@@ -50,6 +50,7 @@ "rand_distr",
  "rug",
  "sampling",
  "utils",
+ "zstd",
 ]
 
 [[package]]
@@ -82,6 +83,8 @@ version = "1.2.31"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "c3a42d84bb6b69d3a8b3eaacf0d88f179e1929695e1ad012b6cf64d9caaa5fd2"
 dependencies = [
+ "jobserver",
+ "libc",
  "shlex",
 ]
 
@@ -160,6 +163,7 @@ "backend",
  "byteorder",
  "criterion",
  "itertools 0.14.0",
+ "rand_core",
  "rand_distr",
  "rug",
  "sampling",
@@ -298,6 +302,15 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "d75a2a4b1b190afb6f5425f10f6a8f959d2ea0b9c2b1d79553551850539e4674"
 
 [[package]]
+name = "jobserver"
+version = "0.1.32"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "48d1dbcbbeb6a7fec7e059840aa538bd62aaccf972c7346c4d9d2059312853d0"
+dependencies = [
+ "libc",
+]
+
+[[package]]
 name = "js-sys"
 version = "0.3.76"
 source = "registry+https://github.com/rust-lang/crates.io-index"
@@ -358,6 +371,12 @@ name = "paste"
 version = "1.0.15"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "57c0d7b74b563b49d38dae00a0c37d4d6de9b432382b2892f0574ddcae73fd0a"
+
+[[package]]
+name = "pkg-config"
+version = "0.3.32"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7edddbd0b52d732b21ad9a5fab5c704c14cd949e5e9a1ec5929a24fded1b904c"
 
 [[package]]
 name = "plotters"
@@ -819,3 +838,31 @@ "proc-macro2",
  "quote",
  "syn",
 ]
+
+[[package]]
+name = "zstd"
+version = "0.13.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "e91ee311a569c327171651566e07972200e76fcfe2242a4fa446149a3881c08a"
+dependencies = [
+ "zstd-safe",
+]
+
+[[package]]
+name = "zstd-safe"
+version = "7.2.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "8f49c4d5f0abb602a93fb8736af2a4f4dd9512e36f7f570d66e65ff867ed3b9d"
+dependencies = [
+ "zstd-sys",
+]
+
+[[package]]
+name = "zstd-sys"
+version = "2.0.15+zstd.1.5.7"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "eb81183ddd97d0c74cedf1d50d85c8d08c1b8b68ee863bdee9e706eedba1a237"
+dependencies = [
+ "cc",
+ "pkg-config",
+]

@@ -11,3 +11,4 @@ rand_distr = "0.5.1"
 itertools = "0.14.0"
 criterion = "0.7.0"
 byteorder = "1.5.0"
+zstd = "0.13.3"

@@ -1,11 +0,0 @@
-{
-    "github.copilot.enable": {
-        "*": false,
-        "plaintext": false,
-        "markdown": false,
-        "scminput": false
-    },
-    "files.associations": {
-        "random": "c"
-    }
-}

@@ -14,7 +14,8 @@ rand_core = {workspace = true}
 sampling = { path = "../sampling" }
 utils = { path = "../utils" }
 paste = "1.0.15"
-byteorder = {workspace = true} 
+byteorder = {workspace = true}
+zstd = {workspace = true}
 
 [build-dependencies]
 cmake = "0.1.54"

@@ -1,7 +1,9 @@
 use std::path::PathBuf;
 
 pub fn build() {
-    let dst: PathBuf = cmake::Config::new("src/implementation/cpu_spqlios/spqlios-arithmetic").define("ENABLE_TESTING", "FALSE").build();
+    let dst: PathBuf = cmake::Config::new("src/implementation/cpu_spqlios/spqlios-arithmetic")
+        .define("ENABLE_TESTING", "FALSE")
+        .build();
 
     let lib_dir: PathBuf = dst.join("lib");
 

@@ -1,4 +1,4 @@
-use crate::hal::layouts::{ScalarZnxOwned, ScalarZnxToMut, ScalarZnxToRef};
+use crate::hal::layouts::ScalarZnxOwned;
 
 /// Allocates as [crate::hal::layouts::ScalarZnx].
 pub trait ScalarZnxAlloc {
@@ -15,33 +15,3 @@ /// User must ensure that bytes is memory aligned and that it length is equal to [ScalarZnxAllocBytes].
 pub trait ScalarZnxFromBytes {
     fn scalar_znx_from_bytes(&self, cols: usize, bytes: Vec<u8>) -> ScalarZnxOwned;
 }
-
-/// Applies the mapping X -> X^k to a\[a_col\] and write the result on res\[res_col\].
-pub trait ScalarZnxAutomorphism {
-    fn scalar_znx_automorphism<R, A>(&self, k: i64, res: &mut R, res_col: usize, a: &A, a_col: usize)
-    where
-        R: ScalarZnxToMut,
-        A: ScalarZnxToRef;
-}
-
-/// Applies the mapping X -> X^k on res\[res_col\].
-pub trait ScalarZnxAutomorphismInplace {
-    fn scalar_znx_automorphism_inplace<R>(&self, k: i64, res: &mut R, res_col: usize)
-    where
-        R: ScalarZnxToMut;
-}
-
-/// Multiply a\[a_col\] with (X^p - 1) and write the result on res\[res_col\].
-pub trait ScalarZnxMulXpMinusOne {
-    fn scalar_znx_mul_xp_minus_one<R, A>(&self, p: i64, r: &mut R, r_col: usize, a: &A, a_col: usize)
-    where
-        R: ScalarZnxToMut,
-        A: ScalarZnxToRef;
-}
-
-/// Multiply res\[res_col\] with (X^p - 1).
-pub trait ScalarZnxMulXpMinusOneInplace {
-    fn scalar_znx_mul_xp_minus_one_inplace<R>(&self, p: i64, res: &mut R, res_col: usize)
-    where
-        R: ScalarZnxToMut;
-}

@@ -20,12 +20,12 @@ fn vec_znx_big_from_bytes(&self, cols: usize, size: usize, bytes: Vec<u8>) -> VecZnxBigOwned<B>;
 }
 
 /// Add a discrete normal distribution on res.
-/// 
+///
 /// # Arguments
 /// * `basek`: base two logarithm of the bivariate representation
 /// * `res`: receiver.
 /// * `res_col`: column of the receiver on which the operation is performed/stored.
-/// * `k`: 
+/// * `k`:
 /// * `source`: random coin source.
 /// * `sigma`: standard deviation of the discrete normal distribution.
 /// * `bound`: rejection sampling bound.

