@@ -90,7 +90,7 @@ // Add noise to ct[0]
     // ct[0] <- ct[0] + e
     ct.add_normal(
         basek,
-        0,                    // Selects the first column of ct (ct[0])
+        0,               // Selects the first column of ct (ct[0])
         basek * ct_size, // Scaling of the noise: 2^{-basek * limbs}
         &mut source,
         3.2,  // Standard deviation

@@ -1,232 +1,232 @@
-use crate::znx_base::ZnxInfos;
-use crate::{Backend, DataView, DataViewMut, FFT64, Module, ZnxSliceSize, ZnxView, alloc_aligned};
-use std::marker::PhantomData;
-
-/// Vector Matrix Product Prepared Matrix: a vector of [VecZnx],
-/// stored as a 3D matrix in the DFT domain in a single contiguous array.
-/// Each col of the [MatZnxDft] can be seen as a collection of [VecZnxDft].
-///
-/// [MatZnxDft] is used to permform a vector matrix product between a [VecZnx]/[VecZnxDft] and a [MatZnxDft].
-/// See the trait [MatZnxDftOps] for additional information.
-pub struct MatZnxDft<D, B: Backend> {
-    data: D,
-    n: usize,
-    size: usize,
-    rows: usize,
-    cols_in: usize,
-    cols_out: usize,
-    _phantom: PhantomData<B>,
-}
-
-impl<D, B: Backend> ZnxInfos for MatZnxDft<D, B> {
-    fn cols(&self) -> usize {
-        self.cols_in
-    }
-
-    fn rows(&self) -> usize {
-        self.rows
-    }
-
-    fn n(&self) -> usize {
-        self.n
-    }
-
-    fn size(&self) -> usize {
-        self.size
-    }
-}
-
-impl<D> ZnxSliceSize for MatZnxDft<D, FFT64> {
-    fn sl(&self) -> usize {
-        self.n() * self.cols_out()
-    }
-}
-
-impl<D, B: Backend> DataView for MatZnxDft<D, B> {
-    type D = D;
-    fn data(&self) -> &Self::D {
-        &self.data
-    }
-}
-
-impl<D, B: Backend> DataViewMut for MatZnxDft<D, B> {
-    fn data_mut(&mut self) -> &mut Self::D {
-        &mut self.data
-    }
-}
-
-impl<D: AsRef<[u8]>> ZnxView for MatZnxDft<D, FFT64> {
-    type Scalar = f64;
-}
-
-impl<D, B: Backend> MatZnxDft<D, B> {
-    pub fn cols_in(&self) -> usize {
-        self.cols_in
-    }
-
-    pub fn cols_out(&self) -> usize {
-        self.cols_out
-    }
-}
-
-impl<D: From<Vec<u8>>, B: Backend> MatZnxDft<D, B> {
-    pub(crate) fn bytes_of(module: &Module<B>, rows: usize, cols_in: usize, cols_out: usize, size: usize) -> usize {
-        unsafe {
-            crate::ffi::vmp::bytes_of_vmp_pmat(
-                module.ptr,
-                (rows * cols_in) as u64,
-                (size * cols_out) as u64,
-            ) as usize
-        }
-    }
-
-    pub(crate) fn new(module: &Module<B>, rows: usize, cols_in: usize, cols_out: usize, size: usize) -> Self {
-        let data: Vec<u8> = alloc_aligned(Self::bytes_of(module, rows, cols_in, cols_out, size));
-        Self {
-            data: data.into(),
-            n: module.n(),
-            size,
-            rows,
-            cols_in,
-            cols_out,
-            _phantom: PhantomData,
-        }
-    }
-
-    pub(crate) fn new_from_bytes(
-        module: &Module<B>,
-        rows: usize,
-        cols_in: usize,
-        cols_out: usize,
-        size: usize,
-        bytes: impl Into<Vec<u8>>,
-    ) -> Self {
-        let data: Vec<u8> = bytes.into();
-        assert!(data.len() == Self::bytes_of(module, rows, cols_in, cols_out, size));
-        Self {
-            data: data.into(),
-            n: module.n(),
-            size,
-            rows,
-            cols_in,
-            cols_out,
-            _phantom: PhantomData,
-        }
-    }
-}
-
-impl<D: AsRef<[u8]>> MatZnxDft<D, FFT64> {
-    /// Returns a copy of the backend array at index (i, j) of the [MatZnxDft].
-    ///
-    /// # Arguments
-    ///
-    /// * `row`: row index (i).
-    /// * `col`: col index (j).
-    #[allow(dead_code)]
-    fn at(&self, row: usize, col: usize) -> Vec<f64> {
-        let n: usize = self.n();
-
-        let mut res: Vec<f64> = alloc_aligned(n);
-
-        if n < 8 {
-            res.copy_from_slice(&self.raw()[(row + col * self.rows()) * n..(row + col * self.rows()) * (n + 1)]);
-        } else {
-            (0..n >> 3).for_each(|blk| {
-                res[blk * 8..(blk + 1) * 8].copy_from_slice(&self.at_block(row, col, blk)[..8]);
-            });
-        }
-
-        res
-    }
-
-    #[allow(dead_code)]
-    fn at_block(&self, row: usize, col: usize, blk: usize) -> &[f64] {
-        let nrows: usize = self.rows();
-        let nsize: usize = self.size();
-        if col == (nsize - 1) && (nsize & 1 == 1) {
