diff --git a/backend/spqlios-arithmetic b/backend/spqlios-arithmetic
index b919282..d604503 160000
--- a/backend/spqlios-arithmetic
+++ b/backend/spqlios-arithmetic
@@ -1 +1 @@
-Subproject commit b919282c9b913e8b11418df6afdb0baa02debc9b
+Subproject commit d6045033e510315437c46ed2ddb80cfbb454950b
diff --git a/backend/src/ffi/vmp.rs b/backend/src/ffi/vmp.rs
index fc8a7ae..4f58e9b 100644
--- a/backend/src/ffi/vmp.rs
+++ b/backend/src/ffi/vmp.rs
@@ -47,6 +47,7 @@ unsafe extern "C" {
         pmat: *const VMP_PMAT,
         nrows: u64,
         ncols: u64,
+        pmat_scale: u64,
         tmp_space: *mut u8,
     );
 }
@@ -79,6 +80,7 @@ unsafe extern "C" {
         pmat: *const VMP_PMAT,
         nrows: u64,
         ncols: u64,
+        pmat_scale: u64,
         tmp_space: *mut u8,
     );
 }
diff --git a/backend/src/mat_znx_dft_ops.rs b/backend/src/mat_znx_dft_ops.rs
index 5ad724f..d0316a9 100644
--- a/backend/src/mat_znx_dft_ops.rs
+++ b/backend/src/mat_znx_dft_ops.rs
@@ -101,7 +101,7 @@ pub trait MatZnxDftOps<BACKEND: Backend> {
         B: MatZnxToRef<FFT64>;
 
     // Same as [MatZnxDftOps::vmp_apply] except result is added on R instead of overwritting R.
-    fn vmp_apply_add<R, A, B>(&self, res: &mut R, a: &A, b: &B, scratch: &mut Scratch)
+    fn vmp_apply_add<R, A, B>(&self, res: &mut R, a: &A, b: &B, scale: usize, scratch: &mut Scratch)
     where
         R: VecZnxDftToMut<FFT64>,
         A: VecZnxDftToRef<FFT64>,
@@ -309,7 +309,7 @@ impl MatZnxDftOps<FFT64> for Module<FFT64> {
         }
     }
 
-    fn vmp_apply_add<R, A, B>(&self, res: &mut R, a: &A, b: &B, scratch: &mut Scratch)
+    fn vmp_apply_add<R, A, B>(&self, res: &mut R, a: &A, b: &B, scale: usize, scratch: &mut Scratch)
     where
         R: VecZnxDftToMut<FFT64>,
         A: VecZnxDftToRef<FFT64>,
@@ -358,6 +358,7 @@ impl MatZnxDftOps<FFT64> for Module<FFT64> {
                 b.as_ptr() as *const vmp::vmp_pmat_t,
                 (b.rows() * b.cols_in()) as u64,
                 (b.size() * b.cols_out()) as u64,
+                scale as u64,
                 tmp_bytes.as_mut_ptr(),
             )
         }
@@ -368,6 +369,7 @@ mod tests {
     use crate::{
         Decoding, FFT64, FillUniform, MatZnxDft, MatZnxDftOps, Module, ScratchOwned, VecZnx, VecZnxAlloc, VecZnxBig,
         VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDft, VecZnxDftAlloc, VecZnxDftOps, ZnxInfos, ZnxView, ZnxViewMut,
+        ZnxZero,
     };
     use sampling::source::Source;
 
@@ -409,7 +411,7 @@ mod tests {
         let basek: usize = 15;
         let a_size: usize = 5;
         let mat_size: usize = 6;
-        let res_size: usize = 5;
+        let res_size: usize = a_size;
 
         [1, 2].iter().for_each(|in_cols| {
             [1, 2].iter().for_each(|out_cols| {
@@ -419,7 +421,6 @@ mod tests {
                 let mat_rows: usize = a_size;
                 let mat_cols_in: usize = a_cols;
                 let mat_cols_out: usize = res_cols;
-                let res_cols: usize = mat_cols_out;
 
                 let mut scratch: ScratchOwned = ScratchOwned::new(
                     module.vmp_apply_tmp_bytes(
@@ -435,7 +436,7 @@ mod tests {
                 let mut a: VecZnx<Vec<u8>> = module.new_vec_znx(a_cols, a_size);
 
                 (0..a_cols).for_each(|i| {
-                    a.at_mut(i, 2)[i + 1] = 1;
+                    a.at_mut(i, a_size - 1)[i + 1] = 1;
                 });
 
