@@ -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,
 };
 
@@ -68,7 +68,7 @@ &self,
         module: &Module<FFT64>,
         row_i: usize,
         col_j: usize,
-        res: &mut GLWECiphertextFourier<R, FFT64>,
+        res: &mut FourierGLWECiphertext<R, FFT64>,
     ) {
         module.mat_znx_dft_get_row(&mut res.data, &self.key.0.data, row_i, col_j);
     }
@@ -80,7 +80,7 @@ &mut self,
         module: &Module<FFT64>,
         row_i: usize,
         col_j: usize,
-        a: &GLWECiphertextFourier<R, FFT64>,
+        a: &FourierGLWECiphertext<R, FFT64>,
     ) {
         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

@@ -23,6 +23,10 @@ dist: SecretDistribution::NONE,
         }
     }
 
+    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)
+    }
+
     pub fn generate_from_sk<DataSkGLWE, DataSkLWE>(
         &mut self,
         module: &Module<FFT64>,

@@ -1,6 +1,6 @@
 use backend::{Backend, Module, ZnxInfos};
 
-use crate::GLWECiphertextFourier;
+use crate::{FourierGLWECiphertext, div_ceil};
 
 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]>;
 }

@@ -4,7 +4,7 @@ ZnxInfos, ZnxZero,
 };
 use sampling::source::Source;
 
-use crate::{GLWECiphertext, GLWECiphertextFourier, GLWESecret, GetRow, Infos, ScratchCore, SetRow};
+use crate::{FourierGLWECiphertext, GLWECiphertext, GLWESecret, GetRow, Infos, ScratchCore, SetRow, div_ceil};
 
 pub struct GGLWECiphertext<C, B: Backend> {
     pub(crate) data: MatZnxDft<C, B>,
@@ -217,7 +217,7 @@ &self,
         module: &Module<FFT64>,
         row_i: usize,
         col_j: usize,
-        res: &mut GLWECiphertextFourier<R, FFT64>,
+        res: &mut FourierGLWECiphertext<R, FFT64>,
     ) {
         module.mat_znx_dft_get_row(&mut res.data, &self.data, row_i, col_j);
     }
@@ -229,7 +229,7 @@ &mut self,
         module: &Module<FFT64>,
         row_i: usize,
         col_j: usize,
-        a: &GLWECiphertextFourier<R, FFT64>,
+        a: &FourierGLWECiphertext<R, FFT64>,
     ) {
         module.mat_znx_dft_set_row(&mut self.data, row_i, col_j, &a.data);
     }

@@ -6,8 +6,8 @@ };
 use sampling::source::Source;
 
 use crate::{
-    AutomorphismKey, GLWECiphertext, GLWECiphertextFourier, GLWESecret, GLWESwitchingKey, GetRow, Infos, ScratchCore, SetRow,
-    TensorKey,
+    AutomorphismKey, FourierGLWECiphertext, GLWECiphertext, GLWESecret, GLWESwitchingKey, GetRow, Infos, ScratchCore, SetRow,
+    TensorKey, div_ceil,
 };
 
 pub struct GGSWCiphertext<C, B: Backend> {
@@ -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
     }
 }
@@ -686,7 +686,7 @@ &self,
         module: &Module<FFT64>,
         row_i: usize,
         col_j: usize,
-        res: &mut GLWECiphertextFourier<R, FFT64>,
+        res: &mut FourierGLWECiphertext<R, FFT64>,
     ) {
         module.mat_znx_dft_get_row(&mut res.data, &self.data, row_i, col_j);
     }
@@ -698,7 +698,7 @@ &mut self,
         module: &Module<FFT64>,
         row_i: usize,
         col_j: usize,
-        a: &GLWECiphertextFourier<R, FFT64>,
+        a: &FourierGLWECiphertext<R, FFT64>,
     ) {
         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::{AutomorphismKey, 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: &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);
+        }
+    }
+}

@@ -0,0 +1,115 @@
+use backend::{
+    Backend, FFT64, Module, VecZnx, VecZnxAlloc, VecZnxBigAlloc, VecZnxBigScratch, VecZnxDftAlloc, VecZnxDftOps, VecZnxToMut,
+    VecZnxToRef,
+};
+
+use crate::{FourierGLWECiphertext, GLWEOps, Infos, SetMetaData, div_ceil};
+
+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, div_ceil(k, basek)),
+            basek,
+            k,
+        }
+    }
+
+    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
+        module.bytes_of_vec_znx(rank + 1, div_ceil(k, 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 GLWECiphertext<Vec<u8>> {
+    pub fn decrypt_scratch_space(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
+        let size: usize = div_ceil(k, 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: 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 +1,56 @@
+use backend::{FFT64, Module, ScalarZnxDftOps, Scratch, VecZnxBigOps, VecZnxDftOps, ZnxZero};
+
+use crate::{GLWECiphertext, GLWEPlaintext, GLWESecret, Infos};
+
+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());
+    }
+}

@@ -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::{GLWECiphertext, GLWEPlaintext, GLWEPublicKey, GLWESecret, Infos, SIX_SIGMA, div_ceil, keys::SecretDistribution};
+
+impl GLWECiphertext<Vec<u8>> {
+    pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
+        let size: usize = div_ceil(k, 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 = div_ceil(k, 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: &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(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::BinaryFixed(hw) => u.fill_binary_hw(0, hw, source_xu),
+                SecretDistribution::BinaryProb(prob) => u.fill_binary_prob(0, prob, source_xu),
+                SecretDistribution::BinaryBlock(block_size) => u.fill_binary_block(0, block_size, 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);
+        });
+    }
+}

