diff --git a/base2k/src/module.rs b/base2k/src/module.rs
index 0e7d124..aab18b4 100644
--- a/base2k/src/module.rs
+++ b/base2k/src/module.rs
@@ -1,106 +1,107 @@
-use crate::GALOISGENERATOR;
-use crate::ffi::module::{MODULE, delete_module_info, module_info_t, new_module_info};
-use std::marker::PhantomData;
-
-#[derive(Copy, Clone)]
-#[repr(u8)]
-pub enum BACKEND {
-    FFT64,
-    NTT120,
-}
-
-pub trait Backend {
-    const KIND: BACKEND;
-    fn module_type() -> u32;
-}
-
-pub struct FFT64;
-pub struct NTT120;
-
-impl Backend for FFT64 {
-    const KIND: BACKEND = BACKEND::FFT64;
-    fn module_type() -> u32 {
-        0
-    }
-}
-
-impl Backend for NTT120 {
-    const KIND: BACKEND = BACKEND::NTT120;
-    fn module_type() -> u32 {
-        1
-    }
-}
-
-pub struct Module<B: Backend> {
-    pub ptr: *mut MODULE,
-    n: usize,
-    _marker: PhantomData<B>,
-}
-
-impl<B: Backend> Module<B> {
-    // Instantiates a new module.
-    pub fn new(n: usize) -> Self {
-        unsafe {
-            let m: *mut module_info_t = new_module_info(n as u64, B::module_type());
-            if m.is_null() {
-                panic!("Failed to create module.");
-            }
-            Self {
-                ptr: m,
-                n: n,
-                _marker: PhantomData,
-            }
-        }
-    }
-
-    pub fn n(&self) -> usize {
-        self.n
-    }
-
-    pub fn log_n(&self) -> usize {
-        (usize::BITS - (self.n() - 1).leading_zeros()) as _
-    }
-
-    pub fn cyclotomic_order(&self) -> u64 {
-        (self.n() << 1) as _
-    }
-
-    // Returns GALOISGENERATOR^|generator| * sign(generator)
-    pub fn galois_element(&self, generator: i64) -> i64 {
-        if generator == 0 {
-            return 1;
-        }
-        ((mod_exp_u64(GALOISGENERATOR, generator.abs() as usize) & (self.cyclotomic_order() - 1)) as i64) * generator.signum()
-    }
-
-    // Returns gen^-1
-    pub fn galois_element_inv(&self, generator: i64) -> i64 {
-        if generator == 0 {
-            panic!("cannot invert 0")
-        }
-        ((mod_exp_u64(
-            generator.abs() as u64,
-            (self.cyclotomic_order() - 1) as usize,
-        ) & (self.cyclotomic_order() - 1)) as i64)
-            * generator.signum()
-    }
-
-    pub fn free(self) {
-        unsafe { delete_module_info(self.ptr) }
-        drop(self);
-    }
-}
-
-fn mod_exp_u64(x: u64, e: usize) -> u64 {
-    let mut y: u64 = 1;
-    let mut x_pow: u64 = x;
-    let mut exp = e;
-    while exp > 0 {
-        if exp & 1 == 1 {
-            y = y.wrapping_mul(x_pow);
-        }
-        x_pow = x_pow.wrapping_mul(x_pow);
-        exp >>= 1;
-    }
-    y
-}
+use crate::GALOISGENERATOR;
+use crate::ffi::module::{MODULE, delete_module_info, module_info_t, new_module_info};
+use std::marker::PhantomData;
+
+#[derive(Copy, Clone)]
+#[repr(u8)]
+pub enum BACKEND {
+    FFT64,
+    NTT120,
+}
+
+pub trait Backend {
+    const KIND: BACKEND;
+    fn module_type() -> u32;
+}
+
+pub struct FFT64;
+pub struct NTT120;
+
+impl Backend for FFT64 {
+    const KIND: BACKEND = BACKEND::FFT64;
+    fn module_type() -> u32 {
+        0
+    }
+}
+
+impl Backend for NTT120 {
+    const KIND: BACKEND = BACKEND::NTT120;
+    fn module_type() -> u32 {
+        1
+    }
+}
+
+pub struct Module<B: Backend> {
+    pub ptr: *mut MODULE,
+    n: usize,
+    _marker: PhantomData<B>,
+}
+
+impl<B: Backend> Module<B> {
+    // Instantiates a new module.
+    pub fn new(n: usize) -> Self {
+        unsafe {
+            let m: *mut module_info_t = new_module_info(n as u64, B::module_type());
+            if m.is_null() {
+                panic!("Failed to create module.");
+            }
+            Self {
+                ptr: m,
+                n: n,
+                _marker: PhantomData,
+            }
+        }
+    }
+
+    pub fn n(&self) -> usize {
+        self.n
+    }
+
+    pub fn log_n(&self) -> usize {
+        (usize::BITS - (self.n() - 1).leading_zeros()) as _
+    }
+
+    pub fn cyclotomic_order(&self) -> u64 {
+        (self.n() << 1) as _
+    }
+
+    // Returns GALOISGENERATOR^|generator| * sign(generator)
+    pub fn galois_element(&self, generator: i64) -> i64 {
+        if generator == 0 {
+            return 1;
+        }
+        ((mod_exp_u64(GALOISGENERATOR, generator.abs() as usize) & (self.cyclotomic_order() - 1)) as i64) * generator.signum()
+    }
+
+    // Returns gen^-1
+    pub fn galois_element_inv(&self, generator: i64) -> i64 {
+        if generator == 0 {
+            panic!("cannot invert 0")
+        }
+        ((mod_exp_u64(
+            generator.abs() as u64,
+            (self.cyclotomic_order() - 1) as usize,
+        ) & (self.cyclotomic_order() - 1)) as i64)
+            * generator.signum()
+    }
+}
+
+impl<B: Backend> Drop for Module<B> {
+    fn drop(&mut self) {
+         unsafe { delete_module_info(self.ptr) }
+    }
+}
+
+fn mod_exp_u64(x: u64, e: usize) -> u64 {
+    let mut y: u64 = 1;
+    let mut x_pow: u64 = x;
+    let mut exp = e;
+    while exp > 0 {
+        if exp & 1 == 1 {
+            y = y.wrapping_mul(x_pow);
+        }
+        x_pow = x_pow.wrapping_mul(x_pow);
+        exp >>= 1;
+    }
+    y
+}
diff --git a/core/Cargo.toml b/core/Cargo.toml
index 692c4fb..a54bd5a 100644
--- a/core/Cargo.toml
+++ b/core/Cargo.toml
@@ -10,3 +10,11 @@ base2k = {path="../base2k"}
 sampling = {path="../sampling"}
 rand_distr = {workspace = true}
 itertools = {workspace = true}
+
+[[bench]]
+name = "external_product_glwe_fft64"
+harness = false
+
+[[bench]]
+name = "keyswitch_glwe_fft64"
+harness = false
\ No newline at end of file
diff --git a/core/benches/external_product_glwe_fft64.rs b/core/benches/external_product_glwe_fft64.rs
new file mode 100644
index 0000000..4462fab
--- /dev/null
+++ b/core/benches/external_product_glwe_fft64.rs
@@ -0,0 +1,205 @@
+use base2k::{FFT64, Module, ScalarZnxAlloc, ScratchOwned};
+use criterion::{BenchmarkId, Criterion, black_box, criterion_group, criterion_main};
+use rlwe::{
+    elem::Infos,
+    encryption::EncryptSkScratchSpace,
+    external_product::{
+        ExternalProduct, ExternalProductInplace, ExternalProductInplaceScratchSpace, ExternalProductScratchSpace,
+    },
+    ggsw::GGSWCiphertext,
+    glwe::GLWECiphertext,
+    keys::{SecretKey, SecretKeyFourier},
+};
+use sampling::source::Source;
+
+fn bench_external_product_glwe_fft64(c: &mut Criterion) {
+    let mut group = c.benchmark_group("external_product_glwe_fft64");
+
+    struct Params {
+        log_n: usize,
+        basek: usize,
+        k_rlwe_in: usize,
+        k_rlwe_out: usize,
+        k_rgsw: usize,
+    }
+
+    fn runner(p: Params) -> impl FnMut() {
+        let module: Module<FFT64> = Module::<FFT64>::new(1 << p.log_n);
+
+        let basek: usize = p.basek;
+        let k_rlwe_in: usize = p.k_rlwe_in;
+        let k_rlwe_out: usize = p.k_rlwe_out;
+        let k_rgsw: usize = p.k_rgsw;
+
+        let rows: usize = (p.k_rlwe_in + p.basek - 1) / p.basek;
+        let sigma: f64 = 3.2;
+        let bound: f64 = sigma * 6.0;
+
+        let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, basek, k_rgsw, rows);
+        let mut ct_rlwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_rlwe_in);
+        let mut ct_rlwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_rlwe_out);
+        let pt_rgsw: base2k::ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
+
+        let mut scratch = ScratchOwned::new(
+            GGSWCiphertext::encrypt_sk_scratch_space(&module, ct_rgsw.size())
+                | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe_in.size())
+                | GLWECiphertext::external_product_scratch_space(
+                    &module,
+                    ct_rlwe_out.size(),
+                    ct_rlwe_in.size(),
+                    ct_rgsw.size(),
+                ),
+        );
+
+        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: SecretKey<Vec<u8>> = SecretKey::new(&module);
+        sk.fill_ternary_prob(0.5, &mut source_xs);
+        let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
+        sk_dft.dft(&module, &sk);
+
+        ct_rgsw.encrypt_sk(
+            &module,
+            &pt_rgsw,
+            &sk_dft,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            bound,
+            scratch.borrow(),
+        );
+
+        ct_rlwe_in.encrypt_zero_sk(
+            &module,
+            &sk_dft,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            bound,
+            scratch.borrow(),
+        );
+
+        move || {
+            ct_rlwe_out.external_product(
+                black_box(&module),
+                black_box(&ct_rlwe_in),
+                black_box(&ct_rgsw),
+                black_box(scratch.borrow()),
+            );
+        }
+    }
+
+    let params_set: Vec<Params> = vec![Params {
+        log_n: 10,
+        basek: 7,
+        k_rlwe_in: 27,
+        k_rlwe_out: 27,
+        k_rgsw: 27,
+    }];
+
+    for params in params_set {
+        let id = BenchmarkId::new("EXTERNAL_PRODUCT_GLWE_FFT64", "");
+        let mut runner = runner(params);
+        group.bench_with_input(id, &(), |b, _| b.iter(&mut runner));
+    }
+
+    group.finish();
+}
+
+fn bench_external_product_glwe_inplace_fft64(c: &mut Criterion) {
+    let mut group = c.benchmark_group("external_product_glwe_inplace_fft64");
+
+    struct Params {
+        log_n: usize,
+        basek: usize,
+        k_rlwe: usize,
+        k_rgsw: usize,
+    }
+
+    fn runner(p: Params) -> impl FnMut() {
+        let module: Module<FFT64> = Module::<FFT64>::new(1 << p.log_n);
+
+        let basek: usize = p.basek;
+        let k_rlwe: usize = p.k_rlwe;
+        let k_rgsw: usize = p.k_rgsw;
+
+        let rows: usize = (p.k_rlwe + p.basek - 1) / p.basek;
+        let sigma: f64 = 3.2;
+        let bound: f64 = sigma * 6.0;
+
+        let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, basek, k_rgsw, rows);
+        let mut ct_rlwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_rlwe);
+        let pt_rgsw: base2k::ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
+
+        let mut scratch = ScratchOwned::new(
+            GGSWCiphertext::encrypt_sk_scratch_space(&module, ct_rgsw.size())
+                | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe.size())
+                | GLWECiphertext::external_product_inplace_scratch_space(&module, ct_rlwe.size(), ct_rgsw.size()),
+        );
+
+        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: SecretKey<Vec<u8>> = SecretKey::new(&module);
+        sk.fill_ternary_prob(0.5, &mut source_xs);
+        let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
+        sk_dft.dft(&module, &sk);
+
+        ct_rgsw.encrypt_sk(
+            &module,
+            &pt_rgsw,
+            &sk_dft,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            bound,
+            scratch.borrow(),
+        );
+
+        ct_rlwe.encrypt_zero_sk(
+            &module,
+            &sk_dft,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            bound,
+            scratch.borrow(),
+        );
+
+        move || {
+            let scratch_borrow = scratch.borrow();
+            (0..1374).for_each(|i| {
+                ct_rlwe.external_product_inplace(
+                    black_box(&module),
+                    black_box(&ct_rgsw),
+                    black_box(scratch_borrow),
+                );
+            });
+        }
+    }
+
+    let params_set: Vec<Params> = vec![Params {
+        log_n: 9,
+        basek: 18,
+        k_rlwe: 27,
+        k_rgsw: 27,
+    }];
+
+    for params in params_set {
+        let id = BenchmarkId::new("EXTERNAL_PRODUCT_GLWE_INPLACE_FFT64", "");
+        let mut runner = runner(params);
+        group.bench_with_input(id, &(), |b, _| b.iter(&mut runner));
+    }
+
+    group.finish();
+}
+
+criterion_group!(
+    benches,
+    bench_external_product_glwe_fft64,
+    bench_external_product_glwe_inplace_fft64
+);
+criterion_main!(benches);
diff --git a/core/benches/keyswitch_glwe_fft64.rs b/core/benches/keyswitch_glwe_fft64.rs
new file mode 100644
index 0000000..3a25360
--- /dev/null
+++ b/core/benches/keyswitch_glwe_fft64.rs
@@ -0,0 +1,200 @@
+use base2k::{FFT64, Module, ScalarZnxAlloc, ScratchOwned};
+use criterion::{BenchmarkId, Criterion, black_box, criterion_group, criterion_main};
+use rlwe::{
+    elem::Infos,
+    encryption::EncryptSkScratchSpace,
+    glwe::GLWECiphertext,
+    keys::{SecretKey, SecretKeyFourier},
+    keyswitch::{KeySwitch, KeySwitchInplace, KeySwitchInplaceScratchSpace, KeySwitchScratchSpace},
+    keyswitch_key::GLWEKeySwitchKey,
+};
+use sampling::source::Source;
+
+fn bench_keyswitch_glwe_fft64(c: &mut Criterion) {
+    let mut group = c.benchmark_group("keyswitch_glwe_fft64");
+
+    struct Params {
+        log_n: usize,
+        basek: usize,
+        k_rlwe_in: usize,
+        k_rlwe_out: usize,
+        k_grlwe: usize,
+    }
+
+    fn runner(p: Params) -> impl FnMut() {
+        let module: Module<FFT64> = Module::<FFT64>::new(1 << p.log_n);
+
+        let basek: usize = p.basek;
+        let k_rlwe_in: usize = p.k_rlwe_in;
+        let k_rlwe_out: usize = p.k_rlwe_out;
+        let k_grlwe: usize = p.k_grlwe;
+
+        let rows: usize = (p.k_rlwe_in + p.basek - 1) / p.basek;
+        let sigma: f64 = 3.2;
+        let bound: f64 = sigma * 6.0;
+
+        let mut ct_grlwe: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, basek, k_grlwe, rows);
+        let mut ct_rlwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_rlwe_in);
+        let mut ct_rlwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_rlwe_out);
+        let pt_grlwe: base2k::ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
+
+        let mut scratch = ScratchOwned::new(
+            GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_grlwe.size())
+                | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe_in.size())
+                | GLWECiphertext::keyswitch_scratch_space(
+                    &module,
+                    ct_rlwe_out.size(),
+                    ct_rlwe_in.size(),
+                    ct_grlwe.size(),
+                ),
+        );
+
+        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: SecretKey<Vec<u8>> = SecretKey::new(&module);
+        sk.fill_ternary_prob(0.5, &mut source_xs);
+        let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
+        sk_dft.dft(&module, &sk);
+
+        ct_grlwe.encrypt_sk(
+            &module,
+            &pt_grlwe,
+            &sk_dft,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            bound,
+            scratch.borrow(),
+        );
+
+        ct_rlwe_in.encrypt_zero_sk(
+            &module,
+            &sk_dft,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            bound,
+            scratch.borrow(),
+        );
+
+        move || {
+            ct_rlwe_out.keyswitch(
+                black_box(&module),
+                black_box(&ct_rlwe_in),
+                black_box(&ct_grlwe),
+                black_box(scratch.borrow()),
+            );
+        }
+    }
+
+    let params_set: Vec<Params> = vec![Params {
+        log_n: 16,
+        basek: 50,
+        k_rlwe_in: 1250,
+        k_rlwe_out: 1250,
+        k_grlwe: 1250 + 66,
+    }];
+
+    for params in params_set {
+        let id = BenchmarkId::new("KEYSWITCH_GLWE_FFT64", "");
+        let mut runner = runner(params);
+        group.bench_with_input(id, &(), |b, _| b.iter(&mut runner));
+    }
+
+    group.finish();
+}
+
+fn bench_keyswitch_glwe_inplace_fft64(c: &mut Criterion) {
+    let mut group = c.benchmark_group("keyswitch_glwe_inplace_fft64");
+
+    struct Params {
+        log_n: usize,
+        basek: usize,
+        k_rlwe: usize,
+        k_grlwe: usize,
+    }
+
+    fn runner(p: Params) -> impl FnMut() {
+        let module: Module<FFT64> = Module::<FFT64>::new(1 << p.log_n);
+
+        let basek: usize = p.basek;
+        let k_rlwe: usize = p.k_rlwe;
+        let k_grlwe: usize = p.k_grlwe;
+
+        let rows: usize = (p.k_rlwe + p.basek - 1) / p.basek;
+        let sigma: f64 = 3.2;
+        let bound: f64 = sigma * 6.0;
+
+        let mut ct_grlwe: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, basek, k_grlwe, rows);
+        let mut ct_rlwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_rlwe);
+        let pt_grlwe: base2k::ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
+
+        let mut scratch = ScratchOwned::new(
+            GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_grlwe.size())
+                | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe.size())
+                | GLWECiphertext::keyswitch_inplace_scratch_space(&module, ct_rlwe.size(), ct_grlwe.size()),
+        );
+
+        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: SecretKey<Vec<u8>> = SecretKey::new(&module);
+        sk.fill_ternary_prob(0.5, &mut source_xs);
+        let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
+        sk_dft.dft(&module, &sk);
+
+        ct_grlwe.encrypt_sk(
+            &module,
+            &pt_grlwe,
+            &sk_dft,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            bound,
+            scratch.borrow(),
+        );
+
+        ct_rlwe.encrypt_zero_sk(
+            &module,
+            &sk_dft,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            bound,
+            scratch.borrow(),
+        );
+
+        move || {
+            ct_rlwe.keyswitch_inplace(
+                black_box(&module),
+                black_box(&ct_grlwe),
+                black_box(scratch.borrow()),
+            );
+        }
+    }
+
+    let params_set: Vec<Params> = vec![Params {
+        log_n: 9,
+        basek: 18,
+        k_rlwe: 27,
+        k_grlwe: 27,
+    }];
+
+    for params in params_set {
+        let id = BenchmarkId::new("KEYSWITCH_GLWE_INPLACE_FFT64", "");
+        let mut runner = runner(params);
+        group.bench_with_input(id, &(), |b, _| b.iter(&mut runner));
+    }
+
+    group.finish();
+}
+
+criterion_group!(
+    benches,
+    bench_keyswitch_glwe_fft64,
+    bench_keyswitch_glwe_inplace_fft64
+);
+criterion_main!(benches);
diff --git a/core/src/elem.rs b/core/src/elem.rs
index b66c86d..bf5ca1e 100644
--- a/core/src/elem.rs
+++ b/core/src/elem.rs
@@ -1,14 +1,6 @@
-use base2k::{
-    Backend, FFT64, MatZnxDft, MatZnxDftToRef, Module, Scratch, VecZnx, VecZnxAlloc, VecZnxDft, VecZnxDftAlloc, VecZnxDftOps,
-    VecZnxDftToMut, VecZnxDftToRef, VecZnxToMut, VecZnxToRef, ZnxInfos, ZnxZero,
-};
+use base2k::{Backend, Module, VecZnxDft, VecZnxDftToMut, VecZnxDftToRef, ZnxInfos};
 
-use crate::{
-    grlwe::GRLWECt,
-    rgsw::RGSWCt,
-    rlwe::{RLWECt, RLWECtDft},
-    utils::derive_size,
-};
+use crate::{glwe::GLWECiphertextFourier, utils::derive_size};
 
 pub trait Infos {
     type Inner: ZnxInfos;
@@ -31,244 +23,37 @@ pub trait Infos {
     }
 
     /// Returns the number of polynomials in each row.
-    fn cols(&self) -> usize {
+    fn rank(&self) -> usize {
         self.inner().cols()
     }
 
     /// Returns the number of size per polynomial.
     fn size(&self) -> usize {
         let size: usize = self.inner().size();
-        debug_assert_eq!(size, derive_size(self.log_base2k(), self.log_k()));
+        debug_assert_eq!(size, derive_size(self.basek(), self.k()));
         size
     }
 
     /// Returns the total number of small polynomials.
     fn poly_count(&self) -> usize {
-        self.rows() * self.cols() * self.size()
+        self.rows() * self.rank() * self.size()
     }
 
     /// Returns the base 2 logarithm of the ciphertext base.
-    fn log_base2k(&self) -> usize;
+    fn basek(&self) -> usize;
 