                 let mut mat_znx_dft: MatZnxDft<Vec<u8>, FFT64> =
@@ -479,7 +480,100 @@ mod tests {
                     (0..a_cols).for_each(|i| {
                         res_want_vi64[(i + 1) + (1 + i * mat_cols_out + col_i)] = 1;
                     });
-                    res_have.decode_vec_i64(col_i, basek, basek * 3, &mut res_have_vi64);
+                    res_have.decode_vec_i64(col_i, basek, basek * a_size, &mut res_have_vi64);
+                    assert_eq!(res_have_vi64, res_want_vi64);
+                });
+            });
+        });
+    }
+
+    #[test]
+    fn vmp_apply_add() {
+        let log_n: i32 = 5;
+        let n: usize = 1 << log_n;
+
+        let module: Module<FFT64> = Module::<FFT64>::new(n);
+        let basek: usize = 15;
+        let a_size: usize = 5;
+        let mat_size: usize = 6;
+        let res_size: usize = a_size;
+
+        [1, 2].iter().for_each(|in_cols| {
+            [1, 2].iter().for_each(|out_cols| {
+                let a_cols: usize = *in_cols;
+                let res_cols: usize = *out_cols;
+
+                let mat_rows: usize = a_size;
+                let mat_cols_in: usize = a_cols;
+                let mat_cols_out: usize = res_cols;
+
+                let mut scratch: ScratchOwned = ScratchOwned::new(
+                    module.vmp_apply_tmp_bytes(
+                        res_size,
+                        a_size,
+                        mat_rows,
+                        mat_cols_in,
+                        mat_cols_out,
+                        mat_size,
+                    ) | module.vec_znx_big_normalize_tmp_bytes(),
+                );
+
+                let mut a: VecZnx<Vec<u8>> = module.new_vec_znx(a_cols, a_size);
+
+                (0..a_cols).for_each(|i| {
+                    a.at_mut(i, a_size - 1)[i + 1] = 1;
+                });
+
+                let mut mat_znx_dft: MatZnxDft<Vec<u8>, FFT64> =
+                    module.new_mat_znx_dft(mat_rows, mat_cols_in, mat_cols_out, mat_size);
+
+                let mut c_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(mat_cols_out, mat_size);
+                let mut c_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(mat_cols_out, mat_size);
+
+                let mut tmp: VecZnx<Vec<u8>> = module.new_vec_znx(mat_cols_out, mat_size);
+
+                // Construts a [VecZnxMatDft] that performs cyclic rotations on each submatrix.
+                (0..a.size()).for_each(|row_i| {
+                    (0..mat_cols_in).for_each(|col_in_i| {
+                        (0..mat_cols_out).for_each(|col_out_i| {
+                            let idx = 1 + col_in_i * mat_cols_out + col_out_i;
+                            tmp.at_mut(col_out_i, row_i)[idx] = 1 as i64; // X^{idx}
+                            module.vec_znx_dft(&mut c_dft, col_out_i, &tmp, col_out_i);
+                            tmp.at_mut(col_out_i, row_i)[idx] = 0 as i64;
+                        });
+                        module.vmp_prepare_row(&mut mat_znx_dft, row_i, col_in_i, &c_dft);
+                    });
+                });
+
+                let mut a_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(a_cols, a_size);
+                (0..a_cols).for_each(|i| {
+                    module.vec_znx_dft(&mut a_dft, i, &a, i);
+                });
+
+                c_dft.zero();
+                (0..c_dft.cols()).for_each(|i| {
+                    module.vec_znx_dft(&mut c_dft, i, &a, 0);
+                });
+
+                module.vmp_apply_add(&mut c_dft, &a_dft, &mat_znx_dft, 0, scratch.borrow());
+
+                let mut res_have_vi64: Vec<i64> = vec![i64::default(); n];
+
+                let mut res_have: VecZnx<Vec<u8>> = module.new_vec_znx(res_cols, res_size);
+                (0..mat_cols_out).for_each(|i| {
+                    module.vec_znx_idft_tmp_a(&mut c_big, i, &mut c_dft, i);
+                    module.vec_znx_big_normalize(basek, &mut res_have, i, &c_big, i, scratch.borrow());
+                });
+
+                (0..mat_cols_out).for_each(|col_i| {
+                    let mut res_want_vi64: Vec<i64> = vec![i64::default(); n];
+                    (0..a_cols).for_each(|i| {
+                        res_want_vi64[(i + 1) + (1 + i * mat_cols_out + col_i)] = 1;
+                    });
+
+                    res_want_vi64[1] += 1;
+
+                    res_have.decode_vec_i64(col_i, basek, basek * a_size, &mut res_have_vi64);
                     assert_eq!(res_have_vi64, res_want_vi64);
                 });
             });
diff --git a/core/src/automorphism.rs b/core/src/automorphism.rs
index 339535c..a4165e6 100644
--- a/core/src/automorphism.rs
+++ b/core/src/automorphism.rs
@@ -12,15 +12,15 @@ pub struct AutomorphismKey<Data, B: Backend> {
 }
 
 impl AutomorphismKey<Vec<u8>, FFT64> {
-    pub fn alloc(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, rank: usize) -> Self {
+    pub fn alloc(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self {
         AutomorphismKey {
-            key: GLWESwitchingKey::alloc(module, basek, k, rows, rank, rank),
+            key: GLWESwitchingKey::alloc(module, basek, k, rows, digits, rank, rank),
             p: 0,
         }
     }
 
-    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, rank: usize) -> usize {
-        GLWESwitchingKey::<Vec<u8>, FFT64>::bytes_of(module, basek, k, rows, rank, rank)
+    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize {
+        GLWESwitchingKey::<Vec<u8>, FFT64>::bytes_of(module, basek, k, rows, digits,rank, rank)
     }
 }
 
@@ -45,6 +45,10 @@ impl<T, B: Backend> AutomorphismKey<T, B> {
         self.p
     }
 