-            &self.raw()[blk * nrows * nsize * 8 + col * nrows * 8 + row * 8..]
-        } else {
-            &self.raw()[blk * nrows * nsize * 8 + (col / 2) * (2 * nrows) * 8 + row * 2 * 8 + (col % 2) * 8..]
-        }
-    }
-}
-
-pub type MatZnxDftOwned<B> = MatZnxDft<Vec<u8>, B>;
-
-pub trait MatZnxDftToRef<B: Backend> {
-    fn to_ref(&self) -> MatZnxDft<&[u8], B>;
-}
-
-pub trait MatZnxDftToMut<B: Backend> {
-    fn to_mut(&mut self) -> MatZnxDft<&mut [u8], B>;
-}
-
-impl<B: Backend> MatZnxDftToMut<B> for MatZnxDft<Vec<u8>, B> {
-    fn to_mut(&mut self) -> MatZnxDft<&mut [u8], B> {
-        MatZnxDft {
-            data: self.data.as_mut_slice(),
-            n: self.n,
-            rows: self.rows,
-            cols_in: self.cols_in,
-            cols_out: self.cols_out,
-            size: self.size,
-            _phantom: PhantomData,
-        }
-    }
-}
-
-impl<B: Backend> MatZnxDftToRef<B> for MatZnxDft<Vec<u8>, B> {
-    fn to_ref(&self) -> MatZnxDft<&[u8], B> {
-        MatZnxDft {
-            data: self.data.as_slice(),
-            n: self.n,
-            rows: self.rows,
-            cols_in: self.cols_in,
-            cols_out: self.cols_out,
-            size: self.size,
-            _phantom: PhantomData,
-        }
-    }
-}
-
-impl<B: Backend> MatZnxDftToMut<B> for MatZnxDft<&mut [u8], B> {
-    fn to_mut(&mut self) -> MatZnxDft<&mut [u8], B> {
-        MatZnxDft {
-            data: self.data,
-            n: self.n,
-            rows: self.rows,
-            cols_in: self.cols_in,
-            cols_out: self.cols_out,
-            size: self.size,
-            _phantom: PhantomData,
-        }
-    }
-}
-
-impl<B: Backend> MatZnxDftToRef<B> for MatZnxDft<&mut [u8], B> {
-    fn to_ref(&self) -> MatZnxDft<&[u8], B> {
-        MatZnxDft {
-            data: self.data,
-            n: self.n,
-            rows: self.rows,
-            cols_in: self.cols_in,
-            cols_out: self.cols_out,
-            size: self.size,
-            _phantom: PhantomData,
-        }
-    }
-}
-
-impl<B: Backend> MatZnxDftToRef<B> for MatZnxDft<&[u8], B> {
-    fn to_ref(&self) -> MatZnxDft<&[u8], B> {
-        MatZnxDft {
-            data: self.data,
-            n: self.n,
-            rows: self.rows,
-            cols_in: self.cols_in,
-            cols_out: self.cols_out,
-            size: self.size,
-            _phantom: PhantomData,
-        }
-    }
-}
+use crate::znx_base::ZnxInfos;
+use crate::{Backend, DataView, DataViewMut, FFT64, Module, ZnxSliceSize, ZnxView, alloc_aligned};
+use std::marker::PhantomData;
+
+/// Vector Matrix Product Prepared Matrix: a vector of [VecZnx],
+/// stored as a 3D matrix in the DFT domain in a single contiguous array.
+/// Each col of the [MatZnxDft] can be seen as a collection of [VecZnxDft].
+///
+/// [MatZnxDft] is used to permform a vector matrix product between a [VecZnx]/[VecZnxDft] and a [MatZnxDft].
+/// See the trait [MatZnxDftOps] for additional information.
+pub struct MatZnxDft<D, B: Backend> {
+    data: D,
+    n: usize,
+    size: usize,
+    rows: usize,
+    cols_in: usize,
+    cols_out: usize,
+    _phantom: PhantomData<B>,
+}
+
+impl<D, B: Backend> ZnxInfos for MatZnxDft<D, B> {
+    fn cols(&self) -> usize {
+        self.cols_in
+    }
+
+    fn rows(&self) -> usize {
+        self.rows
+    }
+
+    fn n(&self) -> usize {
+        self.n
+    }
+
+    fn size(&self) -> usize {
+        self.size
+    }
+}
+
+impl<D> ZnxSliceSize for MatZnxDft<D, FFT64> {
+    fn sl(&self) -> usize {
+        self.n() * self.cols_out()
+    }
+}
+
+impl<D, B: Backend> DataView for MatZnxDft<D, B> {
+    type D = D;
+    fn data(&self) -> &Self::D {
+        &self.data
+    }
+}
+
+impl<D, B: Backend> DataViewMut for MatZnxDft<D, B> {
+    fn data_mut(&mut self) -> &mut Self::D {
+        &mut self.data
+    }
+}
+
+impl<D: AsRef<[u8]>> ZnxView for MatZnxDft<D, FFT64> {
+    type Scalar = f64;
+}
+
+impl<D, B: Backend> MatZnxDft<D, B> {
+    pub fn cols_in(&self) -> usize {
+        self.cols_in
+    }
+
+    pub fn cols_out(&self) -> usize {
+        self.cols_out
+    }
+}
+
+impl<D: From<Vec<u8>>, B: Backend> MatZnxDft<D, B> {
+    pub(crate) fn bytes_of(module: &Module<B>, rows: usize, cols_in: usize, cols_out: usize, size: usize) -> usize {
+        unsafe {
+            crate::ffi::vmp::bytes_of_vmp_pmat(
+                module.ptr,
+                (rows * cols_in) as u64,
+                (size * cols_out) as u64,
