@@ -157,18 +157,22 @@ assert!(col_i < a.cols());
     }
     data.copy_from_slice(a.at(col_i, 0));
     let rem: usize = basek - (k % basek);
-    (1..size).for_each(|i| {
-        if i == size - 1 && rem != basek {
-            let k_rem: usize = basek - rem;
-            izip!(a.at(col_i, i).iter(), data.iter_mut()).for_each(|(x, y)| {
-                *y = (*y << k_rem) + (x >> rem);
-            });
-        } else {
-            izip!(a.at(col_i, i).iter(), data.iter_mut()).for_each(|(x, y)| {
-                *y = (*y << basek) + x;
-            });
-        }
-    })
+    if k < basek {
+        data.iter_mut().for_each(|x| *x >>= rem);
+    } else {
+        (1..size).for_each(|i| {
+            if i == size - 1 && rem != basek {
+                let k_rem: usize = basek - rem;
+                izip!(a.at(col_i, i).iter(), data.iter_mut()).for_each(|(x, y)| {
+                    *y = (*y << k_rem) + (x >> rem);
+                });
+            } else {
+                izip!(a.at(col_i, i).iter(), data.iter_mut()).for_each(|(x, y)| {
+                    *y = (*y << basek) + x;
+                });
+            }
+        })
+    }
 }
 
 fn decode_vec_float<D: AsRef<[u8]>>(a: &VecZnx<D>, col_i: usize, basek: usize, data: &mut [Float]) {
@@ -268,7 +272,7 @@ let data: &[i64] = a.raw();
     let mut res: i64 = data[i];
     let rem: usize = basek - (k % basek);
     let slice_size: usize = a.n() * a.cols();
-    (1..size).for_each(|i| {
+    (0..size).for_each(|i| {
         let x: i64 = data[i * slice_size];
         if i == size - 1 && rem != basek {
             let k_rem: usize = basek - rem;
@@ -316,18 +320,25 @@ let n: usize = 8;
         let module: Module<FFT64> = Module::<FFT64>::new(n);
         let basek: usize = 17;
         let size: usize = 5;
-        let k: usize = size * basek - 5;
-        let mut a: VecZnx<_> = module.new_vec_znx(2, size);
-        let mut source = Source::new([0u8; 32]);
-        let raw: &mut [i64] = a.raw_mut();
-        raw.iter_mut().enumerate().for_each(|(i, x)| *x = i as i64);
-        (0..a.cols()).for_each(|col_i| {
-            let mut have: Vec<i64> = vec![i64::default(); n];
-            have.iter_mut().for_each(|x| *x = source.next_i64());
-            a.encode_vec_i64(col_i, basek, k, &have, 64);
-            let mut want = vec![i64::default(); n];
-            a.decode_vec_i64(col_i, basek, k, &mut want);
-            izip!(want, have).for_each(|(a, b)| assert_eq!(a, b, "{} != {}", a, b));
-        })
+        for k in [size * basek - 5] {
+            let mut a: VecZnx<_> = module.new_vec_znx(2, size);
+            let mut source = Source::new([0u8; 32]);
+            let raw: &mut [i64] = a.raw_mut();
+            raw.iter_mut().enumerate().for_each(|(i, x)| *x = i as i64);
+            (0..a.cols()).for_each(|col_i| {
+                let mut have: Vec<i64> = vec![i64::default(); n];
+                have.iter_mut().for_each(|x| {
+                    if k < 64 {
+                        *x = source.next_u64n(1 << k, (1 << k) - 1) as i64;
+                    } else {
+                        *x = source.next_i64();
+                    }
+                });
+                a.encode_vec_i64(col_i, basek, k, &have, std::cmp::min(k, 64));
+                let mut want = vec![i64::default(); n];
+                a.decode_vec_i64(col_i, basek, k, &mut want);
+                izip!(want, have).for_each(|(a, b)| assert_eq!(a, b, "{} != {}", a, b));
+            })
+        }
     }
 }

@@ -103,7 +103,7 @@ /// Allocates a block of T aligned with [DEFAULTALIGN].
 /// Size of T * size msut be a multiple of [DEFAULTALIGN].
 pub fn alloc_aligned_custom<T>(size: usize, align: usize) -> Vec<T> {
     assert_eq!(
-        (size * size_of::<T>()) % align,
+        (size * size_of::<T>()) % (align / size_of::<T>()),
         0,
         "size={} must be a multiple of align={}",
         size,
@@ -121,7 +121,7 @@ /// Allocates an aligned vector of size equal to the smallest multiple
 /// of [DEFAULTALIGN]/size_of::<T>() that is equal or greater to `size`.
 pub fn alloc_aligned<T>(size: usize) -> Vec<T> {
     alloc_aligned_custom::<T>(
-        size + (size % (DEFAULTALIGN / size_of::<T>())),
+        size + (DEFAULTALIGN - (size % (DEFAULTALIGN / size_of::<T>()))),
         DEFAULTALIGN,
     )
 }
@@ -231,6 +231,23 @@ Self::new(rem_slice),
         )
     }
 
+    pub fn tmp_slice_vec_znx_dft<B: Backend>(
+        &mut self,
+        slice_size: usize,
+        module: &Module<B>,
+        cols: usize,
+        size: usize,
+    ) -> (Vec<VecZnxDft<&mut [u8], B>>, &mut Self) {
+        let mut scratch: &mut Scratch = self;
+        let mut slice: Vec<VecZnxDft<&mut [u8], B>> = Vec::with_capacity(slice_size);
+        for _ in 0..slice_size {
+            let (znx, new_scratch) = scratch.tmp_vec_znx_dft(module, cols, size);
+            scratch = new_scratch;
+            slice.push(znx);
+        }
+        (slice, scratch)
+    }
+
     pub fn tmp_vec_znx_big<B: Backend>(
         &mut self,
         module: &Module<B>,
@@ -251,6 +268,23 @@ (
             VecZnx::from_data(take_slice, module.n(), cols, size),
             Self::new(rem_slice),
         )
+    }
+
+    pub fn tmp_slice_vec_znx<B: Backend>(
+        &mut self,
+        slice_size: usize,
+        module: &Module<B>,
+        cols: usize,
+        size: usize,
+    ) -> (Vec<VecZnx<&mut [u8]>>, &mut Self) {
+        let mut scratch: &mut Scratch = self;
+        let mut slice: Vec<VecZnx<&mut [u8]>> = Vec::with_capacity(slice_size);
+        for _ in 0..slice_size {
+            let (znx, new_scratch) = scratch.tmp_vec_znx(module, cols, size);
+            scratch = new_scratch;
+            slice.push(znx);
+        }
+        (slice, scratch)
     }
 
     pub fn tmp_mat_znx_dft<B: Backend>(

@@ -2,8 +2,8 @@ use crate::ffi::vec_znx_dft::vec_znx_dft_t;
 use crate::ffi::vmp;
 use crate::znx_base::{ZnxInfos, ZnxView, ZnxViewMut};
 use crate::{
-    Backend, FFT64, MatZnxDft, MatZnxDftOwned, MatZnxToMut, MatZnxToRef, Module, Scratch, VecZnxDft, VecZnxDftToMut,
-    VecZnxDftToRef,
+    Backend, FFT64, MatZnxDft, MatZnxDftOwned, MatZnxToMut, MatZnxToRef, Module, ScalarZnxAlloc, ScalarZnxDftAlloc,
+    ScalarZnxDftOps, Scratch, VecZnxDft, VecZnxDftAlloc, VecZnxDftOps, VecZnxDftToMut, VecZnxDftToRef, VecZnxOps,
 };
 
 pub trait MatZnxDftAlloc<B: Backend> {
@@ -38,6 +38,8 @@ b_cols_in: usize,
         b_cols_out: usize,
         b_size: usize,
     ) -> usize;
+
+    fn mat_znx_dft_mul_x_pow_minus_one_scratch_space(&self, size: usize, cols_out: usize) -> usize;
 }
 
 /// This trait implements methods for vector matrix product,
@@ -52,7 +54,7 @@ /// * `a`: the [VecZnxDft] to encode on the [MatZnxDft].
     /// * `row_i`: the index of the row to prepare.
     ///
     /// The size of buf can be obtained with [MatZnxDftOps::vmp_prepare_tmp_bytes].
-    fn vmp_prepare_row<R, A>(&self, res: &mut R, res_row: usize, res_col_in: usize, a: &A)
+    fn mat_znx_dft_set_row<R, A>(&self, res: &mut R, res_row: usize, res_col_in: usize, a: &A)
     where
         R: MatZnxToMut<FFT64>,
         A: VecZnxDftToRef<FFT64>;
@@ -64,11 +66,28 @@ ///
     /// * `res`: the [VecZnxDft] to on which to extract the row of the [MatZnxDft].
     /// * `a`: [MatZnxDft] on which the values are encoded.
     /// * `row_i`: the index of the row to extract.
-    fn vmp_extract_row<R, A>(&self, res: &mut R, a: &A, a_row: usize, a_col_in: usize)
+    fn mat_znx_dft_get_row<R, A>(&self, res: &mut R, a: &A, a_row: usize, a_col_in: usize)
     where
         R: VecZnxDftToMut<FFT64>,
         A: MatZnxToRef<FFT64>;
 
+    /// Multiplies A by (X^{k} - 1) and stores the result on R.
+    fn mat_znx_dft_mul_x_pow_minus_one<R, A>(&self, k: i64, res: &mut R, a: &A, scratch: &mut Scratch)
+    where
+        R: MatZnxToMut<FFT64>,
+        A: MatZnxToRef<FFT64>;
+
+    /// Multiplies A by (X^{k} - 1).
+    fn mat_znx_dft_mul_x_pow_minus_one_inplace<A>(&self, k: i64, a: &mut A, scratch: &mut Scratch)
+    where
+        A: MatZnxToMut<FFT64>;
+
+    /// Multiplies A by (X^{k} - 1).
+    fn mat_znx_dft_mul_x_pow_minus_one_add_inplace<R, A>(&self, k: i64, res: &mut R, a: &A, scratch: &mut Scratch)
+    where
+        R: MatZnxToMut<FFT64>,
+        A: MatZnxToRef<FFT64>;
+
     /// Applies the vector matrix product [VecZnxDft] x [MatZnxDft].
     /// The size of `buf` is given by [MatZnxDftOps::vmp_apply_dft_to_dft_tmp_bytes].
     ///
@@ -149,10 +168,142 @@ (b_size * b_cols_out) as u64,
             ) as usize
         }
     }
+
+    fn mat_znx_dft_mul_x_pow_minus_one_scratch_space(&self, size: usize, cols_out: usize) -> usize {
+        let xpm1_dft: usize = self.bytes_of_scalar_znx(1);
+        let xpm1: usize = self.bytes_of_scalar_znx_dft(1);
+        let tmp: usize = self.bytes_of_vec_znx_dft(cols_out, size);
+        xpm1_dft + (xpm1 | 2 * tmp)
+    }
 }
 
 impl MatZnxDftOps<FFT64> for Module<FFT64> {
-    fn vmp_prepare_row<R, A>(&self, res: &mut R, res_row: usize, res_col_in: usize, a: &A)
+    fn mat_znx_dft_mul_x_pow_minus_one<R, A>(&self, k: i64, res: &mut R, a: &A, scratch: &mut Scratch)
+    where
+        R: MatZnxToMut<FFT64>,
+        A: MatZnxToRef<FFT64>,
+    {
+        let mut res: MatZnxDft<&mut [u8], FFT64> = res.to_mut();
+        let a: MatZnxDft<&[u8], FFT64> = a.to_ref();
+
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(res.n(), self.n());
+            assert_eq!(a.n(), self.n());
+            assert_eq!(res.rows(), a.rows());
+            assert_eq!(res.cols_in(), a.cols_in());
+            assert_eq!(res.cols_out(), a.cols_out());
+        }
+
+        let (mut xpm1_dft, scratch1) = scratch.tmp_scalar_znx_dft(self, 1);
+
+        {
+            let (mut xpm1, _) = scratch1.tmp_scalar_znx(self, 1);
+            xpm1.data[0] = 1;
+            self.vec_znx_rotate_inplace(k, &mut xpm1, 0);
+            self.svp_prepare(&mut xpm1_dft, 0, &xpm1, 0);
+        }
+
+        let (mut tmp_0, scratch2) = scratch1.tmp_vec_znx_dft(self, res.cols_out(), res.size());
+        let (mut tmp_1, _) = scratch2.tmp_vec_znx_dft(self, res.cols_out(), res.size());
+
+        (0..res.rows()).for_each(|row_i| {
+            (0..res.cols_in()).for_each(|col_j| {
+                self.mat_znx_dft_get_row(&mut tmp_0, &a, row_i, col_j);
+
+                (0..tmp_0.cols()).for_each(|i| {
+                    self.svp_apply(&mut tmp_1, i, &xpm1_dft, 0, &tmp_0, i);
+                    self.vec_znx_dft_sub_ab_inplace(&mut tmp_1, i, &tmp_0, i);
+                });
+
+                self.mat_znx_dft_set_row(&mut res, row_i, col_j, &tmp_1);
+            });
+        });
+    }
+
+    fn mat_znx_dft_mul_x_pow_minus_one_inplace<A>(&self, k: i64, a: &mut A, scratch: &mut Scratch)
+    where
+        A: MatZnxToMut<FFT64>,
+    {
+        let mut a: MatZnxDft<&mut [u8], FFT64> = a.to_mut();
+
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(a.n(), self.n());
+        }
+
+        let (mut xpm1_dft, scratch1) = scratch.tmp_scalar_znx_dft(self, 1);
+
+        {
+            let (mut xpm1, _) = scratch1.tmp_scalar_znx(self, 1);
+            xpm1.data[0] = 1;
+            self.vec_znx_rotate_inplace(k, &mut xpm1, 0);
+            self.svp_prepare(&mut xpm1_dft, 0, &xpm1, 0);
+        }
+
+        let (mut tmp_0, scratch2) = scratch1.tmp_vec_znx_dft(self, a.cols_out(), a.size());
+        let (mut tmp_1, _) = scratch2.tmp_vec_znx_dft(self, a.cols_out(), a.size());
+
+        (0..a.rows()).for_each(|row_i| {
+            (0..a.cols_in()).for_each(|col_j| {
+                self.mat_znx_dft_get_row(&mut tmp_0, &a, row_i, col_j);
+
+                (0..tmp_0.cols()).for_each(|i| {
+                    self.svp_apply(&mut tmp_1, i, &xpm1_dft, 0, &tmp_0, i);
+                    self.vec_znx_dft_sub_ab_inplace(&mut tmp_1, i, &tmp_0, i);
+                });
+
+                self.mat_znx_dft_set_row(&mut a, row_i, col_j, &tmp_1);
+            });
+        });
+    }
+
+    fn mat_znx_dft_mul_x_pow_minus_one_add_inplace<R, A>(&self, k: i64, res: &mut R, a: &A, scratch: &mut Scratch)
+    where
+        R: MatZnxToMut<FFT64>,
+        A: MatZnxToRef<FFT64>,
+    {
+        let mut res: MatZnxDft<&mut [u8], FFT64> = res.to_mut();
+        let a: MatZnxDft<&[u8], FFT64> = a.to_ref();
+
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(a.n(), self.n());
+        }
+
+        let (mut xpm1_dft, scratch1) = scratch.tmp_scalar_znx_dft(self, 1);
+
+        {
+            let (mut xpm1, _) = scratch1.tmp_scalar_znx(self, 1);
+            xpm1.data[0] = 1;
+            self.vec_znx_rotate_inplace(k, &mut xpm1, 0);
+            self.svp_prepare(&mut xpm1_dft, 0, &xpm1, 0);
+        }
+
+        let (mut tmp_0, scratch2) = scratch1.tmp_vec_znx_dft(self, a.cols_out(), a.size());
+        let (mut tmp_1, _) = scratch2.tmp_vec_znx_dft(self, a.cols_out(), a.size());
+
+        (0..a.rows()).for_each(|row_i| {
+            (0..a.cols_in()).for_each(|col_j| {
+                self.mat_znx_dft_get_row(&mut tmp_0, &a, row_i, col_j);
+
+                (0..tmp_0.cols()).for_each(|i| {
+                    self.svp_apply(&mut tmp_1, i, &xpm1_dft, 0, &tmp_0, i);
+                    self.vec_znx_dft_sub_ab_inplace(&mut tmp_1, i, &tmp_0, i);
+                });
+
+                self.mat_znx_dft_get_row(&mut tmp_0, &res, row_i, col_j);
+
+                (0..tmp_0.cols()).for_each(|i| {
+                    self.vec_znx_dft_add_inplace(&mut tmp_0, i, &tmp_1, i);
+                });
+
+                self.mat_znx_dft_set_row(&mut res, row_i, col_j, &tmp_0);
+            });
+        });
+    }
+
+    fn mat_znx_dft_set_row<R, A>(&self, res: &mut R, res_row: usize, res_col_in: usize, a: &A)
     where
         R: MatZnxToMut<FFT64>,
         A: VecZnxDftToRef<FFT64>,
@@ -204,7 +355,7 @@ );
         }
     }
 
-    fn vmp_extract_row<R, A>(&self, res: &mut R, a: &A, a_row: usize, a_col_in: usize)
+    fn mat_znx_dft_get_row<R, A>(&self, res: &mut R, a: &A, a_row: usize, a_col_in: usize)
     where
         R: VecZnxDftToMut<FFT64>,
         A: MatZnxToRef<FFT64>,
@@ -376,7 +527,7 @@
     use super::{MatZnxDftAlloc, MatZnxDftScratch};
 
     #[test]
-    fn vmp_prepare_row() {
+    fn vmp_set_row() {
         let module: Module<FFT64> = Module::<FFT64>::new(16);
         let basek: usize = 8;
         let mat_rows: usize = 4;
@@ -395,8 +546,8 @@ (0..mat_cols_out).for_each(|col_out| {
                     a.fill_uniform(basek, col_out, mat_size, &mut source);
                     module.vec_znx_dft(1, 0, &mut a_dft, col_out, &a, col_out);
                 });
-                module.vmp_prepare_row(&mut mat, row_i, col_in, &a_dft);
-                module.vmp_extract_row(&mut b_dft, &mat, row_i, col_in);
+                module.mat_znx_dft_set_row(&mut mat, row_i, col_in, &a_dft);
+                module.mat_znx_dft_get_row(&mut b_dft, &mat, row_i, col_in);
                 assert_eq!(a_dft.raw(), b_dft.raw());
             }
         }
@@ -413,10 +564,10 @@ 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;
+        [1, 2].iter().for_each(|cols_in| {
+            [1, 2].iter().for_each(|cols_out| {
+                let a_cols: usize = *cols_in;
+                let res_cols: usize = *cols_out;
 
                 let mat_rows: usize = a_size;
                 let mat_cols_in: usize = a_cols;
@@ -456,7 +607,7 @@ tmp.at_mut(col_out_i, row_i)[idx] = 1 as i64; // X^{idx}
                             module.vec_znx_dft(1, 0, &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);
+                        module.mat_znx_dft_set_row(&mut mat_znx_dft, row_i, col_in_i, &c_dft);
                     });
                 });
 
@@ -499,11 +650,11 @@ let mat_size: usize = 5;
         let res_size: usize = a_size;
         let mut source: Source = Source::new([0u8; 32]);
 
-        [1, 2].iter().for_each(|in_cols| {
-            [1, 2].iter().for_each(|out_cols| {
+        [1, 2].iter().for_each(|cols_in| {
+            [1, 2].iter().for_each(|cols_out| {
                 (0..res_size).for_each(|shift| {
-                    let a_cols: usize = *in_cols;
-                    let res_cols: usize = *out_cols;
+                    let a_cols: usize = *cols_in;
+                    let res_cols: usize = *cols_out;
 
                     let mat_rows: usize = a_size;
                     let mat_cols_in: usize = a_cols;
@@ -543,7 +694,7 @@ tmp.at_mut(col_out_i, row_i)[idx] = 1 as i64; // X^{idx}
                                 module.vec_znx_dft(1, 0, &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);
+                            module.mat_znx_dft_set_row(&mut mat_znx_dft, row_i, col_in_i, &c_dft);
                         });
                     });
 
@@ -601,13 +752,13 @@ let a_size: usize = 6;
         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| {
+        [1, 2].iter().for_each(|cols_in| {
+            [1, 2].iter().for_each(|cols_out| {
                 [1, 3, 6].iter().for_each(|digits| {
                     let mut source: Source = Source::new([0u8; 32]);
 
-                    let a_cols: usize = *in_cols;
-                    let res_cols: usize = *out_cols;
+                    let a_cols: usize = *cols_in;
+                    let res_cols: usize = *cols_out;
 
                     let mat_rows: usize = a_size;
                     let mat_cols_in: usize = a_cols;
@@ -652,7 +803,7 @@ tmp.at_mut(col_out_i, limb)[idx] = 1 as i64; // X^{idx}
                                 module.vec_znx_dft(1, 0, &mut c_dft, col_out_i, &tmp, col_out_i);
                                 tmp.at_mut(col_out_i, limb)[idx] = 0 as i64;
                             });
-                            module.vmp_prepare_row(&mut mat_znx_dft, row_i, col_in_i, &c_dft);
+                            module.mat_znx_dft_set_row(&mut mat_znx_dft, row_i, col_in_i, &c_dft);
                         });
                     });
 
@@ -694,6 +845,151 @@ });
 
                     assert_eq!(res_have, res_want)
                 });
+            });
+        });
+    }
+
+    #[test]
+    fn mat_znx_dft_mul_x_pow_minus_one() {
+        let log_n: i32 = 5;
+        let n: usize = 1 << log_n;
+
+        let module: Module<FFT64> = Module::<FFT64>::new(n);
+        let basek: usize = 8;
+        let rows: usize = 2;
+        let cols_in: usize = 2;
+        let cols_out: usize = 2;
+        let size: usize = 4;
+
+        let mut scratch: ScratchOwned = ScratchOwned::new(module.mat_znx_dft_mul_x_pow_minus_one_scratch_space(size, cols_out));
+
+        let mut mat_want: MatZnxDft<Vec<u8>, FFT64> = module.new_mat_znx_dft(rows, cols_in, cols_out, size);
+        let mut mat_have: MatZnxDft<Vec<u8>, FFT64> = module.new_mat_znx_dft(rows, cols_in, cols_out, size);
+
+        let mut tmp: VecZnx<Vec<u8>> = module.new_vec_znx(1, size);
+        let mut tmp_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(cols_out, size);
+
+        let mut source: Source = Source::new([0u8; 32]);
+
+        (0..mat_want.rows()).for_each(|row_i| {
+            (0..mat_want.cols_in()).for_each(|col_i| {
+                (0..cols_out).for_each(|j| {
+                    tmp.fill_uniform(basek, 0, size, &mut source);
+                    module.vec_znx_dft(1, 0, &mut tmp_dft, j, &tmp, 0);
+                });
+
+                module.mat_znx_dft_set_row(&mut mat_want, row_i, col_i, &tmp_dft);
+            });
+        });
+
+        let k: i64 = 1;
+
+        module.mat_znx_dft_mul_x_pow_minus_one(k, &mut mat_have, &mat_want, scratch.borrow());
+
+        let mut have: VecZnx<Vec<u8>> = module.new_vec_znx(cols_out, size);
+        let mut want: VecZnx<Vec<u8>> = module.new_vec_znx(cols_out, size);
+        let mut tmp_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, size);
+
+        (0..mat_want.rows()).for_each(|row_i| {
+            (0..mat_want.cols_in()).for_each(|col_i| {
+                module.mat_znx_dft_get_row(&mut tmp_dft, &mat_want, row_i, col_i);
+
+                (0..cols_out).for_each(|j| {
+                    module.vec_znx_idft(&mut tmp_big, 0, &tmp_dft, j, scratch.borrow());
+                    module.vec_znx_big_normalize(basek, &mut tmp, 0, &tmp_big, 0, scratch.borrow());
+                    module.vec_znx_rotate(k, &mut want, j, &tmp, 0);
+                    module.vec_znx_sub_ab_inplace(&mut want, j, &tmp, 0);
+                    module.vec_znx_normalize_inplace(basek, &mut want, j, scratch.borrow());
+                });
+
+                module.mat_znx_dft_get_row(&mut tmp_dft, &mat_have, row_i, col_i);
+
+                (0..cols_out).for_each(|j| {
+                    module.vec_znx_idft(&mut tmp_big, 0, &tmp_dft, j, scratch.borrow());
+                    module.vec_znx_big_normalize(basek, &mut have, j, &tmp_big, 0, scratch.borrow());
+                });
+
+                assert_eq!(have, want)
+            });
+        });
+    }
+
+    #[test]
+    fn mat_znx_dft_mul_x_pow_minus_one_add_inplace() {
+        let log_n: i32 = 5;
+        let n: usize = 1 << log_n;
+
+        let module: Module<FFT64> = Module::<FFT64>::new(n);
+        let basek: usize = 8;
+        let rows: usize = 2;
+        let cols_in: usize = 2;
+        let cols_out: usize = 2;
+        let size: usize = 4;
+
+        let mut scratch: ScratchOwned = ScratchOwned::new(module.mat_znx_dft_mul_x_pow_minus_one_scratch_space(size, cols_out));
+
+        let mut mat_want: MatZnxDft<Vec<u8>, FFT64> = module.new_mat_znx_dft(rows, cols_in, cols_out, size);
+        let mut mat_have: MatZnxDft<Vec<u8>, FFT64> = module.new_mat_znx_dft(rows, cols_in, cols_out, size);
+
+        let mut tmp: VecZnx<Vec<u8>> = module.new_vec_znx(1, size);
+        let mut tmp_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(cols_out, size);
+
+        let mut source: Source = Source::new([0u8; 32]);
+
+        (0..mat_have.rows()).for_each(|row_i| {
+            (0..mat_have.cols_in()).for_each(|col_i| {
+                (0..cols_out).for_each(|j| {
+                    tmp.fill_uniform(basek, 0, size, &mut source);
+                    module.vec_znx_dft(1, 0, &mut tmp_dft, j, &tmp, 0);
+                });
+
+                module.mat_znx_dft_set_row(&mut mat_have, row_i, col_i, &tmp_dft);
+            });
+        });
+
+        (0..mat_want.rows()).for_each(|row_i| {
+            (0..mat_want.cols_in()).for_each(|col_i| {
+                (0..cols_out).for_each(|j| {
+                    tmp.fill_uniform(basek, 0, size, &mut source);
+                    module.vec_znx_dft(1, 0, &mut tmp_dft, j, &tmp, 0);
+                });
+
+                module.mat_znx_dft_set_row(&mut mat_want, row_i, col_i, &tmp_dft);
+            });
+        });
+
+        let k: i64 = 1;
+
+        module.mat_znx_dft_mul_x_pow_minus_one_add_inplace(k, &mut mat_have, &mat_want, scratch.borrow());
+
+        let mut have: VecZnx<Vec<u8>> = module.new_vec_znx(cols_out, size);
+        let mut want: VecZnx<Vec<u8>> = module.new_vec_znx(cols_out, size);
+        let mut tmp_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, size);
+
+        let mut source: Source = Source::new([0u8; 32]);
+        (0..mat_want.rows()).for_each(|row_i| {
+            (0..mat_want.cols_in()).for_each(|col_i| {
+                module.mat_znx_dft_get_row(&mut tmp_dft, &mat_want, row_i, col_i);
+
+                (0..cols_out).for_each(|j| {
+                    module.vec_znx_idft(&mut tmp_big, 0, &tmp_dft, j, scratch.borrow());
+                    module.vec_znx_big_normalize(basek, &mut tmp, 0, &tmp_big, 0, scratch.borrow());
+                    module.vec_znx_rotate(k, &mut want, j, &tmp, 0);
+                    module.vec_znx_sub_ab_inplace(&mut want, j, &tmp, 0);
+
+                    tmp.fill_uniform(basek, 0, size, &mut source);
+                    module.vec_znx_add_inplace(&mut want, j, &tmp, 0);
+                    module.vec_znx_normalize_inplace(basek, &mut want, j, scratch.borrow());
+                });
+
+                module.mat_znx_dft_get_row(&mut tmp_dft, &mat_have, row_i, col_i);
+
+                (0..cols_out).for_each(|j| {
+                    module.vec_znx_idft(&mut tmp_big, 0, &tmp_dft, j, scratch.borrow());
+                    module.vec_znx_big_normalize(basek, &mut have, j, &tmp_big, 0, scratch.borrow());
+                });
+
+                assert_eq!(have, want)
             });
         });
     }

@@ -72,15 +72,44 @@ .iter_mut()
             .for_each(|x: &mut i64| *x = (((source.next_u32() & 1) as i64) << 1) - 1);
         self.at_mut(col, 0).shuffle(source);
     }
+
+    pub fn fill_binary_prob(&mut self, col: usize, prob: f64, source: &mut Source) {
+        let choices: [i64; 2] = [0, 1];
+        let weights: [f64; 2] = [1.0 - prob, prob];
+        let dist: WeightedIndex<f64> = WeightedIndex::new(&weights).unwrap();
+        self.at_mut(col, 0)
+            .iter_mut()
+            .for_each(|x: &mut i64| *x = choices[dist.sample(source)]);
+    }
+
+    pub fn fill_binary_hw(&mut self, col: usize, hw: usize, source: &mut Source) {
+        assert!(hw <= self.n());
+        self.at_mut(col, 0)[..hw]
+            .iter_mut()
+            .for_each(|x: &mut i64| *x = (source.next_u32() & 1) as i64);
+        self.at_mut(col, 0).shuffle(source);
+    }
+
+    pub fn fill_binary_block(&mut self, col: usize, block_size: usize, source: &mut Source) {
+        assert!(self.n() % block_size == 0);
+        let max_idx: u64 = (block_size + 1) as u64;
+        let mask_idx: u64 = (1 << ((u64::BITS - max_idx.leading_zeros()) as u64)) - 1;
+        for block in self.at_mut(col, 0).chunks_mut(block_size) {
+            let idx: usize = source.next_u64n(max_idx, mask_idx) as usize;
+            if idx != block_size {
+                block[idx] = 1;
+            }
+        }
+    }
 }
 
 impl<D: From<Vec<u8>>> ScalarZnx<D> {
-    pub(crate) fn bytes_of<S: Sized>(n: usize, cols: usize) -> usize {
-        n * cols * size_of::<S>()
+    pub(crate) fn bytes_of(n: usize, cols: usize) -> usize {
+        n * cols * size_of::<i64>()
     }
 
-    pub(crate) fn new<S: Sized>(n: usize, cols: usize) -> Self {
-        let data = alloc_aligned::<u8>(Self::bytes_of::<S>(n, cols));
+    pub fn new(n: usize, cols: usize) -> Self {
+        let data: Vec<u8> = alloc_aligned::<u8>(Self::bytes_of(n, cols));
         Self {
             data: data.into(),
             n,
@@ -88,9 +117,9 @@ cols,
         }
     }
 