+    pub fn digits(&self) -> usize {
+        self.key.digits()
+    }
+
     pub fn rank(&self) -> usize {
         self.key.rank()
     }
diff --git a/core/src/elem.rs b/core/src/elem.rs
index fdfd5bd..9a3a285 100644
--- a/core/src/elem.rs
+++ b/core/src/elem.rs
@@ -1,6 +1,6 @@
 use backend::{Backend, Module, ZnxInfos};
 
-use crate::{GLWECiphertextFourier, derive_size};
+use crate::{GLWECiphertextFourier, div_ceil};
 
 pub trait Infos {
     type Inner: ZnxInfos;
@@ -34,7 +34,7 @@ pub trait Infos {
     /// Returns the number of size per polynomial.
     fn size(&self) -> usize {
         let size: usize = self.inner().size();
-        debug_assert_eq!(size, derive_size(self.basek(), self.k()));
+        debug_assert_eq!(size, div_ceil(self.basek(), self.k()));
         size
     }
 
diff --git a/core/src/gglwe_ciphertext.rs b/core/src/gglwe_ciphertext.rs
index 0ab99ed..1650f59 100644
--- a/core/src/gglwe_ciphertext.rs
+++ b/core/src/gglwe_ciphertext.rs
@@ -4,25 +4,27 @@ use backend::{
 };
 use sampling::source::Source;
 
-use crate::{GLWECiphertext, GLWECiphertextFourier, GLWESecret, GetRow, Infos, ScratchCore, SetRow, derive_size};
+use crate::{GLWECiphertext, GLWECiphertextFourier, GLWESecret, GetRow, Infos, ScratchCore, SetRow, div_ceil};
 
 pub struct GGLWECiphertext<C, B: Backend> {
     pub(crate) data: MatZnxDft<C, B>,
     pub(crate) basek: usize,
     pub(crate) k: usize,
+    pub(crate) digits: usize,
 }
 
 impl<B: Backend> GGLWECiphertext<Vec<u8>, B> {
-    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, rank_in: usize, rank_out: usize) -> Self {
+    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank_in: usize, rank_out: usize) -> Self {
         Self {
-            data: module.new_mat_znx_dft(rows, rank_in, rank_out + 1, derive_size(basek, k)),
+            data: module.new_mat_znx_dft(div_ceil(rows, digits), rank_in, rank_out + 1, div_ceil(basek, k)),
             basek: basek,
             k,
+            digits,
         }
     }
 
-    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, rank_in: usize, rank_out: usize) -> usize {
-        module.bytes_of_mat_znx_dft(rows, rank_in, rank_out + 1, derive_size(basek, k))
+    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, digits: usize, rank_in: usize, rank_out: usize) -> usize {
+        module.bytes_of_mat_znx_dft(div_ceil(rows, digits), rank_in, rank_out + 1, div_ceil(basek, k))
     }
 }
 
@@ -47,6 +49,10 @@ impl<T, B: Backend> GGLWECiphertext<T, B> {
         self.data.cols_out() - 1
     }
 
+    pub fn digits(&self) -> usize{
+        self.digits
+    }
+
     pub fn rank_in(&self) -> usize {
         self.data.cols_in()
     }
@@ -58,7 +64,7 @@ impl<T, B: Backend> GGLWECiphertext<T, B> {
 
 impl GGLWECiphertext<Vec<u8>, FFT64> {
     pub fn generate_from_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
-        let size = derive_size(basek, k);
+        let size = div_ceil(basek, k);
         GLWECiphertext::encrypt_sk_scratch_space(module, basek, k)
             + module.bytes_of_vec_znx(rank + 1, size)
             + module.bytes_of_vec_znx(1, size)
@@ -101,6 +107,7 @@ impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GGLWECiphertext<DataSelf, FFT64> {
         }
 
         let rows: usize = self.rows();
+        let digits: usize = self.digits();
         let basek: usize = self.basek();
         let k: usize = self.k();
         let rank_in: usize = self.rank_in();
@@ -125,7 +132,7 @@ impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GGLWECiphertext<DataSelf, FFT64> {
             (0..rows).for_each(|row_i| {
                 // Adds the scalar_znx_pt to the i-th limb of the vec_znx_pt
                 tmp_pt.data.zero(); // zeroes for next iteration
-                module.vec_znx_add_scalar_inplace(&mut tmp_pt.data, 0, row_i, pt, col_i); // Selects the i-th
+                module.vec_znx_add_scalar_inplace(&mut tmp_pt.data, 0, row_i * digits, pt, col_i);
                 module.vec_znx_normalize_inplace(basek, &mut tmp_pt.data, 0, scratch_3);
 