+            ) as usize
+        }
+    }
+
+    pub(crate) fn new(module: &Module<B>, rows: usize, cols_in: usize, cols_out: usize, size: usize) -> Self {
+        let data: Vec<u8> = alloc_aligned(Self::bytes_of(module, rows, cols_in, cols_out, size));
+        Self {
+            data: data.into(),
+            n: module.n(),
+            size,
+            rows,
+            cols_in,
+            cols_out,
+            _phantom: PhantomData,
+        }
+    }
+
+    pub(crate) fn new_from_bytes(
+        module: &Module<B>,
+        rows: usize,
+        cols_in: usize,
+        cols_out: usize,
+        size: usize,
+        bytes: impl Into<Vec<u8>>,
+    ) -> Self {
+        let data: Vec<u8> = bytes.into();
+        assert!(data.len() == Self::bytes_of(module, rows, cols_in, cols_out, size));
+        Self {
+            data: data.into(),
+            n: module.n(),
+            size,
+            rows,
+            cols_in,
+            cols_out,
+            _phantom: PhantomData,
+        }
+    }
+}
+
+impl<D: AsRef<[u8]>> MatZnxDft<D, FFT64> {
+    /// Returns a copy of the backend array at index (i, j) of the [MatZnxDft].
+    ///
+    /// # Arguments
+    ///
+    /// * `row`: row index (i).
+    /// * `col`: col index (j).
+    #[allow(dead_code)]
+    fn at(&self, row: usize, col: usize) -> Vec<f64> {
+        let n: usize = self.n();
+
+        let mut res: Vec<f64> = alloc_aligned(n);
+
+        if n < 8 {
+            res.copy_from_slice(&self.raw()[(row + col * self.rows()) * n..(row + col * self.rows()) * (n + 1)]);
+        } else {
+            (0..n >> 3).for_each(|blk| {
+                res[blk * 8..(blk + 1) * 8].copy_from_slice(&self.at_block(row, col, blk)[..8]);
+            });
+        }
+
+        res
+    }
+
+    #[allow(dead_code)]
+    fn at_block(&self, row: usize, col: usize, blk: usize) -> &[f64] {
+        let nrows: usize = self.rows();
+        let nsize: usize = self.size();
+        if col == (nsize - 1) && (nsize & 1 == 1) {
+            &self.raw()[blk * nrows * nsize * 8 + col * nrows * 8 + row * 8..]
+        } else {
+            &self.raw()[blk * nrows * nsize * 8 + (col / 2) * (2 * nrows) * 8 + row * 2 * 8 + (col % 2) * 8..]
+        }
+    }
+}
+
+pub type MatZnxDftOwned<B> = MatZnxDft<Vec<u8>, B>;
+
+pub trait MatZnxDftToRef<B: Backend> {
+    fn to_ref(&self) -> MatZnxDft<&[u8], B>;
+}
+
+pub trait MatZnxDftToMut<B: Backend>: MatZnxDftToRef<B> {
+    fn to_mut(&mut self) -> MatZnxDft<&mut [u8], B>;
+}
+
+impl<B: Backend> MatZnxDftToMut<B> for MatZnxDft<Vec<u8>, B> {
+    fn to_mut(&mut self) -> MatZnxDft<&mut [u8], B> {
+        MatZnxDft {
+            data: self.data.as_mut_slice(),
+            n: self.n,
+            rows: self.rows,
+            cols_in: self.cols_in,
+            cols_out: self.cols_out,
+            size: self.size,
+            _phantom: PhantomData,
+        }
+    }
+}
+
+impl<B: Backend> MatZnxDftToRef<B> for MatZnxDft<Vec<u8>, B> {
+    fn to_ref(&self) -> MatZnxDft<&[u8], B> {
+        MatZnxDft {
+            data: self.data.as_slice(),
+            n: self.n,
+            rows: self.rows,
+            cols_in: self.cols_in,
+            cols_out: self.cols_out,
+            size: self.size,
+            _phantom: PhantomData,
+        }
+    }
+}
+
+impl<B: Backend> MatZnxDftToMut<B> for MatZnxDft<&mut [u8], B> {
+    fn to_mut(&mut self) -> MatZnxDft<&mut [u8], B> {
+        MatZnxDft {
+            data: self.data,
+            n: self.n,
+            rows: self.rows,
+            cols_in: self.cols_in,
+            cols_out: self.cols_out,
+            size: self.size,
+            _phantom: PhantomData,
+        }
+    }
+}
+
+impl<B: Backend> MatZnxDftToRef<B> for MatZnxDft<&mut [u8], B> {
+    fn to_ref(&self) -> MatZnxDft<&[u8], B> {
+        MatZnxDft {
+            data: self.data,
+            n: self.n,
+            rows: self.rows,
+            cols_in: self.cols_in,
+            cols_out: self.cols_out,
+            size: self.size,
+            _phantom: PhantomData,
+        }
+    }
+}
+
+impl<B: Backend> MatZnxDftToRef<B> for MatZnxDft<&[u8], B> {
+    fn to_ref(&self) -> MatZnxDft<&[u8], B> {
+        MatZnxDft {
+            data: self.data,
+            n: self.n,
+            rows: self.rows,
+            cols_in: self.cols_in,
+            cols_out: self.cols_out,
+            size: self.size,
+            _phantom: PhantomData,
+        }
+    }
+}