@@ -0,0 +1,129 @@
+use backend::{
+    FFT64, MatZnxDftOps, MatZnxDftScratch, Module, Scratch, VecZnxBig, VecZnxBigOps, VecZnxDftAlloc, VecZnxDftOps, VecZnxScratch,
+};
+
+use crate::{FourierGLWECiphertext, GGSWCiphertext, GLWECiphertext, Infos, div_ceil};
+
+impl GLWECiphertext<Vec<u8>> {
+    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 = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank);
+        let in_size: usize = div_ceil(div_ceil(k_in, basek), digits);
+        let out_size: usize = div_ceil(k_out, basek);
+        let ggsw_size: usize = div_ceil(ggsw_k, 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,
+        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: 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 +1,244 @@
+use backend::{
+    FFT64, MatZnxDftOps, MatZnxDftScratch, Module, Scratch, VecZnxBig, VecZnxBigOps, VecZnxBigScratch, VecZnxDftAlloc,
+    VecZnxDftOps, ZnxZero,
+};
+
+use crate::{FourierGLWECiphertext, GLWECiphertext, GLWESwitchingKey, Infos, div_ceil};
+
+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 = div_ceil(div_ceil(k_in, basek), digits);
+        let out_size: usize = div_ceil(k_out, basek);
+        let ksk_size: usize = div_ceil(k_ksk, 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());
+            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(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.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);
+        });
+    }
+}

@@ -0,0 +1,31 @@
+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;
+
+#[allow(unused_imports)]
+pub use automorphism::*;
+pub use ciphertext::*;
+#[allow(unused_imports)]
+pub use decryption::*;
+#[allow(unused_imports)]
+pub use encryption::*;
+#[allow(unused_imports)]
+pub use external_product::*;
+#[allow(unused_imports)]
+pub use keyswitch::*;
+pub use ops::*;
+pub use packing::*;
+pub use plaintext::*;
+pub use public_key::*;
+pub use secret::*;
+#[allow(unused_imports)]
+pub use trace::*;

@@ -0,0 +1,75 @@
+use backend::{Backend, FFT64, Module, ScratchOwned, VecZnxDft};
+use sampling::source::Source;
+
+use crate::{FourierGLWECiphertext, GLWESecret, Infos, keys::SecretDistribution};
+
+pub struct GLWEPublicKey<D, B: Backend> {
+    pub(crate) data: FourierGLWECiphertext<D, B>,
+    pub(crate) dist: SecretDistribution,
+}
+
+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: SecretDistribution::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: &GLWESecret<S, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            match sk.dist {
+                SecretDistribution::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 +1,93 @@
+use backend::{
+    Backend, FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScalarZnxDft, ScalarZnxDftAlloc, ScalarZnxDftOps, ZnxInfos, ZnxZero,
+};
+use sampling::source::Source;
+
+use crate::keys::SecretDistribution;
+
+pub struct GLWESecret<T, B: Backend> {
+    pub(crate) data: ScalarZnx<T>,
+    pub(crate) data_fourier: ScalarZnxDft<T, B>,
+    pub(crate) dist: SecretDistribution,
+}
+
+impl<B: Backend> GLWESecret<Vec<u8>, B> {
+    pub fn alloc(module: &Module<B>, rank: usize) -> Self {
+        Self {
+            data: module.new_scalar_znx(rank),
+            data_fourier: module.new_scalar_znx_dft(rank),
+            dist: SecretDistribution::NONE,
+        }
+    }
+
+    pub fn bytes_of(module: &Module<B>, rank: usize) -> usize {
+        module.bytes_of_scalar_znx(rank) + module.bytes_of_scalar_znx_dft(rank)
+    }
+}
+
+impl<DataSelf, B: Backend> GLWESecret<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]>> GLWESecret<S, FFT64> {
+    pub fn fill_ternary_prob(&mut self, module: &Module<FFT64>, prob: f64, source: &mut Source) {
+        (0..self.rank()).for_each(|i| {
+            self.data.fill_ternary_prob(i, prob, source);
+        });
+        self.prep_fourier(module);
+        self.dist = SecretDistribution::TernaryProb(prob);
+    }
+
+    pub fn fill_ternary_hw(&mut self, module: &Module<FFT64>, hw: usize, source: &mut Source) {
+        (0..self.rank()).for_each(|i| {
+            self.data.fill_ternary_hw(i, hw, source);
+        });
+        self.prep_fourier(module);
+        self.dist = SecretDistribution::TernaryFixed(hw);
+    }
+
+    pub fn fill_binary_prob(&mut self, module: &Module<FFT64>, prob: f64, source: &mut Source) {
+        (0..self.rank()).for_each(|i| {
+            self.data.fill_binary_prob(i, prob, source);
+        });
+        self.prep_fourier(module);
+        self.dist = SecretDistribution::BinaryProb(prob);
+    }
+
+    pub fn fill_binary_hw(&mut self, module: &Module<FFT64>, hw: usize, source: &mut Source) {
+        (0..self.rank()).for_each(|i| {
+            self.data.fill_binary_hw(i, hw, source);
+        });
+        self.prep_fourier(module);
+        self.dist = SecretDistribution::BinaryFixed(hw);
+    }
+
+    pub fn fill_binary_block(&mut self, module: &Module<FFT64>, block_size: usize, source: &mut Source) {
+        (0..self.rank()).for_each(|i| {
+            self.data.fill_binary_block(i, block_size, source);
+        });
+        self.prep_fourier(module);
+        self.dist = SecretDistribution::BinaryBlock(block_size);
+    }
+
+    pub fn fill_zero(&mut self) {
+        self.data.zero();
+        self.dist = SecretDistribution::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);
+        });
+    }
+}

@@ -1,886 +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::BinaryFixed(hw) => u.fill_binary_hw(0, hw, source_xu),
-                SecretDistribution::BinaryProb(prob) => u.fill_binary_prob(0, prob, source_xu),
-                SecretDistribution::BinaryBlock(block_size) => u.fill_binary_block(0, block_size, 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,
-{
-}