     /// Returns the bit precision of the ciphertext.
-    fn log_k(&self) -> usize;
+    fn k(&self) -> usize;
 }
 
 pub trait GetRow<B: Backend> {
-    fn get_row<R>(&self, module: &Module<B>, row_i: usize, col_j: usize, res: &mut RLWECtDft<R, B>)
+    fn get_row<R>(&self, module: &Module<B>, row_i: usize, col_j: usize, res: &mut GLWECiphertextFourier<R, B>)
     where
         VecZnxDft<R, B>: VecZnxDftToMut<B>;
 }
 
 pub trait SetRow<B: Backend> {
-    fn set_row<A>(&mut self, module: &Module<B>, row_i: usize, col_j: usize, a: &RLWECtDft<A, B>)
+    fn set_row<A>(&mut self, module: &Module<B>, row_i: usize, col_j: usize, a: &GLWECiphertextFourier<A, B>)
     where
         VecZnxDft<A, B>: VecZnxDftToRef<B>;
 }
-
-pub trait ProdInplaceScratchSpace {
-    fn prod_by_grlwe_inplace_scratch_space(module: &Module<FFT64>, lhs: usize, rhs: usize) -> usize;
-    fn prod_by_rgsw_inplace_scratch_space(module: &Module<FFT64>, lhs: usize, rhs: usize) -> usize;
-}
-
-pub trait ProdInplace<MUT, REF>
-where
-    MatZnxDft<REF, FFT64>: MatZnxDftToRef<FFT64>,
-{
-    fn prod_by_grlwe_inplace(&mut self, module: &Module<FFT64>, rhs: &GRLWECt<REF, FFT64>, scratch: &mut Scratch);
-    fn prod_by_rgsw_inplace(&mut self, module: &Module<FFT64>, rhs: &RGSWCt<REF, FFT64>, scratch: &mut Scratch);
-}
-
-pub trait ProdScratchSpace {
-    fn prod_by_grlwe_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize;
-    fn prod_by_rgsw_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize;
-}
-
-pub trait Product<MUT, REF>
-where
-    MatZnxDft<REF, FFT64>: MatZnxDftToRef<FFT64>,
-{
-    type Lhs;
-
-    fn prod_by_grlwe(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &GRLWECt<REF, FFT64>, scratch: &mut Scratch);
-    fn prod_by_rgsw(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &RGSWCt<REF, FFT64>, scratch: &mut Scratch);
-}
-
-pub(crate) trait MatRLWEProductScratchSpace {
-    fn prod_with_rlwe_scratch_space(module: &Module<FFT64>, res_size: usize, a_size: usize, grlwe_size: usize) -> usize;
-
-    fn prod_with_rlwe_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, mat_size: usize) -> usize {
-        Self::prod_with_rlwe_scratch_space(module, res_size, res_size, mat_size)
-    }
-
-    fn prod_with_rlwe_dft_scratch_space(module: &Module<FFT64>, res_size: usize, a_size: usize, mat_size: usize) -> usize {
-        (Self::prod_with_rlwe_scratch_space(module, res_size, a_size, mat_size) | module.vec_znx_idft_tmp_bytes())
-            + module.bytes_of_vec_znx(2, a_size)
-            + module.bytes_of_vec_znx(2, res_size)
-    }
-
-    fn prod_with_rlwe_dft_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, mat_size: usize) -> usize {
-        (Self::prod_with_rlwe_inplace_scratch_space(module, res_size, mat_size) | module.vec_znx_idft_tmp_bytes())
-            + module.bytes_of_vec_znx(2, res_size)
-    }
-
-    fn prod_with_mat_rlwe_scratch_space(module: &Module<FFT64>, res_size: usize, a_size: usize, mat_size: usize) -> usize {
-        Self::prod_with_rlwe_dft_scratch_space(module, res_size, a_size, mat_size)
-            + module.bytes_of_vec_znx_dft(2, a_size)
-            + module.bytes_of_vec_znx_dft(2, res_size)
-    }
-
-    fn prod_with_mat_rlwe_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, mat_size: usize) -> usize {
-        Self::prod_with_rlwe_dft_inplace_scratch_space(module, res_size, mat_size) + module.bytes_of_vec_znx_dft(2, res_size)
-    }
-}
-
-pub(crate) trait MatRLWEProduct: Infos {
-    fn prod_with_rlwe<MUT, REF>(&self, module: &Module<FFT64>, res: &mut RLWECt<MUT>, a: &RLWECt<REF>, scratch: &mut Scratch)
-    where
-        VecZnx<MUT>: VecZnxToMut,
-        VecZnx<REF>: VecZnxToRef;
-
-    fn prod_with_rlwe_inplace<MUT>(&self, module: &Module<FFT64>, res: &mut RLWECt<MUT>, scratch: &mut Scratch)
-    where
-        VecZnx<MUT>: VecZnxToMut + VecZnxToRef,
-    {
-        unsafe {
-            let res_ptr: *mut RLWECt<MUT> = res as *mut RLWECt<MUT>; // This is ok because [Self::mul_rlwe] only updates res at the end.
-            self.prod_with_rlwe(&module, &mut *res_ptr, &*res_ptr, scratch);
-        }
-    }
-
-    fn prod_with_rlwe_dft<MUT, REF>(
-        &self,
-        module: &Module<FFT64>,
-        res: &mut RLWECtDft<MUT, FFT64>,
-        a: &RLWECtDft<REF, FFT64>,
-        scratch: &mut Scratch,
-    ) where
-        VecZnxDft<MUT, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64> + ZnxInfos,
-        VecZnxDft<REF, FFT64>: VecZnxDftToRef<FFT64> + ZnxInfos,
-    {
-        let log_base2k: usize = self.log_base2k();
-
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(res.log_base2k(), log_base2k);
-            assert_eq!(self.n(), module.n());
-            assert_eq!(res.n(), module.n());
-        }
-
-        let (a_data, scratch_1) = scratch.tmp_vec_znx(module, 2, a.size());
-
-        let mut a_idft: RLWECt<&mut [u8]> = RLWECt::<&mut [u8]> {
-            data: a_data,
-            log_base2k: a.log_base2k(),
-            log_k: a.log_k(),
-        };
-
-        a.idft(module, &mut a_idft, scratch_1);
-
-        let (res_data, scratch_2) = scratch_1.tmp_vec_znx(module, 2, res.size());
-
-        let mut res_idft: RLWECt<&mut [u8]> = RLWECt::<&mut [u8]> {
-            data: res_data,
-            log_base2k: res.log_base2k(),
-            log_k: res.log_k(),
-        };
-
-        self.prod_with_rlwe(module, &mut res_idft, &a_idft, scratch_2);
-
-        module.vec_znx_dft(res, 0, &res_idft, 0);
-        module.vec_znx_dft(res, 1, &res_idft, 1);
-    }
-
-    fn prod_with_rlwe_dft_inplace<MUT>(&self, module: &Module<FFT64>, res: &mut RLWECtDft<MUT, FFT64>, scratch: &mut Scratch)
-    where
-        VecZnxDft<MUT, FFT64>: VecZnxDftToRef<FFT64> + VecZnxDftToMut<FFT64>,
-    {
-        let log_base2k: usize = self.log_base2k();
-
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(res.log_base2k(), log_base2k);
-            assert_eq!(self.n(), module.n());
-            assert_eq!(res.n(), module.n());
-        }
-
-        let (res_data, scratch_1) = scratch.tmp_vec_znx(module, 2, res.size());
-
-        let mut res_idft: RLWECt<&mut [u8]> = RLWECt::<&mut [u8]> {
-            data: res_data,
-            log_base2k: res.log_base2k(),
-            log_k: res.log_k(),
-        };
-
-        res.idft(module, &mut res_idft, scratch_1);
-
-        self.prod_with_rlwe_inplace(module, &mut res_idft, scratch_1);
-
-        module.vec_znx_dft(res, 0, &res_idft, 0);
-        module.vec_znx_dft(res, 1, &res_idft, 1);
-    }
-
-    fn prod_with_mat_rlwe<RES, LHS>(&self, module: &Module<FFT64>, res: &mut RES, a: &LHS, scratch: &mut Scratch)
-    where
-        LHS: GetRow<FFT64> + Infos,
-        RES: SetRow<FFT64> + Infos,
-    {
-        let (tmp_row_data, scratch1) = scratch.tmp_vec_znx_dft(module, 2, a.size());
-
-        let mut tmp_a_row: RLWECtDft<&mut [u8], FFT64> = RLWECtDft::<&mut [u8], FFT64> {
-            data: tmp_row_data,
-            log_base2k: a.log_base2k(),
-            log_k: a.log_k(),
-        };
-
-        let (tmp_res_data, scratch2) = scratch1.tmp_vec_znx_dft(module, 2, res.size());
-
-        let mut tmp_res_row: RLWECtDft<&mut [u8], FFT64> = RLWECtDft::<&mut [u8], FFT64> {
-            data: tmp_res_data,
-            log_base2k: res.log_base2k(),
-            log_k: res.log_k(),
-        };
-
-        let min_rows: usize = res.rows().min(a.rows());
-
-        (0..res.rows()).for_each(|row_i| {
-            (0..res.cols()).for_each(|col_j| {
-                a.get_row(module, row_i, col_j, &mut tmp_a_row);
-                self.prod_with_rlwe_dft(module, &mut tmp_res_row, &tmp_a_row, scratch2);
-                res.set_row(module, row_i, col_j, &tmp_res_row);
-            });
-        });
-
-        tmp_res_row.data.zero();
-
-        (min_rows..res.rows()).for_each(|row_i| {
-            (0..self.cols()).for_each(|col_j| {
-                res.set_row(module, row_i, col_j, &tmp_res_row);
-            });
-        });
-    }
-
-    fn prod_with_mat_rlwe_inplace<RES>(&self, module: &Module<FFT64>, res: &mut RES, scratch: &mut Scratch)
-    where
-        RES: GetRow<FFT64> + SetRow<FFT64> + Infos,
-    {
-        let (tmp_row_data, scratch1) = scratch.tmp_vec_znx_dft(module, 2, res.size());
-
-        let mut tmp_row: RLWECtDft<&mut [u8], FFT64> = RLWECtDft::<&mut [u8], FFT64> {
-            data: tmp_row_data,
-            log_base2k: res.log_base2k(),
-            log_k: res.log_k(),
-        };
-
-        (0..res.rows()).for_each(|row_i| {
-            (0..res.cols()).for_each(|col_j| {
-                res.get_row(module, row_i, col_j, &mut tmp_row);
-                self.prod_with_rlwe_dft_inplace(module, &mut tmp_row, scratch1);
-                res.set_row(module, row_i, col_j, &tmp_row);
-            });
-        });
-    }
-}
diff --git a/core/src/encryption.rs b/core/src/encryption.rs
new file mode 100644
index 0000000..915834c
--- /dev/null
+++ b/core/src/encryption.rs
@@ -0,0 +1,105 @@
+use base2k::{Backend, Module, Scratch};
+use sampling::source::Source;
+
+pub trait EncryptSkScratchSpace {
+    fn encrypt_sk_scratch_space<B: Backend>(module: &Module<B>, ct_size: usize) -> usize;
+}
+
+pub trait EncryptSk<DataCt, DataPt, DataSk, B: Backend> {
+    type Ciphertext;
+    type Plaintext;
+    type SecretKey;
+
+    fn encrypt_sk(
+        &self,
+        module: &Module<B>,
+        ct: &mut Self::Ciphertext,
+        pt: &Self::Plaintext,
+        sk: &Self::SecretKey,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        bound: f64,
+        scratch: &mut Scratch,
+    );
+}
+
+pub trait EncryptZeroSkScratchSpace {
+    fn encrypt_zero_sk_scratch_space<B: Backend>(module: &Module<B>, ct_size: usize) -> usize;
+}
+
+pub trait EncryptZeroSk<DatCt, DataSk, B: Backend> {
+    type Ciphertext;
+    type SecretKey;
+
+    fn encrypt_zero_sk(
+        &self,
+        module: &Module<B>,
+        ct: &mut Self::Ciphertext,
+        sk: &Self::SecretKey,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        bound: f64,
+        scratch: &mut Scratch,
+    );
+}
+
+pub trait EncryptPkScratchSpace {
+    fn encrypt_pk_scratch_space<B: Backend>(module: &Module<B>, ct_size: usize) -> usize;
+}
+
+pub trait EncryptPk<DataCt, DataPt, DataPk, B: Backend> {
+    type Ciphertext;
+    type Plaintext;
+    type PublicKey;
+
+    fn encrypt_pk(
+        &self,
+        module: &Module<B>,
+        ct: &mut Self::Ciphertext,
+        pt: &Self::Plaintext,
+        pk: &Self::PublicKey,
+        source_xu: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        bound: f64,
+        scratch: &mut Scratch,
+    );
+}
+
+pub trait EncryptZeroPkScratchSpace {
+    fn encrypt_zero_pk_scratch_space<B: Backend>(module: &Module<B>, ct_size: usize) -> usize;
+}
+
+pub trait EncryptZeroPk<DataCt, DataPk, B: Backend> {
+    type Ciphertext;
+    type PublicKey;
+
+    fn encrypt_zero_pk(
+        &self,
+        module: &Module<B>,
+        ct: &mut Self::Ciphertext,
+        pk: &Self::PublicKey,
+        source_xu: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        bound: f64,
+        scratch: &mut Scratch,
+    );
+}
+
+pub trait Decrypt<DataPt, DataCt, DataSk, B: Backend> {
+    type Plaintext;
+    type Ciphertext;
+    type SecretKey;
+
+    fn decrypt(
+        &self,
+        module: &Module<B>,
+        pt: &mut Self::Plaintext,
+        ct: &Self::Ciphertext,
+        sk: &Self::SecretKey,
+        scratch: &mut Scratch,
+    );
+}
diff --git a/core/src/external_product.rs b/core/src/external_product.rs
new file mode 100644
index 0000000..e8d0a7e
--- /dev/null
+++ b/core/src/external_product.rs
@@ -0,0 +1,19 @@
+use base2k::{FFT64, Module, Scratch};
+
+pub trait ExternalProductScratchSpace {
+    fn external_product_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize;
+}
+
+pub trait ExternalProduct<DataLhs, DataRhs> {
+    type Lhs;
+    type Rhs;
+    fn external_product(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &Self::Rhs, scratch: &mut Scratch);
+}
+pub trait ExternalProductInplaceScratchSpace {
+    fn external_product_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize;
+}
+
+pub trait ExternalProductInplace<DataRhs> {
+    type Rhs;
+    fn external_product_inplace(&mut self, module: &Module<FFT64>, rhs: &Self::Rhs, scratch: &mut Scratch);
+}
diff --git a/core/src/rgsw.rs b/core/src/ggsw.rs
similarity index 51%
rename from core/src/rgsw.rs
rename to core/src/ggsw.rs
index b866252..79b12a5 100644
--- a/core/src/rgsw.rs
+++ b/core/src/ggsw.rs
@@ -7,23 +7,26 @@ use base2k::{
 use sampling::source::Source;
 
 use crate::{
-    elem::{
-        GetRow, Infos, MatRLWEProduct, MatRLWEProductScratchSpace, ProdInplace, ProdInplaceScratchSpace, ProdScratchSpace,
-        Product, SetRow,
+    elem::{GetRow, Infos, SetRow},
+    encryption::EncryptSkScratchSpace,
+    external_product::{
+        ExternalProduct, ExternalProductInplace, ExternalProductInplaceScratchSpace, ExternalProductScratchSpace,
     },
-    grlwe::GRLWECt,
-    keys::SecretKeyDft,
-    rlwe::{RLWECt, RLWECtDft, RLWEPt, encrypt_rlwe_sk},
+    glwe::{GLWECiphertext, GLWECiphertextFourier, GLWEPlaintext, encrypt_glwe_sk},
+    keys::SecretKeyFourier,
+    keyswitch::{KeySwitch, KeySwitchInplace, KeySwitchInplaceScratchSpace, KeySwitchScratchSpace},
+    keyswitch_key::GLWEKeySwitchKey,
     utils::derive_size,
+    vec_glwe_product::{VecGLWEProduct, VecGLWEProductScratchSpace},
 };
 
-pub struct RGSWCt<C, B: Backend> {
+pub struct GGSWCiphertext<C, B: Backend> {
     pub data: MatZnxDft<C, B>,
     pub log_base2k: usize,
     pub log_k: usize,
 }
 
-impl<B: Backend> RGSWCt<Vec<u8>, B> {
+impl<B: Backend> GGSWCiphertext<Vec<u8>, B> {
     pub fn new(module: &Module<B>, log_base2k: usize, log_k: usize, rows: usize) -> Self {
         Self {
             data: module.new_mat_znx_dft(rows, 2, 2, derive_size(log_base2k, log_k)),
@@ -33,23 +36,23 @@ impl<B: Backend> RGSWCt<Vec<u8>, B> {
     }
 }
 
-impl<T, B: Backend> Infos for RGSWCt<T, B> {
+impl<T, B: Backend> Infos for GGSWCiphertext<T, B> {
     type Inner = MatZnxDft<T, B>;
 
     fn inner(&self) -> &Self::Inner {
         &self.data
     }
 
-    fn log_base2k(&self) -> usize {
+    fn basek(&self) -> usize {
         self.log_base2k
     }
 
-    fn log_k(&self) -> usize {
+    fn k(&self) -> usize {
         self.log_k
     }
 }
 
-impl<C, B: Backend> MatZnxDftToMut<B> for RGSWCt<C, B>
+impl<C, B: Backend> MatZnxDftToMut<B> for GGSWCiphertext<C, B>
 where
     MatZnxDft<C, B>: MatZnxDftToMut<B>,
 {
@@ -58,7 +61,7 @@ where
     }
 }
 
-impl<C, B: Backend> MatZnxDftToRef<B> for RGSWCt<C, B>
+impl<C, B: Backend> MatZnxDftToRef<B> for GGSWCiphertext<C, B>
 where
     MatZnxDft<C, B>: MatZnxDftToRef<B>,
 {
@@ -67,9 +70,9 @@ where
     }
 }
 
-impl RGSWCt<Vec<u8>, FFT64> {
+impl GGSWCiphertext<Vec<u8>, FFT64> {
     pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, size: usize) -> usize {
-        RLWECt::encrypt_sk_scratch_space(module, size)
+        GLWECiphertext::encrypt_sk_scratch_space(module, size)
             + module.bytes_of_vec_znx(2, size)
             + module.bytes_of_vec_znx(1, size)
             + module.bytes_of_vec_znx_dft(2, size)
@@ -78,9 +81,9 @@ impl RGSWCt<Vec<u8>, FFT64> {
 
 pub fn encrypt_rgsw_sk<C, P, S>(
     module: &Module<FFT64>,
-    ct: &mut RGSWCt<C, FFT64>,
+    ct: &mut GGSWCiphertext<C, FFT64>,
     pt: &ScalarZnx<P>,
-    sk_dft: &SecretKeyDft<S, FFT64>,
+    sk_dft: &SecretKeyFourier<S, FFT64>,
     source_xa: &mut Source,
     source_xe: &mut Source,
     sigma: f64,
@@ -92,21 +95,21 @@ pub fn encrypt_rgsw_sk<C, P, S>(
     ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
 {
     let size: usize = ct.size();
-    let log_base2k: usize = ct.log_base2k();
+    let log_base2k: usize = ct.basek();
 
     let (tmp_znx_pt, scratch_1) = scratch.tmp_vec_znx(module, 1, size);
     let (tmp_znx_ct, scrach_2) = scratch_1.tmp_vec_znx(module, 2, size);
 
-    let mut vec_znx_pt: RLWEPt<&mut [u8]> = RLWEPt {
+    let mut vec_znx_pt: GLWEPlaintext<&mut [u8]> = GLWEPlaintext {
         data: tmp_znx_pt,
         log_base2k: log_base2k,
-        log_k: ct.log_k(),
+        log_k: ct.k(),
     };
 
-    let mut vec_znx_ct: RLWECt<&mut [u8]> = RLWECt {
+    let mut vec_znx_ct: GLWECiphertext<&mut [u8]> = GLWECiphertext {
         data: tmp_znx_ct,
         log_base2k: log_base2k,
-        log_k: ct.log_k(),
+        log_k: ct.k(),
     };
 
     (0..ct.rows()).for_each(|row_j| {
@@ -114,9 +117,9 @@ pub fn encrypt_rgsw_sk<C, P, S>(
         module.vec_znx_add_scalar_inplace(&mut vec_znx_pt, 0, row_j, pt, 0);
         module.vec_znx_normalize_inplace(log_base2k, &mut vec_znx_pt, 0, scrach_2);
 
-        (0..ct.cols()).for_each(|col_i| {
+        (0..ct.rank()).for_each(|col_i| {
             // rlwe encrypt of vec_znx_pt into vec_znx_ct
-            encrypt_rlwe_sk(
+            encrypt_glwe_sk(
                 module,
                 &mut vec_znx_ct,
                 Some((&vec_znx_pt, col_i)),
@@ -141,12 +144,12 @@ pub fn encrypt_rgsw_sk<C, P, S>(
     });
 }
 
-impl<C> RGSWCt<C, FFT64> {
+impl<C> GGSWCiphertext<C, FFT64> {
     pub fn encrypt_sk<P, S>(
         &mut self,
         module: &Module<FFT64>,
         pt: &ScalarZnx<P>,
-        sk_dft: &SecretKeyDft<S, FFT64>,
+        sk_dft: &SecretKeyFourier<S, FFT64>,
         source_xa: &mut Source,
         source_xe: &mut Source,
         sigma: f64,
@@ -163,11 +166,11 @@ impl<C> RGSWCt<C, FFT64> {
     }
 }
 
-impl<C> GetRow<FFT64> for RGSWCt<C, FFT64>
+impl<C> GetRow<FFT64> for GGSWCiphertext<C, FFT64>
 where
     MatZnxDft<C, FFT64>: MatZnxDftToRef<FFT64>,
 {
-    fn get_row<R>(&self, module: &Module<FFT64>, row_i: usize, col_j: usize, res: &mut RLWECtDft<R, FFT64>)
+    fn get_row<R>(&self, module: &Module<FFT64>, row_i: usize, col_j: usize, res: &mut GLWECiphertextFourier<R, FFT64>)
     where
         VecZnxDft<R, FFT64>: VecZnxDftToMut<FFT64>,
     {
@@ -175,11 +178,11 @@ where
     }
 }
 
-impl<C> SetRow<FFT64> for RGSWCt<C, FFT64>
+impl<C> SetRow<FFT64> for GGSWCiphertext<C, FFT64>
 where
     MatZnxDft<C, FFT64>: MatZnxDftToMut<FFT64>,
 {
-    fn set_row<R>(&mut self, module: &Module<FFT64>, row_i: usize, col_j: usize, a: &RLWECtDft<R, FFT64>)
+    fn set_row<R>(&mut self, module: &Module<FFT64>, row_i: usize, col_j: usize, a: &GLWECiphertextFourier<R, FFT64>)
     where
         VecZnxDft<R, FFT64>: VecZnxDftToRef<FFT64>,
     {
@@ -187,30 +190,118 @@ where
     }
 }
 
-impl MatRLWEProductScratchSpace for RGSWCt<Vec<u8>, FFT64> {
-    fn prod_with_rlwe_scratch_space(module: &Module<FFT64>, res_size: usize, a_size: usize, rgsw_size: usize) -> usize {
+impl KeySwitchScratchSpace for GGSWCiphertext<Vec<u8>, FFT64> {
+    fn keyswitch_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
+        <GLWEKeySwitchKey<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_vec_glwe_scratch_space(
+            module, res_size, lhs, rhs,
+        )
+    }
+}
+
+impl<DataSelf, DataLhs, DataRhs> KeySwitch<DataLhs, DataRhs> for GGSWCiphertext<DataSelf, FFT64>
+where
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataLhs, FFT64>: MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Lhs = GGSWCiphertext<DataLhs, FFT64>;
+    type Rhs = GLWEKeySwitchKey<DataRhs, FFT64>;
+
+    fn keyswitch(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_vec_glwe(module, self, lhs, scratch);
+    }
+}
+
+impl KeySwitchInplaceScratchSpace for GGSWCiphertext<Vec<u8>, FFT64> {
+    fn keyswitch_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize {
+        <GLWEKeySwitchKey<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_vec_glwe_inplace_scratch_space(
+            module, res_size, rhs,
+        )
+    }
+}
+
+impl<DataSelf, DataRhs> KeySwitchInplace<DataRhs> for GGSWCiphertext<DataSelf, FFT64>
+where
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Rhs = GLWEKeySwitchKey<DataRhs, FFT64>;
+
+    fn keyswitch_inplace(&mut self, module: &Module<FFT64>, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_vec_glwe(module, self, rhs, scratch);
+    }
+}
+
+impl ExternalProductScratchSpace for GGSWCiphertext<Vec<u8>, FFT64> {
+    fn external_product_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
+        <GGSWCiphertext<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_vec_glwe_scratch_space(
+            module, res_size, lhs, rhs,
+        )
+    }
+}
+
+impl<DataSelf, DataLhs, DataRhs> ExternalProduct<DataLhs, DataRhs> for GGSWCiphertext<DataSelf, FFT64>
+where
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataLhs, FFT64>: MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Lhs = GGSWCiphertext<DataLhs, FFT64>;
+    type Rhs = GGSWCiphertext<DataRhs, FFT64>;
+
+    fn external_product(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_vec_glwe(module, self, lhs, scratch);
+    }
+}
+
+impl ExternalProductInplaceScratchSpace for GGSWCiphertext<Vec<u8>, FFT64> {
+    fn external_product_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize {
+        <GGSWCiphertext<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_glwe_inplace_scratch_space(
+            module, res_size, rhs,
+        )
+    }
+}
+
+impl<DataSelf, DataRhs> ExternalProductInplace<DataRhs> for GGSWCiphertext<DataSelf, FFT64>
+where
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Rhs = GGSWCiphertext<DataRhs, FFT64>;
+
+    fn external_product_inplace(&mut self, module: &Module<FFT64>, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_vec_glwe_inplace(module, self, scratch);
+    }
+}
+
+impl VecGLWEProductScratchSpace for GGSWCiphertext<Vec<u8>, FFT64> {
+    fn prod_with_glwe_scratch_space(module: &Module<FFT64>, res_size: usize, a_size: usize, rgsw_size: usize) -> usize {
         module.bytes_of_vec_znx_dft(2, rgsw_size)
             + ((module.bytes_of_vec_znx_dft(2, a_size) + module.vmp_apply_tmp_bytes(res_size, a_size, a_size, 2, 2, rgsw_size))
                 | module.vec_znx_big_normalize_tmp_bytes())
     }
 }
 
-impl<C> MatRLWEProduct for RGSWCt<C, FFT64>
+impl<C> VecGLWEProduct for GGSWCiphertext<C, FFT64>
 where
     MatZnxDft<C, FFT64>: MatZnxDftToRef<FFT64> + ZnxInfos,
 {
-    fn prod_with_rlwe<R, A>(&self, module: &Module<FFT64>, res: &mut RLWECt<R>, a: &RLWECt<A>, scratch: &mut Scratch)
-    where
-        MatZnxDft<C, FFT64>: MatZnxDftToRef<FFT64>,
+    fn prod_with_glwe<R, A>(
+        &self,
+        module: &Module<FFT64>,
+        res: &mut GLWECiphertext<R>,
+        a: &GLWECiphertext<A>,
+        scratch: &mut Scratch,
+    ) where
         VecZnx<R>: VecZnxToMut,
         VecZnx<A>: VecZnxToRef,
     {
-        let log_base2k: usize = self.log_base2k();
+        let log_base2k: usize = self.basek();
 
