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

@@ -1,5 +1,5 @@
 use backend::{FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned};
-use core::{GGSWCiphertext, GLWECiphertext, GLWESecret, Infos};
+use core::{FourierGLWESecret, GGSWCiphertext, GLWECiphertext, GLWESecret, Infos};
 use criterion::{BenchmarkId, Criterion, criterion_group, criterion_main};
 use sampling::source::Source;
 use std::hint::black_box;
@@ -52,13 +52,14 @@ let mut source_xs = Source::new([0u8; 32]);
         let mut source_xe = Source::new([0u8; 32]);
         let mut source_xa = Source::new([0u8; 32]);
 
-        let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-        sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+        let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+        sk.fill_ternary_prob(0.5, &mut source_xs);
+        let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
         ct_ggsw.encrypt_sk(
             &module,
             &pt_rgsw,
-            &sk,
+            &sk_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,
@@ -67,7 +68,7 @@ );
 
         ct_glwe_in.encrypt_zero_sk(
             &module,
-            &sk,
+            &sk_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,
@@ -134,13 +135,14 @@ let mut source_xs = Source::new([0u8; 32]);
         let mut source_xe = Source::new([0u8; 32]);
         let mut source_xa = Source::new([0u8; 32]);
 
-        let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-        sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+        let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+        sk.fill_ternary_prob(0.5, &mut source_xs);
+        let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
         ct_ggsw.encrypt_sk(
             &module,
             &pt_rgsw,
-            &sk,
+            &sk_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,
@@ -149,7 +151,7 @@ );
 
         ct_glwe.encrypt_zero_sk(
             &module,
-            &sk,
+            &sk_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,

@@ -1,5 +1,5 @@
 use backend::{FFT64, Module, ScratchOwned};
-use core::{AutomorphismKey, GLWECiphertext, GLWESecret, GLWESwitchingKey, Infos};
+use core::{FourierGLWESecret, GLWEAutomorphismKey, GLWECiphertext, GLWESecret, GLWESwitchingKey, Infos};
 use criterion::{BenchmarkId, Criterion, criterion_group, criterion_main};
 use sampling::source::Source;
 use std::{hint::black_box, time::Duration};
@@ -32,7 +32,8 @@
         let rows: usize = (p.k_ct_in + (p.basek * digits) - 1) / (p.basek * digits);
         let sigma: f64 = 3.2;
 
-        let mut ksk: AutomorphismKey<Vec<u8>, FFT64> = AutomorphismKey::alloc(&module, basek, k_grlwe, rows, digits, rank_out);
+        let mut ksk: GLWEAutomorphismKey<Vec<u8>, FFT64> =
+            GLWEAutomorphismKey::alloc(&module, basek, k_grlwe, rows, digits, rank_out);
         let mut ct_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_rlwe_in, rank_in);
         let mut ct_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_rlwe_out, rank_out);
 
@@ -55,11 +56,12 @@ let mut source_xs = Source::new([0u8; 32]);
         let mut source_xe = Source::new([0u8; 32]);
         let mut source_xa = Source::new([0u8; 32]);
 
-        let mut sk_in: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_in);
-        sk_in.fill_ternary_prob(&module, 0.5, &mut source_xs);
+        let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_in);
+        sk_in.fill_ternary_prob(0.5, &mut source_xs);
+        let sk_in_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_in);
 
-        let mut sk_out: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_out);
-        sk_out.fill_ternary_prob(&module, 0.5, &mut source_xs);
+        let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_out);
+        sk_out.fill_ternary_prob(0.5, &mut source_xs);
 
         ksk.generate_from_sk(
             &module,
@@ -73,7 +75,7 @@ );
 
         ct_in.encrypt_zero_sk(
             &module,
-            &sk_in,
+            &sk_in_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,
@@ -146,16 +148,18 @@ let mut source_xs: Source = Source::new([0u8; 32]);
         let mut source_xe: Source = Source::new([0u8; 32]);
         let mut source_xa: Source = Source::new([0u8; 32]);
 
-        let mut sk_in: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-        sk_in.fill_ternary_prob(&&module, 0.5, &mut source_xs);
+        let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+        sk_in.fill_ternary_prob(0.5, &mut source_xs);
+        let sk_in_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_in);
 
-        let mut sk_out: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-        sk_out.fill_ternary_prob(&&module, 0.5, &mut source_xs);
+        let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+        sk_out.fill_ternary_prob(0.5, &mut source_xs);
+        let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
 
         ksk.generate_from_sk(
             &module,
             &sk_in,
-            &sk_out,
+            &sk_out_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,
@@ -164,7 +168,7 @@ );
 
         ct.encrypt_zero_sk(
             &module,
-            &sk_in,
+            &sk_in_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,

@@ -1,16 +1,16 @@
 use backend::{Backend, FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScalarZnxToRef, Scratch, ZnxView, ZnxViewMut};
 use sampling::source::Source;
 
-use crate::{AutomorphismKey, GGSWCiphertext, GLWESecret, LWESecret, SecretDistribution};
+use crate::{Distribution, FourierGLWESecret, GGSWCiphertext, GLWEAutomorphismKey, LWESecret};
 
 pub struct BlindRotationKeyCGGI<B: Backend> {
     pub(crate) data: Vec<GGSWCiphertext<Vec<u8>, B>>,
-    pub(crate) dist: SecretDistribution,
+    pub(crate) dist: Distribution,
 }
 
 pub struct BlindRotationKeyFHEW<B: Backend> {
     pub(crate) data: Vec<GGSWCiphertext<Vec<u8>, B>>,
-    pub(crate) auto: Vec<AutomorphismKey<Vec<u8>, B>>,
+    pub(crate) auto: Vec<GLWEAutomorphismKey<Vec<u8>, B>>,
 }
 
 impl BlindRotationKeyCGGI<FFT64> {
@@ -19,7 +19,7 @@ let mut data: Vec<GGSWCiphertext<Vec<u8>, FFT64>> = Vec::with_capacity(lwe_degree);
         (0..lwe_degree).for_each(|_| data.push(GGSWCiphertext::alloc(module, basek, k, rows, 1, rank)));
         Self {
             data,
-            dist: SecretDistribution::NONE,
+            dist: Distribution::NONE,
         }
     }
 
@@ -30,7 +30,7 @@
     pub fn generate_from_sk<DataSkGLWE, DataSkLWE>(
         &mut self,
         module: &Module<FFT64>,
-        sk_glwe: &GLWESecret<DataSkGLWE, FFT64>,
+        sk_glwe: &FourierGLWESecret<DataSkGLWE, FFT64>,
         sk_lwe: &LWESecret<DataSkLWE>,
         source_xa: &mut Source,
         source_xe: &mut Source,
@@ -46,7 +46,7 @@ assert_eq!(self.data.len(), sk_lwe.n());
             assert_eq!(sk_glwe.n(), module.n());
             assert_eq!(sk_glwe.rank(), self.data[0].rank());
             match sk_lwe.dist {
-                SecretDistribution::BinaryBlock(_) | SecretDistribution::BinaryFixed(_) | SecretDistribution::BinaryProb(_) => {}
+                Distribution::BinaryBlock(_) | Distribution::BinaryFixed(_) | Distribution::BinaryProb(_) => {}
                 _ => panic!("invalid GLWESecret distribution: must be BinaryBlock, BinaryFixed or BinaryProb"),
             }
         }

@@ -0,0 +1,45 @@
+use backend::{Backend, Module, VecZnxDft, VecZnxDftAlloc};
+
+use crate::{Infos, div_ceil};
+
+pub struct FourierGLWECiphertext<C, B: Backend> {
+    pub data: VecZnxDft<C, B>,
+    pub basek: usize,
+    pub k: usize,
+}
+
+impl<B: Backend> FourierGLWECiphertext<Vec<u8>, B> {
+    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rank: usize) -> Self {
+        Self {
+            data: module.new_vec_znx_dft(rank + 1, div_ceil(k, basek)),
+            basek: basek,
+            k: k,
+        }
+    }
+
+    pub fn bytes_of(module: &Module<B>, basek: usize, k: usize, rank: usize) -> usize {
+        module.bytes_of_vec_znx_dft(rank + 1, div_ceil(k, basek))
+    }
+}
+
+impl<T, B: Backend> Infos for FourierGLWECiphertext<T, B> {
+    type Inner = VecZnxDft<T, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.data
+    }
+
+    fn basek(&self) -> usize {
+        self.basek
+    }
+
+    fn k(&self) -> usize {
+        self.k
+    }
+}
+
+impl<T, B: Backend> FourierGLWECiphertext<T, B> {
+    pub fn rank(&self) -> usize {
+        self.cols() - 1
+    }
+}

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

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

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

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

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

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

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

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

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

@@ -0,0 +1,136 @@
+use backend::{FFT64, Module, Scratch, VecZnx, VecZnxDftOps, VecZnxOps, ZnxZero};
+
+use crate::{FourierGLWECiphertext, GLWEAutomorphismKey, GLWECiphertext, GetRow, Infos, ScratchCore, SetRow};
+
+impl GLWEAutomorphismKey<Vec<u8>, FFT64> {
+    pub fn automorphism_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_in: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        let tmp_dft: usize = FourierGLWECiphertext::bytes_of(module, basek, k_in, rank);
+        let tmp_idft: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank);
+        let idft: usize = module.vec_znx_idft_tmp_bytes();
+        let keyswitch: usize = GLWECiphertext::keyswitch_inplace_scratch_space(module, basek, k_out, k_ksk, digits, rank);
+        tmp_dft + tmp_idft + idft + keyswitch
+    }
+
+    pub fn automorphism_inplace_scratch_space(
+        module: &Module<FFT64>,
+        basek: usize,
+        k_out: usize,
+        k_ksk: usize,
+        digits: usize,
+        rank: usize,
+    ) -> usize {
+        GLWEAutomorphismKey::automorphism_scratch_space(module, basek, k_out, k_out, k_ksk, digits, rank)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWEAutomorphismKey<DataSelf, FFT64> {
+    pub fn automorphism<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWEAutomorphismKey<DataLhs, FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(
+                self.rank_in(),
+                lhs.rank_in(),
+                "ksk_out input rank: {} != ksk_in input rank: {}",
+                self.rank_in(),
+                lhs.rank_in()
+            );
+            assert_eq!(
+                lhs.rank_out(),
+                rhs.rank_in(),
+                "ksk_in output rank: {} != ksk_apply input rank: {}",
+                self.rank_out(),
+                rhs.rank_in()
+            );
+            assert_eq!(
+                self.rank_out(),
+                rhs.rank_out(),
+                "ksk_out output rank: {} != ksk_apply output rank: {}",
+                self.rank_out(),
+                rhs.rank_out()
+            );
+        }
+
+        let cols_out: usize = rhs.rank_out() + 1;
+
+        let (mut tmp_dft, scratch1) = scratch.tmp_glwe_fourier(module, lhs.basek(), lhs.k(), lhs.rank());
+
+        (0..self.rank_in()).for_each(|col_i| {
+            (0..self.rows()).for_each(|row_j| {
+                // Extracts relevant row
+                lhs.get_row(module, row_j, col_i, &mut tmp_dft);
+
+                // Get a VecZnxBig from scratch space
+                let (mut tmp_idft_data, scratch2) = scratch1.tmp_vec_znx_big(module, cols_out, self.size());
+
+                // Switches input outside of DFT
+                (0..cols_out).for_each(|i| {
+                    module.vec_znx_idft(&mut tmp_idft_data, i, &tmp_dft.data, i, scratch2);
+                });
+
+                // Consumes to small vec znx
+                let mut tmp_idft_small_data: VecZnx<&mut [u8]> = tmp_idft_data.to_vec_znx_small();
+
+                // Reverts the automorphis key from (-pi^{-1}_{k}(s)a + s, a) to (-sa + pi_{k}(s), a)
+                (0..cols_out).for_each(|i| {
+                    module.vec_znx_automorphism_inplace(lhs.p(), &mut tmp_idft_small_data, i);
+                });
+
+                // Wraps into ciphertext
+                let mut tmp_idft: GLWECiphertext<&mut [u8]> = GLWECiphertext::<&mut [u8]> {
+                    data: tmp_idft_small_data,
+                    basek: self.basek(),
+                    k: self.k(),
+                };
+
+                // Key-switch (-sa + pi_{k}(s), a) to (-pi^{-1}_{k'}(s)a + pi_{k}(s), a)
+                tmp_idft.keyswitch_inplace(module, &rhs.key, scratch2);
+
+                // Applies back the automorphism X^{k}: (-pi^{-1}_{k'}(s)a + pi_{k}(s), a) -> (-pi^{-1}_{k'+k}(s)a + s, a)
+                // and switches back to DFT domain
+                (0..self.rank_out() + 1).for_each(|i| {
+                    module.vec_znx_automorphism_inplace(lhs.p(), &mut tmp_idft.data, i);
+                    module.vec_znx_dft(1, 0, &mut tmp_dft.data, i, &tmp_idft.data, i);
+                });
+
+                // Sets back the relevant row
+                self.set_row(module, row_j, col_i, &tmp_dft);
+            });
+        });
+
+        tmp_dft.data.zero();
+
+        (self.rows().min(lhs.rows())..self.rows()).for_each(|row_i| {
+            (0..self.rank_in()).for_each(|col_j| {
+                self.set_row(module, row_i, col_j, &tmp_dft);
+            });
+        });
+
+        self.p = (lhs.p * rhs.p) % (module.cyclotomic_order() as i64);
+    }
+
+    pub fn automorphism_inplace<DataRhs: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) {
+        unsafe {
+            let self_ptr: *mut GLWEAutomorphismKey<DataSelf, FFT64> = self as *mut GLWEAutomorphismKey<DataSelf, FFT64>;
+            self.automorphism(&module, &*self_ptr, rhs, scratch);
+        }
+    }
+}