-    pub(crate) fn new_from_bytes<S: Sized>(n: usize, cols: usize, bytes: impl Into<Vec<u8>>) -> Self {
+    pub(crate) fn new_from_bytes(n: usize, cols: usize, bytes: impl Into<Vec<u8>>) -> Self {
         let data: Vec<u8> = bytes.into();
-        assert!(data.len() == Self::bytes_of::<S>(n, cols));
+        assert!(data.len() == Self::bytes_of(n, cols));
         Self {
             data: data.into(),
             n,
@@ -102,7 +131,7 @@
 pub type ScalarZnxOwned = ScalarZnx<Vec<u8>>;
 
 pub(crate) fn bytes_of_scalar_znx<B: Backend>(module: &Module<B>, cols: usize) -> usize {
-    ScalarZnxOwned::bytes_of::<i64>(module.n(), cols)
+    ScalarZnxOwned::bytes_of(module.n(), cols)
 }
 
 pub trait ScalarZnxAlloc {
@@ -113,13 +142,13 @@ }
 
 impl<B: Backend> ScalarZnxAlloc for Module<B> {
     fn bytes_of_scalar_znx(&self, cols: usize) -> usize {
-        ScalarZnxOwned::bytes_of::<i64>(self.n(), cols)
+        ScalarZnxOwned::bytes_of(self.n(), cols)
     }
     fn new_scalar_znx(&self, cols: usize) -> ScalarZnxOwned {
-        ScalarZnxOwned::new::<i64>(self.n(), cols)
+        ScalarZnxOwned::new(self.n(), cols)
     }
     fn new_scalar_znx_from_bytes(&self, cols: usize, bytes: Vec<u8>) -> ScalarZnxOwned {
-        ScalarZnxOwned::new_from_bytes::<i64>(self.n(), cols, bytes)
+        ScalarZnxOwned::new_from_bytes(self.n(), cols, bytes)
     }
 }
 

@@ -29,7 +29,7 @@ where
         R: VecZnxDftToMut<BACKEND>,
         A: ScalarZnxDftToRef<BACKEND>;
 
-    fn svp_idft<R, A>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize, scratch: &mut Scratch)
+    fn scalar_znx_idft<R, A>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize, scratch: &mut Scratch)
     where
         R: ScalarZnxToMut,
         A: ScalarZnxDftToRef<BACKEND>;
@@ -50,7 +50,7 @@ }
 }
 
 impl ScalarZnxDftOps<FFT64> for Module<FFT64> {
-    fn svp_idft<R, A>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize, scratch: &mut Scratch)
+    fn scalar_znx_idft<R, A>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize, scratch: &mut Scratch)
     where
         R: ScalarZnxToMut,
         A: ScalarZnxDftToRef<FFT64>,

@@ -111,6 +111,16 @@ .for_each(|x: &mut i64| *x &= mask)
         }
     }
 
+    pub fn rotate(&mut self, k: i64) {
+        unsafe {
+            (0..self.cols()).for_each(|i| {
+                (0..self.size()).for_each(|j| {
+                    znx::znx_rotate_inplace_i64(self.n() as u64, k, self.at_mut_ptr(i, j));
+                });
+            })
+        }
+    }
+
     pub fn rsh(&mut self, basek: usize, k: usize, scratch: &mut Scratch) {
         let n: usize = self.n();
         let cols: usize = self.cols();
@@ -177,7 +187,7 @@ pub(crate) fn bytes_of<Scalar: Sized>(n: usize, cols: usize, size: usize) -> usize {
         n * cols * size * size_of::<Scalar>()
     }
 
-    pub(crate) fn new<Scalar: Sized>(n: usize, cols: usize, size: usize) -> Self {
+    pub fn new<Scalar: Sized>(n: usize, cols: usize, size: usize) -> Self {
         let data = alloc_aligned::<u8>(Self::bytes_of::<Scalar>(n, cols, size));
         Self {
             data: data.into(),
@@ -243,7 +253,12 @@ fn normalize_tmp_bytes(n: usize) -> usize {
     n * std::mem::size_of::<i64>()
 }
 
-#[allow(dead_code)]
+impl<D: AsRef<[u8]> + AsMut<[u8]>> VecZnx<D> {
+    pub fn normalize(&mut self, basek: usize, a_col: usize, tmp_bytes: &mut [u8]) {
+        normalize(basek, self, a_col, tmp_bytes);
+    }
+}
+
 fn normalize<D: AsMut<[u8]> + AsRef<[u8]>>(basek: usize, a: &mut VecZnx<D>, a_col: usize, tmp_bytes: &mut [u8]) {
     let n: usize = a.n();
 

@@ -53,6 +53,22 @@ where
         R: VecZnxDftToMut<B>,
         A: VecZnxDftToRef<B>;
 
+    fn vec_znx_dft_sub<R, A, D>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize, b: &D, b_col: usize)
+    where
+        R: VecZnxDftToMut<B>,
+        A: VecZnxDftToRef<B>,
+        D: VecZnxDftToRef<B>;
+
+    fn vec_znx_dft_sub_ab_inplace<R, A>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize)
+    where
+        R: VecZnxDftToMut<B>,
+        A: VecZnxDftToRef<B>;
+
+    fn vec_znx_dft_sub_ba_inplace<R, A>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize)
+    where
+        R: VecZnxDftToMut<B>,
+        A: VecZnxDftToRef<B>;
+
     fn vec_znx_dft_copy<R, A>(&self, step: usize, offset: usize, res: &mut R, res_col: usize, a: &A, a_col: usize)
     where
         R: VecZnxDftToMut<B>,
@@ -144,6 +160,86 @@ 1,
                     res_mut.at_ptr(res_col, j) as *const vec_znx_dft::vec_znx_dft_t,
                     1,
                     a_ref.at_ptr(a_col, j) as *const vec_znx_dft::vec_znx_dft_t,
+                    1,
+                );
+            });
+        }
+    }
+
+    fn vec_znx_dft_sub<R, A, D>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize, b: &D, b_col: usize)
+    where
+        R: VecZnxDftToMut<FFT64>,
+        A: VecZnxDftToRef<FFT64>,
+        D: VecZnxDftToRef<FFT64>,
+    {
+        let mut res_mut: VecZnxDft<&mut [u8], FFT64> = res.to_mut();
+        let a_ref: VecZnxDft<&[u8], FFT64> = a.to_ref();
+        let b_ref: VecZnxDft<&[u8], FFT64> = b.to_ref();
+
+        let min_size: usize = res_mut.size().min(a_ref.size()).min(b_ref.size());
+
+        unsafe {
+            (0..min_size).for_each(|j| {
+                vec_znx_dft::vec_dft_sub(
+                    self.ptr,
+                    res_mut.at_mut_ptr(res_col, j) as *mut vec_znx_dft::vec_znx_dft_t,
+                    1,
+                    a_ref.at_ptr(a_col, j) as *const vec_znx_dft::vec_znx_dft_t,
+                    1,
+                    b_ref.at_ptr(b_col, j) as *const vec_znx_dft::vec_znx_dft_t,
+                    1,
+                );
+            });
+        }
+        (min_size..res_mut.size()).for_each(|j| {
+            res_mut.zero_at(res_col, j);
+        })
+    }
+
+    fn vec_znx_dft_sub_ab_inplace<R, A>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize)
+    where
+        R: VecZnxDftToMut<FFT64>,
+        A: VecZnxDftToRef<FFT64>,
+    {
+        let mut res_mut: VecZnxDft<&mut [u8], FFT64> = res.to_mut();
+        let a_ref: VecZnxDft<&[u8], FFT64> = a.to_ref();
+
+        let min_size: usize = res_mut.size().min(a_ref.size());
+
+        unsafe {
+            (0..min_size).for_each(|j| {
+                vec_znx_dft::vec_dft_sub(
+                    self.ptr,
+                    res_mut.at_mut_ptr(res_col, j) as *mut vec_znx_dft::vec_znx_dft_t,
+                    1,
+                    res_mut.at_ptr(res_col, j) as *const vec_znx_dft::vec_znx_dft_t,
+                    1,
+                    a_ref.at_ptr(a_col, j) as *const vec_znx_dft::vec_znx_dft_t,
+                    1,
+                );
+            });
+        }
+    }
+
+    fn vec_znx_dft_sub_ba_inplace<R, A>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize)
+    where
+        R: VecZnxDftToMut<FFT64>,
+        A: VecZnxDftToRef<FFT64>,
+    {
+        let mut res_mut: VecZnxDft<&mut [u8], FFT64> = res.to_mut();
+        let a_ref: VecZnxDft<&[u8], FFT64> = a.to_ref();
+
+        let min_size: usize = res_mut.size().min(a_ref.size());
+
+        unsafe {
+            (0..min_size).for_each(|j| {
+                vec_znx_dft::vec_dft_sub(
+                    self.ptr,
+                    res_mut.at_mut_ptr(res_col, j) as *mut vec_znx_dft::vec_znx_dft_t,
+                    1,
+                    a_ref.at_ptr(a_col, j) as *const vec_znx_dft::vec_znx_dft_t,
+                    1,
+                    res_mut.at_ptr(res_col, j) as *const vec_znx_dft::vec_znx_dft_t,
                     1,
                 );
             });

@@ -57,8 +57,8 @@ /// Returns a non-mutable pointer starting at the j-th small polynomial of the i-th column.
     fn at_ptr(&self, i: usize, j: usize) -> *const Self::Scalar {
         #[cfg(debug_assertions)]
         {
-            assert!(i < self.cols());
-            assert!(j < self.size());
+            assert!(i < self.cols(), "{} >= {}", i, self.cols());
+            assert!(j < self.size(), "{} >= {}", j, self.size());
         }
         let offset: usize = self.n() * (j * self.cols() + i);
         unsafe { self.as_ptr().add(offset) }
@@ -85,8 +85,8 @@ /// Returns a mutable pointer starting at the j-th small polynomial of the i-th column.
     fn at_mut_ptr(&mut self, i: usize, j: usize) -> *mut Self::Scalar {
         #[cfg(debug_assertions)]
         {
-            assert!(i < self.cols());
-            assert!(j < self.size());
+            assert!(i < self.cols(), "{} >= {}", i, self.cols());
+            assert!(j < self.size(), "{} >= {}", j, self.size());
         }
         let offset: usize = self.n() * (j * self.cols() + i);
         unsafe { self.as_mut_ptr().add(offset) }

@@ -1,5 +1,5 @@
 use backend::{FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned};
-use core::{GGSWCiphertext, GLWECiphertext, GLWESecret, Infos};
+use core::{FourierGLWESecret, GGSWCiphertext, GLWECiphertext, GLWESecret, Infos};
 use criterion::{BenchmarkId, Criterion, criterion_group, criterion_main};
 use sampling::source::Source;
 use std::hint::black_box;
@@ -26,7 +26,7 @@ let k_ggsw: usize = p.k_ggsw;
         let rank: usize = p.rank;
         let digits: usize = 1;
 
-        let rows: usize = (p.k_ct_in + p.basek - 1) / p.basek;
+        let rows: usize = 1; //(p.k_ct_in + p.basek - 1) / p.basek;
         let sigma: f64 = 3.2;
 
         let mut ct_ggsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k_ggsw, rows, digits, rank);
@@ -52,13 +52,14 @@ let mut source_xs = Source::new([0u8; 32]);
         let mut source_xe = Source::new([0u8; 32]);
         let mut source_xa = Source::new([0u8; 32]);
 
-        let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-        sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+        let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+        sk.fill_ternary_prob(0.5, &mut source_xs);
+        let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
         ct_ggsw.encrypt_sk(
             &module,
             &pt_rgsw,
-            &sk,
+            &sk_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,
@@ -67,7 +68,7 @@ );
 
         ct_glwe_in.encrypt_zero_sk(
             &module,
-            &sk,
+            &sk_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,
@@ -80,11 +81,11 @@ }
     }
 
     let params_set: Vec<Params> = vec![Params {
-        log_n: 10,
-        basek: 7,
-        k_ct_in: 27,
-        k_ct_out: 27,
-        k_ggsw: 27,
+        log_n: 11,
+        basek: 22,
+        k_ct_in: 44,
+        k_ct_out: 44,
+        k_ggsw: 54,
         rank: 1,
     }];
 
@@ -134,13 +135,14 @@ let mut source_xs = Source::new([0u8; 32]);
         let mut source_xe = Source::new([0u8; 32]);
         let mut source_xa = Source::new([0u8; 32]);
 
-        let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-        sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+        let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+        sk.fill_ternary_prob(0.5, &mut source_xs);
+        let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
         ct_ggsw.encrypt_sk(
             &module,
             &pt_rgsw,
-            &sk,
+            &sk_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,
@@ -149,7 +151,7 @@ );
 
         ct_glwe.encrypt_zero_sk(
             &module,
-            &sk,
+            &sk_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,

@@ -1,5 +1,5 @@
 use backend::{FFT64, Module, ScratchOwned};
-use core::{AutomorphismKey, GLWECiphertext, GLWESecret, GLWESwitchingKey, Infos};
+use core::{FourierGLWESecret, GLWEAutomorphismKey, GLWECiphertext, GLWESecret, GLWESwitchingKey, Infos};
 use criterion::{BenchmarkId, Criterion, criterion_group, criterion_main};
 use sampling::source::Source;
 use std::{hint::black_box, time::Duration};
@@ -32,12 +32,13 @@
         let rows: usize = (p.k_ct_in + (p.basek * digits) - 1) / (p.basek * digits);
         let sigma: f64 = 3.2;
 
-        let mut ksk: AutomorphismKey<Vec<u8>, FFT64> = AutomorphismKey::alloc(&module, basek, k_grlwe, rows, digits, rank_out);
+        let mut ksk: GLWEAutomorphismKey<Vec<u8>, FFT64> =
+            GLWEAutomorphismKey::alloc(&module, basek, k_grlwe, rows, digits, rank_out);
         let mut ct_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_rlwe_in, rank_in);
         let mut ct_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_rlwe_out, rank_out);
 
         let mut scratch = ScratchOwned::new(
-            GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ksk.k(), rank_out)
+            GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ksk.k(), rank_in, rank_out)
                 | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_in.k())
                 | GLWECiphertext::keyswitch_scratch_space(
                     &module,
@@ -55,13 +56,14 @@ let mut source_xs = Source::new([0u8; 32]);
         let mut source_xe = Source::new([0u8; 32]);
         let mut source_xa = Source::new([0u8; 32]);
 
-        let mut sk_in: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_in);
-        sk_in.fill_ternary_prob(&module, 0.5, &mut source_xs);
+        let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_in);
+        sk_in.fill_ternary_prob(0.5, &mut source_xs);
+        let sk_in_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_in);
 
-        let mut sk_out: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_out);
-        sk_out.fill_ternary_prob(&module, 0.5, &mut source_xs);
+        let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_out);
+        sk_out.fill_ternary_prob(0.5, &mut source_xs);
 
-        ksk.generate_from_sk(
+        ksk.encrypt_sk(
             &module,
             -1,
             &sk_in,
@@ -73,7 +75,7 @@ );
 
         ct_in.encrypt_zero_sk(
             &module,
-            &sk_in,
+            &sk_in_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,
@@ -137,7 +139,7 @@ let mut ksk: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, digits, rank, rank);
         let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
 
         let mut scratch = ScratchOwned::new(
-            GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ksk.k(), rank)
+            GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ksk.k(), rank, rank)
                 | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
                 | GLWECiphertext::keyswitch_inplace_scratch_space(&module, basek, ct.k(), ksk.k(), digits, rank),
         );
@@ -146,16 +148,18 @@ let mut source_xs: Source = Source::new([0u8; 32]);
         let mut source_xe: Source = Source::new([0u8; 32]);
         let mut source_xa: Source = Source::new([0u8; 32]);
 
-        let mut sk_in: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-        sk_in.fill_ternary_prob(&&module, 0.5, &mut source_xs);
+        let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+        sk_in.fill_ternary_prob(0.5, &mut source_xs);
+        let sk_in_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_in);
 
-        let mut sk_out: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-        sk_out.fill_ternary_prob(&&module, 0.5, &mut source_xs);
+        let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+        sk_out.fill_ternary_prob(0.5, &mut source_xs);
+        let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
 
-        ksk.generate_from_sk(
+        ksk.encrypt_sk(
             &module,
             &sk_in,
-            &sk_out,
+            &sk_out_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,
@@ -164,7 +168,7 @@ );
 
         ct.encrypt_zero_sk(
             &module,
-            &sk_in,
+            &sk_in_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,

@@ -2,7 +2,7 @@ use backend::{Backend, FFT64, MatZnxDft, MatZnxDftOps, Module, ScalarZnxOps, Scratch, VecZnx, VecZnxDftOps, VecZnxOps, ZnxZero};
 use sampling::source::Source;
 
 use crate::{
-    GGLWECiphertext, GGSWCiphertext, GLWECiphertext, GLWECiphertextFourier, GLWESecret, GLWESwitchingKey, GetRow, Infos,
+    FourierGLWECiphertext, GGLWECiphertext, GGSWCiphertext, GLWECiphertext, GLWESecret, GLWESwitchingKey, GetRow, Infos,
     ScratchCore, SetRow,
 };
 
@@ -68,9 +68,9 @@ &self,
         module: &Module<FFT64>,
         row_i: usize,
         col_j: usize,
-        res: &mut GLWECiphertextFourier<R, FFT64>,
+        res: &mut FourierGLWECiphertext<R, FFT64>,
     ) {
-        module.vmp_extract_row(&mut res.data, &self.key.0.data, row_i, col_j);
+        module.mat_znx_dft_get_row(&mut res.data, &self.key.0.data, row_i, col_j);
     }
 }
 
@@ -80,9 +80,9 @@ &mut self,
         module: &Module<FFT64>,
         row_i: usize,
         col_j: usize,
-        a: &GLWECiphertextFourier<R, FFT64>,
+        a: &FourierGLWECiphertext<R, FFT64>,
     ) {
-        module.vmp_prepare_row(&mut self.key.0.data, row_i, col_j, &a.data);
+        module.mat_znx_dft_set_row(&mut self.key.0.data, row_i, col_j, &a.data);
     }
 }
 
@@ -127,8 +127,8 @@ k_ksk: usize,
         digits: usize,
         rank: usize,
     ) -> usize {
-        let tmp_dft: usize = GLWECiphertextFourier::bytes_of(module, basek, k_in, rank);
-        let tmp_idft: usize = GLWECiphertextFourier::bytes_of(module, basek, k_out, rank);
+        let tmp_dft: usize = FourierGLWECiphertext::bytes_of(module, basek, k_in, rank);
+        let tmp_idft: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank);
         let idft: usize = module.vec_znx_idft_tmp_bytes();
         let keyswitch: usize = GLWECiphertext::keyswitch_inplace_scratch_space(module, basek, k_out, k_ksk, digits, rank);
         tmp_dft + tmp_idft + idft + keyswitch

@@ -0,0 +1,463 @@
+use backend::{
+    FFT64, MatZnxDftOps, MatZnxDftScratch, Module, ScalarZnxDft, ScalarZnxDftAlloc, ScalarZnxDftOps,
+    Scratch, VecZnxAlloc, VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDftAlloc, VecZnxDftOps, VecZnxOps, ZnxView,
+    ZnxViewMut, ZnxZero,
+};
+use itertools::izip;
+
+use crate::{
+    GLWECiphertext, GLWECiphertextToMut, GLWEOps, Infos, LWECiphertext, ScratchCore,
+    blind_rotation::{key::BlindRotationKeyCGGI, lut::LookUpTable},
+    dist::Distribution,
+    lwe::ciphertext::LWECiphertextToRef,
+};
+
+pub fn cggi_blind_rotate_scratch_space(
+    module: &Module<FFT64>,
+    block_size: usize,
+    extension_factor: usize,
+    basek: usize,
+    k_res: usize,
+    k_brk: usize,
+    rows: usize,
+    rank: usize,
+) -> usize {
+    let brk_size: usize = k_brk.div_ceil(basek);
+
+    if block_size > 1 {
+        let cols: usize = rank + 1;
+        let acc_dft: usize = module.bytes_of_vec_znx_dft(cols, rows) * extension_factor;
+        let acc_big: usize = module.bytes_of_vec_znx_big(1, brk_size);
+        let vmp_res: usize = module.bytes_of_vec_znx_dft(cols, brk_size) * extension_factor;
+        let acc_dft_add: usize = vmp_res;
+        let xai_plus_y: usize = module.bytes_of_scalar_znx_dft(1);
+        let xai_plus_y_dft: usize = module.bytes_of_scalar_znx_dft(1);
+        let vmp: usize = module.vmp_apply_tmp_bytes(brk_size, rows, rows, 2, 2, brk_size); // GGSW product: (1 x 2) x (2 x 2)
+
+        let acc: usize;
+        if extension_factor > 1 {
+            acc = module.bytes_of_vec_znx(cols, k_res.div_ceil(basek)) * extension_factor;
+        } else {
+            acc = 0;
+        }
+
+        return acc
+            + acc_dft
+            + acc_dft_add
+            + vmp_res
+            + xai_plus_y
+            + xai_plus_y_dft
+            + (vmp | (acc_big + (module.vec_znx_big_normalize_tmp_bytes() | module.vec_znx_idft_tmp_bytes())));
+    } else {
+        2 * GLWECiphertext::bytes_of(module, basek, k_res, rank)
+            + GLWECiphertext::external_product_scratch_space(module, basek, k_res, k_res, k_brk, 1, rank)
+    }
+}
+
+pub fn cggi_blind_rotate<DataRes, DataIn, DataBrk>(
+    module: &Module<FFT64>,
+    res: &mut GLWECiphertext<DataRes>,
+    lwe: &LWECiphertext<DataIn>,
+    lut: &LookUpTable,
+    brk: &BlindRotationKeyCGGI<DataBrk, FFT64>,
+    scratch: &mut Scratch,
+) where
+    DataRes: AsRef<[u8]> + AsMut<[u8]>,
+    DataIn: AsRef<[u8]>,
+    DataBrk: AsRef<[u8]>,
+{
+    match brk.dist {
+        Distribution::BinaryBlock(_) | Distribution::BinaryFixed(_) | Distribution::BinaryProb(_) | Distribution::ZERO => {
+            if lut.extension_factor() > 1 {
+                cggi_blind_rotate_block_binary_extended(module, res, lwe, lut, brk, scratch);
+            } else if brk.block_size() > 1 {
+                cggi_blind_rotate_block_binary(module, res, lwe, lut, brk, scratch);
+            } else {
+                cggi_blind_rotate_binary_standard(module, res, lwe, lut, brk, scratch);
+            }
+        }
+        // TODO: ternary distribution ?
+        _ => panic!(
+            "invalid BlindRotationKeyCGGI distribution: must be BinaryBlock, BinaryFixed or BinaryProb (or ZERO for debugging)"
+        ),
+    }
+}
+
+pub(crate) fn cggi_blind_rotate_block_binary_extended<DataRes, DataIn, DataBrk>(
+    module: &Module<FFT64>,
+    res: &mut GLWECiphertext<DataRes>,
+    lwe: &LWECiphertext<DataIn>,
+    lut: &LookUpTable,
+    brk: &BlindRotationKeyCGGI<DataBrk, FFT64>,
+    scratch: &mut Scratch,
+) where
+    DataRes: AsRef<[u8]> + AsMut<[u8]>,
+    DataIn: AsRef<[u8]>,
+    DataBrk: AsRef<[u8]>,
+{
+    let extension_factor: usize = lut.extension_factor();
+    let basek: usize = res.basek();
+    let rows: usize = brk.rows();
+    let cols: usize = res.rank() + 1;
+
+    let (mut acc, scratch1) = scratch.tmp_slice_vec_znx(extension_factor, module, cols, res.size());
+    let (mut acc_dft, scratch2) = scratch1.tmp_slice_vec_znx_dft(extension_factor, module, cols, rows);
+    let (mut vmp_res, scratch3) = scratch2.tmp_slice_vec_znx_dft(extension_factor, module, cols, brk.size());
+    let (mut acc_add_dft, scratch4) = scratch3.tmp_slice_vec_znx_dft(extension_factor, module, cols, brk.size());
+    let (mut minus_one, scratch5) = scratch4.tmp_scalar_znx_dft(module, 1);
+    let (mut xai_plus_y_dft, scratch6) = scratch5.tmp_scalar_znx_dft(module, 1);
+
+    minus_one.raw_mut()[..module.n() >> 1].fill(-1.0);
+
+    (0..extension_factor).for_each(|i| {
+        acc[i].zero();
+    });
+
+    let x_pow_a: &Vec<ScalarZnxDft<Vec<u8>, FFT64>>;
+    if let Some(b) = &brk.x_pow_a {
+        x_pow_a = b
+    } else {
+        panic!("invalid key: x_pow_a has not been initialized")
+    }
+
+    let mut lwe_2n: Vec<i64> = vec![0i64; lwe.n() + 1]; // TODO: from scratch space
+    let lwe_ref: LWECiphertext<&[u8]> = lwe.to_ref();
+
+    let two_n: usize = 2 * module.n();
+    let two_n_ext: usize = 2 * lut.domain_size();
+
+    negate_and_mod_switch_2n(two_n_ext, &mut lwe_2n, &lwe_ref);
+
+    let a: &[i64] = &lwe_2n[1..];
+    let b_pos: usize = ((lwe_2n[0] + two_n_ext as i64) & (two_n_ext - 1) as i64) as usize;
+
+    let b_hi: usize = b_pos / extension_factor;
+    let b_lo: usize = b_pos & (extension_factor - 1);
+
+    for (i, j) in (0..b_lo).zip(extension_factor - b_lo..extension_factor) {
+        module.vec_znx_rotate(b_hi as i64 + 1, &mut acc[i], 0, &lut.data[j], 0);
+    }
+    for (i, j) in (b_lo..extension_factor).zip(0..extension_factor - b_lo) {
+        module.vec_znx_rotate(b_hi as i64, &mut acc[i], 0, &lut.data[j], 0);
+    }
+
+    let block_size: usize = brk.block_size();
+
+    izip!(
+        a.chunks_exact(block_size),
+        brk.data.chunks_exact(block_size)
+    )
+    .for_each(|(ai, ski)| {
+        (0..extension_factor).for_each(|i| {
+            (0..cols).for_each(|j| {
+                module.vec_znx_dft(1, 0, &mut acc_dft[i], j, &acc[i], j);
+            });
+            acc_add_dft[i].zero();
+        });
+
+        // TODO: first & last iterations can be optimized
+        izip!(ai.iter(), ski.iter()).for_each(|(aii, skii)| {
+            let ai_pos: usize = ((aii + two_n_ext as i64) & (two_n_ext - 1) as i64) as usize;
+            let ai_hi: usize = ai_pos / extension_factor;
+            let ai_lo: usize = ai_pos & (extension_factor - 1);
+
+            // vmp_res = DFT(acc) * BRK[i]
+            (0..extension_factor).for_each(|i| {
+                module.vmp_apply(&mut vmp_res[i], &acc_dft[i], &skii.data, scratch6);
+            });
+
+            // Trivial case: no rotation between polynomials, we can directly multiply with (X^{-ai} - 1)
+            if ai_lo == 0 {
+                // Sets acc_add_dft[i] = (acc[i] * sk) * (X^{-ai} - 1)
+                if ai_hi != 0 {
+                    // DFT X^{-ai}
+                    module.vec_znx_dft_add(&mut xai_plus_y_dft, 0, &x_pow_a[ai_hi], 0, &minus_one, 0);
+                    (0..extension_factor).for_each(|j| {
+                        (0..cols).for_each(|i| {
+                            module.svp_apply_inplace(&mut vmp_res[j], i, &xai_plus_y_dft, 0);
+                            module.vec_znx_dft_add_inplace(&mut acc_add_dft[j], i, &vmp_res[j], i);
+                        });
+                    });
+                }
+
+            // Non trivial case: rotation between polynomials
+            // In this case we can't directly multiply with (X^{-ai} - 1) because of the
+            // ring homomorphism R^{N} -> prod R^{N/extension_factor}, so we split the
+            // computation in two steps: acc_add_dft = (acc * sk) * (-1) + (acc * sk) * X^{-ai}
+            } else {
+                // Sets acc_add_dft[i] = acc[i] * sk
+
+                // Sets acc_add_dft[0..ai_lo] -= acc[..ai_lo] * sk
+                if (ai_hi + 1) & (two_n - 1) != 0 {
+                    for i in 0..ai_lo {
+                        (0..cols).for_each(|k| {
+                            module.vec_znx_dft_sub_ab_inplace(&mut acc_add_dft[i], k, &vmp_res[i], k);
+                        });
+                    }
+                }
+
+                // Sets acc_add_dft[ai_lo..extension_factor] -= acc[ai_lo..extension_factor] * sk
+                if ai_hi != 0 {
+                    for i in ai_lo..extension_factor {
+                        (0..cols).for_each(|k: usize| {
+                            module.vec_znx_dft_sub_ab_inplace(&mut acc_add_dft[i], k, &vmp_res[i], k);
+                        });
+                    }
+                }
+
+                // Sets acc_add_dft[0..ai_lo] += (acc[extension_factor - ai_lo..extension_factor] * sk) * X^{-ai+1}
+                if (ai_hi + 1) & (two_n - 1) != 0 {
+                    for (i, j) in (0..ai_lo).zip(extension_factor - ai_lo..extension_factor) {
+                        (0..cols).for_each(|k| {
+                            module.svp_apply_inplace(&mut vmp_res[j], k, &x_pow_a[ai_hi + 1], 0);
+                            module.vec_znx_dft_add_inplace(&mut acc_add_dft[i], k, &vmp_res[j], k);
+                        });
+                    }
+                }
+
+                // Sets acc_add_dft[ai_lo..extension_factor] += (acc[0..extension_factor - ai_lo] * sk) * X^{-ai}
+                if ai_hi != 0 {
+                    // Sets acc_add_dft[ai_lo..extension_factor] += (acc[0..extension_factor - ai_lo] * sk) * X^{-ai}
+                    for (i, j) in (ai_lo..extension_factor).zip(0..extension_factor - ai_lo) {
+                        (0..cols).for_each(|k| {
+                            module.svp_apply_inplace(&mut vmp_res[j], k, &x_pow_a[ai_hi], 0);
+                            module.vec_znx_dft_add_inplace(&mut acc_add_dft[i], k, &vmp_res[j], k);
+                        });
+                    }
+                }
+            }
+        });
+
+        {
+            let (mut acc_add_big, scratch7) = scratch6.tmp_vec_znx_big(module, 1, brk.size());
+
+            (0..extension_factor).for_each(|j| {
+                (0..cols).for_each(|i| {
+                    module.vec_znx_idft(&mut acc_add_big, 0, &acc_add_dft[j], i, scratch7);
+                    module.vec_znx_big_add_small_inplace(&mut acc_add_big, 0, &acc[j], i);
+                    module.vec_znx_big_normalize(basek, &mut acc[j], i, &acc_add_big, 0, scratch7);
+                });
+            });
+        }
+    });
+
+    (0..cols).for_each(|i| {
+        module.vec_znx_copy(&mut res.data, i, &acc[0], i);
+    });
+}
+
+pub(crate) fn cggi_blind_rotate_block_binary<DataRes, DataIn, DataBrk>(
+    module: &Module<FFT64>,
+    res: &mut GLWECiphertext<DataRes>,
+    lwe: &LWECiphertext<DataIn>,
+    lut: &LookUpTable,
+    brk: &BlindRotationKeyCGGI<DataBrk, FFT64>,
+    scratch: &mut Scratch,
+) where
+    DataRes: AsRef<[u8]> + AsMut<[u8]>,
+    DataIn: AsRef<[u8]>,
+    DataBrk: AsRef<[u8]>,
+{
+    let mut lwe_2n: Vec<i64> = vec![0i64; lwe.n() + 1]; // TODO: from scratch space
+    let mut out_mut: GLWECiphertext<&mut [u8]> = res.to_mut();
+    let lwe_ref: LWECiphertext<&[u8]> = lwe.to_ref();
+    let two_n: usize = module.n() << 1;
+    let basek: usize = brk.basek();
+    let rows = brk.rows();
+
+    let cols: usize = out_mut.rank() + 1;
+
+    negate_and_mod_switch_2n(2 * lut.domain_size(), &mut lwe_2n, &lwe_ref);
+
+    let a: &[i64] = &lwe_2n[1..];
+    let b: i64 = lwe_2n[0];
+
+    out_mut.data.zero();
+
+    // Initialize out to X^{b} * LUT(X)
+    module.vec_znx_rotate(b, &mut out_mut.data, 0, &lut.data[0], 0);
+
+    let block_size: usize = brk.block_size();
+
+    // ACC + [sum DFT(X^ai -1) * (DFT(ACC) x BRKi)]
+
+    let (mut acc_dft, scratch1) = scratch.tmp_vec_znx_dft(module, cols, rows);
+    let (mut vmp_res, scratch2) = scratch1.tmp_vec_znx_dft(module, cols, brk.size());
+    let (mut acc_add_dft, scratch3) = scratch2.tmp_vec_znx_dft(module, cols, brk.size());
+    let (mut minus_one, scratch4) = scratch3.tmp_scalar_znx_dft(module, 1);
+    let (mut xai_plus_y_dft, scratch5) = scratch4.tmp_scalar_znx_dft(module, 1);
+
+    minus_one.raw_mut()[..module.n() >> 1].fill(-1.0);
+
+    let x_pow_a: &Vec<ScalarZnxDft<Vec<u8>, FFT64>>;
+    if let Some(b) = &brk.x_pow_a {
+        x_pow_a = b
+    } else {
+        panic!("invalid key: x_pow_a has not been initialized")
+    }
+
+    izip!(
+        a.chunks_exact(block_size),
+        brk.data.chunks_exact(block_size)
+    )
+    .for_each(|(ai, ski)| {
+        (0..cols).for_each(|j| {
+            module.vec_znx_dft(1, 0, &mut acc_dft, j, &out_mut.data, j);
+        });
+
+        acc_add_dft.zero();
+
+        izip!(ai.iter(), ski.iter()).for_each(|(aii, skii)| {
+            let ai_pos: usize = ((aii + two_n as i64) & (two_n - 1) as i64) as usize;
+
+            // vmp_res = DFT(acc) * BRK[i]
+            module.vmp_apply(&mut vmp_res, &acc_dft, &skii.data, scratch5);
+
+            // DFT(X^ai -1)
+            module.vec_znx_dft_add(&mut xai_plus_y_dft, 0, &x_pow_a[ai_pos], 0, &minus_one, 0);
+
+            // DFT(X^ai -1) * (DFT(acc) * BRK[i])
+            (0..cols).for_each(|i| {
+                module.svp_apply_inplace(&mut vmp_res, i, &xai_plus_y_dft, 0);
+                module.vec_znx_dft_add_inplace(&mut acc_add_dft, i, &vmp_res, i);
+            });
+        });
+
+        {
+            let (mut acc_add_big, scratch6) = scratch5.tmp_vec_znx_big(module, 1, brk.size());
+
+            (0..cols).for_each(|i| {
+                module.vec_znx_idft(&mut acc_add_big, 0, &acc_add_dft, i, scratch6);
+                module.vec_znx_big_add_small_inplace(&mut acc_add_big, 0, &out_mut.data, i);
+                module.vec_znx_big_normalize(basek, &mut out_mut.data, i, &acc_add_big, 0, scratch6);
+            });
+        }
+    });
+}
+
+pub(crate) fn cggi_blind_rotate_binary_standard<DataRes, DataIn, DataBrk>(
+    module: &Module<FFT64>,
+    res: &mut GLWECiphertext<DataRes>,
+    lwe: &LWECiphertext<DataIn>,
+    lut: &LookUpTable,
+    brk: &BlindRotationKeyCGGI<DataBrk, FFT64>,
+    scratch: &mut Scratch,
+) where
+    DataRes: AsRef<[u8]> + AsMut<[u8]>,
+    DataIn: AsRef<[u8]>,
+    DataBrk: AsRef<[u8]>,
+{
+    #[cfg(debug_assertions)]
+    {
+        assert_eq!(
+            res.n(),
+            module.n(),
+            "res.n(): {} != brk.n(): {}",
+            res.n(),
+            module.n()
+        );
+        assert_eq!(
+            lut.domain_size(),
+            module.n(),
+            "lut.n(): {} != brk.n(): {}",
+            lut.domain_size(),
+            module.n()
+        );
+        assert_eq!(
+            brk.n(),
+            module.n(),
+            "brk.n(): {} != brk.n(): {}",
+            brk.n(),
+            module.n()
+        );
+        assert_eq!(
+            res.rank(),
+            brk.rank(),
+            "res.rank(): {} != brk.rank(): {}",
+            res.rank(),
+            brk.rank()
+        );
+        assert_eq!(
+            lwe.n(),
+            brk.data.len(),
+            "lwe.n(): {} != brk.data.len(): {}",
+            lwe.n(),
+            brk.data.len()
+        );
+    }
+
+    let mut lwe_2n: Vec<i64> = vec![0i64; lwe.n() + 1]; // TODO: from scratch space
+    let mut out_mut: GLWECiphertext<&mut [u8]> = res.to_mut();
+    let lwe_ref: LWECiphertext<&[u8]> = lwe.to_ref();
+    let basek: usize = brk.basek();
+
+    negate_and_mod_switch_2n(2 * lut.domain_size(), &mut lwe_2n, &lwe_ref);
+
+    let a: &[i64] = &lwe_2n[1..];
+    let b: i64 = lwe_2n[0];
+
+    out_mut.data.zero();
+
+    // Initialize out to X^{b} * LUT(X)
+    module.vec_znx_rotate(b, &mut out_mut.data, 0, &lut.data[0], 0);
+
+    // ACC + [sum DFT(X^ai -1) * (DFT(ACC) x BRKi)]
+    let (mut acc_tmp, scratch1) = scratch.tmp_glwe_ct(module, basek, out_mut.k(), out_mut.rank());
+    let (mut acc_tmp_rot, scratch2) = scratch1.tmp_glwe_ct(module, basek, out_mut.k(), out_mut.rank());
+
+    // TODO: see if faster by skipping normalization in external product and keeping acc in big coeffs
+    // TODO: first iteration can be optimized to be a gglwe product
+    izip!(a.iter(), brk.data.iter()).for_each(|(ai, ski)| {
+        // acc_tmp = sk[i] * acc
+        acc_tmp.external_product(module, &out_mut, ski, scratch2);
+
+        // acc_tmp = (sk[i] * acc) * X^{ai}
+        acc_tmp_rot.rotate(module, *ai, &acc_tmp);
+
+        // acc = acc + (sk[i] * acc) * X^{ai}
+        out_mut.add_inplace(module, &acc_tmp_rot);
+
+        // acc = acc + (sk[i] * acc) * X^{ai} - (sk[i] * acc) = acc + (sk[i] * acc) * (X^{ai} - 1)
+        out_mut.sub_inplace_ab(module, &acc_tmp);
+    });
+
+    // We can normalize only at the end because we add normalized values in [-2^{basek-1}, 2^{basek-1}]
+    // on top of each others, thus ~ 2^{63-basek} additions are supported before overflow.
+    out_mut.normalize_inplace(module, scratch2);
+}
+
+pub(crate) fn negate_and_mod_switch_2n(n: usize, res: &mut [i64], lwe: &LWECiphertext<&[u8]>) {
+    let basek: usize = lwe.basek();
+
+    let log2n: usize = usize::BITS as usize - (n - 1).leading_zeros() as usize + 1;
+
+    res.copy_from_slice(&lwe.data.at(0, 0));
+    res.iter_mut().for_each(|x| *x = -*x);
+
+    if basek > log2n {
+        let diff: usize = basek - log2n;
+        res.iter_mut().for_each(|x| {
+            *x = div_round_by_pow2(x, diff);
+        })
+    } else {
+        let rem: usize = basek - (log2n % basek);
+        let size: usize = log2n.div_ceil(basek);
+        (1..size).for_each(|i| {
+            if i == size - 1 && rem != basek {
+                let k_rem: usize = basek - rem;
+                izip!(lwe.data.at(0, i).iter(), res.iter_mut()).for_each(|(x, y)| {
+                    *y = (*y << k_rem) + (x >> rem);
+                });
+            } else {
+                izip!(lwe.data.at(0, i).iter(), res.iter_mut()).for_each(|(x, y)| {
+                    *y = (*y << basek) + x;
+                });
+            }
+        })
+    }
+}
+
+#[inline(always)]
+fn div_round_by_pow2(x: &i64, k: usize) -> i64 {
+    (x + (1 << (k - 1))) >> k
+}