@@ -6,13 +6,13 @@ use sampling::source::Source;
 
 use crate::{GGSWCiphertext, GLWECiphertext, GLWEPlaintext, GLWESecret, GLWESwitchingKey, Infos, ScratchCore};
 
-pub struct GLWECiphertextFourier<C, B: Backend> {
+pub struct FourierGLWECiphertext<C, B: Backend> {
     pub data: VecZnxDft<C, B>,
     pub basek: usize,
     pub k: usize,
 }
 
-impl<B: Backend> GLWECiphertextFourier<Vec<u8>, B> {
+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)),
@@ -26,7 +26,7 @@ module.bytes_of_vec_znx_dft(rank + 1, k.div_ceil(basek))
     }
 }
 
-impl<T, B: Backend> Infos for GLWECiphertextFourier<T, B> {
+impl<T, B: Backend> Infos for FourierGLWECiphertext<T, B> {
     type Inner = VecZnxDft<T, B>;
 
     fn inner(&self) -> &Self::Inner {
@@ -42,13 +42,13 @@ self.k
     }
 }
 
-impl<T, B: Backend> GLWECiphertextFourier<T, B> {
+impl<T, B: Backend> FourierGLWECiphertext<T, B> {
     pub fn rank(&self) -> usize {
         self.cols() - 1
     }
 }
 
-impl GLWECiphertextFourier<Vec<u8>, FFT64> {
+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))
@@ -125,7 +125,7 @@ Self::external_product_scratch_space(module, basek, k_out, k_out, k_ggsw, digits, rank)
     }
 }
 
-impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWECiphertextFourier<DataSelf, FFT64> {
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> FourierGLWECiphertext<DataSelf, FFT64> {
     pub fn encrypt_zero_sk<DataSk: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
@@ -143,7 +143,7 @@
     pub fn keyswitch<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
-        lhs: &GLWECiphertextFourier<DataLhs, FFT64>,
+        lhs: &FourierGLWECiphertext<DataLhs, FFT64>,
         rhs: &GLWESwitchingKey<DataRhs, FFT64>,
         scratch: &mut Scratch,
     ) {
@@ -159,7 +159,7 @@ rhs: &GLWESwitchingKey<DataRhs, FFT64>,
         scratch: &mut Scratch,
     ) {
         unsafe {
-            let self_ptr: *mut GLWECiphertextFourier<DataSelf, FFT64> = self as *mut GLWECiphertextFourier<DataSelf, FFT64>;
+            let self_ptr: *mut FourierGLWECiphertext<DataSelf, FFT64> = self as *mut FourierGLWECiphertext<DataSelf, FFT64>;
             self.keyswitch(&module, &*self_ptr, rhs, scratch);
         }
     }
@@ -167,7 +167,7 @@
     pub fn external_product<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
-        lhs: &GLWECiphertextFourier<DataLhs, FFT64>,
+        lhs: &FourierGLWECiphertext<DataLhs, FFT64>,
         rhs: &GGSWCiphertext<DataRhs, FFT64>,
         scratch: &mut Scratch,
     ) {
@@ -184,7 +184,7 @@ assert_eq!(self.n(), module.n());
             assert_eq!(lhs.n(), module.n());
             assert!(
                 scratch.available()
-                    >= GLWECiphertextFourier::external_product_scratch_space(
+                    >= FourierGLWECiphertext::external_product_scratch_space(
                         module,
                         self.basek(),
                         self.k(),
@@ -246,13 +246,13 @@ rhs: &GGSWCiphertext<DataRhs, FFT64>,
         scratch: &mut Scratch,
     ) {
         unsafe {
-            let self_ptr: *mut GLWECiphertextFourier<DataSelf, FFT64> = self as *mut GLWECiphertextFourier<DataSelf, FFT64>;
+            let self_ptr: *mut FourierGLWECiphertext<DataSelf, FFT64> = self as *mut FourierGLWECiphertext<DataSelf, FFT64>;
             self.external_product(&module, &*self_ptr, rhs, scratch);
         }
     }
 }
 
-impl<DataSelf: AsRef<[u8]>> GLWECiphertextFourier<DataSelf, FFT64> {
+impl<DataSelf: AsRef<[u8]>> FourierGLWECiphertext<DataSelf, FFT64> {
     pub fn decrypt<DataPt: AsRef<[u8]> + AsMut<[u8]>, DataSk: AsRef<[u8]>>(
         &self,
         module: &Module<FFT64>,

@@ -1,6 +1,10 @@
 use backend::{Backend, FFT64, Module, VecZnx, VecZnxAlloc, VecZnxToMut, VecZnxToRef};
 
-use crate::{GLWECiphertext, GLWECiphertextToMut, GLWECiphertextToRef, GLWEOps, Infos, SetMetaData};
+use crate::{
+    GLWEOps, Infos, SetMetaData,
+    ciphertext::{GLWECiphertext, GLWECiphertextToMut, GLWECiphertextToRef},
+    div_ceil,
+};
 