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

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

@@ -0,0 +1,253 @@
+use backend::{
+    FFT64, Module, ScalarZnx, ScalarZnxDftOps, ScalarZnxOps, Scratch, VecZnxAlloc, VecZnxDftAlloc, VecZnxOps, ZnxInfos, ZnxZero,
+};
+use sampling::source::Source;
+
+use crate::{
+    FourierGLWESecret, GGLWECiphertext, GLWEAutomorphismKey, GLWECiphertext, GLWESecret, GLWESwitchingKey, GLWETensorKey, Infos,
+    ScratchCore, SetRow, div_ceil,
+};
+
+impl GGLWECiphertext<Vec<u8>, FFT64> {
+    pub fn generate_from_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
+        let size = div_ceil(k, basek);
+        GLWECiphertext::encrypt_sk_scratch_space(module, basek, k)
+            + module.bytes_of_vec_znx(rank + 1, size)
+            + module.bytes_of_vec_znx(1, size)
+            + module.bytes_of_vec_znx_dft(rank + 1, size)
+    }
+
+    pub fn generate_from_pk_scratch_space(_module: &Module<FFT64>, _basek: usize, _k: usize, _rank: usize) -> usize {
+        unimplemented!()
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GGLWECiphertext<DataSelf, FFT64> {
+    pub fn encrypt_sk<DataPt: AsRef<[u8]>, DataSk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        pt: &ScalarZnx<DataPt>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank_in(), pt.cols());
+            assert_eq!(self.rank_out(), sk.rank());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(sk.n(), module.n());
+            assert_eq!(pt.n(), module.n());
+            assert!(
+                scratch.available()
+                    >= GGLWECiphertext::generate_from_sk_scratch_space(module, self.basek(), self.k(), self.rank()),
+                "scratch.available: {} < GGLWECiphertext::generate_from_sk_scratch_space(module, self.rank()={}, \
+                 self.size()={}): {}",
+                scratch.available(),
+                self.rank(),
+                self.size(),
+                GGLWECiphertext::generate_from_sk_scratch_space(module, self.basek(), self.k(), self.rank())
+            );
+            assert!(
+                self.rows() * self.digits() * self.basek() <= self.k(),
+                "self.rows() : {} * self.digits() : {} * self.basek() : {} = {} >= self.k() = {}",
+                self.rows(),
+                self.digits(),
+                self.basek(),
+                self.rows() * self.digits() * self.basek(),
+                self.k()
+            );
+        }
+
+        let rows: usize = self.rows();
+        let digits: usize = self.digits();
+        let basek: usize = self.basek();
+        let k: usize = self.k();
+        let rank_in: usize = self.rank_in();
+        let rank_out: usize = self.rank_out();
+
+        let (mut tmp_pt, scrach_1) = scratch.tmp_glwe_pt(module, basek, k);
+        let (mut tmp_ct, scrach_2) = scrach_1.tmp_glwe_ct(module, basek, k, rank_out);
+        let (mut tmp_ct_dft, scratch_3) = scrach_2.tmp_glwe_fourier(module, basek, k, rank_out);
+
+        // For each input column (i.e. rank) produces a GGLWE ciphertext of rank_out+1 columns
+        //
+        // Example for ksk rank 2 to rank 3:
+        //
+        // (-(a0*s0 + a1*s1 + a2*s2) + s0', a0, a1, a2)
+        // (-(b0*s0 + b1*s1 + b2*s2) + s0', b0, b1, b2)
+        //
+        // Example ksk rank 2 to rank 1
+        //
+        // (-(a*s) + s0, a)
+        // (-(b*s) + s1, b)
+        (0..rank_in).for_each(|col_i| {
+            (0..rows).for_each(|row_i| {
+                // Adds the scalar_znx_pt to the i-th limb of the vec_znx_pt
+                tmp_pt.data.zero(); // zeroes for next iteration
+                module.vec_znx_add_scalar_inplace(
+                    &mut tmp_pt.data,
+                    0,
+                    (digits - 1) + row_i * digits,
+                    pt,
+                    col_i,
+                );
+                module.vec_znx_normalize_inplace(basek, &mut tmp_pt.data, 0, scratch_3);
+
+                // rlwe encrypt of vec_znx_pt into vec_znx_ct
+                tmp_ct.encrypt_sk(module, &tmp_pt, sk, source_xa, source_xe, sigma, scratch_3);
+
+                // Switch vec_znx_ct into DFT domain
+                tmp_ct.dft(module, &mut tmp_ct_dft);
+
+                // Stores vec_znx_dft_ct into thw i-th row of the MatZnxDft
+                self.set_row(module, row_i, col_i, &tmp_ct_dft);
+            });
+        });
+    }
+}
+
+impl GLWESwitchingKey<Vec<u8>, FFT64> {
+    pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
+        GGLWECiphertext::generate_from_sk_scratch_space(module, basek, k, rank)
+    }
+
+    pub fn encrypt_pk_scratch_space(module: &Module<FFT64>, _basek: usize, _k: usize, _rank: usize) -> usize {
+        GGLWECiphertext::generate_from_pk_scratch_space(module, _basek, _k, _rank)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWESwitchingKey<DataSelf, FFT64> {
+    pub fn generate_from_sk<DataSkIn: AsRef<[u8]>, DataSkOut: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        sk_in: &GLWESecret<DataSkIn>,
+        sk_out: &FourierGLWESecret<DataSkOut, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        self.0.encrypt_sk(
+            module,
+            &sk_in.data,
+            sk_out,
+            source_xa,
+            source_xe,
+            sigma,
+            scratch,
+        );
+    }
+}
+
+impl GLWEAutomorphismKey<Vec<u8>, FFT64> {
+    pub fn generate_from_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
+        GGLWECiphertext::generate_from_sk_scratch_space(module, basek, k, rank) + GLWESecret::bytes_of(module, rank)
+    }
+
+    pub fn generate_from_pk_scratch_space(module: &Module<FFT64>, _basek: usize, _k: usize, _rank: usize) -> usize {
+        GGLWECiphertext::generate_from_pk_scratch_space(module, _basek, _k, _rank)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWEAutomorphismKey<DataSelf, FFT64> {
+    pub fn generate_from_sk<DataSk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        p: i64,
+        sk: &GLWESecret<DataSk>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.n(), module.n());
+            assert_eq!(sk.n(), module.n());
+            assert_eq!(self.rank_out(), self.rank_in());
+            assert_eq!(sk.rank(), self.rank());
+            assert!(
+                scratch.available()
+                    >= GLWEAutomorphismKey::generate_from_sk_scratch_space(module, self.basek(), self.k(), self.rank()),
+                "scratch.available(): {} < AutomorphismKey::generate_from_sk_scratch_space(module, self.rank()={}, \
+                 self.size()={}): {}",
+                scratch.available(),
+                self.rank(),
+                self.size(),
+                GLWEAutomorphismKey::generate_from_sk_scratch_space(module, self.basek(), self.k(), self.rank())
+            )
+        }
+
+        let (mut sk_out_dft, scratch_1) = scratch.tmp_fourier_sk(module, sk.rank());
+
+        {
+            let (mut sk_out, _) = scratch_1.tmp_sk(module, sk.rank());
+            (0..self.rank()).for_each(|i| {
+                module.scalar_znx_automorphism(
+                    module.galois_element_inv(p),
+                    &mut sk_out.data,
+                    i,
+                    &sk.data,
+                    i,
+                );
+            });
+            sk_out_dft.set(module, &sk_out);
+        }
+
+        self.key.generate_from_sk(
+            module,
+            &sk,
+            &sk_out_dft,
+            source_xa,
+            source_xe,
+            sigma,
+            scratch_1,
+        );
+
+        self.p = p;
+    }
+}
+
+impl GLWETensorKey<Vec<u8>, FFT64> {
+    pub fn generate_from_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
+        GLWESecret::bytes_of(module, 1)
+            + FourierGLWESecret::bytes_of(module, 1)
+            + GLWESwitchingKey::encrypt_sk_scratch_space(module, basek, k, rank)
+    }
+}
+
+impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWETensorKey<DataSelf, FFT64> {
+    pub fn generate_from_sk<DataSk: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), sk.rank());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(sk.n(), module.n());
+        }
+
+        let rank: usize = self.rank();
+
+        let (mut sk_ij, scratch1) = scratch.tmp_sk(module, 1);
+        let (mut sk_ij_dft, scratch2) = scratch1.tmp_fourier_sk(module, 1);
+
+        (0..rank).for_each(|i| {
+            (i..rank).for_each(|j| {
+                module.svp_apply(&mut sk_ij_dft.data, 0, &sk.data, i, &sk.data, j);
+                module.scalar_znx_idft(&mut sk_ij.data, 0, &sk_ij_dft.data, 0, scratch2);
+                self.at_mut(i, j)
+                    .generate_from_sk(module, &sk_ij, sk, source_xa, source_xe, sigma, scratch2);
+            });
+        })
+    }
+}

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

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

@@ -0,0 +1,91 @@
+use backend::{Backend, FFT64, MatZnxDft, MatZnxDftOps, Module};
+
+use crate::{FourierGLWECiphertext, GGLWECiphertext, GetRow, Infos, SetRow};
+
+pub struct GLWESwitchingKey<Data, B: Backend>(pub(crate) GGLWECiphertext<Data, B>);
+
+impl GLWESwitchingKey<Vec<u8>, FFT64> {
+    pub fn alloc(
+        module: &Module<FFT64>,
+        basek: usize,
+        k: usize,
+        rows: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> Self {
+        GLWESwitchingKey(GGLWECiphertext::alloc(
+            module, basek, k, rows, digits, rank_in, rank_out,
+        ))
+    }
+
+    pub fn bytes_of(
+        module: &Module<FFT64>,
+        basek: usize,
+        k: usize,
+        rows: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> usize {
+        GGLWECiphertext::<Vec<u8>, FFT64>::bytes_of(module, basek, k, rows, digits, rank_in, rank_out)
+    }
+}
+
+impl<T, B: Backend> Infos for GLWESwitchingKey<T, B> {
+    type Inner = MatZnxDft<T, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        self.0.inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.0.basek()
+    }
+
+    fn k(&self) -> usize {
+        self.0.k()
+    }
+}
+
+impl<T, B: Backend> GLWESwitchingKey<T, B> {
+    pub fn rank(&self) -> usize {
+        self.0.data.cols_out() - 1
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.0.data.cols_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.0.data.cols_out() - 1
+    }
+
+    pub fn digits(&self) -> usize {
+        self.0.digits()
+    }
+}
+
+impl<C: AsRef<[u8]>> GetRow<FFT64> for GLWESwitchingKey<C, FFT64> {
+    fn get_row<R: AsMut<[u8]> + AsRef<[u8]>>(
+        &self,
+        module: &Module<FFT64>,
+        row_i: usize,
+        col_j: usize,
+        res: &mut FourierGLWECiphertext<R, FFT64>,
+    ) {
+        module.mat_znx_dft_get_row(&mut res.data, &self.0.data, row_i, col_j);
+    }
+}
+
+impl<C: AsMut<[u8]> + AsRef<[u8]>> SetRow<FFT64> for GLWESwitchingKey<C, FFT64> {
+    fn set_row<R: AsRef<[u8]>>(
+        &mut self,
+        module: &Module<FFT64>,
+        row_i: usize,
+        col_j: usize,
+        a: &FourierGLWECiphertext<R, FFT64>,
+    ) {
+        module.mat_znx_dft_set_row(&mut self.0.data, row_i, col_j, &a.data);
+    }
+}

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

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

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

@@ -6,8 +6,8 @@ };
 use sampling::source::Source;
 
 use crate::{
-    AutomorphismKey, FourierGLWECiphertext, GLWECiphertext, GLWESecret, GLWESwitchingKey, GetRow, Infos, ScratchCore, SetRow,
-    TensorKey, div_ceil,
+    FourierGLWECiphertext, FourierGLWESecret, GLWEAutomorphismKey, GLWECiphertext, GLWESwitchingKey, GLWETensorKey, GetRow,
+    Infos, ScratchCore, SetRow, div_ceil,
 };
 
 pub struct GGSWCiphertext<C, B: Backend> {
@@ -246,7 +246,7 @@ pub fn encrypt_sk<DataPt: AsRef<[u8]>, DataSk: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
         pt: &ScalarZnx<DataPt>,
-        sk: &GLWESecret<DataSk, FFT64>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
         source_xa: &mut Source,
         source_xe: &mut Source,
         sigma: f64,
@@ -304,7 +304,7 @@ module: &Module<FFT64>,
         col_j: usize,
         res: &mut R,
         ci_dft: &VecZnxDft<DataCi, FFT64>,
-        tsk: &TensorKey<DataTsk, FFT64>,
+        tsk: &GLWETensorKey<DataTsk, FFT64>,
         scratch: &mut Scratch,
     ) where
         R: VecZnxToMut,
@@ -408,7 +408,7 @@ &mut self,
         module: &Module<FFT64>,
         lhs: &GGSWCiphertext<DataLhs, FFT64>,
         ksk: &GLWESwitchingKey<DataKsk, FFT64>,
-        tsk: &TensorKey<DataTsk, FFT64>,
+        tsk: &GLWETensorKey<DataTsk, FFT64>,
         scratch: &mut Scratch,
     ) {
         let rank: usize = self.rank();
@@ -449,7 +449,7 @@ pub fn keyswitch_inplace<DataKsk: AsRef<[u8]>, DataTsk: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
         ksk: &GLWESwitchingKey<DataKsk, FFT64>,
-        tsk: &TensorKey<DataTsk, FFT64>,
+        tsk: &GLWETensorKey<DataTsk, FFT64>,
         scratch: &mut Scratch,
     ) {
         unsafe {
@@ -462,8 +462,8 @@ pub fn automorphism<DataLhs: AsRef<[u8]>, DataAk: AsRef<[u8]>, DataTsk: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
         lhs: &GGSWCiphertext<DataLhs, FFT64>,
-        auto_key: &AutomorphismKey<DataAk, FFT64>,
-        tensor_key: &TensorKey<DataTsk, FFT64>,
+        auto_key: &GLWEAutomorphismKey<DataAk, FFT64>,
+        tensor_key: &GLWETensorKey<DataTsk, FFT64>,
         scratch: &mut Scratch,
     ) {
         #[cfg(debug_assertions)]
@@ -551,8 +551,8 @@
     pub fn automorphism_inplace<DataKsk: AsRef<[u8]>, DataTsk: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
-        auto_key: &AutomorphismKey<DataKsk, FFT64>,
-        tensor_key: &TensorKey<DataTsk, FFT64>,
+        auto_key: &GLWEAutomorphismKey<DataKsk, FFT64>,
+        tensor_key: &GLWETensorKey<DataTsk, FFT64>,
         scratch: &mut Scratch,
     ) {
         unsafe {

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

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

@@ -1,6 +1,6 @@
 use backend::{FFT64, Module, Scratch, VecZnxOps};
 
-use crate::{AutomorphismKey, GLWECiphertext};
+use crate::{GLWEAutomorphismKey, GLWECiphertext};
 
 impl GLWECiphertext<Vec<u8>> {
     pub fn automorphism_scratch_space(
@@ -32,7 +32,7 @@ pub fn automorphism<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
         lhs: &GLWECiphertext<DataLhs>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
         scratch: &mut Scratch,
     ) {
         self.keyswitch(module, lhs, &rhs.key, scratch);
@@ -44,7 +44,7 @@
     pub fn automorphism_inplace<DataRhs: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
         scratch: &mut Scratch,
     ) {
         self.keyswitch_inplace(module, &rhs.key, scratch);
@@ -57,7 +57,7 @@ pub fn automorphism_add<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
         lhs: &GLWECiphertext<DataLhs>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
         scratch: &mut Scratch,
     ) {
         Self::keyswitch_private::<_, _, 1>(self, rhs.p(), module, lhs, &rhs.key, scratch);
@@ -66,7 +66,7 @@
     pub fn automorphism_add_inplace<DataRhs: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
         scratch: &mut Scratch,
     ) {
         unsafe {
@@ -79,7 +79,7 @@ pub fn automorphism_sub_ab<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
         lhs: &GLWECiphertext<DataLhs>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
         scratch: &mut Scratch,
     ) {
         Self::keyswitch_private::<_, _, 2>(self, rhs.p(), module, lhs, &rhs.key, scratch);
@@ -88,7 +88,7 @@
     pub fn automorphism_sub_ab_inplace<DataRhs: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
         scratch: &mut Scratch,
     ) {
         unsafe {
@@ -101,7 +101,7 @@ pub fn automorphism_sub_ba<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
         lhs: &GLWECiphertext<DataLhs>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
         scratch: &mut Scratch,
     ) {
         Self::keyswitch_private::<_, _, 3>(self, rhs.p(), module, lhs, &rhs.key, scratch);
@@ -110,7 +110,7 @@
     pub fn automorphism_sub_ba_inplace<DataRhs: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
-        rhs: &AutomorphismKey<DataRhs, FFT64>,
+        rhs: &GLWEAutomorphismKey<DataRhs, FFT64>,
         scratch: &mut Scratch,
     ) {
         unsafe {

@@ -1,6 +1,6 @@
 use backend::{FFT64, Module, ScalarZnxDftOps, Scratch, VecZnxBigOps, VecZnxDftOps, ZnxZero};
 
-use crate::{GLWECiphertext, GLWEPlaintext, GLWESecret, Infos};
+use crate::{FourierGLWESecret, GLWECiphertext, GLWEPlaintext, Infos};
 
 impl<DataSelf: AsRef<[u8]>> GLWECiphertext<DataSelf> {
     pub fn clone(&self) -> GLWECiphertext<Vec<u8>> {
@@ -15,7 +15,7 @@ pub fn decrypt<DataPt: AsMut<[u8]> + AsRef<[u8]>, DataSk: AsRef<[u8]>>(
         &self,
         module: &Module<FFT64>,
         pt: &mut GLWEPlaintext<DataPt>,
-        sk: &GLWESecret<DataSk, FFT64>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
         scratch: &mut Scratch,
     ) {
         #[cfg(debug_assertions)]
@@ -36,7 +36,7 @@ (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);
+                module.svp_apply_inplace(&mut ci_dft, 0, &sk.data, i - 1);
                 let ci_big = module.vec_znx_idft_consume(ci_dft);
 
                 // c0_big += a[i] * s[i]

@@ -4,7 +4,7 @@ VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDftAlloc, VecZnxDftOps, VecZnxOps, ZnxZero,
 };
 use sampling::source::Source;
 
-use crate::{GLWECiphertext, GLWEPlaintext, GLWEPublicKey, GLWESecret, Infos, SIX_SIGMA, div_ceil, keys::SecretDistribution};
+use crate::{FourierGLWESecret, GLWECiphertext, GLWEPlaintext, GLWEPublicKey, Infos, SIX_SIGMA, dist::Distribution, div_ceil};
 
 impl GLWECiphertext<Vec<u8>> {
     pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize) -> usize {
@@ -24,7 +24,7 @@ pub fn encrypt_sk<DataPt: AsRef<[u8]>, DataSk: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
         pt: &GLWEPlaintext<DataPt>,
-        sk: &GLWESecret<DataSk, FFT64>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
         source_xa: &mut Source,
         source_xe: &mut Source,
         sigma: f64,
@@ -44,7 +44,7 @@
     pub fn encrypt_zero_sk<DataSk: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
-        sk: &GLWESecret<DataSk, FFT64>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
         source_xa: &mut Source,
         source_xe: &mut Source,
         sigma: f64,
@@ -106,7 +106,7 @@ 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>,
+        sk: &FourierGLWESecret<DataSk, FFT64>,
         source_xa: &mut Source,
         source_xe: &mut Source,
         sigma: f64,
@@ -148,7 +148,7 @@ 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);
+                module.svp_apply_inplace(&mut ci_dft, 0, &sk.data, i - 1);
                 let ci_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume(ci_dft);
 