@@ -1,5 +1,6 @@
 use crate::hal::layouts::{Data, DataMut, DataRef};
 use rand_distr::num_traits::Zero;
+use sampling::source::Source;
 
 pub trait ZnxInfos {
     /// Returns the ring degree of the polynomials.
@@ -108,3 +109,7 @@ {
     fn zero(&mut self);
     fn zero_at(&mut self, i: usize, j: usize);
 }
+
+pub trait FillUniform {
+    fn fill_uniform(&mut self, source: &mut Source);
+}

@@ -1,13 +1,7 @@
 use crate::hal::{
-    api::{
-        ScalarZnxAlloc, ScalarZnxAllocBytes, ScalarZnxAutomorphism, ScalarZnxAutomorphismInplace, ScalarZnxFromBytes,
-        ScalarZnxMulXpMinusOne, ScalarZnxMulXpMinusOneInplace,
-    },
-    layouts::{Backend, Module, ScalarZnxOwned, ScalarZnxToMut, ScalarZnxToRef},
-    oep::{
-        ScalarZnxAllocBytesImpl, ScalarZnxAllocImpl, ScalarZnxAutomorphismImpl, ScalarZnxAutomorphismInplaceIml,
-        ScalarZnxFromBytesImpl, ScalarZnxMulXpMinusOneImpl, ScalarZnxMulXpMinusOneInplaceImpl,
-    },
+    api::{ScalarZnxAlloc, ScalarZnxAllocBytes},
+    layouts::{Backend, Module, ScalarZnxOwned},
+    oep::{ScalarZnxAllocBytesImpl, ScalarZnxAllocImpl},
 };
 
 impl<B> ScalarZnxAllocBytes for Module<B>
@@ -27,62 +21,3 @@ fn scalar_znx_alloc(&self, cols: usize) -> ScalarZnxOwned {
         B::scalar_znx_alloc_impl(self.n(), cols)
     }
 }
-
-impl<B> ScalarZnxFromBytes for Module<B>
-where
-    B: Backend + ScalarZnxFromBytesImpl<B>,
-{
-    fn scalar_znx_from_bytes(&self, cols: usize, bytes: Vec<u8>) -> ScalarZnxOwned {
-        B::scalar_znx_from_bytes_impl(self.n(), cols, bytes)
-    }
-}
-
-impl<B> ScalarZnxAutomorphism for Module<B>
-where
-    B: Backend + ScalarZnxAutomorphismImpl<B>,
-{
-    fn scalar_znx_automorphism<R, A>(&self, k: i64, res: &mut R, res_col: usize, a: &A, a_col: usize)
-    where
-        R: ScalarZnxToMut,
-        A: ScalarZnxToRef,
-    {
-        B::scalar_znx_automorphism_impl(self, k, res, res_col, a, a_col);
-    }
-}
-
-impl<B> ScalarZnxAutomorphismInplace for Module<B>
-where
-    B: Backend + ScalarZnxAutomorphismInplaceIml<B>,
-{
-    fn scalar_znx_automorphism_inplace<A>(&self, k: i64, a: &mut A, a_col: usize)
-    where
-        A: ScalarZnxToMut,
-    {
-        B::scalar_znx_automorphism_inplace_impl(self, k, a, a_col);
-    }
-}
-
-impl<B> ScalarZnxMulXpMinusOne for Module<B>
-where
-    B: Backend + ScalarZnxMulXpMinusOneImpl<B>,
-{
-    fn scalar_znx_mul_xp_minus_one<R, A>(&self, p: i64, r: &mut R, r_col: usize, a: &A, a_col: usize)
-    where
-        R: ScalarZnxToMut,
-        A: ScalarZnxToRef,
-    {
-        B::scalar_znx_mul_xp_minus_one_impl(self, p, r, r_col, a, a_col);
-    }
-}
-
-impl<B> ScalarZnxMulXpMinusOneInplace for Module<B>
-where
-    B: Backend + ScalarZnxMulXpMinusOneInplaceImpl<B>,
-{
-    fn scalar_znx_mul_xp_minus_one_inplace<R>(&self, p: i64, r: &mut R, r_col: usize)
-    where
-        R: ScalarZnxToMut,
-    {
-        B::scalar_znx_mul_xp_minus_one_inplace_impl(self, p, r, r_col);
-    }
-}

@@ -1,12 +1,17 @@
 use crate::{
     alloc_aligned,
     hal::{
-        api::{DataView, DataViewMut, ZnxInfos, ZnxSliceSize, ZnxView},
+        api::{DataView, DataViewMut, FillUniform, ZnxInfos, ZnxSliceSize, ZnxView, ZnxViewMut, ZnxZero},
         layouts::{Data, DataMut, DataRef, ReaderFrom, VecZnx, WriterTo},
     },
 };
+use std::fmt;
 
-#[derive(PartialEq, Eq)]
+use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
+use rand::RngCore;
+use sampling::source::Source;
+
+#[derive(PartialEq, Eq, Clone)]
 pub struct MatZnx<D: Data> {
     data: D,
     n: usize,
@@ -16,6 +21,12 @@ cols_in: usize,
     cols_out: usize,
 }
 
+impl<D: DataRef> fmt::Debug for MatZnx<D> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "{}", self)
+    }
+}
+
 impl<D: Data> ZnxInfos for MatZnx<D> {
     fn cols(&self) -> usize {
         self.cols_in
@@ -74,7 +85,7 @@ }
 }
 
 impl<D: DataRef + From<Vec<u8>>> MatZnx<D> {
-    pub(crate) fn new(n: usize, rows: usize, cols_in: usize, cols_out: usize, size: usize) -> Self {
+    pub(crate) fn alloc(n: usize, rows: usize, cols_in: usize, cols_out: usize, size: usize) -> Self {
         let data: Vec<u8> = alloc_aligned(Self::bytes_of(n, rows, cols_in, cols_out, size));
         Self {
             data: data.into(),
@@ -86,7 +97,7 @@ cols_out,
         }
     }
 
-    pub(crate) fn new_from_bytes(
+    pub(crate) fn from_bytes(
         n: usize,
         rows: usize,
         cols_in: usize,
@@ -158,6 +169,12 @@ }
     }
 }
 
+impl<D: DataMut> FillUniform for MatZnx<D> {
+    fn fill_uniform(&mut self, source: &mut Source) {
+        source.fill_bytes(self.data.as_mut());
+    }
+}
+
 pub type MatZnxOwned = MatZnx<Vec<u8>>;
 pub type MatZnxMut<'a> = MatZnx<&'a mut [u8]>;
 pub type MatZnxRef<'a> = MatZnx<&'a [u8]>;
@@ -209,8 +226,6 @@ }
     }
 }
 
