda/src/crypto/ciphertext.cu
+++ b/backends/tfhe-cuda-backend/cuda/src/crypto/ciphertext.cu
@@ -24,7 +24,7 @@ void cuda_convert_lwe_ciphertext_vector_to_cpu_64(void *stream,
 void cuda_glwe_sample_extract_64(void *stream, uint32_t gpu_index,
                                  void *lwe_array_out, void const *glwe_array_in,
                                  uint32_t const *nth_array, uint32_t num_nths,
-                                 uint32_t glwe_dimension,
+                                 uint32_t lwe_per_glwe, uint32_t glwe_dimension,
                                  uint32_t polynomial_size) {
 
   switch (polynomial_size) {
@@ -32,43 +32,43 @@ void cuda_glwe_sample_extract_64(void *stream, uint32_t gpu_index,
     host_sample_extract<uint64_t, AmortizedDegree<256>>(
         static_cast<cudaStream_t>(stream), gpu_index, (uint64_t *)lwe_array_out,
         (uint64_t const *)glwe_array_in, (uint32_t const *)nth_array, num_nths,
-        glwe_dimension);
+        lwe_per_glwe, glwe_dimension);
     break;
   case 512:
     host_sample_extract<uint64_t, AmortizedDegree<512>>(
         static_cast<cudaStream_t>(stream), gpu_index, (uint64_t *)lwe_array_out,
         (uint64_t const *)glwe_array_in, (uint32_t const *)nth_array, num_nths,
-        glwe_dimension);
+        lwe_per_glwe, glwe_dimension);
     break;
   case 1024:
     host_sample_extract<uint64_t, AmortizedDegree<1024>>(
         static_cast<cudaStream_t>(stream), gpu_index, (uint64_t *)lwe_array_out,
         (uint64_t const *)glwe_array_in, (uint32_t const *)nth_array, num_nths,
-        glwe_dimension);
+        lwe_per_glwe, glwe_dimension);
     break;
   case 2048:
     host_sample_extract<uint64_t, AmortizedDegree<2048>>(
         static_cast<cudaStream_t>(stream), gpu_index, (uint64_t *)lwe_array_out,
         (uint64_t const *)glwe_array_in, (uint32_t const *)nth_array, num_nths,
-        glwe_dimension);
+        lwe_per_glwe, glwe_dimension);
     break;
   case 4096:
     host_sample_extract<uint64_t, AmortizedDegree<4096>>(
         static_cast<cudaStream_t>(stream), gpu_index, (uint64_t *)lwe_array_out,
         (uint64_t const *)glwe_array_in, (uint32_t const *)nth_array, num_nths,
-        glwe_dimension);
+        lwe_per_glwe, glwe_dimension);
     break;
   case 8192:
     host_sample_extract<uint64_t, AmortizedDegree<8192>>(
         static_cast<cudaStream_t>(stream), gpu_index, (uint64_t *)lwe_array_out,
         (uint64_t const *)glwe_array_in, (uint32_t const *)nth_array, num_nths,
-        glwe_dimension);
+        lwe_per_glwe, glwe_dimension);
     break;
   case 16384:
     host_sample_extract<uint64_t, AmortizedDegree<16384>>(
         static_cast<cudaStream_t>(stream), gpu_index, (uint64_t *)lwe_array_out,
         (uint64_t const *)glwe_array_in, (uint32_t const *)nth_array, num_nths,
-        glwe_dimension);
+        lwe_per_glwe, glwe_dimension);
     break;
   default:
     PANIC("Cuda error: unsupported polynomial size. Supported "
diff --git a/backends/tfhe-cuda-backend/cuda/src/crypto/ciphertext.cuh b/backends/tfhe-cuda-backend/cuda/src/crypto/ciphertext.cuh
index 3ccda68731..d33fd83019 100644
--- a/backends/tfhe-cuda-backend/cuda/src/crypto/ciphertext.cuh
+++ b/backends/tfhe-cuda-backend/cuda/src/crypto/ciphertext.cuh
@@ -28,7 +28,7 @@ void cuda_convert_lwe_ciphertext_vector_to_cpu(cudaStream_t stream,
 
 template <typename Torus, class params>
 __global__ void sample_extract(Torus *lwe_array_out, Torus const *glwe_array_in,
-                               uint32_t const *nth_array,
+                               uint32_t const *nth_array, uint32_t lwe_per_glwe,
                                uint32_t glwe_dimension) {
 
   const int input_id = blockIdx.x;
@@ -39,28 +39,29 @@ __global__ void sample_extract(Torus *lwe_array_out, Torus const *glwe_array_in,
   auto lwe_out = lwe_array_out + input_id * lwe_output_size;
 
   // We assume each GLWE will store the first polynomial_size inputs
-  uint32_t lwe_per_glwe = params::degree;
   auto glwe_in = glwe_array_in + (input_id / lwe_per_glwe) * glwe_input_size;
 