                 // use c[0] as buffer, which is overwritten later by the normalization step
@@ -213,16 +213,16 @@
         {
             let (mut u, _) = scratch_1.tmp_scalar_znx(module, 1);
             match pk.dist {
-                SecretDistribution::NONE => panic!(
+                Distribution::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 => {}
+                Distribution::TernaryFixed(hw) => u.fill_ternary_hw(0, hw, source_xu),
+                Distribution::TernaryProb(prob) => u.fill_ternary_prob(0, prob, source_xu),
+                Distribution::BinaryFixed(hw) => u.fill_binary_hw(0, hw, source_xu),
+                Distribution::BinaryProb(prob) => u.fill_binary_prob(0, prob, source_xu),
+                Distribution::BinaryBlock(block_size) => u.fill_binary_block(0, block_size, source_xu),
+                Distribution::ZERO => {}
             }
 
             module.svp_prepare(&mut u_dft, 0, &u, 0);

@@ -11,24 +11,13 @@ 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::*;
+pub use ciphertext::GLWECiphertext;
+pub(crate) use ciphertext::{GLWECiphertextToMut, GLWECiphertextToRef};
+pub use ops::GLWEOps;
+pub use packing::GLWEPacker;
+pub use plaintext::GLWEPlaintext;
+pub use public_key::GLWEPublicKey;
+pub use secret::GLWESecret;
 
 #[cfg(test)]
 mod test_fft64;

@@ -1,4 +1,4 @@
-use crate::{AutomorphismKey, GLWECiphertext, GLWEOps, Infos, ScratchCore};
+use crate::{GLWEAutomorphismKey, GLWECiphertext, GLWEOps, Infos, ScratchCore};
 use std::collections::HashMap;
 
 use backend::{FFT64, Module, Scratch};
@@ -7,7 +7,7 @@ /// [StreamPacker] enables only the fly GLWE packing
 /// with constant memory of Log(N) ciphertexts.
 /// Main difference with usual GLWE packing is that
 /// the output is bit-reversed.
-pub struct StreamPacker {
+pub struct GLWEPacker {
     accumulators: Vec<Accumulator>,
     log_batch: usize,
     counter: usize,
@@ -39,7 +39,7 @@ }
     }
 }
 
-impl StreamPacker {
+impl GLWEPacker {
     /// Instantiates a new [StreamPacker].
     ///
     /// #Arguments
@@ -98,7 +98,7 @@ &mut self,
         module: &Module<FFT64>,
         res: &mut Vec<GLWECiphertext<Vec<u8>>>,
         a: Option<&GLWECiphertext<DataA>>,
-        auto_keys: &HashMap<i64, AutomorphismKey<DataAK, FFT64>>,
+        auto_keys: &HashMap<i64, GLWEAutomorphismKey<DataAK, FFT64>>,
         scratch: &mut Scratch,
     ) {
         pack_core(
@@ -125,7 +125,7 @@ pub fn flush<DataAK: AsRef<[u8]>>(
         &mut self,
         module: &Module<FFT64>,
         res: &mut Vec<GLWECiphertext<Vec<u8>>>,
-        auto_keys: &HashMap<i64, AutomorphismKey<DataAK, FFT64>>,
+        auto_keys: &HashMap<i64, GLWEAutomorphismKey<DataAK, FFT64>>,
         scratch: &mut Scratch,
     ) {
         if self.counter != 0 {
@@ -151,7 +151,7 @@ module: &Module<FFT64>,
     a: Option<&GLWECiphertext<D>>,
     accumulators: &mut [Accumulator],
     i: usize,
-    auto_keys: &HashMap<i64, AutomorphismKey<DataAK, FFT64>>,
+    auto_keys: &HashMap<i64, GLWEAutomorphismKey<DataAK, FFT64>>,
     scratch: &mut Scratch,
 ) {
     let log_n: usize = module.log_n();
@@ -215,7 +215,7 @@ module: &Module<FFT64>,
     acc: &mut Accumulator,
     b: Option<&GLWECiphertext<D>>,
     i: usize,
-    auto_keys: &HashMap<i64, AutomorphismKey<DataAK, FFT64>>,
+    auto_keys: &HashMap<i64, GLWEAutomorphismKey<DataAK, FFT64>>,
     scratch: &mut Scratch,
 ) {
     let log_n: usize = module.log_n();

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

@@ -1,18 +1,18 @@
 use backend::{Backend, FFT64, Module, ScratchOwned, VecZnxDft};
 use sampling::source::Source;
 
-use crate::{FourierGLWECiphertext, GLWESecret, Infos, keys::SecretDistribution};
+use crate::{FourierGLWECiphertext, FourierGLWESecret, Infos, dist::Distribution};
 
 pub struct GLWEPublicKey<D, B: Backend> {
     pub(crate) data: FourierGLWECiphertext<D, B>,
-    pub(crate) dist: SecretDistribution,
+    pub(crate) dist: Distribution,
 }
 
 impl<B: Backend> GLWEPublicKey<Vec<u8>, B> {
     pub fn alloc(module: &Module<B>, basek: usize, k: usize, rank: usize) -> Self {
         Self {
             data: FourierGLWECiphertext::alloc(module, basek, k, rank),
-            dist: SecretDistribution::NONE,
+            dist: Distribution::NONE,
         }
     }
 
@@ -47,7 +47,7 @@ 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>,
+        sk: &FourierGLWESecret<S, FFT64>,
         source_xa: &mut Source,
         source_xe: &mut Source,
         sigma: f64,
@@ -55,7 +55,7 @@ ) {
         #[cfg(debug_assertions)]
         {
             match sk.dist {
-                SecretDistribution::NONE => panic!("invalid sk: SecretDistribution::NONE"),
+                Distribution::NONE => panic!("invalid sk: SecretDistribution::NONE"),
                 _ => {}
             }
         }

@@ -1,31 +1,27 @@
-use backend::{
-    Backend, FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScalarZnxDft, ScalarZnxDftAlloc, ScalarZnxDftOps, ZnxInfos, ZnxZero,
-};
+use backend::{Backend, Module, ScalarZnx, ScalarZnxAlloc, ZnxInfos, ZnxZero};
 use sampling::source::Source;
 
-use crate::keys::SecretDistribution;
+use crate::dist::Distribution;
 
-pub struct GLWESecret<T, B: Backend> {
+pub struct GLWESecret<T> {
     pub(crate) data: ScalarZnx<T>,
-    pub(crate) data_fourier: ScalarZnxDft<T, B>,
-    pub(crate) dist: SecretDistribution,
+    pub(crate) dist: Distribution,
 }
 
-impl<B: Backend> GLWESecret<Vec<u8>, B> {
-    pub fn alloc(module: &Module<B>, rank: usize) -> Self {
+impl GLWESecret<Vec<u8>> {
+    pub fn alloc<B: Backend>(module: &Module<B>, rank: usize) -> Self {
         Self {
             data: module.new_scalar_znx(rank),
-            data_fourier: module.new_scalar_znx_dft(rank),
-            dist: SecretDistribution::NONE,
+            dist: Distribution::NONE,
         }
     }
 
-    pub fn bytes_of(module: &Module<B>, rank: usize) -> usize {
-        module.bytes_of_scalar_znx(rank) + module.bytes_of_scalar_znx_dft(rank)
+    pub fn bytes_of<B: Backend>(module: &Module<B>, rank: usize) -> usize {
+        module.bytes_of_scalar_znx(rank)
     }
 }
 
-impl<DataSelf, B: Backend> GLWESecret<DataSelf, B> {
+impl<DataSelf> GLWESecret<DataSelf> {
     pub fn n(&self) -> usize {
         self.data.n()
     }
@@ -39,55 +35,50 @@ 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) {
+impl<S: AsMut<[u8]> + AsRef<[u8]>> GLWESecret<S> {
+    pub fn fill_ternary_prob(&mut self, prob: f64, source: &mut Source) {
         (0..self.rank()).for_each(|i| {
             self.data.fill_ternary_prob(i, prob, source);
         });
-        self.prep_fourier(module);
-        self.dist = SecretDistribution::TernaryProb(prob);
+        self.dist = Distribution::TernaryProb(prob);
     }
 
-    pub fn fill_ternary_hw(&mut self, module: &Module<FFT64>, hw: usize, source: &mut Source) {
+    pub fn fill_ternary_hw(&mut self, hw: usize, source: &mut Source) {
         (0..self.rank()).for_each(|i| {
             self.data.fill_ternary_hw(i, hw, source);
         });
-        self.prep_fourier(module);
-        self.dist = SecretDistribution::TernaryFixed(hw);
+        self.dist = Distribution::TernaryFixed(hw);
     }
 
-    pub fn fill_binary_prob(&mut self, module: &Module<FFT64>, prob: f64, source: &mut Source) {
+    pub fn fill_binary_prob(&mut self, prob: f64, source: &mut Source) {
         (0..self.rank()).for_each(|i| {
             self.data.fill_binary_prob(i, prob, source);
         });
-        self.prep_fourier(module);
-        self.dist = SecretDistribution::BinaryProb(prob);
+        self.dist = Distribution::BinaryProb(prob);
     }
 
-    pub fn fill_binary_hw(&mut self, module: &Module<FFT64>, hw: usize, source: &mut Source) {
+    pub fn fill_binary_hw(&mut self, hw: usize, source: &mut Source) {
         (0..self.rank()).for_each(|i| {
             self.data.fill_binary_hw(i, hw, source);
         });
-        self.prep_fourier(module);
-        self.dist = SecretDistribution::BinaryFixed(hw);
+        self.dist = Distribution::BinaryFixed(hw);
     }
 
-    pub fn fill_binary_block(&mut self, module: &Module<FFT64>, block_size: usize, source: &mut Source) {
+    pub fn fill_binary_block(&mut self, block_size: usize, source: &mut Source) {
         (0..self.rank()).for_each(|i| {
             self.data.fill_binary_block(i, block_size, source);
         });
-        self.prep_fourier(module);
-        self.dist = SecretDistribution::BinaryBlock(block_size);
+        self.dist = Distribution::BinaryBlock(block_size);
     }
 
     pub fn fill_zero(&mut self) {
         self.data.zero();
-        self.dist = SecretDistribution::ZERO;
+        self.dist = Distribution::ZERO;
     }
 
-    pub(crate) fn prep_fourier(&mut self, module: &Module<FFT64>) {
-        (0..self.rank()).for_each(|i| {
-            module.svp_prepare(&mut self.data_fourier, i, &self.data, i);
-        });
-    }
+    // 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);
+    // });
+    // }
 }

@@ -1,1 +1,224 @@
+use backend::{FFT64, FillUniform, Module, ScratchOwned, Stats, VecZnxOps};
 
+use sampling::source::Source;
+
+use crate::{
+    FourierGLWESecret, GLWEAutomorphismKey, GLWECiphertext, GLWEPlaintext, GLWESecret, Infos, div_ceil,
+    noise::log2_std_noise_gglwe_product,
+};
+
+#[test]
+fn apply_inplace() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_ct: usize = 60;
+    let digits: usize = div_ceil(k_ct, basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_ct + basek * di;
+            println!("test automorphism_inplace digits: {} rank: {}", di, rank);
+            test_automorphism_inplace(log_n, basek, -5, k_ct, k_ksk, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn apply() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_in: usize = 60;
+    let digits: usize = div_ceil(k_in, basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_in + basek * di;
+            let k_out: usize = k_ksk; // Better capture noise.
+            println!("test automorphism digits: {} rank: {}", di, rank);
+            test_automorphism(log_n, basek, -5, k_out, k_in, k_ksk, di, rank, 3.2);
+        })
+    });
+}
+
+fn test_automorphism(
+    log_n: usize,
+    basek: usize,
+    p: i64,
+    k_out: usize,
+    k_in: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = div_ceil(k_in, basek * digits);
+
+    let mut autokey: GLWEAutomorphismKey<Vec<u8>, FFT64> = GLWEAutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
+    let mut ct_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_in, rank);
+    let mut ct_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_out, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWEAutomorphismKey::generate_from_sk_scratch_space(&module, basek, autokey.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_out.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_in.k())
+            | GLWECiphertext::automorphism_scratch_space(
+                &module,
+                basek,
+                ct_out.k(),
+                ct_in.k(),
+                autokey.k(),
+                digits,
+                rank,
+            ),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
+
+    autokey.generate_from_sk(
+        &module,
+        p,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_in.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_out.automorphism(&module, &ct_in, &autokey, scratch.borrow());
+    ct_out.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
+    module.vec_znx_automorphism_inplace(p, &mut pt_want.data, 0);
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+    module.vec_znx_normalize_inplace(basek, &mut pt_have.data, 0, scratch.borrow());
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+
+    println!("{}", noise_have);
+
+    let noise_want: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank as f64,
+        k_in,
+        k_ksk,
+    );
+
+    assert!(
+        noise_have <= noise_want + 1.0,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_automorphism_inplace(
+    log_n: usize,
+    basek: usize,
+    p: i64,
+    k_ct: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = div_ceil(k_ct, basek * digits);
+
+    let mut autokey: GLWEAutomorphismKey<Vec<u8>, FFT64> = GLWEAutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWEAutomorphismKey::generate_from_sk_scratch_space(&module, basek, autokey.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
+            | GLWECiphertext::automorphism_inplace_scratch_space(&module, basek, ct.k(), autokey.k(), digits, rank),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
+
+    autokey.generate_from_sk(
+        &module,
+        p,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct.automorphism_inplace(&module, &autokey, scratch.borrow());
+    ct.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
+    module.vec_znx_automorphism_inplace(p, &mut pt_want.data, 0);
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+    module.vec_znx_normalize_inplace(basek, &mut pt_have.data, 0, scratch.borrow());
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+    let noise_want: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank as f64,
+        k_ct,
+        k_ksk,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}

@@ -2,7 +2,7 @@ use backend::{Decoding, Encoding, FFT64, Module, ScratchOwned, Stats, VecZnxOps, ZnxZero};
 use itertools::izip;
 use sampling::source::Source;
 
-use crate::{FourierGLWECiphertext, GLWECiphertext, GLWEPlaintext, GLWEPublicKey, GLWESecret, Infos};
+use crate::{FourierGLWECiphertext, FourierGLWESecret, GLWECiphertext, GLWEPlaintext, GLWEPublicKey, GLWESecret, Infos};
 
 #[test]
 fn encrypt_sk() {
@@ -46,8 +46,9 @@ GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
             | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k()),
     );
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     let mut data_want: Vec<i64> = vec![0i64; module.n()];
 
@@ -60,7 +61,7 @@
     ct.encrypt_sk(
         &module,
         &pt,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -69,7 +70,7 @@ );
 
     pt.data.zero();
 
-    ct.decrypt(&module, &mut pt, &sk, scratch.borrow());
+    ct.decrypt(&module, &mut pt, &sk_dft, scratch.borrow());
 
     let mut data_have: Vec<i64> = vec![0i64; module.n()];
 
@@ -98,8 +99,9 @@ let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([1u8; 32]);
     let mut source_xa: Source = Source::new([0u8; 32]);
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     let mut ct_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank);
 
@@ -110,13 +112,13 @@ );
 
     ct_dft.encrypt_zero_sk(
         &module,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
         scratch.borrow(),
     );
-    ct_dft.decrypt(&module, &mut pt, &sk, scratch.borrow());
+    ct_dft.decrypt(&module, &mut pt, &sk_dft, scratch.borrow());
 
     assert!((sigma - pt.data.std(0, basek) * (k_ct as f64).exp2()) <= 0.2);
 }
@@ -132,11 +134,12 @@ let mut source_xe: Source = Source::new([0u8; 32]);
     let mut source_xa: Source = Source::new([0u8; 32]);
     let mut source_xu: Source = Source::new([0u8; 32]);
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     let mut pk: GLWEPublicKey<Vec<u8>, FFT64> = GLWEPublicKey::alloc(&module, basek, k_pk, rank);
-    pk.generate_from_sk(&module, &sk, &mut source_xa, &mut source_xe, sigma);
+    pk.generate_from_sk(&module, &sk_dft, &mut source_xa, &mut source_xe, sigma);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
@@ -164,7 +167,7 @@ );
 
     let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
 
-    ct.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+    ct.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
 
     module.vec_znx_sub_ab_inplace(&mut pt_want.data, 0, &pt_have.data, 0);
 

@@ -1,86 +1,16 @@
-use backend::{
-    Decoding, Encoding, FFT64, FillUniform, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned, Stats, VecZnxOps, ZnxViewMut,
-    ZnxZero,
-};
-use itertools::izip;
+use backend::{FFT64, FillUniform, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned, Stats, VecZnxOps, ZnxViewMut};
 use sampling::source::Source;
 
 use crate::{
-    FourierGLWECiphertext, GGSWCiphertext, GLWECiphertext, GLWEPlaintext, GLWEPublicKey, GLWESecret, Infos,
-    automorphism::AutomorphismKey,
-    keyswitch_key::GLWESwitchingKey,
-    test_fft64::{log2_std_noise_gglwe_product, noise_ggsw_product},
+    FourierGLWESecret, GGSWCiphertext, GLWECiphertext, GLWEPlaintext, GLWESecret, Infos, div_ceil, noise::noise_ggsw_product,
 };
 