@@ -313,7 +313,7 @@ pub trait VecZnxToRef {
     fn to_ref(&self) -> VecZnx<&[u8]>;
 }
 
-pub trait VecZnxToMut {
+pub trait VecZnxToMut: VecZnxToRef {
     fn to_mut(&mut self) -> VecZnx<&mut [u8]>;
 }
 

@@ -125,15 +125,8 @@ /// # Arguments
     ///
     /// * `basek`: normalization basis.
     /// * `tmp_bytes`: scratch space of size at least [VecZnxBigOps::vec_znx_big_normalize].
-    fn vec_znx_big_normalize<R, A>(
-        &self,
-        basek: usize,
-        res: &mut R,
-        res_col: usize,
-        a: &A,
-        a_col: usize,
-        scratch: &mut Scratch,
-    ) where
+    fn vec_znx_big_normalize<R, A>(&self, basek: usize, res: &mut R, res_col: usize, a: &A, a_col: usize, scratch: &mut Scratch)
+    where
         R: VecZnxToMut,
         A: VecZnxBigToRef<BACKEND>;
 
@@ -530,15 +523,8 @@ )
         }
     }
 
-    fn vec_znx_big_normalize<R, A>(
-        &self,
-        basek: usize,
-        res: &mut R,
-        res_col: usize,
-        a: &A,
-        a_col: usize,
-        scratch: &mut Scratch,
-    ) where
+    fn vec_znx_big_normalize<R, A>(&self, basek: usize, res: &mut R, res_col: usize, a: &A, a_col: usize, scratch: &mut Scratch)
+    where
         R: VecZnxToMut,
         A: VecZnxBigToRef<FFT64>,
     {

@@ -142,7 +142,7 @@ pub trait VecZnxDftToRef<B: Backend> {
     fn to_ref(&self) -> VecZnxDft<&[u8], B>;
 }
 
-pub trait VecZnxDftToMut<B: Backend> {
+pub trait VecZnxDftToMut<B: Backend>: VecZnxDftToRef<B> {
     fn to_mut(&mut self) -> VecZnxDft<&mut [u8], B>;
 }
 

@@ -152,6 +152,11 @@ fn switch_degree<R, A>(&self, r: &mut R, col_b: usize, a: &A, col_a: usize)
     where
         R: VecZnxToMut,
         A: VecZnxToRef;
+
+    fn vec_znx_copy<R, A>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize)
+    where
+        R: VecZnxToMut,
+        A: VecZnxToRef;
 }
 
 pub trait VecZnxScratch {
@@ -174,6 +179,26 @@ }
 }
 
 impl<BACKEND: Backend> VecZnxOps for Module<BACKEND> {
+    fn vec_znx_copy<R, A>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize)
+    where
+        R: VecZnxToMut,
+        A: VecZnxToRef,
+    {
+        let mut res_mut: VecZnx<&mut [u8]> = res.to_mut();
+        let a_ref: VecZnx<&[u8]> = a.to_ref();
+
+        let min_size: usize = min(res_mut.size(), a_ref.size());
+
+        (0..min_size).for_each(|j| {
+            res_mut
+                .at_mut(res_col, j)
+                .copy_from_slice(a_ref.at(a_col, j));
+        });
+        (min_size..res_mut.size()).for_each(|j| {
+            res_mut.zero_at(res_col, j);
+        })
+    }
+
     fn vec_znx_normalize<R, A>(&self, basek: usize, res: &mut R, res_col: usize, a: &A, a_col: usize, scratch: &mut Scratch)
     where
         R: VecZnxToMut,