         #[cfg(debug_assertions)]
         {
-            assert_eq!(res.log_base2k(), log_base2k);
-            assert_eq!(a.log_base2k(), log_base2k);
+            assert_eq!(res.basek(), log_base2k);
+            assert_eq!(a.basek(), log_base2k);
             assert_eq!(self.n(), module.n());
             assert_eq!(res.n(), module.n());
             assert_eq!(a.n(), module.n());
@@ -231,53 +322,3 @@ where
         module.vec_znx_big_normalize(log_base2k, res, 1, &res_big, 1, scratch1);
     }
 }
-
-impl ProdInplaceScratchSpace for RGSWCt<Vec<u8>, FFT64> {
-    fn prod_by_grlwe_inplace_scratch_space(module: &Module<FFT64>, lhs: usize, rhs: usize) -> usize {
-        <GRLWECt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_mat_rlwe_inplace_scratch_space(module, lhs, rhs)
-    }
-
-    fn prod_by_rgsw_inplace_scratch_space(module: &Module<FFT64>, lhs: usize, rhs: usize) -> usize {
-        <RGSWCt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_mat_rlwe_inplace_scratch_space(module, lhs, rhs)
-    }
-}
-
-impl ProdScratchSpace for RGSWCt<Vec<u8>, FFT64> {
-    fn prod_by_grlwe_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
-        <GRLWECt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_mat_rlwe_scratch_space(module, res_size, lhs, rhs)
-    }
-
-    fn prod_by_rgsw_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
-        <RGSWCt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_mat_rlwe_scratch_space(module, res_size, lhs, rhs)
-    }
-}
-
-impl<MUT, REF> ProdInplace<MUT, REF> for RGSWCt<MUT, FFT64>
-where
-    RGSWCt<MUT, FFT64>: GetRow<FFT64> + SetRow<FFT64> + Infos,
-    MatZnxDft<REF, FFT64>: MatZnxDftToRef<FFT64>,
-{
-    fn prod_by_grlwe_inplace(&mut self, module: &Module<FFT64>, rhs: &GRLWECt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_mat_rlwe_inplace(module, self, scratch);
-    }
-
-    fn prod_by_rgsw_inplace(&mut self, module: &Module<FFT64>, rhs: &RGSWCt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_mat_rlwe_inplace(module, self, scratch);
-    }
-}
-
-impl<MUT, REF> Product<MUT, REF> for RGSWCt<MUT, FFT64>
-where
-    MatZnxDft<MUT, FFT64>: MatZnxDftToRef<FFT64> + MatZnxDftToMut<FFT64>,
-    MatZnxDft<REF, FFT64>: MatZnxDftToRef<FFT64>,
-{
-    type Lhs = RGSWCt<REF, FFT64>;
-
-    fn prod_by_grlwe(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &GRLWECt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_mat_rlwe(module, self, lhs, scratch);
-    }
-
-    fn prod_by_rgsw(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &RGSWCt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_mat_rlwe(module, self, lhs, scratch);
-    }
-}
diff --git a/core/src/glwe.rs b/core/src/glwe.rs
new file mode 100644
index 0000000..e50582d
--- /dev/null
+++ b/core/src/glwe.rs
@@ -0,0 +1,845 @@
+use base2k::{
+    AddNormal, Backend, FFT64, FillUniform, MatZnxDft, MatZnxDftToRef, Module, ScalarZnxAlloc, ScalarZnxDft, ScalarZnxDftAlloc,
+    ScalarZnxDftOps, ScalarZnxDftToRef, Scratch, VecZnx, VecZnxAlloc, VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDft,
+    VecZnxDftAlloc, VecZnxDftOps, VecZnxDftToMut, VecZnxDftToRef, VecZnxOps, VecZnxToMut, VecZnxToRef, ZnxInfos,
+};
+use sampling::source::Source;
+
+use crate::{
+    elem::Infos,
+    encryption::{EncryptSk, EncryptSkScratchSpace, EncryptZeroSkScratchSpace},
+    external_product::{
+        ExternalProduct, ExternalProductInplace, ExternalProductInplaceScratchSpace, ExternalProductScratchSpace,
+    },
+    ggsw::GGSWCiphertext,
+    keys::{PublicKey, SecretDistribution, SecretKeyFourier},
+    keyswitch::{KeySwitch, KeySwitchInplace, KeySwitchInplaceScratchSpace, KeySwitchScratchSpace},
+    keyswitch_key::GLWEKeySwitchKey,
+    utils::derive_size,
+    vec_glwe_product::{VecGLWEProduct, VecGLWEProductScratchSpace},
+};
+
+pub struct GLWECiphertext<C> {
+    pub data: VecZnx<C>,
+    pub log_base2k: usize,
+    pub log_k: usize,
+}
+
+impl GLWECiphertext<Vec<u8>> {
+    pub fn new<B: Backend>(module: &Module<B>, log_base2k: usize, log_k: usize) -> Self {
+        Self {
+            data: module.new_vec_znx(2, derive_size(log_base2k, log_k)),
+            log_base2k: log_base2k,
+            log_k: log_k,
+        }
+    }
+}
+
+impl<T> Infos for GLWECiphertext<T> {
+    type Inner = VecZnx<T>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.data
+    }
+
+    fn basek(&self) -> usize {
+        self.log_base2k
+    }
+
+    fn k(&self) -> usize {
+        self.log_k
+    }
+}
+
+impl<C> VecZnxToMut for GLWECiphertext<C>
+where
+    VecZnx<C>: VecZnxToMut,
+{
+    fn to_mut(&mut self) -> VecZnx<&mut [u8]> {
+        self.data.to_mut()
+    }
+}
+
+impl<C> VecZnxToRef for GLWECiphertext<C>
+where
+    VecZnx<C>: VecZnxToRef,
+{
+    fn to_ref(&self) -> VecZnx<&[u8]> {
+        self.data.to_ref()
+    }
+}
+
+impl<C> GLWECiphertext<C>
+where
+    VecZnx<C>: VecZnxToRef,
+{
+    #[allow(dead_code)]
+    pub(crate) fn dft<R>(&self, module: &Module<FFT64>, res: &mut GLWECiphertextFourier<R, FFT64>)
+    where
+        VecZnxDft<R, FFT64>: VecZnxDftToMut<FFT64> + ZnxInfos,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), 2);
+            assert_eq!(res.rank(), 2);
+            assert_eq!(self.basek(), res.basek())
+        }
+
+        module.vec_znx_dft(res, 0, self, 0);
+        module.vec_znx_dft(res, 1, self, 1);
+    }
+}
+
+impl KeySwitchScratchSpace for GLWECiphertext<Vec<u8>> {
+    fn keyswitch_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
+        <GLWEKeySwitchKey<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_glwe_scratch_space(module, res_size, lhs, rhs)
+    }
+}
+
+impl<DataSelf, DataLhs, DataRhs> KeySwitch<DataLhs, DataRhs> for GLWECiphertext<DataSelf>
+where
+    VecZnx<DataSelf>: VecZnxToMut + VecZnxToRef,
+    VecZnx<DataLhs>: VecZnxToRef,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Lhs = GLWECiphertext<DataLhs>;
+    type Rhs = GLWEKeySwitchKey<DataRhs, FFT64>;
+
+    fn keyswitch(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_glwe(module, self, lhs, scratch);
+    }
+}
+
+impl KeySwitchInplaceScratchSpace for GLWECiphertext<Vec<u8>> {
+    fn keyswitch_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize {
+        <GLWEKeySwitchKey<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_glwe_inplace_scratch_space(
+            module, res_size, rhs,
+        )
+    }
+}
+
+impl<DataSelf, DataRhs> KeySwitchInplace<DataRhs> for GLWECiphertext<DataSelf>
+where
+    VecZnx<DataSelf>: VecZnxToMut + VecZnxToRef,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Rhs = GLWEKeySwitchKey<DataRhs, FFT64>;
+
+    fn keyswitch_inplace(&mut self, module: &Module<FFT64>, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_glwe_inplace(module, self, scratch);
+    }
+}
+
+impl ExternalProductScratchSpace for GLWECiphertext<Vec<u8>> {
+    fn external_product_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
+        <GGSWCiphertext<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_glwe_scratch_space(module, res_size, lhs, rhs)
+    }
+}
+
+impl<DataSelf, DataLhs, DataRhs> ExternalProduct<DataLhs, DataRhs> for GLWECiphertext<DataSelf>
+where
+    VecZnx<DataSelf>: VecZnxToMut + VecZnxToRef,
+    VecZnx<DataLhs>: VecZnxToRef,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Lhs = GLWECiphertext<DataLhs>;
+    type Rhs = GGSWCiphertext<DataRhs, FFT64>;
+
+    fn external_product(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_glwe(module, self, lhs, scratch);
+    }
+}
+
+impl ExternalProductInplaceScratchSpace for GLWECiphertext<Vec<u8>> {
+    fn external_product_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize {
+        <GGSWCiphertext<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_glwe_inplace_scratch_space(
+            module, res_size, rhs,
+        )
+    }
+}
+
+impl<DataSelf, DataRhs> ExternalProductInplace<DataRhs> for GLWECiphertext<DataSelf>
+where
+    VecZnx<DataSelf>: VecZnxToMut + VecZnxToRef,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64> + ZnxInfos,
+{
+    type Rhs = GGSWCiphertext<DataRhs, FFT64>;
+
+    fn external_product_inplace(&mut self, module: &Module<FFT64>, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_glwe_inplace(module, self, scratch);
+    }
+}
+
+impl GLWECiphertext<Vec<u8>> {
+    pub fn encrypt_pk_scratch_space<B: Backend>(module: &Module<B>, pk_size: usize) -> usize {
+        ((module.bytes_of_vec_znx_dft(1, pk_size) + module.bytes_of_vec_znx_big(1, pk_size)) | module.bytes_of_scalar_znx(1))
+            + module.bytes_of_scalar_znx_dft(1)
+            + module.vec_znx_big_normalize_tmp_bytes()
+    }
+
+    pub fn decrypt_scratch_space<B: Backend>(module: &Module<B>, size: usize) -> usize {
+        (module.vec_znx_big_normalize_tmp_bytes() | module.bytes_of_vec_znx_dft(1, size)) + module.bytes_of_vec_znx_big(1, size)
+    }
+}
+
+impl EncryptSkScratchSpace for GLWECiphertext<Vec<u8>> {
+    fn encrypt_sk_scratch_space<B: Backend>(module: &Module<B>, size: usize) -> usize {
+        (module.vec_znx_big_normalize_tmp_bytes() | module.bytes_of_vec_znx_dft(1, size)) + module.bytes_of_vec_znx_big(1, size)
+    }
+}
+
+impl<DataCt, DataPt, DataSk> EncryptSk<DataCt, DataPt, DataSk, FFT64> for GLWECiphertext<DataCt>
+where
+    VecZnx<DataCt>: VecZnxToMut + VecZnxToRef,
+    VecZnx<DataPt>: VecZnxToRef,
+    ScalarZnxDft<DataSk, FFT64>: ScalarZnxDftToRef<FFT64>,
+{
+    type Ciphertext = GLWECiphertext<DataCt>;
+    type Plaintext = GLWEPlaintext<DataPt>;
+    type SecretKey = SecretKeyFourier<DataSk, FFT64>;
+
+    fn encrypt_sk(
+        &self,
+        module: &Module<FFT64>,
+        ct: &mut Self::Ciphertext,
+        pt: &Self::Plaintext,
+        sk: &Self::SecretKey,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        bound: f64,
+        scratch: &mut Scratch,
+    ) {
+        encrypt_glwe_sk(
+            module,
+            ct,
+            Some((pt, 0)),
+            sk,
+            source_xa,
+            source_xe,
+            sigma,
+            bound,
+            scratch,
+        );
+    }
+}
+
+pub(crate) fn encrypt_glwe_sk<DataCt, DataPt, DataSk>(
+    module: &Module<FFT64>,
+    ct: &mut GLWECiphertext<DataCt>,
+    pt: Option<(&GLWEPlaintext<DataPt>, usize)>,
+    sk_dft: &SecretKeyFourier<DataSk, FFT64>,
+    source_xa: &mut Source,
+    source_xe: &mut Source,
+    sigma: f64,
+    bound: f64,
+    scratch: &mut Scratch,
+) where
+    VecZnx<DataCt>: VecZnxToMut + VecZnxToRef,
+    VecZnx<DataPt>: VecZnxToRef,
+    ScalarZnxDft<DataSk, FFT64>: ScalarZnxDftToRef<FFT64>,
+{
+    let log_base2k: usize = ct.basek();
+    let log_k: usize = ct.k();
+    let size: usize = ct.size();
+
+    // c1 = a
+    ct.data.fill_uniform(log_base2k, 1, size, source_xa);
+
+    let (mut c0_big, scratch_1) = scratch.tmp_vec_znx_big(module, 1, size);
+
+    {
+        let (mut c0_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, size);
+        module.vec_znx_dft(&mut c0_dft, 0, ct, 1);
+
+        // c0_dft = DFT(a) * DFT(s)
+        module.svp_apply_inplace(&mut c0_dft, 0, sk_dft, 0);
+
+        // c0_big = IDFT(c0_dft)
+        module.vec_znx_idft_tmp_a(&mut c0_big, 0, &mut c0_dft, 0);
+    }
+
+    // c0_big = m - c0_big
+    if let Some((pt, col)) = pt {
+        match col {
+            0 => module.vec_znx_big_sub_small_b_inplace(&mut c0_big, 0, pt, 0),
+            1 => {
+                module.vec_znx_big_negate_inplace(&mut c0_big, 0);
+                module.vec_znx_add_inplace(ct, 1, pt, 0);
+                module.vec_znx_normalize_inplace(log_base2k, ct, 1, scratch_1);
+            }
+            _ => panic!("invalid target column: {}", col),
+        }
+    } else {
+        module.vec_znx_big_negate_inplace(&mut c0_big, 0);
+    }
+    // c0_big += e
+    c0_big.add_normal(log_base2k, 0, log_k, source_xe, sigma, bound);
+
+    // c0 = norm(c0_big = -as + m + e)
+    module.vec_znx_big_normalize(log_base2k, ct, 0, &c0_big, 0, scratch_1);
+}
+
+pub fn decrypt_glwe<P, C, S>(
+    module: &Module<FFT64>,
+    pt: &mut GLWEPlaintext<P>,
+    ct: &GLWECiphertext<C>,
+    sk_dft: &SecretKeyFourier<S, FFT64>,
+    scratch: &mut Scratch,
+) where
+    VecZnx<P>: VecZnxToMut + VecZnxToRef,
+    VecZnx<C>: VecZnxToRef,
+    ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
+{
+    let (mut c0_big, scratch_1) = scratch.tmp_vec_znx_big(module, 1, ct.size()); // TODO optimize size when pt << ct
+
+    {
+        let (mut c0_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, ct.size()); // TODO optimize size when pt << ct
+        module.vec_znx_dft(&mut c0_dft, 0, ct, 1);
+
+        // c0_dft = DFT(a) * DFT(s)
+        module.svp_apply_inplace(&mut c0_dft, 0, sk_dft, 0);
+
+        // c0_big = IDFT(c0_dft)
+        module.vec_znx_idft_tmp_a(&mut c0_big, 0, &mut c0_dft, 0);
+    }
+
+    // c0_big = (a * s) + (-a * s + m + e) = BIG(m + e)
+    module.vec_znx_big_add_small_inplace(&mut c0_big, 0, ct, 0);
+
+    // pt = norm(BIG(m + e))
+    module.vec_znx_big_normalize(ct.basek(), pt, 0, &mut c0_big, 0, scratch_1);
+
+    pt.log_base2k = ct.basek();
+    pt.log_k = pt.k().min(ct.k());
+}
+
+impl<MUT> GLWECiphertext<MUT>
+where
+    VecZnx<MUT>: VecZnxToMut + VecZnxToRef,
+{
+    pub fn encrypt_sk<R0, R1>(
+        &mut self,
+        module: &Module<FFT64>,
+        pt: &GLWEPlaintext<R0>,
+        sk_dft: &SecretKeyFourier<R1, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        bound: f64,
+        scratch: &mut Scratch,
+    ) where
+        VecZnx<R0>: VecZnxToRef,
+        ScalarZnxDft<R1, FFT64>: ScalarZnxDftToRef<FFT64>,
+    {
+        encrypt_glwe_sk(
+            module,
+            self,
+            Some((pt, 0)),
+            sk_dft,
+            source_xa,
+            source_xe,
+            sigma,
+            bound,
+            scratch,
+        )
+    }
+
+    pub fn encrypt_zero_sk<R>(
+        &mut self,
+        module: &Module<FFT64>,
+        sk_dft: &SecretKeyFourier<R, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        bound: f64,
+        scratch: &mut Scratch,
+    ) where
+        ScalarZnxDft<R, FFT64>: ScalarZnxDftToRef<FFT64>,
+    {
+        encrypt_glwe_sk::<MUT, _, R>(
+            module, self, None, sk_dft, source_xa, source_xe, sigma, bound, scratch,
+        )
+    }
+
+    pub fn encrypt_pk<R0, R1>(
+        &mut self,
+        module: &Module<FFT64>,
+        pt: &GLWEPlaintext<R0>,
+        pk: &PublicKey<R1, FFT64>,
+        source_xu: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        bound: f64,
+        scratch: &mut Scratch,
+    ) where
+        VecZnx<R0>: VecZnxToRef,
+        VecZnxDft<R1, FFT64>: VecZnxDftToRef<FFT64>,
+    {
+        encrypt_glwe_pk(
+            module,
+            self,
+            Some(pt),
+            pk,
+            source_xu,
+            source_xe,
+            sigma,
+            bound,
+            scratch,
+        )
+    }
+
+    pub fn encrypt_zero_pk<R>(
+        &mut self,
+        module: &Module<FFT64>,
+        pk: &PublicKey<R, FFT64>,
+        source_xu: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        bound: f64,
+        scratch: &mut Scratch,
+    ) where
+        VecZnxDft<R, FFT64>: VecZnxDftToRef<FFT64>,
+    {
+        encrypt_glwe_pk::<MUT, _, R>(
+            module, self, None, pk, source_xu, source_xe, sigma, bound, scratch,
+        )
+    }
+}
+
+impl<REF> GLWECiphertext<REF>
+where
+    VecZnx<REF>: VecZnxToRef,
+{
+    pub fn decrypt<MUT, REF1>(
+        &self,
+        module: &Module<FFT64>,
+        pt: &mut GLWEPlaintext<MUT>,
+        sk_dft: &SecretKeyFourier<REF1, FFT64>,
+        scratch: &mut Scratch,
+    ) where
+        VecZnx<MUT>: VecZnxToMut + VecZnxToRef,
+        ScalarZnxDft<REF1, FFT64>: ScalarZnxDftToRef<FFT64>,
+    {
+        decrypt_glwe(module, pt, self, sk_dft, scratch);
+    }
+}
+
+pub(crate) fn encrypt_glwe_pk<C, P, S>(
+    module: &Module<FFT64>,
+    ct: &mut GLWECiphertext<C>,
+    pt: Option<&GLWEPlaintext<P>>,
+    pk: &PublicKey<S, FFT64>,
+    source_xu: &mut Source,
+    source_xe: &mut Source,
+    sigma: f64,
+    bound: f64,
+    scratch: &mut Scratch,
+) where
+    VecZnx<C>: VecZnxToMut + VecZnxToRef,
+    VecZnx<P>: VecZnxToRef,
+    VecZnxDft<S, FFT64>: VecZnxDftToRef<FFT64>,
+{
+    #[cfg(debug_assertions)]
+    {
+        assert_eq!(ct.basek(), pk.basek());
+        assert_eq!(ct.n(), module.n());
+        assert_eq!(pk.n(), module.n());
+        if let Some(pt) = pt {
+            assert_eq!(pt.basek(), pk.basek());
+            assert_eq!(pt.n(), module.n());
+        }
+    }
+
+    let log_base2k: usize = pk.basek();
+    let size_pk: usize = pk.size();
+
+    // Generates u according to the underlying secret distribution.
+    let (mut u_dft, scratch_1) = scratch.tmp_scalar_znx_dft(module, 1);
+
+    {
+        let (mut u, _) = scratch_1.tmp_scalar_znx(module, 1);
+        match pk.dist {
+            SecretDistribution::NONE => panic!(
+                "invalid public key: SecretDistribution::NONE, ensure it has been correctly intialized through Self::generate"
+            ),
+            SecretDistribution::TernaryFixed(hw) => u.fill_ternary_hw(0, hw, source_xu),
+            SecretDistribution::TernaryProb(prob) => u.fill_ternary_prob(0, prob, source_xu),
+            SecretDistribution::ZERO => {}
+        }
+
+        module.svp_prepare(&mut u_dft, 0, &u, 0);
+    }
+
+    let (mut tmp_big, scratch_2) = scratch_1.tmp_vec_znx_big(module, 1, size_pk); // TODO optimize size (e.g. when encrypting at low homomorphic capacity)
+    let (mut tmp_dft, scratch_3) = scratch_2.tmp_vec_znx_dft(module, 1, size_pk); // TODO optimize size (e.g. when encrypting at low homomorphic capacity)
+
+    // ct[0] = pk[0] * u + m + e0
+    module.svp_apply(&mut tmp_dft, 0, &u_dft, 0, pk, 0);
+    module.vec_znx_idft_tmp_a(&mut tmp_big, 0, &mut tmp_dft, 0);
+    tmp_big.add_normal(log_base2k, 0, pk.k(), source_xe, sigma, bound);
+
+    if let Some(pt) = pt {
+        module.vec_znx_big_add_small_inplace(&mut tmp_big, 0, pt, 0);
+    }
+
+    module.vec_znx_big_normalize(log_base2k, ct, 0, &tmp_big, 0, scratch_3);
+
+    // ct[1] = pk[1] * u + e1
+    module.svp_apply(&mut tmp_dft, 0, &u_dft, 0, pk, 1);
+    module.vec_znx_idft_tmp_a(&mut tmp_big, 0, &mut tmp_dft, 0);
+    tmp_big.add_normal(log_base2k, 0, pk.k(), source_xe, sigma, bound);
+    module.vec_znx_big_normalize(log_base2k, ct, 1, &tmp_big, 0, scratch_3);
+}
+
+pub struct GLWEPlaintext<C> {
+    pub data: VecZnx<C>,
+    pub log_base2k: usize,
+    pub log_k: usize,
+}
+
+impl<T> Infos for GLWEPlaintext<T> {
+    type Inner = VecZnx<T>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.data
+    }
+
+    fn basek(&self) -> usize {
+        self.log_base2k
+    }
+
+    fn k(&self) -> usize {
+        self.log_k
+    }
+}
+
+impl<C> VecZnxToMut for GLWEPlaintext<C>
+where
+    VecZnx<C>: VecZnxToMut,
+{
+    fn to_mut(&mut self) -> VecZnx<&mut [u8]> {
+        self.data.to_mut()
+    }
+}
+
+impl<C> VecZnxToRef for GLWEPlaintext<C>
+where
+    VecZnx<C>: VecZnxToRef,
+{
+    fn to_ref(&self) -> VecZnx<&[u8]> {
+        self.data.to_ref()
+    }
+}
+
+impl GLWEPlaintext<Vec<u8>> {
+    pub fn new<B: Backend>(module: &Module<B>, log_base2k: usize, log_k: usize) -> Self {
+        Self {
+            data: module.new_vec_znx(1, derive_size(log_base2k, log_k)),
+            log_base2k: log_base2k,
+            log_k: log_k,
+        }
+    }
+}
+
+pub struct GLWECiphertextFourier<C, B: Backend> {
+    pub data: VecZnxDft<C, B>,
+    pub log_base2k: usize,
+    pub log_k: usize,
+}
+
+impl<B: Backend> GLWECiphertextFourier<Vec<u8>, B> {
+    pub fn new(module: &Module<B>, log_base2k: usize, log_k: usize) -> Self {
+        Self {
+            data: module.new_vec_znx_dft(2, derive_size(log_base2k, log_k)),
+            log_base2k: log_base2k,
+            log_k: log_k,
+        }
+    }
+}
+
+impl<T, B: Backend> Infos for GLWECiphertextFourier<T, B> {
+    type Inner = VecZnxDft<T, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.data
+    }
+
+    fn basek(&self) -> usize {
+        self.log_base2k
+    }
+
+    fn k(&self) -> usize {
+        self.log_k
+    }
+}
+
+impl<C, B: Backend> VecZnxDftToMut<B> for GLWECiphertextFourier<C, B>
+where
+    VecZnxDft<C, B>: VecZnxDftToMut<B>,
+{
+    fn to_mut(&mut self) -> VecZnxDft<&mut [u8], B> {
+        self.data.to_mut()
+    }
+}
+
+impl<C, B: Backend> VecZnxDftToRef<B> for GLWECiphertextFourier<C, B>
+where
+    VecZnxDft<C, B>: VecZnxDftToRef<B>,
+{
+    fn to_ref(&self) -> VecZnxDft<&[u8], B> {
+        self.data.to_ref()
+    }
+}
+
+impl<C> GLWECiphertextFourier<C, FFT64>
+where
+    GLWECiphertextFourier<C, FFT64>: VecZnxDftToRef<FFT64>,
+{
+    #[allow(dead_code)]
+    pub(crate) fn idft_scratch_space(module: &Module<FFT64>, size: usize) -> usize {
+        module.bytes_of_vec_znx(2, size) + (module.vec_znx_big_normalize_tmp_bytes() | module.vec_znx_idft_tmp_bytes())
+    }
+
+    pub(crate) fn idft<R>(&self, module: &Module<FFT64>, res: &mut GLWECiphertext<R>, scratch: &mut Scratch)
+    where
+        GLWECiphertext<R>: VecZnxToMut,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), 2);
+            assert_eq!(res.rank(), 2);
+            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, 2, min_size);
+
+        module.vec_znx_idft(&mut res_big, 0, self, 0, scratch1);
+        module.vec_znx_idft(&mut res_big, 1, self, 1, scratch1);
+        module.vec_znx_big_normalize(self.basek(), res, 0, &res_big, 0, scratch1);
+        module.vec_znx_big_normalize(self.basek(), res, 1, &res_big, 1, scratch1);
+    }
+}
+
+pub(crate) fn encrypt_zero_glwe_dft_sk<C, S>(
+    module: &Module<FFT64>,
+    ct: &mut GLWECiphertextFourier<C, FFT64>,
+    sk: &SecretKeyFourier<S, FFT64>,
+    source_xa: &mut Source,
+    source_xe: &mut Source,
+    sigma: f64,
+    bound: f64,
+    scratch: &mut Scratch,
+) where
+    VecZnxDft<C, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64>,
+    ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
+{
+    let log_base2k: usize = ct.basek();
+    let log_k: usize = ct.k();
+    let size: usize = ct.size();
+
+    #[cfg(debug_assertions)]
+    {
+        match sk.dist {
+            SecretDistribution::NONE => panic!("invalid sk.dist = SecretDistribution::NONE"),
+            _ => {}
+        }
+        assert_eq!(ct.rank(), 2);
+    }
+
+    // ct[1] = DFT(a)
+    {
+        let (mut tmp_znx, _) = scratch.tmp_vec_znx(module, 1, size);
+        tmp_znx.fill_uniform(log_base2k, 0, size, source_xa);
+        module.vec_znx_dft(ct, 1, &tmp_znx, 0);
+    }
+
+    let (mut c0_big, scratch_1) = scratch.tmp_vec_znx_big(module, 1, size);
+
+    {
+        let (mut tmp_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, size);
+        // c0_dft = ct[1] * DFT(s)
+        module.svp_apply(&mut tmp_dft, 0, sk, 0, ct, 1);
+
+        // c0_big = IDFT(c0_dft)
+        module.vec_znx_idft_tmp_a(&mut c0_big, 0, &mut tmp_dft, 0);
+    }
+
+    // c0_big += e
+    c0_big.add_normal(log_base2k, 0, log_k, source_xe, sigma, bound);
+
+    // c0 = norm(c0_big = -as - e), NOTE: e is centered at 0.
+    let (mut tmp_znx, scratch_2) = scratch_1.tmp_vec_znx(module, 1, size);
+    module.vec_znx_big_normalize(log_base2k, &mut tmp_znx, 0, &c0_big, 0, scratch_2);
+    module.vec_znx_negate_inplace(&mut tmp_znx, 0);
+    // ct[0] = DFT(-as + e)
+    module.vec_znx_dft(ct, 0, &tmp_znx, 0);
+}
+
+impl GLWECiphertextFourier<Vec<u8>, FFT64> {
+    pub fn encrypt_zero_sk_scratch_space(module: &Module<FFT64>, size: usize) -> usize {
+        (module.bytes_of_vec_znx(1, size) | module.bytes_of_vec_znx_dft(1, size))
+            + module.bytes_of_vec_znx_big(1, size)
+            + module.bytes_of_vec_znx(1, size)
+            + module.vec_znx_big_normalize_tmp_bytes()
+    }
+
+    pub fn decrypt_scratch_space(module: &Module<FFT64>, size: usize) -> usize {
+        (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)
+    }
+}
+
+pub fn decrypt_rlwe_dft<P, C, S>(
+    module: &Module<FFT64>,
+    pt: &mut GLWEPlaintext<P>,
+    ct: &GLWECiphertextFourier<C, FFT64>,
+    sk: &SecretKeyFourier<S, FFT64>,
+    scratch: &mut Scratch,
+) where
+    VecZnx<P>: VecZnxToMut + VecZnxToRef,
+    VecZnxDft<C, FFT64>: VecZnxDftToRef<FFT64>,
+    ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
+{
+    let (mut c0_big, scratch_1) = scratch.tmp_vec_znx_big(module, 1, ct.size()); // TODO optimize size when pt << ct
+
+    {
+        let (mut c0_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, ct.size()); // TODO optimize size when pt << ct
+        // c0_dft = DFT(a) * DFT(s)
+        module.svp_apply(&mut c0_dft, 0, sk, 0, ct, 1);
+        // c0_big = IDFT(c0_dft)
+        module.vec_znx_idft_tmp_a(&mut c0_big, 0, &mut c0_dft, 0);
+    }
+
+    {
+        let (mut c1_big, scratch_2) = scratch_1.tmp_vec_znx_big(module, 1, ct.size());
+        // c0_big = (a * s) + (-a * s + m + e) = BIG(m + e)
+        module.vec_znx_idft(&mut c1_big, 0, ct, 0, scratch_2);
+        module.vec_znx_big_add_inplace(&mut c0_big, 0, &c1_big, 0);
+    }
+
+    // pt = norm(BIG(m + e))
+    module.vec_znx_big_normalize(ct.basek(), pt, 0, &mut c0_big, 0, scratch_1);
+
+    pt.log_base2k = ct.basek();
+    pt.log_k = pt.k().min(ct.k());
+}
+
+impl<C> GLWECiphertextFourier<C, FFT64>
+where
+    VecZnxDft<C, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64>,
+{
+    pub(crate) fn encrypt_zero_sk<S>(
+        &mut self,
+        module: &Module<FFT64>,
+        sk_dft: &SecretKeyFourier<S, FFT64>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        bound: f64,
+        scratch: &mut Scratch,
+    ) where
+        ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
+    {
+        encrypt_zero_glwe_dft_sk(
+            module, self, sk_dft, source_xa, source_xe, sigma, bound, scratch,
+        )
+    }
+
+    pub fn decrypt<P, S>(
+        &self,
+        module: &Module<FFT64>,
+        pt: &mut GLWEPlaintext<P>,
+        sk_dft: &SecretKeyFourier<S, FFT64>,
+        scratch: &mut Scratch,
+    ) where
+        VecZnx<P>: VecZnxToMut + VecZnxToRef,
+        ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
+    {
+        decrypt_rlwe_dft(module, pt, self, sk_dft, scratch);
+    }
+}
+
+impl KeySwitchScratchSpace for GLWECiphertextFourier<Vec<u8>, FFT64> {
+    fn keyswitch_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
+        <GLWEKeySwitchKey<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_glwe_scratch_space(module, res_size, lhs, rhs)
+    }
+}
+
+impl<DataSelf, DataLhs, DataRhs> KeySwitch<DataLhs, DataRhs> for GLWECiphertextFourier<DataSelf, FFT64>
+where
+    VecZnxDft<DataSelf, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64>,
+    VecZnxDft<DataLhs, FFT64>: VecZnxDftToRef<FFT64>,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Lhs = GLWECiphertextFourier<DataLhs, FFT64>;
+    type Rhs = GLWEKeySwitchKey<DataRhs, FFT64>;
+
+    fn keyswitch(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_glwe_fourier(module, self, lhs, scratch);
+    }
+}
+
+impl KeySwitchInplaceScratchSpace for GLWECiphertextFourier<Vec<u8>, FFT64> {
+    fn keyswitch_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize {
+        <GLWEKeySwitchKey<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_glwe_inplace_scratch_space(
+            module, res_size, rhs,
+        )
+    }
+}
+
+impl<DataSelf, DataRhs> KeySwitchInplace<DataRhs> for GLWECiphertextFourier<DataSelf, FFT64>
+where
+    VecZnxDft<DataSelf, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64>,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Rhs = GLWEKeySwitchKey<DataRhs, FFT64>;
+
+    fn keyswitch_inplace(&mut self, module: &Module<FFT64>, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_glwe_fourier_inplace(module, self, scratch);
+    }
+}
+
+impl ExternalProductScratchSpace for GLWECiphertextFourier<Vec<u8>, FFT64> {
+    fn external_product_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
+        <GGSWCiphertext<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_glwe_scratch_space(module, res_size, lhs, rhs)
+    }
+}
+
+impl<DataSelf, DataLhs, DataRhs> ExternalProduct<DataLhs, DataRhs> for GLWECiphertextFourier<DataSelf, FFT64>
+where
+    VecZnxDft<DataSelf, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64>,
+    VecZnxDft<DataLhs, FFT64>: VecZnxDftToRef<FFT64>,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Lhs = GLWECiphertextFourier<DataLhs, FFT64>;
+    type Rhs = GGSWCiphertext<DataRhs, FFT64>;
+
+    fn external_product(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_glwe_fourier(module, self, lhs, scratch);
+    }
+}
+
+impl ExternalProductInplaceScratchSpace for GLWECiphertextFourier<Vec<u8>, FFT64> {
+    fn external_product_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize {
+        <GGSWCiphertext<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_glwe_inplace_scratch_space(
+            module, res_size, rhs,
+        )
+    }
+}
+
+impl<DataSelf, DataRhs> ExternalProductInplace<DataRhs> for GLWECiphertextFourier<DataSelf, FFT64>
+where
+    VecZnxDft<DataSelf, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64>,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64> + ZnxInfos,
+{
+    type Rhs = GGSWCiphertext<DataRhs, FFT64>;
+
+    fn external_product_inplace(&mut self, module: &Module<FFT64>, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_glwe_fourier_inplace(module, self, scratch);
+    }
+}
diff --git a/core/src/keys.rs b/core/src/keys.rs
index 8285f85..eaa569e 100644
--- a/core/src/keys.rs
+++ b/core/src/keys.rs
@@ -5,7 +5,7 @@ use base2k::{
 };
 use sampling::source::Source;
 