 #[test]
-fn encrypt_sk() {
-    let log_n: usize = 8;
-    (1..4).for_each(|rank| {
-        println!("test encrypt_sk rank: {}", rank);
-        test_encrypt_sk(log_n, 8, 54, 30, 3.2, rank);
-    });
-}
-
-#[test]
-fn encrypt_zero_sk() {
-    let log_n: usize = 8;
-    (1..4).for_each(|rank| {
-        println!("test encrypt_zero_sk rank: {}", rank);
-        test_encrypt_zero_sk(log_n, 8, 64, 3.2, rank);
-    });
-}
-
-#[test]
-fn encrypt_pk() {
-    let log_n: usize = 8;
-    (1..4).for_each(|rank| {
-        println!("test encrypt_pk rank: {}", rank);
-        test_encrypt_pk(log_n, 8, 64, 64, 3.2, rank)
-    });
-}
-
-#[test]
-fn keyswitch() {
+fn apply() {
     let log_n: usize = 8;
     let basek: usize = 12;
     let k_in: usize = 45;
-    let digits: usize = k_in.div_ceil(basek);
-    (1..4).for_each(|rank_in| {
-        (1..4).for_each(|rank_out| {
-            (1..digits + 1).for_each(|di| {
-                let k_ksk: usize = k_in + basek * di;
-                let k_out: usize = k_ksk; // better capture noise
-                println!(
-                    "test keyswitch digits: {} rank_in: {} rank_out: {}",
-                    di, rank_in, rank_out
-                );
-                test_keyswitch(log_n, basek, k_out, k_in, k_ksk, di, rank_in, rank_out, 3.2);
-            })
-        });
-    });
-}
-
-#[test]
-fn keyswitch_inplace() {
-    let log_n: usize = 8;
-    let basek: usize = 12;
-    let k_ct: usize = 45;
-    let digits: usize = k_ct.div_ceil(basek);
-    (1..4).for_each(|rank| {
-        (1..digits + 1).for_each(|di| {
-            let k_ksk: usize = k_ct + basek * di;
-            println!("test keyswitch_inplace digits: {} rank: {}", di, rank);
-            test_keyswitch_inplace(log_n, basek, k_ct, k_ksk, di, rank, 3.2);
-        });
-    });
-}
-
-#[test]
-fn external_product() {
-    let log_n: usize = 8;
-    let basek: usize = 12;
-    let k_in: usize = 45;
-    let digits: usize = k_in.div_ceil(basek);
+    let digits: usize = div_ceil(k_in, basek);
     (1..4).for_each(|rank| {
         (1..digits + 1).for_each(|di| {
             let k_ggsw: usize = k_in + basek * di;
@@ -92,7 +22,7 @@ });
 }
 
 #[test]
-fn external_product_inplace() {
+fn apply_inplace() {
     let log_n: usize = 8;
     let basek: usize = 12;
     let k_ct: usize = 60;
@@ -106,548 +36,6 @@ });
     });
 }
 
-#[test]
-fn automorphism_inplace() {
-    let log_n: usize = 8;
-    let basek: usize = 12;
-    let k_ct: usize = 60;
-    let digits: usize = k_ct.div_ceil(basek);
-    (1..4).for_each(|rank| {
-        (1..digits + 1).for_each(|di| {
-            let k_ksk: usize = k_ct + basek * di;
-            println!("test automorphism_inplace digits: {} rank: {}", di, rank);
-            test_automorphism_inplace(log_n, basek, -5, k_ct, k_ksk, di, rank, 3.2);
-        });
-    });
-}
-
-#[test]
-fn automorphism() {
-    let log_n: usize = 8;
-    let basek: usize = 12;
-    let k_in: usize = 60;
-    let digits: usize = k_in.div_ceil(basek);
-    (1..4).for_each(|rank| {
-        (1..digits + 1).for_each(|di| {
-            let k_ksk: usize = k_in + basek * di;
-            let k_out: usize = k_ksk; // Better capture noise.
-            println!("test automorphism digits: {} rank: {}", di, rank);
-            test_automorphism(log_n, basek, -5, k_out, k_in, k_ksk, di, rank, 3.2);
-        })
-    });
-}
-
-fn test_encrypt_sk(log_n: usize, basek: usize, k_ct: usize, k_pt: usize, sigma: f64, rank: usize) {
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-
-    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
-    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_pt);
-
-    let mut source_xs: Source = Source::new([0u8; 32]);
-    let mut source_xe: Source = Source::new([0u8; 32]);
-    let mut source_xa: Source = Source::new([0u8; 32]);
-
-    let mut scratch: ScratchOwned = ScratchOwned::new(
-        GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
-            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k()),
-    );
-
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
-
-    let mut data_want: Vec<i64> = vec![0i64; module.n()];
-
-    data_want
-        .iter_mut()
-        .for_each(|x| *x = source_xa.next_i64() & 0xFF);
-
-    pt.data.encode_vec_i64(0, basek, k_pt, &data_want, 10);
-
-    ct.encrypt_sk(
-        &module,
-        &pt,
-        &sk,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    pt.data.zero();
-
-    ct.decrypt(&module, &mut pt, &sk, scratch.borrow());
-
-    let mut data_have: Vec<i64> = vec![0i64; module.n()];
-
-    pt.data
-        .decode_vec_i64(0, basek, pt.size() * basek, &mut data_have);
-
-    // TODO: properly assert the decryption noise through std(dec(ct) - pt)
-    let scale: f64 = (1 << (pt.size() * basek - k_pt)) as f64;
-    izip!(data_want.iter(), data_have.iter()).for_each(|(a, b)| {
-        let b_scaled = (*b as f64) / scale;
-        assert!(
-            (*a as f64 - b_scaled).abs() < 0.1,
-            "{} {}",
-            *a as f64,
-            b_scaled
-        )
-    });
-}
-
-fn test_encrypt_zero_sk(log_n: usize, basek: usize, k_ct: usize, sigma: f64, rank: usize) {
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-
-    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
-
-    let mut source_xs: Source = Source::new([0u8; 32]);
-    let mut source_xe: Source = Source::new([1u8; 32]);
-    let mut source_xa: Source = Source::new([0u8; 32]);
-
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
-
-    let mut ct_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank);
-
-    let mut scratch: ScratchOwned = ScratchOwned::new(
-        FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ct)
-            | FourierGLWECiphertext::encrypt_sk_scratch_space(&module, basek, k_ct, rank),
-    );
-
-    ct_dft.encrypt_zero_sk(
-        &module,
-        &sk,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-    ct_dft.decrypt(&module, &mut pt, &sk, scratch.borrow());
-
-    assert!((sigma - pt.data.std(0, basek) * (k_ct as f64).exp2()) <= 0.2);
-}
-
-fn test_encrypt_pk(log_n: usize, basek: usize, k_ct: usize, k_pk: usize, sigma: f64, rank: usize) {
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-
-    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
-    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
-
-    let mut source_xs: Source = Source::new([0u8; 32]);
-    let mut source_xe: Source = Source::new([0u8; 32]);
-    let mut source_xa: Source = Source::new([0u8; 32]);
-    let mut source_xu: Source = Source::new([0u8; 32]);
-
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
-
-    let mut pk: GLWEPublicKey<Vec<u8>, FFT64> = GLWEPublicKey::alloc(&module, basek, k_pk, rank);
-    pk.generate_from_sk(&module, &sk, &mut source_xa, &mut source_xe, sigma);
-
-    let mut scratch: ScratchOwned = ScratchOwned::new(
-        GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
-            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k())
-            | GLWECiphertext::encrypt_pk_scratch_space(&module, basek, pk.k()),
-    );
-
-    let mut data_want: Vec<i64> = vec![0i64; module.n()];
-
-    data_want
-        .iter_mut()
-        .for_each(|x| *x = source_xa.next_i64() & 0);
-
-    pt_want.data.encode_vec_i64(0, basek, k_ct, &data_want, 10);
-
-    ct.encrypt_pk(
-        &module,
-        &pt_want,
-        &pk,
-        &mut source_xu,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
-
-    ct.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
-
-    module.vec_znx_sub_ab_inplace(&mut pt_want.data, 0, &pt_have.data, 0);
-
-    let noise_have: f64 = pt_want.data.std(0, basek).log2();
-    let noise_want: f64 = ((((rank as f64) + 1.0) * module.n() as f64 * 0.5 * sigma * sigma).sqrt()).log2() - (k_ct as f64);
-
-    assert!(
-        (noise_have - noise_want).abs() < 0.2,
-        "{} {}",
-        noise_have,
-        noise_want
-    );
-}
-
-fn test_keyswitch(
-    log_n: usize,
-    basek: usize,
-    k_out: usize,
-    k_in: usize,
-    k_ksk: usize,
-    digits: usize,
-    rank_in: usize,
-    rank_out: usize,
-    sigma: f64,
-) {
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-
-    let rows: usize = k_in.div_ceil(basek * digits);
-
-    let mut ksk: GLWESwitchingKey<Vec<u8>, FFT64> =
-        GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, digits, rank_in, rank_out);
-    let mut ct_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_in, rank_in);
-    let mut ct_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_out, rank_out);
-    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
-    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
-
-    let mut source_xs: Source = Source::new([0u8; 32]);
-    let mut source_xe: Source = Source::new([0u8; 32]);
-    let mut source_xa: Source = Source::new([0u8; 32]);
-
-    pt_want
-        .data
-        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
-
-    let mut scratch: ScratchOwned = ScratchOwned::new(
-        GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ksk.k(), rank_out)
-            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_out.k())
-            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_in.k())
-            | GLWECiphertext::keyswitch_scratch_space(
-                &module,
-                basek,
-                ct_out.k(),
-                ct_in.k(),
-                ksk.k(),
-                digits,
-                rank_in,
-                rank_out,
-            ),
-    );
-
-    let mut sk_in: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_in);
-    sk_in.fill_ternary_prob(&module, 0.5, &mut source_xs);
-
-    let mut sk_out: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_out);
-    sk_out.fill_ternary_prob(&module, 0.5, &mut source_xs);
-
-    ksk.generate_from_sk(
-        &module,
-        &sk_in,
-        &sk_out,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    ct_in.encrypt_sk(
-        &module,
-        &pt_want,
-        &sk_in,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    ct_out.keyswitch(&module, &ct_in, &ksk, scratch.borrow());
-    ct_out.decrypt(&module, &mut pt_have, &sk_out, scratch.borrow());
-
-    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
-
-    let noise_have: f64 = pt_have.data.std(0, basek).log2();
-    let noise_want: f64 = log2_std_noise_gglwe_product(
-        module.n() as f64,
-        basek * digits,
-        0.5,
-        0.5,
-        0f64,
-        sigma * sigma,
-        0f64,
-        rank_in as f64,
-        k_in,
-        k_ksk,
-    );
-
-    println!("{} vs. {}", noise_have, noise_want);
-
-    assert!(
-        (noise_have - noise_want).abs() <= 0.5,
-        "{} {}",
-        noise_have,
-        noise_want
-    );
-}
-
-fn test_keyswitch_inplace(log_n: usize, basek: usize, k_ct: usize, k_ksk: usize, digits: usize, rank: usize, sigma: f64) {
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-
-    let rows: usize = k_ct.div_ceil(basek * digits);
-
-    let mut ct_grlwe: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, digits, rank, rank);
-    let mut ct_glwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
-    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
-    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
-
-    let mut source_xs: Source = Source::new([0u8; 32]);
-    let mut source_xe: Source = Source::new([0u8; 32]);
-    let mut source_xa: Source = Source::new([0u8; 32]);
-
-    pt_want
-        .data
-        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
-
-    let mut scratch: ScratchOwned = ScratchOwned::new(
-        GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ct_grlwe.k(), rank)
-            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_glwe.k())
-            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_glwe.k())
-            | GLWECiphertext::keyswitch_inplace_scratch_space(&module, basek, ct_glwe.k(), ct_grlwe.k(), digits, rank),
-    );
-
-    let mut sk0: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk0.fill_ternary_prob(&module, 0.5, &mut source_xs);
-
-    let mut sk1: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk1.fill_ternary_prob(&module, 0.5, &mut source_xs);
-
-    ct_grlwe.generate_from_sk(
-        &module,
-        &sk0,
-        &sk1,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    ct_glwe.encrypt_sk(
-        &module,
-        &pt_want,
-        &sk0,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    ct_glwe.keyswitch_inplace(&module, &ct_grlwe, scratch.borrow());
-
-    ct_glwe.decrypt(&module, &mut pt_have, &sk1, scratch.borrow());
-
-    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
-
-    let noise_have: f64 = pt_have.data.std(0, basek).log2();
-    let noise_want: f64 = log2_std_noise_gglwe_product(
-        module.n() as f64,
-        basek * digits,
-        0.5,
-        0.5,
-        0f64,
-        sigma * sigma,
-        0f64,
-        rank as f64,
-        k_ct,
-        k_ksk,
-    );
-
-    assert!(
-        (noise_have - noise_want).abs() <= 0.5,
-        "{} {}",
-        noise_have,
-        noise_want
-    );
-}
-
-fn test_automorphism(
-    log_n: usize,
-    basek: usize,
-    p: i64,
-    k_out: usize,
-    k_in: usize,
-    k_ksk: usize,
-    digits: usize,
-    rank: usize,
-    sigma: f64,
-) {
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-
-    let rows: usize = k_in.div_ceil(basek * digits);
-
-    let mut autokey: AutomorphismKey<Vec<u8>, FFT64> = AutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
-    let mut ct_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_in, rank);
-    let mut ct_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_out, rank);
-    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
-    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
-
-    let mut source_xs: Source = Source::new([0u8; 32]);
-    let mut source_xe: Source = Source::new([0u8; 32]);
-    let mut source_xa: Source = Source::new([0u8; 32]);
-
-    pt_want
-        .data
-        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
-
-    let mut scratch: ScratchOwned = ScratchOwned::new(
-        AutomorphismKey::generate_from_sk_scratch_space(&module, basek, autokey.k(), rank)
-            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_out.k())
-            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_in.k())
-            | GLWECiphertext::automorphism_scratch_space(
-                &module,
-                basek,
-                ct_out.k(),
-                ct_in.k(),
-                autokey.k(),
-                digits,
-                rank,
-            ),
-    );
-
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
-
-    autokey.generate_from_sk(
-        &module,
-        p,
-        &sk,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    ct_in.encrypt_sk(
-        &module,
-        &pt_want,
-        &sk,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    ct_out.automorphism(&module, &ct_in, &autokey, scratch.borrow());
-    ct_out.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
-    module.vec_znx_automorphism_inplace(p, &mut pt_want.data, 0);
-    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
-    module.vec_znx_normalize_inplace(basek, &mut pt_have.data, 0, scratch.borrow());
-
-    let noise_have: f64 = pt_have.data.std(0, basek).log2();
-
-    println!("{}", noise_have);
-
-    let noise_want: f64 = log2_std_noise_gglwe_product(
-        module.n() as f64,
-        basek * digits,
-        0.5,
-        0.5,
-        0f64,
-        sigma * sigma,
-        0f64,
-        rank as f64,
-        k_in,
-        k_ksk,
-    );
-
-    assert!(
-        noise_have <= noise_want + 1.0,
-        "{} {}",
-        noise_have,
-        noise_want
-    );
-}
-
-fn test_automorphism_inplace(
-    log_n: usize,
-    basek: usize,
-    p: i64,
-    k_ct: usize,
-    k_ksk: usize,
-    digits: usize,
-    rank: usize,
-    sigma: f64,
-) {
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-
-    let rows: usize = k_ct.div_ceil(basek * digits);
-
-    let mut autokey: AutomorphismKey<Vec<u8>, FFT64> = AutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
-    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
-    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
-    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
-
-    let mut source_xs: Source = Source::new([0u8; 32]);
-    let mut source_xe: Source = Source::new([0u8; 32]);
-    let mut source_xa: Source = Source::new([0u8; 32]);
-
-    pt_want
-        .data
-        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
-
-    let mut scratch: ScratchOwned = ScratchOwned::new(
-        AutomorphismKey::generate_from_sk_scratch_space(&module, basek, autokey.k(), rank)
-            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k())
-            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
-            | GLWECiphertext::automorphism_inplace_scratch_space(&module, basek, ct.k(), autokey.k(), digits, rank),
-    );
-
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
-
-    autokey.generate_from_sk(
-        &module,
-        p,
-        &sk,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    ct.encrypt_sk(
-        &module,
-        &pt_want,
-        &sk,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    ct.automorphism_inplace(&module, &autokey, scratch.borrow());
-    ct.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
-    module.vec_znx_automorphism_inplace(p, &mut pt_want.data, 0);
-    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
-    module.vec_znx_normalize_inplace(basek, &mut pt_have.data, 0, scratch.borrow());
-
-    let noise_have: f64 = pt_have.data.std(0, basek).log2();
-    let noise_want: f64 = log2_std_noise_gglwe_product(
-        module.n() as f64,
-        basek * digits,
-        0.5,
-        0.5,
-        0f64,
-        sigma * sigma,
-        0f64,
-        rank as f64,
-        k_ct,
-        k_ksk,
-    );
-
-    assert!(
-        (noise_have - noise_want).abs() <= 0.5,
-        "{} {}",
-        noise_have,
-        noise_want
-    );
-}
-
 fn test_external_product(
     log_n: usize,
     basek: usize,
@@ -699,13 +87,14 @@ rank,
             ),
     );
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     ct_ggsw.encrypt_sk(
         &module,
         &pt_rgsw,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -715,7 +104,7 @@
     ct_glwe_in.encrypt_sk(
         &module,
         &pt_want,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -724,7 +113,7 @@ );
 
     ct_glwe_out.external_product(&module, &ct_glwe_in, &ct_ggsw, scratch.borrow());
 