@@ -0,0 +1,159 @@
+use backend::{
+    Backend, FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScalarZnxDft, ScalarZnxDftAlloc, ScalarZnxDftOps, ScalarZnxToRef, Scratch,
+    ZnxView, ZnxViewMut,
+};
+use sampling::source::Source;
+
+use crate::{Distribution, FourierGLWESecret, GGSWCiphertext, Infos, LWESecret};
+
+pub struct BlindRotationKeyCGGI<D, B: Backend> {
+    pub(crate) data: Vec<GGSWCiphertext<D, B>>,
+    pub(crate) dist: Distribution,
+    pub(crate) x_pow_a: Option<Vec<ScalarZnxDft<Vec<u8>, B>>>,
+}
+
+// pub struct BlindRotationKeyFHEW<B: Backend> {
+//    pub(crate) data: Vec<GGSWCiphertext<Vec<u8>, B>>,
+//    pub(crate) auto: Vec<GLWEAutomorphismKey<Vec<u8>, B>>,
+//}
+
+impl BlindRotationKeyCGGI<Vec<u8>, FFT64> {
+    pub fn allocate(module: &Module<FFT64>, n_lwe: usize, basek: usize, k: usize, rows: usize, rank: usize) -> Self {
+        let mut data: Vec<GGSWCiphertext<Vec<u8>, FFT64>> = Vec::with_capacity(n_lwe);
+        (0..n_lwe).for_each(|_| data.push(GGSWCiphertext::alloc(module, basek, k, rows, 1, rank)));
+        Self {
+            data,
+            dist: Distribution::NONE,
+            x_pow_a: None::<Vec<ScalarZnxDft<Vec<u8>, FFT64>>>,
+        }
+    }
+
+    pub fn generate_from_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
+        GGSWCiphertext::encrypt_sk_scratch_space(module, basek, k, rank)
+    }
+}
+
+impl<D: AsRef<[u8]>> BlindRotationKeyCGGI<D, FFT64> {
+    #[allow(dead_code)]
+    pub(crate) fn n(&self) -> usize {
+        self.data[0].n()
+    }
+
+    #[allow(dead_code)]
+    pub(crate) fn rows(&self) -> usize {
+        self.data[0].rows()
+    }
+
+    #[allow(dead_code)]
+    pub(crate) fn k(&self) -> usize {
+        self.data[0].k()
+    }
+
+    #[allow(dead_code)]
+    pub(crate) fn size(&self) -> usize {
+        self.data[0].size()
+    }
+
+    #[allow(dead_code)]
+    pub(crate) fn rank(&self) -> usize {
+        self.data[0].rank()
+    }
+
+    pub(crate) fn basek(&self) -> usize {
+        self.data[0].basek()
+    }
+
+    pub(crate) fn block_size(&self) -> usize {
+        match self.dist {
+            Distribution::BinaryBlock(value) => value,
+            _ => 1,
+        }
+    }
+}
+
+impl<D: AsRef<[u8]> + AsMut<[u8]>> BlindRotationKeyCGGI<D, FFT64> {
+    pub fn generate_from_sk<DataSkGLWE, DataSkLWE>(
+        &mut self,
+        module: &Module<FFT64>,
+        sk_glwe: &FourierGLWESecret<DataSkGLWE, FFT64>,
+        sk_lwe: &LWESecret<DataSkLWE>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) where
+        DataSkGLWE: AsRef<[u8]>,
+        DataSkLWE: AsRef<[u8]>,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.data.len(), sk_lwe.n());
+            assert_eq!(sk_glwe.n(), module.n());
+            assert_eq!(sk_glwe.rank(), self.data[0].rank());
+            match sk_lwe.dist {
+                Distribution::BinaryBlock(_)
+                | Distribution::BinaryFixed(_)
+                | Distribution::BinaryProb(_)
+                | Distribution::ZERO => {}
+                _ => panic!(
+                    "invalid GLWESecret distribution: must be BinaryBlock, BinaryFixed or BinaryProb (or ZERO for debugging)"
+                ),
+            }
+        }
+
+        self.dist = sk_lwe.dist;
+
+        let mut pt: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
+        let sk_ref: ScalarZnx<&[u8]> = sk_lwe.data.to_ref();
+
+        self.data.iter_mut().enumerate().for_each(|(i, ggsw)| {
+            pt.at_mut(0, 0)[0] = sk_ref.at(0, 0)[i];
+            ggsw.encrypt_sk(module, &pt, sk_glwe, source_xa, source_xe, sigma, scratch);
+        });
+
+        match sk_lwe.dist {
+            Distribution::BinaryBlock(_) => {
+                let mut x_pow_a: Vec<ScalarZnxDft<Vec<u8>, FFT64>> = Vec::with_capacity(module.n() << 1);
+                let mut buf: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
+                (0..module.n() << 1).for_each(|i| {
+                    let mut res: ScalarZnxDft<Vec<u8>, FFT64> = module.new_scalar_znx_dft(1);
+                    set_xai_plus_y(module, i, 0, &mut res, &mut buf);
+                    x_pow_a.push(res);
+                });
+                self.x_pow_a = Some(x_pow_a);
+            }
+            _ => {}
+        }
+    }
+}
+
+pub fn set_xai_plus_y<A, B>(module: &Module<FFT64>, ai: usize, y: i64, res: &mut ScalarZnxDft<A, FFT64>, buf: &mut ScalarZnx<B>)
+where
+    A: AsRef<[u8]> + AsMut<[u8]>,
+    B: AsRef<[u8]> + AsMut<[u8]>,
+{
+    let n: usize = module.n();
+
+    {
+        let raw: &mut [i64] = buf.at_mut(0, 0);
+        if ai < n {
+            raw[ai] = 1;
+        } else {
+            raw[(ai - n) & (n - 1)] = -1;
+        }
+        raw[0] += y;
+    }
+
+    module.svp_prepare(res, 0, buf, 0);
+
+    {
+        let raw: &mut [i64] = buf.at_mut(0, 0);
+
+        if ai < n {
+            raw[ai] = 0;
+        } else {
+            raw[(ai - n) & (n - 1)] = 0;
+        }
+        raw[0] = 0;
+    }
+}

@@ -0,0 +1,126 @@
+use backend::{FFT64, Module, VecZnx, VecZnxAlloc, VecZnxOps, ZnxInfos, ZnxViewMut, alloc_aligned};
+
+pub struct LookUpTable {
+    pub(crate) data: Vec<VecZnx<Vec<u8>>>,
+    pub(crate) basek: usize,
+    pub(crate) k: usize,
+}
+
+impl LookUpTable {
+    pub fn alloc(module: &Module<FFT64>, basek: usize, k: usize, extension_factor: usize) -> Self {
+        #[cfg(debug_assertions)]
+        {
+            assert!(
+                extension_factor & (extension_factor - 1) == 0,
+                "extension_factor must be a power of two but is: {}",
+                extension_factor
+            );
+        }
+        let size: usize = k.div_ceil(basek);
+        let mut data: Vec<VecZnx<Vec<u8>>> = Vec::with_capacity(extension_factor);
+        (0..extension_factor).for_each(|_| {
+            data.push(module.new_vec_znx(1, size));
+        });
+        Self { data, basek, k }
+    }
+
+    pub fn log_extension_factor(&self) -> usize {
+        (usize::BITS - (self.extension_factor() - 1).leading_zeros()) as _
+    }
+
+    pub fn extension_factor(&self) -> usize {
+        self.data.len()
+    }
+
+    pub fn domain_size(&self) -> usize {
+        self.data.len() * self.data[0].n()
+    }
+
+    pub fn set(&mut self, module: &Module<FFT64>, f: &Vec<i64>, k: usize) {
+        assert!(f.len() <= module.n());
+
+        let basek: usize = self.basek;
+
+        // Get the number minimum limb to store the message modulus
+        let limbs: usize = k.div_ceil(1 << basek);
+
+        #[cfg(debug_assertions)]
+        {
+            assert!(limbs <= self.data[0].size());
+        }
+
+        // Scaling factor
+        let scale: i64 = 1 << (k % basek) as i64;
+
+        // #elements in lookup table
+        let f_len: usize = f.len();
+
+        // If LUT size > module.n()
+        let domain_size: usize = self.domain_size();
+
+        let size: usize = self.k.div_ceil(self.basek);
+
+        // Equivalent to AUTO([f(0), -f(n-1), -f(n-2), ..., -f(1)], -1)
+        let mut lut_full: VecZnx<Vec<u8>> = VecZnx::new::<i64>(domain_size, 1, size);
+
+        let lut_at: &mut [i64] = lut_full.at_mut(0, limbs - 1);
+
+        f.iter().enumerate().for_each(|(i, fi)| {
+            let start: usize = (i * domain_size).div_round(f_len);
+            let end: usize = ((i + 1) * domain_size).div_round(f_len);
+            lut_at[start..end].fill(fi * scale);
+        });
+
+        // Rotates half the step to the left
+        let half_step: usize = domain_size.div_round(f_len << 1);
+
+        lut_full.rotate(-(half_step as i64));
+
+        let mut tmp_bytes: Vec<u8> = alloc_aligned(lut_full.n() * size_of::<i64>());
+        lut_full.normalize(self.basek, 0, &mut tmp_bytes);
+
+        if self.extension_factor() > 1 {
+            (0..self.extension_factor()).for_each(|i| {
+                module.switch_degree(&mut self.data[i], 0, &lut_full, 0);
+                if i < self.extension_factor() {
+                    lut_full.rotate(-1);
+                }
+            });
+        } else {
+            module.vec_znx_copy(&mut self.data[0], 0, &lut_full, 0);
+        }
+    }
+
+    #[allow(dead_code)]
+    pub(crate) fn rotate(&mut self, k: i64) {
+        let extension_factor: usize = self.extension_factor();
+        let two_n: usize = 2 * self.data[0].n();
+        let two_n_ext: usize = two_n * extension_factor;
+
+        let k_pos: usize = ((k + two_n_ext as i64) % two_n_ext as i64) as usize;
+
+        let k_hi: usize = k_pos / extension_factor;
+        let k_lo: usize = k_pos % extension_factor;
+
+        (0..extension_factor - k_lo).for_each(|i| {
+            self.data[i].rotate(k_hi as i64);
+        });
+
+        (extension_factor - k_lo..extension_factor).for_each(|i| {
+            self.data[i].rotate(k_hi as i64 + 1);
+        });
+
+        self.data.rotate_right(k_lo as usize);
+    }
+}
+
+pub(crate) trait DivRound {
+    fn div_round(self, rhs: Self) -> Self;
+}
+
+impl DivRound for usize {
+    #[inline]
+    fn div_round(self, rhs: Self) -> Self {
+        (self + rhs / 2) / rhs
+    }
+}

@@ -0,0 +1,10 @@
+pub mod cggi;
+pub mod key;
+pub mod lut;
+
+pub use cggi::{cggi_blind_rotate, cggi_blind_rotate_scratch_space};
+pub use key::BlindRotationKeyCGGI;
+pub use lut::LookUpTable;
+
+#[cfg(test)]
+pub mod test_fft64;

@@ -0,0 +1,125 @@
+use backend::{Encoding, FFT64, Module, ScratchOwned, ZnxView};
+use sampling::source::Source;
+
+use crate::{
+    FourierGLWESecret, GLWECiphertext, GLWEPlaintext, GLWESecret, Infos, LWECiphertext, LWESecret,
+    blind_rotation::{
+        cggi::{cggi_blind_rotate, cggi_blind_rotate_scratch_space, negate_and_mod_switch_2n},
+        key::BlindRotationKeyCGGI,
+        lut::LookUpTable,
+    },
+    lwe::{LWEPlaintext, ciphertext::LWECiphertextToRef},
+};
+
+#[test]
+fn standard() {
+    blind_rotatio_test(224, 1, 1);
+}
+
+#[test]
+fn block_binary() {
+    blind_rotatio_test(224, 7, 1);
+}
+
+#[test]
+fn block_binary_extended() {
+    blind_rotatio_test(224, 7, 2);
+}
+
+fn blind_rotatio_test(n_lwe: usize, block_size: usize, extension_factor: usize) {
+    let module: Module<FFT64> = Module::<FFT64>::new(512);
+    let basek: usize = 19;
+
+    let k_lwe: usize = 24;
+    let k_brk: usize = 3 * basek;
+    let rows_brk: usize = 2; // Ensures first limb is noise-free.
+    let k_lut: usize = 1 * basek;
+    let k_res: usize = 2 * basek;
+    let rank: usize = 1;
+
+    let message_modulus: usize = 1 << 4;
+
+    let mut source_xs: Source = Source::new([2u8; 32]);
+    let mut source_xe: Source = Source::new([2u8; 32]);
+    let mut source_xa: Source = Source::new([1u8; 32]);
+
+    let mut sk_glwe: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_glwe.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_glwe_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_glwe);
+
+    let mut sk_lwe: LWESecret<Vec<u8>> = LWESecret::alloc(n_lwe);
+    sk_lwe.fill_binary_block(block_size, &mut source_xs);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(BlindRotationKeyCGGI::generate_from_sk_scratch_space(
+        &module, basek, k_brk, rank,
+    ));
+
+    let mut scratch_br: ScratchOwned = ScratchOwned::new(cggi_blind_rotate_scratch_space(
+        &module,
+        block_size,
+        extension_factor,
+        basek,
+        k_res,
+        k_brk,
+        rows_brk,
+        rank,
+    ));
+
+    let mut brk: BlindRotationKeyCGGI<Vec<u8>, FFT64> =
+        BlindRotationKeyCGGI::allocate(&module, n_lwe, basek, k_brk, rows_brk, rank);
+
+    brk.generate_from_sk(
+        &module,
+        &sk_glwe_dft,
+        &sk_lwe,
+        &mut source_xa,
+        &mut source_xe,
+        3.2,
+        scratch.borrow(),
+    );
+
+    let mut lwe: LWECiphertext<Vec<u8>> = LWECiphertext::alloc(n_lwe, basek, k_lwe);
+
+    let mut pt_lwe: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc(basek, k_lwe);
+
+    let x: i64 = 2;
+    let bits: usize = 8;
+
+    pt_lwe.data.encode_coeff_i64(0, basek, bits, 0, x, bits);
+
+    lwe.encrypt_sk(&pt_lwe, &sk_lwe, &mut source_xa, &mut source_xe, 3.2);
+
+    let mut f: Vec<i64> = vec![0i64; message_modulus];
+    f.iter_mut()
+        .enumerate()
+        .for_each(|(i, x)| *x = 2 * (i as i64) + 1);
+
+    let mut lut: LookUpTable = LookUpTable::alloc(&module, basek, k_lut, extension_factor);
+    lut.set(&module, &f, message_modulus);
+
+    let mut res: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_res, rank);
+
+    cggi_blind_rotate(&module, &mut res, &lwe, &lut, &brk, scratch_br.borrow());
+
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_res);
+
+    res.decrypt(&module, &mut pt_have, &sk_glwe_dft, scratch.borrow());
+
+    let mut lwe_2n: Vec<i64> = vec![0i64; lwe.n() + 1]; // TODO: from scratch space
+
+    negate_and_mod_switch_2n(2 * lut.domain_size(), &mut lwe_2n, &lwe.to_ref());
+
+    let pt_want: i64 = (lwe_2n[0]
+        + lwe_2n[1..]
+            .iter()
+            .zip(sk_lwe.data.at(0, 0))
+            .map(|(x, y)| x * y)
+            .sum::<i64>())
+        & (2 * lut.domain_size() - 1) as i64;
+
+    lut.rotate(pt_want);
+
+    // First limb should be exactly equal (test are parameterized such that the noise does not reach
+    // the first limb)
+    assert_eq!(pt_have.data.at(0, 0), lut.data[0].at(0, 0));
+}

@@ -0,0 +1,73 @@
+use std::vec;
+
+use backend::{FFT64, Module, ZnxView};
+
+use crate::blind_rotation::lut::{DivRound, LookUpTable};
+
+#[test]
+fn standard() {
+    let module: Module<FFT64> = Module::<FFT64>::new(32);
+    let basek: usize = 20;
+    let k_lut: usize = 40;
+    let message_modulus: usize = 16;
+    let extension_factor: usize = 1;
+
+    let log_scale: usize = basek + 1;
+
+    let mut f: Vec<i64> = vec![0i64; message_modulus];
+    f.iter_mut()
+        .enumerate()
+        .for_each(|(i, x)| *x = (i as i64) - 8);
+
+    let mut lut: LookUpTable = LookUpTable::alloc(&module, basek, k_lut, extension_factor);
+    lut.set(&module, &f, log_scale);
+
+    let half_step: i64 = lut.domain_size().div_round(message_modulus << 1) as i64;
+    lut.rotate(half_step);
+
+    let step: usize = lut.domain_size().div_round(message_modulus);
+
+    (0..lut.domain_size()).step_by(step).for_each(|i| {
+        (0..step).for_each(|_| {
+            assert_eq!(
+                f[i / step] % message_modulus as i64,
+                lut.data[0].raw()[0] / (1 << (log_scale % basek)) as i64
+            );
+            lut.rotate(-1);
+        });
+    });
+}
+
+#[test]
+fn extended() {
+    let module: Module<FFT64> = Module::<FFT64>::new(32);
+    let basek: usize = 20;
+    let k_lut: usize = 40;
+    let message_modulus: usize = 16;
+    let extension_factor: usize = 4;
+
+    let log_scale: usize = basek + 1;
+
+    let mut f: Vec<i64> = vec![0i64; message_modulus];
+    f.iter_mut()
+        .enumerate()
+        .for_each(|(i, x)| *x = (i as i64) - 8);
+
+    let mut lut: LookUpTable = LookUpTable::alloc(&module, basek, k_lut, extension_factor);
+    lut.set(&module, &f, log_scale);
+
+    let half_step: i64 = lut.domain_size().div_round(message_modulus << 1) as i64;
+    lut.rotate(half_step);
+
+    let step: usize = lut.domain_size().div_round(message_modulus);
+
+    (0..lut.domain_size()).step_by(step).for_each(|i| {
+        (0..step).for_each(|_| {
+            assert_eq!(
+                f[i / step] % message_modulus as i64,
+                lut.data[0].raw()[0] / (1 << (log_scale % basek)) as i64
+            );
+            lut.rotate(-1);
+        });
+    });
+}

@@ -0,0 +1,2 @@
+pub mod cggi;
+pub mod lut;

@@ -0,0 +1,10 @@
+#[derive(Clone, Copy, Debug)]
+pub(crate) enum Distribution {
+    TernaryFixed(usize), // Ternary with fixed Hamming weight
+    TernaryProb(f64),    // Ternary with probabilistic Hamming weight
+    BinaryFixed(usize),  // Binary with fixed Hamming weight
+    BinaryProb(f64),     // Binary with probabilistic Hamming weight
+    BinaryBlock(usize),  // Binary split in block of size 2^k
+    ZERO,                // Debug mod
+    NONE,                // Unitialized
+}

@@ -1,6 +1,6 @@
 use backend::{Backend, Module, ZnxInfos};
 
-use crate::GLWECiphertextFourier;
+use crate::FourierGLWECiphertext;
 
 pub trait Infos {
     type Inner: ZnxInfos;
@@ -56,13 +56,13 @@ fn set_k(&mut self, k: usize);
 }
 
 pub trait GetRow<B: Backend> {
-    fn get_row<R>(&self, module: &Module<B>, row_i: usize, col_j: usize, res: &mut GLWECiphertextFourier<R, B>)
+    fn get_row<R>(&self, module: &Module<B>, row_i: usize, col_j: usize, res: &mut FourierGLWECiphertext<R, B>)
     where
         R: AsMut<[u8]> + AsRef<[u8]>;
 }
 
 pub trait SetRow<B: Backend> {
-    fn set_row<R>(&mut self, module: &Module<B>, row_i: usize, col_j: usize, a: &GLWECiphertextFourier<R, B>)
+    fn set_row<R>(&mut self, module: &Module<B>, row_i: usize, col_j: usize, a: &FourierGLWECiphertext<R, B>)
     where
         R: AsRef<[u8]>;
 }

@@ -0,0 +1,45 @@
+use backend::{Backend, Module, VecZnxDft, VecZnxDftAlloc};
+
+use crate::Infos;
+
+pub struct FourierGLWECiphertext<C, B: Backend> {
+    pub data: VecZnxDft<C, B>,
+    pub basek: usize,
+    pub k: usize,
+}
+
+impl<B: Backend> FourierGLWECiphertext<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, k.div_ceil(basek)),
+            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, k.div_ceil(basek))
+    }
+}
+
+impl<T, B: Backend> Infos for FourierGLWECiphertext<T, B> {
+    type Inner = VecZnxDft<T, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.data
+    }
+
+    fn basek(&self) -> usize {
+        self.basek
+    }
+
+    fn k(&self) -> usize {
+        self.k
+    }
+}
+
+impl<T, B: Backend> FourierGLWECiphertext<T, B> {
+    pub fn rank(&self) -> usize {
+        self.cols() - 1
+    }
+}