 pub struct GLWEPlaintext<C> {
     pub data: VecZnx<C>,

@@ -1,11 +1,3 @@
-use backend::{
-    Backend, FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScalarZnxDft, ScalarZnxDftAlloc, ScalarZnxDftOps, ScratchOwned, VecZnxDft,
-    ZnxInfos, ZnxZero,
-};
-use sampling::source::Source;
-
-use crate::{GLWECiphertextFourier, Infos};
-
 #[derive(Clone, Copy, Debug)]
 pub(crate) enum SecretDistribution {
     TernaryFixed(usize), // Ternary with fixed Hamming weight
@@ -16,221 +8,3 @@ BinaryBlock(usize),  // Binary split in block of size 2^k
     ZERO,                // Debug mod
     NONE,                // Unitialized
 }
-
-pub struct LWESecret<T> {
-    pub(crate) data: ScalarZnx<T>,
-    pub(crate) dist: SecretDistribution,
-}
-
-impl LWESecret<Vec<u8>> {
-    pub fn alloc(n: usize) -> Self {
-        Self {
-            data: ScalarZnx::new(n, 1),
-            dist: SecretDistribution::NONE,
-        }
-    }
-}
-
-impl<DataSelf> LWESecret<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<D: AsRef<[u8]> + AsMut<[u8]>> LWESecret<D> {
-    pub fn fill_ternary_prob(&mut self, prob: f64, source: &mut Source) {
-        self.data.fill_ternary_prob(0, prob, source);
-        self.dist = SecretDistribution::TernaryProb(prob);
-    }
-
-    pub fn fill_ternary_hw(&mut self, hw: usize, source: &mut Source) {
-        self.data.fill_ternary_hw(0, hw, source);
-        self.dist = SecretDistribution::TernaryFixed(hw);
-    }
-
-    pub fn fill_binary_prob(&mut self, prob: f64, source: &mut Source) {
-        self.data.fill_binary_prob(0, prob, source);
-        self.dist = SecretDistribution::BinaryProb(prob);
-    }
-
-    pub fn fill_binary_hw(&mut self, hw: usize, source: &mut Source) {
-        self.data.fill_binary_hw(0, hw, source);
-        self.dist = SecretDistribution::BinaryFixed(hw);
-    }
-
-    pub fn fill_binary_block(&mut self, block_size: usize, source: &mut Source) {
-        self.data.fill_binary_block(0, block_size, source);
-        self.dist = SecretDistribution::BinaryBlock(block_size);
-    }
-
-    pub fn fill_zero(&mut self) {
-        self.data.zero();
-        self.dist = SecretDistribution::ZERO;
-    }
-}
-
-pub struct GLWESecret<T, B: Backend> {
-    pub(crate) data: ScalarZnx<T>,
-    pub(crate) data_fourier: ScalarZnxDft<T, B>,
-    pub(crate) dist: SecretDistribution,
-}
-
-impl<B: Backend> GLWESecret<Vec<u8>, B> {
-    pub fn alloc(module: &Module<B>, rank: usize) -> Self {
-        Self {
-            data: module.new_scalar_znx(rank),
-            data_fourier: module.new_scalar_znx_dft(rank),
-            dist: SecretDistribution::NONE,
-        }
-    }
-
-    pub fn bytes_of(module: &Module<B>, rank: usize) -> usize {
-        module.bytes_of_scalar_znx(rank) + module.bytes_of_scalar_znx_dft(rank)
-    }
-}
-
-impl<DataSelf, B: Backend> GLWESecret<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]>> GLWESecret<S, FFT64> {
-    pub fn fill_ternary_prob(&mut self, module: &Module<FFT64>, prob: f64, source: &mut Source) {
-        (0..self.rank()).for_each(|i| {
-            self.data.fill_ternary_prob(i, prob, source);
-        });
-        self.prep_fourier(module);
-        self.dist = SecretDistribution::TernaryProb(prob);
-    }
-
-    pub fn fill_ternary_hw(&mut self, module: &Module<FFT64>, hw: usize, source: &mut Source) {
-        (0..self.rank()).for_each(|i| {
-            self.data.fill_ternary_hw(i, hw, source);
-        });
-        self.prep_fourier(module);
-        self.dist = SecretDistribution::TernaryFixed(hw);
-    }
-
-    pub fn fill_binary_prob(&mut self, module: &Module<FFT64>, prob: f64, source: &mut Source) {
-        (0..self.rank()).for_each(|i| {
-            self.data.fill_binary_prob(i, prob, source);
-        });
-        self.prep_fourier(module);
-        self.dist = SecretDistribution::BinaryProb(prob);
-    }
-
-    pub fn fill_binary_hw(&mut self, module: &Module<FFT64>, hw: usize, source: &mut Source) {
-        (0..self.rank()).for_each(|i| {
-            self.data.fill_binary_hw(i, hw, source);
-        });
-        self.prep_fourier(module);
-        self.dist = SecretDistribution::BinaryFixed(hw);
-    }
-
-    pub fn fill_binary_block(&mut self, module: &Module<FFT64>, block_size: usize, source: &mut Source) {
-        (0..self.rank()).for_each(|i| {
-            self.data.fill_binary_block(i, block_size, source);
-        });
-        self.prep_fourier(module);
-        self.dist = SecretDistribution::BinaryBlock(block_size);
-    }
-
-    pub fn fill_zero(&mut self) {
-        self.data.zero();
-        self.dist = SecretDistribution::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);
-        });
-    }
-}
-
-pub struct GLWEPublicKey<D, B: Backend> {
-    pub(crate) data: GLWECiphertextFourier<D, B>,
-    pub(crate) dist: SecretDistribution,
-}
-
-impl<B: Backend> GLWEPublicKey<Vec<u8>, B> {
-    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rank: usize) -> Self {
-        Self {
-            data: GLWECiphertextFourier::alloc(module, basek, k, rank),
-            dist: SecretDistribution::NONE,
-        }
-    }
-
-    pub fn bytes_of(module: &Module<B>, basek: usize, k: usize, rank: usize) -> usize {
-        GLWECiphertextFourier::<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: &GLWESecret<S, FFT64>,
-        source_xa: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-    ) {
-        #[cfg(debug_assertions)]
-        {
-            match sk.dist {
-                SecretDistribution::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(GLWECiphertextFourier::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;
-    }
-}

@@ -1,7 +1,7 @@
 use backend::{Backend, FFT64, MatZnxDft, MatZnxDftOps, Module, Scratch, ZnxZero};
 use sampling::source::Source;
 
-use crate::{GGLWECiphertext, GGSWCiphertext, GLWECiphertextFourier, GLWESecret, GetRow, Infos, ScratchCore, SetRow};
+use crate::{FourierGLWECiphertext, GGLWECiphertext, GGSWCiphertext, GLWESecret, GetRow, Infos, ScratchCore, SetRow};
 
 pub struct GLWESwitchingKey<Data, B: Backend>(pub(crate) GGLWECiphertext<Data, B>);
 