                 // rlwe encrypt of vec_znx_pt into vec_znx_ct
diff --git a/core/src/ggsw_ciphertext.rs b/core/src/ggsw_ciphertext.rs
index 062954c..98edf89 100644
--- a/core/src/ggsw_ciphertext.rs
+++ b/core/src/ggsw_ciphertext.rs
@@ -7,26 +7,28 @@ use sampling::source::Source;
 
 use crate::{
     AutomorphismKey, GLWECiphertext, GLWECiphertextFourier, GLWESecret, GLWESwitchingKey, GetRow, Infos, ScratchCore, SetRow,
-    TensorKey, derive_size,
+    TensorKey, div_ceil,
 };
 
 pub struct GGSWCiphertext<C, B: Backend> {
-    pub data: MatZnxDft<C, B>,
-    pub basek: usize,
-    pub k: usize,
+    pub(crate) data: MatZnxDft<C, B>,
+    pub(crate) basek: usize,
+    pub(crate) k: usize,
+    pub(crate) digits: usize,
 }
 
 impl<B: Backend> GGSWCiphertext<Vec<u8>, B> {
-    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, rank: usize) -> Self {
+    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self {
         Self {
-            data: module.new_mat_znx_dft(rows, rank + 1, rank + 1, derive_size(basek, k)),
-            basek: basek,
+            data: module.new_mat_znx_dft(div_ceil(rows, digits), rank + 1, rank + 1, div_ceil(basek, k)),
+            basek,
             k: k,
+            digits,
         }
     }
 
-    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, rank: usize) -> usize {
-        module.bytes_of_mat_znx_dft(rows, rank + 1, rank + 1, derive_size(basek, k))
+    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize {
+        module.bytes_of_mat_znx_dft(div_ceil(rows, digits), rank + 1, rank + 1, div_ceil(basek, k))
     }
 }
 
@@ -50,11 +52,15 @@ impl<T, B: Backend> GGSWCiphertext<T, B> {
     pub fn rank(&self) -> usize {
         self.data.cols_out() - 1
     }
+
+    pub fn digits(&self) -> usize {
+        self.digits
+    }
 }
 
 impl GGSWCiphertext<Vec<u8>, FFT64> {
     pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
-        let size = derive_size(basek, k);
+        let size = div_ceil(basek, k);
         GLWECiphertext::encrypt_sk_scratch_space(module, basek, k)
             + module.bytes_of_vec_znx(rank + 1, size)
             + module.bytes_of_vec_znx(1, size)
@@ -68,8 +74,8 @@ impl GGSWCiphertext<Vec<u8>, FFT64> {
         tsk_k: usize,
         rank: usize,
     ) -> usize {
-        let tsk_size: usize = derive_size(basek, tsk_k);
-        let self_size: usize = derive_size(basek, self_k);
+        let tsk_size: usize = div_ceil(basek, tsk_k);
+        let self_size: usize = div_ceil(basek, self_k);
         let tmp_dft_i: usize = module.bytes_of_vec_znx_dft(rank + 1, tsk_size);
         let tmp_dft_col_data: usize = module.bytes_of_vec_znx_dft(1, self_size);
         let vmp: usize = tmp_dft_col_data + module.vmp_apply_tmp_bytes(self_size, self_size, self_size, rank, rank, tsk_size);
@@ -87,7 +93,7 @@ impl GGSWCiphertext<Vec<u8>, FFT64> {
         rank: usize,
     ) -> usize {
         GLWECiphertext::keyswitch_from_fourier_scratch_space(module, basek, out_k, rank, in_k, rank, ksk_k)
-            + module.bytes_of_vec_znx_dft(rank + 1, derive_size(basek, in_k))
+            + module.bytes_of_vec_znx_dft(rank + 1, div_ceil(basek, in_k))
     }
 
     pub fn keyswitch_scratch_space(
@@ -99,7 +105,7 @@ impl GGSWCiphertext<Vec<u8>, FFT64> {
         tsk_k: usize,
         rank: usize,
     ) -> usize {
-        let out_size: usize = derive_size(basek, out_k);
+        let out_size: usize = div_ceil(basek, out_k);
 
         let res_znx: usize = module.bytes_of_vec_znx(rank + 1, out_size);
         let ci_dft: usize = module.bytes_of_vec_znx_dft(rank + 1, out_size);
@@ -130,7 +136,7 @@ impl GGSWCiphertext<Vec<u8>, FFT64> {
         rank: usize,
     ) -> usize {
         let cols: usize = rank + 1;
-        let out_size: usize = derive_size(basek, out_k);
+        let out_size: usize = div_ceil(basek, out_k);
         let res: usize = module.bytes_of_vec_znx(cols, out_size);
         let res_dft: usize = module.bytes_of_vec_znx_dft(cols, out_size);
         let ci_dft: usize = module.bytes_of_vec_znx_dft(cols, out_size);
@@ -199,6 +205,7 @@ impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GGSWCiphertext<DataSelf, FFT64> {
         let basek: usize = self.basek();
         let k: usize = self.k();
         let rank: usize = self.rank();
+        let digits: usize = self.digits();
 
         let (mut tmp_pt, scratch1) = scratch.tmp_glwe_pt(module, basek, k);
         let (mut tmp_ct, scratch2) = scratch1.tmp_glwe_ct(module, basek, k, rank);
@@ -207,7 +214,7 @@ impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GGSWCiphertext<DataSelf, FFT64> {
             tmp_pt.data.zero();
 
             // Adds the scalar_znx_pt to the i-th limb of the vec_znx_pt
-            module.vec_znx_add_scalar_inplace(&mut tmp_pt.data, 0, row_i, pt, 0);
+            module.vec_znx_add_scalar_inplace(&mut tmp_pt.data, 0, row_i * digits, pt, 0);
             module.vec_znx_normalize_inplace(basek, &mut tmp_pt.data, 0, scratch2);
 