@@ -1,11 +1,11 @@
-use backend::{Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned, FFT64};
-use criterion::{BenchmarkId, Criterion, black_box, criterion_group, criterion_main};
+use backend::{FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned};
 use core::{
     elem::Infos,
     ggsw_ciphertext::GGSWCiphertext,
     glwe_ciphertext::GLWECiphertext,
     keys::{SecretKey, SecretKeyFourier},
 };
+use criterion::{BenchmarkId, Criterion, black_box, criterion_group, criterion_main};
 use sampling::source::Source;
 
 fn bench_external_product_glwe_fft64(c: &mut Criterion) {

@@ -1,11 +1,11 @@
 use backend::{FFT64, Module, ScratchOwned};
-use criterion::{BenchmarkId, Criterion, black_box, criterion_group, criterion_main};
 use core::{
     elem::Infos,
     glwe_ciphertext::GLWECiphertext,
     keys::{SecretKey, SecretKeyFourier},
     keyswitch_key::GLWESwitchingKey,
 };
+use criterion::{BenchmarkId, Criterion, black_box, criterion_group, criterion_main};
 use sampling::source::Source;
 
 fn bench_keyswitch_glwe_fft64(c: &mut Criterion) {

@@ -168,7 +168,7 @@ }
 
 impl<DataSelf> AutomorphismKey<DataSelf, FFT64>
 where
-    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64>,
 {
     pub fn generate_from_sk<DataSk>(
         &mut self,
@@ -221,7 +221,7 @@ }
 
 impl<DataSelf> AutomorphismKey<DataSelf, FFT64>
 where
-    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64>,
 {
     pub fn automorphism<DataLhs, DataRhs>(
         &mut self,

@@ -27,6 +27,10 @@ fn cols(&self) -> usize {
         self.inner().cols()
     }
 
+    fn rank(&self) -> usize {
+        self.cols() - 1
+    }
+
     /// Returns the number of size per polynomial.
     fn size(&self) -> usize {
         let size: usize = self.inner().size();
@@ -44,6 +48,11 @@ fn basek(&self) -> usize;
 
     /// Returns the bit precision of the ciphertext.
     fn k(&self) -> usize;
+}
+
+pub trait SetMetaData {
+    fn set_basek(&mut self, basek: usize);
+    fn set_k(&mut self, k: usize);
 }
 
 pub trait GetRow<B: Backend> {

@@ -1,8 +1,8 @@
 use backend::{
     Backend, FFT64, MatZnxDft, MatZnxDftAlloc, MatZnxDftOps, MatZnxDftScratch, MatZnxDftToMut, MatZnxDftToRef, Module, ScalarZnx,
     ScalarZnxDft, ScalarZnxDftToRef, ScalarZnxToRef, Scratch, VecZnx, VecZnxAlloc, VecZnxBigAlloc, VecZnxBigOps,
-    VecZnxBigScratch, VecZnxDft, VecZnxDftAlloc, VecZnxDftOps, VecZnxDftToMut, VecZnxDftToRef, VecZnxOps, VecZnxToMut,
-    VecZnxToRef, ZnxInfos, ZnxZero,
+    VecZnxBigScratch, VecZnxDft, VecZnxDftAlloc, VecZnxDftOps, VecZnxDftToMut, VecZnxDftToRef, VecZnxOps, VecZnxToMut, ZnxInfos,
+    ZnxZero,
 };
 use sampling::source::Source;
 
@@ -196,7 +196,7 @@ }
 
 impl<DataSelf> GGSWCiphertext<DataSelf, FFT64>
 where
-    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64>,
 {
     pub fn encrypt_sk<DataPt, DataSk>(
         &mut self,
@@ -639,7 +639,7 @@ res: &mut GLWECiphertext<DataRes>,
         ksk: &GLWESwitchingKey<DataKsk, FFT64>,
         scratch: &mut Scratch,
     ) where
-        VecZnx<DataRes>: VecZnxToMut + VecZnxToRef,
+        VecZnx<DataRes>: VecZnxToMut,
         MatZnxDft<DataKsk, FFT64>: MatZnxDftToRef<FFT64>,
     {
         #[cfg(debug_assertions)]

@@ -2,16 +2,17 @@ use backend::{
     AddNormal, Backend, FFT64, FillUniform, MatZnxDft, MatZnxDftOps, MatZnxDftScratch, MatZnxDftToRef, Module, ScalarZnxAlloc,
     ScalarZnxDft, ScalarZnxDftAlloc, ScalarZnxDftOps, ScalarZnxDftToRef, Scratch, VecZnx, VecZnxAlloc, VecZnxBig, VecZnxBigAlloc,
     VecZnxBigOps, VecZnxBigScratch, VecZnxDft, VecZnxDftAlloc, VecZnxDftOps, VecZnxDftToMut, VecZnxDftToRef, VecZnxOps,
-    VecZnxToMut, VecZnxToRef, ZnxInfos, ZnxZero, copy_vec_znx_from,
+    VecZnxToMut, VecZnxToRef, ZnxInfos, ZnxZero,
 };
 use sampling::source::Source;
 
 use crate::{
     SIX_SIGMA,
     automorphism::AutomorphismKey,
-    elem::Infos,
+    elem::{Infos, SetMetaData},
     ggsw_ciphertext::GGSWCiphertext,
     glwe_ciphertext_fourier::GLWECiphertextFourier,
+    glwe_ops::GLWEOps,
     glwe_plaintext::GLWEPlaintext,
     keys::{GLWEPublicKey, SecretDistribution, SecretKeyFourier},
     keyswitch_key::GLWESwitchingKey,
@@ -201,9 +202,24 @@ GLWECiphertext::external_product_scratch_space(module, out_size, out_rank, out_size, ggsw_size)
     }
 }
 