-use crate::{elem::Infos, rlwe::RLWECtDft};
+use crate::{elem::Infos, glwe::GLWECiphertextFourier};
 
 #[derive(Clone, Copy, Debug)]
 pub enum SecretDistribution {
@@ -67,12 +67,12 @@ where
     }
 }
 
-pub struct SecretKeyDft<T, B: Backend> {
+pub struct SecretKeyFourier<T, B: Backend> {
     pub data: ScalarZnxDft<T, B>,
     pub dist: SecretDistribution,
 }
 
-impl<B: Backend> SecretKeyDft<Vec<u8>, B> {
+impl<B: Backend> SecretKeyFourier<Vec<u8>, B> {
     pub fn new(module: &Module<B>) -> Self {
         Self {
             data: module.new_scalar_znx_dft(1),
@@ -82,7 +82,7 @@ impl<B: Backend> SecretKeyDft<Vec<u8>, B> {
 
     pub fn dft<S>(&mut self, module: &Module<FFT64>, sk: &SecretKey<S>)
     where
-        SecretKeyDft<Vec<u8>, B>: ScalarZnxDftToMut<base2k::FFT64>,
+        SecretKeyFourier<Vec<u8>, B>: ScalarZnxDftToMut<base2k::FFT64>,
         SecretKey<S>: ScalarZnxToRef,
     {
         #[cfg(debug_assertions)]
@@ -98,7 +98,7 @@ impl<B: Backend> SecretKeyDft<Vec<u8>, B> {
     }
 }
 
-impl<C, B: Backend> ScalarZnxDftToMut<B> for SecretKeyDft<C, B>
+impl<C, B: Backend> ScalarZnxDftToMut<B> for SecretKeyFourier<C, B>
 where
     ScalarZnxDft<C, B>: ScalarZnxDftToMut<B>,
 {
@@ -107,7 +107,7 @@ where
     }
 }
 
-impl<C, B: Backend> ScalarZnxDftToRef<B> for SecretKeyDft<C, B>
+impl<C, B: Backend> ScalarZnxDftToRef<B> for SecretKeyFourier<C, B>
 where
     ScalarZnxDft<C, B>: ScalarZnxDftToRef<B>,
 {
@@ -117,14 +117,14 @@ where
 }
 
 pub struct PublicKey<D, B: Backend> {
-    pub data: RLWECtDft<D, B>,
+    pub data: GLWECiphertextFourier<D, B>,
     pub dist: SecretDistribution,
 }
 
 impl<B: Backend> PublicKey<Vec<u8>, B> {
     pub fn new(module: &Module<B>, log_base2k: usize, log_k: usize) -> Self {
         Self {
-            data: RLWECtDft::new(module, log_base2k, log_k),
+            data: GLWECiphertextFourier::new(module, log_base2k, log_k),
             dist: SecretDistribution::NONE,
         }
     }
@@ -137,11 +137,11 @@ impl<T, B: Backend> Infos for PublicKey<T, B> {
         &self.data.data
     }
 
-    fn log_base2k(&self) -> usize {
+    fn basek(&self) -> usize {
         self.data.log_base2k
     }
 
-    fn log_k(&self) -> usize {
+    fn k(&self) -> usize {
         self.data.log_k
     }
 }
@@ -168,7 +168,7 @@ impl<C> PublicKey<C, FFT64> {
     pub fn generate<S>(
         &mut self,
         module: &Module<FFT64>,
-        sk_dft: &SecretKeyDft<S, FFT64>,
+        sk_dft: &SecretKeyFourier<S, FFT64>,
         source_xa: &mut Source,
         source_xe: &mut Source,
         sigma: f64,
@@ -186,7 +186,7 @@ impl<C> PublicKey<C, FFT64> {
         }
 
         // Its ok to allocate scratch space here since pk is usually generated only once.
-        let mut scratch: ScratchOwned = ScratchOwned::new(RLWECtDft::encrypt_zero_sk_scratch_space(
+        let mut scratch: ScratchOwned = ScratchOwned::new(GLWECiphertextFourier::encrypt_zero_sk_scratch_space(
             module,
             self.size(),
         ));
diff --git a/core/src/keyswitch.rs b/core/src/keyswitch.rs
new file mode 100644
index 0000000..c77ccb4
--- /dev/null
+++ b/core/src/keyswitch.rs
@@ -0,0 +1,20 @@
+use base2k::{FFT64, Module, Scratch};
+
+pub trait KeySwitchScratchSpace {
+    fn keyswitch_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize;
+}
+
+pub trait KeySwitch<DataLhs, DataRhs> {
+    type Lhs;
+    type Rhs;
+    fn keyswitch(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &Self::Rhs, scratch: &mut Scratch);
+}
+
+pub trait KeySwitchInplaceScratchSpace {
+    fn keyswitch_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize;
+}
+
+pub trait KeySwitchInplace<DataRhs> {
+    type Rhs;
+    fn keyswitch_inplace(&mut self, module: &Module<FFT64>, rhs: &Self::Rhs, scratch: &mut Scratch);
+}
diff --git a/core/src/grlwe.rs b/core/src/keyswitch_key.rs
similarity index 51%
rename from core/src/grlwe.rs
rename to core/src/keyswitch_key.rs
index 80c976d..cb4c248 100644
--- a/core/src/grlwe.rs
+++ b/core/src/keyswitch_key.rs
@@ -7,23 +7,26 @@ use base2k::{
 use sampling::source::Source;
 
 use crate::{
-    elem::{
-        GetRow, Infos, MatRLWEProduct, MatRLWEProductScratchSpace, ProdInplace, ProdInplaceScratchSpace, ProdScratchSpace,
-        Product, SetRow,
+    elem::{GetRow, Infos, SetRow},
+    encryption::EncryptSkScratchSpace,
+    external_product::{
+        ExternalProduct, ExternalProductInplace, ExternalProductInplaceScratchSpace, ExternalProductScratchSpace,
     },
-    keys::SecretKeyDft,
-    rgsw::RGSWCt,
-    rlwe::{RLWECt, RLWECtDft, RLWEPt},
+    ggsw::GGSWCiphertext,
+    glwe::{GLWECiphertext, GLWECiphertextFourier, GLWEPlaintext},
+    keys::SecretKeyFourier,
+    keyswitch::{KeySwitch, KeySwitchInplace, KeySwitchInplaceScratchSpace, KeySwitchScratchSpace},
     utils::derive_size,
+    vec_glwe_product::{VecGLWEProduct, VecGLWEProductScratchSpace},
 };
 
-pub struct GRLWECt<C, B: Backend> {
+pub struct GLWEKeySwitchKey<C, B: Backend> {
     pub data: MatZnxDft<C, B>,
     pub log_base2k: usize,
     pub log_k: usize,
 }
 
-impl<B: Backend> GRLWECt<Vec<u8>, B> {
+impl<B: Backend> GLWEKeySwitchKey<Vec<u8>, B> {
     pub fn new(module: &Module<B>, log_base2k: usize, log_k: usize, rows: usize) -> Self {
         Self {
             data: module.new_mat_znx_dft(rows, 1, 2, derive_size(log_base2k, log_k)),
@@ -33,23 +36,23 @@ impl<B: Backend> GRLWECt<Vec<u8>, B> {
     }
 }
 
-impl<T, B: Backend> Infos for GRLWECt<T, B> {
+impl<T, B: Backend> Infos for GLWEKeySwitchKey<T, B> {
     type Inner = MatZnxDft<T, B>;
 
     fn inner(&self) -> &Self::Inner {
         &self.data
     }
 
-    fn log_base2k(&self) -> usize {
+    fn basek(&self) -> usize {
         self.log_base2k
     }
 
-    fn log_k(&self) -> usize {
+    fn k(&self) -> usize {
         self.log_k
     }
 }
 
-impl<C, B: Backend> MatZnxDftToMut<B> for GRLWECt<C, B>
+impl<C, B: Backend> MatZnxDftToMut<B> for GLWEKeySwitchKey<C, B>
 where
     MatZnxDft<C, B>: MatZnxDftToMut<B>,
 {
@@ -58,7 +61,7 @@ where
     }
 }
 
-impl<C, B: Backend> MatZnxDftToRef<B> for GRLWECt<C, B>
+impl<C, B: Backend> MatZnxDftToRef<B> for GLWEKeySwitchKey<C, B>
 where
     MatZnxDft<C, B>: MatZnxDftToRef<B>,
 {
@@ -67,20 +70,20 @@ where
     }
 }
 
-impl GRLWECt<Vec<u8>, FFT64> {
+impl GLWEKeySwitchKey<Vec<u8>, FFT64> {
     pub fn encrypt_sk_scratch_space(module: &Module<FFT64>, size: usize) -> usize {
-        RLWECt::encrypt_sk_scratch_space(module, size)
+        GLWECiphertext::encrypt_sk_scratch_space(module, size)
             + module.bytes_of_vec_znx(2, size)
             + module.bytes_of_vec_znx(1, size)
             + module.bytes_of_vec_znx_dft(2, size)
     }
 }
 
-pub fn encrypt_grlwe_sk<C, P, S>(
+pub fn encrypt_glwe_key_switch_key_sk<C, P, S>(
     module: &Module<FFT64>,
-    ct: &mut GRLWECt<C, FFT64>,
+    ct: &mut GLWEKeySwitchKey<C, FFT64>,
     pt: &ScalarZnx<P>,
-    sk_dft: &SecretKeyDft<S, FFT64>,
+    sk_dft: &SecretKeyFourier<S, FFT64>,
     source_xa: &mut Source,
     source_xe: &mut Source,
     sigma: f64,
@@ -93,22 +96,22 @@ pub fn encrypt_grlwe_sk<C, P, S>(
 {
     let rows: usize = ct.rows();
     let size: usize = ct.size();
-    let log_base2k: usize = ct.log_base2k();
+    let log_base2k: usize = ct.basek();
 
     let (tmp_znx_pt, scrach_1) = scratch.tmp_vec_znx(module, 1, size);
     let (tmp_znx_ct, scrach_2) = scrach_1.tmp_vec_znx(module, 2, size);
     let (mut vec_znx_dft_ct, scratch_3) = scrach_2.tmp_vec_znx_dft(module, 2, size);
 
-    let mut vec_znx_pt: RLWEPt<&mut [u8]> = RLWEPt {
+    let mut vec_znx_pt: GLWEPlaintext<&mut [u8]> = GLWEPlaintext {
         data: tmp_znx_pt,
         log_base2k: log_base2k,
-        log_k: ct.log_k(),
+        log_k: ct.k(),
     };
 
-    let mut vec_znx_ct: RLWECt<&mut [u8]> = RLWECt {
+    let mut vec_znx_ct: GLWECiphertext<&mut [u8]> = GLWECiphertext {
         data: tmp_znx_ct,
         log_base2k: log_base2k,
-        log_k: ct.log_k(),
+        log_k: ct.k(),
     };
 
     (0..rows).for_each(|row_i| {
@@ -119,7 +122,7 @@ pub fn encrypt_grlwe_sk<C, P, S>(
         // rlwe encrypt of vec_znx_pt into vec_znx_ct
         vec_znx_ct.encrypt_sk(
             module,
-            Some(&vec_znx_pt),
+            &vec_znx_pt,
             sk_dft,
             source_xa,
             source_xe,
@@ -139,12 +142,12 @@ pub fn encrypt_grlwe_sk<C, P, S>(
     });
 }
 
-impl<C> GRLWECt<C, FFT64> {
+impl<C> GLWEKeySwitchKey<C, FFT64> {
     pub fn encrypt_sk<P, S>(
         &mut self,
         module: &Module<FFT64>,
         pt: &ScalarZnx<P>,
-        sk_dft: &SecretKeyDft<S, FFT64>,
+        sk_dft: &SecretKeyFourier<S, FFT64>,
         source_xa: &mut Source,
         source_xe: &mut Source,
         sigma: f64,
@@ -155,17 +158,17 @@ impl<C> GRLWECt<C, FFT64> {
         ScalarZnx<P>: ScalarZnxToRef,
         ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
     {
-        encrypt_grlwe_sk(
+        encrypt_glwe_key_switch_key_sk(
             module, self, pt, sk_dft, source_xa, source_xe, sigma, bound, scratch,
         )
     }
 }
 
-impl<C> GetRow<FFT64> for GRLWECt<C, FFT64>
+impl<C> GetRow<FFT64> for GLWEKeySwitchKey<C, FFT64>
 where
     MatZnxDft<C, FFT64>: MatZnxDftToRef<FFT64>,
 {
-    fn get_row<R>(&self, module: &Module<FFT64>, row_i: usize, col_j: usize, res: &mut RLWECtDft<R, FFT64>)
+    fn get_row<R>(&self, module: &Module<FFT64>, row_i: usize, col_j: usize, res: &mut GLWECiphertextFourier<R, FFT64>)
     where
         VecZnxDft<R, FFT64>: VecZnxDftToMut<FFT64>,
     {
@@ -177,11 +180,11 @@ where
     }
 }
 
-impl<C> SetRow<FFT64> for GRLWECt<C, FFT64>
+impl<C> SetRow<FFT64> for GLWEKeySwitchKey<C, FFT64>
 where
     MatZnxDft<C, FFT64>: MatZnxDftToMut<FFT64>,
 {
-    fn set_row<R>(&mut self, module: &Module<FFT64>, row_i: usize, col_j: usize, a: &RLWECtDft<R, FFT64>)
+    fn set_row<R>(&mut self, module: &Module<FFT64>, row_i: usize, col_j: usize, a: &GLWECiphertextFourier<R, FFT64>)
     where
         VecZnxDft<R, FFT64>: VecZnxDftToRef<FFT64>,
     {
@@ -193,8 +196,92 @@ where
     }
 }
 