             (0..rank + 1).for_each(|col_j| {
diff --git a/core/src/glwe_ciphertext.rs b/core/src/glwe_ciphertext.rs
index d5f8c47..a084b91 100644
--- a/core/src/glwe_ciphertext.rs
+++ b/core/src/glwe_ciphertext.rs
@@ -7,7 +7,7 @@ use sampling::source::Source;
 
 use crate::{
     AutomorphismKey, GGSWCiphertext, GLWECiphertextFourier, GLWEOps, GLWEPlaintext, GLWEPublicKey, GLWESecret, GLWESwitchingKey,
-    Infos, SIX_SIGMA, SecretDistribution, SetMetaData, derive_size,
+    Infos, SIX_SIGMA, SecretDistribution, SetMetaData, div_ceil,
 };
 
 pub struct GLWECiphertext<C> {
@@ -19,14 +19,14 @@ pub struct GLWECiphertext<C> {
 impl GLWECiphertext<Vec<u8>> {
     pub fn alloc<B: Backend>(module: &Module<B>, basek: usize, k: usize, rank: usize) -> Self {
         Self {
-            data: module.new_vec_znx(rank + 1, derive_size(basek, k)),
+            data: module.new_vec_znx(rank + 1, div_ceil(basek, k)),
             basek,
             k,
         }
     }
 
     pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
-        module.bytes_of_vec_znx(rank + 1, derive_size(basek, k))
+        module.bytes_of_vec_znx(rank + 1, div_ceil(basek, k))
     }
 }
 
@@ -69,18 +69,18 @@ impl<C: AsRef<[u8]>> GLWECiphertext<C> {
 
 impl GLWECiphertext<Vec<u8>> {
     pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
-        let size: usize = derive_size(basek, k);
+        let size: usize = div_ceil(basek, k);
         module.vec_znx_big_normalize_tmp_bytes() + module.bytes_of_vec_znx_dft(1, size) + module.bytes_of_vec_znx(1, size)
     }
     pub fn encrypt_pk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
-        let size: usize = derive_size(basek, k);
+        let size: usize = div_ceil(basek, k);
         ((module.bytes_of_vec_znx_dft(1, size) + module.bytes_of_vec_znx_big(1, size)) | module.bytes_of_scalar_znx(1))
             + module.bytes_of_scalar_znx_dft(1)
             + module.vec_znx_big_normalize_tmp_bytes()
     }
 
     pub fn decrypt_scratch_space(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
-        let size: usize = derive_size(basek, k);
+        let size: usize = div_ceil(basek, k);
         (module.vec_znx_big_normalize_tmp_bytes() | module.bytes_of_vec_znx_dft(1, size)) + module.bytes_of_vec_znx_big(1, size)
     }
 
@@ -94,9 +94,9 @@ impl GLWECiphertext<Vec<u8>> {
         ksk_k: usize,
     ) -> usize {
         let res_dft: usize = GLWECiphertextFourier::bytes_of(module, basek, out_k, out_rank);
-        let in_size: usize = derive_size(basek, in_k);
-        let out_size: usize = derive_size(basek, out_k);
-        let ksk_size: usize = derive_size(basek, ksk_k);
+        let in_size: usize = div_ceil(basek, in_k);
+        let out_size: usize = div_ceil(basek, out_k);
+        let ksk_size: usize = div_ceil(basek, ksk_k);
         let vmp: usize = module.vmp_apply_tmp_bytes(out_size, in_size, in_size, in_rank, out_rank + 1, ksk_size)
             + module.bytes_of_vec_znx_dft(in_rank, in_size);
         let normalize: usize = module.vec_znx_big_normalize_tmp_bytes();
@@ -155,9 +155,9 @@ impl GLWECiphertext<Vec<u8>> {
         rank: usize,
     ) -> usize {
         let res_dft: usize = GLWECiphertextFourier::bytes_of(module, basek, out_k, rank);
-        let in_size: usize = derive_size(basek, in_k);
-        let out_size: usize = derive_size(basek, out_k);
-        let ggsw_size: usize = derive_size(basek, ggsw_k);
+        let in_size: usize = div_ceil(basek, in_k);
+        let out_size: usize = div_ceil(basek, out_k);
+        let ggsw_size: usize = div_ceil(basek, ggsw_k);
         let vmp: usize = module.bytes_of_vec_znx_dft(rank + 1, in_size)
             + module.vmp_apply_tmp_bytes(
                 out_size,
diff --git a/core/src/glwe_ciphertext_fourier.rs b/core/src/glwe_ciphertext_fourier.rs
index 92864d3..4fe7e1e 100644
--- a/core/src/glwe_ciphertext_fourier.rs
+++ b/core/src/glwe_ciphertext_fourier.rs
@@ -4,7 +4,7 @@ use backend::{
 };
 use sampling::source::Source;
 