@@ -0,0 +1,84 @@
+use backend::{
+    FFT64, Module, ScalarZnxDftOps, Scratch, VecZnxBig, VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDftAlloc,
+    VecZnxDftOps, ZnxZero,
+};
+
+use crate::{FourierGLWECiphertext, FourierGLWESecret, GLWECiphertext, GLWEPlaintext, Infos};
+
+impl FourierGLWECiphertext<Vec<u8>, FFT64> {
+    pub fn decrypt_scratch_space(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
+        let size: usize = k.div_ceil(basek);
+        (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()))
+            + module.bytes_of_vec_znx_big(1, size)
+    }
+}
+
+impl<DataSelf: AsRef<[u8]>> FourierGLWECiphertext<DataSelf, FFT64> {
+    pub fn decrypt<DataPt: AsRef<[u8]> + AsMut<[u8]>, DataSk: AsRef<[u8]>>(
+        &self,
+        module: &Module<FFT64>,
+        pt: &mut GLWEPlaintext<DataPt>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), sk.rank());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(pt.n(), module.n());
+            assert_eq!(sk.n(), module.n());
+        }
+
+        let cols = self.rank() + 1;
+
+        let (mut pt_big, scratch_1) = scratch.tmp_vec_znx_big(module, 1, self.size()); // TODO optimize size when pt << ct
+        pt_big.zero();
+
+        {
+            (1..cols).for_each(|i| {
+                let (mut ci_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, self.size()); // TODO optimize size when pt << ct
+                module.svp_apply(&mut ci_dft, 0, &sk.data, i - 1, &self.data, i);
+                let ci_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume(ci_dft);
+                module.vec_znx_big_add_inplace(&mut pt_big, 0, &ci_big, 0);
+            });
+        }
+
+        {
+            let (mut c0_big, scratch_2) = scratch_1.tmp_vec_znx_big(module, 1, self.size());
+            // c0_big = (a * s) + (-a * s + m + e) = BIG(m + e)
+            module.vec_znx_idft(&mut c0_big, 0, &self.data, 0, scratch_2);
+            module.vec_znx_big_add_inplace(&mut pt_big, 0, &c0_big, 0);
+        }
+
+        // pt = norm(BIG(m + e))
+        module.vec_znx_big_normalize(self.basek(), &mut pt.data, 0, &mut pt_big, 0, scratch_1);
+
+        pt.basek = self.basek();
+        pt.k = pt.k().min(self.k());
+    }
+
+    #[allow(dead_code)]
+    pub(crate) fn idft<DataRes: AsRef<[u8]> + AsMut<[u8]>>(
+        &self,
+        module: &Module<FFT64>,
+        res: &mut GLWECiphertext<DataRes>,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), res.rank());
+            assert_eq!(self.basek(), res.basek())
+        }
+
+        let min_size: usize = self.size().min(res.size());
+
+        let (mut res_big, scratch1) = scratch.tmp_vec_znx_big(module, 1, min_size);
+
+        (0..self.rank() + 1).for_each(|i| {
+            module.vec_znx_idft(&mut res_big, 0, &self.data, i, scratch1);
+            module.vec_znx_big_normalize(self.basek(), &mut res.data, i, &res_big, 0, scratch1);
+        });
+    }
+}

@@ -0,0 +1,32 @@
+use backend::{FFT64, Module, Scratch, VecZnxAlloc, VecZnxBigScratch, VecZnxDftOps};
+use sampling::source::Source;
+
+use crate::{FourierGLWECiphertext, FourierGLWESecret, GLWECiphertext, Infos, ScratchCore};
+
+impl FourierGLWECiphertext<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, k.div_ceil(basek))
+            + (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, k.div_ceil(basek)) + GLWECiphertext::encrypt_sk_scratch_space(module, basek, k)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> FourierGLWECiphertext<DataSelf, FFT64> {
+    pub fn encrypt_zero_sk<DataSk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        let (mut tmp_ct, scratch1) = scratch.tmp_glwe_ct(module, self.basek(), self.k(), self.rank());
+        tmp_ct.encrypt_zero_sk(module, sk, source_xa, source_xe, sigma, scratch1);
+        tmp_ct.dft(module, self);
+    }
+}

@@ -0,0 +1,129 @@
+use backend::{
+    FFT64, MatZnxDftOps, MatZnxDftScratch, Module, Scratch, VecZnxAlloc, VecZnxBig, VecZnxBigOps, VecZnxBigScratch,
+    VecZnxDftAlloc, VecZnxDftOps,
+};
+
+use crate::{FourierGLWECiphertext, GGSWCiphertext, Infos};
+
+impl FourierGLWECiphertext<Vec<u8>, FFT64> {
+    // WARNING TODO: UPDATE
+    pub fn external_product_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        _k_out: usize,
+        k_in: usize,
+        k_ggsw: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        let ggsw_size: usize = k_ggsw.div_ceil(basek);
+        let res_dft: usize = module.bytes_of_vec_znx_dft(rank + 1, ggsw_size);
+        let in_size: usize = k_in.div_ceil(basek).div_ceil(digits);
+        let ggsw_size: usize = k_ggsw.div_ceil(basek);
+        let vmp: usize = module.bytes_of_vec_znx_dft(rank + 1, in_size)
+            + module.vmp_apply_tmp_bytes(ggsw_size, in_size, in_size, rank + 1, rank + 1, ggsw_size);
+        let res_small: usize = module.bytes_of_vec_znx(rank + 1, ggsw_size);
+        let normalize: usize = module.vec_znx_big_normalize_tmp_bytes();
+        res_dft + (vmp | (res_small + normalize))
+    }
+
+    pub fn external_product_inplace_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_ggsw: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        Self::external_product_scratch_space(module, basek, k_out, k_out, k_ggsw, digits, rank)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> FourierGLWECiphertext<DataSelf, FFT64> {
+    pub fn external_product<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &FourierGLWECiphertext<DataLhs, FFT64>,
+        rhs: &GGSWCiphertext<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        let basek: usize = self.basek();
+
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(rhs.rank(), lhs.rank());
+            assert_eq!(rhs.rank(), self.rank());
+            assert_eq!(self.basek(), basek);
+            assert_eq!(lhs.basek(), basek);
+            assert_eq!(rhs.n(), module.n());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(lhs.n(), module.n());
+            assert!(
+                scratch.available()
+                    >= FourierGLWECiphertext::external_product_scratch_space(
+                        module,
+                        self.basek(),
+                        self.k(),
+                        lhs.k(),
+                        rhs.k(),
+                        rhs.digits(),
+                        rhs.rank(),
+                    )
+            );
+        }
+
+        let cols: usize = rhs.rank() + 1;
+        let digits = rhs.digits();
+
+        // Space for VMP result in DFT domain and high precision
+        let (mut res_dft, scratch1) = scratch.tmp_vec_znx_dft(module, cols, rhs.size());
+        let (mut a_dft, scratch2) = scratch1.tmp_vec_znx_dft(module, cols, (lhs.size() + digits - 1) / digits);
+
+        {
+            (0..digits).for_each(|di| {
+                a_dft.set_size((lhs.size() + di) / digits);
+
+                // Small optimization for digits > 2
+                // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
+                // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(digits-1) * B}.
+                // As such we can ignore the last digits-2 limbs safely of the sum of vmp products.
+                // It is possible to further ignore the last digits-1 limbs, but this introduce
+                // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
+                // noise is kept with respect to the ideal functionality.
+                res_dft.set_size(rhs.size() - ((digits - di) as isize - 2).max(0) as usize);
+
+                (0..cols).for_each(|col_i| {
+                    module.vec_znx_dft_copy(digits, digits - 1 - di, &mut a_dft, col_i, &lhs.data, col_i);
+                });
+
+                if di == 0 {
+                    module.vmp_apply(&mut res_dft, &a_dft, &rhs.data, scratch2);
+                } else {
+                    module.vmp_apply_add(&mut res_dft, &a_dft, &rhs.data, di, scratch2);
+                }
+            });
+        }
+
+        // VMP result in high precision
+        let res_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume::<&mut [u8]>(res_dft);
+
+        // Space for VMP result normalized
+        let (mut res_small, scratch2) = scratch1.tmp_vec_znx(module, cols, rhs.size());
+        (0..cols).for_each(|i| {
+            module.vec_znx_big_normalize(basek, &mut res_small, i, &res_big, i, scratch2);
+            module.vec_znx_dft(1, 0, &mut self.data, i, &res_small, i);
+        });
+    }
+
+    pub fn external_product_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GGSWCiphertext<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        unsafe {
+            let self_ptr: *mut FourierGLWECiphertext<DataSelf, FFT64> = self as *mut FourierGLWECiphertext<DataSelf, FFT64>;
+            self.external_product(&module, &*self_ptr, rhs, scratch);
+        }
+    }
+}

@@ -0,0 +1,56 @@
+use backend::{FFT64, Module, Scratch};
+
+use crate::{FourierGLWECiphertext, GLWECiphertext, GLWESwitchingKey, Infos, ScratchCore};
+
+impl FourierGLWECiphertext<Vec<u8>, FFT64> {
+    pub fn keyswitch_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_in: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> usize {
+        GLWECiphertext::bytes_of(module, basek, k_out, rank_out)
+            + GLWECiphertext::keyswitch_from_fourier_scratch_space(module, basek, k_out, k_in, k_ksk, digits, rank_in, rank_out)
+    }
+
+    pub fn keyswitch_inplace_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        Self::keyswitch_scratch_space(module, basek, k_out, k_out, k_ksk, digits, rank, rank)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> FourierGLWECiphertext<DataSelf, FFT64> {
+    pub fn keyswitch<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &FourierGLWECiphertext<DataLhs, FFT64>,
+        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        let (mut tmp_ct, scratch1) = scratch.tmp_glwe_ct(module, self.basek(), self.k(), self.rank());
+        tmp_ct.keyswitch_from_fourier(module, lhs, rhs, scratch1);
+        tmp_ct.dft(module, self);
+    }
+
+    pub fn keyswitch_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        unsafe {
+            let self_ptr: *mut FourierGLWECiphertext<DataSelf, FFT64> = self as *mut FourierGLWECiphertext<DataSelf, FFT64>;
+            self.keyswitch(&module, &*self_ptr, rhs, scratch);
+        }
+    }
+}

@@ -0,0 +1,12 @@
+pub mod ciphertext;
+pub mod decryption;
+pub mod encryption;
+pub mod external_product;
+pub mod keyswitch;
+pub mod secret;
+
+pub use ciphertext::FourierGLWECiphertext;
+pub use secret::FourierGLWESecret;
+
+#[cfg(test)]
+pub mod test_fft64;

@@ -0,0 +1,58 @@
+use backend::{Backend, FFT64, Module, ScalarZnxDft, ScalarZnxDftAlloc, ScalarZnxDftOps, ZnxInfos};
+
+use crate::{GLWESecret, dist::Distribution};
+
+pub struct FourierGLWESecret<T, B: Backend> {
+    pub(crate) data: ScalarZnxDft<T, B>,
+    pub(crate) dist: Distribution,
+}
+
+impl<B: Backend> FourierGLWESecret<Vec<u8>, B> {
+    pub fn alloc(module: &Module<B>, rank: usize) -> Self {
+        Self {
+            data: module.new_scalar_znx_dft(rank),
+            dist: Distribution::NONE,
+        }
+    }
+
+    pub fn bytes_of(module: &Module<B>, rank: usize) -> usize {
+        module.bytes_of_scalar_znx_dft(rank)
+    }
+}
+
+impl FourierGLWESecret<Vec<u8>, FFT64> {
+    pub fn from<D>(module: &Module<FFT64>, sk: &GLWESecret<D>) -> Self
+    where
+        D: AsRef<[u8]>,
+    {
+        let mut sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = Self::alloc(module, sk.rank());
+        sk_dft.set(module, sk);
+        sk_dft
+    }
+}
+
+impl<DataSelf, B: Backend> FourierGLWESecret<DataSelf, B> {
+    pub fn n(&self) -> usize {
+        self.data.n()
+    }
+
+    pub fn log_n(&self) -> usize {
+        self.data.log_n()
+    }
+
+    pub fn rank(&self) -> usize {
+        self.data.cols()
+    }
+}
+
+impl<S: AsMut<[u8]> + AsRef<[u8]>> FourierGLWESecret<S, FFT64> {
+    pub(crate) fn set<D>(&mut self, module: &Module<FFT64>, sk: &GLWESecret<D>)
+    where
+        D: AsRef<[u8]>,
+    {
+        (0..self.rank()).for_each(|i| {
+            module.svp_prepare(&mut self.data, i, &sk.data, i);
+        });
+        self.dist = sk.dist
+    }
+}

@@ -0,0 +1,246 @@
+use crate::{
+    FourierGLWECiphertext, FourierGLWESecret, GGSWCiphertext, GLWECiphertext, GLWEOps, GLWEPlaintext, GLWESecret, Infos,
+    noise::noise_ggsw_product,
+};
+use backend::{FFT64, FillUniform, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned, Stats, VecZnxOps, ZnxViewMut};
+use sampling::source::Source;
+
+#[test]
+fn apply() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_in: usize = 45;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ggsw: usize = k_in + basek * di;
+            println!("test external_product digits: {} rank: {}", di, rank);
+            let k_out: usize = k_ggsw; // Better capture noise.
+            test_apply(log_n, basek, k_out, k_in, k_ggsw, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn apply_inplace() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_ct: usize = 60;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ggsw: usize = k_ct + basek * di;
+            println!("test external_product digits: {} rank: {}", di, rank);
+            test_apply_inplace(log_n, basek, k_ct, k_ggsw, di, rank, 3.2);
+        });
+    });
+}
+
+fn test_apply(log_n: usize, basek: usize, k_out: usize, k_in: usize, k_ggsw: usize, digits: usize, rank: usize, sigma: f64) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_in.div_ceil(digits * basek);
+
+    let mut ct_ggsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k_ggsw, rows, digits, rank);
+    let mut ct_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_in, rank);
+    let mut ct_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_out, rank);
+    let mut ct_in_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_in, rank);
+    let mut ct_out_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_out, rank);
+    let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    // Random input plaintext
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    pt_want.data.at_mut(0, 0)[1] = 1;
+
+    let k: i64 = 1;
+
+    pt_rgsw.raw_mut()[0] = 1; // X^{0}
+    module.vec_znx_rotate_inplace(k, &mut pt_rgsw, 0); // X^{k}
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, ct_ggsw.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_out.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_in.k())
+            | FourierGLWECiphertext::external_product_scratch_space(
+                &module,
+                basek,
+                ct_out.k(),
+                ct_in.k(),
+                ct_ggsw.k(),
+                digits,
+                rank,
+            ),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
+
+    ct_ggsw.encrypt_sk(
+        &module,
+        &pt_rgsw,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_in.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_in.dft(&module, &mut ct_in_dft);
+    ct_out_dft.external_product(&module, &ct_in_dft, &ct_ggsw, scratch.borrow());
+    ct_out_dft.idft(&module, &mut ct_out, scratch.borrow());
+
+    ct_out.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
+
+    pt_want.rotate_inplace(&module, k);
+    pt_have.sub_inplace_ab(&module, &pt_want);
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+
+    let var_gct_err_lhs: f64 = sigma * sigma;
+    let var_gct_err_rhs: f64 = 0f64;
+
+    let var_msg: f64 = 1f64 / module.n() as f64; // X^{k}
+    let var_a0_err: f64 = sigma * sigma;
+    let var_a1_err: f64 = 1f64 / 12f64;
+
+    let noise_want: f64 = noise_ggsw_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        var_msg,
+        var_a0_err,
+        var_a1_err,
+        var_gct_err_lhs,
+        var_gct_err_rhs,
+        rank as f64,
+        k_in,
+        k_ggsw,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_apply_inplace(log_n: usize, basek: usize, k_ct: usize, k_ggsw: usize, digits: usize, rank: usize, sigma: f64) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let rows: usize = k_ct.div_ceil(digits * basek);
+
+    let mut ct_ggsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k_ggsw, rows, digits, rank);
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut ct_rlwe_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    // Random input plaintext
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    pt_want.data.at_mut(0, 0)[1] = 1;
+
+    let k: i64 = 1;
+
+    pt_rgsw.raw_mut()[0] = 1; // X^{0}
+    module.vec_znx_rotate_inplace(k, &mut pt_rgsw, 0); // X^{k}
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, ct_ggsw.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
+            | FourierGLWECiphertext::external_product_inplace_scratch_space(&module, basek, ct.k(), ct_ggsw.k(), digits, rank),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
+
+    ct_ggsw.encrypt_sk(
+        &module,
+        &pt_rgsw,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct.dft(&module, &mut ct_rlwe_dft);
+    ct_rlwe_dft.external_product_inplace(&module, &ct_ggsw, scratch.borrow());
+    ct_rlwe_dft.idft(&module, &mut ct, scratch.borrow());
+
+    ct.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
+
+    pt_want.rotate_inplace(&module, k);
+    pt_have.sub_inplace_ab(&module, &pt_want);
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+
+    let var_gct_err_lhs: f64 = sigma * sigma;
+    let var_gct_err_rhs: f64 = 0f64;
+
+    let var_msg: f64 = 1f64 / module.n() as f64; // X^{k}
+    let var_a0_err: f64 = sigma * sigma;
+    let var_a1_err: f64 = 1f64 / 12f64;
+
+    let noise_want: f64 = noise_ggsw_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        var_msg,
+        var_a0_err,
+        var_a1_err,
+        var_gct_err_lhs,
+        var_gct_err_rhs,
+        rank as f64,
+        k_ct,
+        k_ggsw,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+
+    println!("{} {}", noise_have, noise_want);
+}

@@ -0,0 +1,235 @@
+use crate::{
+    FourierGLWECiphertext, FourierGLWESecret, GLWECiphertext, GLWEPlaintext, GLWESecret, GLWESwitchingKey, Infos,
+    noise::log2_std_noise_gglwe_product,
+};
+use backend::{FFT64, FillUniform, Module, ScratchOwned, Stats, VecZnxOps};
+use sampling::source::Source;
+
+#[test]
+fn apply() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_in: usize = 45;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank_in| {
+        (1..4).for_each(|rank_out| {
+            (1..digits + 1).for_each(|di| {
+                let k_ksk: usize = k_in + basek * di;
+                println!(
+                    "test keyswitch digits: {} rank_in: {} rank_out: {}",
+                    di, rank_in, rank_out
+                );
+                let k_out: usize = k_ksk; // Better capture noise.
+                test_apply(log_n, basek, k_in, k_out, k_ksk, di, rank_in, rank_out, 3.2);
+            })
+        });
+    });
+}
+
+#[test]
+fn apply_inplace() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_ct: usize = 45;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_ct + basek * di;
+            println!("test keyswitch_inplace digits: {} rank: {}", di, rank);
+            test_apply_inplace(log_n, basek, k_ct, k_ksk, di, rank, 3.2);
+        });
+    });
+}
+
+fn test_apply(
+    log_n: usize,
+    basek: usize,
+    k_in: usize,
+    k_out: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank_in: usize,
+    rank_out: usize,
+    sigma: f64,
+) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_in.div_ceil(basek * digits);
+
+    let mut ksk: GLWESwitchingKey<Vec<u8>, FFT64> =
+        GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, digits, rank_in, rank_out);
+    let mut ct_glwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_in, rank_in);
+    let mut ct_glwe_dft_in: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_in, rank_in);
+    let mut ct_glwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_out, rank_out);
+    let mut ct_glwe_dft_out: FourierGLWECiphertext<Vec<u8>, FFT64> =
+        FourierGLWECiphertext::alloc(&module, basek, k_out, rank_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    // Random input plaintext
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_ksk, rank_in, rank_out)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, k_out)
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, k_in)
+            | FourierGLWECiphertext::keyswitch_scratch_space(
+                &module,
+                basek,
+                ct_glwe_out.k(),
+                ksk.k(),
+                ct_glwe_in.k(),
+                digits,
+                rank_in,
+                rank_out,
+            ),
+    );
+
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_in);
+    sk_in.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_in_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_in);
+
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_out);
+    sk_out.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
+
+    ksk.encrypt_sk(
+        &module,
+        &sk_in,
+        &sk_out_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe_in.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_in_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe_in.dft(&module, &mut ct_glwe_dft_in);
+    ct_glwe_dft_out.keyswitch(&module, &ct_glwe_dft_in, &ksk, scratch.borrow());
+    ct_glwe_dft_out.idft(&module, &mut ct_glwe_out, scratch.borrow());
+
+    ct_glwe_out.decrypt(&module, &mut pt_have, &sk_out_dft, scratch.borrow());
+
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+    let noise_want: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank_in as f64,
+        k_in,
+        k_ksk,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_apply_inplace(log_n: usize, basek: usize, k_ct: usize, k_ksk: usize, digits: usize, rank: usize, sigma: f64) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_ct.div_ceil(basek * digits);
+
+    let mut ksk: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, digits, rank, rank);
+    let mut ct_glwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut ct_rlwe_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    // Random input plaintext
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ksk.k(), rank, rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_glwe.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_glwe.k())
+            | FourierGLWECiphertext::keyswitch_inplace_scratch_space(&module, basek, ct_rlwe_dft.k(), ksk.k(), digits, rank),
+    );
+
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_in.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_in_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_in);
+
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_out.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
+
+    ksk.encrypt_sk(
+        &module,
+        &sk_in,
+        &sk_out_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_in_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.dft(&module, &mut ct_rlwe_dft);
+    ct_rlwe_dft.keyswitch_inplace(&module, &ksk, scratch.borrow());
+    ct_rlwe_dft.idft(&module, &mut ct_glwe, scratch.borrow());
+
+    ct_glwe.decrypt(&module, &mut pt_have, &sk_out_dft, scratch.borrow());
+
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+    let noise_want: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank as f64,
+        k_ct,
+        k_ksk,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}

@@ -0,0 +1,2 @@
+pub mod external_product;
+pub mod keyswitch;

@@ -0,0 +1,150 @@
+use backend::{FFT64, Module, Scratch, VecZnx, VecZnxDftOps, VecZnxOps, ZnxZero};
+
+use crate::{FourierGLWECiphertext, GLWEAutomorphismKey, GLWECiphertext, GetRow, Infos, ScratchCore, SetRow};
+
+impl GLWEAutomorphismKey<Vec<u8>, FFT64> {
+    pub fn automorphism_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_in: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        let tmp_dft: usize = FourierGLWECiphertext::bytes_of(module, basek, k_in, rank);
+        let tmp_idft: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank);
+        let idft: usize = module.vec_znx_idft_tmp_bytes();
+        let keyswitch: usize = GLWECiphertext::keyswitch_inplace_scratch_space(module, basek, k_out, k_ksk, digits, rank);
+        tmp_dft + tmp_idft + idft + keyswitch
+    }
+
+    pub fn automorphism_inplace_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        GLWEAutomorphismKey::automorphism_scratch_space(module, basek, k_out, k_out, k_ksk, digits, rank)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWEAutomorphismKey<DataSelf, FFT64> {
+    pub fn automorphism<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWEAutomorphismKey<DataLhs, FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(
+                self.rank_in(),
+                lhs.rank_in(),
+                "ksk_out input rank: {} != ksk_in input rank: {}",
+                self.rank_in(),
+                lhs.rank_in()
+            );
+            assert_eq!(
+                lhs.rank_out(),
+                rhs.rank_in(),
+                "ksk_in output rank: {} != ksk_apply input rank: {}",
+                self.rank_out(),
+                rhs.rank_in()
+            );
+            assert_eq!(
+                self.rank_out(),
+                rhs.rank_out(),
+                "ksk_out output rank: {} != ksk_apply output rank: {}",
+                self.rank_out(),
+                rhs.rank_out()
+            );
+            assert!(
+                self.k() <= lhs.k(),
+                "output k={} cannot be greater than input k={}",
+                self.k(),
+                lhs.k()
+            )
+        }
+
+        let cols_out: usize = rhs.rank_out() + 1;
+
+        (0..self.rank_in()).for_each(|col_i| {
+            (0..self.rows()).for_each(|row_j| {
+                let (mut tmp_idft_data, scratct1) = scratch.tmp_vec_znx_big(module, cols_out, self.size());
+
+                {
+                    let (mut tmp_dft, scratch2) = scratct1.tmp_fourier_glwe_ct(module, lhs.basek(), lhs.k(), lhs.rank());
+
+                    // Extracts relevant row
+                    lhs.get_row(module, row_j, col_i, &mut tmp_dft);
+
+                    // Get a VecZnxBig from scratch space
+
+                    // Switches input outside of DFT
+                    (0..cols_out).for_each(|i| {
+                        module.vec_znx_idft(&mut tmp_idft_data, i, &tmp_dft.data, i, scratch2);
+                    });
+                }
+
+                // Consumes to small vec znx
+                let mut tmp_idft_small_data: VecZnx<&mut [u8]> = tmp_idft_data.to_vec_znx_small();
+
+                // Reverts the automorphis key from (-pi^{-1}_{k}(s)a + s, a) to (-sa + pi_{k}(s), a)
+                (0..cols_out).for_each(|i| {
+                    module.vec_znx_automorphism_inplace(lhs.p(), &mut tmp_idft_small_data, i);
+                });
+
+                // Wraps into ciphertext
+                let mut tmp_idft: GLWECiphertext<&mut [u8]> = GLWECiphertext::<&mut [u8]> {
+                    data: tmp_idft_small_data,
+                    basek: self.basek(),
+                    k: self.k(),
+                };
+
+                // Key-switch (-sa + pi_{k}(s), a) to (-pi^{-1}_{k'}(s)a + pi_{k}(s), a)
+                tmp_idft.keyswitch_inplace(module, &rhs.key, scratct1);
+
+                {
+                    let (mut tmp_dft, _) = scratct1.tmp_fourier_glwe_ct(module, self.basek(), self.k(), self.rank());
+
+                    // Applies back the automorphism X^{k}: (-pi^{-1}_{k'}(s)a + pi_{k}(s), a) -> (-pi^{-1}_{k'+k}(s)a + s, a)
+                    // and switches back to DFT domain
+                    (0..self.rank_out() + 1).for_each(|i| {
+                        module.vec_znx_automorphism_inplace(lhs.p(), &mut tmp_idft.data, i);
+                        module.vec_znx_dft(1, 0, &mut tmp_dft.data, i, &tmp_idft.data, i);
+                    });
+
+                    // Sets back the relevant row
+                    self.set_row(module, row_j, col_i, &tmp_dft);
+                }
+            });
+        });
+
+        let (mut tmp_dft, _) = scratch.tmp_fourier_glwe_ct(module, self.basek(), self.k(), self.rank());
+        tmp_dft.data.zero();
+
+        (self.rows().min(lhs.rows())..self.rows()).for_each(|row_i| {
+            (0..self.rank_in()).for_each(|col_j| {
+                self.set_row(module, row_i, col_j, &tmp_dft);
+            });
+        });
+
+        self.p = (lhs.p * rhs.p) % (module.cyclotomic_order() as i64);
+    }
+
+    pub fn automorphism_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        unsafe {
+            let self_ptr: *mut GLWEAutomorphismKey<DataSelf, FFT64> = self as *mut GLWEAutomorphismKey<DataSelf, FFT64>;
+            self.automorphism(&module, &*self_ptr, rhs, scratch);
+        }
+    }
+}

@@ -0,0 +1,83 @@
+use backend::{Backend, FFT64, MatZnxDft, MatZnxDftOps, Module};
+
+use crate::{FourierGLWECiphertext, GLWESwitchingKey, GetRow, Infos, SetRow};
+
+pub struct GLWEAutomorphismKey<Data, B: Backend> {
+    pub(crate) key: GLWESwitchingKey<Data, B>,
+    pub(crate) p: i64,
+}
+
+impl GLWEAutomorphismKey<Vec<u8>, FFT64> {
+    pub fn alloc(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self {
+        GLWEAutomorphismKey {
+            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, digits: usize, rank: usize) -> usize {
+        GLWESwitchingKey::<Vec<u8>, FFT64>::bytes_of(module, basek, k, rows, digits, rank, rank)
+    }
+}
+
+impl<T, B: Backend> Infos for GLWEAutomorphismKey<T, B> {
+    type Inner = MatZnxDft<T, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.key.inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.key.basek()
+    }
+
+    fn k(&self) -> usize {
+        self.key.k()
+    }
+}
+
+impl<T, B: Backend> GLWEAutomorphismKey<T, B> {
+    pub fn p(&self) -> i64 {
+        self.p
+    }
+
+    pub fn digits(&self) -> usize {
+        self.key.digits()
+    }
+
+    pub fn rank(&self) -> usize {
+        self.key.rank()
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.key.rank_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.key.rank_out()
+    }
+}
+
+impl<C: AsRef<[u8]>> GetRow<FFT64> for GLWEAutomorphismKey<C, FFT64> {
+    fn get_row<R: AsMut<[u8]> + AsRef<[u8]>>(
+        &self,
+        module: &Module<FFT64>,
+        row_i: usize,
+        col_j: usize,
+        res: &mut FourierGLWECiphertext<R, FFT64>,
+    ) {
+        module.mat_znx_dft_get_row(&mut res.data, &self.key.key.data, row_i, col_j);
+    }
+}
+
+impl<C: AsMut<[u8]> + AsRef<[u8]>> SetRow<FFT64> for GLWEAutomorphismKey<C, FFT64> {
+    fn set_row<R: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        row_i: usize,
+        col_j: usize,
+        a: &FourierGLWECiphertext<R, FFT64>,
+    ) {
+        module.mat_znx_dft_set_row(&mut self.key.key.data, row_i, col_j, &a.data);
+    }
+}

@@ -0,0 +1,131 @@
+use backend::{Backend, FFT64, MatZnxDft, MatZnxDftAlloc, MatZnxDftOps, Module};
+
+use crate::{FourierGLWECiphertext, GetRow, Infos, SetRow};
+
+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,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> Self {
+        let size: usize = k.div_ceil(basek);
+        debug_assert!(
+            size > digits,
+            "invalid gglwe: ceil(k/basek): {} <= digits: {}",
+            size,
+            digits
+        );
+
+        assert!(
+            rows * digits <= size,
+            "invalid gglwe: rows: {} * digits:{} > ceil(k/basek): {}",
+            rows,
+            digits,
+            size
+        );
+
+        Self {
+            data: module.new_mat_znx_dft(rows, rank_in, rank_out + 1, size),
+            basek: basek,
+            k,
+            digits,
+        }
+    }
+
+    pub fn bytes_of(
+        module: &Module<FFT64>,
+        basek: usize,
+        k: usize,
+        rows: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> usize {
+        let size: usize = k.div_ceil(basek);
+        debug_assert!(
+            size > digits,
+            "invalid gglwe: ceil(k/basek): {} <= digits: {}",
+            size,
+            digits
+        );
+
+        assert!(
+            rows * digits <= size,
+            "invalid gglwe: rows: {} * digits:{} > ceil(k/basek): {}",
+            rows,
+            digits,
+            size
+        );
+
+        module.bytes_of_mat_znx_dft(rows, rank_in, rank_out + 1, rows)
+    }
+}
+
+impl<T, B: Backend> Infos for GGLWECiphertext<T, B> {
+    type Inner = MatZnxDft<T, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.data
+    }
+
+    fn basek(&self) -> usize {
+        self.basek
+    }
+
+    fn k(&self) -> usize {
+        self.k
+    }
+}
+
+impl<T, B: Backend> GGLWECiphertext<T, B> {
+    pub fn rank(&self) -> usize {
+        self.data.cols_out() - 1
+    }
+
+    pub fn digits(&self) -> usize {
+        self.digits
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.data.cols_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.data.cols_out() - 1
+    }
+}
+
+impl<C: AsRef<[u8]>> GetRow<FFT64> for GGLWECiphertext<C, FFT64> {
+    fn get_row<R: AsMut<[u8]> + AsRef<[u8]>>(
+        &self,
+        module: &Module<FFT64>,
+        row_i: usize,
+        col_j: usize,
+        res: &mut FourierGLWECiphertext<R, FFT64>,
+    ) {
+        module.mat_znx_dft_get_row(&mut res.data, &self.data, row_i, col_j);
+    }
+}
+
+impl<C: AsMut<[u8]> + AsRef<[u8]>> SetRow<FFT64> for GGLWECiphertext<C, FFT64> {
+    fn set_row<R: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        row_i: usize,
+        col_j: usize,
+        a: &FourierGLWECiphertext<R, FFT64>,
+    ) {
+        module.mat_znx_dft_set_row(&mut self.data, row_i, col_j, &a.data);
+    }
+}