@@ -73,7 +73,7 @@ &self,
         module: &Module<FFT64>,
         row_i: usize,
         col_j: usize,
-        res: &mut GLWECiphertextFourier<R, FFT64>,
+        res: &mut FourierGLWECiphertext<R, FFT64>,
     ) {
         module.mat_znx_dft_get_row(&mut res.data, &self.0.data, row_i, col_j);
     }
@@ -85,7 +85,7 @@ &mut self,
         module: &Module<FFT64>,
         row_i: usize,
         col_j: usize,
-        a: &GLWECiphertextFourier<R, FFT64>,
+        a: &FourierGLWECiphertext<R, FFT64>,
     ) {
         module.mat_znx_dft_set_row(&mut self.0.data, row_i, col_j, &a.data);
     }
@@ -110,10 +110,10 @@ digits: usize,
         rank_in: usize,
         rank_out: usize,
     ) -> usize {
-        let tmp_in: usize = GLWECiphertextFourier::bytes_of(module, basek, k_in, rank_in);
-        let tmp_out: usize = GLWECiphertextFourier::bytes_of(module, basek, k_out, rank_out);
+        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 =
-            GLWECiphertextFourier::keyswitch_scratch_space(module, basek, k_out, k_in, k_ksk, digits, rank_in, rank_out);
+            FourierGLWECiphertext::keyswitch_scratch_space(module, basek, k_out, k_in, k_ksk, digits, rank_in, rank_out);
         tmp_in + tmp_out + ksk
     }
 
@@ -125,8 +125,8 @@ k_ksk: usize,
         digits: usize,
         rank: usize,
     ) -> usize {
-        let tmp: usize = GLWECiphertextFourier::bytes_of(module, basek, k_out, rank);
-        let ksk: usize = GLWECiphertextFourier::keyswitch_inplace_scratch_space(module, basek, k_out, k_ksk, digits, rank);
+        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
     }
 
@@ -139,9 +139,9 @@ 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
     }
 
@@ -153,9 +153,9 @@ 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
     }
 }

@@ -1,38 +1,35 @@
 pub mod automorphism;
 pub mod blind_rotation;
 pub mod elem;
-pub mod gglwe_ciphertext;
-pub mod ggsw_ciphertext;
-pub mod glwe_ciphertext;
-pub mod glwe_ciphertext_fourier;
-pub mod glwe_ops;
-pub mod glwe_packing;
-pub mod glwe_plaintext;
+pub mod fourier_glwe;
+pub mod gglwe;
+pub mod ggsw;
+pub mod glwe;
 pub mod keys;
 pub mod keyswitch_key;
+pub mod lwe;
 pub mod tensor_key;
 #[cfg(test)]
 mod test_fft64;
-pub mod trace;
+mod utils;
 
 pub use automorphism::*;
 use backend::Backend;
 use backend::FFT64;
 use backend::Module;
 pub use elem::*;
-pub use gglwe_ciphertext::*;
-pub use ggsw_ciphertext::*;
-pub use glwe_ciphertext::*;
-pub use glwe_ciphertext_fourier::*;
-pub use glwe_ops::*;
-pub use glwe_packing::*;
-pub use glwe_plaintext::*;
-pub use keys::*;
+pub use fourier_glwe::*;
+pub use gglwe::*;
+pub use ggsw::*;
+pub use glwe::*;
 pub use keyswitch_key::*;
+pub use lwe::*;
 pub use tensor_key::*;
 
 pub use backend::Scratch;
 pub use backend::ScratchOwned;
+
+use crate::keys::SecretDistribution;
 
 pub(crate) const SIX_SIGMA: f64 = 6.0;
 
@@ -64,7 +61,7 @@ module: &Module<B>,
         basek: usize,
         k: usize,
         rank: usize,
-    ) -> (GLWECiphertextFourier<&mut [u8], B>, &mut Self);
+    ) -> (FourierGLWECiphertext<&mut [u8], B>, &mut Self);
     fn tmp_sk(&mut self, module: &Module<B>, rank: usize) -> (GLWESecret<&mut [u8], B>, &mut Self);
     fn tmp_glwe_pk(
         &mut self,
@@ -181,9 +178,9 @@ module: &Module<FFT64>,
         basek: usize,
         k: usize,
         rank: usize,
-    ) -> (GLWECiphertextFourier<&mut [u8], FFT64>, &mut Self) {
-        let (data, scratch) = self.tmp_vec_znx_dft(module, rank + 1, k.div_ceil(basek));
-        (GLWECiphertextFourier { data, basek, k }, scratch)
+    ) -> (FourierGLWECiphertext<&mut [u8], FFT64>, &mut Self) {
+        let (data, scratch) = self.tmp_vec_znx_dft(module, rank + 1, div_ceil(k, basek));
+        (FourierGLWECiphertext { data, basek, k }, scratch)
     }
 