-use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
-
 impl<D: DataMut> ReaderFrom for MatZnx<D> {
     fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
         self.n = reader.read_u64::<LittleEndian>()? as usize;
@@ -244,3 +259,32 @@ writer.write_all(buf)?;
         Ok(())
     }
 }
+
+impl<D: DataRef> fmt::Display for MatZnx<D> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        writeln!(
+            f,
+            "MatZnx(n={}, rows={}, cols_in={}, cols_out={}, size={})",
+            self.n, self.rows, self.cols_in, self.cols_out, self.size
+        )?;
+
+        for row_i in 0..self.rows {
+            writeln!(f, "Row {}:", row_i)?;
+            for col_i in 0..self.cols_in {
+                writeln!(f, "cols_in {}:", col_i)?;
+                writeln!(f, "{}:", self.at(row_i, col_i))?;
+            }
+        }
+        Ok(())
+    }
+}
+
+impl<D: DataMut> ZnxZero for MatZnx<D> {
+    fn zero(&mut self) {
+        self.raw_mut().fill(0)
+    }
+
+    fn zero_at(&mut self, i: usize, j: usize) {
+        self.at_mut(i, j).zero();
+    }
+}

@@ -6,12 +6,12 @@
 use crate::{
     alloc_aligned,
     hal::{
-        api::{DataView, DataViewMut, ZnxInfos, ZnxSliceSize, ZnxView, ZnxViewMut, ZnxZero},
-        layouts::{Data, DataMut, DataRef, ReaderFrom, VecZnx, VecZnxToMut, VecZnxToRef, WriterTo},
+        api::{DataView, DataViewMut, FillUniform, ZnxInfos, ZnxSliceSize, ZnxView, ZnxViewMut, ZnxZero},
+        layouts::{Data, DataMut, DataRef, ReaderFrom, VecZnx, WriterTo},
     },
 };
 
-#[derive(PartialEq, Eq)]
+#[derive(PartialEq, Eq, Debug, Clone)]
 pub struct ScalarZnx<D: Data> {
     pub(crate) data: D,
     pub(crate) n: usize,
@@ -114,7 +114,7 @@ }
 }
 
 impl<D: DataRef + From<Vec<u8>>> ScalarZnx<D> {
-    pub fn new(n: usize, cols: usize) -> Self {
+    pub fn alloc(n: usize, cols: usize) -> Self {
         let data: Vec<u8> = alloc_aligned::<u8>(Self::bytes_of(n, cols));
         Self {
             data: data.into(),
@@ -123,7 +123,7 @@ cols,
         }
     }
 
-    pub(crate) fn new_from_bytes(n: usize, cols: usize, bytes: impl Into<Vec<u8>>) -> Self {
+    pub(crate) fn from_bytes(n: usize, cols: usize, bytes: impl Into<Vec<u8>>) -> Self {
         let data: Vec<u8> = bytes.into();
         assert!(data.len() == Self::bytes_of(n, cols));
         Self {
@@ -143,6 +143,12 @@ self.at_mut(i, j).fill(0);
     }
 }
 
+impl<D: DataMut> FillUniform for ScalarZnx<D> {
+    fn fill_uniform(&mut self, source: &mut Source) {
+        source.fill_bytes(self.data.as_mut());
+    }
+}
+
 pub type ScalarZnxOwned = ScalarZnx<Vec<u8>>;
 
 impl<D: Data> ScalarZnx<D> {
@@ -179,8 +185,8 @@ }
     }
 }
 
-impl<D: DataRef> VecZnxToRef for ScalarZnx<D> {
-    fn to_ref(&self) -> VecZnx<&[u8]> {
+impl<D: DataRef> ScalarZnx<D> {
+    pub fn as_vec_znx(&self) -> VecZnx<&[u8]> {
         VecZnx {
             data: self.data.as_ref(),
             n: self.n,
@@ -191,8 +197,8 @@ }
     }
 }
 
-impl<D: DataMut> VecZnxToMut for ScalarZnx<D> {
-    fn to_mut(&mut self) -> VecZnx<&mut [u8]> {
+impl<D: DataMut> ScalarZnx<D> {
+    pub fn as_vec_znx_mut(&mut self) -> VecZnx<&mut [u8]> {
         VecZnx {
             data: self.data.as_mut(),
             n: self.n,

@@ -3,12 +3,12 @@
 use crate::{
     alloc_aligned,
     hal::{
-        api::{DataView, DataViewMut, ZnxInfos, ZnxSliceSize, ZnxView, ZnxViewMut, ZnxZero},
+        api::{DataView, DataViewMut, FillUniform, ZnxInfos, ZnxSliceSize, ZnxView, ZnxViewMut, ZnxZero},
         layouts::{Data, DataMut, DataRef, ReaderFrom, WriterTo},
     },
 };
 
-#[derive(PartialEq, Eq)]
+#[derive(PartialEq, Eq, Clone)]
 pub struct VecZnx<D: Data> {
     pub(crate) data: D,
     pub(crate) n: usize,
@@ -86,7 +86,7 @@ }
 }
 
 impl<D: DataRef + From<Vec<u8>>> VecZnx<D> {
-    pub fn new<Scalar: Sized>(n: usize, cols: usize, size: usize) -> Self {
+    pub fn alloc<Scalar: Sized>(n: usize, cols: usize, size: usize) -> Self {
         let data: Vec<u8> = alloc_aligned::<u8>(Self::alloc_bytes::<Scalar>(n, cols, size));
         Self {
             data: data.into(),
@@ -157,6 +157,12 @@ Ok(())
     }
 }
 
+impl<D: DataMut> FillUniform for VecZnx<D> {
+    fn fill_uniform(&mut self, source: &mut Source) {
+        source.fill_bytes(self.data.as_mut());
+    }
+}
+
 pub type VecZnxOwned = VecZnx<Vec<u8>>;
 pub type VecZnxMut<'a> = VecZnx<&'a mut [u8]>;
 pub type VecZnxRef<'a> = VecZnx<&'a [u8]>;
@@ -207,6 +213,8 @@ }
 }
 
 use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
+use rand::RngCore;
+use sampling::source::Source;
 
 impl<D: DataMut> ReaderFrom for VecZnx<D> {
     fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {

@@ -1,4 +1,4 @@
-use crate::hal::layouts::{Backend, Module, ScalarZnxOwned, ScalarZnxToMut, ScalarZnxToRef};
+use crate::hal::layouts::{Backend, ScalarZnxOwned};
 
 pub unsafe trait ScalarZnxFromBytesImpl<B: Backend> {
     fn scalar_znx_from_bytes_impl(n: usize, cols: usize, bytes: Vec<u8>) -> ScalarZnxOwned;
@@ -11,29 +11,3 @@
 pub unsafe trait ScalarZnxAllocImpl<B: Backend> {
     fn scalar_znx_alloc_impl(n: usize, cols: usize) -> ScalarZnxOwned;
 }
-
-pub unsafe trait ScalarZnxAutomorphismImpl<B: Backend> {
-    fn scalar_znx_automorphism_impl<R, A>(module: &Module<B>, k: i64, res: &mut R, res_col: usize, a: &A, a_col: usize)
-    where
-        R: ScalarZnxToMut,
-        A: ScalarZnxToRef;
-}
-
-pub unsafe trait ScalarZnxAutomorphismInplaceIml<B: Backend> {
-    fn scalar_znx_automorphism_inplace_impl<A>(module: &Module<B>, k: i64, a: &mut A, a_col: usize)
-    where
-        A: ScalarZnxToMut;
-}
-
-pub unsafe trait ScalarZnxMulXpMinusOneImpl<B: Backend> {
-    fn scalar_znx_mul_xp_minus_one_impl<R, A>(module: &Module<B>, p: i64, r: &mut R, r_col: usize, a: &A, a_col: usize)
-    where
-        R: ScalarZnxToMut,
-        A: ScalarZnxToRef;
-}
-
-pub unsafe trait ScalarZnxMulXpMinusOneInplaceImpl<B: Backend> {
-    fn scalar_znx_mul_xp_minus_one_inplace_impl<R>(module: &Module<B>, p: i64, r: &mut R, r_col: usize)
-    where
-        R: ScalarZnxToMut;
-}

@@ -1,1 +1,2 @@
+pub mod serialization;
 pub mod vec_znx;

@@ -0,0 +1,56 @@
+use std::fmt::Debug;
+
+use sampling::source::Source;
+
+use crate::hal::{
+    api::{FillUniform, ZnxZero},
+    layouts::{ReaderFrom, WriterTo},
+};
+
+/// Generic test for serialization and deserialization.
+///
+/// - `T` must implement I/O traits, zeroing, cloning, and random filling.
+pub fn test_reader_writer_interface<T>(mut original: T)
+where
+    T: WriterTo + ReaderFrom + PartialEq + Eq + Debug + Clone + ZnxZero + FillUniform,
+{
+    // Fill original with uniform random data
+    let mut source = Source::new([0u8; 32]);
+    original.fill_uniform(&mut source);
+
+    // Serialize into a buffer
+    let mut buffer = Vec::new();
+    original.write_to(&mut buffer).expect("write_to failed");
+
+    // Prepare receiver: same shape, but zeroed
+    let mut receiver = original.clone();
+    receiver.zero();
+
+    // Deserialize from buffer
+    let mut reader: &[u8] = &buffer;
+    receiver.read_from(&mut reader).expect("read_from failed");
+
+    // Ensure serialization round-trip correctness
+    assert_eq!(
+        &original, &receiver,
+        "Deserialized object does not match the original"
+    );
+}
+
+#[test]
+fn scalar_znx_serialize() {
+    let original: crate::hal::layouts::ScalarZnx<Vec<u8>> = crate::hal::layouts::ScalarZnx::alloc(1024, 3);
+    test_reader_writer_interface(original);
+}
+
+#[test]
+fn vec_znx_serialize() {
+    let original: crate::hal::layouts::VecZnx<Vec<u8>> = crate::hal::layouts::VecZnx::alloc::<i64>(1024, 3, 4);
+    test_reader_writer_interface(original);
+}
+
+#[test]
+fn mat_znx_serialize() {
+    let original: crate::hal::layouts::MatZnx<Vec<u8>> = crate::hal::layouts::MatZnx::alloc(1024, 3, 2, 2, 4);
+    test_reader_writer_interface(original);
+}

@@ -11,7 +11,7 @@ where
     B: CPUAVX,
 {
     fn mat_znx_alloc_impl(module: &Module<B>, rows: usize, cols_in: usize, cols_out: usize, size: usize) -> MatZnxOwned {
-        MatZnxOwned::new(module.n(), rows, cols_in, cols_out, size)
+        MatZnxOwned::alloc(module.n(), rows, cols_in, cols_out, size)
     }
 }
 
@@ -36,6 +36,6 @@ cols_out: usize,
         size: usize,
         bytes: Vec<u8>,
     ) -> MatZnxOwned {
-        MatZnxOwned::new_from_bytes(module.n(), rows, cols_in, cols_out, size, bytes)
+        MatZnxOwned::from_bytes(module.n(), rows, cols_in, cols_out, size, bytes)
     }
 }

@@ -21,6 +21,9 @@ pub use module_fft64::*;
 pub use module_ntt120::*;
 
 /// For external documentation
-pub use vec_znx::{vec_znx_copy_ref, vec_znx_lsh_inplace_ref, vec_znx_merge_ref, vec_znx_rsh_inplace_ref, vec_znx_split_ref, vec_znx_switch_degree_ref};
+pub use vec_znx::{
+    vec_znx_copy_ref, vec_znx_lsh_inplace_ref, vec_znx_merge_ref, vec_znx_rsh_inplace_ref, vec_znx_split_ref,
+    vec_znx_switch_degree_ref,
+};
 
 pub trait CPUAVX {}

@@ -1,16 +1,9 @@
 use crate::{
     hal::{
-        api::{ZnxInfos, ZnxSliceSize, ZnxView, ZnxViewMut},
-        layouts::{Backend, Module, ScalarZnx, ScalarZnxOwned, ScalarZnxToMut, ScalarZnxToRef},
-        oep::{
-            ScalarZnxAllocBytesImpl, ScalarZnxAllocImpl, ScalarZnxAutomorphismImpl, ScalarZnxAutomorphismInplaceIml,
-            ScalarZnxFromBytesImpl,
-        },
+        layouts::{Backend, ScalarZnxOwned},
+        oep::{ScalarZnxAllocBytesImpl, ScalarZnxAllocImpl, ScalarZnxFromBytesImpl},
     },
-    implementation::cpu_spqlios::{
-        CPUAVX,
-        ffi::{module::module_info_t, vec_znx},
-    },
+    implementation::cpu_spqlios::CPUAVX,
 };
 
 unsafe impl<B: Backend> ScalarZnxAllocBytesImpl<B> for B
@@ -27,7 +20,7 @@ where
     B: CPUAVX,
 {
     fn scalar_znx_alloc_impl(n: usize, cols: usize) -> ScalarZnxOwned {
-        ScalarZnxOwned::new(n, cols)
+        ScalarZnxOwned::alloc(n, cols)
     }
 }
 