+impl<DataSelf> SetMetaData for GLWECiphertext<DataSelf>
+where
+    VecZnx<DataSelf>: VecZnxToMut,
+{
+    fn set_k(&mut self, k: usize) {
+        self.k = k
+    }
+
+    fn set_basek(&mut self, basek: usize) {
+        self.basek = basek
+    }
+}
+
+impl<DataSelf> GLWEOps<FFT64> for GLWECiphertext<DataSelf> where VecZnx<DataSelf>: VecZnxToMut {}
+
 impl<DataSelf> GLWECiphertext<DataSelf>
 where
-    VecZnx<DataSelf>: VecZnxToMut + VecZnxToRef,
+    VecZnx<DataSelf>: VecZnxToMut,
 {
     pub fn encrypt_sk<DataPt, DataSk>(
         &mut self,
@@ -279,21 +295,6 @@ ) where
         VecZnxDft<DataPk, FFT64>: VecZnxDftToRef<FFT64>,
     {
         self.encrypt_pk_private(module, None, pk, source_xu, source_xe, sigma, scratch);
-    }
-
-    pub fn copy<DataOther>(&mut self, other: &GLWECiphertext<DataOther>)
-    where
-        VecZnx<DataOther>: VecZnxToRef,
-    {
-        copy_vec_znx_from(&mut self.data.to_mut(), &other.to_ref());
-        self.k = other.k;
-        self.basek = other.basek;
-    }
-
-    pub fn rsh(&mut self, k: usize, scratch: &mut Scratch) {
-        let basek: usize = self.basek();
-        let mut self_mut: VecZnx<&mut [u8]> = self.data.to_mut();
-        self_mut.rsh(basek, k, scratch);
     }
 
     pub fn automorphism<DataLhs, DataRhs>(

@@ -1,7 +1,7 @@
 use backend::{
     Backend, FFT64, MatZnxDft, MatZnxDftOps, MatZnxDftScratch, MatZnxDftToRef, Module, ScalarZnxDft, ScalarZnxDftOps,
     ScalarZnxDftToRef, Scratch, VecZnx, VecZnxAlloc, VecZnxBig, VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDft,
-    VecZnxDftAlloc, VecZnxDftOps, VecZnxDftToMut, VecZnxDftToRef, VecZnxToMut, VecZnxToRef, ZnxZero,
+    VecZnxDftAlloc, VecZnxDftOps, VecZnxDftToMut, VecZnxDftToRef, VecZnxToMut, ZnxZero,
 };
 use sampling::source::Source;
 
@@ -126,7 +126,7 @@ }
 
 impl<DataSelf> GLWECiphertextFourier<DataSelf, FFT64>
 where
-    VecZnxDft<DataSelf, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64>,
+    VecZnxDft<DataSelf, FFT64>: VecZnxDftToMut<FFT64>,
 {
     pub fn encrypt_zero_sk<DataSk>(
         &mut self,
@@ -261,7 +261,7 @@ pt: &mut GLWEPlaintext<DataPt>,
         sk_dft: &SecretKeyFourier<DataSk, FFT64>,
         scratch: &mut Scratch,
     ) where
-        VecZnx<DataPt>: VecZnxToMut + VecZnxToRef,
+        VecZnx<DataPt>: VecZnxToMut,
         ScalarZnxDft<DataSk, FFT64>: ScalarZnxDftToRef<FFT64>,
     {
         #[cfg(debug_assertions)]