-  // nth is ensured to be in [0, lwe_per_glwe)
-  auto nth = nth_array[input_id] % lwe_per_glwe;
+  // nth is ensured to be in [0, params::degree)
+  auto nth = nth_array[input_id] % params::degree;
 
   sample_extract_mask<Torus, params>(lwe_out, glwe_in, glwe_dimension, nth);
   sample_extract_body<Torus, params>(lwe_out, glwe_in, glwe_dimension, nth);
 }
 
+// lwe_per_glwe LWEs will be extracted per GLWE ciphertext, thus we need to have
+// enough indexes
 template <typename Torus, class params>
-__host__ void host_sample_extract(cudaStream_t stream, uint32_t gpu_index,
-                                  Torus *lwe_array_out,
-                                  Torus const *glwe_array_in,
-                                  uint32_t const *nth_array, uint32_t num_nths,
-                                  uint32_t glwe_dimension) {
+__host__ void
+host_sample_extract(cudaStream_t stream, uint32_t gpu_index,
+                    Torus *lwe_array_out, Torus const *glwe_array_in,
+                    uint32_t const *nth_array, uint32_t num_nths,
+                    uint32_t lwe_per_glwe, uint32_t glwe_dimension) {
   cuda_set_device(gpu_index);
 
   dim3 grid(num_nths);
   dim3 thds(params::degree / params::opt);
   sample_extract<Torus, params><<<grid, thds, 0, stream>>>(
-      lwe_array_out, glwe_array_in, nth_array, glwe_dimension);
+      lwe_array_out, glwe_array_in, nth_array, lwe_per_glwe, glwe_dimension);
   check_cuda_error(cudaGetLastError());
 }
 
diff --git a/backends/tfhe-cuda-backend/cuda/src/integer/compression/compression.cuh b/backends/tfhe-cuda-backend/cuda/src/integer/compression/compression.cuh
index ddbaf173dc..54d60f3b6e 100644
--- a/backends/tfhe-cuda-backend/cuda/src/integer/compression/compression.cuh
+++ b/backends/tfhe-cuda-backend/cuda/src/integer/compression/compression.cuh
@@ -279,10 +279,10 @@ __host__ void host_integer_decompress(
     extracted_glwe = max_idx_and_glwe.second;
 
     auto num_lwes = last_idx + 1 - current_idx;
-    cuda_glwe_sample_extract_64(streams[0], gpu_indexes[0], extracted_lwe,
-                                extracted_glwe, d_indexes_array_chunk, num_lwes,
-                                compression_params.glwe_dimension,
-                                compression_params.polynomial_size);
+    cuda_glwe_sample_extract_64(
+        streams[0], gpu_indexes[0], extracted_lwe, extracted_glwe,
+        d_indexes_array_chunk, num_lwes, compression_params.polynomial_size,
+        compression_params.glwe_dimension, compression_params.polynomial_size);
     d_indexes_array_chunk += num_lwes;
     extracted_lwe += num_lwes * lwe_accumulator_size;
     current_idx = last_idx;
diff --git a/backends/tfhe-cuda-backend/src/bindings.rs b/backends/tfhe-cuda-backend/src/bindings.rs
index 58d3ffebab..f57e3ebdc3 100644
--- a/backends/tfhe-cuda-backend/src/bindings.rs
+++ b/backends/tfhe-cuda-backend/src/bindings.rs
@@ -30,6 +30,7 @@ unsafe extern "C" {
         glwe_array_in: *const ffi::c_void,
         nth_array: *const u32,
         num_nths: u32,
+        lwe_per_glwe: u32,
         glwe_dimension: u32,
         polynomial_size: u32,
     );
diff --git a/tfhe/src/core_crypto/gpu/algorithms/glwe_sample_extraction.rs b/tfhe/src/core_crypto/gpu/algorithms/glwe_sample_extraction.rs
index 216c73dc8e..ed6de52fb8 100644
--- a/tfhe/src/core_crypto/gpu/algorithms/glwe_sample_extraction.rs
+++ b/tfhe/src/core_crypto/gpu/algorithms/glwe_sample_extraction.rs
@@ -13,6 +13,7 @@ pub unsafe fn cuda_extract_lwe_samples_from_glwe_ciphertext_list_async<Scalar>(
     input_glwe_list: &CudaGlweCiphertextList<Scalar>,
     output_lwe_list: &mut CudaLweCiphertextList<Scalar>,
     vec_nth: &[MonomialDegree],
+    lwe_per_glwe: u32,
     streams: &CudaStreams,
 ) where
     Scalar: UnsignedTorus,
@@ -29,9 +30,10 @@ pub unsafe fn cuda_extract_lwe_samples_from_glwe_ciphertext_list_async<Scalar>(
         Got {in_lwe_dim:?} for input and {out_lwe_dim:?} for output.",
     );
 
+    // lwe_per_glwe LWEs will be extracted per GLWE ciphertext, thus we need to have enough indexes
     assert_eq!(
         vec_nth.len(),
-        input_glwe_list.glwe_ciphertext_count().0 * input_glwe_list.polynomial_size().0,
+        input_glwe_list.glwe_ciphertext_count().0 * lwe_per_glwe as usize,
         "Mismatch between number of nths and number of GLWEs provided.",
     );
 