     fn tmp_glwe_pk(

@@ -0,0 +1,64 @@
+use backend::{ScalarZnx, ZnxInfos, ZnxZero};
+use sampling::source::Source;
+
+use crate::SecretDistribution;
+
+pub struct LWESecret<T> {
+    pub(crate) data: ScalarZnx<T>,
+    pub(crate) dist: SecretDistribution,
+}
+
+impl LWESecret<Vec<u8>> {
+    pub fn alloc(n: usize) -> Self {
+        Self {
+            data: ScalarZnx::new(n, 1),
+            dist: SecretDistribution::NONE,
+        }
+    }
+}
+
+impl<DataSelf> LWESecret<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<D: AsRef<[u8]> + AsMut<[u8]>> LWESecret<D> {
+    pub fn fill_ternary_prob(&mut self, prob: f64, source: &mut Source) {
+        self.data.fill_ternary_prob(0, prob, source);
+        self.dist = SecretDistribution::TernaryProb(prob);
+    }
+
+    pub fn fill_ternary_hw(&mut self, hw: usize, source: &mut Source) {
+        self.data.fill_ternary_hw(0, hw, source);
+        self.dist = SecretDistribution::TernaryFixed(hw);
+    }
+
+    pub fn fill_binary_prob(&mut self, prob: f64, source: &mut Source) {
+        self.data.fill_binary_prob(0, prob, source);
+        self.dist = SecretDistribution::BinaryProb(prob);
+    }
+
+    pub fn fill_binary_hw(&mut self, hw: usize, source: &mut Source) {
+        self.data.fill_binary_hw(0, hw, source);
+        self.dist = SecretDistribution::BinaryFixed(hw);
+    }
+
+    pub fn fill_binary_block(&mut self, block_size: usize, source: &mut Source) {
+        self.data.fill_binary_block(0, block_size, source);
+        self.dist = SecretDistribution::BinaryBlock(block_size);
+    }
+
+    pub fn fill_zero(&mut self) {
+        self.data.zero();
+        self.dist = SecretDistribution::ZERO;
+    }
+}

@@ -2,7 +2,8 @@ use backend::{FFT64, Module, ScalarZnxOps, ScratchOwned, Stats, VecZnxOps};
 use sampling::source::Source;
 
 use crate::{
-    AutomorphismKey, GLWECiphertextFourier, GLWEPlaintext, GLWESecret, GetRow, Infos, test_fft64::log2_std_noise_gglwe_product,
+    AutomorphismKey, FourierGLWECiphertext, GLWEPlaintext, GLWESecret, GetRow, Infos, div_ceil,
+    test_fft64::log2_std_noise_gglwe_product,
 };
 
 #[test]
@@ -69,7 +70,7 @@ let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         AutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_apply, rank)
-            | GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_out)
+            | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_out)
             | AutomorphismKey::automorphism_scratch_space(&module, basek, k_out, k_in, k_apply, digits, rank),
     );
 
@@ -101,7 +102,7 @@
     // gglwe_{s1}(s0) (x) gglwe_{s2}(s1) = gglwe_{s2}(s0)
     auto_key_out.automorphism(&module, &auto_key_in, &auto_key_apply, scratch.borrow());
 
-    let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_out, rank);
+    let mut ct_glwe_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_out, rank);
     let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
 
     let mut sk_auto: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
@@ -183,7 +184,7 @@ let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         AutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_apply, rank)
-            | GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_in)
+            | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_in)
             | AutomorphismKey::automorphism_inplace_scratch_space(&module, basek, k_in, k_apply, digits, rank),
     );
 
@@ -215,7 +216,7 @@
     // gglwe_{s1}(s0) (x) gglwe_{s2}(s1) = gglwe_{s2}(s0)
     auto_key.automorphism_inplace(&module, &auto_key_apply, scratch.borrow());
 
-    let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_in, rank);
+    let mut ct_glwe_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_in, rank);
     let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
 
     let mut sk_auto: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);

@@ -2,7 +2,7 @@ use backend::{FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScalarZnxToMut, ScratchOwned, Stats, VecZnxOps, ZnxViewMut};
 use sampling::source::Source;
 
 use crate::{
-    GGSWCiphertext, GLWECiphertextFourier, GLWEPlaintext, GLWESecret, GLWESwitchingKey, GetRow, Infos,
+    FourierGLWECiphertext, GGSWCiphertext, GLWEPlaintext, GLWESecret, GLWESwitchingKey, GetRow, Infos, div_ceil,
     test_fft64::{log2_std_noise_gglwe_product, noise_ggsw_product},
 };
 
@@ -145,7 +145,7 @@ let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_ksk, rank_out)
-            | GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_ksk),
+            | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ksk),
     );
 
     let mut sk_in: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_in);
@@ -164,8 +164,8 @@ sigma,
         scratch.borrow(),
     );
 
-    let mut ct_glwe_fourier: GLWECiphertextFourier<Vec<u8>, FFT64> =
-        GLWECiphertextFourier::alloc(&module, basek, k_ksk, rank_out);
+    let mut ct_glwe_fourier: FourierGLWECiphertext<Vec<u8>, FFT64> =
+        FourierGLWECiphertext::alloc(&module, basek, k_ksk, rank_out);
 
     (0..ksk.rank_in()).for_each(|col_i| {
         (0..ksk.rows()).for_each(|row_i| {
@@ -234,7 +234,7 @@ let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_ksk, rank_in_s0s1 | rank_out_s0s1)
-            | GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_out)
+            | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_out)
             | GLWESwitchingKey::keyswitch_scratch_space(
                 &module,
                 basek,
@@ -281,8 +281,8 @@
     // gglwe_{s1}(s0) (x) gglwe_{s2}(s1) = gglwe_{s2}(s0)
     ct_gglwe_s0s2.keyswitch(&module, &ct_gglwe_s0s1, &ct_gglwe_s1s2, scratch.borrow());
 
-    let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> =
-        GLWECiphertextFourier::alloc(&module, basek, k_out, rank_out_s1s2);
+    let mut ct_glwe_dft: FourierGLWECiphertext<Vec<u8>, FFT64> =
+        FourierGLWECiphertext::alloc(&module, basek, k_out, rank_out_s1s2);
     let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
 
     (0..ct_gglwe_s0s2.rank_in()).for_each(|col_i| {
@@ -346,7 +346,7 @@ let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_ksk, rank_out)
-            | GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_ksk)
+            | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ksk)
             | GLWESwitchingKey::keyswitch_inplace_scratch_space(&module, basek, k_ct, k_ksk, digits, rank_out),
     );
 