@@ -0,0 +1,302 @@
+use backend::{
+    FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScalarZnxDftOps, ScalarZnxOps, Scratch, VecZnxAlloc, VecZnxDftAlloc, VecZnxOps,
+    ZnxInfos, ZnxView, ZnxViewMut, ZnxZero,
+};
+use sampling::source::Source;
+
+use crate::{
+    FourierGLWESecret, GGLWECiphertext, GLWEAutomorphismKey, GLWECiphertext, GLWESecret, GLWESwitchingKey, GLWETensorKey, Infos,
+    ScratchCore, SetRow,
+};
+
+impl GGLWECiphertext<Vec<u8>, FFT64> {
+    pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
+        let size = k.div_ceil(basek);
+        GLWECiphertext::encrypt_sk_scratch_space(module, basek, k)
+            + module.bytes_of_vec_znx(rank + 1, size)
+            + module.bytes_of_vec_znx(1, size)
+            + module.bytes_of_vec_znx_dft(rank + 1, size)
+    }
+
+    pub fn encrypt_pk_scratch_space(_module: &Module<FFT64>, _basek: usize, _k: usize, _rank: usize) -> usize {
+        unimplemented!()
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GGLWECiphertext<DataSelf, FFT64> {
+    pub fn encrypt_sk<DataPt: AsRef<[u8]>, DataSk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        pt: &ScalarZnx<DataPt>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(
+                self.rank_in(),
+                pt.cols(),
+                "self.rank_in(): {} != pt.cols(): {}",
+                self.rank_in(),
+                pt.cols()
+            );
+            assert_eq!(
+                self.rank_out(),
+                sk.rank(),
+                "self.rank_out(): {} != sk.rank(): {}",
+                self.rank_out(),
+                sk.rank()
+            );
+            assert_eq!(self.n(), module.n());
+            assert_eq!(sk.n(), module.n());
+            assert_eq!(pt.n(), module.n());
+            assert!(
+                scratch.available() >= GGLWECiphertext::encrypt_sk_scratch_space(module, self.basek(), self.k(), self.rank()),
+                "scratch.available: {} < GGLWECiphertext::encrypt_sk_scratch_space(module, self.rank()={}, self.size()={}): {}",
+                scratch.available(),
+                self.rank(),
+                self.size(),
+                GGLWECiphertext::encrypt_sk_scratch_space(module, self.basek(), self.k(), self.rank())
+            );
+            assert!(
+                self.rows() * self.digits() * self.basek() <= self.k(),
+                "self.rows() : {} * self.digits() : {} * self.basek() : {} = {} >= self.k() = {}",
+                self.rows(),
+                self.digits(),
+                self.basek(),
+                self.rows() * self.digits() * self.basek(),
+                self.k()
+            );
+        }
+
+        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();
+        let rank_out: usize = self.rank_out();
+
+        let (mut tmp_pt, scrach_1) = scratch.tmp_glwe_pt(module, basek, k);
+        let (mut tmp_ct, scrach_2) = scrach_1.tmp_glwe_ct(module, basek, k, rank_out);
+        let (mut tmp_ct_dft, scratch_3) = scrach_2.tmp_fourier_glwe_ct(module, basek, k, rank_out);
+
+        // For each input column (i.e. rank) produces a GGLWE ciphertext of rank_out+1 columns
+        //
+        // Example for ksk rank 2 to rank 3:
+        //
+        // (-(a0*s0 + a1*s1 + a2*s2) + s0', a0, a1, a2)
+        // (-(b0*s0 + b1*s1 + b2*s2) + s0', b0, b1, b2)
+        //
+        // Example ksk rank 2 to rank 1
+        //
+        // (-(a*s) + s0, a)
+        // (-(b*s) + s1, b)
+        (0..rank_in).for_each(|col_i| {
+            (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,
+                    (digits - 1) + 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
+                tmp_ct.encrypt_sk(module, &tmp_pt, sk, source_xa, source_xe, sigma, scratch_3);
+
+                // Switch vec_znx_ct into DFT domain
+                tmp_ct.dft(module, &mut tmp_ct_dft);
+
+                // Stores vec_znx_dft_ct into thw i-th row of the MatZnxDft
+                self.set_row(module, row_i, col_i, &tmp_ct_dft);
+            });
+        });
+    }
+}
+
+impl GLWESwitchingKey<Vec<u8>, FFT64> {
+    pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank_in: usize, rank_out: usize) -> usize {
+        GGLWECiphertext::encrypt_sk_scratch_space(module, basek, k, rank_out)
+            + module.bytes_of_scalar_znx(rank_in)
+            + FourierGLWESecret::bytes_of(module, rank_out)
+    }
+
+    pub fn encrypt_pk_scratch_space(
+        module: &Module<FFT64>,
+        _basek: usize,
+        _k: usize,
+        _rank_in: usize,
+        _rank_out: usize,
+    ) -> usize {
+        GGLWECiphertext::encrypt_pk_scratch_space(module, _basek, _k, _rank_out)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWESwitchingKey<DataSelf, FFT64> {
+    pub fn encrypt_sk<DataSkIn: AsRef<[u8]>, DataSkOut: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        sk_in: &GLWESecret<DataSkIn>,
+        sk_out: &FourierGLWESecret<DataSkOut, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert!(sk_in.n() <= module.n());
+            assert!(sk_out.n() <= module.n());
+        }
+
+        let (mut sk_in_tmp, scratch1) = scratch.tmp_scalar_znx(module, sk_in.rank());
+        sk_in_tmp.zero();
+
+        (0..sk_in.rank()).for_each(|i| {
+            sk_in_tmp
+                .at_mut(i, 0)
+                .iter_mut()
+                .step_by(module.n() / sk_in.n())
+                .zip(sk_in.data.at(i, 0).iter())
+                .for_each(|(x, y)| *x = *y);
+        });
+
+        let (mut sk_out_tmp, scratch2) = scratch1.tmp_fourier_glwe_secret(module, sk_out.rank());
+        (0..sk_out.rank()).for_each(|i| {
+            sk_out_tmp
+                .data
+                .at_mut(i, 0)
+                .chunks_exact_mut(module.n() / sk_out.n())
+                .zip(sk_out.data.at(i, 0).iter())
+                .for_each(|(a_chunk, &b_elem)| {
+                    a_chunk.fill(b_elem);
+                });
+        });
+
+        self.key.encrypt_sk(
+            module,
+            &sk_in_tmp,
+            &sk_out_tmp,
+            source_xa,
+            source_xe,
+            sigma,
+            scratch2,
+        );
+        self.sk_in_n = sk_in.n();
+        self.sk_out_n = sk_out.n();
+    }
+}
+
+impl GLWEAutomorphismKey<Vec<u8>, FFT64> {
+    pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
+        GLWESwitchingKey::encrypt_sk_scratch_space(module, basek, k, rank, rank) + GLWESecret::bytes_of(module, rank)
+    }
+
+    pub fn encrypt_pk_scratch_space(module: &Module<FFT64>, _basek: usize, _k: usize, _rank: usize) -> usize {
+        GLWESwitchingKey::encrypt_pk_scratch_space(module, _basek, _k, _rank, _rank)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWEAutomorphismKey<DataSelf, FFT64> {
+    pub fn encrypt_sk<DataSk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        p: i64,
+        sk: &GLWESecret<DataSk>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.n(), module.n());
+            assert_eq!(sk.n(), module.n());
+            assert_eq!(self.rank_out(), self.rank_in());
+            assert_eq!(sk.rank(), self.rank());
+            assert!(
+                scratch.available() >= GLWEAutomorphismKey::encrypt_sk_scratch_space(module, self.basek(), self.k(), self.rank()),
+                "scratch.available(): {} < AutomorphismKey::encrypt_sk_scratch_space(module, self.rank()={}, self.size()={}): {}",
+                scratch.available(),
+                self.rank(),
+                self.size(),
+                GLWEAutomorphismKey::encrypt_sk_scratch_space(module, self.basek(), self.k(), self.rank())
+            )
+        }
+
+        let (mut sk_out_dft, scratch_1) = scratch.tmp_fourier_glwe_secret(module, sk.rank());
+
+        {
+            let (mut sk_out, _) = scratch_1.tmp_glwe_secret(module, sk.rank());
+            (0..self.rank()).for_each(|i| {
+                module.scalar_znx_automorphism(
+                    module.galois_element_inv(p),
+                    &mut sk_out.data,
+                    i,
+                    &sk.data,
+                    i,
+                );
+            });
+            sk_out_dft.set(module, &sk_out);
+        }
+
+        self.key.encrypt_sk(
+            module,
+            &sk,
+            &sk_out_dft,
+            source_xa,
+            source_xe,
+            sigma,
+            scratch_1,
+        );
+
+        self.p = p;
+    }
+}
+
+impl GLWETensorKey<Vec<u8>, FFT64> {
+    pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
+        GLWESecret::bytes_of(module, 1)
+            + FourierGLWESecret::bytes_of(module, 1)
+            + GLWESwitchingKey::encrypt_sk_scratch_space(module, basek, k, rank, rank)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWETensorKey<DataSelf, FFT64> {
+    pub fn encrypt_sk<DataSk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), sk.rank());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(sk.n(), module.n());
+        }
+
+        let rank: usize = self.rank();
+
+        let (mut sk_ij, scratch1) = scratch.tmp_glwe_secret(module, 1);
+        let (mut sk_ij_dft, scratch2) = scratch1.tmp_fourier_glwe_secret(module, 1);
+
+        (0..rank).for_each(|i| {
+            (i..rank).for_each(|j| {
+                module.svp_apply(&mut sk_ij_dft.data, 0, &sk.data, i, &sk.data, j);
+                module.scalar_znx_idft(&mut sk_ij.data, 0, &sk_ij_dft.data, 0, scratch2);
+                self.at_mut(i, j)
+                    .encrypt_sk(module, &sk_ij, sk, source_xa, source_xe, sigma, scratch2);
+            });
+        })
+    }
+}

@@ -0,0 +1,162 @@
+use backend::{FFT64, Module, Scratch, ZnxZero};
+
+use crate::{FourierGLWECiphertext, GGSWCiphertext, GLWEAutomorphismKey, GLWESwitchingKey, GetRow, Infos, ScratchCore, SetRow};
+
+impl GLWESwitchingKey<Vec<u8>, FFT64> {
+    pub fn external_product_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_in: usize,
+        k_ggsw: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        let tmp_in: usize = FourierGLWECiphertext::bytes_of(module, basek, k_in, rank);
+        let tmp_out: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank);
+        let ggsw: usize = FourierGLWECiphertext::external_product_scratch_space(module, basek, k_out, k_in, k_ggsw, digits, rank);
+        tmp_in + tmp_out + ggsw
+    }
+
+    pub fn external_product_inplace_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_ggsw: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        let tmp: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank);
+        let ggsw: usize =
+            FourierGLWECiphertext::external_product_inplace_scratch_space(module, basek, k_out, k_ggsw, digits, rank);
+        tmp + ggsw
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWESwitchingKey<DataSelf, FFT64> {
+    pub fn external_product<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWESwitchingKey<DataLhs, FFT64>,
+        rhs: &GGSWCiphertext<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(
+                self.rank_in(),
+                lhs.rank_in(),
+                "ksk_out input rank: {} != ksk_in input rank: {}",
+                self.rank_in(),
+                lhs.rank_in()
+            );
+            assert_eq!(
+                lhs.rank_out(),
+                rhs.rank(),
+                "ksk_in output rank: {} != ggsw rank: {}",
+                self.rank_out(),
+                rhs.rank()
+            );
+            assert_eq!(
+                self.rank_out(),
+                rhs.rank(),
+                "ksk_out output rank: {} != ggsw rank: {}",
+                self.rank_out(),
+                rhs.rank()
+            );
+        }
+
+        let (mut tmp_in, scratch1) = scratch.tmp_fourier_glwe_ct(module, lhs.basek(), lhs.k(), lhs.rank());
+        let (mut tmp_out, scratch2) = scratch1.tmp_fourier_glwe_ct(module, self.basek(), self.k(), self.rank());
+
+        (0..self.rank_in()).for_each(|col_i| {
+            (0..self.rows()).for_each(|row_j| {
+                lhs.get_row(module, row_j, col_i, &mut tmp_in);
+                tmp_out.external_product(module, &tmp_in, rhs, scratch2);
+                self.set_row(module, row_j, col_i, &tmp_out);
+            });
+        });
+
+        tmp_out.data.zero();
+
+        (self.rows().min(lhs.rows())..self.rows()).for_each(|row_i| {
+            (0..self.rank_in()).for_each(|col_j| {
+                self.set_row(module, row_i, col_j, &tmp_out);
+            });
+        });
+    }
+
+    pub fn external_product_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GGSWCiphertext<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(
+                self.rank_out(),
+                rhs.rank(),
+                "ksk_out output rank: {} != ggsw rank: {}",
+                self.rank_out(),
+                rhs.rank()
+            );
+        }
+
+        let (mut tmp, scratch1) = scratch.tmp_fourier_glwe_ct(module, self.basek(), self.k(), self.rank());
+        println!("tmp: {}", tmp.size());
+        (0..self.rank_in()).for_each(|col_i| {
+            (0..self.rows()).for_each(|row_j| {
+                self.get_row(module, row_j, col_i, &mut tmp);
+                tmp.external_product_inplace(module, rhs, scratch1);
+                self.set_row(module, row_j, col_i, &tmp);
+            });
+        });
+    }
+}
+
+impl GLWEAutomorphismKey<Vec<u8>, FFT64> {
+    pub fn external_product_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_in: usize,
+        ggsw_k: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        GLWESwitchingKey::external_product_scratch_space(module, basek, k_out, k_in, ggsw_k, digits, rank)
+    }
+
+    pub fn external_product_inplace_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        ggsw_k: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        GLWESwitchingKey::external_product_inplace_scratch_space(module, basek, k_out, ggsw_k, digits, rank)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWEAutomorphismKey<DataSelf, FFT64> {
+    pub fn external_product<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWEAutomorphismKey<DataLhs, FFT64>,
+        rhs: &GGSWCiphertext<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        self.key.external_product(module, &lhs.key, rhs, scratch);
+    }
+
+    pub fn external_product_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GGSWCiphertext<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        self.key.external_product_inplace(module, rhs, scratch);
+    }
+}

@@ -0,0 +1,163 @@
+use backend::{FFT64, Module, Scratch, ZnxZero};
+
+use crate::{FourierGLWECiphertext, GLWEAutomorphismKey, GLWESwitchingKey, GetRow, Infos, ScratchCore, SetRow};
+
+impl GLWEAutomorphismKey<Vec<u8>, FFT64> {
+    pub fn keyswitch_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_in: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        GLWESwitchingKey::keyswitch_scratch_space(module, basek, k_out, k_in, k_ksk, digits, rank, rank)
+    }
+
+    pub fn keyswitch_inplace_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        GLWESwitchingKey::keyswitch_inplace_scratch_space(module, basek, k_out, k_ksk, digits, rank)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWEAutomorphismKey<DataSelf, FFT64> {
+    pub fn keyswitch<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWEAutomorphismKey<DataLhs, FFT64>,
+        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        self.key.keyswitch(module, &lhs.key, rhs, scratch);
+    }
+
+    pub fn keyswitch_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        self.key.keyswitch_inplace(module, &rhs.key, scratch);
+    }
+}
+
+impl GLWESwitchingKey<Vec<u8>, FFT64> {
+    pub fn keyswitch_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_in: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> usize {
+        let tmp_in: usize = FourierGLWECiphertext::bytes_of(module, basek, k_in, rank_in);
+        let tmp_out: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank_out);
+        let ksk: usize =
+            FourierGLWECiphertext::keyswitch_scratch_space(module, basek, k_out, k_in, k_ksk, digits, rank_in, rank_out);
+        tmp_in + tmp_out + ksk
+    }
+
+    pub fn keyswitch_inplace_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        let tmp: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank);
+        let ksk: usize = FourierGLWECiphertext::keyswitch_inplace_scratch_space(module, basek, k_out, k_ksk, digits, rank);
+        tmp + ksk
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWESwitchingKey<DataSelf, FFT64> {
+    pub fn keyswitch<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWESwitchingKey<DataLhs, FFT64>,
+        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(
+                self.rank_in(),
+                lhs.rank_in(),
+                "ksk_out input rank: {} != ksk_in input rank: {}",
+                self.rank_in(),
+                lhs.rank_in()
+            );
+            assert_eq!(
+                lhs.rank_out(),
+                rhs.rank_in(),
+                "ksk_in output rank: {} != ksk_apply input rank: {}",
+                self.rank_out(),
+                rhs.rank_in()
+            );
+            assert_eq!(
+                self.rank_out(),
+                rhs.rank_out(),
+                "ksk_out output rank: {} != ksk_apply output rank: {}",
+                self.rank_out(),
+                rhs.rank_out()
+            );
+        }
+
+        let (mut tmp_in, scratch1) = scratch.tmp_fourier_glwe_ct(module, lhs.basek(), lhs.k(), lhs.rank());
+        let (mut tmp_out, scratch2) = scratch1.tmp_fourier_glwe_ct(module, self.basek(), self.k(), self.rank());
+
+        (0..self.rank_in()).for_each(|col_i| {
+            (0..self.rows()).for_each(|row_j| {
+                lhs.get_row(module, row_j, col_i, &mut tmp_in);
+                tmp_out.keyswitch(module, &tmp_in, rhs, scratch2);
+                self.set_row(module, row_j, col_i, &tmp_out);
+            });
+        });
+
+        tmp_out.data.zero();
+
+        (self.rows().min(lhs.rows())..self.rows()).for_each(|row_i| {
+            (0..self.rank_in()).for_each(|col_j| {
+                self.set_row(module, row_i, col_j, &tmp_out);
+            });
+        });
+    }
+
+    pub fn keyswitch_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(
+                self.rank_out(),
+                rhs.rank_out(),
+                "ksk_out output rank: {} != ksk_apply output rank: {}",
+                self.rank_out(),
+                rhs.rank_out()
+            );
+        }
+
+        let (mut tmp, scratch1) = scratch.tmp_fourier_glwe_ct(module, self.basek(), self.k(), self.rank());
+
+        (0..self.rank_in()).for_each(|col_i| {
+            (0..self.rows()).for_each(|row_j| {
+                self.get_row(module, row_j, col_i, &mut tmp);
+                tmp.keyswitch_inplace(module, rhs, scratch1);
+                self.set_row(module, row_j, col_i, &tmp);
+            });
+        });
+    }
+}

@@ -0,0 +1,105 @@
+use backend::{Backend, FFT64, MatZnxDft, MatZnxDftOps, Module};
+
+use crate::{FourierGLWECiphertext, GGLWECiphertext, GetRow, Infos, SetRow};
+
+pub struct GLWESwitchingKey<Data, B: Backend> {
+    pub(crate) key: GGLWECiphertext<Data, B>,
+    pub(crate) sk_in_n: usize,  // Degree of sk_in
+    pub(crate) sk_out_n: usize, // Degree of sk_out
+}
+
+impl GLWESwitchingKey<Vec<u8>, FFT64> {
+    pub fn alloc(
+        module: &Module<FFT64>,
+        basek: usize,
+        k: usize,
+        rows: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> Self {
+        GLWESwitchingKey {
+            key: GGLWECiphertext::alloc(module, basek, k, rows, digits, rank_in, rank_out),
+            sk_in_n: 0,
+            sk_out_n: 0,
+        }
+    }
+
+    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)
+    }
+}
+
+impl<T, B: Backend> Infos for GLWESwitchingKey<T, B> {
+    type Inner = MatZnxDft<T, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        self.key.inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.key.basek()
+    }
+
+    fn k(&self) -> usize {
+        self.key.k()
+    }
+}
+
+impl<T, B: Backend> GLWESwitchingKey<T, B> {
+    pub fn rank(&self) -> usize {
+        self.key.data.cols_out() - 1
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.key.data.cols_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.key.data.cols_out() - 1
+    }
+
+    pub fn digits(&self) -> usize {
+        self.key.digits()
+    }
+
+    pub fn sk_degree_in(&self) -> usize {
+        self.sk_in_n
+    }
+
+    pub fn sk_degree_out(&self) -> usize {
+        self.sk_out_n
+    }
+}
+
+impl<C: AsRef<[u8]>> GetRow<FFT64> for GLWESwitchingKey<C, FFT64> {
+    fn get_row<R: AsMut<[u8]> + AsRef<[u8]>>(
+        &self,
+        module: &Module<FFT64>,
+        row_i: usize,
+        col_j: usize,
+        res: &mut FourierGLWECiphertext<R, FFT64>,
+    ) {
+        module.mat_znx_dft_get_row(&mut res.data, &self.key.data, row_i, col_j);
+    }
+}
+
+impl<C: AsMut<[u8]> + AsRef<[u8]>> SetRow<FFT64> for GLWESwitchingKey<C, FFT64> {
+    fn set_row<R: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        row_i: usize,
+        col_j: usize,
+        a: &FourierGLWECiphertext<R, FFT64>,
+    ) {
+        module.mat_znx_dft_set_row(&mut self.key.data, row_i, col_j, &a.data);
+    }
+}

@@ -0,0 +1,16 @@
+pub mod automorphism;
+pub mod automorphism_key;
+pub mod ciphertext;
+pub mod encryption;
+pub mod external_product;
+pub mod keyswitch;
+pub mod keyswitch_key;
+pub mod tensor_key;
+
+pub use automorphism_key::GLWEAutomorphismKey;
+pub use ciphertext::GGLWECiphertext;
+pub use keyswitch_key::GLWESwitchingKey;
+pub use tensor_key::GLWETensorKey;
+
+#[cfg(test)]
+mod test_fft64;

@@ -0,0 +1,81 @@
+use backend::{Backend, FFT64, MatZnxDft, Module};
+
+use crate::{GLWESwitchingKey, Infos};
+
+pub struct GLWETensorKey<C, B: Backend> {
+    pub(crate) keys: Vec<GLWESwitchingKey<C, B>>,
+}
+
+impl GLWETensorKey<Vec<u8>, FFT64> {
+    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, digits, 1, rank,
+            ));
+        });
+        Self { keys: keys }
+    }
+
+    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, digits, 1, rank)
+    }
+}
+
+impl<T, B: Backend> Infos for GLWETensorKey<T, B> {
+    type Inner = MatZnxDft<T, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.keys[0].inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.keys[0].basek()
+    }
+
+    fn k(&self) -> usize {
+        self.keys[0].k()
+    }
+}
+
+impl<T, B: Backend> GLWETensorKey<T, B> {
+    pub fn rank(&self) -> usize {
+        self.keys[0].rank()
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.keys[0].rank_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.keys[0].rank_out()
+    }
+
+    pub fn digits(&self) -> usize {
+        self.keys[0].digits()
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWETensorKey<DataSelf, FFT64> {
+    // Returns a mutable reference to GLWESwitchingKey_{s}(s[i] * s[j])
+    pub fn at_mut(&mut self, mut i: usize, mut j: usize) -> &mut GLWESwitchingKey<DataSelf, FFT64> {
+        if i > j {
+            std::mem::swap(&mut i, &mut j);
+        };
+        let rank: usize = self.rank();
+        &mut self.keys[i * rank + j - (i * (i + 1) / 2)]
+    }
+}
+
+impl<DataSelf: AsRef<[u8]>> GLWETensorKey<DataSelf, FFT64> {
+    // Returns a reference to GLWESwitchingKey_{s}(s[i] * s[j])
+    pub fn at(&self, mut i: usize, mut j: usize) -> &GLWESwitchingKey<DataSelf, FFT64> {
+        if i > j {
+            std::mem::swap(&mut i, &mut j);
+        };
+        let rank: usize = self.rank();
+        &self.keys[i * rank + j - (i * (i + 1) / 2)]
+    }
+}

@@ -0,0 +1,3 @@
+pub mod automorphism_key;
+pub mod gglwe;
+pub mod tensor_key;

@@ -1,236 +0,0 @@
-use backend::{
-    Backend, FFT64, MatZnxDft, MatZnxDftAlloc, MatZnxDftOps, Module, ScalarZnx, Scratch, VecZnxAlloc, VecZnxDftAlloc, VecZnxOps,
-    ZnxInfos, ZnxZero,
-};
-use sampling::source::Source;
-
-use crate::{GLWECiphertext, GLWECiphertextFourier, GLWESecret, GetRow, Infos, ScratchCore, SetRow};
-
-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,
-        digits: usize,
-        rank_in: usize,
-        rank_out: usize,
-    ) -> Self {
-        let size: usize = k.div_ceil(basek);
-        debug_assert!(
-            size > digits,
-            "invalid gglwe: ceil(k/basek): {} <= digits: {}",
-            size,
-            digits
-        );
-
-        debug_assert!(
-            rows * digits <= size,
-            "invalid gglwe: rows: {} * digits:{} > ceil(k/basek): {}",
-            rows,
-            digits,
-            size
-        );
-
-        Self {
-            data: module.new_mat_znx_dft(rows, rank_in, rank_out + 1, size),
-            basek: basek,
-            k,
-            digits,
-        }
-    }
-
-    pub fn bytes_of(
-        module: &Module<FFT64>,
-        basek: usize,
-        k: usize,
-        rows: usize,
-        digits: usize,
-        rank_in: usize,
-        rank_out: usize,
-    ) -> usize {
-        let size: usize = k.div_ceil(basek);
-        debug_assert!(
-            size > digits,
-            "invalid gglwe: ceil(k/basek): {} <= digits: {}",
-            size,
-            digits
-        );
-
-        assert!(
-            rows * digits <= size,
-            "invalid gglwe: rows: {} * digits:{} > ceil(k/basek): {}",
-            rows,
-            digits,
-            size
-        );
-
-        module.bytes_of_mat_znx_dft(rows, rank_in, rank_out + 1, size)
-    }
-}
-
-impl<T, B: Backend> Infos for GGLWECiphertext<T, B> {
-    type Inner = MatZnxDft<T, B>;
-
-    fn inner(&self) -> &Self::Inner {
-        &self.data
-    }
-
-    fn basek(&self) -> usize {
-        self.basek
-    }
-
-    fn k(&self) -> usize {
-        self.k
-    }
-}
-
-impl<T, B: Backend> GGLWECiphertext<T, B> {
-    pub fn rank(&self) -> usize {
-        self.data.cols_out() - 1
-    }
-
-    pub fn digits(&self) -> usize {
-        self.digits
-    }
-
-    pub fn rank_in(&self) -> usize {
-        self.data.cols_in()
-    }
-
-    pub fn rank_out(&self) -> usize {
-        self.data.cols_out() - 1
-    }
-}
-
-impl GGLWECiphertext<Vec<u8>, FFT64> {
-    pub fn generate_from_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
-        let size = k.div_ceil(basek);
-        GLWECiphertext::encrypt_sk_scratch_space(module, basek, k)
-            + module.bytes_of_vec_znx(rank + 1, size)
-            + module.bytes_of_vec_znx(1, size)
-            + module.bytes_of_vec_znx_dft(rank + 1, size)
-    }
-
-    pub fn generate_from_pk_scratch_space(_module: &Module<FFT64>, _basek: usize, _k: usize, _rank: usize) -> usize {
-        unimplemented!()
-    }
-}
-
-impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GGLWECiphertext<DataSelf, FFT64> {
-    pub fn encrypt_sk<DataPt: AsRef<[u8]>, DataSk: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        pt: &ScalarZnx<DataPt>,
-        sk: &GLWESecret<DataSk, FFT64>,
-        source_xa: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-        scratch: &mut Scratch,
-    ) {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(self.rank_in(), pt.cols());
-            assert_eq!(self.rank_out(), sk.rank());
-            assert_eq!(self.n(), module.n());
-            assert_eq!(sk.n(), module.n());
-            assert_eq!(pt.n(), module.n());
-            assert!(
-                scratch.available()
-                    >= GGLWECiphertext::generate_from_sk_scratch_space(module, self.basek(), self.k(), self.rank()),
-                "scratch.available: {} < GGLWECiphertext::generate_from_sk_scratch_space(module, self.rank()={}, \
-                 self.size()={}): {}",
-                scratch.available(),
-                self.rank(),
-                self.size(),
-                GGLWECiphertext::generate_from_sk_scratch_space(module, self.basek(), self.k(), self.rank())
-            );
-            assert!(
-                self.rows() * self.digits() * self.basek() <= self.k(),
-                "self.rows() : {} * self.digits() : {} * self.basek() : {} = {} >= self.k() = {}",
-                self.rows(),
-                self.digits(),
-                self.basek(),
-                self.rows() * self.digits() * self.basek(),
-                self.k()
-            );
-        }
-
-        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();
-        let rank_out: usize = self.rank_out();
-
-        let (mut tmp_pt, scrach_1) = scratch.tmp_glwe_pt(module, basek, k);
-        let (mut tmp_ct, scrach_2) = scrach_1.tmp_glwe_ct(module, basek, k, rank_out);
-        let (mut tmp_ct_dft, scratch_3) = scrach_2.tmp_glwe_fourier(module, basek, k, rank_out);
-
-        // For each input column (i.e. rank) produces a GGLWE ciphertext of rank_out+1 columns
-        //
-        // Example for ksk rank 2 to rank 3:
-        //
-        // (-(a0*s0 + a1*s1 + a2*s2) + s0', a0, a1, a2)
-        // (-(b0*s0 + b1*s1 + b2*s2) + s0', b0, b1, b2)
-        //
-        // Example ksk rank 2 to rank 1
-        //
-        // (-(a*s) + s0, a)
-        // (-(b*s) + s1, b)
-        (0..rank_in).for_each(|col_i| {
-            (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,
-                    (digits - 1) + 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
-                tmp_ct.encrypt_sk(module, &tmp_pt, sk, source_xa, source_xe, sigma, scratch_3);
-
-                // Switch vec_znx_ct into DFT domain
-                tmp_ct.dft(module, &mut tmp_ct_dft);
-
-                // Stores vec_znx_dft_ct into thw i-th row of the MatZnxDft
-                self.set_row(module, row_i, col_i, &tmp_ct_dft);
-            });
-        });
-    }
-}
-
-impl<C: AsRef<[u8]>> GetRow<FFT64> for GGLWECiphertext<C, FFT64> {
-    fn get_row<R: AsMut<[u8]> + AsRef<[u8]>>(
-        &self,
-        module: &Module<FFT64>,
-        row_i: usize,
-        col_j: usize,
-        res: &mut GLWECiphertextFourier<R, FFT64>,
-    ) {
-        module.vmp_extract_row(&mut res.data, &self.data, row_i, col_j);
-    }
-}
-
-impl<C: AsMut<[u8]> + AsRef<[u8]>> SetRow<FFT64> for GGLWECiphertext<C, FFT64> {
-    fn set_row<R: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        row_i: usize,
-        col_j: usize,
-        a: &GLWECiphertextFourier<R, FFT64>,
-    ) {
-        module.vmp_prepare_row(&mut self.data, row_i, col_j, &a.data);
-    }
-}