-impl MatRLWEProductScratchSpace for GRLWECt<Vec<u8>, FFT64> {
-    fn prod_with_rlwe_scratch_space(module: &Module<FFT64>, res_size: usize, a_size: usize, grlwe_size: usize) -> usize {
+impl KeySwitchScratchSpace for GLWEKeySwitchKey<Vec<u8>, FFT64> {
+    fn keyswitch_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
+        <GLWEKeySwitchKey<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_vec_glwe_scratch_space(
+            module, res_size, lhs, rhs,
+        )
+    }
+}
+
+impl<DataSelf, DataLhs, DataRhs> KeySwitch<DataLhs, DataRhs> for GLWEKeySwitchKey<DataSelf, FFT64>
+where
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataLhs, FFT64>: MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Lhs = GLWEKeySwitchKey<DataLhs, FFT64>;
+    type Rhs = GLWEKeySwitchKey<DataRhs, FFT64>;
+
+    fn keyswitch(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_vec_glwe(module, self, lhs, scratch);
+    }
+}
+
+impl KeySwitchInplaceScratchSpace for GLWEKeySwitchKey<Vec<u8>, FFT64> {
+    fn keyswitch_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize {
+        <GLWEKeySwitchKey<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_vec_glwe_inplace_scratch_space(
+            module, res_size, rhs,
+        )
+    }
+}
+
+impl<DataSelf, DataRhs> KeySwitchInplace<DataRhs> for GLWEKeySwitchKey<DataSelf, FFT64>
+where
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Rhs = GLWEKeySwitchKey<DataRhs, FFT64>;
+
+    fn keyswitch_inplace(&mut self, module: &Module<FFT64>, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_vec_glwe(module, self, rhs, scratch);
+    }
+}
+
+impl ExternalProductScratchSpace for GLWEKeySwitchKey<Vec<u8>, FFT64> {
+    fn external_product_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
+        <GGSWCiphertext<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_vec_glwe_scratch_space(
+            module, res_size, lhs, rhs,
+        )
+    }
+}
+
+impl<DataSelf, DataLhs, DataRhs> ExternalProduct<DataLhs, DataRhs> for GLWEKeySwitchKey<DataSelf, FFT64>
+where
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataLhs, FFT64>: MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Lhs = GLWEKeySwitchKey<DataLhs, FFT64>;
+    type Rhs = GGSWCiphertext<DataRhs, FFT64>;
+
+    fn external_product(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_vec_glwe(module, self, lhs, scratch);
+    }
+}
+
+impl ExternalProductInplaceScratchSpace for GLWEKeySwitchKey<Vec<u8>, FFT64> {
+    fn external_product_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize {
+        <GGSWCiphertext<Vec<u8>, FFT64> as VecGLWEProductScratchSpace>::prod_with_glwe_inplace_scratch_space(
+            module, res_size, rhs,
+        )
+    }
+}
+
+impl<DataSelf, DataRhs> ExternalProductInplace<DataRhs> for GLWEKeySwitchKey<DataSelf, FFT64>
+where
+    MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
+    MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+{
+    type Rhs = GGSWCiphertext<DataRhs, FFT64>;
+
+    fn external_product_inplace(&mut self, module: &Module<FFT64>, rhs: &Self::Rhs, scratch: &mut Scratch) {
+        rhs.prod_with_vec_glwe_inplace(module, self, scratch);
+    }
+}
+
+impl VecGLWEProductScratchSpace for GLWEKeySwitchKey<Vec<u8>, FFT64> {
+    fn prod_with_glwe_scratch_space(module: &Module<FFT64>, res_size: usize, a_size: usize, grlwe_size: usize) -> usize {
         module.bytes_of_vec_znx_dft(2, grlwe_size)
             + (module.vec_znx_big_normalize_tmp_bytes()
                 | (module.vmp_apply_tmp_bytes(res_size, a_size, a_size, 1, 2, grlwe_size)
@@ -202,22 +289,27 @@ impl MatRLWEProductScratchSpace for GRLWECt<Vec<u8>, FFT64> {
     }
 }
 
-impl<C> MatRLWEProduct for GRLWECt<C, FFT64>
+impl<C> VecGLWEProduct for GLWEKeySwitchKey<C, FFT64>
 where
     MatZnxDft<C, FFT64>: MatZnxDftToRef<FFT64> + ZnxInfos,
 {
-    fn prod_with_rlwe<R, A>(&self, module: &Module<FFT64>, res: &mut RLWECt<R>, a: &RLWECt<A>, scratch: &mut Scratch)
-    where
+    fn prod_with_glwe<R, A>(
+        &self,
+        module: &Module<FFT64>,
+        res: &mut GLWECiphertext<R>,
+        a: &GLWECiphertext<A>,
+        scratch: &mut Scratch,
+    ) where
         MatZnxDft<C, FFT64>: MatZnxDftToRef<FFT64>,
         VecZnx<R>: VecZnxToMut,
         VecZnx<A>: VecZnxToRef,
     {
-        let log_base2k: usize = self.log_base2k();
+        let log_base2k: usize = self.basek();
 
         #[cfg(debug_assertions)]
         {
-            assert_eq!(res.log_base2k(), log_base2k);
-            assert_eq!(a.log_base2k(), log_base2k);
+            assert_eq!(res.basek(), log_base2k);
+            assert_eq!(a.basek(), log_base2k);
             assert_eq!(self.n(), module.n());
             assert_eq!(res.n(), module.n());
             assert_eq!(a.n(), module.n());
@@ -239,53 +331,3 @@ where
         module.vec_znx_big_normalize(log_base2k, res, 1, &res_big, 1, scratch1);
     }
 }
-
-impl ProdInplaceScratchSpace for GRLWECt<Vec<u8>, FFT64> {
-    fn prod_by_grlwe_inplace_scratch_space(module: &Module<FFT64>, lhs: usize, rhs: usize) -> usize {
-        <GRLWECt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_mat_rlwe_inplace_scratch_space(module, lhs, rhs)
-    }
-
-    fn prod_by_rgsw_inplace_scratch_space(module: &Module<FFT64>, lhs: usize, rhs: usize) -> usize {
-        <RGSWCt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_mat_rlwe_inplace_scratch_space(module, lhs, rhs)
-    }
-}
-
-impl ProdScratchSpace for GRLWECt<Vec<u8>, FFT64> {
-    fn prod_by_grlwe_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
-        <GRLWECt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_mat_rlwe_scratch_space(module, res_size, lhs, rhs)
-    }
-
-    fn prod_by_rgsw_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
-        <RGSWCt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_mat_rlwe_scratch_space(module, res_size, lhs, rhs)
-    }
-}
-
-impl<MUT, REF> ProdInplace<MUT, REF> for GRLWECt<MUT, FFT64>
-where
-    GRLWECt<MUT, FFT64>: GetRow<FFT64> + SetRow<FFT64> + Infos,
-    MatZnxDft<REF, FFT64>: MatZnxDftToRef<FFT64>,
-{
-    fn prod_by_grlwe_inplace(&mut self, module: &Module<FFT64>, rhs: &GRLWECt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_mat_rlwe_inplace(module, self, scratch);
-    }
-
-    fn prod_by_rgsw_inplace(&mut self, module: &Module<FFT64>, rhs: &RGSWCt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_mat_rlwe_inplace(module, self, scratch);
-    }
-}
-
-impl<MUT, REF> Product<MUT, REF> for GRLWECt<MUT, FFT64>
-where
-    MatZnxDft<MUT, FFT64>: MatZnxDftToRef<FFT64> + MatZnxDftToMut<FFT64>,
-    MatZnxDft<REF, FFT64>: MatZnxDftToRef<FFT64>,
-{
-    type Lhs = GRLWECt<REF, FFT64>;
-
-    fn prod_by_grlwe(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &GRLWECt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_mat_rlwe(module, self, lhs, scratch);
-    }
-
-    fn prod_by_rgsw(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &RGSWCt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_mat_rlwe(module, self, lhs, scratch);
-    }
-}
diff --git a/core/src/lib.rs b/core/src/lib.rs
index bed71cc..97db860 100644
--- a/core/src/lib.rs
+++ b/core/src/lib.rs
@@ -1,8 +1,12 @@
 pub mod elem;
-pub mod grlwe;
+pub mod encryption;
+pub mod external_product;
+pub mod ggsw;
+pub mod glwe;
 pub mod keys;
-pub mod rgsw;
-pub mod rlwe;
+pub mod keyswitch;
+pub mod keyswitch_key;
 #[cfg(test)]
 mod test_fft64;
 mod utils;
+pub mod vec_glwe_product;
diff --git a/core/src/rlwe.rs b/core/src/rlwe.rs
deleted file mode 100644
index 2dab803..0000000
--- a/core/src/rlwe.rs
+++ /dev/null
@@ -1,701 +0,0 @@
-use base2k::{
-    AddNormal, Backend, FFT64, FillUniform, MatZnxDft, MatZnxDftToRef, Module, ScalarZnxAlloc, ScalarZnxDft, ScalarZnxDftAlloc,
-    ScalarZnxDftOps, ScalarZnxDftToRef, Scratch, VecZnx, VecZnxAlloc, VecZnxBigAlloc, VecZnxBigOps, VecZnxBigScratch, VecZnxDft,
-    VecZnxDftAlloc, VecZnxDftOps, VecZnxDftToMut, VecZnxDftToRef, VecZnxOps, VecZnxToMut, VecZnxToRef, ZnxInfos,
-};
-use sampling::source::Source;
-
-use crate::{
-    elem::{Infos, MatRLWEProduct, MatRLWEProductScratchSpace, ProdInplace, ProdInplaceScratchSpace, ProdScratchSpace, Product},
-    grlwe::GRLWECt,
-    keys::{PublicKey, SecretDistribution, SecretKeyDft},
-    rgsw::RGSWCt,
-    utils::derive_size,
-};
-
-pub struct RLWECt<C> {
-    pub data: VecZnx<C>,
-    pub log_base2k: usize,
-    pub log_k: usize,
-}
-
-impl RLWECt<Vec<u8>> {
-    pub fn new<B: Backend>(module: &Module<B>, log_base2k: usize, log_k: usize) -> Self {
-        Self {
-            data: module.new_vec_znx(2, derive_size(log_base2k, log_k)),
-            log_base2k: log_base2k,
-            log_k: log_k,
-        }
-    }
-}
-
-impl<T> Infos for RLWECt<T> {
-    type Inner = VecZnx<T>;
-
-    fn inner(&self) -> &Self::Inner {
-        &self.data
-    }
-
-    fn log_base2k(&self) -> usize {
-        self.log_base2k
-    }
-
-    fn log_k(&self) -> usize {
-        self.log_k
-    }
-}
-
-impl<C> VecZnxToMut for RLWECt<C>
-where
-    VecZnx<C>: VecZnxToMut,
-{
-    fn to_mut(&mut self) -> VecZnx<&mut [u8]> {
-        self.data.to_mut()
-    }
-}
-
-impl<C> VecZnxToRef for RLWECt<C>
-where
-    VecZnx<C>: VecZnxToRef,
-{
-    fn to_ref(&self) -> VecZnx<&[u8]> {
-        self.data.to_ref()
-    }
-}
-
-impl<C> RLWECt<C>
-where
-    VecZnx<C>: VecZnxToRef,
-{
-    #[allow(dead_code)]
-    pub(crate) fn dft<R>(&self, module: &Module<FFT64>, res: &mut RLWECtDft<R, FFT64>)
-    where
-        VecZnxDft<R, FFT64>: VecZnxDftToMut<FFT64> + ZnxInfos,
-    {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(self.cols(), 2);
-            assert_eq!(res.cols(), 2);
-            assert_eq!(self.log_base2k(), res.log_base2k())
-        }
-
-        module.vec_znx_dft(res, 0, self, 0);
-        module.vec_znx_dft(res, 1, self, 1);
-    }
-}
-
-impl ProdInplaceScratchSpace for RLWECt<Vec<u8>> {
-    fn prod_by_grlwe_inplace_scratch_space(module: &Module<FFT64>, lhs: usize, rhs: usize) -> usize {
-        <GRLWECt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_rlwe_inplace_scratch_space(module, lhs, rhs)
-    }
-
-    fn prod_by_rgsw_inplace_scratch_space(module: &Module<FFT64>, lhs: usize, rhs: usize) -> usize {
-        <RGSWCt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_rlwe_inplace_scratch_space(module, lhs, rhs)
-    }
-}
-
-impl ProdScratchSpace for RLWECt<Vec<u8>> {
-    fn prod_by_grlwe_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
-        <GRLWECt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_rlwe_scratch_space(module, res_size, lhs, rhs)
-    }
-
-    fn prod_by_rgsw_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
-        <RGSWCt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_rlwe_scratch_space(module, res_size, lhs, rhs)
-    }
-}
-
-impl<MUT, REF> ProdInplace<MUT, REF> for RLWECt<MUT>
-where
-    VecZnx<MUT>: VecZnxToMut + VecZnxToRef,
-    MatZnxDft<REF, FFT64>: MatZnxDftToRef<FFT64>,
-{
-    fn prod_by_grlwe_inplace(&mut self, module: &Module<FFT64>, rhs: &GRLWECt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_rlwe_inplace(module, self, scratch);
-    }
-
-    fn prod_by_rgsw_inplace(&mut self, module: &Module<FFT64>, rhs: &RGSWCt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_rlwe_inplace(module, self, scratch);
-    }
-}
-
-impl<MUT, REF> Product<MUT, REF> for RLWECt<MUT>
-where
-    VecZnx<MUT>: VecZnxToMut + VecZnxToRef,
-    VecZnx<REF>: VecZnxToRef,
-    MatZnxDft<REF, FFT64>: MatZnxDftToRef<FFT64>,
-{
-    type Lhs = RLWECt<REF>;
-
-    fn prod_by_grlwe(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &GRLWECt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_rlwe(module, self, lhs, scratch);
-    }
-
-    fn prod_by_rgsw(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &RGSWCt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_rlwe(module, self, lhs, scratch);
-    }
-}
-
-impl RLWECt<Vec<u8>> {
-    pub fn encrypt_sk_scratch_space<B: Backend>(module: &Module<B>, size: usize) -> usize {
-        (module.vec_znx_big_normalize_tmp_bytes() | module.bytes_of_vec_znx_dft(1, size)) + module.bytes_of_vec_znx_big(1, size)
-    }
-
-    pub fn encrypt_pk_scratch_space<B: Backend>(module: &Module<B>, pk_size: usize) -> usize {
-        ((module.bytes_of_vec_znx_dft(1, pk_size) + module.bytes_of_vec_znx_big(1, pk_size)) | module.bytes_of_scalar_znx(1))
-            + module.bytes_of_scalar_znx_dft(1)
-            + module.vec_znx_big_normalize_tmp_bytes()
-    }
-
-    pub fn decrypt_scratch_space<B: Backend>(module: &Module<B>, size: usize) -> usize {
-        (module.vec_znx_big_normalize_tmp_bytes() | module.bytes_of_vec_znx_dft(1, size)) + module.bytes_of_vec_znx_big(1, size)
-    }
-}
-
-pub fn encrypt_rlwe_sk<C, P, S>(
-    module: &Module<FFT64>,
-    ct: &mut RLWECt<C>,
-    pt: Option<(&RLWEPt<P>, usize)>,
-    sk_dft: &SecretKeyDft<S, FFT64>,
-    source_xa: &mut Source,
-    source_xe: &mut Source,
-    sigma: f64,
-    bound: f64,
-    scratch: &mut Scratch,
-) where
-    VecZnx<C>: VecZnxToMut + VecZnxToRef,
-    VecZnx<P>: VecZnxToRef,
-    ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
-{
-    let log_base2k: usize = ct.log_base2k();
-    let log_k: usize = ct.log_k();
-    let size: usize = ct.size();
-
-    // c1 = a
-    ct.data.fill_uniform(log_base2k, 1, size, source_xa);
-
-    let (mut c0_big, scratch_1) = scratch.tmp_vec_znx_big(module, 1, size);
-
-    {
-        let (mut c0_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, size);
-        module.vec_znx_dft(&mut c0_dft, 0, ct, 1);
-
-        // c0_dft = DFT(a) * DFT(s)
-        module.svp_apply_inplace(&mut c0_dft, 0, sk_dft, 0);
-
-        // c0_big = IDFT(c0_dft)
-        module.vec_znx_idft_tmp_a(&mut c0_big, 0, &mut c0_dft, 0);
-    }
-
-    // c0_big = m - c0_big
-    if let Some((pt, col)) = pt {
-        match col {
-            0 => module.vec_znx_big_sub_small_b_inplace(&mut c0_big, 0, pt, 0),
-            1 => {
-                module.vec_znx_big_negate_inplace(&mut c0_big, 0);
-                module.vec_znx_add_inplace(ct, 1, pt, 0);
-                module.vec_znx_normalize_inplace(log_base2k, ct, 1, scratch_1);
-            }
-            _ => panic!("invalid target column: {}", col),
-        }
-    } else {
-        module.vec_znx_big_negate_inplace(&mut c0_big, 0);
-    }
-    // c0_big += e
-    c0_big.add_normal(log_base2k, 0, log_k, source_xe, sigma, bound);
-
-    // c0 = norm(c0_big = -as + m + e)
-    module.vec_znx_big_normalize(log_base2k, ct, 0, &c0_big, 0, scratch_1);
-}
-
-pub fn decrypt_rlwe<P, C, S>(
-    module: &Module<FFT64>,
-    pt: &mut RLWEPt<P>,
-    ct: &RLWECt<C>,
-    sk_dft: &SecretKeyDft<S, FFT64>,
-    scratch: &mut Scratch,
-) where
-    VecZnx<P>: VecZnxToMut + VecZnxToRef,
-    VecZnx<C>: VecZnxToRef,
-    ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
-{
-    let (mut c0_big, scratch_1) = scratch.tmp_vec_znx_big(module, 1, ct.size()); // TODO optimize size when pt << ct
-
-    {
-        let (mut c0_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, ct.size()); // TODO optimize size when pt << ct
-        module.vec_znx_dft(&mut c0_dft, 0, ct, 1);
-
-        // c0_dft = DFT(a) * DFT(s)
-        module.svp_apply_inplace(&mut c0_dft, 0, sk_dft, 0);
-
-        // c0_big = IDFT(c0_dft)
-        module.vec_znx_idft_tmp_a(&mut c0_big, 0, &mut c0_dft, 0);
-    }
-
-    // c0_big = (a * s) + (-a * s + m + e) = BIG(m + e)
-    module.vec_znx_big_add_small_inplace(&mut c0_big, 0, ct, 0);
-
-    // pt = norm(BIG(m + e))
-    module.vec_znx_big_normalize(ct.log_base2k(), pt, 0, &mut c0_big, 0, scratch_1);
-
-    pt.log_base2k = ct.log_base2k();
-    pt.log_k = pt.log_k().min(ct.log_k());
-}
-
-impl<C> RLWECt<C> {
-    pub fn encrypt_sk<P, S>(
-        &mut self,
-        module: &Module<FFT64>,
-        pt: Option<&RLWEPt<P>>,
-        sk_dft: &SecretKeyDft<S, FFT64>,
-        source_xa: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-        bound: f64,
-        scratch: &mut Scratch,
-    ) where
-        VecZnx<C>: VecZnxToMut + VecZnxToRef,
-        VecZnx<P>: VecZnxToRef,
-        ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
-    {
-        if let Some(pt) = pt {
-            encrypt_rlwe_sk(
-                module,
-                self,
-                Some((pt, 0)),
-                sk_dft,
-                source_xa,
-                source_xe,
-                sigma,
-                bound,
-                scratch,
-            )
-        } else {
-            encrypt_rlwe_sk::<C, P, S>(
-                module, self, None, sk_dft, source_xa, source_xe, sigma, bound, scratch,
-            )
-        }
-    }
-
-    pub fn decrypt<P, S>(
-        &self,
-        module: &Module<FFT64>,
-        pt: &mut RLWEPt<P>,
-        sk_dft: &SecretKeyDft<S, FFT64>,
-        scratch: &mut Scratch,
-    ) where
-        VecZnx<P>: VecZnxToMut + VecZnxToRef,
-        VecZnx<C>: VecZnxToRef,
-        ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
-    {
-        decrypt_rlwe(module, pt, self, sk_dft, scratch);
-    }
-
-    pub fn encrypt_pk<P, S>(
-        &mut self,
-        module: &Module<FFT64>,
-        pt: Option<&RLWEPt<P>>,
-        pk: &PublicKey<S, FFT64>,
-        source_xu: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-        bound: f64,
-        scratch: &mut Scratch,
-    ) where
-        VecZnx<C>: VecZnxToMut + VecZnxToRef,
-        VecZnx<P>: VecZnxToRef,
-        VecZnxDft<S, FFT64>: VecZnxDftToRef<FFT64>,
-    {
-        encrypt_rlwe_pk(
-            module, self, pt, pk, source_xu, source_xe, sigma, bound, scratch,
-        )
-    }
-}
-
-pub(crate) fn encrypt_rlwe_pk<C, P, S>(
-    module: &Module<FFT64>,
-    ct: &mut RLWECt<C>,
-    pt: Option<&RLWEPt<P>>,
-    pk: &PublicKey<S, FFT64>,
-    source_xu: &mut Source,
-    source_xe: &mut Source,
-    sigma: f64,
-    bound: f64,
-    scratch: &mut Scratch,
-) where
-    VecZnx<C>: VecZnxToMut + VecZnxToRef,
-    VecZnx<P>: VecZnxToRef,
-    VecZnxDft<S, FFT64>: VecZnxDftToRef<FFT64>,
-{
-    #[cfg(debug_assertions)]
-    {
-        assert_eq!(ct.log_base2k(), pk.log_base2k());
-        assert_eq!(ct.n(), module.n());
-        assert_eq!(pk.n(), module.n());
-        if let Some(pt) = pt {
-            assert_eq!(pt.log_base2k(), pk.log_base2k());
-            assert_eq!(pt.n(), module.n());
-        }
-    }
-
-    let log_base2k: usize = pk.log_base2k();
-    let size_pk: usize = pk.size();
-
-    // Generates u according to the underlying secret distribution.
-    let (mut u_dft, scratch_1) = scratch.tmp_scalar_znx_dft(module, 1);
-
-    {
-        let (mut u, _) = scratch_1.tmp_scalar_znx(module, 1);
-        match pk.dist {
-            SecretDistribution::NONE => panic!(
-                "invalid public key: SecretDistribution::NONE, ensure it has been correctly intialized through Self::generate"
-            ),
-            SecretDistribution::TernaryFixed(hw) => u.fill_ternary_hw(0, hw, source_xu),
-            SecretDistribution::TernaryProb(prob) => u.fill_ternary_prob(0, prob, source_xu),
-            SecretDistribution::ZERO => {}
-        }
-
-        module.svp_prepare(&mut u_dft, 0, &u, 0);
-    }
-
-    let (mut tmp_big, scratch_2) = scratch_1.tmp_vec_znx_big(module, 1, size_pk); // TODO optimize size (e.g. when encrypting at low homomorphic capacity)
-    let (mut tmp_dft, scratch_3) = scratch_2.tmp_vec_znx_dft(module, 1, size_pk); // TODO optimize size (e.g. when encrypting at low homomorphic capacity)
-
-    // ct[0] = pk[0] * u + m + e0
-    module.svp_apply(&mut tmp_dft, 0, &u_dft, 0, pk, 0);
-    module.vec_znx_idft_tmp_a(&mut tmp_big, 0, &mut tmp_dft, 0);
-    tmp_big.add_normal(log_base2k, 0, pk.log_k(), source_xe, sigma, bound);
-
-    if let Some(pt) = pt {
-        module.vec_znx_big_add_small_inplace(&mut tmp_big, 0, pt, 0);
-    }
-
-    module.vec_znx_big_normalize(log_base2k, ct, 0, &tmp_big, 0, scratch_3);
-
-    // ct[1] = pk[1] * u + e1
-    module.svp_apply(&mut tmp_dft, 0, &u_dft, 0, pk, 1);
-    module.vec_znx_idft_tmp_a(&mut tmp_big, 0, &mut tmp_dft, 0);
-    tmp_big.add_normal(log_base2k, 0, pk.log_k(), source_xe, sigma, bound);
-    module.vec_znx_big_normalize(log_base2k, ct, 1, &tmp_big, 0, scratch_3);
-}
-
-pub struct RLWEPt<C> {
-    pub data: VecZnx<C>,
-    pub log_base2k: usize,
-    pub log_k: usize,
-}
-
-impl<T> Infos for RLWEPt<T> {
-    type Inner = VecZnx<T>;
-
-    fn inner(&self) -> &Self::Inner {
-        &self.data
-    }
-
-    fn log_base2k(&self) -> usize {
-        self.log_base2k
-    }
-
-    fn log_k(&self) -> usize {
-        self.log_k
-    }
-}
-
-impl<C> VecZnxToMut for RLWEPt<C>
-where
-    VecZnx<C>: VecZnxToMut,
-{
-    fn to_mut(&mut self) -> VecZnx<&mut [u8]> {
-        self.data.to_mut()
-    }
-}
-
-impl<C> VecZnxToRef for RLWEPt<C>
-where
-    VecZnx<C>: VecZnxToRef,
-{
-    fn to_ref(&self) -> VecZnx<&[u8]> {
-        self.data.to_ref()
-    }
-}
-
-impl RLWEPt<Vec<u8>> {
-    pub fn new<B: Backend>(module: &Module<B>, log_base2k: usize, log_k: usize) -> Self {
-        Self {
-            data: module.new_vec_znx(1, derive_size(log_base2k, log_k)),
-            log_base2k: log_base2k,
-            log_k: log_k,
-        }
-    }
-}
-
-pub struct RLWECtDft<C, B: Backend> {
-    pub data: VecZnxDft<C, B>,
-    pub log_base2k: usize,
-    pub log_k: usize,
-}
-
-impl<B: Backend> RLWECtDft<Vec<u8>, B> {
-    pub fn new(module: &Module<B>, log_base2k: usize, log_k: usize) -> Self {
-        Self {
-            data: module.new_vec_znx_dft(2, derive_size(log_base2k, log_k)),
-            log_base2k: log_base2k,
-            log_k: log_k,
-        }
-    }
-}
-
-impl<T, B: Backend> Infos for RLWECtDft<T, B> {
-    type Inner = VecZnxDft<T, B>;
-
-    fn inner(&self) -> &Self::Inner {
-        &self.data
-    }
-
-    fn log_base2k(&self) -> usize {
-        self.log_base2k
-    }
-
-    fn log_k(&self) -> usize {
-        self.log_k
-    }
-}
-
-impl<C, B: Backend> VecZnxDftToMut<B> for RLWECtDft<C, B>
-where
-    VecZnxDft<C, B>: VecZnxDftToMut<B>,
-{
-    fn to_mut(&mut self) -> VecZnxDft<&mut [u8], B> {
-        self.data.to_mut()
-    }
-}
-
-impl<C, B: Backend> VecZnxDftToRef<B> for RLWECtDft<C, B>
-where
-    VecZnxDft<C, B>: VecZnxDftToRef<B>,
-{
-    fn to_ref(&self) -> VecZnxDft<&[u8], B> {
-        self.data.to_ref()
-    }
-}
-
-impl<C> RLWECtDft<C, FFT64>
-where
-    RLWECtDft<C, FFT64>: VecZnxDftToRef<FFT64>,
-{
-    #[allow(dead_code)]
-    pub(crate) fn idft_scratch_space(module: &Module<FFT64>, size: usize) -> usize {
-        module.bytes_of_vec_znx(2, size) + (module.vec_znx_big_normalize_tmp_bytes() | module.vec_znx_idft_tmp_bytes())
-    }
-
-    pub(crate) fn idft<R>(&self, module: &Module<FFT64>, res: &mut RLWECt<R>, scratch: &mut Scratch)
-    where
-        RLWECt<R>: VecZnxToMut,
-    {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(self.cols(), 2);
-            assert_eq!(res.cols(), 2);
-            assert_eq!(self.log_base2k(), res.log_base2k())
-        }
-
-        let min_size: usize = self.size().min(res.size());
-
-        let (mut res_big, scratch1) = scratch.tmp_vec_znx_big(module, 2, min_size);
-
-        module.vec_znx_idft(&mut res_big, 0, self, 0, scratch1);
-        module.vec_znx_idft(&mut res_big, 1, self, 1, scratch1);
-        module.vec_znx_big_normalize(self.log_base2k(), res, 0, &res_big, 0, scratch1);
-        module.vec_znx_big_normalize(self.log_base2k(), res, 1, &res_big, 1, scratch1);
-    }
-}
-
-pub(crate) fn encrypt_zero_rlwe_dft_sk<C, S>(
-    module: &Module<FFT64>,
-    ct: &mut RLWECtDft<C, FFT64>,
-    sk: &SecretKeyDft<S, FFT64>,
-    source_xa: &mut Source,
-    source_xe: &mut Source,
-    sigma: f64,
-    bound: f64,
-    scratch: &mut Scratch,
-) where
-    VecZnxDft<C, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64>,
-    ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
-{
-    let log_base2k: usize = ct.log_base2k();
-    let log_k: usize = ct.log_k();
-    let size: usize = ct.size();
-
-    #[cfg(debug_assertions)]
-    {
-        match sk.dist {
-            SecretDistribution::NONE => panic!("invalid sk.dist = SecretDistribution::NONE"),
-            _ => {}
-        }
-        assert_eq!(ct.cols(), 2);
-    }
-
-    // ct[1] = DFT(a)
-    {
-        let (mut tmp_znx, _) = scratch.tmp_vec_znx(module, 1, size);
-        tmp_znx.fill_uniform(log_base2k, 0, size, source_xa);
-        module.vec_znx_dft(ct, 1, &tmp_znx, 0);
-    }
-
-    let (mut c0_big, scratch_1) = scratch.tmp_vec_znx_big(module, 1, size);
-
-    {
-        let (mut tmp_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, size);
-        // c0_dft = ct[1] * DFT(s)
-        module.svp_apply(&mut tmp_dft, 0, sk, 0, ct, 1);
-
-        // c0_big = IDFT(c0_dft)
-        module.vec_znx_idft_tmp_a(&mut c0_big, 0, &mut tmp_dft, 0);
-    }
-
-    // c0_big += e
-    c0_big.add_normal(log_base2k, 0, log_k, source_xe, sigma, bound);
-
-    // c0 = norm(c0_big = -as - e), NOTE: e is centered at 0.
-    let (mut tmp_znx, scratch_2) = scratch_1.tmp_vec_znx(module, 1, size);
-    module.vec_znx_big_normalize(log_base2k, &mut tmp_znx, 0, &c0_big, 0, scratch_2);
-    module.vec_znx_negate_inplace(&mut tmp_znx, 0);
-    // ct[0] = DFT(-as + e)
-    module.vec_znx_dft(ct, 0, &tmp_znx, 0);
-}
-
-impl RLWECtDft<Vec<u8>, FFT64> {
-    pub fn encrypt_zero_sk_scratch_space(module: &Module<FFT64>, size: usize) -> usize {
-        (module.bytes_of_vec_znx(1, size) | module.bytes_of_vec_znx_dft(1, size))
-            + module.bytes_of_vec_znx_big(1, size)
-            + module.bytes_of_vec_znx(1, size)
-            + module.vec_znx_big_normalize_tmp_bytes()
-    }
-
-    pub fn decrypt_scratch_space(module: &Module<FFT64>, size: usize) -> usize {
-        (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)
-    }
-}
-
-pub fn decrypt_rlwe_dft<P, C, S>(
-    module: &Module<FFT64>,
-    pt: &mut RLWEPt<P>,
-    ct: &RLWECtDft<C, FFT64>,
-    sk: &SecretKeyDft<S, FFT64>,
-    scratch: &mut Scratch,
-) where
-    VecZnx<P>: VecZnxToMut + VecZnxToRef,
-    VecZnxDft<C, FFT64>: VecZnxDftToRef<FFT64>,
-    ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
-{
-    let (mut c0_big, scratch_1) = scratch.tmp_vec_znx_big(module, 1, ct.size()); // TODO optimize size when pt << ct
-
-    {
-        let (mut c0_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, ct.size()); // TODO optimize size when pt << ct
-        // c0_dft = DFT(a) * DFT(s)
-        module.svp_apply(&mut c0_dft, 0, sk, 0, ct, 1);
-        // c0_big = IDFT(c0_dft)
-        module.vec_znx_idft_tmp_a(&mut c0_big, 0, &mut c0_dft, 0);
-    }
-
-    {
-        let (mut c1_big, scratch_2) = scratch_1.tmp_vec_znx_big(module, 1, ct.size());
-        // c0_big = (a * s) + (-a * s + m + e) = BIG(m + e)
-        module.vec_znx_idft(&mut c1_big, 0, ct, 0, scratch_2);
-        module.vec_znx_big_add_inplace(&mut c0_big, 0, &c1_big, 0);
-    }
-
-    // pt = norm(BIG(m + e))
-    module.vec_znx_big_normalize(ct.log_base2k(), pt, 0, &mut c0_big, 0, scratch_1);
-
-    pt.log_base2k = ct.log_base2k();
-    pt.log_k = pt.log_k().min(ct.log_k());
-}
-
-impl<C> RLWECtDft<C, FFT64> {
-    pub(crate) fn encrypt_zero_sk<S>(
-        &mut self,
-        module: &Module<FFT64>,
-        sk_dft: &SecretKeyDft<S, FFT64>,
-        source_xa: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-        bound: f64,
-        scratch: &mut Scratch,
-    ) where
-        VecZnxDft<C, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64>,
-        ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
-    {
-        encrypt_zero_rlwe_dft_sk(
-            module, self, sk_dft, source_xa, source_xe, sigma, bound, scratch,
-        )
-    }
-
-    pub fn decrypt<P, S>(
-        &self,
-        module: &Module<FFT64>,
-        pt: &mut RLWEPt<P>,
-        sk_dft: &SecretKeyDft<S, FFT64>,
-        scratch: &mut Scratch,
-    ) where
-        VecZnx<P>: VecZnxToMut + VecZnxToRef,
-        VecZnxDft<C, FFT64>: VecZnxDftToRef<FFT64>,
-        ScalarZnxDft<S, FFT64>: ScalarZnxDftToRef<FFT64>,
-    {
-        decrypt_rlwe_dft(module, pt, self, sk_dft, scratch);
-    }
-}
-
-impl ProdInplaceScratchSpace for RLWECtDft<Vec<u8>, FFT64> {
-    fn prod_by_grlwe_inplace_scratch_space(module: &Module<FFT64>, lhs: usize, rhs: usize) -> usize {
-        <GRLWECt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_rlwe_dft_inplace_scratch_space(module, lhs, rhs)
-    }
-
-    fn prod_by_rgsw_inplace_scratch_space(module: &Module<FFT64>, lhs: usize, rhs: usize) -> usize {
-        <RGSWCt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_rlwe_dft_inplace_scratch_space(module, lhs, rhs)
-    }
-}
-
-impl ProdScratchSpace for RLWECtDft<Vec<u8>, FFT64> {
-    fn prod_by_grlwe_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
-        <GRLWECt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_rlwe_dft_scratch_space(module, res_size, lhs, rhs)
-    }
-
-    fn prod_by_rgsw_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
-        <RGSWCt<Vec<u8>, FFT64> as MatRLWEProductScratchSpace>::prod_with_rlwe_dft_scratch_space(module, res_size, lhs, rhs)
-    }
-}
-
-impl<MUT, REF> ProdInplace<MUT, REF> for RLWECtDft<MUT, FFT64>
-where
-    VecZnxDft<MUT, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64>,
-    MatZnxDft<REF, FFT64>: MatZnxDftToRef<FFT64>,
-{
-    fn prod_by_grlwe_inplace(&mut self, module: &Module<FFT64>, rhs: &GRLWECt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_rlwe_dft_inplace(module, self, scratch);
-    }
-
-    fn prod_by_rgsw_inplace(&mut self, module: &Module<FFT64>, rhs: &RGSWCt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_rlwe_dft_inplace(module, self, scratch);
-    }
-}
-
-impl<MUT, REF> Product<MUT, REF> for RLWECtDft<MUT, FFT64>
-where
-    VecZnxDft<MUT, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64>,
-    VecZnxDft<REF, FFT64>: VecZnxDftToRef<FFT64>,
-    MatZnxDft<REF, FFT64>: MatZnxDftToRef<FFT64>,
-{
-    type Lhs = RLWECtDft<REF, FFT64>;
-
-    fn prod_by_grlwe(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &GRLWECt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_rlwe_dft(module, self, lhs, scratch);
-    }
-
-    fn prod_by_rgsw(&mut self, module: &Module<FFT64>, lhs: &Self::Lhs, rhs: &RGSWCt<REF, FFT64>, scratch: &mut Scratch) {
-        rhs.prod_with_rlwe_dft(module, self, lhs, scratch);
-    }
-}
diff --git a/core/src/test_fft64/grlwe.rs b/core/src/test_fft64/grlwe.rs
index 81c1023..9d9a077 100644
--- a/core/src/test_fft64/grlwe.rs
+++ b/core/src/test_fft64/grlwe.rs
@@ -2,11 +2,15 @@ use base2k::{FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned, Stats, VecZ
 use sampling::source::Source;
 