-use crate::{GGSWCiphertext, GLWECiphertext, GLWEPlaintext, GLWESecret, GLWESwitchingKey, Infos, ScratchCore, derive_size};
+use crate::{GGSWCiphertext, GLWECiphertext, GLWEPlaintext, GLWESecret, GLWESwitchingKey, Infos, ScratchCore, div_ceil};
 
 pub struct GLWECiphertextFourier<C, B: Backend> {
     pub data: VecZnxDft<C, B>,
@@ -15,14 +15,14 @@ pub struct GLWECiphertextFourier<C, B: Backend> {
 impl<B: Backend> GLWECiphertextFourier<Vec<u8>, B> {
     pub fn alloc(module: &Module<B>, basek: usize, k: usize, rank: usize) -> Self {
         Self {
-            data: module.new_vec_znx_dft(rank + 1, derive_size(basek, k)),
+            data: module.new_vec_znx_dft(rank + 1, div_ceil(basek, k)),
             basek: basek,
             k: k,
         }
     }
 
     pub fn bytes_of(module: &Module<B>, basek: usize, k: usize, rank: usize) -> usize {
-        module.bytes_of_vec_znx_dft(rank + 1, derive_size(basek, k))
+        module.bytes_of_vec_znx_dft(rank + 1, div_ceil(basek, k))
     }
 }
 
@@ -51,16 +51,16 @@ impl<T, B: Backend> GLWECiphertextFourier<T, B> {
 impl GLWECiphertextFourier<Vec<u8>, FFT64> {
     #[allow(dead_code)]
     pub(crate) fn idft_scratch_space(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
-        module.bytes_of_vec_znx(1, derive_size(basek, k))
+        module.bytes_of_vec_znx(1, div_ceil(basek, k))
             + (module.vec_znx_big_normalize_tmp_bytes() | module.vec_znx_idft_tmp_bytes())
     }
 
     pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
-        module.bytes_of_vec_znx(rank + 1, derive_size(basek, k)) + GLWECiphertext::encrypt_sk_scratch_space(module, basek, k)
+        module.bytes_of_vec_znx(rank + 1, div_ceil(basek, k)) + GLWECiphertext::encrypt_sk_scratch_space(module, basek, k)
     }
 
     pub fn decrypt_scratch_space(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
-        let size: usize = derive_size(basek, k);
+        let size: usize = div_ceil(basek, k);
         (module.vec_znx_big_normalize_tmp_bytes()
             | module.bytes_of_vec_znx_dft(1, size)
             | (module.bytes_of_vec_znx_big(1, size) + module.vec_znx_idft_tmp_bytes()))
@@ -99,9 +99,9 @@ impl GLWECiphertextFourier<Vec<u8>, FFT64> {
         rank: usize,
     ) -> usize {
         let res_dft: usize = GLWECiphertextFourier::bytes_of(module, basek, out_k, rank);
-        let out_size: usize = derive_size(basek, out_k);
-        let in_size: usize = derive_size(basek, in_k);
-        let ggsw_size: usize = derive_size(basek, ggsw_k);
+        let out_size: usize = div_ceil(basek, out_k);
+        let in_size: usize = div_ceil(basek, in_k);
+        let ggsw_size: usize = div_ceil(basek, ggsw_k);
         let vmp: usize = module.vmp_apply_tmp_bytes(out_size, in_size, in_size, rank + 1, rank + 1, ggsw_size);
         let res_small: usize = GLWECiphertext::bytes_of(module, basek, out_k, rank);
         let normalize: usize = module.vec_znx_big_normalize_tmp_bytes();
diff --git a/core/src/glwe_plaintext.rs b/core/src/glwe_plaintext.rs
index 0aa846f..058c9a5 100644
--- a/core/src/glwe_plaintext.rs
+++ b/core/src/glwe_plaintext.rs
@@ -1,6 +1,6 @@
 use backend::{Backend, FFT64, Module, VecZnx, VecZnxAlloc, VecZnxToMut, VecZnxToRef};
 
-use crate::{GLWECiphertext, GLWECiphertextToMut, GLWECiphertextToRef, GLWEOps, Infos, SetMetaData, derive_size};
+use crate::{GLWECiphertext, GLWECiphertextToMut, GLWECiphertextToRef, GLWEOps, Infos, SetMetaData, div_ceil};
 
 pub struct GLWEPlaintext<C> {
     pub data: VecZnx<C>,
@@ -37,14 +37,14 @@ impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> SetMetaData for GLWEPlaintext<DataSelf
 impl GLWEPlaintext<Vec<u8>> {
     pub fn alloc<B: Backend>(module: &Module<B>, basek: usize, k: usize) -> Self {
         Self {
-            data: module.new_vec_znx(1, derive_size(basek, k)),
+            data: module.new_vec_znx(1, div_ceil(basek, k)),
             basek: basek,
             k,
         }
     }
 
     pub fn byte_of(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
-        module.bytes_of_vec_znx(1, derive_size(basek, k))
+        module.bytes_of_vec_znx(1, div_ceil(basek, k))
     }
 }
 
diff --git a/core/src/keyswitch_key.rs b/core/src/keyswitch_key.rs
index 0362cd8..bc9baae 100644
--- a/core/src/keyswitch_key.rs
+++ b/core/src/keyswitch_key.rs
@@ -6,14 +6,14 @@ use crate::{GGLWECiphertext, GGSWCiphertext, GLWECiphertextFourier, GLWESecret,
 pub struct GLWESwitchingKey<Data, B: Backend>(pub(crate) GGLWECiphertext<Data, B>);
 
 impl GLWESwitchingKey<Vec<u8>, FFT64> {
-    pub fn alloc(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, rank_in: usize, rank_out: usize) -> Self {
+    pub fn alloc(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, digits: usize, rank_in: usize, rank_out: usize) -> Self {
         GLWESwitchingKey(GGLWECiphertext::alloc(
-            module, basek, k, rows, rank_in, rank_out,
+            module, basek, k, rows, digits, rank_in, rank_out,
         ))
     }
 