@@ -36,65 +29,6 @@ where
     B: CPUAVX,
 {
     fn scalar_znx_from_bytes_impl(n: usize, cols: usize, bytes: Vec<u8>) -> ScalarZnxOwned {
-        ScalarZnxOwned::new_from_bytes(n, cols, bytes)
-    }
-}
-
-unsafe impl<B: Backend> ScalarZnxAutomorphismImpl<B> for B
-where
-    B: CPUAVX,
-{
-    fn scalar_znx_automorphism_impl<R, A>(module: &Module<B>, k: i64, res: &mut R, res_col: usize, a: &A, a_col: usize)
-    where
-        R: ScalarZnxToMut,
-        A: ScalarZnxToRef,
-    {
-        let a: ScalarZnx<&[u8]> = a.to_ref();
-        let mut res: ScalarZnx<&mut [u8]> = res.to_mut();
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(a.n(), module.n());
-            assert_eq!(res.n(), module.n());
-        }
-        unsafe {
-            vec_znx::vec_znx_automorphism(
-                module.ptr() as *const module_info_t,
-                k,
-                res.at_mut_ptr(res_col, 0),
-                res.size() as u64,
-                res.sl() as u64,
-                a.at_ptr(a_col, 0),
-                a.size() as u64,
-                a.sl() as u64,
-            )
-        }
-    }
-}
-
-unsafe impl<B: Backend> ScalarZnxAutomorphismInplaceIml<B> for B
-where
-    B: CPUAVX,
-{
-    fn scalar_znx_automorphism_inplace_impl<A>(module: &Module<B>, k: i64, a: &mut A, a_col: usize)
-    where
-        A: ScalarZnxToMut,
-    {
-        let mut a: ScalarZnx<&mut [u8]> = a.to_mut();
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(a.n(), module.n());
-        }
-        unsafe {
-            vec_znx::vec_znx_automorphism(
-                module.ptr() as *const module_info_t,
-                k,
-                a.at_mut_ptr(a_col, 0),
-                a.size() as u64,
-                a.sl() as u64,
-                a.at_ptr(a_col, 0),
-                a.size() as u64,
-                a.sl() as u64,
-            )
-        }
+        ScalarZnxOwned::from_bytes(n, cols, bytes)
     }
 }

@@ -37,7 +37,7 @@ where
     B: CPUAVX,
 {
     fn vec_znx_alloc_impl(n: usize, cols: usize, size: usize) -> VecZnxOwned {
-        VecZnxOwned::new::<i64>(n, cols, size)
+        VecZnxOwned::alloc::<i64>(n, cols, size)
     }
 }
 

@@ -12,6 +12,7 @@ sampling = {path="../sampling"}
 rand_distr = {workspace = true}
 itertools = {workspace = true}
 byteorder = {workspace = true}
+rand_core = {workspace = true}
 
 [[bench]]
 name = "external_product_glwe_fft64"

@@ -75,7 +75,7 @@
         let size: usize = self.k.div_ceil(self.basek);
 
         // Equivalent to AUTO([f(0), -f(n-1), -f(n-2), ..., -f(1)], -1)
-        let mut lut_full: VecZnx<Vec<u8>> = VecZnx::new::<i64>(domain_size, 1, size);
+        let mut lut_full: VecZnx<Vec<u8>> = VecZnx::alloc::<i64>(domain_size, 1, size);
 
         let lut_at: &mut [i64] = lut_full.at_mut(0, limbs - 1);
 

@@ -1,187 +0,0 @@
-use backend::hal::{
-    api::{MatZnxAlloc, MatZnxAllocBytes},
-    layouts::{Backend, Data, DataMut, DataRef, MatZnx, Module, ReaderFrom, Scratch, VmpPMat, WriterTo},
-};
-
-use crate::{GGLWEExecLayoutFamily, GLWECiphertext, GLWESwitchingKey, GLWESwitchingKeyExec, Infos};
-
-#[derive(PartialEq, Eq)]
-pub struct AutomorphismKey<D: Data> {
-    pub(crate) key: GLWESwitchingKey<D>,
-    pub(crate) p: i64,
-}
-
-impl AutomorphismKey<Vec<u8>> {
-    pub fn alloc<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
-    where
-        Module<B>: MatZnxAlloc,
-    {
-        AutomorphismKey {
-            key: GLWESwitchingKey::alloc(module, basek, k, rows, digits, rank, rank),
-            p: 0,
-        }
-    }
-
-    pub fn bytes_of<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
-    where
-        Module<B>: MatZnxAllocBytes,
-    {
-        GLWESwitchingKey::<Vec<u8>>::bytes_of(module, basek, k, rows, digits, rank, rank)
-    }
-}
-
-impl<D: Data> Infos for AutomorphismKey<D> {
-    type Inner = MatZnx<D>;
-
-    fn inner(&self) -> &Self::Inner {
-        &self.key.inner()
-    }
-
-    fn basek(&self) -> usize {
-        self.key.basek()
-    }
-
-    fn k(&self) -> usize {
-        self.key.k()
-    }
-}
-
-impl<D: Data> AutomorphismKey<D> {
-    pub fn p(&self) -> i64 {
-        self.p
-    }
-
-    pub fn digits(&self) -> usize {
-        self.key.digits()
-    }
-
-    pub fn rank(&self) -> usize {
-        self.key.rank()
-    }
-
-    pub fn rank_in(&self) -> usize {
-        self.key.rank_in()
-    }
-
-    pub fn rank_out(&self) -> usize {
-        self.key.rank_out()
-    }
-}
-
-impl<D: DataRef> AutomorphismKey<D> {
-    pub fn at(&self, row: usize, col: usize) -> GLWECiphertext<&[u8]> {
-        self.key.at(row, col)
-    }
-}
-
-impl<D: DataMut> AutomorphismKey<D> {
-    pub fn at_mut(&mut self, row: usize, col: usize) -> GLWECiphertext<&mut [u8]> {
-        self.key.at_mut(row, col)
-    }
-}
-
-use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
-
-impl<D: DataMut> ReaderFrom for AutomorphismKey<D> {
-    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
-        self.p = reader.read_u64::<LittleEndian>()? as i64;
-        self.key.read_from(reader)
-    }
-}
-
-impl<D: DataRef> WriterTo for AutomorphismKey<D> {
-    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
-        writer.write_u64::<LittleEndian>(self.p as u64)?;
-        self.key.write_to(writer)
-    }
-}
-
-#[derive(PartialEq, Eq)]
-pub struct AutomorphismKeyExec<D: Data, B: Backend> {
-    pub(crate) key: GLWESwitchingKeyExec<D, B>,
-    pub(crate) p: i64,
-}
-
-impl<B: Backend> AutomorphismKeyExec<Vec<u8>, B> {
-    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
-    where
-        Module<B>: GGLWEExecLayoutFamily<B>,
-    {
-        AutomorphismKeyExec::<Vec<u8>, B> {
-            key: GLWESwitchingKeyExec::alloc(module, basek, k, rows, digits, rank, rank),
-            p: 0,
-        }
-    }
-
-    pub fn bytes_of(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
-    where
-        Module<B>: GGLWEExecLayoutFamily<B>,
-    {
-        GLWESwitchingKeyExec::<Vec<u8>, B>::bytes_of(module, basek, k, rows, digits, rank, rank)
-    }
-
-    pub fn from<DataOther: DataRef>(module: &Module<B>, other: &AutomorphismKey<DataOther>, scratch: &mut Scratch<B>) -> Self
-    where
-        Module<B>: GGLWEExecLayoutFamily<B>,
-    {
-        let mut atk_exec: AutomorphismKeyExec<Vec<u8>, B> = Self::alloc(
-            module,
-            other.basek(),
-            other.k(),
-            other.rows(),
-            other.digits(),
-            other.rank(),
-        );
-        atk_exec.prepare(module, other, scratch);
-        atk_exec
-    }
-}
-
-impl<D: DataMut, B: Backend> AutomorphismKeyExec<D, B> {
-    pub fn prepare<DataOther>(&mut self, module: &Module<B>, other: &AutomorphismKey<DataOther>, scratch: &mut Scratch<B>)
-    where
-        DataOther: DataRef,
-        Module<B>: GGLWEExecLayoutFamily<B>,
-    {
-        self.key.prepare(module, &other.key, scratch);
-        self.p = other.p;
-    }
-}
-
-impl<D: Data, B: Backend> Infos for AutomorphismKeyExec<D, B> {
-    type Inner = VmpPMat<D, B>;
-
-    fn inner(&self) -> &Self::Inner {
-        &self.key.inner()
-    }
-
-    fn basek(&self) -> usize {
-        self.key.basek()
-    }
-
-    fn k(&self) -> usize {
-        self.key.k()
-    }
-}
-
-impl<D: Data, B: Backend> AutomorphismKeyExec<D, B> {
-    pub fn p(&self) -> i64 {
-        self.p
-    }
-
-    pub fn digits(&self) -> usize {
-        self.key.digits()
-    }
-
-    pub fn rank(&self) -> usize {
-        self.key.rank()
-    }
-
-    pub fn rank_in(&self) -> usize {
-        self.key.rank_in()
-    }
-
-    pub fn rank_out(&self) -> usize {
-        self.key.rank_out()
-    }
-}