 use crate::{
-    elem::{GetRow, Infos, ProdInplace, ProdInplaceScratchSpace, ProdScratchSpace, Product},
-    grlwe::GRLWECt,
-    keys::{SecretKey, SecretKeyDft},
-    rgsw::RGSWCt,
-    rlwe::{RLWECtDft, RLWEPt},
+    elem::{GetRow, Infos},
+    external_product::{
+        ExternalProduct, ExternalProductInplace, ExternalProductInplaceScratchSpace, ExternalProductScratchSpace,
+    },
+    ggsw::GGSWCiphertext,
+    glwe::{GLWECiphertextFourier, GLWEPlaintext},
+    keys::{SecretKey, SecretKeyFourier},
+    keyswitch::{KeySwitch, KeySwitchInplace, KeySwitchInplaceScratchSpace, KeySwitchScratchSpace},
+    keyswitch_key::GLWEKeySwitchKey,
     test_fft64::rgsw::noise_rgsw_product,
 };
 
@@ -20,8 +24,8 @@ fn encrypt_sk() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_ct, rows);
-    let mut pt: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_ct);
+    let mut ct: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_ct, rows);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_ct);
     let mut pt_scalar: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
@@ -31,13 +35,14 @@ fn encrypt_sk() {
     pt_scalar.fill_ternary_hw(0, module.n(), &mut source_xs);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct.size()) | RLWECtDft::decrypt_scratch_space(&module, ct.size()),
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct.size())
+            | GLWECiphertextFourier::decrypt_scratch_space(&module, ct.size()),
     );
 
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
     ct.encrypt_sk(
@@ -51,7 +56,7 @@ fn encrypt_sk() {
         scratch.borrow(),
     );
 
-    let mut ct_rlwe_dft: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_ct);
+    let mut ct_rlwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::new(&module, log_base2k, log_k_ct);
 
     (0..ct.rows()).for_each(|row_i| {
         ct.get_row(&module, row_i, 0, &mut ct_rlwe_dft);
@@ -60,12 +65,10 @@ fn encrypt_sk() {
         let std_pt: f64 = pt.data.std(0, log_base2k) * (log_k_ct as f64).exp2();
         assert!((sigma - std_pt).abs() <= 0.2, "{} {}", sigma, std_pt);
     });
-
-    module.free();
 }
 
 #[test]
-fn from_prod_by_grlwe() {
+fn keyswitch() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -74,18 +77,18 @@ fn from_prod_by_grlwe() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_grlwe_s0s1: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_grlwe_s1s2: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_grlwe_s0s2: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_grlwe_s0s1: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_grlwe_s1s2: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_grlwe_s0s2: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
 
     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(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct_grlwe_s0s1.size())
-            | RLWECtDft::decrypt_scratch_space(&module, ct_grlwe_s0s2.size())
-            | GRLWECt::prod_by_grlwe_scratch_space(
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_grlwe_s0s1.size())
+            | GLWECiphertextFourier::decrypt_scratch_space(&module, ct_grlwe_s0s2.size())
+            | GLWEKeySwitchKey::keyswitch_scratch_space(
                 &module,
                 ct_grlwe_s0s2.size(),
                 ct_grlwe_s0s1.size(),
@@ -96,19 +99,19 @@ fn from_prod_by_grlwe() {
     let mut sk0: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk0.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk0_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk0_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk0_dft.dft(&module, &sk0);
 
     let mut sk1: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk1.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk1_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk1_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk1_dft.dft(&module, &sk1);
 
     let mut sk2: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk2.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk2_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk2_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk2_dft.dft(&module, &sk2);
 
     // GRLWE_{s1}(s0) = s0 -> s1
@@ -136,10 +139,11 @@ fn from_prod_by_grlwe() {
     );
 
     // GRLWE_{s1}(s0) (x) GRLWE_{s2}(s1) = GRLWE_{s2}(s0)
-    ct_grlwe_s0s2.prod_by_grlwe(&module, &ct_grlwe_s0s1, &ct_grlwe_s1s2, scratch.borrow());
+    ct_grlwe_s0s2.keyswitch(&module, &ct_grlwe_s0s1, &ct_grlwe_s1s2, scratch.borrow());
 
-    let mut ct_rlwe_dft_s0s2: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_grlwe);
-    let mut pt: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_grlwe);
+    let mut ct_rlwe_dft_s0s2: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::new(&module, log_base2k, log_k_grlwe);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_grlwe);
 
     (0..ct_grlwe_s0s2.rows()).for_each(|row_i| {
         ct_grlwe_s0s2.get_row(&module, row_i, 0, &mut ct_rlwe_dft_s0s2);
@@ -166,12 +170,10 @@ fn from_prod_by_grlwe() {
             noise_want
         );
     });
-
-    module.free();
 }
 
 #[test]
-fn prod_by_grlwe() {
+fn keyswitch_inplace() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -180,35 +182,35 @@ fn prod_by_grlwe() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_grlwe_s0s1: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_grlwe_s1s2: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_grlwe_s0s1: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_grlwe_s1s2: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
 
     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(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct_grlwe_s0s1.size())
-            | RLWECtDft::decrypt_scratch_space(&module, ct_grlwe_s0s1.size())
-            | GRLWECt::prod_by_grlwe_inplace_scratch_space(&module, ct_grlwe_s0s1.size(), ct_grlwe_s1s2.size()),
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_grlwe_s0s1.size())
+            | GLWECiphertextFourier::decrypt_scratch_space(&module, ct_grlwe_s0s1.size())
+            | GLWEKeySwitchKey::keyswitch_inplace_scratch_space(&module, ct_grlwe_s0s1.size(), ct_grlwe_s1s2.size()),
     );
 
     let mut sk0: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk0.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk0_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk0_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk0_dft.dft(&module, &sk0);
 
     let mut sk1: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk1.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk1_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk1_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk1_dft.dft(&module, &sk1);
 
     let mut sk2: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk2.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk2_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk2_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk2_dft.dft(&module, &sk2);
 
     // GRLWE_{s1}(s0) = s0 -> s1
@@ -236,12 +238,13 @@ fn prod_by_grlwe() {
     );
 
     // GRLWE_{s1}(s0) (x) GRLWE_{s2}(s1) = GRLWE_{s2}(s0)
-    ct_grlwe_s0s1.prod_by_grlwe_inplace(&module, &ct_grlwe_s1s2, scratch.borrow());
+    ct_grlwe_s0s1.keyswitch_inplace(&module, &ct_grlwe_s1s2, scratch.borrow());
 
-    let ct_grlwe_s0s2: GRLWECt<Vec<u8>, FFT64> = ct_grlwe_s0s1;
+    let ct_grlwe_s0s2: GLWEKeySwitchKey<Vec<u8>, FFT64> = ct_grlwe_s0s1;
 
-    let mut ct_rlwe_dft_s0s2: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_grlwe);
-    let mut pt: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_grlwe);
+    let mut ct_rlwe_dft_s0s2: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::new(&module, log_base2k, log_k_grlwe);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_grlwe);
 
     (0..ct_grlwe_s0s2.rows()).for_each(|row_i| {
         ct_grlwe_s0s2.get_row(&module, row_i, 0, &mut ct_rlwe_dft_s0s2);
@@ -268,12 +271,10 @@ fn prod_by_grlwe() {
             noise_want
         );
     });
-
-    module.free();
 }
 
 #[test]
-fn from_prod_by_rgsw() {
+fn external_product() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -282,9 +283,9 @@ fn from_prod_by_rgsw() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_grlwe_in: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_grlwe_out: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_rgsw: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_grlwe_in: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_grlwe_out: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_grlwe, rows);
 
     let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
     let mut pt_grlwe: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
@@ -294,15 +295,15 @@ fn from_prod_by_rgsw() {
     let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct_grlwe_in.size())
-            | RLWECtDft::decrypt_scratch_space(&module, ct_grlwe_out.size())
-            | GRLWECt::prod_by_rgsw_scratch_space(
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_grlwe_in.size())
+            | GLWECiphertextFourier::decrypt_scratch_space(&module, ct_grlwe_out.size())
+            | GLWEKeySwitchKey::external_product_scratch_space(
                 &module,
                 ct_grlwe_out.size(),
                 ct_grlwe_in.size(),
                 ct_rgsw.size(),
             )
-            | RGSWCt::encrypt_sk_scratch_space(&module, ct_rgsw.size()),
+            | GGSWCiphertext::encrypt_sk_scratch_space(&module, ct_rgsw.size()),
     );
 
     let k: usize = 1;
@@ -314,7 +315,7 @@ fn from_prod_by_rgsw() {
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
     // GRLWE_{s1}(s0) = s0 -> s1
@@ -341,10 +342,11 @@ fn from_prod_by_rgsw() {
     );
 
     // GRLWE_(m) (x) RGSW_(X^k) = GRLWE_(m * X^k)
-    ct_grlwe_out.prod_by_rgsw(&module, &ct_grlwe_in, &ct_rgsw, scratch.borrow());
+    ct_grlwe_out.external_product(&module, &ct_grlwe_in, &ct_rgsw, scratch.borrow());
 
-    let mut ct_rlwe_dft_s0s2: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_grlwe);
-    let mut pt: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_grlwe);
+    let mut ct_rlwe_dft_s0s2: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::new(&module, log_base2k, log_k_grlwe);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_grlwe);
 
     module.vec_znx_rotate_inplace(k as i64, &mut pt_grlwe, 0);
 
@@ -382,12 +384,10 @@ fn from_prod_by_rgsw() {
             noise_want
         );
     });
-
-    module.free();
 }
 
 #[test]
-fn prod_by_rgsw() {
+fn external_product_inplace() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -396,8 +396,8 @@ fn prod_by_rgsw() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_grlwe: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_rgsw: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_grlwe: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_grlwe, rows);
 
     let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
     let mut pt_grlwe: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
@@ -407,10 +407,10 @@ fn prod_by_rgsw() {
     let mut source_xa: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct_grlwe.size())
-            | RLWECtDft::decrypt_scratch_space(&module, ct_grlwe.size())
-            | GRLWECt::prod_by_rgsw_inplace_scratch_space(&module, ct_grlwe.size(), ct_rgsw.size())
-            | RGSWCt::encrypt_sk_scratch_space(&module, ct_rgsw.size()),
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_grlwe.size())
+            | GLWECiphertextFourier::decrypt_scratch_space(&module, ct_grlwe.size())
+            | GLWEKeySwitchKey::external_product_inplace_scratch_space(&module, ct_grlwe.size(), ct_rgsw.size())
+            | GGSWCiphertext::encrypt_sk_scratch_space(&module, ct_rgsw.size()),
     );
 
     let k: usize = 1;
@@ -422,7 +422,7 @@ fn prod_by_rgsw() {
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
     // GRLWE_{s1}(s0) = s0 -> s1
@@ -449,10 +449,11 @@ fn prod_by_rgsw() {
     );
 
     // GRLWE_(m) (x) RGSW_(X^k) = GRLWE_(m * X^k)
-    ct_grlwe.prod_by_rgsw_inplace(&module, &ct_rgsw, scratch.borrow());
+    ct_grlwe.external_product_inplace(&module, &ct_rgsw, scratch.borrow());
 
-    let mut ct_rlwe_dft_s0s2: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_grlwe);
-    let mut pt: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_grlwe);
+    let mut ct_rlwe_dft_s0s2: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::new(&module, log_base2k, log_k_grlwe);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_grlwe);
 
     module.vec_znx_rotate_inplace(k as i64, &mut pt_grlwe, 0);
 
@@ -490,8 +491,6 @@ fn prod_by_rgsw() {
             noise_want
         );
     });
-
-    module.free();
 }
 
 pub(crate) fn noise_grlwe_rlwe_product(
diff --git a/core/src/test_fft64/rgsw.rs b/core/src/test_fft64/rgsw.rs
index 50cd356..820b671 100644
--- a/core/src/test_fft64/rgsw.rs
+++ b/core/src/test_fft64/rgsw.rs
@@ -5,16 +5,20 @@ use base2k::{
 use sampling::source::Source;
 
 use crate::{
-    elem::{GetRow, Infos, ProdInplace, ProdInplaceScratchSpace, ProdScratchSpace, Product},
-    grlwe::GRLWECt,
-    keys::{SecretKey, SecretKeyDft},
-    rgsw::RGSWCt,
-    rlwe::{RLWECtDft, RLWEPt},
+    elem::{GetRow, Infos},
+    external_product::{
+        ExternalProduct, ExternalProductInplace, ExternalProductInplaceScratchSpace, ExternalProductScratchSpace,
+    },
+    ggsw::GGSWCiphertext,
+    glwe::{GLWECiphertextFourier, GLWEPlaintext},
+    keys::{SecretKey, SecretKeyFourier},
+    keyswitch::{KeySwitch, KeySwitchInplace, KeySwitchInplaceScratchSpace, KeySwitchScratchSpace},
+    keyswitch_key::GLWEKeySwitchKey,
     test_fft64::grlwe::noise_grlwe_rlwe_product,
 };
 