@@ -0,0 +1,6 @@
+pub mod ciphertext;
+
+pub use ciphertext::GGSWCiphertext;
+
+#[cfg(test)]
+mod test_fft64;

@@ -0,0 +1,1 @@
+mod ggsw;

@@ -6,8 +6,8 @@ };
 use sampling::source::Source;
 
 use crate::{
-    AutomorphismKey, GLWECiphertext, GLWECiphertextFourier, GLWESecret, GLWESwitchingKey, GetRow, Infos, ScratchCore, SetRow,
-    TensorKey,
+    FourierGLWECiphertext, FourierGLWESecret, GLWEAutomorphismKey, GLWECiphertext, GLWESwitchingKey, GLWETensorKey, GetRow,
+    Infos, ScratchCore, SetRow,
 };
 
 pub struct GGSWCiphertext<C, B: Backend> {
@@ -17,8 +17,8 @@ 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, digits: usize, rank: usize) -> Self {
+impl GGSWCiphertext<Vec<u8>, FFT64> {
+    pub fn alloc(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self {
         let size: usize = k.div_ceil(basek);
         debug_assert!(
             size > digits,
@@ -220,9 +220,9 @@ k_ggsw: usize,
         digits: usize,
         rank: usize,
     ) -> usize {
-        let tmp_in: usize = GLWECiphertextFourier::bytes_of(module, basek, k_in, rank);
-        let tmp_out: usize = GLWECiphertextFourier::bytes_of(module, basek, k_out, rank);
-        let ggsw: usize = GLWECiphertextFourier::external_product_scratch_space(module, basek, k_out, k_in, k_ggsw, digits, rank);
+        let tmp_in: usize = FourierGLWECiphertext::bytes_of(module, basek, k_in, rank);
+        let tmp_out: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank);
+        let ggsw: usize = FourierGLWECiphertext::external_product_scratch_space(module, basek, k_out, k_in, k_ggsw, digits, rank);
         tmp_in + tmp_out + ggsw
     }
 
@@ -234,9 +234,9 @@ k_ggsw: usize,
         digits: usize,
         rank: usize,
     ) -> usize {
-        let tmp: usize = GLWECiphertextFourier::bytes_of(module, basek, k_out, rank);
+        let tmp: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank);
         let ggsw: usize =
-            GLWECiphertextFourier::external_product_inplace_scratch_space(module, basek, k_out, k_ggsw, digits, rank);
+            FourierGLWECiphertext::external_product_inplace_scratch_space(module, basek, k_out, k_ggsw, digits, rank);
         tmp + ggsw
     }
 }
@@ -246,7 +246,7 @@ pub fn encrypt_sk<DataPt: AsRef<[u8]>, DataSk: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
         pt: &ScalarZnx<DataPt>,
-        sk: &GLWESecret<DataSk, FFT64>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
         source_xa: &mut Source,
         source_xe: &mut Source,
         sigma: f64,
@@ -290,7 +290,7 @@ );
 
                 // Switch vec_znx_ct into DFT domain
                 {
-                    let (mut tmp_ct_dft, _) = scratch2.tmp_glwe_fourier(module, basek, k, rank);
+                    let (mut tmp_ct_dft, _) = scratch2.tmp_fourier_glwe_ct(module, basek, k, rank);
                     tmp_ct.dft(module, &mut tmp_ct_dft);
                     self.set_row(module, row_i, col_j, &tmp_ct_dft);
                 }
@@ -304,7 +304,7 @@ module: &Module<FFT64>,
         col_j: usize,
         res: &mut R,
         ci_dft: &VecZnxDft<DataCi, FFT64>,
-        tsk: &TensorKey<DataTsk, FFT64>,
+        tsk: &GLWETensorKey<DataTsk, FFT64>,
         scratch: &mut Scratch,
     ) where
         R: VecZnxToMut,
@@ -361,7 +361,7 @@ // a2 * (-(h0s0 + h1s1 + h1s2) + s0s2, h0, h1, h2) = (-(a2h0s0 + a2h1s1 + a2h1s2) + a2s0s2, a2h0, a2h1, a2h2)
             // =
             // (-(x0s0 + x1s1 + x2s2) + s0(a0s0 + a1s1 + a2s2), x0, x1, x2)
             (1..cols).for_each(|col_i| {
-                let pmat: &MatZnxDft<DataTsk, FFT64> = &tsk.at(col_i - 1, col_j - 1).0.data; // Selects Enc(s[i]s[j])
+                let pmat: &MatZnxDft<DataTsk, FFT64> = &tsk.at(col_i - 1, col_j - 1).key.data; // Selects Enc(s[i]s[j])
 
                 // Extracts a[i] and multipies with Enc(s[i]s[j])
                 (0..digits).for_each(|di| {
@@ -408,7 +408,7 @@ &mut self,
         module: &Module<FFT64>,
         lhs: &GGSWCiphertext<DataLhs, FFT64>,
         ksk: &GLWESwitchingKey<DataKsk, FFT64>,
-        tsk: &TensorKey<DataTsk, FFT64>,
+        tsk: &GLWETensorKey<DataTsk, FFT64>,
         scratch: &mut Scratch,
     ) {
         let rank: usize = self.rank();
@@ -429,7 +429,7 @@ (0..cols).for_each(|col_i| {
                 module.vec_znx_dft(1, 0, &mut ci_dft, col_i, &tmp_res.data, col_i);
             });
 
-            module.vmp_prepare_row(&mut self.data, row_i, 0, &ci_dft);
+            module.mat_znx_dft_set_row(&mut self.data, row_i, 0, &ci_dft);
 
             // Generates
             //
@@ -438,7 +438,7 @@ // col 2: (-(c0s0' + c1s1' + c2s2')    , c0       , c1 + M[i], c2       )
             // col 3: (-(d0s0' + d1s1' + d2s2')    , d0       , d1       , d2 + M[i])
             (1..cols).for_each(|col_j| {
                 self.expand_row(module, col_j, &mut tmp_res.data, &ci_dft, tsk, scratch2);
-                let (mut tmp_res_dft, _) = scratch2.tmp_glwe_fourier(module, basek, self.k(), rank);
+                let (mut tmp_res_dft, _) = scratch2.tmp_fourier_glwe_ct(module, basek, self.k(), rank);
                 tmp_res.dft(module, &mut tmp_res_dft);
                 self.set_row(module, row_i, col_j, &tmp_res_dft);
             });
@@ -449,7 +449,7 @@ pub fn keyswitch_inplace<DataKsk: AsRef<[u8]>, DataTsk: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
         ksk: &GLWESwitchingKey<DataKsk, FFT64>,
-        tsk: &TensorKey<DataTsk, FFT64>,
+        tsk: &GLWETensorKey<DataTsk, FFT64>,
         scratch: &mut Scratch,
     ) {
         unsafe {
@@ -462,8 +462,8 @@ pub fn automorphism<DataLhs: AsRef<[u8]>, DataAk: AsRef<[u8]>, DataTsk: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
         lhs: &GGSWCiphertext<DataLhs, FFT64>,
-        auto_key: &AutomorphismKey<DataAk, FFT64>,
-        tensor_key: &TensorKey<DataTsk, FFT64>,
+        auto_key: &GLWEAutomorphismKey<DataAk, FFT64>,
+        tensor_key: &GLWETensorKey<DataTsk, FFT64>,
         scratch: &mut Scratch,
     ) {
         #[cfg(debug_assertions)]
@@ -525,7 +525,7 @@ module.vec_znx_automorphism_inplace(auto_key.p(), &mut tmp_res.data, col_i);
                 module.vec_znx_dft(1, 0, &mut ci_dft, col_i, &tmp_res.data, col_i);
             });
 
-            module.vmp_prepare_row(&mut self.data, row_i, 0, &ci_dft);
+            module.mat_znx_dft_set_row(&mut self.data, row_i, 0, &ci_dft);
 
             // Generates
             //
@@ -541,7 +541,7 @@ &ci_dft,
                     tensor_key,
                     scratch2,
                 );
-                let (mut tmp_res_dft, _) = scratch2.tmp_glwe_fourier(module, basek, self.k(), rank);
+                let (mut tmp_res_dft, _) = scratch2.tmp_fourier_glwe_ct(module, basek, self.k(), rank);
                 tmp_res.dft(module, &mut tmp_res_dft);
                 self.set_row(module, row_i, col_j, &tmp_res_dft);
             });
@@ -551,8 +551,8 @@
     pub fn automorphism_inplace<DataKsk: AsRef<[u8]>, DataTsk: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
-        auto_key: &AutomorphismKey<DataKsk, FFT64>,
-        tensor_key: &TensorKey<DataTsk, FFT64>,
+        auto_key: &GLWEAutomorphismKey<DataKsk, FFT64>,
+        tensor_key: &GLWETensorKey<DataTsk, FFT64>,
         scratch: &mut Scratch,
     ) {
         unsafe {
@@ -599,8 +599,8 @@ )
             )
         }
 
-        let (mut tmp_ct_in, scratch1) = scratch.tmp_glwe_fourier(module, lhs.basek(), lhs.k(), lhs.rank());
-        let (mut tmp_ct_out, scratch2) = scratch1.tmp_glwe_fourier(module, self.basek(), self.k(), self.rank());
+        let (mut tmp_ct_in, scratch1) = scratch.tmp_fourier_glwe_ct(module, lhs.basek(), lhs.k(), lhs.rank());
+        let (mut tmp_ct_out, scratch2) = scratch1.tmp_fourier_glwe_ct(module, self.basek(), self.k(), self.rank());
 
         (0..self.rank() + 1).for_each(|col_i| {
             (0..self.rows()).for_each(|row_j| {
@@ -636,7 +636,7 @@ rhs.rank()
             );
         }
 
-        let (mut tmp_ct, scratch1) = scratch.tmp_glwe_fourier(module, self.basek(), self.k(), self.rank());
+        let (mut tmp_ct, scratch1) = scratch.tmp_fourier_glwe_ct(module, self.basek(), self.k(), self.rank());
 
         (0..self.rank() + 1).for_each(|col_i| {
             (0..self.rows()).for_each(|row_j| {
@@ -674,7 +674,7 @@ ksk.rank()
                     )
             )
         }
-        let (mut tmp_dft_dft, scratch1) = scratch.tmp_glwe_fourier(module, self.basek(), self.k(), self.rank());
+        let (mut tmp_dft_dft, scratch1) = scratch.tmp_fourier_glwe_ct(module, self.basek(), self.k(), self.rank());
         self.get_row(module, row_i, 0, &mut tmp_dft_dft);
         res.keyswitch_from_fourier(module, &tmp_dft_dft, ksk, scratch1);
     }
@@ -686,9 +686,9 @@ &self,
         module: &Module<FFT64>,
         row_i: usize,
         col_j: usize,
-        res: &mut GLWECiphertextFourier<R, FFT64>,
+        res: &mut FourierGLWECiphertext<R, FFT64>,
     ) {
-        module.vmp_extract_row(&mut res.data, &self.data, row_i, col_j);
+        module.mat_znx_dft_get_row(&mut res.data, &self.data, row_i, col_j);
     }
 }
 
@@ -698,8 +698,8 @@ &mut self,
         module: &Module<FFT64>,
         row_i: usize,
         col_j: usize,
-        a: &GLWECiphertextFourier<R, FFT64>,
+        a: &FourierGLWECiphertext<R, FFT64>,
     ) {
-        module.vmp_prepare_row(&mut self.data, row_i, col_j, &a.data);
+        module.mat_znx_dft_set_row(&mut self.data, row_i, col_j, &a.data);
     }
 }

@@ -0,0 +1,121 @@
+use backend::{FFT64, Module, Scratch, VecZnxOps};
+
+use crate::{GLWEAutomorphismKey, GLWECiphertext};
+
+impl GLWECiphertext<Vec<u8>> {
+    pub fn automorphism_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_in: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        Self::keyswitch_scratch_space(module, basek, k_out, k_in, k_ksk, digits, rank, rank)
+    }
+
+    pub fn automorphism_inplace_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        Self::keyswitch_inplace_scratch_space(module, basek, k_out, k_ksk, digits, rank)
+    }
+}
+
+impl<DataSelf: AsRef<[u8]> + AsMut<[u8]>> GLWECiphertext<DataSelf> {
+    pub fn automorphism<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWECiphertext<DataLhs>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        self.keyswitch(module, lhs, &rhs.key, scratch);
+        (0..self.rank() + 1).for_each(|i| {
+            module.vec_znx_automorphism_inplace(rhs.p(), &mut self.data, i);
+        })
+    }
+
+    pub fn automorphism_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        self.keyswitch_inplace(module, &rhs.key, scratch);
+        (0..self.rank() + 1).for_each(|i| {
+            module.vec_znx_automorphism_inplace(rhs.p(), &mut self.data, i);
+        })
+    }
+
+    pub fn automorphism_add<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWECiphertext<DataLhs>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        Self::keyswitch_private::<_, _, 1>(self, rhs.p(), module, lhs, &rhs.key, scratch);
+    }
+
+    pub fn automorphism_add_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        unsafe {
+            let self_ptr: *mut GLWECiphertext<DataSelf> = self as *mut GLWECiphertext<DataSelf>;
+            Self::keyswitch_private::<_, _, 1>(self, rhs.p(), module, &*self_ptr, &rhs.key, scratch);
+        }
+    }
+
+    pub fn automorphism_sub_ab<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWECiphertext<DataLhs>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        Self::keyswitch_private::<_, _, 2>(self, rhs.p(), module, lhs, &rhs.key, scratch);
+    }
+
+    pub fn automorphism_sub_ab_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        unsafe {
+            let self_ptr: *mut GLWECiphertext<DataSelf> = self as *mut GLWECiphertext<DataSelf>;
+            Self::keyswitch_private::<_, _, 2>(self, rhs.p(), module, &*self_ptr, &rhs.key, scratch);
+        }
+    }
+
+    pub fn automorphism_sub_ba<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWECiphertext<DataLhs>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        Self::keyswitch_private::<_, _, 3>(self, rhs.p(), module, lhs, &rhs.key, scratch);
+    }
+
+    pub fn automorphism_sub_ba_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        unsafe {
+            let self_ptr: *mut GLWECiphertext<DataSelf> = self as *mut GLWECiphertext<DataSelf>;
+            Self::keyswitch_private::<_, _, 3>(self, rhs.p(), module, &*self_ptr, &rhs.key, scratch);
+        }
+    }
+}

@@ -0,0 +1,115 @@
+use backend::{Backend, FFT64, Module, VecZnx, VecZnxAlloc, VecZnxDftOps, VecZnxToMut, VecZnxToRef};
+
+use crate::{FourierGLWECiphertext, GLWEOps, Infos, SetMetaData};
+
+pub struct GLWECiphertext<C> {
+    pub data: VecZnx<C>,
+    pub basek: usize,
+    pub k: usize,
+}
+
+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, k.div_ceil(basek)),
+            basek,
+            k,
+        }
+    }
+
+    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
+        module.bytes_of_vec_znx(rank + 1, k.div_ceil(basek))
+    }
+}
+
+impl<T> Infos for GLWECiphertext<T> {
+    type Inner = VecZnx<T>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.data
+    }
+
+    fn basek(&self) -> usize {
+        self.basek
+    }
+
+    fn k(&self) -> usize {
+        self.k
+    }
+}
+
+impl<T> GLWECiphertext<T> {
+    pub fn rank(&self) -> usize {
+        self.cols() - 1
+    }
+}
+
+impl<C: AsRef<[u8]>> GLWECiphertext<C> {
+    #[allow(dead_code)]
+    pub(crate) fn dft<R: AsMut<[u8]> + AsRef<[u8]>>(&self, module: &Module<FFT64>, res: &mut FourierGLWECiphertext<R, FFT64>) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), res.rank());
+            assert_eq!(self.basek(), res.basek())
+        }
+
+        (0..self.rank() + 1).for_each(|i| {
+            module.vec_znx_dft(1, 0, &mut res.data, i, &self.data, i);
+        })
+    }
+}
+
+impl<DataSelf: AsRef<[u8]>> GLWECiphertext<DataSelf> {
+    pub fn clone(&self) -> GLWECiphertext<Vec<u8>> {
+        GLWECiphertext {
+            data: self.data.clone(),
+            basek: self.basek(),
+            k: self.k(),
+        }
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> SetMetaData for GLWECiphertext<DataSelf> {
+    fn set_k(&mut self, k: usize) {
+        self.k = k
+    }
+
+    fn set_basek(&mut self, basek: usize) {
+        self.basek = basek
+    }
+}
+
+pub trait GLWECiphertextToRef {
+    fn to_ref(&self) -> GLWECiphertext<&[u8]>;
+}
+
+impl<D: AsRef<[u8]>> GLWECiphertextToRef for GLWECiphertext<D> {
+    fn to_ref(&self) -> GLWECiphertext<&[u8]> {
+        GLWECiphertext {
+            data: self.data.to_ref(),
+            basek: self.basek,
+            k: self.k,
+        }
+    }
+}
+
+pub trait GLWECiphertextToMut {
+    fn to_mut(&mut self) -> GLWECiphertext<&mut [u8]>;
+}
+
+impl<D: AsMut<[u8]> + AsRef<[u8]>> GLWECiphertextToMut for GLWECiphertext<D> {
+    fn to_mut(&mut self) -> GLWECiphertext<&mut [u8]> {
+        GLWECiphertext {
+            data: self.data.to_mut(),
+            basek: self.basek,
+            k: self.k,
+        }
+    }
+}
+
+impl<D> GLWEOps for GLWECiphertext<D>
+where
+    D: AsRef<[u8]> + AsMut<[u8]>,
+    GLWECiphertext<D>: GLWECiphertextToMut + Infos + SetMetaData,
+{
+}

@@ -0,0 +1,58 @@
+use backend::{
+    FFT64, Module, ScalarZnxDftOps, Scratch, VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDftAlloc, VecZnxDftOps,
+    ZnxZero,
+};
+
+use crate::{FourierGLWESecret, GLWECiphertext, GLWEPlaintext, Infos};
+
+impl GLWECiphertext<Vec<u8>> {
+    pub fn decrypt_scratch_space(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
+        let size: usize = k.div_ceil(basek);
+        (module.vec_znx_big_normalize_tmp_bytes() | module.bytes_of_vec_znx_dft(1, size)) + module.bytes_of_vec_znx_big(1, size)
+    }
+}
+
+impl<DataSelf: AsRef<[u8]>> GLWECiphertext<DataSelf> {
+    pub fn decrypt<DataPt: AsMut<[u8]> + AsRef<[u8]>, DataSk: AsRef<[u8]>>(
+        &self,
+        module: &Module<FFT64>,
+        pt: &mut GLWEPlaintext<DataPt>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), sk.rank());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(pt.n(), module.n());
+            assert_eq!(sk.n(), module.n());
+        }
+
+        let cols: usize = self.rank() + 1;
+
+        let (mut c0_big, scratch_1) = scratch.tmp_vec_znx_big(module, 1, self.size()); // TODO optimize size when pt << ct
+        c0_big.zero();
+
+        {
+            (1..cols).for_each(|i| {
+                // ci_dft = DFT(a[i]) * DFT(s[i])
+                let (mut ci_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, self.size()); // TODO optimize size when pt << ct
+                module.vec_znx_dft(1, 0, &mut ci_dft, 0, &self.data, i);
+                module.svp_apply_inplace(&mut ci_dft, 0, &sk.data, i - 1);
+                let ci_big = module.vec_znx_idft_consume(ci_dft);
+
+                // c0_big += a[i] * s[i]
+                module.vec_znx_big_add_inplace(&mut c0_big, 0, &ci_big, 0);
+            });
+        }
+
+        // c0_big = (a * s) + (-a * s + m + e) = BIG(m + e)
+        module.vec_znx_big_add_small_inplace(&mut c0_big, 0, &self.data, 0);
+
+        // pt = norm(BIG(m + e))
+        module.vec_znx_big_normalize(self.basek(), &mut pt.data, 0, &mut c0_big, 0, scratch_1);
+
+        pt.basek = self.basek();
+        pt.k = pt.k().min(self.k());
+    }
+}

@@ -0,0 +1,254 @@
+use backend::{
+    AddNormal, FFT64, FillUniform, Module, ScalarZnxAlloc, ScalarZnxDftAlloc, ScalarZnxDftOps, Scratch, VecZnxAlloc, VecZnxBig,
+    VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDftAlloc, VecZnxDftOps, VecZnxOps, ZnxZero,
+};
+use sampling::source::Source;
+
+use crate::{FourierGLWESecret, GLWECiphertext, GLWEPlaintext, GLWEPublicKey, Infos, SIX_SIGMA, dist::Distribution};
+
+impl GLWECiphertext<Vec<u8>> {
+    pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
+        let size: usize = k.div_ceil(basek);
+        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 = k.div_ceil(basek);
+        ((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()
+    }
+}
+
+impl<DataSelf: AsRef<[u8]> + AsMut<[u8]>> GLWECiphertext<DataSelf> {
+    pub fn encrypt_sk<DataPt: AsRef<[u8]>, DataSk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        pt: &GLWEPlaintext<DataPt>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        self.encrypt_sk_private(
+            module,
+            Some((pt, 0)),
+            sk,
+            source_xa,
+            source_xe,
+            sigma,
+            scratch,
+        );
+    }
+
+    pub fn encrypt_zero_sk<DataSk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        self.encrypt_sk_private(
+            module,
+            None::<(&GLWEPlaintext<Vec<u8>>, usize)>,
+            sk,
+            source_xa,
+            source_xe,
+            sigma,
+            scratch,
+        );
+    }
+
+    pub fn encrypt_pk<DataPt: AsRef<[u8]>, DataPk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        pt: &GLWEPlaintext<DataPt>,
+        pk: &GLWEPublicKey<DataPk, FFT64>,
+        source_xu: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        self.encrypt_pk_private::<DataPt, DataPk>(
+            module,
+            Some((pt, 0)),
+            pk,
+            source_xu,
+            source_xe,
+            sigma,
+            scratch,
+        );
+    }
+
+    pub fn encrypt_zero_pk<DataPk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        pk: &GLWEPublicKey<DataPk, FFT64>,
+        source_xu: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        self.encrypt_pk_private::<Vec<u8>, DataPk>(
+            module,
+            None::<(&GLWEPlaintext<Vec<u8>>, usize)>,
+            pk,
+            source_xu,
+            source_xe,
+            sigma,
+            scratch,
+        );
+    }
+
+    pub(crate) fn encrypt_sk_private<DataPt: AsRef<[u8]>, DataSk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        pt: Option<(&GLWEPlaintext<DataPt>, usize)>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), sk.rank());
+            assert_eq!(sk.n(), module.n());
+            assert_eq!(self.n(), module.n());
+            if let Some((pt, col)) = pt {
+                assert_eq!(pt.n(), module.n());
+                assert!(col < self.rank() + 1);
+            }
+            assert!(
+                scratch.available() >= GLWECiphertext::encrypt_sk_scratch_space(module, self.basek(), self.k()),
+                "scratch.available(): {} < GLWECiphertext::encrypt_sk_scratch_space: {}",
+                scratch.available(),
+                GLWECiphertext::encrypt_sk_scratch_space(module, self.basek(), self.k())
+            )
+        }
+
+        let basek: usize = self.basek();
+        let k: usize = self.k();
+        let size: usize = self.size();
+        let cols: usize = self.rank() + 1;
+
+        let (mut c0_big, scratch_1) = scratch.tmp_vec_znx(module, 1, size);
+        c0_big.zero();
+
+        {
+            // c[i] = uniform
+            // c[0] -= c[i] * s[i],
+            (1..cols).for_each(|i| {
+                let (mut ci_dft, scratch_2) = scratch_1.tmp_vec_znx_dft(module, 1, size);
+
+                // c[i] = uniform
+                self.data.fill_uniform(basek, i, size, source_xa);
+
+                // c[i] = norm(IDFT(DFT(c[i]) * DFT(s[i])))
+                module.vec_znx_dft(1, 0, &mut ci_dft, 0, &self.data, i);
+                module.svp_apply_inplace(&mut ci_dft, 0, &sk.data, i - 1);
+                let ci_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume(ci_dft);
+
+                // use c[0] as buffer, which is overwritten later by the normalization step
+                module.vec_znx_big_normalize(basek, &mut self.data, 0, &ci_big, 0, scratch_2);
+
+                // c0_tmp = -c[i] * s[i] (use c[0] as buffer)
+                module.vec_znx_sub_ab_inplace(&mut c0_big, 0, &self.data, 0);
+
+                // c[i] += m if col = i
+                if let Some((pt, col)) = pt {
+                    if i == col {
+                        module.vec_znx_add_inplace(&mut self.data, i, &pt.data, 0);
+                        module.vec_znx_normalize_inplace(basek, &mut self.data, i, scratch_2);
+                    }
+                }
+            });
+        }
+
+        // c[0] += e
+        c0_big.add_normal(basek, 0, k, source_xe, sigma, sigma * SIX_SIGMA);
+
+        // c[0] += m if col = 0
+        if let Some((pt, col)) = pt {
+            if col == 0 {
+                module.vec_znx_add_inplace(&mut c0_big, 0, &pt.data, 0);
+            }
+        }
+
+        // c[0] = norm(c[0])
+        module.vec_znx_normalize(basek, &mut self.data, 0, &c0_big, 0, scratch_1);
+    }
+
+    pub(crate) fn encrypt_pk_private<DataPt: AsRef<[u8]>, DataPk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        pt: Option<(&GLWEPlaintext<DataPt>, usize)>,
+        pk: &GLWEPublicKey<DataPk, FFT64>,
+        source_xu: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.basek(), pk.basek());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(pk.n(), module.n());
+            assert_eq!(self.rank(), pk.rank());
+            if let Some((pt, _)) = pt {
+                assert_eq!(pt.basek(), pk.basek());
+                assert_eq!(pt.n(), module.n());
+            }
+        }
+
+        let basek: usize = pk.basek();
+        let size_pk: usize = pk.size();
+        let cols: usize = self.rank() + 1;
+
+        // Generates u according to the underlying secret distribution.
+        let (mut u_dft, scratch_1) = scratch.tmp_scalar_znx_dft(module, 1);
+
+        {
+            let (mut u, _) = scratch_1.tmp_scalar_znx(module, 1);
+            match pk.dist {
+                Distribution::NONE => panic!(
+                    "invalid public key: SecretDistribution::NONE, ensure it has been correctly intialized through \
+                     Self::generate"
+                ),
+                Distribution::TernaryFixed(hw) => u.fill_ternary_hw(0, hw, source_xu),
+                Distribution::TernaryProb(prob) => u.fill_ternary_prob(0, prob, source_xu),
+                Distribution::BinaryFixed(hw) => u.fill_binary_hw(0, hw, source_xu),
+                Distribution::BinaryProb(prob) => u.fill_binary_prob(0, prob, source_xu),
+                Distribution::BinaryBlock(block_size) => u.fill_binary_block(0, block_size, source_xu),
+                Distribution::ZERO => {}
+            }
+
+            module.svp_prepare(&mut u_dft, 0, &u, 0);
+        }
+
+        // ct[i] = pk[i] * u + ei (+ m if col = i)
+        (0..cols).for_each(|i| {
+            let (mut ci_dft, scratch_2) = scratch_1.tmp_vec_znx_dft(module, 1, size_pk);
+            // ci_dft = DFT(u) * DFT(pk[i])
+            module.svp_apply(&mut ci_dft, 0, &u_dft, 0, &pk.data.data, i);
+
+            // ci_big = u * p[i]
+            let mut ci_big = module.vec_znx_idft_consume(ci_dft);
+
+            // ci_big = u * pk[i] + e
+            ci_big.add_normal(basek, 0, pk.k(), source_xe, sigma, sigma * SIX_SIGMA);
+
+            // ci_big = u * pk[i] + e + m (if col = i)
+            if let Some((pt, col)) = pt {
+                if col == i {
+                    module.vec_znx_big_add_small_inplace(&mut ci_big, 0, &pt.data, 0);
+                }
+            }
+
+            // ct[i] = norm(ci_big)
+            module.vec_znx_big_normalize(basek, &mut self.data, i, &ci_big, 0, scratch_2);
+        });
+    }
+}