@@ -386,7 +386,7 @@ ct_gglwe_s0s1.keyswitch_inplace(&module, &ct_gglwe_s1s2, scratch.borrow());
 
     let ct_gglwe_s0s2: GLWESwitchingKey<Vec<u8>, FFT64> = ct_gglwe_s0s1;
 
-    let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_ct, rank_out);
+    let mut ct_glwe_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank_out);
     let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
 
     (0..ct_gglwe_s0s2.rank_in()).for_each(|col_i| {
@@ -455,7 +455,7 @@ let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_in, rank_out)
-            | GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_out)
+            | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_out)
             | GLWESwitchingKey::external_product_scratch_space(&module, basek, k_out, k_in, k_ggsw, digits, rank_out)
             | GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_ggsw, rank_out),
     );
@@ -494,7 +494,7 @@
     // gglwe_(m) (x) RGSW_(X^k) = gglwe_(m * X^k)
     ct_gglwe_out.external_product(&module, &ct_gglwe_in, &ct_rgsw, scratch.borrow());
 
-    let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_out, rank_out);
+    let mut ct_glwe_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_out, rank_out);
     let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
 
     (0..rank_in).for_each(|i| {
@@ -575,7 +575,7 @@ let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_ct, rank_out)
-            | GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_ct)
+            | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ct)
             | GLWESwitchingKey::external_product_inplace_scratch_space(&module, basek, k_ct, k_ggsw, digits, rank_out)
             | GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_ggsw, rank_out),
     );
@@ -614,7 +614,7 @@
     // gglwe_(m) (x) RGSW_(X^k) = gglwe_(m * X^k)
     ct_gglwe.external_product_inplace(&module, &ct_rgsw, scratch.borrow());
 
-    let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_ct, rank_out);
+    let mut ct_glwe_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank_out);
     let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
 
     (0..rank_in).for_each(|i| {

@@ -5,7 +5,7 @@ };
 use sampling::source::Source;
 
 use crate::{
-    GGSWCiphertext, GLWECiphertextFourier, GLWEPlaintext, GLWESecret, GLWESwitchingKey, GetRow, Infos, TensorKey,
+    FourierGLWECiphertext, GGSWCiphertext, GLWEPlaintext, GLWESecret, GLWESwitchingKey, GetRow, Infos, TensorKey,
     automorphism::AutomorphismKey,
     test_fft64::{noise_ggsw_keyswitch, noise_ggsw_product},
 };
@@ -139,7 +139,7 @@ pt_scalar.fill_ternary_hw(0, module.n(), &mut source_xs);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k, rank)
-            | GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k),
+            | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k),
     );
 
     let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
@@ -155,7 +155,7 @@ sigma,
         scratch.borrow(),
     );
 
-    let mut ct_glwe_fourier: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k, rank);
+    let mut ct_glwe_fourier: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k, rank);
     let mut pt_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(1, ct.size());
     let mut pt_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, ct.size());
 
@@ -221,7 +221,7 @@ let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_in, rank)
-            | GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_out)
+            | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_out)
             | GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_ksk, rank)
             | TensorKey::generate_from_sk_scratch_space(&module, basek, k_tsk, rank)
             | GGSWCiphertext::keyswitch_scratch_space(
@@ -269,7 +269,7 @@ );
 
     ct_out.keyswitch(&module, &ct_in, &ksk, &tsk, scratch.borrow());
 
-    let mut ct_glwe_fourier: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_out, rank);
+    let mut ct_glwe_fourier: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_out, rank);
     let mut pt_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(1, ct_out.size());
     let mut pt_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, ct_out.size());
 
@@ -348,7 +348,7 @@ let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_ct, rank)
-            | GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_ct)
+            | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ct)
             | GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_ksk, rank)
             | TensorKey::generate_from_sk_scratch_space(&module, basek, k_tsk, rank)
             | GGSWCiphertext::keyswitch_inplace_scratch_space(&module, basek, k_ct, k_ksk, digits, k_tsk, digits, rank),
@@ -394,7 +394,7 @@ );
 
     ct.keyswitch_inplace(&module, &ksk, &tsk, scratch.borrow());
 
-    let mut ct_glwe_fourier: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_ct, rank);
+    let mut ct_glwe_fourier: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank);
     let mut pt_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(1, ct.size());
     let mut pt_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, ct.size());
 
@@ -483,7 +483,7 @@ let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_in, rank)
-            | GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_out)
+            | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_out)
             | AutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_ksk, rank)
             | TensorKey::generate_from_sk_scratch_space(&module, basek, k_tsk, rank)
             | GGSWCiphertext::automorphism_scratch_space(
@@ -530,7 +530,7 @@ ct_out.automorphism(&module, &ct_in, &auto_key, &tensor_key, scratch.borrow());
 
     module.scalar_znx_automorphism_inplace(p, &mut pt_scalar, 0);
 
-    let mut ct_glwe_fourier: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_out, rank);
+    let mut ct_glwe_fourier: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_out, rank);
     let mut pt_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(1, ct_out.size());
     let mut pt_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, ct_out.size());
 
@@ -608,7 +608,7 @@ let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_ct, rank)
-            | GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_ct)
+            | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ct)
             | AutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_ksk, rank)
             | TensorKey::generate_from_sk_scratch_space(&module, basek, k_tsk, rank)
             | GGSWCiphertext::automorphism_inplace_scratch_space(&module, basek, k_ct, k_ksk, digits, k_tsk, digits, rank),
@@ -653,7 +653,7 @@ ct.automorphism_inplace(&module, &auto_key, &tensor_key, scratch.borrow());
 
     module.scalar_znx_automorphism_inplace(p, &mut pt_scalar, 0);
 
-    let mut ct_glwe_fourier: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_ct, rank);
+    let mut ct_glwe_fourier: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank);
     let mut pt_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(1, ct.size());
     let mut pt_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, ct.size());
 