-    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, rank_in: usize, rank_out: usize) -> usize {
-        GGLWECiphertext::<Vec<u8>, FFT64>::bytes_of(module, basek, k, rows, rank_in, rank_out)
+    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, digits: usize, rank_in: usize, rank_out: usize) -> usize {
+        GGLWECiphertext::<Vec<u8>, FFT64>::bytes_of(module, basek, k, rows, digits, rank_in, rank_out)
     }
 }
 
@@ -45,6 +45,10 @@ impl<T, B: Backend> GLWESwitchingKey<T, B> {
     pub fn rank_out(&self) -> usize {
         self.0.data.cols_out() - 1
     }
+
+    pub fn digits(&self) -> usize {
+        self.0.digits()
+    }
 }
 
 impl<C: AsRef<[u8]>> GetRow<FFT64> for GLWESwitchingKey<C, FFT64> {
diff --git a/core/src/lib.rs b/core/src/lib.rs
index 3854e21..b82f82a 100644
--- a/core/src/lib.rs
+++ b/core/src/lib.rs
@@ -33,7 +33,7 @@ pub use tensor_key::*;
 
 pub use backend::Scratch;
 pub use backend::ScratchOwned;
-use utils::derive_size;
+use utils::div_ceil;
 
 pub(crate) const SIX_SIGMA: f64 = 6.0;
 
@@ -46,6 +46,7 @@ pub trait ScratchCore<B: Backend> {
         basek: usize,
         k: usize,
         rows: usize,
+        digits: usize,
         rank_in: usize,
         rank_out: usize,
     ) -> (GGLWECiphertext<&mut [u8], B>, &mut Self);
@@ -55,6 +56,7 @@ pub trait ScratchCore<B: Backend> {
         basek: usize,
         k: usize,
         rows: usize,
+        digits: usize,
         rank: usize,
     ) -> (GGSWCiphertext<&mut [u8], B>, &mut Self);
     fn tmp_glwe_fourier(
@@ -78,6 +80,7 @@ pub trait ScratchCore<B: Backend> {
         basek: usize,
         k: usize,
         rows: usize,
+        digits: usize,
         rank_in: usize,
         rank_out: usize,
     ) -> (GLWESwitchingKey<&mut [u8], B>, &mut Self);
@@ -87,6 +90,7 @@ pub trait ScratchCore<B: Backend> {
         basek: usize,
         k: usize,
         rows: usize,
+        digits: usize,
         rank: usize,
     ) -> (TensorKey<&mut [u8], B>, &mut Self);
     fn tmp_autokey(
@@ -95,6 +99,7 @@ pub trait ScratchCore<B: Backend> {
         basek: usize,
         k: usize,
         rows: usize,
+        digits: usize,
         rank: usize,
     ) -> (AutomorphismKey<&mut [u8], B>, &mut Self);
 }
@@ -107,12 +112,12 @@ impl ScratchCore<FFT64> for Scratch {
         k: usize,
         rank: usize,
     ) -> (GLWECiphertext<&mut [u8]>, &mut Self) {
-        let (data, scratch) = self.tmp_vec_znx(module, rank + 1, derive_size(basek, k));
+        let (data, scratch) = self.tmp_vec_znx(module, rank + 1, div_ceil(basek, k));
         (GLWECiphertext { data, basek, k }, scratch)
     }
 
     fn tmp_glwe_pt(&mut self, module: &Module<FFT64>, basek: usize, k: usize) -> (GLWEPlaintext<&mut [u8]>, &mut Self) {
-        let (data, scratch) = self.tmp_vec_znx(module, 1, derive_size(basek, k));
+        let (data, scratch) = self.tmp_vec_znx(module, 1, div_ceil(basek, k));
         (GLWEPlaintext { data, basek, k }, scratch)
     }
 
@@ -122,15 +127,17 @@ impl ScratchCore<FFT64> for Scratch {
         basek: usize,
         k: usize,
         rows: usize,
+        digits: usize,
         rank_in: usize,
         rank_out: usize,
     ) -> (GGLWECiphertext<&mut [u8], FFT64>, &mut Self) {
-        let (data, scratch) = self.tmp_mat_znx_dft(module, rows, rank_in, rank_out + 1, derive_size(basek, k));
+        let (data, scratch) = self.tmp_mat_znx_dft(module, div_ceil(rows, digits), rank_in, rank_out + 1, div_ceil(basek, k));
         (
             GGLWECiphertext {
                 data: data,
                 basek: basek,
                 k,
+                digits,
             },
             scratch,
         )
@@ -142,14 +149,16 @@ impl ScratchCore<FFT64> for Scratch {
         basek: usize,
         k: usize,
         rows: usize,
+        digits: usize,
         rank: usize,
     ) -> (GGSWCiphertext<&mut [u8], FFT64>, &mut Self) {
-        let (data, scratch) = self.tmp_mat_znx_dft(module, rows, rank + 1, rank + 1, derive_size(basek, k));
+        let (data, scratch) = self.tmp_mat_znx_dft(module, div_ceil(rows, digits), rank + 1, rank + 1, div_ceil(basek, k));
         (
             GGSWCiphertext {
-                data: data,
-                basek: basek,
+                data,
+                basek,
                 k,
+                digits,
             },
             scratch,
         )
@@ -162,7 +171,7 @@ impl ScratchCore<FFT64> for Scratch {
         k: usize,
         rank: usize,
     ) -> (GLWECiphertextFourier<&mut [u8], FFT64>, &mut Self) {
-        let (data, scratch) = self.tmp_vec_znx_dft(module, rank + 1, derive_size(basek, k));
+        let (data, scratch) = self.tmp_vec_znx_dft(module, rank + 1, div_ceil(basek, k));
         (GLWECiphertextFourier { data, basek, k }, scratch)
     }
 