 #[test]
-fn encrypt_rgsw_sk() {
+fn encrypt_sk() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 8;
     let log_k_ct: usize = 54;
@@ -23,9 +27,9 @@ fn encrypt_rgsw_sk() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_ct, rows);
-    let mut pt_have: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_ct);
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_ct);
+    let mut ct: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_ct, rows);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_ct);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_ct);
     let mut pt_scalar: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
@@ -35,13 +39,14 @@ fn encrypt_rgsw_sk() {
     pt_scalar.fill_ternary_hw(0, module.n(), &mut source_xs);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        RGSWCt::encrypt_sk_scratch_space(&module, ct.size()) | RLWECtDft::decrypt_scratch_space(&module, ct.size()),
+        GGSWCiphertext::encrypt_sk_scratch_space(&module, ct.size())
+            | GLWECiphertextFourier::decrypt_scratch_space(&module, ct.size()),
     );
 
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
     ct.encrypt_sk(
@@ -55,11 +60,11 @@ fn encrypt_rgsw_sk() {
         scratch.borrow(),
     );
 
-    let mut ct_rlwe_dft: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_ct);
+    let mut ct_rlwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::new(&module, log_base2k, log_k_ct);
     let mut pt_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(1, ct.size());
     let mut pt_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, ct.size());
 
-    (0..ct.cols()).for_each(|col_j| {
+    (0..ct.rank()).for_each(|col_j| {
         (0..ct.rows()).for_each(|row_i| {
             module.vec_znx_add_scalar_inplace(&mut pt_want, 0, row_i, &pt_scalar, 0);
 
@@ -82,12 +87,10 @@ fn encrypt_rgsw_sk() {
             pt_want.data.zero();
         });
     });
-
-    module.free();
 }
 
 #[test]
-fn from_prod_by_grlwe() {
+fn keyswitch() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -98,9 +101,9 @@ fn from_prod_by_grlwe() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_grlwe: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_rgsw_in: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_rgsw_in, rows);
-    let mut ct_rgsw_out: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_rgsw_out, rows);
+    let mut ct_grlwe: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_rgsw_in: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_rgsw_in, rows);
+    let mut ct_rgsw_out: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_rgsw_out, rows);
     let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
@@ -111,10 +114,10 @@ fn from_prod_by_grlwe() {
     pt_rgsw.fill_ternary_prob(0, 0.5, &mut source_xs);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct_grlwe.size())
-            | RLWECtDft::decrypt_scratch_space(&module, ct_rgsw_out.size())
-            | RGSWCt::encrypt_sk_scratch_space(&module, ct_rgsw_in.size())
-            | RGSWCt::prod_by_grlwe_scratch_space(
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_grlwe.size())
+            | GLWECiphertextFourier::decrypt_scratch_space(&module, ct_rgsw_out.size())
+            | GGSWCiphertext::encrypt_sk_scratch_space(&module, ct_rgsw_in.size())
+            | GGSWCiphertext::keyswitch_scratch_space(
                 &module,
                 ct_rgsw_out.size(),
                 ct_rgsw_in.size(),
@@ -125,13 +128,13 @@ fn from_prod_by_grlwe() {
     let mut sk0: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk0.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk0_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk0_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk0_dft.dft(&module, &sk0);
 
     let mut sk1: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk1.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk1_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk1_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk1_dft.dft(&module, &sk1);
 
     ct_grlwe.encrypt_sk(
@@ -156,15 +159,15 @@ fn from_prod_by_grlwe() {
         scratch.borrow(),
     );
 
-    ct_rgsw_out.prod_by_grlwe(&module, &ct_rgsw_in, &ct_grlwe, scratch.borrow());
+    ct_rgsw_out.keyswitch(&module, &ct_rgsw_in, &ct_grlwe, scratch.borrow());
 
-    let mut ct_rlwe_dft: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_rgsw_out);
-    let mut pt: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rgsw_out);
+    let mut ct_rlwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::new(&module, log_base2k, log_k_rgsw_out);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rgsw_out);
     let mut pt_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(1, ct_rgsw_out.size());
     let mut pt_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, ct_rgsw_out.size());
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rgsw_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rgsw_out);
 
-    (0..ct_rgsw_out.cols()).for_each(|col_j| {
+    (0..ct_rgsw_out.rank()).for_each(|col_j| {
         (0..ct_rgsw_out.rows()).for_each(|row_i| {
             module.vec_znx_add_scalar_inplace(&mut pt_want, 0, row_i, &pt_rgsw, 0);
 
@@ -203,12 +206,10 @@ fn from_prod_by_grlwe() {
             pt_want.data.zero();
         });
     });
-
-    module.free();
 }
 
 #[test]
-fn from_prod_by_grlwe_inplace() {
+fn keyswitch_inplace() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -218,8 +219,8 @@ fn from_prod_by_grlwe_inplace() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_grlwe: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_rgsw: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_rgsw, rows);
+    let mut ct_grlwe: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_rgsw, rows);
     let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
@@ -230,22 +231,22 @@ fn from_prod_by_grlwe_inplace() {
     pt_rgsw.fill_ternary_prob(0, 0.5, &mut source_xs);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct_grlwe.size())
-            | RLWECtDft::decrypt_scratch_space(&module, ct_rgsw.size())
-            | RGSWCt::encrypt_sk_scratch_space(&module, ct_rgsw.size())
-            | RGSWCt::prod_by_grlwe_inplace_scratch_space(&module, ct_rgsw.size(), ct_grlwe.size()),
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_grlwe.size())
+            | GLWECiphertextFourier::decrypt_scratch_space(&module, ct_rgsw.size())
+            | GGSWCiphertext::encrypt_sk_scratch_space(&module, ct_rgsw.size())
+            | GGSWCiphertext::keyswitch_inplace_scratch_space(&module, ct_rgsw.size(), ct_grlwe.size()),
     );
 
     let mut sk0: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk0.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk0_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk0_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk0_dft.dft(&module, &sk0);
 
     let mut sk1: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk1.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk1_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk1_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk1_dft.dft(&module, &sk1);
 
     ct_grlwe.encrypt_sk(
@@ -270,15 +271,15 @@ fn from_prod_by_grlwe_inplace() {
         scratch.borrow(),
     );
 
-    ct_rgsw.prod_by_grlwe_inplace(&module, &ct_grlwe, scratch.borrow());
+    ct_rgsw.keyswitch_inplace(&module, &ct_grlwe, scratch.borrow());
 
-    let mut ct_rlwe_dft: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_rgsw);
-    let mut pt: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rgsw);
+    let mut ct_rlwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::new(&module, log_base2k, log_k_rgsw);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rgsw);
     let mut pt_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(1, ct_rgsw.size());
     let mut pt_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, ct_rgsw.size());
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rgsw);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rgsw);
 
-    (0..ct_rgsw.cols()).for_each(|col_j| {
+    (0..ct_rgsw.rank()).for_each(|col_j| {
         (0..ct_rgsw.rows()).for_each(|row_i| {
             module.vec_znx_add_scalar_inplace(&mut pt_want, 0, row_i, &pt_rgsw, 0);
 
@@ -317,12 +318,10 @@ fn from_prod_by_grlwe_inplace() {
             pt_want.data.zero();
         });
     });
-
-    module.free();
 }
 
 #[test]
-fn from_prod_by_rgsw() {
+fn external_product() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_rgsw_rhs: usize = 60;
@@ -333,9 +332,9 @@ fn from_prod_by_rgsw() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_rgsw_rhs: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_rgsw_rhs, rows);
-    let mut ct_rgsw_lhs_in: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_rgsw_lhs_in, rows);
-    let mut ct_rgsw_lhs_out: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_rgsw_lhs_out, rows);
+    let mut ct_rgsw_rhs: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_rgsw_rhs, rows);
+    let mut ct_rgsw_lhs_in: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_rgsw_lhs_in, rows);
+    let mut ct_rgsw_lhs_out: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_rgsw_lhs_out, rows);
     let mut pt_rgsw_lhs: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
     let mut pt_rgsw_rhs: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
 
@@ -351,10 +350,10 @@ fn from_prod_by_rgsw() {
     pt_rgsw_rhs.to_mut().raw_mut()[k] = 1; //X^{k}
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct_rgsw_rhs.size())
-            | RLWECtDft::decrypt_scratch_space(&module, ct_rgsw_lhs_out.size())
-            | RGSWCt::encrypt_sk_scratch_space(&module, ct_rgsw_lhs_in.size())
-            | RGSWCt::prod_by_rgsw_scratch_space(
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_rgsw_rhs.size())
+            | GLWECiphertextFourier::decrypt_scratch_space(&module, ct_rgsw_lhs_out.size())
+            | GGSWCiphertext::encrypt_sk_scratch_space(&module, ct_rgsw_lhs_in.size())
+            | GGSWCiphertext::external_product_scratch_space(
                 &module,
                 ct_rgsw_lhs_out.size(),
                 ct_rgsw_lhs_in.size(),
@@ -365,7 +364,7 @@ fn from_prod_by_rgsw() {
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
     ct_rgsw_rhs.encrypt_sk(
@@ -390,17 +389,18 @@ fn from_prod_by_rgsw() {
         scratch.borrow(),
     );
 
-    ct_rgsw_lhs_out.prod_by_rgsw(&module, &ct_rgsw_lhs_in, &ct_rgsw_rhs, scratch.borrow());
+    ct_rgsw_lhs_out.external_product(&module, &ct_rgsw_lhs_in, &ct_rgsw_rhs, scratch.borrow());
 
-    let mut ct_rlwe_dft: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_rgsw_lhs_out);
-    let mut pt: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rgsw_lhs_out);
+    let mut ct_rlwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::new(&module, log_base2k, log_k_rgsw_lhs_out);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rgsw_lhs_out);
     let mut pt_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(1, ct_rgsw_lhs_out.size());
     let mut pt_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, ct_rgsw_lhs_out.size());
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rgsw_lhs_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rgsw_lhs_out);
 
     module.vec_znx_rotate_inplace(k as i64, &mut pt_rgsw_lhs, 0);
 
-    (0..ct_rgsw_lhs_out.cols()).for_each(|col_j| {
+    (0..ct_rgsw_lhs_out.rank()).for_each(|col_j| {
         (0..ct_rgsw_lhs_out.rows()).for_each(|row_i| {
             module.vec_znx_add_scalar_inplace(&mut pt_want, 0, row_i, &pt_rgsw_lhs, 0);
 
@@ -448,12 +448,10 @@ fn from_prod_by_rgsw() {
             pt_want.data.zero();
         });
     });
-
-    module.free();
 }
 
 #[test]
-fn from_prod_by_rgsw_inplace() {
+fn external_product_inplace() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_rgsw_rhs: usize = 60;
@@ -463,8 +461,8 @@ fn from_prod_by_rgsw_inplace() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_rgsw_rhs: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_rgsw_rhs, rows);
-    let mut ct_rgsw_lhs: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_rgsw_lhs, rows);
+    let mut ct_rgsw_rhs: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_rgsw_rhs, rows);
+    let mut ct_rgsw_lhs: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_rgsw_lhs, rows);
     let mut pt_rgsw_lhs: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
     let mut pt_rgsw_rhs: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
 
@@ -480,16 +478,16 @@ fn from_prod_by_rgsw_inplace() {
     pt_rgsw_rhs.to_mut().raw_mut()[k] = 1; //X^{k}
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct_rgsw_rhs.size())
-            | RLWECtDft::decrypt_scratch_space(&module, ct_rgsw_lhs.size())
-            | RGSWCt::encrypt_sk_scratch_space(&module, ct_rgsw_lhs.size())
-            | RGSWCt::prod_by_rgsw_inplace_scratch_space(&module, ct_rgsw_lhs.size(), ct_rgsw_rhs.size()),
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_rgsw_rhs.size())
+            | GLWECiphertextFourier::decrypt_scratch_space(&module, ct_rgsw_lhs.size())
+            | GGSWCiphertext::encrypt_sk_scratch_space(&module, ct_rgsw_lhs.size())
+            | GGSWCiphertext::external_product_inplace_scratch_space(&module, ct_rgsw_lhs.size(), ct_rgsw_rhs.size()),
     );
 
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
     ct_rgsw_rhs.encrypt_sk(
@@ -514,17 +512,17 @@ fn from_prod_by_rgsw_inplace() {
         scratch.borrow(),
     );
 
-    ct_rgsw_lhs.prod_by_rgsw_inplace(&module, &ct_rgsw_rhs, scratch.borrow());
+    ct_rgsw_lhs.external_product_inplace(&module, &ct_rgsw_rhs, scratch.borrow());
 
-    let mut ct_rlwe_dft: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_rgsw_lhs);
-    let mut pt: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rgsw_lhs);
+    let mut ct_rlwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::new(&module, log_base2k, log_k_rgsw_lhs);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rgsw_lhs);
     let mut pt_dft: VecZnxDft<Vec<u8>, FFT64> = module.new_vec_znx_dft(1, ct_rgsw_lhs.size());
     let mut pt_big: VecZnxBig<Vec<u8>, FFT64> = module.new_vec_znx_big(1, ct_rgsw_lhs.size());
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rgsw_lhs);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rgsw_lhs);
 
     module.vec_znx_rotate_inplace(k as i64, &mut pt_rgsw_lhs, 0);
 
-    (0..ct_rgsw_lhs.cols()).for_each(|col_j| {
+    (0..ct_rgsw_lhs.rank()).for_each(|col_j| {
         (0..ct_rgsw_lhs.rows()).for_each(|row_i| {
             module.vec_znx_add_scalar_inplace(&mut pt_want, 0, row_i, &pt_rgsw_lhs, 0);
 
@@ -572,8 +570,6 @@ fn from_prod_by_rgsw_inplace() {
             pt_want.data.zero();
         });
     });
-
-    module.free();
 }
 
 pub(crate) fn noise_rgsw_product(
diff --git a/core/src/test_fft64/rlwe.rs b/core/src/test_fft64/rlwe.rs
index a2fabb9..6958925 100644
--- a/core/src/test_fft64/rlwe.rs
+++ b/core/src/test_fft64/rlwe.rs
@@ -6,11 +6,16 @@ use itertools::izip;
 use sampling::source::Source;
 
 use crate::{
-    elem::{Infos, ProdInplace, ProdInplaceScratchSpace, ProdScratchSpace, Product},
-    grlwe::GRLWECt,
-    keys::{PublicKey, SecretKey, SecretKeyDft},
-    rgsw::RGSWCt,
-    rlwe::{RLWECt, RLWECtDft, RLWEPt},
+    elem::Infos,
+    encryption::EncryptSkScratchSpace,
+    external_product::{
+        ExternalProduct, ExternalProductInplace, ExternalProductInplaceScratchSpace, ExternalProductScratchSpace,
+    },
+    ggsw::GGSWCiphertext,
+    glwe::{GLWECiphertext, GLWECiphertextFourier, GLWEPlaintext},
+    keys::{PublicKey, SecretKey, SecretKeyFourier},
+    keyswitch::{KeySwitch, KeySwitchInplace, KeySwitchInplaceScratchSpace, KeySwitchScratchSpace},
+    keyswitch_key::GLWEKeySwitchKey,
     test_fft64::{grlwe::noise_grlwe_rlwe_product, rgsw::noise_rgsw_product},
 };
 
@@ -24,21 +29,21 @@ fn encrypt_sk() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_ct);
-    let mut pt: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_pt);
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_ct);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_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(
-        RLWECt::encrypt_sk_scratch_space(&module, ct.size()) | RLWECt::decrypt_scratch_space(&module, ct.size()),
+        GLWECiphertext::encrypt_sk_scratch_space(&module, ct.size()) | GLWECiphertext::decrypt_scratch_space(&module, ct.size()),
     );
 
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
     let mut data_want: Vec<i64> = vec![0i64; module.n()];
@@ -52,7 +57,7 @@ fn encrypt_sk() {
 
     ct.encrypt_sk(
         &module,
-        Some(&pt),
+        &pt,
         &sk_dft,
         &mut source_xa,
         &mut source_xe,
@@ -81,8 +86,6 @@ fn encrypt_sk() {
             b_scaled
         )
     });
-
-    module.free();
 }
 
 #[test]
@@ -94,7 +97,7 @@ fn encrypt_zero_sk() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut pt: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_ct);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_ct);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([1u8; 32]);
@@ -102,14 +105,14 @@ fn encrypt_zero_sk() {
 
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
-    let mut ct_dft: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_ct);
+    let mut ct_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::new(&module, log_base2k, log_k_ct);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        RLWECtDft::decrypt_scratch_space(&module, ct_dft.size())
-            | RLWECtDft::encrypt_zero_sk_scratch_space(&module, ct_dft.size()),
+        GLWECiphertextFourier::decrypt_scratch_space(&module, ct_dft.size())
+            | GLWECiphertextFourier::encrypt_zero_sk_scratch_space(&module, ct_dft.size()),
     );
 
     ct_dft.encrypt_zero_sk(
@@ -124,7 +127,6 @@ fn encrypt_zero_sk() {
     ct_dft.decrypt(&module, &mut pt, &sk_dft, scratch.borrow());
 
     assert!((sigma - pt.data.std(0, log_base2k) * (log_k_ct as f64).exp2()) <= 0.2);
-    module.free();
 }
 
 #[test]
@@ -137,8 +139,8 @@ fn encrypt_pk() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_ct);
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_ct);
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_ct);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_ct);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -147,7 +149,7 @@ fn encrypt_pk() {
 
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
     let mut pk: PublicKey<Vec<u8>, FFT64> = PublicKey::new(&module, log_base2k, log_k_pk);
@@ -161,9 +163,9 @@ fn encrypt_pk() {
     );
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        RLWECt::encrypt_sk_scratch_space(&module, ct.size())
-            | RLWECt::decrypt_scratch_space(&module, ct.size())
-            | RLWECt::encrypt_pk_scratch_space(&module, pk.size()),
+        GLWECiphertext::encrypt_sk_scratch_space(&module, ct.size())
+            | GLWECiphertext::decrypt_scratch_space(&module, ct.size())
+            | GLWECiphertext::encrypt_pk_scratch_space(&module, pk.size()),
     );
 
     let mut data_want: Vec<i64> = vec![0i64; module.n()];
@@ -178,7 +180,7 @@ fn encrypt_pk() {
 
     ct.encrypt_pk(
         &module,
-        Some(&pt_want),
+        &pt_want,
         &pk,
         &mut source_xu,
         &mut source_xe,
@@ -187,19 +189,17 @@ fn encrypt_pk() {
         scratch.borrow(),
     );
 
-    let mut pt_have: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_ct);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_ct);
 
     ct.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
 
     module.vec_znx_sub_ab_inplace(&mut pt_want, 0, &pt_have, 0);
 
     assert!(((1.0f64 / 12.0).sqrt() - pt_want.data.std(0, log_base2k) * (log_k_ct as f64).exp2()).abs() < 0.2);
-
-    module.free();
 }
 
 #[test]
-fn prod_by_grlwe() {
+fn keyswitch() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -210,11 +210,11 @@ fn prod_by_grlwe() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_grlwe: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_rlwe_in: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_rlwe_in);
-    let mut ct_rlwe_out: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_rlwe_out);
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe_in);
-    let mut pt_have: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe_out);
+    let mut ct_grlwe: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_rlwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_in);
+    let mut ct_rlwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_out);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -226,10 +226,10 @@ fn prod_by_grlwe() {
         .fill_uniform(log_base2k, 0, pt_want.size(), &mut source_xa);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct_grlwe.size())
-            | RLWECt::decrypt_scratch_space(&module, ct_rlwe_out.size())
-            | RLWECt::encrypt_sk_scratch_space(&module, ct_rlwe_in.size())
-            | RLWECt::prod_by_grlwe_scratch_space(
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_grlwe.size())
+            | GLWECiphertext::decrypt_scratch_space(&module, ct_rlwe_out.size())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe_in.size())
+            | GLWECiphertext::keyswitch_scratch_space(
                 &module,
                 ct_rlwe_out.size(),
                 ct_rlwe_in.size(),
@@ -240,13 +240,13 @@ fn prod_by_grlwe() {
     let mut sk0: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk0.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk0_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk0_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk0_dft.dft(&module, &sk0);
 
     let mut sk1: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk1.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk1_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk1_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk1_dft.dft(&module, &sk1);
 
     ct_grlwe.encrypt_sk(
@@ -262,7 +262,7 @@ fn prod_by_grlwe() {
 
     ct_rlwe_in.encrypt_sk(
         &module,
-        Some(&pt_want),
+        &pt_want,
         &sk0_dft,
         &mut source_xa,
         &mut source_xe,
@@ -271,7 +271,7 @@ fn prod_by_grlwe() {
         scratch.borrow(),
     );
 
-    ct_rlwe_out.prod_by_grlwe(&module, &ct_rlwe_in, &ct_grlwe, scratch.borrow());
+    ct_rlwe_out.keyswitch(&module, &ct_rlwe_in, &ct_grlwe, scratch.borrow());
 
     ct_rlwe_out.decrypt(&module, &mut pt_have, &sk1_dft, scratch.borrow());
 
@@ -296,12 +296,10 @@ fn prod_by_grlwe() {
         noise_have,
         noise_want
     );
-
-    module.free();
 }
 
 #[test]
-fn prod_by_grlwe_inplace() {
+fn keyswich_inplace() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -311,10 +309,10 @@ fn prod_by_grlwe_inplace() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_grlwe: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_rlwe: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_rlwe);
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe);
-    let mut pt_have: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe);
+    let mut ct_grlwe: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_rlwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -326,22 +324,22 @@ fn prod_by_grlwe_inplace() {
         .fill_uniform(log_base2k, 0, pt_want.size(), &mut source_xa);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct_grlwe.size())
-            | RLWECt::decrypt_scratch_space(&module, ct_rlwe.size())
-            | RLWECt::encrypt_sk_scratch_space(&module, ct_rlwe.size())
-            | RLWECt::prod_by_grlwe_inplace_scratch_space(&module, ct_rlwe.size(), ct_grlwe.size()),
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_grlwe.size())
+            | GLWECiphertext::decrypt_scratch_space(&module, ct_rlwe.size())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe.size())
+            | GLWECiphertext::keyswitch_inplace_scratch_space(&module, ct_rlwe.size(), ct_grlwe.size()),
     );
 
     let mut sk0: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk0.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk0_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk0_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk0_dft.dft(&module, &sk0);
 
     let mut sk1: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk1.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk1_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk1_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk1_dft.dft(&module, &sk1);
 
     ct_grlwe.encrypt_sk(
@@ -357,7 +355,7 @@ fn prod_by_grlwe_inplace() {
 
     ct_rlwe.encrypt_sk(
         &module,
-        Some(&pt_want),
+        &pt_want,
         &sk0_dft,
         &mut source_xa,
         &mut source_xe,
@@ -366,7 +364,7 @@ fn prod_by_grlwe_inplace() {
         scratch.borrow(),
     );
 
-    ct_rlwe.prod_by_grlwe_inplace(&module, &ct_grlwe, scratch.borrow());
+    ct_rlwe.keyswitch_inplace(&module, &ct_grlwe, scratch.borrow());
 
     ct_rlwe.decrypt(&module, &mut pt_have, &sk1_dft, scratch.borrow());
 
@@ -391,12 +389,10 @@ fn prod_by_grlwe_inplace() {
         noise_have,
         noise_want
     );
-
-    module.free();
 }
 
 #[test]
-fn prod_by_rgsw() {
+fn external_product() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -407,12 +403,12 @@ fn prod_by_rgsw() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_rgsw: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_rlwe_in: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_rlwe_in);
-    let mut ct_rlwe_out: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_rlwe_out);
+    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_rlwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_in);
+    let mut ct_rlwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_out);
     let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe_in);
-    let mut pt_have: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_out);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -430,10 +426,10 @@ fn prod_by_rgsw() {
     pt_rgsw.raw_mut()[k] = 1; // X^{k}
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        RGSWCt::encrypt_sk_scratch_space(&module, ct_rgsw.size())
-            | RLWECt::decrypt_scratch_space(&module, ct_rlwe_out.size())
-            | RLWECt::encrypt_sk_scratch_space(&module, ct_rlwe_in.size())
-            | RLWECt::prod_by_grlwe_scratch_space(
+        GGSWCiphertext::encrypt_sk_scratch_space(&module, ct_rgsw.size())
+            | GLWECiphertext::decrypt_scratch_space(&module, ct_rlwe_out.size())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe_in.size())
+            | GLWECiphertext::external_product_scratch_space(
                 &module,
                 ct_rlwe_out.size(),
                 ct_rlwe_in.size(),
@@ -444,7 +440,7 @@ fn prod_by_rgsw() {
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
     ct_rgsw.encrypt_sk(
@@ -460,7 +456,7 @@ fn prod_by_rgsw() {
 
     ct_rlwe_in.encrypt_sk(
         &module,
-        Some(&pt_want),
+        &pt_want,
         &sk_dft,
         &mut source_xa,
         &mut source_xe,
@@ -469,7 +465,7 @@ fn prod_by_rgsw() {
         scratch.borrow(),
     );
 