@@ -0,0 +1,213 @@
+use backend::{Backend, Module, Scratch, VecZnx, VecZnxOps, VecZnxToMut, VecZnxToRef, ZnxZero};
+
+use crate::elem::{Infos, SetMetaData};
+
+pub trait GLWEOps<BACKEND: Backend>
+where
+    Self: Sized + VecZnxToMut + SetMetaData + Infos,
+{
+    fn add<A, B>(&mut self, module: &Module<BACKEND>, a: &A, b: &B)
+    where
+        A: VecZnxToRef + Infos,
+        B: VecZnxToRef + Infos,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(a.n(), module.n());
+            assert_eq!(b.n(), module.n());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(a.basek(), b.basek());
+            assert!(self.rank() >= a.rank().max(b.rank()));
+        }
+
+        let min_col: usize = a.rank().min(b.rank()) + 1;
+        let max_col: usize = a.rank().max(b.rank() + 1);
+        let self_col: usize = self.rank() + 1;
+
+        (0..min_col).for_each(|i| {
+            module.vec_znx_add(self, i, a, i, b, i);
+        });
+
+        if a.rank() > b.rank() {
+            (min_col..max_col).for_each(|i| {
+                module.vec_znx_copy(self, i, a, i);
+            });
+        } else {
+            (min_col..max_col).for_each(|i| {
+                module.vec_znx_copy(self, i, b, i);
+            });
+        }
+
+        let size: usize = self.size();
+        let mut self_mut: VecZnx<&mut [u8]> = self.to_mut();
+        (max_col..self_col).for_each(|i| {
+            (0..size).for_each(|j| {
+                self_mut.zero_at(i, j);
+            });
+        });
+
+        self.set_basek(a.basek());
+        self.set_k(a.k().max(b.k()));
+    }
+
+    fn add_inplace<A>(&mut self, module: &Module<BACKEND>, a: &A)
+    where
+        A: VecZnxToRef + Infos,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(a.n(), module.n());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(self.basek(), a.basek());
+            assert!(self.rank() >= a.rank())
+        }
+
+        (0..a.rank() + 1).for_each(|i| {
+            module.vec_znx_add_inplace(self, i, a, i);
+        });
+
+        self.set_k(a.k().max(self.k()));
+    }
+
+    fn sub<A, B>(&mut self, module: &Module<BACKEND>, a: &A, b: &B)
+    where
+        A: VecZnxToRef + Infos,
+        B: VecZnxToRef + Infos,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(a.n(), module.n());
+            assert_eq!(b.n(), module.n());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(a.basek(), b.basek());
+            assert!(self.rank() >= a.rank().max(b.rank()));
+        }
+
+        let min_col: usize = a.rank().min(b.rank()) + 1;
+        let max_col: usize = a.rank().max(b.rank() + 1);
+        let self_col: usize = self.rank() + 1;
+
+        (0..min_col).for_each(|i| {
+            module.vec_znx_sub(self, i, a, i, b, i);
+        });
+
+        if a.rank() > b.rank() {
+            (min_col..max_col).for_each(|i| {
+                module.vec_znx_copy(self, i, a, i);
+            });
+        } else {
+            (min_col..max_col).for_each(|i| {
+                module.vec_znx_copy(self, i, b, i);
+                module.vec_znx_negate_inplace(self, i);
+            });
+        }
+
+        let size: usize = self.size();
+        let mut self_mut: VecZnx<&mut [u8]> = self.to_mut();
+        (max_col..self_col).for_each(|i| {
+            (0..size).for_each(|j| {
+                self_mut.zero_at(i, j);
+            });
+        });
+
+        self.set_basek(a.basek());
+        self.set_k(a.k().max(b.k()));
+    }
+
+    fn sub_inplace_ab<A>(&mut self, module: &Module<BACKEND>, a: &A)
+    where
+        A: VecZnxToRef + Infos,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(a.n(), module.n());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(self.basek(), a.basek());
+            assert!(self.rank() >= a.rank())
+        }
+
+        (0..a.rank() + 1).for_each(|i| {
+            module.vec_znx_sub_ab_inplace(self, i, a, i);
+        });
+
+        self.set_k(a.k().max(self.k()));
+    }
+
+    fn sub_inplace_ba<A>(&mut self, module: &Module<BACKEND>, a: &A)
+    where
+        A: VecZnxToRef + Infos,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(a.n(), module.n());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(self.basek(), a.basek());
+            assert!(self.rank() >= a.rank())
+        }
+
+        (0..a.rank() + 1).for_each(|i| {
+            module.vec_znx_sub_ba_inplace(self, i, a, i);
+        });
+
+        self.set_k(a.k().max(self.k()));
+    }
+
+    fn rotate<A>(&mut self, module: &Module<BACKEND>, k: i64, a: &A)
+    where
+        A: VecZnxToRef + Infos,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(a.n(), module.n());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(self.basek(), a.basek());
+            assert_eq!(self.rank(), a.rank())
+        }
+
+        (0..a.rank() + 1).for_each(|i| {
+            module.vec_znx_rotate(k, self, i, a, i);
+        });
+
+        self.set_k(a.k());
+    }
+
+    fn rotate_inplace<A>(&mut self, module: &Module<BACKEND>, k: i64)
+    where
+        A: VecZnxToRef + Infos,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.n(), module.n());
+        }
+
+        (0..self.rank() + 1).for_each(|i| {
+            module.vec_znx_rotate_inplace(k, self, i);
+        });
+    }
+
+    fn copy<A>(&mut self, module: &Module<BACKEND>, a: &A)
+    where
+        A: VecZnxToRef + Infos,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.n(), module.n());
+            assert_eq!(a.n(), module.n());
+        }
+
+        let cols: usize = self.rank().min(a.rank()) + 1;
+
+        (0..cols).for_each(|i| {
+            module.vec_znx_copy(self, i, a, i);
+        });
+
+        self.set_k(a.k());
+        self.set_basek(a.basek());
+    }
+
+    fn rsh(&mut self, k: usize, scratch: &mut Scratch) {
+        let basek: usize = self.basek();
+        let mut self_mut: VecZnx<&mut [u8]> = self.to_mut();
+        self_mut.rsh(basek, k, scratch);
+    }
+}