@@ -202,10 +211,11 @@ impl ScratchCore<FFT64> for Scratch {
         basek: usize,
         k: usize,
         rows: usize,
+        digits: usize,
         rank_in: usize,
         rank_out: usize,
     ) -> (GLWESwitchingKey<&mut [u8], FFT64>, &mut Self) {
-        let (data, scratch) = self.tmp_gglwe(module, basek, k, rows, rank_in, rank_out);
+        let (data, scratch) = self.tmp_gglwe(module, basek, k, rows, digits, rank_in, rank_out);
         (GLWESwitchingKey(data), scratch)
     }
 
@@ -215,9 +225,10 @@ impl ScratchCore<FFT64> for Scratch {
         basek: usize,
         k: usize,
         rows: usize,
+        digits: usize,
         rank: usize,
     ) -> (AutomorphismKey<&mut [u8], FFT64>, &mut Self) {
-        let (data, scratch) = self.tmp_glwe_ksk(module, basek, k, rows, rank, rank);
+        let (data, scratch) = self.tmp_glwe_ksk(module, basek, k, rows, digits, rank, rank);
         (AutomorphismKey { key: data, p: 0 }, scratch)
     }
 
@@ -227,6 +238,7 @@ impl ScratchCore<FFT64> for Scratch {
         basek: usize,
         k: usize,
         rows: usize,
+        digits: usize,
         rank: usize,
     ) -> (TensorKey<&mut [u8], FFT64>, &mut Self) {
         let mut keys: Vec<GLWESwitchingKey<&mut [u8], FFT64>> = Vec::new();
@@ -235,12 +247,12 @@ impl ScratchCore<FFT64> for Scratch {
         let mut scratch: &mut Scratch = self;
 
         if pairs != 0 {
-            let (gglwe, s) = scratch.tmp_glwe_ksk(module, basek, k, rows, 1, rank);
+            let (gglwe, s) = scratch.tmp_glwe_ksk(module, basek, k, rows, digits, 1, rank);
             scratch = s;
             keys.push(gglwe);
         }
         for _ in 1..pairs {
-            let (gglwe, s) = scratch.tmp_glwe_ksk(module, basek, k, rows, 1, rank);
+            let (gglwe, s) = scratch.tmp_glwe_ksk(module, basek, k, rows, digits, 1, rank);
             scratch = s;
             keys.push(gglwe);
         }
diff --git a/core/src/tensor_key.rs b/core/src/tensor_key.rs
index fca6b2e..c7e9bf4 100644
--- a/core/src/tensor_key.rs
+++ b/core/src/tensor_key.rs
@@ -8,18 +8,18 @@ pub struct TensorKey<C, B: Backend> {
 }
 
 impl TensorKey<Vec<u8>, FFT64> {
-    pub fn alloc(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, rank: usize) -> Self {
+    pub fn alloc(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self {
         let mut keys: Vec<GLWESwitchingKey<Vec<u8>, FFT64>> = Vec::new();
         let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
         (0..pairs).for_each(|_| {
-            keys.push(GLWESwitchingKey::alloc(module, basek, k, rows, 1, rank));
+            keys.push(GLWESwitchingKey::alloc(module, basek, k, rows, digits,1, rank));
         });
         Self { keys: keys }
     }
 
-    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, rank: usize) -> usize {
+    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize {
         let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
-        pairs * GLWESwitchingKey::<Vec<u8>, FFT64>::bytes_of(module, basek, k, rows, 1, rank)
+        pairs * GLWESwitchingKey::<Vec<u8>, FFT64>::bytes_of(module, basek, k, rows, digits,1, rank)
     }
 }
 
@@ -51,6 +51,10 @@ impl<T, B: Backend> TensorKey<T, B> {
     pub fn rank_out(&self) -> usize {
         self.keys[0].rank_out()
     }
+
+    pub fn digits(&self) -> usize {
+        self.keys[0].digits()
+    }
 }
 
 impl TensorKey<Vec<u8>, FFT64> {
diff --git a/core/src/utils.rs b/core/src/utils.rs
index c3bc5d5..62164c3 100644
--- a/core/src/utils.rs
+++ b/core/src/utils.rs
@@ -1,3 +1,3 @@
-pub(crate) fn derive_size(basek: usize, k: usize) -> usize {
-    (k + basek - 1) / basek
+pub(crate) fn div_ceil(a: usize, b: usize) -> usize {
+    (a + b - 1) / b
 }