@@ -1,7 +1,7 @@
 use backend::hal::{
     api::{
-        ScalarZnxAllocBytes, ScalarZnxAutomorphism, ScratchAvailable, SvpApply, TakeScalarZnx, TakeVecZnx, TakeVecZnxBig,
-        TakeVecZnxDft, VecZnxAddScalarInplace, VecZnxAllocBytes, VecZnxBigAllocBytes, VecZnxDftToVecZnxBigTmpA,
+        ScalarZnxAllocBytes, ScratchAvailable, SvpApply, TakeScalarZnx, TakeVecZnx, TakeVecZnxBig, TakeVecZnxDft,
+        VecZnxAddScalarInplace, VecZnxAllocBytes, VecZnxAutomorphism, VecZnxBigAllocBytes, VecZnxDftToVecZnxBigTmpA,
         VecZnxNormalizeInplace, VecZnxNormalizeTmpBytes, VecZnxSwithcDegree, ZnxZero,
     },
     layouts::{Backend, DataMut, DataRef, Module, ScalarZnx, Scratch},
@@ -9,8 +9,10 @@ };
 use sampling::source::Source;
 
 use crate::{
-    AutomorphismKey, GGLWECiphertext, GLWECiphertext, GLWEDecryptFamily, GLWEEncryptSkFamily, GLWEPlaintext, GLWESecret,
-    GLWESecretExec, GLWESecretFamily, GLWESwitchingKey, GLWETensorKey, Infos, TakeGLWEPt, TakeGLWESecret, TakeGLWESecretExec,
+    AutomorphismKey, AutomorphismKeyCompressed, GGLWECiphertext, GGLWECiphertextCompressed, GLWECiphertext, GLWEDecryptFamily,
+    GLWEEncryptSkFamily, GLWEPlaintext, GLWESecret, GLWESecretExec, GLWESecretFamily, GLWESwitchingKey,
+    GLWESwitchingKeyCompressed, GLWETensorKey, GLWETensorKeyCompressed, Infos, TakeGLWEPt, TakeGLWESecret, TakeGLWESecretExec,
+    encrypt_sk_internal,
 };
 
 pub trait GGLWEEncryptSkFamily<B: Backend> = GLWEEncryptSkFamily<B> + GLWESecretFamily<B>;
@@ -122,6 +124,112 @@ });
     }
 }
 