@@ -0,0 +1,129 @@
+use backend::{
+    FFT64, MatZnxDftOps, MatZnxDftScratch, Module, Scratch, VecZnxBig, VecZnxBigOps, VecZnxDftAlloc, VecZnxDftOps, VecZnxScratch,
+};
+
+use crate::{FourierGLWECiphertext, GGSWCiphertext, GLWECiphertext, Infos};
+
+impl GLWECiphertext<Vec<u8>> {
+    pub fn external_product_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_in: usize,
+        k_ggsw: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        let res_dft: usize = FourierGLWECiphertext::bytes_of(module, basek, k_ggsw, rank);
+        let in_size: usize = k_in.div_ceil(basek).div_ceil(digits);
+        let out_size: usize = k_out.div_ceil(basek);
+        let ggsw_size: usize = k_ggsw.div_ceil(basek);
+        let vmp: usize = module.bytes_of_vec_znx_dft(rank + 1, in_size)
+            + module.vmp_apply_tmp_bytes(
+                out_size,
+                in_size,
+                in_size,  // rows
+                rank + 1, // cols in
+                rank + 1, // cols out
+                ggsw_size,
+            );
+        let normalize: usize = module.vec_znx_normalize_tmp_bytes();
+        res_dft + (vmp | normalize)
+    }
+
+    pub fn external_product_inplace_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_ggsw: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        Self::external_product_scratch_space(module, basek, k_out, k_out, k_ggsw, digits, rank)
+    }
+}
+
+impl<DataSelf: AsRef<[u8]> + AsMut<[u8]>> GLWECiphertext<DataSelf> {
+    pub fn external_product<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWECiphertext<DataLhs>,
+        rhs: &GGSWCiphertext<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        let basek: usize = self.basek();
+
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(rhs.rank(), lhs.rank());
+            assert_eq!(rhs.rank(), self.rank());
+            assert_eq!(self.basek(), basek);
+            assert_eq!(lhs.basek(), basek);
+            assert_eq!(rhs.n(), module.n());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(lhs.n(), module.n());
+            assert!(
+                scratch.available()
+                    >= GLWECiphertext::external_product_scratch_space(
+                        module,
+                        self.basek(),
+                        self.k(),
+                        lhs.k(),
+                        rhs.k(),
+                        rhs.digits(),
+                        rhs.rank(),
+                    )
+            );
+        }
+
+        let cols: usize = rhs.rank() + 1;
+        let digits: usize = rhs.digits();
+
+        let (mut res_dft, scratch1) = scratch.tmp_vec_znx_dft(module, cols, rhs.size()); // Todo optimise
+        let (mut a_dft, scratch2) = scratch1.tmp_vec_znx_dft(module, cols, (lhs.size() + digits - 1) / digits);
+
+        {
+            (0..digits).for_each(|di| {
+                // (lhs.size() + di) / digits = (a - (digit - di - 1) + digit - 1) / digits
+                a_dft.set_size((lhs.size() + di) / digits);
+
+                // Small optimization for digits > 2
+                // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
+                // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(digits-1) * B}.
+                // As such we can ignore the last digits-2 limbs safely of the sum of vmp products.
+                // It is possible to further ignore the last digits-1 limbs, but this introduce
+                // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
+                // noise is kept with respect to the ideal functionality.
+                res_dft.set_size(rhs.size() - ((digits - di) as isize - 2).max(0) as usize);
+
+                (0..cols).for_each(|col_i| {
+                    module.vec_znx_dft(digits, digits - 1 - di, &mut a_dft, col_i, &lhs.data, col_i);
+                });
+
+                if di == 0 {
+                    module.vmp_apply(&mut res_dft, &a_dft, &rhs.data, scratch2);
+                } else {
+                    module.vmp_apply_add(&mut res_dft, &a_dft, &rhs.data, di, scratch2);
+                }
+            });
+        }
+
+        let res_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume(res_dft);
+
+        (0..cols).for_each(|i| {
+            module.vec_znx_big_normalize(basek, &mut self.data, i, &res_big, i, scratch1);
+        });
+    }
+
+    pub fn external_product_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GGSWCiphertext<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        unsafe {
+            let self_ptr: *mut GLWECiphertext<DataSelf> = self as *mut GLWECiphertext<DataSelf>;
+            self.external_product(&module, &*self_ptr, rhs, scratch);
+        }
+    }
+}

@@ -0,0 +1,256 @@
+use backend::{
+    FFT64, MatZnxDftOps, MatZnxDftScratch, Module, Scratch, VecZnxBig, VecZnxBigOps, VecZnxBigScratch, VecZnxDftAlloc,
+    VecZnxDftOps, ZnxZero,
+};
+
+use crate::{FourierGLWECiphertext, GLWECiphertext, GLWESwitchingKey, Infos};
+
+impl GLWECiphertext<Vec<u8>> {
+    pub fn keyswitch_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_in: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> usize {
+        let res_dft: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank_out + 1);
+        let in_size: usize = k_in.div_ceil(basek).div_ceil(digits);
+        let out_size: usize = k_out.div_ceil(basek);
+        let ksk_size: usize = k_ksk.div_ceil(basek);
+        let ai_dft: usize = module.bytes_of_vec_znx_dft(rank_in, in_size);
+        let vmp: usize = module.vmp_apply_tmp_bytes(out_size, in_size, in_size, rank_in, rank_out + 1, ksk_size)
+            + module.bytes_of_vec_znx_dft(rank_in, in_size);
+        let normalize: usize = module.vec_znx_big_normalize_tmp_bytes();
+        return res_dft + ((ai_dft + vmp) | normalize);
+    }
+
+    pub fn keyswitch_from_fourier_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_in: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> usize {
+        Self::keyswitch_scratch_space(module, basek, k_out, k_in, k_ksk, digits, rank_in, rank_out)
+    }
+
+    pub fn keyswitch_inplace_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        Self::keyswitch_scratch_space(module, basek, k_out, k_out, k_ksk, digits, rank, rank)
+    }
+}
+
+impl<DataSelf: AsRef<[u8]> + AsMut<[u8]>> GLWECiphertext<DataSelf> {
+    pub fn keyswitch<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWECiphertext<DataLhs>,
+        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        Self::keyswitch_private::<_, _, 0>(self, 0, module, lhs, rhs, scratch);
+    }
+
+    pub fn keyswitch_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        unsafe {
+            let self_ptr: *mut GLWECiphertext<DataSelf> = self as *mut GLWECiphertext<DataSelf>;
+            self.keyswitch(&module, &*self_ptr, rhs, scratch);
+        }
+    }
+
+    pub(crate) fn keyswitch_private<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>, const OP: u8>(
+        &mut self,
+        apply_auto: i64,
+        module: &Module<FFT64>,
+        lhs: &GLWECiphertext<DataLhs>,
+        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        let basek: usize = self.basek();
+
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(
+                lhs.rank(),
+                rhs.rank_in(),
+                "lhs.rank(): {} != rhs.rank_in(): {}",
+                lhs.rank(),
+                rhs.rank_in()
+            );
+            assert_eq!(
+                self.rank(),
+                rhs.rank_out(),
+                "self.rank(): {} != rhs.rank_out(): {}",
+                self.rank(),
+                rhs.rank_out()
+            );
+            assert_eq!(self.basek(), basek);
+            assert_eq!(lhs.basek(), basek);
+            assert_eq!(rhs.n(), module.n());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(lhs.n(), module.n());
+            assert!(
+                scratch.available()
+                    >= GLWECiphertext::keyswitch_scratch_space(
+                        module,
+                        self.basek(),
+                        self.k(),
+                        lhs.k(),
+                        rhs.k(),
+                        rhs.digits(),
+                        rhs.rank_in(),
+                        rhs.rank_out(),
+                    )
+            );
+        }
+
+        let cols_in: usize = rhs.rank_in();
+        let cols_out: usize = rhs.rank_out() + 1;
+        let digits: usize = rhs.digits();
+
+        let (mut res_dft, scratch1) = scratch.tmp_vec_znx_dft(module, cols_out, rhs.size()); // Todo optimise
+        let (mut ai_dft, scratch2) = scratch1.tmp_vec_znx_dft(module, cols_in, (lhs.size() + digits - 1) / digits);
+        ai_dft.zero();
+        {
+            (0..digits).for_each(|di| {
+                ai_dft.set_size((lhs.size() + di) / digits);
+
+                // Small optimization for digits > 2
+                // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
+                // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(digits-1) * B}.
+                // As such we can ignore the last digits-2 limbs safely of the sum of vmp products.
+                // It is possible to further ignore the last digits-1 limbs, but this introduce
+                // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
+                // noise is kept with respect to the ideal functionality.
+                res_dft.set_size(rhs.size() - ((digits - di) as isize - 2).max(0) as usize);
+
+                (0..cols_in).for_each(|col_i| {
+                    module.vec_znx_dft(
+                        digits,
+                        digits - di - 1,
+                        &mut ai_dft,
+                        col_i,
+                        &lhs.data,
+                        col_i + 1,
+                    );
+                });
+
+                if di == 0 {
+                    module.vmp_apply(&mut res_dft, &ai_dft, &rhs.key.data, scratch2);
+                } else {
+                    module.vmp_apply_add(&mut res_dft, &ai_dft, &rhs.key.data, di, scratch2);
+                }
+            });
+        }
+
+        let mut res_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume(res_dft);
+
+        module.vec_znx_big_add_small_inplace(&mut res_big, 0, &lhs.data, 0);
+
+        (0..cols_out).for_each(|i| {
+            if apply_auto != 0 {
+                module.vec_znx_big_automorphism_inplace(apply_auto, &mut res_big, i);
+            }
+
+            match OP {
+                1 => module.vec_znx_big_add_small_inplace(&mut res_big, i, &lhs.data, i),
+                2 => module.vec_znx_big_sub_small_a_inplace(&mut res_big, i, &lhs.data, i),
+                3 => module.vec_znx_big_sub_small_b_inplace(&mut res_big, i, &lhs.data, i),
+                _ => {}
+            }
+            module.vec_znx_big_normalize(basek, &mut self.data, i, &res_big, i, scratch1);
+        });
+    }
+
+    pub(crate) fn keyswitch_from_fourier<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &FourierGLWECiphertext<DataLhs, FFT64>,
+        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        let basek: usize = self.basek();
+
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(lhs.rank(), rhs.rank_in());
+            assert_eq!(self.rank(), rhs.rank_out());
+            assert_eq!(self.basek(), basek);
+            assert_eq!(lhs.basek(), basek);
+            assert_eq!(rhs.n(), module.n());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(lhs.n(), module.n());
+            assert!(
+                scratch.available()
+                    >= GLWECiphertext::keyswitch_from_fourier_scratch_space(
+                        module,
+                        self.basek(),
+                        self.k(),
+                        lhs.k(),
+                        rhs.k(),
+                        rhs.digits(),
+                        rhs.rank_in(),
+                        rhs.rank_out(),
+                    )
+            );
+        }
+
+        let cols_in: usize = rhs.rank_in();
+        let cols_out: usize = rhs.rank_out() + 1;
+
+        // Buffer of the result of VMP in DFT
+        let (mut res_dft, scratch1) = scratch.tmp_vec_znx_dft(module, cols_out, rhs.size()); // Todo optimise
+
+        {
+            let digits = rhs.digits();
+
+            (0..digits).for_each(|di| {
+                // (lhs.size() + di) / digits = (a - (digit - di - 1) + digit - 1) / digits
+                let (mut ai_dft, scratch2) = scratch1.tmp_vec_znx_dft(module, cols_in, (lhs.size() + di) / digits);
+
+                (0..cols_in).for_each(|col_i| {
+                    module.vec_znx_dft_copy(
+                        digits,
+                        digits - 1 - di,
+                        &mut ai_dft,
+                        col_i,
+                        &lhs.data,
+                        col_i + 1,
+                    );
+                });
+
+                if di == 0 {
+                    module.vmp_apply(&mut res_dft, &ai_dft, &rhs.key.data, scratch2);
+                } else {
+                    module.vmp_apply_add(&mut res_dft, &ai_dft, &rhs.key.data, di, scratch2);
+                }
+            });
+        }
+
+        module.vec_znx_dft_add_inplace(&mut res_dft, 0, &lhs.data, 0);
+
+        // Switches result of VMP outside of DFT
+        let res_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume::<&mut [u8]>(res_dft);
+
+        (0..cols_out).for_each(|i| {
+            module.vec_znx_big_normalize(basek, &mut self.data, i, &res_big, i, scratch1);
+        });
+    }
+}

@@ -0,0 +1,23 @@
+pub mod automorphism;
+pub mod ciphertext;
+pub mod decryption;
+pub mod encryption;
+pub mod external_product;
+pub mod keyswitch;
+pub mod ops;
+pub mod packing;
+pub mod plaintext;
+pub mod public_key;
+pub mod secret;
+pub mod trace;
+
+pub use ciphertext::GLWECiphertext;
+pub(crate) use ciphertext::{GLWECiphertextToMut, GLWECiphertextToRef};
+pub use ops::GLWEOps;
+pub use packing::GLWEPacker;
+pub use plaintext::GLWEPlaintext;
+pub use public_key::GLWEPublicKey;
+pub use secret::GLWESecret;
+
+#[cfg(test)]
+mod test_fft64;

@@ -0,0 +1,75 @@
+use backend::{Backend, FFT64, Module, ScratchOwned, VecZnxDft};
+use sampling::source::Source;
+
+use crate::{FourierGLWECiphertext, FourierGLWESecret, Infos, dist::Distribution};
+
+pub struct GLWEPublicKey<D, B: Backend> {
+    pub(crate) data: FourierGLWECiphertext<D, B>,
+    pub(crate) dist: Distribution,
+}
+
+impl<B: Backend> GLWEPublicKey<Vec<u8>, B> {
+    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rank: usize) -> Self {
+        Self {
+            data: FourierGLWECiphertext::alloc(module, basek, k, rank),
+            dist: Distribution::NONE,
+        }
+    }
+
+    pub fn bytes_of(module: &Module<B>, basek: usize, k: usize, rank: usize) -> usize {
+        FourierGLWECiphertext::<Vec<u8>, B>::bytes_of(module, basek, k, rank)
+    }
+}
+
+impl<T, B: Backend> Infos for GLWEPublicKey<T, B> {
+    type Inner = VecZnxDft<T, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.data.data
+    }
+
+    fn basek(&self) -> usize {
+        self.data.basek
+    }
+
+    fn k(&self) -> usize {
+        self.data.k
+    }
+}
+
+impl<T, B: Backend> GLWEPublicKey<T, B> {
+    pub fn rank(&self) -> usize {
+        self.cols() - 1
+    }
+}
+
+impl<C: AsRef<[u8]> + AsMut<[u8]>> GLWEPublicKey<C, FFT64> {
+    pub fn generate_from_sk<S: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        sk: &FourierGLWESecret<S, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            match sk.dist {
+                Distribution::NONE => panic!("invalid sk: SecretDistribution::NONE"),
+                _ => {}
+            }
+        }
+
+        // Its ok to allocate scratch space here since pk is usually generated only once.
+        let mut scratch: ScratchOwned = ScratchOwned::new(FourierGLWECiphertext::encrypt_sk_scratch_space(
+            module,
+            self.basek(),
+            self.k(),
+            self.rank(),
+        ));
+
+        self.data
+            .encrypt_zero_sk(module, sk, source_xa, source_xe, sigma, scratch.borrow());
+        self.dist = sk.dist;
+    }
+}

@@ -0,0 +1,84 @@
+use backend::{Backend, Module, ScalarZnx, ScalarZnxAlloc, ZnxInfos, ZnxZero};
+use sampling::source::Source;
+
+use crate::dist::Distribution;
+
+pub struct GLWESecret<T> {
+    pub(crate) data: ScalarZnx<T>,
+    pub(crate) dist: Distribution,
+}
+
+impl GLWESecret<Vec<u8>> {
+    pub fn alloc<B: Backend>(module: &Module<B>, rank: usize) -> Self {
+        Self {
+            data: module.new_scalar_znx(rank),
+            dist: Distribution::NONE,
+        }
+    }
+
+    pub fn bytes_of<B: Backend>(module: &Module<B>, rank: usize) -> usize {
+        module.bytes_of_scalar_znx(rank)
+    }
+}
+
+impl<DataSelf> GLWESecret<DataSelf> {
+    pub fn n(&self) -> usize {
+        self.data.n()
+    }
+
+    pub fn log_n(&self) -> usize {
+        self.data.log_n()
+    }
+
+    pub fn rank(&self) -> usize {
+        self.data.cols()
+    }
+}
+
+impl<S: AsMut<[u8]> + AsRef<[u8]>> GLWESecret<S> {
+    pub fn fill_ternary_prob(&mut self, prob: f64, source: &mut Source) {
+        (0..self.rank()).for_each(|i| {
+            self.data.fill_ternary_prob(i, prob, source);
+        });
+        self.dist = Distribution::TernaryProb(prob);
+    }
+
+    pub fn fill_ternary_hw(&mut self, hw: usize, source: &mut Source) {
+        (0..self.rank()).for_each(|i| {
+            self.data.fill_ternary_hw(i, hw, source);
+        });
+        self.dist = Distribution::TernaryFixed(hw);
+    }
+
+    pub fn fill_binary_prob(&mut self, prob: f64, source: &mut Source) {
+        (0..self.rank()).for_each(|i| {
+            self.data.fill_binary_prob(i, prob, source);
+        });
+        self.dist = Distribution::BinaryProb(prob);
+    }
+
+    pub fn fill_binary_hw(&mut self, hw: usize, source: &mut Source) {
+        (0..self.rank()).for_each(|i| {
+            self.data.fill_binary_hw(i, hw, source);
+        });
+        self.dist = Distribution::BinaryFixed(hw);
+    }
+
+    pub fn fill_binary_block(&mut self, block_size: usize, source: &mut Source) {
+        (0..self.rank()).for_each(|i| {
+            self.data.fill_binary_block(i, block_size, source);
+        });
+        self.dist = Distribution::BinaryBlock(block_size);
+    }
+
+    pub fn fill_zero(&mut self) {
+        self.data.zero();
+        self.dist = Distribution::ZERO;
+    }
+
+    // pub(crate) fn prep_fourier(&mut self, module: &Module<FFT64>) {
+    // (0..self.rank()).for_each(|i| {
+    // module.svp_prepare(&mut self.data_fourier, i, &self.data, i);
+    // });
+    // }
+}

@@ -0,0 +1,223 @@
+use backend::{FFT64, FillUniform, Module, ScratchOwned, Stats, VecZnxOps};
+
+use sampling::source::Source;
+
+use crate::{
+    FourierGLWESecret, GLWEAutomorphismKey, GLWECiphertext, GLWEPlaintext, GLWESecret, Infos, noise::log2_std_noise_gglwe_product,
+};
+
+#[test]
+fn apply_inplace() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_ct: usize = 60;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_ct + basek * di;
+            println!("test automorphism_inplace digits: {} rank: {}", di, rank);
+            test_automorphism_inplace(log_n, basek, -5, k_ct, k_ksk, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn apply() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_in: usize = 60;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_in + basek * di;
+            let k_out: usize = k_ksk; // Better capture noise.
+            println!("test automorphism digits: {} rank: {}", di, rank);
+            test_automorphism(log_n, basek, -5, k_out, k_in, k_ksk, di, rank, 3.2);
+        })
+    });
+}
+
+fn test_automorphism(
+    log_n: usize,
+    basek: usize,
+    p: i64,
+    k_out: usize,
+    k_in: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_in.div_ceil(basek * digits);
+
+    let mut autokey: GLWEAutomorphismKey<Vec<u8>, FFT64> = GLWEAutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
+    let mut ct_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_in, rank);
+    let mut ct_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_out, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWEAutomorphismKey::encrypt_sk_scratch_space(&module, basek, autokey.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_out.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_in.k())
+            | GLWECiphertext::automorphism_scratch_space(
+                &module,
+                basek,
+                ct_out.k(),
+                ct_in.k(),
+                autokey.k(),
+                digits,
+                rank,
+            ),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
+
+    autokey.encrypt_sk(
+        &module,
+        p,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_in.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_out.automorphism(&module, &ct_in, &autokey, scratch.borrow());
+    ct_out.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
+    module.vec_znx_automorphism_inplace(p, &mut pt_want.data, 0);
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+    module.vec_znx_normalize_inplace(basek, &mut pt_have.data, 0, scratch.borrow());
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+
+    println!("{}", noise_have);
+
+    let noise_want: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank as f64,
+        k_in,
+        k_ksk,
+    );
+
+    assert!(
+        noise_have <= noise_want + 1.0,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_automorphism_inplace(
+    log_n: usize,
+    basek: usize,
+    p: i64,
+    k_ct: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_ct.div_ceil(basek * digits);
+
+    let mut autokey: GLWEAutomorphismKey<Vec<u8>, FFT64> = GLWEAutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWEAutomorphismKey::encrypt_sk_scratch_space(&module, basek, autokey.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
+            | GLWECiphertext::automorphism_inplace_scratch_space(&module, basek, ct.k(), autokey.k(), digits, rank),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
+
+    autokey.encrypt_sk(
+        &module,
+        p,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct.automorphism_inplace(&module, &autokey, scratch.borrow());
+    ct.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
+    module.vec_znx_automorphism_inplace(p, &mut pt_want.data, 0);
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+    module.vec_znx_normalize_inplace(basek, &mut pt_have.data, 0, scratch.borrow());
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+    let noise_want: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank as f64,
+        k_ct,
+        k_ksk,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}

@@ -0,0 +1,183 @@
+use backend::{Decoding, Encoding, FFT64, Module, ScratchOwned, Stats, VecZnxOps, ZnxZero};
+use itertools::izip;
+use sampling::source::Source;
+
+use crate::{FourierGLWECiphertext, FourierGLWESecret, GLWECiphertext, GLWEPlaintext, GLWEPublicKey, GLWESecret, Infos};
+
+#[test]
+fn encrypt_sk() {
+    let log_n: usize = 8;
+    (1..4).for_each(|rank| {
+        println!("test encrypt_sk rank: {}", rank);
+        test_encrypt_sk(log_n, 8, 54, 30, 3.2, rank);
+    });
+}
+
+#[test]
+fn encrypt_zero_sk() {
+    let log_n: usize = 8;
+    (1..4).for_each(|rank| {
+        println!("test encrypt_zero_sk rank: {}", rank);
+        test_encrypt_zero_sk(log_n, 8, 64, 3.2, rank);
+    });
+}
+
+#[test]
+fn encrypt_pk() {
+    let log_n: usize = 8;
+    (1..4).for_each(|rank| {
+        println!("test encrypt_pk rank: {}", rank);
+        test_encrypt_pk(log_n, 8, 64, 64, 3.2, rank)
+    });
+}
+
+fn test_encrypt_sk(log_n: usize, basek: usize, k_ct: usize, k_pt: usize, sigma: f64, rank: usize) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_pt);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k()),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
+
+    let mut data_want: Vec<i64> = vec![0i64; module.n()];
+
+    data_want
+        .iter_mut()
+        .for_each(|x| *x = source_xa.next_i64() & 0xFF);
+
+    pt.data.encode_vec_i64(0, basek, k_pt, &data_want, 10);
+
+    ct.encrypt_sk(
+        &module,
+        &pt,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    pt.data.zero();
+
+    ct.decrypt(&module, &mut pt, &sk_dft, scratch.borrow());
+
+    let mut data_have: Vec<i64> = vec![0i64; module.n()];
+
+    pt.data
+        .decode_vec_i64(0, basek, pt.size() * basek, &mut data_have);
+
+    // TODO: properly assert the decryption noise through std(dec(ct) - pt)
+    let scale: f64 = (1 << (pt.size() * basek - k_pt)) as f64;
+    izip!(data_want.iter(), data_have.iter()).for_each(|(a, b)| {
+        let b_scaled = (*b as f64) / scale;
+        assert!(
+            (*a as f64 - b_scaled).abs() < 0.1,
+            "{} {}",
+            *a as f64,
+            b_scaled
+        )
+    });
+}
+
+fn test_encrypt_zero_sk(log_n: usize, basek: usize, k_ct: usize, sigma: f64, rank: usize) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([1u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
+
+    let mut ct_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ct)
+            | FourierGLWECiphertext::encrypt_sk_scratch_space(&module, basek, k_ct, rank),
+    );
+
+    ct_dft.encrypt_zero_sk(
+        &module,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+    ct_dft.decrypt(&module, &mut pt, &sk_dft, scratch.borrow());
+
+    assert!((sigma - pt.data.std(0, basek) * (k_ct as f64).exp2()) <= 0.2);
+}
+
+fn test_encrypt_pk(log_n: usize, basek: usize, k_ct: usize, k_pk: usize, sigma: f64, rank: usize) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+    let mut source_xu: Source = Source::new([0u8; 32]);
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
+
+    let mut pk: GLWEPublicKey<Vec<u8>, FFT64> = GLWEPublicKey::alloc(&module, basek, k_pk, rank);
+    pk.generate_from_sk(&module, &sk_dft, &mut source_xa, &mut source_xe, sigma);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k())
+            | GLWECiphertext::encrypt_pk_scratch_space(&module, basek, pk.k()),
+    );
+
+    let mut data_want: Vec<i64> = vec![0i64; module.n()];
+
+    data_want
+        .iter_mut()
+        .for_each(|x| *x = source_xa.next_i64() & 0);
+
+    pt_want.data.encode_vec_i64(0, basek, k_ct, &data_want, 10);
+
+    ct.encrypt_pk(
+        &module,
+        &pt_want,
+        &pk,
+        &mut source_xu,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    ct.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
+
+    module.vec_znx_sub_ab_inplace(&mut pt_want.data, 0, &pt_have.data, 0);
+
+    let noise_have: f64 = pt_want.data.std(0, basek).log2();
+    let noise_want: f64 = ((((rank as f64) + 1.0) * module.n() as f64 * 0.5 * sigma * sigma).sqrt()).log2() - (k_ct as f64);
+
+    assert!(
+        (noise_have - noise_want).abs() < 0.2,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}

@@ -0,0 +1,244 @@
+use backend::{FFT64, FillUniform, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned, Stats, VecZnxOps, ZnxViewMut};
+use sampling::source::Source;
+
+use crate::{FourierGLWESecret, GGSWCiphertext, GLWECiphertext, GLWEPlaintext, GLWESecret, Infos, noise::noise_ggsw_product};
+
+#[test]
+fn apply() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_in: usize = 45;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ggsw: usize = k_in + basek * di;
+            let k_out: usize = k_ggsw; // Better capture noise
+            println!("test external_product digits: {} rank: {}", di, rank);
+            test_external_product(log_n, basek, k_out, k_in, k_ggsw, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn apply_inplace() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_ct: usize = 60;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ggsw: usize = k_ct + basek * di;
+            println!("test external_product digits: {} rank: {}", di, rank);
+            test_external_product_inplace(log_n, basek, k_ct, k_ggsw, di, rank, 3.2);
+        });
+    });
+}
+
+fn test_external_product(
+    log_n: usize,
+    basek: usize,
+    k_out: usize,
+    k_in: usize,
+    k_ggsw: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_in.div_ceil(basek * digits);
+
+    let mut ct_ggsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k_ggsw, rows, digits, rank);
+    let mut ct_glwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_in, rank);
+    let mut ct_glwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_out, rank);
+    let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    // Random input plaintext
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    pt_want.data.at_mut(0, 0)[1] = 1;
+
+    let k: usize = 1;
+
+    pt_rgsw.raw_mut()[k] = 1; // X^{k}
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, ct_ggsw.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_glwe_out.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_glwe_in.k())
+            | GLWECiphertext::external_product_scratch_space(
+                &module,
+                basek,
+                ct_glwe_out.k(),
+                ct_glwe_in.k(),
+                ct_ggsw.k(),
+                digits,
+                rank,
+            ),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
+
+    ct_ggsw.encrypt_sk(
+        &module,
+        &pt_rgsw,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe_in.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe_out.external_product(&module, &ct_glwe_in, &ct_ggsw, scratch.borrow());
+
+    ct_glwe_out.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
+
+    module.vec_znx_rotate_inplace(k as i64, &mut pt_want.data, 0);
+
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+
+    let var_gct_err_lhs: f64 = sigma * sigma;
+    let var_gct_err_rhs: f64 = 0f64;
+
+    let var_msg: f64 = 1f64 / module.n() as f64; // X^{k}
+    let var_a0_err: f64 = sigma * sigma;
+    let var_a1_err: f64 = 1f64 / 12f64;
+
+    let noise_want: f64 = noise_ggsw_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        var_msg,
+        var_a0_err,
+        var_a1_err,
+        var_gct_err_lhs,
+        var_gct_err_rhs,
+        rank as f64,
+        k_in,
+        k_ggsw,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_external_product_inplace(log_n: usize, basek: usize, k_ct: usize, k_ggsw: usize, digits: usize, rank: usize, sigma: f64) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let rows: usize = k_ct.div_ceil(basek * digits);
+
+    let mut ct_ggsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k_ggsw, rows, digits, rank);
+    let mut ct_glwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    // Random input plaintext
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    pt_want.data.at_mut(0, 0)[1] = 1;
+
+    let k: usize = 1;
+
+    pt_rgsw.raw_mut()[k] = 1; // X^{k}
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, ct_ggsw.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_glwe.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_glwe.k())
+            | GLWECiphertext::external_product_inplace_scratch_space(&module, basek, ct_glwe.k(), ct_ggsw.k(), digits, rank),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
+
+    ct_ggsw.encrypt_sk(
+        &module,
+        &pt_rgsw,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.external_product_inplace(&module, &ct_ggsw, scratch.borrow());
+
+    ct_glwe.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
+
+    module.vec_znx_rotate_inplace(k as i64, &mut pt_want.data, 0);
+
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+
+    let var_gct_err_lhs: f64 = sigma * sigma;
+    let var_gct_err_rhs: f64 = 0f64;
+
+    let var_msg: f64 = 1f64 / module.n() as f64; // X^{k}
+    let var_a0_err: f64 = sigma * sigma;
+    let var_a1_err: f64 = 1f64 / 12f64;
+
+    let noise_want: f64 = noise_ggsw_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        var_msg,
+        var_a0_err,
+        var_a1_err,
+        var_gct_err_lhs,
+        var_gct_err_rhs,
+        rank as f64,
+        k_ct,
+        k_ggsw,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}

@@ -0,0 +1,226 @@
+use backend::{FFT64, FillUniform, Module, ScratchOwned, Stats, VecZnxOps};
+use sampling::source::Source;
+
+use crate::{
+    FourierGLWESecret, GLWECiphertext, GLWEPlaintext, GLWESecret, GLWESwitchingKey, Infos, noise::log2_std_noise_gglwe_product,
+};
+
+#[test]
+fn apply() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_in: usize = 45;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank_in| {
+        (1..4).for_each(|rank_out| {
+            (1..digits + 1).for_each(|di| {
+                let k_ksk: usize = k_in + basek * di;
+                let k_out: usize = k_ksk; // better capture noise
+                println!(
+                    "test keyswitch digits: {} rank_in: {} rank_out: {}",
+                    di, rank_in, rank_out
+                );
+                test_keyswitch(log_n, basek, k_out, k_in, k_ksk, di, rank_in, rank_out, 3.2);
+            })
+        });
+    });
+}
+
+#[test]
+fn apply_inplace() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_ct: usize = 45;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_ct + basek * di;
+            println!("test keyswitch_inplace digits: {} rank: {}", di, rank);
+            test_keyswitch_inplace(log_n, basek, k_ct, k_ksk, di, rank, 3.2);
+        });
+    });
+}
+
+fn test_keyswitch(
+    log_n: usize,
+    basek: usize,
+    k_out: usize,
+    k_in: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank_in: usize,
+    rank_out: usize,
+    sigma: f64,
+) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_in.div_ceil(basek * digits);
+
+    let mut ksk: GLWESwitchingKey<Vec<u8>, FFT64> =
+        GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, digits, rank_in, rank_out);
+    let mut ct_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_in, rank_in);
+    let mut ct_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_out, rank_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ksk.k(), rank_in, rank_out)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_out.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_in.k())
+            | GLWECiphertext::keyswitch_scratch_space(
+                &module,
+                basek,
+                ct_out.k(),
+                ct_in.k(),
+                ksk.k(),
+                digits,
+                rank_in,
+                rank_out,
+            ),
+    );
+
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_in);
+    sk_in.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_in_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_in);
+
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_out);
+    sk_out.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
+
+    ksk.encrypt_sk(
+        &module,
+        &sk_in,
+        &sk_out_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_in.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_in_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_out.keyswitch(&module, &ct_in, &ksk, scratch.borrow());
+    ct_out.decrypt(&module, &mut pt_have, &sk_out_dft, scratch.borrow());
+
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+    let noise_want: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank_in as f64,
+        k_in,
+        k_ksk,
+    );
+
+    println!("{} vs. {}", noise_have, noise_want);
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_keyswitch_inplace(log_n: usize, basek: usize, k_ct: usize, k_ksk: usize, digits: usize, rank: usize, sigma: f64) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_ct.div_ceil(basek * digits);
+
+    let mut ct_grlwe: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, digits, rank, rank);
+    let mut ct_glwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ct_grlwe.k(), rank, rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_glwe.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_glwe.k())
+            | GLWECiphertext::keyswitch_inplace_scratch_space(&module, basek, ct_glwe.k(), ct_grlwe.k(), digits, rank),
+    );
+
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_in.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_in_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_in);
+
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_out.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
+
+    ct_grlwe.encrypt_sk(
+        &module,
+        &sk_in,
+        &sk_out_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_in_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.keyswitch_inplace(&module, &ct_grlwe, scratch.borrow());
+
+    ct_glwe.decrypt(&module, &mut pt_have, &sk_out_dft, scratch.borrow());
+
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+    let noise_want: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank as f64,
+        k_ct,
+        k_ksk,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}