-    ct_rlwe_out.prod_by_rgsw(&module, &ct_rlwe_in, &ct_rgsw, scratch.borrow());
+    ct_rlwe_out.external_product(&module, &ct_rlwe_in, &ct_rgsw, scratch.borrow());
 
     ct_rlwe_out.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
 
@@ -505,12 +501,10 @@ fn prod_by_rgsw() {
         noise_have,
         noise_want
     );
-
-    module.free();
 }
 
 #[test]
-fn prod_by_rgsw_inplace() {
+fn external_product_inplace() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -521,11 +515,11 @@ fn prod_by_rgsw_inplace() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_rgsw: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_rlwe: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_rlwe_in);
+    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_rlwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_in);
     let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe_in);
-    let mut pt_have: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_out);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -543,16 +537,16 @@ fn prod_by_rgsw_inplace() {
     pt_rgsw.raw_mut()[k] = 1; // X^{k}
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        RGSWCt::encrypt_sk_scratch_space(&module, ct_rgsw.size())
-            | RLWECt::decrypt_scratch_space(&module, ct_rlwe.size())
-            | RLWECt::encrypt_sk_scratch_space(&module, ct_rlwe.size())
-            | RLWECt::prod_by_rgsw_inplace_scratch_space(&module, ct_rlwe.size(), ct_rgsw.size()),
+        GGSWCiphertext::encrypt_sk_scratch_space(&module, ct_rgsw.size())
+            | GLWECiphertext::decrypt_scratch_space(&module, ct_rlwe.size())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe.size())
+            | GLWECiphertext::external_product_inplace_scratch_space(&module, ct_rlwe.size(), ct_rgsw.size()),
     );
 
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
     ct_rgsw.encrypt_sk(
@@ -568,7 +562,7 @@ fn prod_by_rgsw_inplace() {
 
     ct_rlwe.encrypt_sk(
         &module,
-        Some(&pt_want),
+        &pt_want,
         &sk_dft,
         &mut source_xa,
         &mut source_xe,
@@ -577,7 +571,7 @@ fn prod_by_rgsw_inplace() {
         scratch.borrow(),
     );
 
-    ct_rlwe.prod_by_rgsw_inplace(&module, &ct_rgsw, scratch.borrow());
+    ct_rlwe.external_product_inplace(&module, &ct_rgsw, scratch.borrow());
 
     ct_rlwe.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
 
@@ -613,6 +607,4 @@ fn prod_by_rgsw_inplace() {
         noise_have,
         noise_want
     );
-
-    module.free();
 }
diff --git a/core/src/test_fft64/rlwe_dft.rs b/core/src/test_fft64/rlwe_dft.rs
index fe71a09..06359b1 100644
--- a/core/src/test_fft64/rlwe_dft.rs
+++ b/core/src/test_fft64/rlwe_dft.rs
@@ -1,16 +1,21 @@
 use crate::{
-    elem::{Infos, ProdInplace, ProdInplaceScratchSpace, ProdScratchSpace, Product},
-    grlwe::GRLWECt,
-    keys::{SecretKey, SecretKeyDft},
-    rgsw::RGSWCt,
-    rlwe::{RLWECt, RLWECtDft, RLWEPt},
+    elem::Infos,
+    encryption::EncryptSkScratchSpace,
+    external_product::{
+        ExternalProduct, ExternalProductInplace, ExternalProductInplaceScratchSpace, ExternalProductScratchSpace,
+    },
+    ggsw::GGSWCiphertext,
+    glwe::{GLWECiphertext, GLWECiphertextFourier, GLWEPlaintext},
+    keys::{SecretKey, SecretKeyFourier},
+    keyswitch::{KeySwitch, KeySwitchInplace, KeySwitchInplaceScratchSpace, KeySwitchScratchSpace},
+    keyswitch_key::GLWEKeySwitchKey,
     test_fft64::{grlwe::noise_grlwe_rlwe_product, rgsw::noise_rgsw_product},
 };
 use base2k::{FFT64, FillUniform, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned, Stats, VecZnxOps, VecZnxToMut, ZnxViewMut};
 use sampling::source::Source;
 
 #[test]
-fn by_grlwe_inplace() {
+fn keyswitch() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -21,13 +26,15 @@ fn by_grlwe_inplace() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_grlwe: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_rlwe_in: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_rlwe_in);
-    let mut ct_rlwe_in_dft: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_rlwe_in);
-    let mut ct_rlwe_out: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_rlwe_out);
-    let mut ct_rlwe_out_dft: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_rlwe_out);
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe_in);
-    let mut pt_have: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe_out);
+    let mut ct_grlwe: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_rlwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_in);
+    let mut ct_rlwe_in_dft: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::new(&module, log_base2k, log_k_rlwe_in);
+    let mut ct_rlwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_out);
+    let mut ct_rlwe_out_dft: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::new(&module, log_base2k, log_k_rlwe_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_out);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -39,10 +46,10 @@ fn by_grlwe_inplace() {
         .fill_uniform(log_base2k, 0, pt_want.size(), &mut source_xa);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct_grlwe.size())
-            | RLWECt::decrypt_scratch_space(&module, ct_rlwe_out.size())
-            | RLWECt::encrypt_sk_scratch_space(&module, ct_rlwe_in.size())
-            | RLWECtDft::prod_by_grlwe_scratch_space(
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_grlwe.size())
+            | GLWECiphertext::decrypt_scratch_space(&module, ct_rlwe_out.size())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe_in.size())
+            | GLWECiphertextFourier::keyswitch_scratch_space(
                 &module,
                 ct_rlwe_out.size(),
                 ct_rlwe_in.size(),
@@ -53,13 +60,13 @@ fn by_grlwe_inplace() {
     let mut sk0: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk0.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk0_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk0_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk0_dft.dft(&module, &sk0);
 
     let mut sk1: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk1.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk1_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk1_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk1_dft.dft(&module, &sk1);
 
     ct_grlwe.encrypt_sk(
@@ -75,7 +82,7 @@ fn by_grlwe_inplace() {
 
     ct_rlwe_in.encrypt_sk(
         &module,
-        Some(&pt_want),
+        &pt_want,
         &sk0_dft,
         &mut source_xa,
         &mut source_xe,
@@ -85,7 +92,7 @@ fn by_grlwe_inplace() {
     );
 
     ct_rlwe_in.dft(&module, &mut ct_rlwe_in_dft);
-    ct_rlwe_out_dft.prod_by_grlwe(&module, &ct_rlwe_in_dft, &ct_grlwe, scratch.borrow());
+    ct_rlwe_out_dft.keyswitch(&module, &ct_rlwe_in_dft, &ct_grlwe, scratch.borrow());
     ct_rlwe_out_dft.idft(&module, &mut ct_rlwe_out, scratch.borrow());
 
     ct_rlwe_out.decrypt(&module, &mut pt_have, &sk1_dft, scratch.borrow());
@@ -111,12 +118,10 @@ fn by_grlwe_inplace() {
         noise_have,
         noise_want
     );
-
-    module.free();
 }
 
 #[test]
-fn prod_by_grlwe_inplace() {
+fn keyswich_inplace() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -126,11 +131,11 @@ fn prod_by_grlwe_inplace() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_grlwe: GRLWECt<Vec<u8>, FFT64> = GRLWECt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_rlwe: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_rlwe);
-    let mut ct_rlwe_dft: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_rlwe);
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe);
-    let mut pt_have: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe);
+    let mut ct_grlwe: GLWEKeySwitchKey<Vec<u8>, FFT64> = GLWEKeySwitchKey::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_rlwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe);
+    let mut ct_rlwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::new(&module, log_base2k, log_k_rlwe);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -142,22 +147,22 @@ fn prod_by_grlwe_inplace() {
         .fill_uniform(log_base2k, 0, pt_want.size(), &mut source_xa);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        GRLWECt::encrypt_sk_scratch_space(&module, ct_grlwe.size())
-            | RLWECt::decrypt_scratch_space(&module, ct_rlwe.size())
-            | RLWECt::encrypt_sk_scratch_space(&module, ct_rlwe.size())
-            | RLWECtDft::prod_by_grlwe_inplace_scratch_space(&module, ct_rlwe_dft.size(), ct_grlwe.size()),
+        GLWEKeySwitchKey::encrypt_sk_scratch_space(&module, ct_grlwe.size())
+            | GLWECiphertext::decrypt_scratch_space(&module, ct_rlwe.size())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe.size())
+            | GLWECiphertextFourier::keyswitch_inplace_scratch_space(&module, ct_rlwe_dft.size(), ct_grlwe.size()),
     );
 
     let mut sk0: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk0.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk0_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk0_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk0_dft.dft(&module, &sk0);
 
     let mut sk1: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk1.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk1_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk1_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk1_dft.dft(&module, &sk1);
 
     ct_grlwe.encrypt_sk(
@@ -173,7 +178,7 @@ fn prod_by_grlwe_inplace() {
 
     ct_rlwe.encrypt_sk(
         &module,
-        Some(&pt_want),
+        &pt_want,
         &sk0_dft,
         &mut source_xa,
         &mut source_xe,
@@ -183,7 +188,7 @@ fn prod_by_grlwe_inplace() {
     );
 
     ct_rlwe.dft(&module, &mut ct_rlwe_dft);
-    ct_rlwe_dft.prod_by_grlwe_inplace(&module, &ct_grlwe, scratch.borrow());
+    ct_rlwe_dft.keyswitch_inplace(&module, &ct_grlwe, scratch.borrow());
     ct_rlwe_dft.idft(&module, &mut ct_rlwe, scratch.borrow());
 
     ct_rlwe.decrypt(&module, &mut pt_have, &sk1_dft, scratch.borrow());
@@ -209,12 +214,10 @@ fn prod_by_grlwe_inplace() {
         noise_have,
         noise_want
     );
-
-    module.free();
 }
 
 #[test]
-fn prod_by_rgsw() {
+fn external_product() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -225,14 +228,16 @@ fn prod_by_rgsw() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_rgsw: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_rlwe_in: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_rlwe_in);
-    let mut ct_rlwe_out: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_rlwe_out);
-    let mut ct_rlwe_dft_in: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_rlwe_in);
-    let mut ct_rlwe_dft_out: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_rlwe_out);
+    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_rlwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_in);
+    let mut ct_rlwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_out);
+    let mut ct_rlwe_dft_in: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::new(&module, log_base2k, log_k_rlwe_in);
+    let mut ct_rlwe_dft_out: GLWECiphertextFourier<Vec<u8>, FFT64> =
+        GLWECiphertextFourier::new(&module, log_base2k, log_k_rlwe_out);
     let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe_in);
-    let mut pt_have: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_out);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -250,10 +255,10 @@ fn prod_by_rgsw() {
     pt_rgsw.raw_mut()[k] = 1; // X^{k}
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        RGSWCt::encrypt_sk_scratch_space(&module, ct_rgsw.size())
-            | RLWECt::decrypt_scratch_space(&module, ct_rlwe_out.size())
-            | RLWECt::encrypt_sk_scratch_space(&module, ct_rlwe_in.size())
-            | RLWECt::prod_by_rgsw_scratch_space(
+        GGSWCiphertext::encrypt_sk_scratch_space(&module, ct_rgsw.size())
+            | GLWECiphertext::decrypt_scratch_space(&module, ct_rlwe_out.size())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe_in.size())
+            | GLWECiphertext::external_product_scratch_space(
                 &module,
                 ct_rlwe_out.size(),
                 ct_rlwe_in.size(),
@@ -264,7 +269,7 @@ fn prod_by_rgsw() {
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
     ct_rgsw.encrypt_sk(
@@ -280,7 +285,7 @@ fn prod_by_rgsw() {
 
     ct_rlwe_in.encrypt_sk(
         &module,
-        Some(&pt_want),
+        &pt_want,
         &sk_dft,
         &mut source_xa,
         &mut source_xe,
@@ -290,7 +295,7 @@ fn prod_by_rgsw() {
     );
 
     ct_rlwe_in.dft(&module, &mut ct_rlwe_dft_in);
-    ct_rlwe_dft_out.prod_by_rgsw(&module, &ct_rlwe_dft_in, &ct_rgsw, scratch.borrow());
+    ct_rlwe_dft_out.external_product(&module, &ct_rlwe_dft_in, &ct_rgsw, scratch.borrow());
     ct_rlwe_dft_out.idft(&module, &mut ct_rlwe_out, scratch.borrow());
 
     ct_rlwe_out.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
@@ -327,12 +332,10 @@ fn prod_by_rgsw() {
         noise_have,
         noise_want
     );
-
-    module.free();
 }
 
 #[test]
-fn prod_by_rgsw_inplace() {
+fn external_product_inplace() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
     let log_base2k: usize = 12;
     let log_k_grlwe: usize = 60;
@@ -343,12 +346,12 @@ fn prod_by_rgsw_inplace() {
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_rgsw: RGSWCt<Vec<u8>, FFT64> = RGSWCt::new(&module, log_base2k, log_k_grlwe, rows);
-    let mut ct_rlwe: RLWECt<Vec<u8>> = RLWECt::new(&module, log_base2k, log_k_rlwe_in);
-    let mut ct_rlwe_dft: RLWECtDft<Vec<u8>, FFT64> = RLWECtDft::new(&module, log_base2k, log_k_rlwe_in);
+    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_grlwe, rows);
+    let mut ct_rlwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_in);
+    let mut ct_rlwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::new(&module, log_base2k, log_k_rlwe_in);
     let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
-    let mut pt_want: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe_in);
-    let mut pt_have: RLWEPt<Vec<u8>> = RLWEPt::new(&module, log_base2k, log_k_rlwe_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_out);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -366,16 +369,16 @@ fn prod_by_rgsw_inplace() {
     pt_rgsw.raw_mut()[k] = 1; // X^{k}
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
-        RGSWCt::encrypt_sk_scratch_space(&module, ct_rgsw.size())
-            | RLWECt::decrypt_scratch_space(&module, ct_rlwe.size())
-            | RLWECt::encrypt_sk_scratch_space(&module, ct_rlwe.size())
-            | RLWECt::prod_by_rgsw_inplace_scratch_space(&module, ct_rlwe.size(), ct_rgsw.size()),
+        GGSWCiphertext::encrypt_sk_scratch_space(&module, ct_rgsw.size())
+            | GLWECiphertext::decrypt_scratch_space(&module, ct_rlwe.size())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe.size())
+            | GLWECiphertext::external_product_inplace_scratch_space(&module, ct_rlwe.size(), ct_rgsw.size()),
     );
 
     let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module);
     sk.fill_ternary_prob(0.5, &mut source_xs);
 
-    let mut sk_dft: SecretKeyDft<Vec<u8>, FFT64> = SecretKeyDft::new(&module);
+    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module);
     sk_dft.dft(&module, &sk);
 
     ct_rgsw.encrypt_sk(
@@ -391,7 +394,7 @@ fn prod_by_rgsw_inplace() {
 
     ct_rlwe.encrypt_sk(
         &module,
-        Some(&pt_want),
+        &pt_want,
         &sk_dft,
         &mut source_xa,
         &mut source_xe,
@@ -401,7 +404,7 @@ fn prod_by_rgsw_inplace() {
     );
 
     ct_rlwe.dft(&module, &mut ct_rlwe_dft);
-    ct_rlwe_dft.prod_by_rgsw_inplace(&module, &ct_rgsw, scratch.borrow());
+    ct_rlwe_dft.external_product_inplace(&module, &ct_rgsw, scratch.borrow());
     ct_rlwe_dft.idft(&module, &mut ct_rlwe, scratch.borrow());
 
     ct_rlwe.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
@@ -438,6 +441,4 @@ fn prod_by_rgsw_inplace() {
         noise_have,
         noise_want
     );
-
-    module.free();
 }
diff --git a/core/src/vec_glwe_product.rs b/core/src/vec_glwe_product.rs
new file mode 100644
index 0000000..7920de9
--- /dev/null
+++ b/core/src/vec_glwe_product.rs
@@ -0,0 +1,197 @@
+use base2k::{
+    FFT64, Module, Scratch, VecZnx, VecZnxAlloc, VecZnxDft, VecZnxDftAlloc, VecZnxDftOps, VecZnxDftToMut, VecZnxDftToRef,
+    VecZnxToMut, VecZnxToRef, ZnxInfos, ZnxZero,
+};
+
+use crate::{
+    elem::{GetRow, Infos, SetRow},
+    glwe::{GLWECiphertext, GLWECiphertextFourier},
+};
+
+pub(crate) trait VecGLWEProductScratchSpace {
+    fn prod_with_glwe_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize;
+
+    fn prod_with_glwe_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize {
+        Self::prod_with_glwe_scratch_space(module, res_size, res_size, rhs)
+    }
+
+    fn prod_with_glwe_dft_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
+        (Self::prod_with_glwe_scratch_space(module, res_size, lhs, rhs) | module.vec_znx_idft_tmp_bytes())
+            + module.bytes_of_vec_znx(2, lhs)
+            + module.bytes_of_vec_znx(2, res_size)
+    }
+
+    fn prod_with_glwe_dft_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize {
+        (Self::prod_with_glwe_inplace_scratch_space(module, res_size, rhs) | module.vec_znx_idft_tmp_bytes())
+            + module.bytes_of_vec_znx(2, res_size)
+    }
+
+    fn prod_with_vec_glwe_scratch_space(module: &Module<FFT64>, res_size: usize, lhs: usize, rhs: usize) -> usize {
+        Self::prod_with_glwe_dft_scratch_space(module, res_size, lhs, rhs)
+            + module.bytes_of_vec_znx_dft(2, lhs)
+            + module.bytes_of_vec_znx_dft(2, res_size)
+    }
+
+    fn prod_with_vec_glwe_inplace_scratch_space(module: &Module<FFT64>, res_size: usize, rhs: usize) -> usize {
+        Self::prod_with_glwe_dft_inplace_scratch_space(module, res_size, rhs) + module.bytes_of_vec_znx_dft(2, res_size)
+    }
+}
+
+pub(crate) trait VecGLWEProduct: Infos {
+    fn prod_with_glwe<MUT, REF>(
+        &self,
+        module: &Module<FFT64>,
+        res: &mut GLWECiphertext<MUT>,
+        a: &GLWECiphertext<REF>,
+        scratch: &mut Scratch,
+    ) where
+        VecZnx<MUT>: VecZnxToMut,
+        VecZnx<REF>: VecZnxToRef;
+
+    fn prod_with_glwe_inplace<MUT>(&self, module: &Module<FFT64>, res: &mut GLWECiphertext<MUT>, scratch: &mut Scratch)
+    where
+        VecZnx<MUT>: VecZnxToMut + VecZnxToRef,
+    {
+        unsafe {
+            let res_ptr: *mut GLWECiphertext<MUT> = res as *mut GLWECiphertext<MUT>; // This is ok because [Self::mul_rlwe] only updates res at the end.
+            self.prod_with_glwe(&module, &mut *res_ptr, &*res_ptr, scratch);
+        }
+    }
+
+    fn prod_with_glwe_fourier<MUT, REF>(
+        &self,
+        module: &Module<FFT64>,
+        res: &mut GLWECiphertextFourier<MUT, FFT64>,
+        a: &GLWECiphertextFourier<REF, FFT64>,
+        scratch: &mut Scratch,
+    ) where
+        VecZnxDft<MUT, FFT64>: VecZnxDftToMut<FFT64> + VecZnxDftToRef<FFT64> + ZnxInfos,
+        VecZnxDft<REF, FFT64>: VecZnxDftToRef<FFT64> + ZnxInfos,
+    {
+        let log_base2k: usize = self.basek();
+
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(res.basek(), log_base2k);
+            assert_eq!(self.n(), module.n());
+            assert_eq!(res.n(), module.n());
+        }
+
+        let (a_data, scratch_1) = scratch.tmp_vec_znx(module, 2, a.size());
+
+        let mut a_idft: GLWECiphertext<&mut [u8]> = GLWECiphertext::<&mut [u8]> {
+            data: a_data,
+            log_base2k: a.basek(),
+            log_k: a.k(),
+        };
+
+        a.idft(module, &mut a_idft, scratch_1);
+
+        let (res_data, scratch_2) = scratch_1.tmp_vec_znx(module, 2, res.size());
+
+        let mut res_idft: GLWECiphertext<&mut [u8]> = GLWECiphertext::<&mut [u8]> {
+            data: res_data,
+            log_base2k: res.basek(),
+            log_k: res.k(),
+        };
+
+        self.prod_with_glwe(module, &mut res_idft, &a_idft, scratch_2);
+
+        module.vec_znx_dft(res, 0, &res_idft, 0);
+        module.vec_znx_dft(res, 1, &res_idft, 1);
+    }
+
+    fn prod_with_glwe_fourier_inplace<MUT>(
+        &self,
+        module: &Module<FFT64>,
+        res: &mut GLWECiphertextFourier<MUT, FFT64>,
+        scratch: &mut Scratch,
+    ) where
+        VecZnxDft<MUT, FFT64>: VecZnxDftToRef<FFT64> + VecZnxDftToMut<FFT64>,
+    {
+        let log_base2k: usize = self.basek();
+
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(res.basek(), log_base2k);
+            assert_eq!(self.n(), module.n());
+            assert_eq!(res.n(), module.n());
+        }
+
+        let (res_data, scratch_1) = scratch.tmp_vec_znx(module, 2, res.size());
+
+        let mut res_idft: GLWECiphertext<&mut [u8]> = GLWECiphertext::<&mut [u8]> {
+            data: res_data,
+            log_base2k: res.basek(),
+            log_k: res.k(),
+        };
+
+        res.idft(module, &mut res_idft, scratch_1);
+
+        self.prod_with_glwe_inplace(module, &mut res_idft, scratch_1);
+
+        module.vec_znx_dft(res, 0, &res_idft, 0);
+        module.vec_znx_dft(res, 1, &res_idft, 1);
+    }
+
+    fn prod_with_vec_glwe<RES, LHS>(&self, module: &Module<FFT64>, res: &mut RES, a: &LHS, scratch: &mut Scratch)
+    where
+        LHS: GetRow<FFT64> + Infos,
+        RES: SetRow<FFT64> + Infos,
+    {
+        let (tmp_row_data, scratch1) = scratch.tmp_vec_znx_dft(module, 2, a.size());
+
+        let mut tmp_a_row: GLWECiphertextFourier<&mut [u8], FFT64> = GLWECiphertextFourier::<&mut [u8], FFT64> {
+            data: tmp_row_data,
+            log_base2k: a.basek(),
+            log_k: a.k(),
+        };
+
+        let (tmp_res_data, scratch2) = scratch1.tmp_vec_znx_dft(module, 2, res.size());
+
+        let mut tmp_res_row: GLWECiphertextFourier<&mut [u8], FFT64> = GLWECiphertextFourier::<&mut [u8], FFT64> {
+            data: tmp_res_data,
+            log_base2k: res.basek(),
+            log_k: res.k(),
+        };
+
+        let min_rows: usize = res.rows().min(a.rows());
+
+        (0..res.rows()).for_each(|row_i| {
+            (0..res.rank()).for_each(|col_j| {
+                a.get_row(module, row_i, col_j, &mut tmp_a_row);
+                self.prod_with_glwe_fourier(module, &mut tmp_res_row, &tmp_a_row, scratch2);
+                res.set_row(module, row_i, col_j, &tmp_res_row);
+            });
+        });
+
+        tmp_res_row.data.zero();
+
+        (min_rows..res.rows()).for_each(|row_i| {
+            (0..self.rank()).for_each(|col_j| {
+                res.set_row(module, row_i, col_j, &tmp_res_row);
+            });
+        });
+    }
+
+    fn prod_with_vec_glwe_inplace<RES>(&self, module: &Module<FFT64>, res: &mut RES, scratch: &mut Scratch)
+    where
+        RES: GetRow<FFT64> + SetRow<FFT64> + Infos,
+    {
+        let (tmp_row_data, scratch1) = scratch.tmp_vec_znx_dft(module, 2, res.size());
+
+        let mut tmp_row: GLWECiphertextFourier<&mut [u8], FFT64> = GLWECiphertextFourier::<&mut [u8], FFT64> {
+            data: tmp_row_data,
+            log_base2k: res.basek(),
+            log_k: res.k(),
+        };
+
+        (0..res.rows()).for_each(|row_i| {
+            (0..res.rank()).for_each(|col_j| {
+                res.get_row(module, row_i, col_j, &mut tmp_row);
+                self.prod_with_glwe_fourier_inplace(module, &mut tmp_row, scratch1);
+                res.set_row(module, row_i, col_j, &tmp_row);
+            });
+        });
+    }
+}