@@ -53,6 +55,7 @@ pub unsafe fn cuda_extract_lwe_samples_from_glwe_ciphertext_list_async<Scalar>(
             &input_glwe_list.0.d_vec,
             &d_nth_array,
             vec_nth.len() as u32,
+            lwe_per_glwe,
             input_glwe_list.glwe_dimension(),
             input_glwe_list.polynomial_size(),
         );
@@ -66,6 +69,7 @@ pub fn cuda_extract_lwe_samples_from_glwe_ciphertext_list<Scalar>(
     input_glwe_list: &CudaGlweCiphertextList<Scalar>,
     output_lwe_list: &mut CudaLweCiphertextList<Scalar>,
     vec_nth: &[MonomialDegree],
+    lwe_per_glwe: u32,
     streams: &CudaStreams,
 ) where
     Scalar: UnsignedTorus,
@@ -75,6 +79,7 @@ pub fn cuda_extract_lwe_samples_from_glwe_ciphertext_list<Scalar>(
             input_glwe_list,
             output_lwe_list,
             vec_nth,
+            lwe_per_glwe,
             streams,
         );
     }
diff --git a/tfhe/src/core_crypto/gpu/algorithms/test/glwe_sample_extraction.rs b/tfhe/src/core_crypto/gpu/algorithms/test/glwe_sample_extraction.rs
index 7f6ac165b8..4384c5ad51 100644
--- a/tfhe/src/core_crypto/gpu/algorithms/test/glwe_sample_extraction.rs
+++ b/tfhe/src/core_crypto/gpu/algorithms/test/glwe_sample_extraction.rs
@@ -75,21 +75,22 @@ fn glwe_encrypt_sample_extract_decrypt_custom_mod<Scalar: UnsignedTorus + Send +
         let input_cuda_glwe_list =
             CudaGlweCiphertextList::from_glwe_ciphertext_list(&glwe_list, &streams);
 
+        let lwe_per_glwe = 2;
         let mut output_cuda_lwe_ciphertext_list = CudaLweCiphertextList::new(
             equivalent_lwe_sk.lwe_dimension(),
-            LweCiphertextCount(msgs.len() * glwe_list.polynomial_size().0),
+            LweCiphertextCount(msgs.len() * lwe_per_glwe),
             ciphertext_modulus,
             &streams,
         );
 
-        let nths = (0..(msgs.len() * glwe_list.polynomial_size().0))
+        let nths = (0..(msgs.len() * lwe_per_glwe))
             .map(|x| MonomialDegree(x % glwe_list.polynomial_size().0))
             .collect_vec();
-
         cuda_extract_lwe_samples_from_glwe_ciphertext_list(
             &input_cuda_glwe_list,
             &mut output_cuda_lwe_ciphertext_list,
             nths.as_slice(),
+            lwe_per_glwe as u32,
             &streams,
         );
 
@@ -107,7 +108,7 @@ fn glwe_encrypt_sample_extract_decrypt_custom_mod<Scalar: UnsignedTorus + Send +
             &mut output_plaintext_list,
         );
 
-        let mut decoded = vec![Scalar::ZERO; plaintext_list.plaintext_count().0];
+        let mut decoded = vec![Scalar::ZERO; msgs.len() * lwe_per_glwe];
 
         decoded
             .iter_mut()
@@ -116,7 +117,7 @@ fn glwe_encrypt_sample_extract_decrypt_custom_mod<Scalar: UnsignedTorus + Send +
 
         let mut count = msg_modulus;
         count = count.wrapping_sub(Scalar::ONE);
-        for result in decoded.chunks_exact(glwe_list.polynomial_size().0) {
+        for result in decoded.chunks_exact(lwe_per_glwe) {
             assert!(result.iter().all(|&x| x == count));
             count = count.wrapping_sub(Scalar::ONE);
         }
diff --git a/tfhe/src/core_crypto/gpu/mod.rs b/tfhe/src/core_crypto/gpu/mod.rs
index 76ea6bb7fd..da68cff2ae 100644
--- a/tfhe/src/core_crypto/gpu/mod.rs
+++ b/tfhe/src/core_crypto/gpu/mod.rs
@@ -402,6 +402,7 @@ pub unsafe fn extract_lwe_samples_from_glwe_ciphertext_list_async<T: UnsignedInt
     glwe_array_in: &CudaVec<T>,
     nth_array: &CudaVec<u32>,
     num_nths: u32,
+    lwe_per_glwe: u32,
     glwe_dimension: GlweDimension,
     polynomial_size: PolynomialSize,
 ) {
@@ -412,6 +413,7 @@ pub unsafe fn extract_lwe_samples_from_glwe_ciphertext_list_async<T: UnsignedInt
         glwe_array_in.as_c_ptr(0),
         nth_array.as_c_ptr(0).cast::<u32>(),
         num_nths,
+        lwe_per_glwe,
         glwe_dimension.0 as u32,
         polynomial_size.0 as u32,
     );