+impl GGLWECiphertextCompressed<Vec<u8>> {
+    pub fn encrypt_sk_scratch_space<B: Backend>(module: &Module<B>, basek: usize, k: usize) -> usize
+    where
+        Module<B>: GLWESwitchingKeyEncryptSkFamily<B> + VecZnxAllocBytes,
+    {
+        GGLWECiphertext::encrypt_sk_scratch_space(module, basek, k)
+    }
+}
+
+impl<D: DataMut> GGLWECiphertextCompressed<D> {
+    pub fn encrypt_sk<DataPt: DataRef, DataSk: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        pt: &ScalarZnx<DataPt>,
+        sk: &GLWESecretExec<DataSk, B>,
+        seed: [u8; 32],
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch<B>,
+    ) where
+        Module<B>: GGLWEEncryptSkFamily<B> + VecZnxAllocBytes + VecZnxAddScalarInplace,
+        Scratch<B>: TakeVecZnxDft<B> + ScratchAvailable + TakeVecZnx<B>,
+    {
+        #[cfg(debug_assertions)]
+        {
+            use backend::hal::api::ZnxInfos;
+
+            assert_eq!(
+                self.rank_in(),
+                pt.cols(),
+                "self.rank_in(): {} != pt.cols(): {}",
+                self.rank_in(),
+                pt.cols()
+            );
+            assert_eq!(
+                self.rank_out(),
+                sk.rank(),
+                "self.rank_out(): {} != sk.rank(): {}",
+                self.rank_out(),
+                sk.rank()
+            );
+            assert_eq!(self.n(), module.n());
+            assert_eq!(sk.n(), module.n());
+            assert_eq!(pt.n(), module.n());
+            assert!(
+                scratch.available() >= GGLWECiphertextCompressed::encrypt_sk_scratch_space(module, self.basek(), self.k()),
+                "scratch.available: {} < GGLWECiphertext::encrypt_sk_scratch_space(module, self.rank()={}, self.size()={}): {}",
+                scratch.available(),
+                self.rank(),
+                self.size(),
+                GGLWECiphertextCompressed::encrypt_sk_scratch_space(module, self.basek(), self.k())
+            );
+            assert!(
+                self.rows() * self.digits() * self.basek() <= self.k(),
+                "self.rows() : {} * self.digits() : {} * self.basek() : {} = {} >= self.k() = {}",
+                self.rows(),
+                self.digits(),
+                self.basek(),
+                self.rows() * self.digits() * self.basek(),
+                self.k()
+            );
+        }
+
+        let rows: usize = self.rows();
+        let digits: usize = self.digits();
+        let basek: usize = self.basek();
+        let k: usize = self.k();
+        let rank_in: usize = self.rank_in();
+
+        let mut source_xa = Source::new(seed);
+
+        let (mut tmp_pt, scrach_1) = scratch.take_glwe_pt(module, basek, k);
+        (0..rank_in).for_each(|col_i| {
+            (0..rows).for_each(|row_i| {
+                // Adds the scalar_znx_pt to the i-th limb of the vec_znx_pt
+                tmp_pt.data.zero(); // zeroes for next iteration
+                module.vec_znx_add_scalar_inplace(
+                    &mut tmp_pt.data,
+                    0,
+                    (digits - 1) + row_i * digits,
+                    pt,
+                    col_i,
+                );
+                module.vec_znx_normalize_inplace(basek, &mut tmp_pt.data, 0, scrach_1);
+
+                let (seed, mut source_xa_tmp) = source_xa.branch();
+                self.seed[col_i * rows + row_i] = seed;
+
+                encrypt_sk_internal(
+                    module,
+                    self.basek(),
+                    self.k(),
+                    &mut self.at_mut(row_i, col_i).data,
+                    true,
+                    Some((&tmp_pt, 0)),
+                    sk,
+                    &mut source_xa_tmp,
+                    source_xe,
+                    sigma,
+                    scrach_1,
+                );
+            });
+        });
+    }
+}
+
 pub trait GLWESwitchingKeyEncryptSkFamily<B: Backend> = GGLWEEncryptSkFamily<B>;
 
 impl GLWESwitchingKey<Vec<u8>> {
@@ -197,14 +305,19 @@ }
 
         let (mut sk_in_tmp, scratch1) = scratch.take_scalar_znx(module, sk_in.rank());
         (0..sk_in.rank()).for_each(|i| {
-            module.vec_znx_switch_degree(&mut sk_in_tmp, i, &sk_in.data, i);
+            module.vec_znx_switch_degree(
+                &mut sk_in_tmp.as_vec_znx_mut(),
+                i,
+                &sk_in.data.as_vec_znx(),
+                i,
+            );
         });
 
         let (mut sk_out_tmp, scratch2) = scratch1.take_glwe_secret_exec(module, sk_out.rank());
         {
             let (mut tmp, _) = scratch2.take_scalar_znx(module, 1);
             (0..sk_out.rank()).for_each(|i| {
-                module.vec_znx_switch_degree(&mut tmp, 0, &sk_out.data, i);
+                module.vec_znx_switch_degree(&mut tmp.as_vec_znx_mut(), 0, &sk_out.data.as_vec_znx(), i);
                 module.svp_prepare(&mut sk_out_tmp.data, i, &tmp, 0);
             });
         }
@@ -223,6 +336,100 @@ self.sk_out_n = sk_out.n();
     }
 }
 
+impl GLWESwitchingKeyCompressed<Vec<u8>> {
+    pub fn encrypt_sk_scratch_space<B: Backend>(
+        module: &Module<B>,
+        basek: usize,
+        k: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> usize
+    where
+        Module<B>: GLWESwitchingKeyEncryptSkFamily<B> + ScalarZnxAllocBytes + VecZnxAllocBytes,
+    {
+        (GGLWECiphertext::encrypt_sk_scratch_space(module, basek, k) | module.scalar_znx_alloc_bytes(1))
+            + module.scalar_znx_alloc_bytes(rank_in)
+            + GLWESecretExec::bytes_of(module, rank_out)
+    }
+}
+
+impl<DataSelf: DataMut> GLWESwitchingKeyCompressed<DataSelf> {
+    pub fn encrypt_sk<DataSkIn: DataRef, DataSkOut: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        sk_in: &GLWESecret<DataSkIn>,
+        sk_out: &GLWESecret<DataSkOut>,
+        seed_xa: [u8; 32],
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch<B>,
+    ) where
+        Module<B>: GLWESwitchingKeyEncryptSkFamily<B>
+            + ScalarZnxAllocBytes
+            + VecZnxSwithcDegree
+            + VecZnxAllocBytes
+            + VecZnxAddScalarInplace,
+        Scratch<B>:
+            ScratchAvailable + TakeScalarZnx<B> + TakeVecZnxDft<B> + TakeGLWESecretExec<B> + ScratchAvailable + TakeVecZnx<B>,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert!(sk_in.n() <= module.n());
+            assert!(sk_out.n() <= module.n());
+            assert!(
+                scratch.available()
+                    >= GLWESwitchingKey::encrypt_sk_scratch_space(
+                        module,
+                        self.basek(),
+                        self.k(),
+                        self.rank_in(),
+                        self.rank_out()
+                    ),
+                "scratch.available()={} < GLWESwitchingKey::encrypt_sk_scratch_space={}",
+                scratch.available(),
+                GLWESwitchingKey::encrypt_sk_scratch_space(
+                    module,
+                    self.basek(),
+                    self.k(),
+                    self.rank_in(),
+                    self.rank_out()
+                )
+            )
+        }
+
+        let (mut sk_in_tmp, scratch1) = scratch.take_scalar_znx(module, sk_in.rank());
+        (0..sk_in.rank()).for_each(|i| {
+            module.vec_znx_switch_degree(
+                &mut sk_in_tmp.as_vec_znx_mut(),
+                i,
+                &sk_in.data.as_vec_znx(),
+                i,
+            );
+        });
+
+        let (mut sk_out_tmp, scratch2) = scratch1.take_glwe_secret_exec(module, sk_out.rank());
+        {
+            let (mut tmp, _) = scratch2.take_scalar_znx(module, 1);
+            (0..sk_out.rank()).for_each(|i| {
+                module.vec_znx_switch_degree(&mut tmp.as_vec_znx_mut(), 0, &sk_out.data.as_vec_znx(), i);
+                module.svp_prepare(&mut sk_out_tmp.data, i, &tmp, 0);
+            });
+        }
+
+        self.key.encrypt_sk(
+            module,
+            &sk_in_tmp,
+            &sk_out_tmp,
+            seed_xa,
+            source_xe,
+            sigma,
+            scratch2,
+        );
+        self.sk_in_n = sk_in.n();
+        self.sk_out_n = sk_out.n();
+    }
+}
+
 pub trait AutomorphismKeyEncryptSkFamily<B: Backend> = GGLWEEncryptSkFamily<B>;
 