@@ -217,7 +217,7 @@ source_xa: &mut Source,
         source_xe: &mut Source,
         sigma: f64,
     ) where
-        VecZnxDft<C, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64>,
+        VecZnxDft<C, FFT64>: VecZnxDftToMut<FFT64>,
         ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64> + ZnxInfos,
     {
         #[cfg(debug_assertions)]

@@ -149,7 +149,7 @@ }
 }
 impl<DataSelf> GLWESwitchingKey<DataSelf, FFT64>
 where
-    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64>,
 {
     pub fn encrypt_sk<DataSkIn, DataSkOut>(
         &mut self,

@@ -4,6 +4,7 @@ pub mod gglwe_ciphertext;
 pub mod ggsw_ciphertext;
 pub mod glwe_ciphertext;
 pub mod glwe_ciphertext_fourier;
+pub mod glwe_ops;
 pub mod glwe_plaintext;
 pub mod keys;
 pub mod keyswitch_key;

@@ -63,7 +63,7 @@ }
 
 impl<DataSelf> TensorKey<DataSelf, FFT64>
 where
-    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64>,
 {
     pub fn encrypt_sk<DataSk>(
         &mut self,

@@ -110,7 +110,8 @@ sigma,
         scratch.borrow(),
     );
 
-    let mut ct_glwe_fourier: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_ksk, rank_out);
+    let mut ct_glwe_fourier: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::alloc(&module, basek, k_ksk, rank_out);
 
     (0..ksk.rank_in()).for_each(|col_i| {
         (0..ksk.rows()).for_each(|row_i| {
@@ -202,7 +203,8 @@
     // gglwe_{s1}(s0) (x) gglwe_{s2}(s1) = gglwe_{s2}(s0)
     ct_gglwe_s0s2.keyswitch(&module, &ct_gglwe_s0s1, &ct_gglwe_s1s2, scratch.borrow());
 
-    let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_ksk, rank_out_s1s2);
+    let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::alloc(&module, basek, k_ksk, rank_out_s1s2);
     let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ksk);
 
     (0..ct_gglwe_s0s2.rank_in()).for_each(|col_i| {
@@ -304,7 +306,8 @@ ct_gglwe_s0s1.keyswitch_inplace(&module, &ct_gglwe_s1s2, scratch.borrow());
 
     let ct_gglwe_s0s2: GLWESwitchingKey<Vec<u8>, FFT64> = ct_gglwe_s0s1;
 
-    let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_ksk, rank_out_s0s1);
+    let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::alloc(&module, basek, k_ksk, rank_out_s0s1);
     let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ksk);
 
     (0..ct_gglwe_s0s2.rank_in()).for_each(|col_i| {

@@ -61,7 +61,8 @@ let rows: usize = (k_ct_in + basek - 1) / basek;
 
     let mut ksk: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, rank_in, rank_out);
     let mut ct_glwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct_in, rank_in);
-    let mut ct_glwe_dft_in: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_ct_in, rank_in);
+    let mut ct_glwe_dft_in: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::alloc(&module, basek, k_ct_in, rank_in);
     let mut ct_glwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct_out, rank_out);
     let mut ct_glwe_dft_out: GLWECiphertextFourier<Vec<u8>, FFT64> =
         GLWECiphertextFourier::alloc(&module, basek, k_ct_out, rank_out);

@@ -1,4 +1,6 @@
-use backend::{Module, ScalarZnx, ScalarZnxDft, ScalarZnxDftAlloc, ScalarZnxDftOps, ScratchOwned, Stats, VecZnxDftOps, VecZnxOps, FFT64};
+use backend::{
+    FFT64, Module, ScalarZnx, ScalarZnxDft, ScalarZnxDftAlloc, ScalarZnxDftOps, ScratchOwned, Stats, VecZnxDftOps, VecZnxOps,
+};
 use sampling::source::Source;
 
 use crate::{

@@ -2,7 +2,7 @@ use std::collections::HashMap;
 
 use backend::{FFT64, MatZnxDft, MatZnxDftToRef, Module, Scratch, VecZnx, VecZnxToMut, VecZnxToRef};
 
-use crate::{automorphism::AutomorphismKey, glwe_ciphertext::GLWECiphertext};
+use crate::{automorphism::AutomorphismKey, glwe_ciphertext::GLWECiphertext, glwe_ops::GLWEOps};
 
 impl GLWECiphertext<Vec<u8>> {
     pub fn trace_galois_elements(module: &Module<FFT64>) -> Vec<i64> {
@@ -34,7 +34,7 @@ }
 
 impl<DataSelf> GLWECiphertext<DataSelf>
 where
-    VecZnx<DataSelf>: VecZnxToMut + VecZnxToRef,
+    VecZnx<DataSelf>: VecZnxToMut,
 {
     pub fn trace<DataLhs, DataAK>(
         &mut self,
@@ -48,7 +48,7 @@ ) where
         VecZnx<DataLhs>: VecZnxToRef,
         MatZnxDft<DataAK, FFT64>: MatZnxDftToRef<FFT64>,
     {
-        self.copy(lhs);
+        self.copy(module, lhs);
         self.trace_inplace(module, start, end, auto_keys, scratch);
     }