-    ct_glwe_out.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+    ct_glwe_out.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
 
     module.vec_znx_rotate_inplace(k as i64, &mut pt_want.data, 0);
 
@@ -793,13 +182,14 @@ | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_glwe.k())
             | GLWECiphertext::external_product_inplace_scratch_space(&module, basek, ct_glwe.k(), ct_ggsw.k(), digits, rank),
     );
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     ct_ggsw.encrypt_sk(
         &module,
         &pt_rgsw,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -809,7 +199,7 @@
     ct_glwe.encrypt_sk(
         &module,
         &pt_want,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -818,7 +208,7 @@ );
 
     ct_glwe.external_product_inplace(&module, &ct_ggsw, scratch.borrow());
 
-    ct_glwe.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+    ct_glwe.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
 
     module.vec_znx_rotate_inplace(k as i64, &mut pt_want.data, 0);
 

@@ -1,1 +1,227 @@
+use backend::{FFT64, FillUniform, Module, ScratchOwned, Stats, VecZnxOps};
+use sampling::source::Source;
 
+use crate::{
+    FourierGLWESecret, GLWECiphertext, GLWEPlaintext, GLWESecret, GLWESwitchingKey, Infos, div_ceil,
+    noise::log2_std_noise_gglwe_product,
+};
+
+#[test]
+fn apply() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_in: usize = 45;
+    let digits: usize = div_ceil(k_in, basek);
+    (1..4).for_each(|rank_in| {
+        (1..4).for_each(|rank_out| {
+            (1..digits + 1).for_each(|di| {
+                let k_ksk: usize = k_in + basek * di;
+                let k_out: usize = k_ksk; // better capture noise
+                println!(
+                    "test keyswitch digits: {} rank_in: {} rank_out: {}",
+                    di, rank_in, rank_out
+                );
+                test_keyswitch(log_n, basek, k_out, k_in, k_ksk, di, rank_in, rank_out, 3.2);
+            })
+        });
+    });
+}
+
+#[test]
+fn apply_inplace() {
+    let log_n: usize = 8;
+    let basek: usize = 12;
+    let k_ct: usize = 45;
+    let digits: usize = div_ceil(k_ct, basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_ct + basek * di;
+            println!("test keyswitch_inplace digits: {} rank: {}", di, rank);
+            test_keyswitch_inplace(log_n, basek, k_ct, k_ksk, di, rank, 3.2);
+        });
+    });
+}
+
+fn test_keyswitch(
+    log_n: usize,
+    basek: usize,
+    k_out: usize,
+    k_in: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank_in: usize,
+    rank_out: usize,
+    sigma: f64,
+) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = div_ceil(k_in, basek * digits);
+
+    let mut ksk: GLWESwitchingKey<Vec<u8>, FFT64> =
+        GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, digits, rank_in, rank_out);
+    let mut ct_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_in, rank_in);
+    let mut ct_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_out, rank_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ksk.k(), rank_out)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_out.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_in.k())
+            | GLWECiphertext::keyswitch_scratch_space(
+                &module,
+                basek,
+                ct_out.k(),
+                ct_in.k(),
+                ksk.k(),
+                digits,
+                rank_in,
+                rank_out,
+            ),
+    );
+
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_in);
+    sk_in.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_in_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_in);
+
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_out);
+    sk_out.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
+
+    ksk.generate_from_sk(
+        &module,
+        &sk_in,
+        &sk_out_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_in.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_in_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_out.keyswitch(&module, &ct_in, &ksk, scratch.borrow());
+    ct_out.decrypt(&module, &mut pt_have, &sk_out_dft, scratch.borrow());
+
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+    let noise_want: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank_in as f64,
+        k_in,
+        k_ksk,
+    );
+
+    println!("{} vs. {}", noise_have, noise_want);
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_keyswitch_inplace(log_n: usize, basek: usize, k_ct: usize, k_ksk: usize, digits: usize, rank: usize, sigma: f64) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = div_ceil(k_ct, basek * digits);
+
+    let mut ct_grlwe: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, digits, rank, rank);
+    let mut ct_glwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ct_grlwe.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_glwe.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_glwe.k())
+            | GLWECiphertext::keyswitch_inplace_scratch_space(&module, basek, ct_glwe.k(), ct_grlwe.k(), digits, rank),
+    );
+
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_in.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_in_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_in);
+
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_out.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
+
+    ct_grlwe.generate_from_sk(
+        &module,
+        &sk_in,
+        &sk_out_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_in_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.keyswitch_inplace(&module, &ct_grlwe, scratch.borrow());
+
+    ct_glwe.decrypt(&module, &mut pt_have, &sk_out_dft, scratch.borrow());
+
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+    let noise_want: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank as f64,
+        k_ct,
+        k_ksk,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}

@@ -1,11 +1,11 @@
-use crate::{AutomorphismKey, GLWECiphertext, GLWEOps, GLWEPlaintext, GLWESecret, StreamPacker};
+use crate::{FourierGLWESecret, GLWEAutomorphismKey, GLWECiphertext, GLWEOps, GLWEPacker, GLWEPlaintext, GLWESecret, div_ceil};
 use std::collections::HashMap;
 
 use backend::{Encoding, FFT64, Module, ScratchOwned, Stats};
 use sampling::source::Source;
 
 #[test]
-fn packing() {
+fn apply() {
     let log_n: usize = 5;
     let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
 
@@ -26,12 +26,13 @@
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWECiphertext::encrypt_sk_scratch_space(&module, basek, k_ct)
             | GLWECiphertext::decrypt_scratch_space(&module, basek, k_ct)
-            | AutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_ksk, rank)
-            | StreamPacker::scratch_space(&module, basek, k_ct, k_ksk, digits, rank),
+            | GLWEAutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_ksk, rank)
+            | GLWEPacker::scratch_space(&module, basek, k_ct, k_ksk, digits, rank),
     );
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
     let mut data: Vec<i64> = vec![0i64; module.n()];
@@ -40,11 +41,11 @@ *x = i as i64;
     });
     pt.data.encode_vec_i64(0, basek, pt_k, &data, 32);
 
-    let gal_els: Vec<i64> = StreamPacker::galois_elements(&module);
+    let gal_els: Vec<i64> = GLWEPacker::galois_elements(&module);
 
-    let mut auto_keys: HashMap<i64, AutomorphismKey<Vec<u8>, FFT64>> = HashMap::new();
+    let mut auto_keys: HashMap<i64, GLWEAutomorphismKey<Vec<u8>, FFT64>> = HashMap::new();
     gal_els.iter().for_each(|gal_el| {
-        let mut key: AutomorphismKey<Vec<u8>, FFT64> = AutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
+        let mut key: GLWEAutomorphismKey<Vec<u8>, FFT64> = GLWEAutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
         key.generate_from_sk(
             &module,
             *gal_el,
@@ -59,14 +60,14 @@ });
 
     let log_batch: usize = 0;
 
-    let mut packer: StreamPacker = StreamPacker::new(&module, log_batch, basek, k_ct, rank);
+    let mut packer: GLWEPacker = GLWEPacker::new(&module, log_batch, basek, k_ct, rank);
 
     let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
 
     ct.encrypt_sk(
         &module,
         &pt,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -79,7 +80,7 @@ (0..module.n() >> log_batch).for_each(|i| {
         ct.encrypt_sk(
             &module,
             &pt,
-            &sk,
+            &sk_dft,
             &mut source_xa,
             &mut source_xe,
             sigma,
@@ -115,7 +116,7 @@ }
         });
         pt_want.data.encode_vec_i64(0, basek, pt_k, &data, 32);
 
-        res_i.decrypt(&module, &mut pt, &sk, scratch.borrow());
+        res_i.decrypt(&module, &mut pt, &sk_dft, scratch.borrow());
 
         if i & 1 == 0 {
             pt.sub_inplace_ab(&module, &pt_want);

@@ -3,10 +3,13 @@
 use backend::{FFT64, FillUniform, Module, ScratchOwned, Stats, VecZnxOps, ZnxView, ZnxViewMut};
 use sampling::source::Source;
 
-use crate::{AutomorphismKey, GLWECiphertext, GLWEPlaintext, GLWESecret, Infos, test_fft64::var_noise_gglwe_product};
+use crate::{
+    FourierGLWESecret, GLWEAutomorphismKey, GLWECiphertext, GLWEPlaintext, GLWESecret, Infos, div_ceil,
+    noise::var_noise_gglwe_product,
+};
 
 #[test]
-fn trace_inplace() {
+fn apply_inplace() {
     let log_n: usize = 8;
     (1..4).for_each(|rank| {
         println!("test trace_inplace rank: {}", rank);
@@ -33,12 +36,13 @@
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
             | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k())
-            | AutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_autokey, rank)
+            | GLWEAutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_autokey, rank)
             | GLWECiphertext::trace_inplace_scratch_space(&module, basek, ct.k(), k_autokey, digits, rank),
     );
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     let mut data_want: Vec<i64> = vec![0i64; module.n()];
 
@@ -53,17 +57,18 @@
     ct.encrypt_sk(
         &module,
         &pt_have,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
         scratch.borrow(),
     );
 
-    let mut auto_keys: HashMap<i64, AutomorphismKey<Vec<u8>, FFT64>> = HashMap::new();
+    let mut auto_keys: HashMap<i64, GLWEAutomorphismKey<Vec<u8>, FFT64>> = HashMap::new();
     let gal_els: Vec<i64> = GLWECiphertext::trace_galois_elements(&module);
     gal_els.iter().for_each(|gal_el| {
-        let mut key: AutomorphismKey<Vec<u8>, FFT64> = AutomorphismKey::alloc(&module, basek, k_autokey, rows, digits, rank);
+        let mut key: GLWEAutomorphismKey<Vec<u8>, FFT64> =
+            GLWEAutomorphismKey::alloc(&module, basek, k_autokey, rows, digits, rank);
         key.generate_from_sk(
             &module,
             *gal_el,
@@ -81,7 +86,7 @@ ct.trace_inplace(&module, 5, log_n, &auto_keys, scratch.borrow());
 
     (0..pt_want.size()).for_each(|i| pt_want.data.at_mut(0, i)[0] = pt_have.data.at(0, i)[0]);
 
-    ct.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+    ct.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
 
     module.vec_znx_sub_ab_inplace(&mut pt_want.data, 0, &pt_have.data, 0);
     module.vec_znx_normalize_inplace(basek, &mut pt_want.data, 0, scratch.borrow());

@@ -2,7 +2,7 @@ use std::collections::HashMap;
 
 use backend::{FFT64, Module, Scratch};
 
-use crate::{AutomorphismKey, GLWECiphertext, GLWECiphertextToMut, GLWECiphertextToRef, GLWEOps, Infos, SetMetaData};
+use crate::{GLWEAutomorphismKey, GLWECiphertext, GLWECiphertextToMut, GLWECiphertextToRef, GLWEOps, Infos, SetMetaData};
 
 impl GLWECiphertext<Vec<u8>> {
     pub fn trace_galois_elements(module: &Module<FFT64>) -> Vec<i64> {
@@ -51,7 +51,7 @@ module: &Module<FFT64>,
         start: usize,
         end: usize,
         lhs: &GLWECiphertext<DataLhs>,
-        auto_keys: &HashMap<i64, AutomorphismKey<DataAK, FFT64>>,
+        auto_keys: &HashMap<i64, GLWEAutomorphismKey<DataAK, FFT64>>,
         scratch: &mut Scratch,
     ) where
         GLWECiphertext<DataLhs>: GLWECiphertextToRef + Infos,
@@ -65,7 +65,7 @@ &mut self,
         module: &Module<FFT64>,
         start: usize,
         end: usize,
-        auto_keys: &HashMap<i64, AutomorphismKey<DataAK, FFT64>>,
+        auto_keys: &HashMap<i64, GLWEAutomorphismKey<DataAK, FFT64>>,
         scratch: &mut Scratch,
     ) {
         (start..end).for_each(|i| {

@@ -1,5 +1,5 @@
 #[derive(Clone, Copy, Debug)]
-pub(crate) enum SecretDistribution {
+pub(crate) enum Distribution {
     TernaryFixed(usize), // Ternary with fixed Hamming weight
     TernaryProb(f64),    // Ternary with probabilistic Hamming weight
     BinaryFixed(usize),  // Binary with fixed Hamming weight