@@ -0,0 +1,6 @@
+pub mod automorphism;
+pub mod encryption;
+pub mod external_product;
+pub mod keyswitch;
+pub mod packing;
+pub mod trace;

@@ -1,883 +0,0 @@
-use backend::{
-    AddNormal, Backend, FFT64, FillUniform, MatZnxDftOps, MatZnxDftScratch, Module, ScalarZnxAlloc, ScalarZnxDftAlloc,
-    ScalarZnxDftOps, Scratch, VecZnx, VecZnxAlloc, VecZnxBig, VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDftAlloc,
-    VecZnxDftOps, VecZnxOps, VecZnxToMut, VecZnxToRef, ZnxZero,
-};
-use sampling::source::Source;
-
-use crate::{
-    AutomorphismKey, GGSWCiphertext, GLWECiphertextFourier, GLWEOps, GLWEPlaintext, GLWEPublicKey, GLWESecret, GLWESwitchingKey,
-    Infos, SIX_SIGMA, SecretDistribution, SetMetaData,
-};
-
-pub struct GLWECiphertext<C> {
-    pub data: VecZnx<C>,
-    pub basek: usize,
-    pub k: usize,
-}
-
-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, k.div_ceil(basek)),
-            basek,
-            k,
-        }
-    }
-
-    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
-        module.bytes_of_vec_znx(rank + 1, k.div_ceil(basek))
-    }
-}
-
-impl<T> Infos for GLWECiphertext<T> {
-    type Inner = VecZnx<T>;
-
-    fn inner(&self) -> &Self::Inner {
-        &self.data
-    }
-
-    fn basek(&self) -> usize {
-        self.basek
-    }
-
-    fn k(&self) -> usize {
-        self.k
-    }
-}
-
-impl<T> GLWECiphertext<T> {
-    pub fn rank(&self) -> usize {
-        self.cols() - 1
-    }
-}
-
-impl<C: AsRef<[u8]>> GLWECiphertext<C> {
-    #[allow(dead_code)]
-    pub(crate) fn dft<R: AsMut<[u8]> + AsRef<[u8]>>(&self, module: &Module<FFT64>, res: &mut GLWECiphertextFourier<R, FFT64>) {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(self.rank(), res.rank());
-            assert_eq!(self.basek(), res.basek())
-        }
-
-        (0..self.rank() + 1).for_each(|i| {
-            module.vec_znx_dft(1, 0, &mut res.data, i, &self.data, i);
-        })
-    }
-}
-
-impl GLWECiphertext<Vec<u8>> {
-    pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
-        let size: usize = k.div_ceil(basek);
-        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 = k.div_ceil(basek);
-        ((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 = k.div_ceil(basek);
-        (module.vec_znx_big_normalize_tmp_bytes() | module.bytes_of_vec_znx_dft(1, size)) + module.bytes_of_vec_znx_big(1, size)
-    }
-
-    pub fn keyswitch_scratch_space(
-        module: &Module<FFT64>,
-        basek: usize,
-        k_out: usize,
-        k_in: usize,
-        k_ksk: usize,
-        digits: usize,
-        rank_in: usize,
-        rank_out: usize,
-    ) -> usize {
-        let res_dft: usize = GLWECiphertextFourier::bytes_of(module, basek, k_out, rank_out + 1);
-        let in_size: usize = k_in.div_ceil(basek).div_ceil(digits);
-        let out_size: usize = k_out.div_ceil(basek);
-        let ksk_size: usize = k_ksk.div_ceil(basek);
-        let ai_dft: usize = module.bytes_of_vec_znx_dft(rank_in, in_size);
-        let vmp: usize = module.vmp_apply_tmp_bytes(out_size, in_size, in_size, rank_in, rank_out + 1, ksk_size)
-            + module.bytes_of_vec_znx_dft(rank_in, in_size);
-        let normalize: usize = module.vec_znx_big_normalize_tmp_bytes();
-        return res_dft + ((ai_dft + vmp) | normalize);
-    }
-
-    pub fn keyswitch_from_fourier_scratch_space(
-        module: &Module<FFT64>,
-        basek: usize,
-        k_out: usize,
-        k_in: usize,
-        k_ksk: usize,
-        digits: usize,
-        rank_in: usize,
-        rank_out: usize,
-    ) -> usize {
-        Self::keyswitch_scratch_space(module, basek, k_out, k_in, k_ksk, digits, rank_in, rank_out)
-    }
-
-    pub fn keyswitch_inplace_scratch_space(
-        module: &Module<FFT64>,
-        basek: usize,
-        k_out: usize,
-        k_ksk: usize,
-        digits: usize,
-        rank: usize,
-    ) -> usize {
-        Self::keyswitch_scratch_space(module, basek, k_out, k_out, k_ksk, digits, rank, rank)
-    }
-
-    pub fn automorphism_scratch_space(
-        module: &Module<FFT64>,
-        basek: usize,
-        k_out: usize,
-        k_in: usize,
-        k_ksk: usize,
-        digits: usize,
-        rank: usize,
-    ) -> usize {
-        Self::keyswitch_scratch_space(module, basek, k_out, k_in, k_ksk, digits, rank, rank)
-    }
-
-    pub fn automorphism_inplace_scratch_space(
-        module: &Module<FFT64>,
-        basek: usize,
-        k_out: usize,
-        k_ksk: usize,
-        digits: usize,
-        rank: usize,
-    ) -> usize {
-        Self::keyswitch_inplace_scratch_space(module, basek, k_out, k_ksk, digits, rank)
-    }
-
-    pub fn external_product_scratch_space(
-        module: &Module<FFT64>,
-        basek: usize,
-        k_out: usize,
-        k_in: usize,
-        ggsw_k: usize,
-        digits: usize,
-        rank: usize,
-    ) -> usize {
-        let res_dft: usize = GLWECiphertextFourier::bytes_of(module, basek, k_out, rank);
-        let in_size: usize = k_in.div_ceil(basek).div_ceil(digits);
-        let out_size: usize = k_out.div_ceil(basek);
-        let ggsw_size: usize = ggsw_k.div_ceil(basek);
-        let vmp: usize = module.bytes_of_vec_znx_dft(rank + 1, in_size)
-            + module.vmp_apply_tmp_bytes(
-                out_size,
-                in_size,
-                in_size,  // rows
-                rank + 1, // cols in
-                rank + 1, // cols out
-                ggsw_size,
-            );
-        let normalize: usize = module.vec_znx_big_normalize_tmp_bytes();
-        res_dft + (vmp | normalize)
-    }
-
-    pub fn external_product_inplace_scratch_space(
-        module: &Module<FFT64>,
-        basek: usize,
-        k_out: usize,
-        ggsw_k: usize,
-        digits: usize,
-        rank: usize,
-    ) -> usize {
-        Self::external_product_scratch_space(module, basek, k_out, k_out, ggsw_k, digits, rank)
-    }
-}
-
-impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> SetMetaData for GLWECiphertext<DataSelf> {
-    fn set_k(&mut self, k: usize) {
-        self.k = k
-    }
-
-    fn set_basek(&mut self, basek: usize) {
-        self.basek = basek
-    }
-}
-
-impl<DataSelf: AsRef<[u8]> + AsMut<[u8]>> GLWECiphertext<DataSelf> {
-    pub fn encrypt_sk<DataPt: AsRef<[u8]>, DataSk: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        pt: &GLWEPlaintext<DataPt>,
-        sk: &GLWESecret<DataSk, FFT64>,
-        source_xa: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-        scratch: &mut Scratch,
-    ) {
-        self.encrypt_sk_private(
-            module,
-            Some((pt, 0)),
-            sk,
-            source_xa,
-            source_xe,
-            sigma,
-            scratch,
-        );
-    }
-
-    pub fn encrypt_zero_sk<DataSk: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        sk: &GLWESecret<DataSk, FFT64>,
-        source_xa: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-        scratch: &mut Scratch,
-    ) {
-        self.encrypt_sk_private(
-            module,
-            None::<(&GLWEPlaintext<Vec<u8>>, usize)>,
-            sk,
-            source_xa,
-            source_xe,
-            sigma,
-            scratch,
-        );
-    }
-
-    pub fn encrypt_pk<DataPt: AsRef<[u8]>, DataPk: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        pt: &GLWEPlaintext<DataPt>,
-        pk: &GLWEPublicKey<DataPk, FFT64>,
-        source_xu: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-        scratch: &mut Scratch,
-    ) {
-        self.encrypt_pk_private(
-            module,
-            Some((pt, 0)),
-            pk,
-            source_xu,
-            source_xe,
-            sigma,
-            scratch,
-        );
-    }
-
-    pub fn encrypt_zero_pk<DataPk: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        pk: &GLWEPublicKey<DataPk, FFT64>,
-        source_xu: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-        scratch: &mut Scratch,
-    ) {
-        self.encrypt_pk_private(
-            module,
-            None::<(&GLWEPlaintext<Vec<u8>>, usize)>,
-            pk,
-            source_xu,
-            source_xe,
-            sigma,
-            scratch,
-        );
-    }
-
-    pub fn automorphism<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        lhs: &GLWECiphertext<DataLhs>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        self.keyswitch(module, lhs, &rhs.key, scratch);
-        (0..self.rank() + 1).for_each(|i| {
-            module.vec_znx_automorphism_inplace(rhs.p(), &mut self.data, i);
-        })
-    }
-
-    pub fn automorphism_inplace<DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        self.keyswitch_inplace(module, &rhs.key, scratch);
-        (0..self.rank() + 1).for_each(|i| {
-            module.vec_znx_automorphism_inplace(rhs.p(), &mut self.data, i);
-        })
-    }
-
-    pub fn automorphism_add<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        lhs: &GLWECiphertext<DataLhs>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        Self::keyswitch_private::<_, _, 1>(self, rhs.p(), module, lhs, &rhs.key, scratch);
-    }
-
-    pub fn automorphism_add_inplace<DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        unsafe {
-            let self_ptr: *mut GLWECiphertext<DataSelf> = self as *mut GLWECiphertext<DataSelf>;
-            Self::keyswitch_private::<_, _, 1>(self, rhs.p(), module, &*self_ptr, &rhs.key, scratch);
-        }
-    }
-
-    pub fn automorphism_sub_ab<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        lhs: &GLWECiphertext<DataLhs>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        Self::keyswitch_private::<_, _, 2>(self, rhs.p(), module, lhs, &rhs.key, scratch);
-    }
-
-    pub fn automorphism_sub_ab_inplace<DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        unsafe {
-            let self_ptr: *mut GLWECiphertext<DataSelf> = self as *mut GLWECiphertext<DataSelf>;
-            Self::keyswitch_private::<_, _, 2>(self, rhs.p(), module, &*self_ptr, &rhs.key, scratch);
-        }
-    }
-
-    pub fn automorphism_sub_ba<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        lhs: &GLWECiphertext<DataLhs>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        Self::keyswitch_private::<_, _, 3>(self, rhs.p(), module, lhs, &rhs.key, scratch);
-    }
-
-    pub fn automorphism_sub_ba_inplace<DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        unsafe {
-            let self_ptr: *mut GLWECiphertext<DataSelf> = self as *mut GLWECiphertext<DataSelf>;
-            Self::keyswitch_private::<_, _, 3>(self, rhs.p(), module, &*self_ptr, &rhs.key, scratch);
-        }
-    }
-
-    pub(crate) fn keyswitch_from_fourier<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        lhs: &GLWECiphertextFourier<DataLhs, FFT64>,
-        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        let basek: usize = self.basek();
-
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(lhs.rank(), rhs.rank_in());
-            assert_eq!(self.rank(), rhs.rank_out());
-            assert_eq!(self.basek(), basek);
-            assert_eq!(lhs.basek(), basek);
-            assert_eq!(rhs.n(), module.n());
-            assert_eq!(self.n(), module.n());
-            assert_eq!(lhs.n(), module.n());
-            assert!(
-                scratch.available()
-                    >= GLWECiphertext::keyswitch_from_fourier_scratch_space(
-                        module,
-                        self.basek(),
-                        self.k(),
-                        lhs.k(),
-                        rhs.k(),
-                        rhs.digits(),
-                        rhs.rank_in(),
-                        rhs.rank_out(),
-                    )
-            );
-        }
-
-        let cols_in: usize = rhs.rank_in();
-        let cols_out: usize = rhs.rank_out() + 1;
-
-        // Buffer of the result of VMP in DFT
-        let (mut res_dft, scratch1) = scratch.tmp_vec_znx_dft(module, cols_out, rhs.size()); // Todo optimise
-
-        {
-            let digits = rhs.digits();
-
-            (0..digits).for_each(|di| {
-                // (lhs.size() + di) / digits = (a - (digit - di - 1) + digit - 1) / digits
-                let (mut ai_dft, scratch2) = scratch1.tmp_vec_znx_dft(module, cols_in, (lhs.size() + di) / digits);
-
-                (0..cols_in).for_each(|col_i| {
-                    module.vec_znx_dft_copy(
-                        digits,
-                        digits - 1 - di,
-                        &mut ai_dft,
-                        col_i,
-                        &lhs.data,
-                        col_i + 1,
-                    );
-                });
-
-                if di == 0 {
-                    module.vmp_apply(&mut res_dft, &ai_dft, &rhs.0.data, scratch2);
-                } else {
-                    module.vmp_apply_add(&mut res_dft, &ai_dft, &rhs.0.data, di, scratch2);
-                }
-            });
-        }
-
-        module.vec_znx_dft_add_inplace(&mut res_dft, 0, &lhs.data, 0);
-
-        // Switches result of VMP outside of DFT
-        let res_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume::<&mut [u8]>(res_dft);
-
-        (0..cols_out).for_each(|i| {
-            module.vec_znx_big_normalize(basek, &mut self.data, i, &res_big, i, scratch1);
-        });
-    }
-
-    pub fn keyswitch<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        lhs: &GLWECiphertext<DataLhs>,
-        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        Self::keyswitch_private::<_, _, 0>(self, 0, module, lhs, rhs, scratch);
-    }
-
-    pub(crate) fn keyswitch_private<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>, const OP: u8>(
-        &mut self,
-        apply_auto: i64,
-        module: &Module<FFT64>,
-        lhs: &GLWECiphertext<DataLhs>,
-        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        let basek: usize = self.basek();
-
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(lhs.rank(), rhs.rank_in());
-            assert_eq!(self.rank(), rhs.rank_out());
-            assert_eq!(self.basek(), basek);
-            assert_eq!(lhs.basek(), basek);
-            assert_eq!(rhs.n(), module.n());
-            assert_eq!(self.n(), module.n());
-            assert_eq!(lhs.n(), module.n());
-            assert!(
-                scratch.available()
-                    >= GLWECiphertext::keyswitch_scratch_space(
-                        module,
-                        self.basek(),
-                        self.k(),
-                        lhs.k(),
-                        rhs.k(),
-                        rhs.digits(),
-                        rhs.rank_in(),
-                        rhs.rank_out(),
-                    )
-            );
-        }
-
-        let cols_in: usize = rhs.rank_in();
-        let cols_out: usize = rhs.rank_out() + 1;
-        let digits: usize = rhs.digits();
-
-        let (mut res_dft, scratch1) = scratch.tmp_vec_znx_dft(module, cols_out, rhs.size()); // Todo optimise
-        let (mut ai_dft, scratch2) = scratch1.tmp_vec_znx_dft(module, cols_in, (lhs.size() + digits - 1) / digits);
-        ai_dft.zero();
-        {
-            (0..digits).for_each(|di| {
-                ai_dft.set_size((lhs.size() + di) / digits);
-
-                // Small optimization for digits > 2
-                // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
-                // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(digits-1) * B}.
-                // As such we can ignore the last digits-2 limbs safely of the sum of vmp products.
-                // It is possible to further ignore the last digits-1 limbs, but this introduce
-                // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
-                // noise is kept with respect to the ideal functionality.
-                res_dft.set_size(rhs.size() - ((digits - di) as isize - 2).max(0) as usize);
-
-                (0..cols_in).for_each(|col_i| {
-                    module.vec_znx_dft(
-                        digits,
-                        digits - di - 1,
-                        &mut ai_dft,
-                        col_i,
-                        &lhs.data,
-                        col_i + 1,
-                    );
-                });
-
-                if di == 0 {
-                    module.vmp_apply(&mut res_dft, &ai_dft, &rhs.0.data, scratch2);
-                } else {
-                    module.vmp_apply_add(&mut res_dft, &ai_dft, &rhs.0.data, di, scratch2);
-                }
-            });
-        }
-
-        let mut res_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume(res_dft);
-
-        module.vec_znx_big_add_small_inplace(&mut res_big, 0, &lhs.data, 0);
-
-        (0..cols_out).for_each(|i| {
-            if apply_auto != 0 {
-                module.vec_znx_big_automorphism_inplace(apply_auto, &mut res_big, i);
-            }
-
-            match OP {
-                1 => module.vec_znx_big_add_small_inplace(&mut res_big, i, &lhs.data, i),
-                2 => module.vec_znx_big_sub_small_a_inplace(&mut res_big, i, &lhs.data, i),
-                3 => module.vec_znx_big_sub_small_b_inplace(&mut res_big, i, &lhs.data, i),
-                _ => {}
-            }
-            module.vec_znx_big_normalize(basek, &mut self.data, i, &res_big, i, scratch1);
-        });
-    }
-
-    pub fn keyswitch_inplace<DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        unsafe {
-            let self_ptr: *mut GLWECiphertext<DataSelf> = self as *mut GLWECiphertext<DataSelf>;
-            self.keyswitch(&module, &*self_ptr, rhs, scratch);
-        }
-    }
-
-    pub fn external_product<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        lhs: &GLWECiphertext<DataLhs>,
-        rhs: &GGSWCiphertext<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        let basek: usize = self.basek();
-
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(rhs.rank(), lhs.rank());
-            assert_eq!(rhs.rank(), self.rank());
-            assert_eq!(self.basek(), basek);
-            assert_eq!(lhs.basek(), basek);
-            assert_eq!(rhs.n(), module.n());
-            assert_eq!(self.n(), module.n());
-            assert_eq!(lhs.n(), module.n());
-            assert!(
-                scratch.available()
-                    >= GLWECiphertext::external_product_scratch_space(
-                        module,
-                        self.basek(),
-                        self.k(),
-                        lhs.k(),
-                        rhs.k(),
-                        rhs.digits(),
-                        rhs.rank(),
-                    )
-            );
-        }
-
-        let cols: usize = rhs.rank() + 1;
-        let digits: usize = rhs.digits();
-
-        let (mut res_dft, scratch1) = scratch.tmp_vec_znx_dft(module, cols, rhs.size()); // Todo optimise
-        let (mut a_dft, scratch2) = scratch1.tmp_vec_znx_dft(module, cols, (lhs.size() + digits - 1) / digits);
-
-        {
-            (0..digits).for_each(|di| {
-                // (lhs.size() + di) / digits = (a - (digit - di - 1) + digit - 1) / digits
-                a_dft.set_size((lhs.size() + di) / digits);
-
-                // Small optimization for digits > 2
-                // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
-                // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(digits-1) * B}.
-                // As such we can ignore the last digits-2 limbs safely of the sum of vmp products.
-                // It is possible to further ignore the last digits-1 limbs, but this introduce
-                // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
-                // noise is kept with respect to the ideal functionality.
-                res_dft.set_size(rhs.size() - ((digits - di) as isize - 2).max(0) as usize);
-
-                (0..cols).for_each(|col_i| {
-                    module.vec_znx_dft(digits, digits - 1 - di, &mut a_dft, col_i, &lhs.data, col_i);
-                });
-
-                if di == 0 {
-                    module.vmp_apply(&mut res_dft, &a_dft, &rhs.data, scratch2);
-                } else {
-                    module.vmp_apply_add(&mut res_dft, &a_dft, &rhs.data, di, scratch2);
-                }
-            });
-        }
-
-        let res_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume(res_dft);
-
-        (0..cols).for_each(|i| {
-            module.vec_znx_big_normalize(basek, &mut self.data, i, &res_big, i, scratch1);
-        });
-    }
-
-    pub fn external_product_inplace<DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        rhs: &GGSWCiphertext<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        unsafe {
-            let self_ptr: *mut GLWECiphertext<DataSelf> = self as *mut GLWECiphertext<DataSelf>;
-            self.external_product(&module, &*self_ptr, rhs, scratch);
-        }
-    }
-
-    pub(crate) fn encrypt_sk_private<DataPt: AsRef<[u8]>, DataSk: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        pt: Option<(&GLWEPlaintext<DataPt>, usize)>,
-        sk: &GLWESecret<DataSk, FFT64>,
-        source_xa: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-        scratch: &mut Scratch,
-    ) {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(self.rank(), sk.rank());
-            assert_eq!(sk.n(), module.n());
-            assert_eq!(self.n(), module.n());
-            if let Some((pt, col)) = pt {
-                assert_eq!(pt.n(), module.n());
-                assert!(col < self.rank() + 1);
-            }
-            assert!(
-                scratch.available() >= GLWECiphertext::encrypt_sk_scratch_space(module, self.basek(), self.k()),
-                "scratch.available(): {} < GLWECiphertext::encrypt_sk_scratch_space: {}",
-                scratch.available(),
-                GLWECiphertext::encrypt_sk_scratch_space(module, self.basek(), self.k())
-            )
-        }
-
-        let basek: usize = self.basek();
-        let k: usize = self.k();
-        let size: usize = self.size();
-        let cols: usize = self.rank() + 1;
-
-        let (mut c0_big, scratch_1) = scratch.tmp_vec_znx(module, 1, size);
-        c0_big.zero();
-
-        {
-            // c[i] = uniform
-            // c[0] -= c[i] * s[i],
-            (1..cols).for_each(|i| {
-                let (mut ci_dft, scratch_2) = scratch_1.tmp_vec_znx_dft(module, 1, size);
-
-                // c[i] = uniform
-                self.data.fill_uniform(basek, i, size, source_xa);
-
-                // c[i] = norm(IDFT(DFT(c[i]) * DFT(s[i])))
-                module.vec_znx_dft(1, 0, &mut ci_dft, 0, &self.data, i);
-                module.svp_apply_inplace(&mut ci_dft, 0, &sk.data_fourier, i - 1);
-                let ci_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume(ci_dft);
-
-                // use c[0] as buffer, which is overwritten later by the normalization step
-                module.vec_znx_big_normalize(basek, &mut self.data, 0, &ci_big, 0, scratch_2);
-
-                // c0_tmp = -c[i] * s[i] (use c[0] as buffer)
-                module.vec_znx_sub_ab_inplace(&mut c0_big, 0, &self.data, 0);
-
-                // c[i] += m if col = i
-                if let Some((pt, col)) = pt {
-                    if i == col {
-                        module.vec_znx_add_inplace(&mut self.data, i, &pt.data, 0);
-                        module.vec_znx_normalize_inplace(basek, &mut self.data, i, scratch_2);
-                    }
-                }
-            });
-        }
-
-        // c[0] += e
-        c0_big.add_normal(basek, 0, k, source_xe, sigma, sigma * SIX_SIGMA);
-
-        // c[0] += m if col = 0
-        if let Some((pt, col)) = pt {
-            if col == 0 {
-                module.vec_znx_add_inplace(&mut c0_big, 0, &pt.data, 0);
-            }
-        }
-
-        // c[0] = norm(c[0])
-        module.vec_znx_normalize(basek, &mut self.data, 0, &c0_big, 0, scratch_1);
-    }
-
-    pub(crate) fn encrypt_pk_private<DataPt: AsRef<[u8]>, DataPk: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        pt: Option<(&GLWEPlaintext<DataPt>, usize)>,
-        pk: &GLWEPublicKey<DataPk, FFT64>,
-        source_xu: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-        scratch: &mut Scratch,
-    ) {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(self.basek(), pk.basek());
-            assert_eq!(self.n(), module.n());
-            assert_eq!(pk.n(), module.n());
-            assert_eq!(self.rank(), pk.rank());
-            if let Some((pt, _)) = pt {
-                assert_eq!(pt.basek(), pk.basek());
-                assert_eq!(pt.n(), module.n());
-            }
-        }
-
-        let basek: usize = pk.basek();
-        let size_pk: usize = pk.size();
-        let cols: usize = self.rank() + 1;
-
-        // Generates u according to the underlying secret distribution.
-        let (mut u_dft, scratch_1) = scratch.tmp_scalar_znx_dft(module, 1);
-
-        {
-            let (mut u, _) = scratch_1.tmp_scalar_znx(module, 1);
-            match pk.dist {
-                SecretDistribution::NONE => panic!(
-                    "invalid public key: SecretDistribution::NONE, ensure it has been correctly intialized through \
-                     Self::generate"
-                ),
-                SecretDistribution::TernaryFixed(hw) => u.fill_ternary_hw(0, hw, source_xu),
-                SecretDistribution::TernaryProb(prob) => u.fill_ternary_prob(0, prob, source_xu),
-                SecretDistribution::ZERO => {}
-            }
-
-            module.svp_prepare(&mut u_dft, 0, &u, 0);
-        }
-
-        // ct[i] = pk[i] * u + ei (+ m if col = i)
-        (0..cols).for_each(|i| {
-            let (mut ci_dft, scratch_2) = scratch_1.tmp_vec_znx_dft(module, 1, size_pk);
-            // ci_dft = DFT(u) * DFT(pk[i])
-            module.svp_apply(&mut ci_dft, 0, &u_dft, 0, &pk.data.data, i);
-
-            // ci_big = u * p[i]
-            let mut ci_big = module.vec_znx_idft_consume(ci_dft);
-
-            // ci_big = u * pk[i] + e
-            ci_big.add_normal(basek, 0, pk.k(), source_xe, sigma, sigma * SIX_SIGMA);
-
-            // ci_big = u * pk[i] + e + m (if col = i)
-            if let Some((pt, col)) = pt {
-                if col == i {
-                    module.vec_znx_big_add_small_inplace(&mut ci_big, 0, &pt.data, 0);
-                }
-            }
-
-            // ct[i] = norm(ci_big)
-            module.vec_znx_big_normalize(basek, &mut self.data, i, &ci_big, 0, scratch_2);
-        });
-    }
-}
-
-impl<DataSelf: AsRef<[u8]>> GLWECiphertext<DataSelf> {
-    pub fn clone(&self) -> GLWECiphertext<Vec<u8>> {
-        GLWECiphertext {
-            data: self.data.clone(),
-            basek: self.basek(),
-            k: self.k(),
-        }
-    }
-
-    pub fn decrypt<DataPt: AsMut<[u8]> + AsRef<[u8]>, DataSk: AsRef<[u8]>>(
-        &self,
-        module: &Module<FFT64>,
-        pt: &mut GLWEPlaintext<DataPt>,
-        sk: &GLWESecret<DataSk, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(self.rank(), sk.rank());
-            assert_eq!(self.n(), module.n());
-            assert_eq!(pt.n(), module.n());
-            assert_eq!(sk.n(), module.n());
-        }
-
-        let cols: usize = self.rank() + 1;
-
-        let (mut c0_big, scratch_1) = scratch.tmp_vec_znx_big(module, 1, self.size()); // TODO optimize size when pt << ct
-        c0_big.zero();
-
-        {
-            (1..cols).for_each(|i| {
-                // ci_dft = DFT(a[i]) * DFT(s[i])
-                let (mut ci_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, self.size()); // TODO optimize size when pt << ct
-                module.vec_znx_dft(1, 0, &mut ci_dft, 0, &self.data, i);
-                module.svp_apply_inplace(&mut ci_dft, 0, &sk.data_fourier, i - 1);
-                let ci_big = module.vec_znx_idft_consume(ci_dft);
-
-                // c0_big += a[i] * s[i]
-                module.vec_znx_big_add_inplace(&mut c0_big, 0, &ci_big, 0);
-            });
-        }
-
-        // c0_big = (a * s) + (-a * s + m + e) = BIG(m + e)
-        module.vec_znx_big_add_small_inplace(&mut c0_big, 0, &self.data, 0);
-
-        // pt = norm(BIG(m + e))
-        module.vec_znx_big_normalize(self.basek(), &mut pt.data, 0, &mut c0_big, 0, scratch_1);
-
-        pt.basek = self.basek();
-        pt.k = pt.k().min(self.k());
-    }
-}
-
-pub trait GLWECiphertextToRef {
-    fn to_ref(&self) -> GLWECiphertext<&[u8]>;
-}
-
-impl<D: AsRef<[u8]>> GLWECiphertextToRef for GLWECiphertext<D> {
-    fn to_ref(&self) -> GLWECiphertext<&[u8]> {
-        GLWECiphertext {
-            data: self.data.to_ref(),
-            basek: self.basek,
-            k: self.k,
-        }
-    }
-}
-
-pub trait GLWECiphertextToMut {
-    fn to_mut(&mut self) -> GLWECiphertext<&mut [u8]>;
-}
-
-impl<D: AsMut<[u8]> + AsRef<[u8]>> GLWECiphertextToMut for GLWECiphertext<D> {
-    fn to_mut(&mut self) -> GLWECiphertext<&mut [u8]> {
-        GLWECiphertext {
-            data: self.data.to_mut(),
-            basek: self.basek,
-            k: self.k,
-        }
-    }
-}
-
-impl<D> GLWEOps for GLWECiphertext<D>
-where
-    D: AsRef<[u8]> + AsMut<[u8]>,
-    GLWECiphertext<D>: GLWECiphertextToMut + Infos + SetMetaData,
-{
-}