@@ -737,7 +737,7 @@
     pt_ggsw_rhs.to_mut().raw_mut()[k] = 1; //X^{k}
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_out)
+        FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_out)
             | GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_ggsw, rank)
             | GGSWCiphertext::external_product_scratch_space(&module, basek, k_out, k_in, k_ggsw, digits, rank),
     );
@@ -767,7 +767,7 @@ );
 
     ct_ggsw_lhs_out.external_product(&module, &ct_ggsw_lhs_in, &ct_ggsw_rhs, scratch.borrow());
 
-    let mut ct_glwe_fourier: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_out, rank);
+    let mut ct_glwe_fourier: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_out, rank);
     let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
     let mut pt_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(1, ct_ggsw_lhs_out.size());
     let mut pt_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, ct_ggsw_lhs_out.size());
@@ -857,7 +857,7 @@
     pt_ggsw_rhs.to_mut().raw_mut()[k] = 1; //X^{k}
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_ct)
+        FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ct)
             | GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_ggsw, rank)
             | GGSWCiphertext::external_product_inplace_scratch_space(&module, basek, k_ct, k_ggsw, digits, rank),
     );
@@ -887,7 +887,7 @@ );
 
     ct_ggsw_lhs.external_product_inplace(&module, &ct_ggsw_rhs, scratch.borrow());
 
-    let mut ct_glwe_fourier: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_ct, rank);
+    let mut ct_glwe_fourier: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank);
     let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
     let mut pt_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(1, ct_ggsw_lhs.size());
     let mut pt_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, ct_ggsw_lhs.size());

@@ -6,7 +6,7 @@ use itertools::izip;
 use sampling::source::Source;
 
 use crate::{
-    GGSWCiphertext, GLWECiphertext, GLWECiphertextFourier, GLWEPlaintext, GLWEPublicKey, GLWESecret, Infos,
+    FourierGLWECiphertext, GGSWCiphertext, GLWECiphertext, GLWEPlaintext, GLWEPublicKey, GLWESecret, Infos,
     automorphism::AutomorphismKey,
     keyswitch_key::GLWESwitchingKey,
     test_fft64::{log2_std_noise_gglwe_product, noise_ggsw_product},
@@ -207,11 +207,11 @@
     let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
     sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
 
-    let mut ct_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_ct, rank);
+    let mut ct_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_ct)
-            | GLWECiphertextFourier::encrypt_sk_scratch_space(&module, basek, k_ct, rank),
+        FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ct)
+            | FourierGLWECiphertext::encrypt_sk_scratch_space(&module, basek, k_ct, rank),
     );
 
     ct_dft.encrypt_zero_sk(

@@ -1,5 +1,5 @@
 use crate::{
-    GGSWCiphertext, GLWECiphertext, GLWECiphertextFourier, GLWEOps, GLWEPlaintext, GLWESecret, GLWESwitchingKey, Infos,
+    FourierGLWECiphertext, GGSWCiphertext, GLWECiphertext, GLWEOps, GLWEPlaintext, GLWESecret, GLWESwitchingKey, Infos, div_ceil,
     test_fft64::{log2_std_noise_gglwe_product, noise_ggsw_product},
 };
 use backend::{FFT64, FillUniform, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned, Stats, VecZnxOps, ZnxViewMut};
@@ -90,10 +90,10 @@
     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: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::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: GLWECiphertextFourier<Vec<u8>, FFT64> =
-        GLWECiphertextFourier::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);
 
@@ -110,7 +110,7 @@ let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_ksk, rank_out)
             | GLWECiphertext::decrypt_scratch_space(&module, basek, k_out)
             | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, k_in)
-            | GLWECiphertextFourier::keyswitch_scratch_space(
+            | FourierGLWECiphertext::keyswitch_scratch_space(
                 &module,
                 basek,
                 ct_glwe_out.k(),
@@ -185,7 +185,7 @@ 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: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::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);
 
@@ -202,7 +202,7 @@ let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ksk.k(), rank)
             | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_glwe.k())
             | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_glwe.k())
-            | GLWECiphertextFourier::keyswitch_inplace_scratch_space(&module, basek, ct_rlwe_dft.k(), ksk.k(), digits, rank),
+            | FourierGLWECiphertext::keyswitch_inplace_scratch_space(&module, basek, ct_rlwe_dft.k(), ksk.k(), digits, rank),
     );
 
     let mut sk_in: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
@@ -278,8 +278,8 @@
     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: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k_in, rank);
-    let mut ct_out_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::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);
@@ -304,7 +304,7 @@ 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())
-            | GLWECiphertextFourier::external_product_scratch_space(
+            | FourierGLWECiphertext::external_product_scratch_space(
                 &module,
                 basek,
                 ct_out.k(),
@@ -384,7 +384,7 @@ 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: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
-    let mut ct_rlwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::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);
@@ -409,7 +409,7 @@ 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())
-            | GLWECiphertextFourier::external_product_inplace_scratch_space(&module, basek, ct.k(), ct_ggsw.k(), digits, rank),
+            | FourierGLWECiphertext::external_product_inplace_scratch_space(&module, basek, ct.k(), ct_ggsw.k(), digits, rank),
     );
 
     let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);

@@ -1,7 +1,7 @@
 use backend::{FFT64, Module, ScalarZnxDftOps, ScratchOwned, Stats, VecZnxOps};
 use sampling::source::Source;
 
-use crate::{GLWECiphertextFourier, GLWEPlaintext, GLWESecret, GetRow, Infos, TensorKey};
+use crate::{FourierGLWECiphertext, GLWEPlaintext, GLWESecret, GetRow, Infos, TensorKey};
 
 #[test]
 fn encrypt_sk() {
@@ -42,7 +42,7 @@ sigma,
         scratch.borrow(),
     );
 
-    let mut ct_glwe_fourier: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k, rank);
+    let mut ct_glwe_fourier: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k, rank);
     let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k);
 
     let mut sk_ij = GLWESecret::alloc(&module, 1);