@@ -1,343 +0,0 @@
-use backend::{Backend, FFT64, MatZnxDft, MatZnxDftOps, Module, Scratch, ZnxZero};
-use sampling::source::Source;
-
-use crate::{FourierGLWECiphertext, GGLWECiphertext, GGSWCiphertext, GLWESecret, GetRow, Infos, ScratchCore, SetRow};
-
-pub struct GLWESwitchingKey<Data, B: Backend>(pub(crate) GGLWECiphertext<Data, B>);
-
-impl GLWESwitchingKey<Vec<u8>, FFT64> {
-    pub fn alloc(
-        module: &Module<FFT64>,
-        basek: usize,
-        k: usize,
-        rows: usize,
-        digits: usize,
-        rank_in: usize,
-        rank_out: usize,
-    ) -> Self {
-        GLWESwitchingKey(GGLWECiphertext::alloc(
-            module, basek, k, rows, digits, rank_in, rank_out,
-        ))
-    }
-
-    pub fn bytes_of(
-        module: &Module<FFT64>,
-        basek: usize,
-        k: usize,
-        rows: usize,
-        digits: usize,
-        rank_in: usize,
-        rank_out: usize,
-    ) -> usize {
-        GGLWECiphertext::<Vec<u8>, FFT64>::bytes_of(module, basek, k, rows, digits, rank_in, rank_out)
-    }
-}
-
-impl<T, B: Backend> Infos for GLWESwitchingKey<T, B> {
-    type Inner = MatZnxDft<T, B>;
-
-    fn inner(&self) -> &Self::Inner {
-        self.0.inner()
-    }
-
-    fn basek(&self) -> usize {
-        self.0.basek()
-    }
-
-    fn k(&self) -> usize {
-        self.0.k()
-    }
-}
-
-impl<T, B: Backend> GLWESwitchingKey<T, B> {
-    pub fn rank(&self) -> usize {
-        self.0.data.cols_out() - 1
-    }
-
-    pub fn rank_in(&self) -> usize {
-        self.0.data.cols_in()
-    }
-
-    pub fn rank_out(&self) -> usize {
-        self.0.data.cols_out() - 1
-    }
-
-    pub fn digits(&self) -> usize {
-        self.0.digits()
-    }
-}
-
-impl<C: AsRef<[u8]>> GetRow<FFT64> for GLWESwitchingKey<C, FFT64> {
-    fn get_row<R: AsMut<[u8]> + AsRef<[u8]>>(
-        &self,
-        module: &Module<FFT64>,
-        row_i: usize,
-        col_j: usize,
-        res: &mut FourierGLWECiphertext<R, FFT64>,
-    ) {
-        module.mat_znx_dft_get_row(&mut res.data, &self.0.data, row_i, col_j);
-    }
-}
-
-impl<C: AsMut<[u8]> + AsRef<[u8]>> SetRow<FFT64> for GLWESwitchingKey<C, FFT64> {
-    fn set_row<R: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        row_i: usize,
-        col_j: usize,
-        a: &FourierGLWECiphertext<R, FFT64>,
-    ) {
-        module.mat_znx_dft_set_row(&mut self.0.data, row_i, col_j, &a.data);
-    }
-}
-
-impl GLWESwitchingKey<Vec<u8>, FFT64> {
-    pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
-        GGLWECiphertext::generate_from_sk_scratch_space(module, basek, k, rank)
-    }
-
-    pub fn encrypt_pk_scratch_space(module: &Module<FFT64>, _basek: usize, _k: usize, _rank: usize) -> usize {
-        GGLWECiphertext::generate_from_pk_scratch_space(module, _basek, _k, _rank)
-    }
-
-    pub fn keyswitch_scratch_space(
-        module: &Module<FFT64>,
-        basek: usize,
-        k_out: usize,
-        k_in: usize,
-        k_ksk: usize,
-        digits: usize,
-        rank_in: usize,
-        rank_out: usize,
-    ) -> usize {
-        let tmp_in: usize = FourierGLWECiphertext::bytes_of(module, basek, k_in, rank_in);
-        let tmp_out: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank_out);
-        let ksk: usize =
-            FourierGLWECiphertext::keyswitch_scratch_space(module, basek, k_out, k_in, k_ksk, digits, rank_in, rank_out);
-        tmp_in + tmp_out + ksk
-    }
-
-    pub fn keyswitch_inplace_scratch_space(
-        module: &Module<FFT64>,
-        basek: usize,
-        k_out: usize,
-        k_ksk: usize,
-        digits: usize,
-        rank: usize,
-    ) -> usize {
-        let tmp: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank);
-        let ksk: usize = FourierGLWECiphertext::keyswitch_inplace_scratch_space(module, basek, k_out, k_ksk, digits, rank);
-        tmp + ksk
-    }
-
-    pub fn external_product_scratch_space(
-        module: &Module<FFT64>,
-        basek: usize,
-        k_out: usize,
-        k_in: usize,
-        k_ggsw: usize,
-        digits: usize,
-        rank: usize,
-    ) -> usize {
-        let tmp_in: usize = FourierGLWECiphertext::bytes_of(module, basek, k_in, rank);
-        let tmp_out: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank);
-        let ggsw: usize = FourierGLWECiphertext::external_product_scratch_space(module, basek, k_out, k_in, k_ggsw, digits, rank);
-        tmp_in + tmp_out + ggsw
-    }
-
-    pub fn external_product_inplace_scratch_space(
-        module: &Module<FFT64>,
-        basek: usize,
-        k_out: usize,
-        k_ggsw: usize,
-        digits: usize,
-        rank: usize,
-    ) -> usize {
-        let tmp: usize = FourierGLWECiphertext::bytes_of(module, basek, k_out, rank);
-        let ggsw: usize =
-            FourierGLWECiphertext::external_product_inplace_scratch_space(module, basek, k_out, k_ggsw, digits, rank);
-        tmp + ggsw
-    }
-}
-impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> GLWESwitchingKey<DataSelf, FFT64> {
-    pub fn generate_from_sk<DataSkIn: AsRef<[u8]>, DataSkOut: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        sk_in: &GLWESecret<DataSkIn, FFT64>,
-        sk_out: &GLWESecret<DataSkOut, FFT64>,
-        source_xa: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-        scratch: &mut Scratch,
-    ) {
-        self.0.encrypt_sk(
-            module,
-            &sk_in.data,
-            sk_out,
-            source_xa,
-            source_xe,
-            sigma,
-            scratch,
-        );
-    }
-
-    pub fn keyswitch<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        lhs: &GLWESwitchingKey<DataLhs, FFT64>,
-        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(
-                self.rank_in(),
-                lhs.rank_in(),
-                "ksk_out input rank: {} != ksk_in input rank: {}",
-                self.rank_in(),
-                lhs.rank_in()
-            );
-            assert_eq!(
-                lhs.rank_out(),
-                rhs.rank_in(),
-                "ksk_in output rank: {} != ksk_apply input rank: {}",
-                self.rank_out(),
-                rhs.rank_in()
-            );
-            assert_eq!(
-                self.rank_out(),
-                rhs.rank_out(),
-                "ksk_out output rank: {} != ksk_apply output rank: {}",
-                self.rank_out(),
-                rhs.rank_out()
-            );
-        }
-
-        let (mut tmp_in, scratch1) = scratch.tmp_glwe_fourier(module, lhs.basek(), lhs.k(), lhs.rank());
-        let (mut tmp_out, scratch2) = scratch1.tmp_glwe_fourier(module, self.basek(), self.k(), self.rank());
-
-        (0..self.rank_in()).for_each(|col_i| {
-            (0..self.rows()).for_each(|row_j| {
-                lhs.get_row(module, row_j, col_i, &mut tmp_in);
-                tmp_out.keyswitch(module, &tmp_in, rhs, scratch2);
-                self.set_row(module, row_j, col_i, &tmp_out);
-            });
-        });
-
-        tmp_out.data.zero();
-
-        (self.rows().min(lhs.rows())..self.rows()).for_each(|row_i| {
-            (0..self.rank_in()).for_each(|col_j| {
-                self.set_row(module, row_i, col_j, &tmp_out);
-            });
-        });
-    }
-
-    pub fn keyswitch_inplace<DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(
-                self.rank_out(),
-                rhs.rank_out(),
-                "ksk_out output rank: {} != ksk_apply output rank: {}",
-                self.rank_out(),
-                rhs.rank_out()
-            );
-        }
-
-        let (mut tmp, scratch1) = scratch.tmp_glwe_fourier(module, self.basek(), self.k(), self.rank());
-
-        (0..self.rank_in()).for_each(|col_i| {
-            (0..self.rows()).for_each(|row_j| {
-                self.get_row(module, row_j, col_i, &mut tmp);
-                tmp.keyswitch_inplace(module, rhs, scratch1);
-                self.set_row(module, row_j, col_i, &tmp);
-            });
-        });
-    }
-
-    pub fn external_product<DataLhs: AsRef<[u8]>, DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        lhs: &GLWESwitchingKey<DataLhs, FFT64>,
-        rhs: &GGSWCiphertext<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(
-                self.rank_in(),
-                lhs.rank_in(),
-                "ksk_out input rank: {} != ksk_in input rank: {}",
-                self.rank_in(),
-                lhs.rank_in()
-            );
-            assert_eq!(
-                lhs.rank_out(),
-                rhs.rank(),
-                "ksk_in output rank: {} != ggsw rank: {}",
-                self.rank_out(),
-                rhs.rank()
-            );
-            assert_eq!(
-                self.rank_out(),
-                rhs.rank(),
-                "ksk_out output rank: {} != ggsw rank: {}",
-                self.rank_out(),
-                rhs.rank()
-            );
-        }
-
-        let (mut tmp_in, scratch1) = scratch.tmp_glwe_fourier(module, lhs.basek(), lhs.k(), lhs.rank());
-        let (mut tmp_out, scratch2) = scratch1.tmp_glwe_fourier(module, self.basek(), self.k(), self.rank());
-
-        (0..self.rank_in()).for_each(|col_i| {
-            (0..self.rows()).for_each(|row_j| {
-                lhs.get_row(module, row_j, col_i, &mut tmp_in);
-                tmp_out.external_product(module, &tmp_in, rhs, scratch2);
-                self.set_row(module, row_j, col_i, &tmp_out);
-            });
-        });
-
-        tmp_out.data.zero();
-
-        (self.rows().min(lhs.rows())..self.rows()).for_each(|row_i| {
-            (0..self.rank_in()).for_each(|col_j| {
-                self.set_row(module, row_i, col_j, &tmp_out);
-            });
-        });
-    }
-
-    pub fn external_product_inplace<DataRhs: AsRef<[u8]>>(
-        &mut self,
-        module: &Module<FFT64>,
-        rhs: &GGSWCiphertext<DataRhs, FFT64>,
-        scratch: &mut Scratch,
-    ) {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(
-                self.rank_out(),
-                rhs.rank(),
-                "ksk_out output rank: {} != ggsw rank: {}",
-                self.rank_out(),
-                rhs.rank()
-            );
-        }
-
-        let (mut tmp, scratch1) = scratch.tmp_glwe_fourier(module, self.basek(), self.k(), self.rank());
-        println!("tmp: {}", tmp.size());
-        (0..self.rank_in()).for_each(|col_i| {
-            (0..self.rows()).for_each(|row_j| {
-                self.get_row(module, row_j, col_i, &mut tmp);
-                tmp.external_product_inplace(module, rhs, scratch1);
-                self.set_row(module, row_j, col_i, &tmp);
-            });
-        });
-    }
-}

@@ -1,35 +1,29 @@
-pub mod automorphism;
 pub mod blind_rotation;
+pub mod dist;
 pub mod elem;
 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 noise;
 mod utils;
 
-pub use automorphism::*;
 use backend::Backend;
 use backend::FFT64;
 use backend::Module;
 pub use elem::*;
-pub use fourier_glwe::*;
-pub use gglwe::*;
+pub use fourier_glwe::{FourierGLWECiphertext, FourierGLWESecret};
+pub use gglwe::{GGLWECiphertext, GLWEAutomorphismKey, GLWESwitchingKey, GLWETensorKey};
 pub use ggsw::*;
-pub use glwe::*;
-pub use keyswitch_key::*;
+pub use glwe::{GLWECiphertext, GLWEOps, GLWEPacker, GLWEPlaintext, GLWEPublicKey, GLWESecret};
+pub(crate) use glwe::{GLWECiphertextToMut, GLWECiphertextToRef};
 pub use lwe::*;
-pub use tensor_key::*;
 
 pub use backend::Scratch;
 pub use backend::ScratchOwned;
 
-use crate::keys::SecretDistribution;
+use crate::dist::Distribution;
 
 pub(crate) const SIX_SIGMA: f64 = 6.0;
 
@@ -62,7 +56,8 @@ basek: usize,
         k: usize,
         rank: usize,
     ) -> (FourierGLWECiphertext<&mut [u8], B>, &mut Self);
-    fn tmp_sk(&mut self, module: &Module<B>, rank: usize) -> (GLWESecret<&mut [u8], B>, &mut Self);
+    fn tmp_sk(&mut self, module: &Module<B>, rank: usize) -> (GLWESecret<&mut [u8]>, &mut Self);
+    fn tmp_fourier_sk(&mut self, module: &Module<B>, rank: usize) -> (FourierGLWESecret<&mut [u8], B>, &mut Self);
     fn tmp_glwe_pk(
         &mut self,
         module: &Module<B>,
@@ -88,7 +83,7 @@ k: usize,
         rows: usize,
         digits: usize,
         rank: usize,
-    ) -> (TensorKey<&mut [u8], B>, &mut Self);
+    ) -> (GLWETensorKey<&mut [u8], B>, &mut Self);
     fn tmp_autokey(
         &mut self,
         module: &Module<B>,
@@ -97,7 +92,7 @@ k: usize,
         rows: usize,
         digits: usize,
         rank: usize,
-    ) -> (AutomorphismKey<&mut [u8], B>, &mut Self);
+    ) -> (GLWEAutomorphismKey<&mut [u8], B>, &mut Self);
 }
 
 impl ScratchCore<FFT64> for Scratch {
@@ -194,22 +189,31 @@ let (data, scratch) = self.tmp_glwe_fourier(module, basek, k, rank);
         (
             GLWEPublicKey {
                 data,
-                dist: SecretDistribution::NONE,
+                dist: Distribution::NONE,
             },
             scratch,
         )
     }
 
-    fn tmp_sk(&mut self, module: &Module<FFT64>, rank: usize) -> (GLWESecret<&mut [u8], FFT64>, &mut Self) {
+    fn tmp_sk(&mut self, module: &Module<FFT64>, rank: usize) -> (GLWESecret<&mut [u8]>, &mut Self) {
         let (data, scratch) = self.tmp_scalar_znx(module, rank);
-        let (data_fourier, scratch1) = scratch.tmp_scalar_znx_dft(module, rank);
         (
             GLWESecret {
                 data,
-                data_fourier,
-                dist: SecretDistribution::NONE,
+                dist: Distribution::NONE,
             },
-            scratch1,
+            scratch,
+        )
+    }
+
+    fn tmp_fourier_sk(&mut self, module: &Module<FFT64>, rank: usize) -> (FourierGLWESecret<&mut [u8], FFT64>, &mut Self) {
+        let (data, scratch) = self.tmp_scalar_znx_dft(module, rank);
+        (
+            FourierGLWESecret {
+                data,
+                dist: Distribution::NONE,
+            },
+            scratch,
         )
     }
 
@@ -235,9 +239,9 @@ k: usize,
         rows: usize,
         digits: usize,
         rank: usize,
-    ) -> (AutomorphismKey<&mut [u8], FFT64>, &mut Self) {
+    ) -> (GLWEAutomorphismKey<&mut [u8], FFT64>, &mut Self) {
         let (data, scratch) = self.tmp_glwe_ksk(module, basek, k, rows, digits, rank, rank);
-        (AutomorphismKey { key: data, p: 0 }, scratch)
+        (GLWEAutomorphismKey { key: data, p: 0 }, scratch)
     }
 
     fn tmp_tsk(
@@ -248,7 +252,7 @@ k: usize,
         rows: usize,
         digits: usize,
         rank: usize,
-    ) -> (TensorKey<&mut [u8], FFT64>, &mut Self) {
+    ) -> (GLWETensorKey<&mut [u8], FFT64>, &mut Self) {
         let mut keys: Vec<GLWESwitchingKey<&mut [u8], FFT64>> = Vec::new();
         let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
 
@@ -264,6 +268,6 @@ let (gglwe, s) = scratch.tmp_glwe_ksk(module, basek, k, rows, digits, 1, rank);
             scratch = s;
             keys.push(gglwe);
         }
-        (TensorKey { keys }, scratch)
+        (GLWETensorKey { keys }, scratch)
     }
 }

@@ -1,18 +1,18 @@
 use backend::{ScalarZnx, ZnxInfos, ZnxZero};
 use sampling::source::Source;
 
-use crate::SecretDistribution;
+use crate::Distribution;
 
 pub struct LWESecret<T> {
     pub(crate) data: ScalarZnx<T>,
-    pub(crate) dist: SecretDistribution,
+    pub(crate) dist: Distribution,
 }
 
 impl LWESecret<Vec<u8>> {
     pub fn alloc(n: usize) -> Self {
         Self {
             data: ScalarZnx::new(n, 1),
-            dist: SecretDistribution::NONE,
+            dist: Distribution::NONE,
         }
     }
 }
@@ -34,31 +34,31 @@
 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);
+        self.dist = Distribution::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);
+        self.dist = Distribution::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);
+        self.dist = Distribution::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);
+        self.dist = Distribution::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);
+        self.dist = Distribution::BinaryBlock(block_size);
     }
 
     pub fn fill_zero(&mut self) {
         self.data.zero();
-        self.dist = SecretDistribution::ZERO;
+        self.dist = Distribution::ZERO;
     }
 }

@@ -0,0 +1,3 @@
+pub mod secret;
+
+pub use secret::LWESecret;

@@ -1,125 +0,0 @@
-use backend::{Backend, FFT64, MatZnxDft, Module, ScalarZnxDftOps, Scratch};
-use sampling::source::Source;
-
-use crate::{GLWESecret, GLWESwitchingKey, Infos, ScratchCore};
-
-pub struct TensorKey<C, B: Backend> {
-    pub(crate) keys: Vec<GLWESwitchingKey<C, B>>,
-}
-
-impl TensorKey<Vec<u8>, FFT64> {
-    pub fn alloc(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self {
-        let mut keys: Vec<GLWESwitchingKey<Vec<u8>, FFT64>> = Vec::new();
-        let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
-        (0..pairs).for_each(|_| {
-            keys.push(GLWESwitchingKey::alloc(
-                module, basek, k, rows, digits, 1, rank,
-            ));
-        });
-        Self { keys: keys }
-    }
-
-    pub fn bytes_of(module: &Module<FFT64>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize {
-        let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
-        pairs * GLWESwitchingKey::<Vec<u8>, FFT64>::bytes_of(module, basek, k, rows, digits, 1, rank)
-    }
-}
-
-impl<T, B: Backend> Infos for TensorKey<T, B> {
-    type Inner = MatZnxDft<T, B>;
-
-    fn inner(&self) -> &Self::Inner {
-        &self.keys[0].inner()
-    }
-
-    fn basek(&self) -> usize {
-        self.keys[0].basek()
-    }
-
-    fn k(&self) -> usize {
-        self.keys[0].k()
-    }
-}
-
-impl<T, B: Backend> TensorKey<T, B> {
-    pub fn rank(&self) -> usize {
-        self.keys[0].rank()
-    }
-
-    pub fn rank_in(&self) -> usize {
-        self.keys[0].rank_in()
-    }
-
-    pub fn rank_out(&self) -> usize {
-        self.keys[0].rank_out()
-    }
-
-    pub fn digits(&self) -> usize {
-        self.keys[0].digits()
-    }
-}
-
-impl TensorKey<Vec<u8>, FFT64> {
-    pub fn generate_from_sk_scratch_space(module: &Module<FFT64>, basek: usize, k: usize, rank: usize) -> usize {
-        GLWESecret::bytes_of(module, 1) + GLWESwitchingKey::encrypt_sk_scratch_space(module, basek, k, rank)
-    }
-}
-
-impl<DataSelf: AsMut<[u8]> + AsRef<[u8]>> TensorKey<DataSelf, FFT64> {
-    pub fn generate_from_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,
-    ) {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(self.rank(), sk.rank());
-            assert_eq!(self.n(), module.n());
-            assert_eq!(sk.n(), module.n());
-        }
-
-        let rank: usize = self.rank();
-
-        let (mut sk_ij, scratch1) = scratch.tmp_sk(module, 1);
-
-        (0..rank).for_each(|i| {
-            (i..rank).for_each(|j| {
-                module.svp_apply(
-                    &mut sk_ij.data_fourier,
-                    0,
-                    &sk.data_fourier,
-                    i,
-                    &sk.data_fourier,
-                    j,
-                );
-                module.svp_idft(&mut sk_ij.data, 0, &sk_ij.data_fourier, 0, scratch1);
-                self.at_mut(i, j)
-                    .generate_from_sk(module, &sk_ij, sk, source_xa, source_xe, sigma, scratch1);
-            });
-        })
-    }
-
-    // Returns a mutable reference to GLWESwitchingKey_{s}(s[i] * s[j])
-    pub fn at_mut(&mut self, mut i: usize, mut j: usize) -> &mut GLWESwitchingKey<DataSelf, FFT64> {
-        if i > j {
-            std::mem::swap(&mut i, &mut j);
-        };
-        let rank: usize = self.rank();
-        &mut self.keys[i * rank + j - (i * (i + 1) / 2)]
-    }
-}
-
-impl<DataSelf: AsRef<[u8]>> TensorKey<DataSelf, FFT64> {
-    // Returns a reference to GLWESwitchingKey_{s}(s[i] * s[j])
-    pub fn at(&self, mut i: usize, mut j: usize) -> &GLWESwitchingKey<DataSelf, FFT64> {
-        if i > j {
-            std::mem::swap(&mut i, &mut j);
-        };
-        let rank: usize = self.rank();
-        &self.keys[i * rank + j - (i * (i + 1) / 2)]
-    }
-}

@@ -2,8 +2,8 @@ use backend::{FFT64, Module, ScalarZnxOps, ScratchOwned, Stats, VecZnxOps};
 use sampling::source::Source;
 
 use crate::{
-    AutomorphismKey, FourierGLWECiphertext, GLWEPlaintext, GLWESecret, GetRow, Infos, div_ceil,
-    test_fft64::log2_std_noise_gglwe_product,
+    FourierGLWECiphertext, FourierGLWESecret, GLWEAutomorphismKey, GLWEPlaintext, GLWESecret, GetRow, Infos, div_ceil,
+    noise::log2_std_noise_gglwe_product,
 };
 
 #[test]
@@ -58,24 +58,25 @@
     let rows_in: usize = k_in / (basek * digits);
     let rows_apply: usize = k_in.div_ceil(basek * digits);
 
-    let mut auto_key_in: AutomorphismKey<Vec<u8>, FFT64> = AutomorphismKey::alloc(&module, basek, k_in, rows_in, digits_in, rank);
-    let mut auto_key_out: AutomorphismKey<Vec<u8>, FFT64> =
-        AutomorphismKey::alloc(&module, basek, k_out, rows_in, digits_in, rank);
-    let mut auto_key_apply: AutomorphismKey<Vec<u8>, FFT64> =
-        AutomorphismKey::alloc(&module, basek, k_apply, rows_apply, digits, rank);
+    let mut auto_key_in: GLWEAutomorphismKey<Vec<u8>, FFT64> =
+        GLWEAutomorphismKey::alloc(&module, basek, k_in, rows_in, digits_in, rank);
+    let mut auto_key_out: GLWEAutomorphismKey<Vec<u8>, FFT64> =
+        GLWEAutomorphismKey::alloc(&module, basek, k_out, rows_in, digits_in, rank);
+    let mut auto_key_apply: GLWEAutomorphismKey<Vec<u8>, FFT64> =
+        GLWEAutomorphismKey::alloc(&module, basek, k_apply, rows_apply, digits, rank);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
     let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        AutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_apply, rank)
+        GLWEAutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_apply, rank)
             | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_out)
-            | AutomorphismKey::automorphism_scratch_space(&module, basek, k_out, k_in, k_apply, digits, rank),
+            | GLWEAutomorphismKey::automorphism_scratch_space(&module, basek, k_out, k_in, k_apply, digits, rank),
     );
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
 
     // gglwe_{s1}(s0) = s0 -> s1
     auto_key_in.generate_from_sk(
@@ -105,7 +106,7 @@
     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);
+    let mut sk_auto: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
     sk_auto.fill_zero(); // Necessary to avoid panic of unfilled sk
     (0..rank).for_each(|i| {
         module.scalar_znx_automorphism(
@@ -117,12 +118,12 @@ i,
         );
     });
 
-    sk_auto.prep_fourier(&module);
+    let sk_auto_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_auto);
 
     (0..auto_key_out.rank_in()).for_each(|col_i| {
         (0..auto_key_out.rows()).for_each(|row_i| {
             auto_key_out.get_row(&module, row_i, col_i, &mut ct_glwe_dft);
-            ct_glwe_dft.decrypt(&module, &mut pt, &sk_auto, scratch.borrow());
+            ct_glwe_dft.decrypt(&module, &mut pt, &sk_auto_dft, scratch.borrow());
 
             module.vec_znx_sub_scalar_inplace(
                 &mut pt.data,
@@ -174,22 +175,23 @@
     let rows_in: usize = k_in / (basek * digits);
     let rows_apply: usize = k_in.div_ceil(basek * digits);
 
-    let mut auto_key: AutomorphismKey<Vec<u8>, FFT64> = AutomorphismKey::alloc(&module, basek, k_in, rows_in, digits_in, rank);
-    let mut auto_key_apply: AutomorphismKey<Vec<u8>, FFT64> =
-        AutomorphismKey::alloc(&module, basek, k_apply, rows_apply, digits, rank);
+    let mut auto_key: GLWEAutomorphismKey<Vec<u8>, FFT64> =
+        GLWEAutomorphismKey::alloc(&module, basek, k_in, rows_in, digits_in, rank);
+    let mut auto_key_apply: GLWEAutomorphismKey<Vec<u8>, FFT64> =
+        GLWEAutomorphismKey::alloc(&module, basek, k_apply, rows_apply, digits, rank);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
     let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        AutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_apply, rank)
+        GLWEAutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_apply, rank)
             | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_in)
-            | AutomorphismKey::automorphism_inplace_scratch_space(&module, basek, k_in, k_apply, digits, rank),
+            | GLWEAutomorphismKey::automorphism_inplace_scratch_space(&module, basek, k_in, k_apply, digits, rank),
     );
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
 
     // gglwe_{s1}(s0) = s0 -> s1
     auto_key.generate_from_sk(
@@ -219,8 +221,9 @@
     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);
+    let mut sk_auto: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
     sk_auto.fill_zero(); // Necessary to avoid panic of unfilled sk
+
     (0..rank).for_each(|i| {
         module.scalar_znx_automorphism(
             module.galois_element_inv(p0 * p1),
@@ -231,13 +234,13 @@ i,
         );
     });
 
-    sk_auto.prep_fourier(&module);
+    let sk_auto_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_auto);
 
     (0..auto_key.rank_in()).for_each(|col_i| {
         (0..auto_key.rows()).for_each(|row_i| {
             auto_key.get_row(&module, row_i, col_i, &mut ct_glwe_dft);
 
-            ct_glwe_dft.decrypt(&module, &mut pt, &sk_auto, scratch.borrow());
+            ct_glwe_dft.decrypt(&module, &mut pt, &sk_auto_dft, scratch.borrow());
             module.vec_znx_sub_scalar_inplace(
                 &mut pt.data,
                 0,

@@ -2,8 +2,9 @@ use backend::{FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScalarZnxToMut, ScratchOwned, Stats, VecZnxOps, ZnxViewMut};
 use sampling::source::Source;
 
 use crate::{
-    FourierGLWECiphertext, GGSWCiphertext, GLWEPlaintext, GLWESecret, GLWESwitchingKey, GetRow, Infos, div_ceil,
-    test_fft64::{log2_std_noise_gglwe_product, noise_ggsw_product},
+    FourierGLWECiphertext, FourierGLWESecret, GGSWCiphertext, GLWEPlaintext, GLWESecret, GLWESwitchingKey, GetRow, Infos,
+    div_ceil,
+    noise::{log2_std_noise_gglwe_product, noise_ggsw_product},
 };
 
 #[test]
@@ -148,16 +149,17 @@ GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_ksk, rank_out)
             | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ksk),
     );
 
-    let mut sk_in: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_in);
-    sk_in.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_in);
+    sk_in.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_out: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_out);
-    sk_out.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_out);
+    sk_out.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
 
     ksk.generate_from_sk(
         &module,
         &sk_in,
-        &sk_out,
+        &sk_out_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -170,7 +172,7 @@
     (0..ksk.rank_in()).for_each(|col_i| {
         (0..ksk.rows()).for_each(|row_i| {
             ksk.get_row(&module, row_i, col_i, &mut ct_glwe_fourier);
-            ct_glwe_fourier.decrypt(&module, &mut pt, &sk_out, scratch.borrow());
+            ct_glwe_fourier.decrypt(&module, &mut pt, &sk_out_dft, scratch.borrow());
             module.vec_znx_sub_scalar_inplace(
                 &mut pt.data,
                 0,
@@ -247,20 +249,22 @@ ct_gglwe_s1s2.rank_out(),
             ),
     );
 
-    let mut sk0: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_in_s0s1);
-    sk0.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk0: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_in_s0s1);
+    sk0.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk1: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_out_s0s1);
-    sk1.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk1: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_out_s0s1);
+    sk1.fill_ternary_prob(0.5, &mut source_xs);
+    let sk1_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk1);
 
-    let mut sk2: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_out_s1s2);
-    sk2.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk2: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_out_s1s2);
+    sk2.fill_ternary_prob(0.5, &mut source_xs);
+    let sk2_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk2);
 
     // gglwe_{s1}(s0) = s0 -> s1
     ct_gglwe_s0s1.generate_from_sk(
         &module,
         &sk0,
-        &sk1,
+        &sk1_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -271,7 +275,7 @@ // gglwe_{s2}(s1) -> s1 -> s2
     ct_gglwe_s1s2.generate_from_sk(
         &module,
         &sk1,
-        &sk2,
+        &sk2_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -288,7 +292,7 @@
     (0..ct_gglwe_s0s2.rank_in()).for_each(|col_i| {
         (0..ct_gglwe_s0s2.rows()).for_each(|row_i| {
             ct_gglwe_s0s2.get_row(&module, row_i, col_i, &mut ct_glwe_dft);
-            ct_glwe_dft.decrypt(&module, &mut pt, &sk2, scratch.borrow());
+            ct_glwe_dft.decrypt(&module, &mut pt, &sk2_dft, scratch.borrow());
             module.vec_znx_sub_scalar_inplace(
                 &mut pt.data,
                 0,
@@ -350,20 +354,22 @@ | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ksk)
             | GLWESwitchingKey::keyswitch_inplace_scratch_space(&module, basek, k_ct, k_ksk, digits, rank_out),
     );
 
-    let mut sk0: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_in);
-    sk0.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk0: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_in);
+    sk0.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk1: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_out);
-    sk1.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk1: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_out);
+    sk1.fill_ternary_prob(0.5, &mut source_xs);
+    let sk1_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk1);
 
-    let mut sk2: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_out);
-    sk2.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk2: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_out);
+    sk2.fill_ternary_prob(0.5, &mut source_xs);
+    let sk2_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk2);
 
     // gglwe_{s1}(s0) = s0 -> s1
     ct_gglwe_s0s1.generate_from_sk(
         &module,
         &sk0,
-        &sk1,
+        &sk1_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -374,7 +380,7 @@ // gglwe_{s2}(s1) -> s1 -> s2
     ct_gglwe_s1s2.generate_from_sk(
         &module,
         &sk1,
-        &sk2,
+        &sk2_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -392,7 +398,7 @@
     (0..ct_gglwe_s0s2.rank_in()).for_each(|col_i| {
         (0..ct_gglwe_s0s2.rows()).for_each(|row_i| {
             ct_gglwe_s0s2.get_row(&module, row_i, col_i, &mut ct_glwe_dft);
-            ct_glwe_dft.decrypt(&module, &mut pt, &sk2, scratch.borrow());
+            ct_glwe_dft.decrypt(&module, &mut pt, &sk2_dft, scratch.borrow());
             module.vec_znx_sub_scalar_inplace(
                 &mut pt.data,
                 0,
@@ -464,17 +470,18 @@ let r: usize = 1;
 
     pt_rgsw.to_mut().raw_mut()[r] = 1; // X^{r}
 
-    let mut sk_in: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_in);
-    sk_in.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_in);
+    sk_in.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_out: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_out);
-    sk_out.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_out);
+    sk_out.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
 
     // gglwe_{s1}(s0) = s0 -> s1
     ct_gglwe_in.generate_from_sk(
         &module,
         &sk_in,
-        &sk_out,
+        &sk_out_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -484,7 +491,7 @@
     ct_rgsw.encrypt_sk(
         &module,
         &pt_rgsw,
-        &sk_out,
+        &sk_out_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -504,7 +511,7 @@
     (0..rank_in).for_each(|col_i| {
         (0..ct_gglwe_out.rows()).for_each(|row_i| {
             ct_gglwe_out.get_row(&module, row_i, col_i, &mut ct_glwe_dft);
-            ct_glwe_dft.decrypt(&module, &mut pt, &sk_out, scratch.borrow());
+            ct_glwe_dft.decrypt(&module, &mut pt, &sk_out_dft, scratch.borrow());
 
             module.vec_znx_sub_scalar_inplace(
                 &mut pt.data,
@@ -584,17 +591,18 @@ let r: usize = 1;
 
     pt_rgsw.to_mut().raw_mut()[r] = 1; // X^{r}
 
-    let mut sk_in: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_in);
-    sk_in.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_in);
+    sk_in.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_out: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_out);
-    sk_out.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank_out);
+    sk_out.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
 
     // gglwe_{s1}(s0) = s0 -> s1
     ct_gglwe.generate_from_sk(
         &module,
         &sk_in,
-        &sk_out,
+        &sk_out_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -604,7 +612,7 @@
     ct_rgsw.encrypt_sk(
         &module,
         &pt_rgsw,
-        &sk_out,
+        &sk_out_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -624,7 +632,7 @@
     (0..rank_in).for_each(|col_i| {
         (0..ct_gglwe.rows()).for_each(|row_i| {
             ct_gglwe.get_row(&module, row_i, col_i, &mut ct_glwe_dft);
-            ct_glwe_dft.decrypt(&module, &mut pt, &sk_out, scratch.borrow());
+            ct_glwe_dft.decrypt(&module, &mut pt, &sk_out_dft, scratch.borrow());
 
             module.vec_znx_sub_scalar_inplace(
                 &mut pt.data,

@@ -5,9 +5,9 @@ };
 use sampling::source::Source;
 
 use crate::{
-    FourierGLWECiphertext, GGSWCiphertext, GLWEPlaintext, GLWESecret, GLWESwitchingKey, GetRow, Infos, TensorKey,
-    automorphism::AutomorphismKey,
-    test_fft64::{noise_ggsw_keyswitch, noise_ggsw_product},
+    FourierGLWECiphertext, FourierGLWESecret, GGSWCiphertext, GLWEAutomorphismKey, GLWEPlaintext, GLWESecret, GLWESwitchingKey,
+    GLWETensorKey, GetRow, Infos, div_ceil,
+    noise::{noise_ggsw_keyswitch, noise_ggsw_product},
 };
 
 #[test]
@@ -142,13 +142,14 @@ GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k, rank)
             | FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k),
     );
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     ct.encrypt_sk(
         &module,
         &pt_scalar,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -172,14 +173,14 @@
             // mul with sk[col_j-1]
             if col_j > 0 {
                 module.vec_znx_dft(1, 0, &mut pt_dft, 0, &pt_want.data, 0);
-                module.svp_apply_inplace(&mut pt_dft, 0, &sk.data_fourier, col_j - 1);
+                module.svp_apply_inplace(&mut pt_dft, 0, &sk_dft.data, col_j - 1);
                 module.vec_znx_idft_tmp_a(&mut pt_big, 0, &mut pt_dft, 0);
                 module.vec_znx_big_normalize(basek, &mut pt_want.data, 0, &pt_big, 0, scratch.borrow());
             }
 
             ct.get_row(&module, row_i, col_j, &mut ct_glwe_fourier);
 
-            ct_glwe_fourier.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+            ct_glwe_fourier.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
 
             module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
 
@@ -209,7 +210,7 @@ let digits_in: usize = 1;
 
     let mut ct_in: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k_in, rows, digits_in, rank);
     let mut ct_out: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k_out, rows, digits_in, rank);
-    let mut tsk: TensorKey<Vec<u8>, FFT64> = TensorKey::alloc(&module, basek, k_ksk, rows, digits, rank);
+    let mut tsk: GLWETensorKey<Vec<u8>, FFT64> = GLWETensorKey::alloc(&module, basek, k_ksk, rows, digits, rank);
     let mut ksk: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, digits, rank, rank);
     let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
     let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
@@ -223,7 +224,7 @@ let mut scratch: ScratchOwned = ScratchOwned::new(
         GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_in, rank)
             | 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)
+            | GLWETensorKey::generate_from_sk_scratch_space(&module, basek, k_tsk, rank)
             | GGSWCiphertext::keyswitch_scratch_space(
                 &module, basek, k_out, k_in, k_ksk, digits, k_tsk, digits, rank,
             ),
@@ -231,16 +232,18 @@ );
 
     let var_xs: f64 = 0.5;
 
-    let mut sk_in: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk_in.fill_ternary_prob(&module, var_xs, &mut source_xs);
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_in.fill_ternary_prob(var_xs, &mut source_xs);
+    let sk_in_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_in);
 
-    let mut sk_out: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk_out.fill_ternary_prob(&module, var_xs, &mut source_xs);
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_out.fill_ternary_prob(var_xs, &mut source_xs);
+    let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
 
     ksk.generate_from_sk(
         &module,
         &sk_in,
-        &sk_out,
+        &sk_out_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -248,7 +251,7 @@ scratch.borrow(),
     );
     tsk.generate_from_sk(
         &module,
-        &sk_out,
+        &sk_out_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -260,7 +263,7 @@
     ct_in.encrypt_sk(
         &module,
         &pt_scalar,
-        &sk_in,
+        &sk_in_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -280,14 +283,14 @@
             // mul with sk[col_j-1]
             if col_j > 0 {
                 module.vec_znx_dft(1, 0, &mut pt_dft, 0, &pt_want.data, 0);
-                module.svp_apply_inplace(&mut pt_dft, 0, &sk_out.data_fourier, col_j - 1);
+                module.svp_apply_inplace(&mut pt_dft, 0, &sk_out_dft.data, col_j - 1);
                 module.vec_znx_idft_tmp_a(&mut pt_big, 0, &mut pt_dft, 0);
                 module.vec_znx_big_normalize(basek, &mut pt_want.data, 0, &pt_big, 0, scratch.borrow());
             }
 
             ct_out.get_row(&module, row_i, col_j, &mut ct_glwe_fourier);
 
-            ct_glwe_fourier.decrypt(&module, &mut pt_have, &sk_out, scratch.borrow());
+            ct_glwe_fourier.decrypt(&module, &mut pt_have, &sk_out_dft, scratch.borrow());
 
             module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
 
@@ -336,7 +339,7 @@
     let digits_in: usize = 1;
 
     let mut ct: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k_ct, rows, digits_in, rank);
-    let mut tsk: TensorKey<Vec<u8>, FFT64> = TensorKey::alloc(&module, basek, k_tsk, rows, digits, rank);
+    let mut tsk: GLWETensorKey<Vec<u8>, FFT64> = GLWETensorKey::alloc(&module, basek, k_tsk, rows, digits, rank);
     let mut ksk: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, digits, rank, rank);
     let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
     let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
@@ -350,22 +353,24 @@ let mut scratch: ScratchOwned = ScratchOwned::new(
         GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_ct, rank)
             | 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)
+            | GLWETensorKey::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),
     );
 
     let var_xs: f64 = 0.5;
 
-    let mut sk_in: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk_in.fill_ternary_prob(&module, var_xs, &mut source_xs);
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_in.fill_ternary_prob(var_xs, &mut source_xs);
+    let sk_in_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_in);
 
-    let mut sk_out: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk_out.fill_ternary_prob(&module, var_xs, &mut source_xs);
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_out.fill_ternary_prob(var_xs, &mut source_xs);
+    let sk_out_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk_out);
 
     ksk.generate_from_sk(
         &module,
         &sk_in,
-        &sk_out,
+        &sk_out_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -373,7 +378,7 @@ scratch.borrow(),
     );
     tsk.generate_from_sk(
         &module,
-        &sk_out,
+        &sk_out_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -385,7 +390,7 @@
     ct.encrypt_sk(
         &module,
         &pt_scalar,
-        &sk_in,
+        &sk_in_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -411,14 +416,14 @@
             // mul with sk[col_j-1]
             if col_j > 0 {
                 module.vec_znx_dft(1, 0, &mut pt_dft, 0, &pt_want.data, 0);
-                module.svp_apply_inplace(&mut pt_dft, 0, &sk_out.data_fourier, col_j - 1);
+                module.svp_apply_inplace(&mut pt_dft, 0, &sk_out_dft.data, col_j - 1);
                 module.vec_znx_idft_tmp_a(&mut pt_big, 0, &mut pt_dft, 0);
                 module.vec_znx_big_normalize(basek, &mut pt_want.data, 0, &pt_big, 0, scratch.borrow());
             }
 
             ct.get_row(&module, row_i, col_j, &mut ct_glwe_fourier);
 
-            ct_glwe_fourier.decrypt(&module, &mut pt_have, &sk_out, scratch.borrow());
+            ct_glwe_fourier.decrypt(&module, &mut pt_have, &sk_out_dft, scratch.borrow());
 
             module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
 
@@ -471,8 +476,8 @@ let digits_in: usize = 1;
 
     let mut ct_in: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k_in, rows_in, digits_in, rank);
     let mut ct_out: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k_out, rows_in, digits_in, rank);
-    let mut tensor_key: TensorKey<Vec<u8>, FFT64> = TensorKey::alloc(&module, basek, k_tsk, rows, digits, rank);
-    let mut auto_key: AutomorphismKey<Vec<u8>, FFT64> = AutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
+    let mut tensor_key: GLWETensorKey<Vec<u8>, FFT64> = GLWETensorKey::alloc(&module, basek, k_tsk, rows, digits, rank);
+    let mut auto_key: GLWEAutomorphismKey<Vec<u8>, FFT64> = GLWEAutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
     let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
     let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
     let mut pt_scalar: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
@@ -484,8 +489,8 @@
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_in, rank)
             | 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)
+            | GLWEAutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_ksk, rank)
+            | GLWETensorKey::generate_from_sk_scratch_space(&module, basek, k_tsk, rank)
             | GGSWCiphertext::automorphism_scratch_space(
                 &module, basek, k_out, k_in, k_ksk, digits, k_tsk, digits, rank,
             ),
@@ -493,8 +498,9 @@ );
 
     let var_xs: f64 = 0.5;
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, var_xs, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(var_xs, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     auto_key.generate_from_sk(
         &module,
@@ -507,7 +513,7 @@ scratch.borrow(),
     );
     tensor_key.generate_from_sk(
         &module,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -519,7 +525,7 @@
     ct_in.encrypt_sk(
         &module,
         &pt_scalar,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -541,14 +547,14 @@
             // mul with sk[col_j-1]
             if col_j > 0 {
                 module.vec_znx_dft(1, 0, &mut pt_dft, 0, &pt_want.data, 0);
-                module.svp_apply_inplace(&mut pt_dft, 0, &sk.data_fourier, col_j - 1);
+                module.svp_apply_inplace(&mut pt_dft, 0, &sk_dft.data, col_j - 1);
                 module.vec_znx_idft_tmp_a(&mut pt_big, 0, &mut pt_dft, 0);
                 module.vec_znx_big_normalize(basek, &mut pt_want.data, 0, &pt_big, 0, scratch.borrow());
             }
 
             ct_out.get_row(&module, row_i, col_j, &mut ct_glwe_fourier);
 
-            ct_glwe_fourier.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+            ct_glwe_fourier.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
 
             module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
 
@@ -596,8 +602,8 @@ let rows_in: usize = k_ct.div_euclid(basek * digits);
     let digits_in: usize = 1;
 
     let mut ct: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k_ct, rows_in, digits_in, rank);
-    let mut tensor_key: TensorKey<Vec<u8>, FFT64> = TensorKey::alloc(&module, basek, k_tsk, rows, digits, rank);
-    let mut auto_key: AutomorphismKey<Vec<u8>, FFT64> = AutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
+    let mut tensor_key: GLWETensorKey<Vec<u8>, FFT64> = GLWETensorKey::alloc(&module, basek, k_tsk, rows, digits, rank);
+    let mut auto_key: GLWEAutomorphismKey<Vec<u8>, FFT64> = GLWEAutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
     let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
     let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
     let mut pt_scalar: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
@@ -609,15 +615,16 @@
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_ct, rank)
             | 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)
+            | GLWEAutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_ksk, rank)
+            | GLWETensorKey::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),
     );
 
     let var_xs: f64 = 0.5;
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, var_xs, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(var_xs, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     auto_key.generate_from_sk(
         &module,
@@ -630,7 +637,7 @@ scratch.borrow(),
     );
     tensor_key.generate_from_sk(
         &module,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -642,7 +649,7 @@
     ct.encrypt_sk(
         &module,
         &pt_scalar,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -664,14 +671,14 @@
             // mul with sk[col_j-1]
             if col_j > 0 {
                 module.vec_znx_dft(1, 0, &mut pt_dft, 0, &pt_want.data, 0);
-                module.svp_apply_inplace(&mut pt_dft, 0, &sk.data_fourier, col_j - 1);
+                module.svp_apply_inplace(&mut pt_dft, 0, &sk_dft.data, col_j - 1);
                 module.vec_znx_idft_tmp_a(&mut pt_big, 0, &mut pt_dft, 0);
                 module.vec_znx_big_normalize(basek, &mut pt_want.data, 0, &pt_big, 0, scratch.borrow());
             }
 
             ct.get_row(&module, row_i, col_j, &mut ct_glwe_fourier);
 
-            ct_glwe_fourier.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+            ct_glwe_fourier.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
 
             module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
 
@@ -742,13 +749,14 @@ | 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),
     );
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     ct_ggsw_rhs.encrypt_sk(
         &module,
         &pt_ggsw_rhs,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -758,7 +766,7 @@
     ct_ggsw_lhs_in.encrypt_sk(
         &module,
         &pt_ggsw_lhs,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -787,13 +795,13 @@ );
 
             if col_j > 0 {
                 module.vec_znx_dft(1, 0, &mut pt_dft, 0, &pt_want.data, 0);
-                module.svp_apply_inplace(&mut pt_dft, 0, &sk.data_fourier, col_j - 1);
+                module.svp_apply_inplace(&mut pt_dft, 0, &sk_dft.data, col_j - 1);
                 module.vec_znx_idft_tmp_a(&mut pt_big, 0, &mut pt_dft, 0);
                 module.vec_znx_big_normalize(basek, &mut pt_want.data, 0, &pt_big, 0, scratch.borrow());
             }
 
             ct_ggsw_lhs_out.get_row(&module, row_i, col_j, &mut ct_glwe_fourier);
-            ct_glwe_fourier.decrypt(&module, &mut pt, &sk, scratch.borrow());
+            ct_glwe_fourier.decrypt(&module, &mut pt, &sk_dft, scratch.borrow());
 
             module.vec_znx_sub_ab_inplace(&mut pt.data, 0, &pt_want.data, 0);
 
@@ -862,13 +870,14 @@ | GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k_ggsw, rank)
             | GGSWCiphertext::external_product_inplace_scratch_space(&module, basek, k_ct, k_ggsw, digits, rank),
     );
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     ct_ggsw_rhs.encrypt_sk(
         &module,
         &pt_ggsw_rhs,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -878,7 +887,7 @@
     ct_ggsw_lhs.encrypt_sk(
         &module,
         &pt_ggsw_lhs,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -907,13 +916,13 @@ );
 
             if col_j > 0 {
                 module.vec_znx_dft(1, 0, &mut pt_dft, 0, &pt_want.data, 0);
-                module.svp_apply_inplace(&mut pt_dft, 0, &sk.data_fourier, col_j - 1);
+                module.svp_apply_inplace(&mut pt_dft, 0, &sk_dft.data, col_j - 1);
                 module.vec_znx_idft_tmp_a(&mut pt_big, 0, &mut pt_dft, 0);
                 module.vec_znx_big_normalize(basek, &mut pt_want.data, 0, &pt_big, 0, scratch.borrow());
             }
 
             ct_ggsw_lhs.get_row(&module, row_i, col_j, &mut ct_glwe_fourier);
-            ct_glwe_fourier.decrypt(&module, &mut pt, &sk, scratch.borrow());
+            ct_glwe_fourier.decrypt(&module, &mut pt, &sk_dft, scratch.borrow());
 
             module.vec_znx_sub_ab_inplace(&mut pt.data, 0, &pt_want.data, 0);
 

@@ -1,9 +1,4 @@
-mod automorphism_key;
-mod gglwe;
-mod ggsw;
-mod glwe_fourier;
-mod tensor_key;
-
+#[allow(dead_code)]
 pub(crate) fn var_noise_gglwe_product(
     n: f64,
     basek: usize,
@@ -34,6 +29,7 @@ noise /= b_scale * b_scale;
     noise
 }
 
+#[allow(dead_code)]
 pub(crate) fn log2_std_noise_gglwe_product(
     n: f64,
     basek: usize,
@@ -62,6 +58,7 @@ noise = noise.sqrt();
     noise.log2().min(-1.0).max(-(a_logq as f64)) // max noise is [-2^{-1}, 2^{-1}]
 }
 
+#[allow(dead_code)]
 pub(crate) fn noise_ggsw_product(
     n: f64,
     basek: usize,
@@ -94,6 +91,7 @@ noise /= b_scale;
     noise.log2().min(-1.0) // max noise is [-2^{-1}, 2^{-1}]
 }
 
+#[allow(dead_code)]
 pub(crate) fn noise_ggsw_keyswitch(
     n: f64,
     basek: usize,

@@ -1,7 +1,7 @@
 use backend::{FFT64, Module, ScalarZnxDftOps, ScratchOwned, Stats, VecZnxOps};
 use sampling::source::Source;
 
-use crate::{FourierGLWECiphertext, GLWEPlaintext, GLWESecret, GetRow, Infos, TensorKey};
+use crate::{FourierGLWECiphertext, FourierGLWESecret, GLWEPlaintext, GLWESecret, GLWETensorKey, GetRow, Infos};
 
 #[test]
 fn encrypt_sk() {
@@ -17,25 +17,26 @@ let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
 
     let rows: usize = k / basek;
 
-    let mut tensor_key: TensorKey<Vec<u8>, FFT64> = TensorKey::alloc(&module, basek, k, rows, 1, rank);
+    let mut tensor_key: GLWETensorKey<Vec<u8>, FFT64> = GLWETensorKey::alloc(&module, basek, k, rows, 1, rank);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
     let mut source_xa: Source = Source::new([0u8; 32]);
 
-    let mut scratch: ScratchOwned = ScratchOwned::new(TensorKey::generate_from_sk_scratch_space(
+    let mut scratch: ScratchOwned = ScratchOwned::new(GLWETensorKey::generate_from_sk_scratch_space(
         &module,
         basek,
         tensor_key.k(),
         rank,
     ));
 
-    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::from(&module, &sk);
 
     tensor_key.generate_from_sk(
         &module,
-        &sk,
+        &sk_dft,
         &mut source_xa,
         &mut source_xe,
         sigma,
@@ -45,25 +46,19 @@
     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);
+    let mut sk_ij_dft: FourierGLWESecret<Vec<u8>, FFT64> = FourierGLWESecret::alloc(&module, 1);
+    let mut sk_ij: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, 1);
 
     (0..rank).for_each(|i| {
         (0..rank).for_each(|j| {
-            module.svp_apply(
-                &mut sk_ij.data_fourier,
-                0,
-                &sk.data_fourier,
-                i,
-                &sk.data_fourier,
-                j,
-            );
-            module.svp_idft(&mut sk_ij.data, 0, &sk_ij.data_fourier, 0, scratch.borrow());
+            module.svp_apply(&mut sk_ij_dft.data, 0, &sk_dft.data, i, &sk_dft.data, j);
+            module.scalar_znx_idft(&mut sk_ij.data, 0, &sk_ij_dft.data, 0, scratch.borrow());
             (0..tensor_key.rank_in()).for_each(|col_i| {
                 (0..tensor_key.rows()).for_each(|row_i| {
                     tensor_key
                         .at(i, j)
                         .get_row(&module, row_i, col_i, &mut ct_glwe_fourier);
-                    ct_glwe_fourier.decrypt(&module, &mut pt, &sk, scratch.borrow());
+                    ct_glwe_fourier.decrypt(&module, &mut pt, &sk_dft, scratch.borrow());
                     module.vec_znx_sub_scalar_inplace(&mut pt.data, 0, row_i, &sk_ij.data, col_i);
                     let std_pt: f64 = pt.data.std(0, basek) * (k as f64).exp2();
                     assert!((sigma - std_pt).abs() <= 0.5, "{} {}", sigma, std_pt);