 impl AutomorphismKey<Vec<u8>> {
@@ -250,9 +457,9 @@ sigma: f64,
         scratch: &mut Scratch<B>,
     ) where
         Module<B>: AutomorphismKeyEncryptSkFamily<B>
-            + ScalarZnxAutomorphism
             + ScalarZnxAllocBytes
             + VecZnxAllocBytes
+            + VecZnxAutomorphism
             + VecZnxSwithcDegree
             + VecZnxAddScalarInplace,
         Scratch<B>: ScratchAvailable + TakeScalarZnx<B> + TakeVecZnxDft<B> + TakeGLWESecretExec<B> + TakeVecZnx<B>,
@@ -277,11 +484,11 @@ let (mut sk_out, scratch_1) = scratch.take_glwe_secret(module, sk.rank());
 
         {
             (0..self.rank()).for_each(|i| {
-                module.scalar_znx_automorphism(
+                module.vec_znx_automorphism(
                     module.galois_element_inv(p),
-                    &mut sk_out.data,
+                    &mut sk_out.data.as_vec_znx_mut(),
                     i,
-                    &sk.data,
+                    &sk.data.as_vec_znx(),
                     i,
                 );
             });
@@ -294,6 +501,72 @@ self.p = p;
     }
 }
 
+impl AutomorphismKeyCompressed<Vec<u8>> {
+    pub fn encrypt_sk_scratch_space<B: Backend>(module: &Module<B>, basek: usize, k: usize, rank: usize) -> usize
+    where
+        Module<B>: AutomorphismKeyEncryptSkFamily<B> + ScalarZnxAllocBytes + VecZnxAllocBytes,
+    {
+        GLWESwitchingKeyCompressed::encrypt_sk_scratch_space(module, basek, k, rank, rank) + GLWESecret::bytes_of(module, rank)
+    }
+}
+
+impl<DataSelf: DataMut> AutomorphismKeyCompressed<DataSelf> {
+    pub fn encrypt_sk<DataSk: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        p: i64,
+        sk: &GLWESecret<DataSk>,
+        seed_xa: [u8; 32],
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch<B>,
+    ) where
+        Module<B>: AutomorphismKeyEncryptSkFamily<B>
+            + ScalarZnxAllocBytes
+            + VecZnxAllocBytes
+            + VecZnxSwithcDegree
+            + VecZnxAutomorphism
+            + VecZnxAddScalarInplace,
+        Scratch<B>: ScratchAvailable + TakeScalarZnx<B> + TakeVecZnxDft<B> + TakeGLWESecretExec<B> + TakeVecZnx<B>,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.n(), module.n());
+            assert_eq!(sk.n(), module.n());
+            assert_eq!(self.rank_out(), self.rank_in());
+            assert_eq!(sk.rank(), self.rank());
+            assert!(
+                scratch.available()
+                    >= AutomorphismKeyCompressed::encrypt_sk_scratch_space(module, self.basek(), self.k(), self.rank()),
+                "scratch.available(): {} < AutomorphismKey::encrypt_sk_scratch_space(module, self.rank()={}, self.size()={}): {}",
+                scratch.available(),
+                self.rank(),
+                self.size(),
+                AutomorphismKeyCompressed::encrypt_sk_scratch_space(module, self.basek(), self.k(), self.rank())
+            )
+        }
+
+        let (mut sk_out, scratch_1) = scratch.take_glwe_secret(module, sk.rank());
+
+        {
+            (0..self.rank()).for_each(|i| {
+                module.vec_znx_automorphism(
+                    module.galois_element_inv(p),
+                    &mut sk_out.data.as_vec_znx_mut(),
+                    i,
+                    &sk.data.as_vec_znx(),
+                    i,
+                );
+            });
+        }
+
+        self.key
+            .encrypt_sk(module, &sk, &sk_out, seed_xa, source_xe, sigma, scratch_1);
+
+        self.p = p;
+    }
+}
+
 pub trait GLWETensorKeyEncryptSkFamily<B: Backend> =
     GGLWEEncryptSkFamily<B> + VecZnxBigAllocBytes + VecZnxDftToVecZnxBigTmpA<B> + SvpApply<B>;
 
@@ -344,7 +617,7 @@
         let (mut sk_dft, scratch2) = scratch1.take_vec_znx_dft(module, rank, 1);
 
         (0..rank).for_each(|i| {
-            module.vec_znx_dft_from_vec_znx(1, 0, &mut sk_dft, i, &sk.data, i);
+            module.vec_znx_dft_from_vec_znx(1, 0, &mut sk_dft, i, &sk.data.as_vec_znx(), i);
         });
 
         let (mut sk_ij_big, scratch3) = scratch2.take_vec_znx_big(module, 1, 1);
@@ -356,7 +629,14 @@ (i..rank).for_each(|j| {
                 module.svp_apply(&mut sk_ij_dft, 0, &sk_dft_prep.data, j, &sk_dft, i);
 
                 module.vec_znx_dft_to_vec_znx_big_tmp_a(&mut sk_ij_big, 0, &mut sk_ij_dft, 0);
-                module.vec_znx_big_normalize(self.basek(), &mut sk_ij.data, 0, &sk_ij_big, 0, scratch5);
+                module.vec_znx_big_normalize(
+                    self.basek(),
+                    &mut sk_ij.data.as_vec_znx_mut(),
+                    0,
+                    &sk_ij_big,
+                    0,
+                    scratch5,
+                );
 
                 self.at_mut(i, j)
                     .encrypt_sk(module, &sk_ij, sk, source_xa, source_xe, sigma, scratch5);
@@ -364,3 +644,77 @@ });
         })
     }
 }
+
+impl GLWETensorKeyCompressed<Vec<u8>> {
+    pub fn encrypt_sk_scratch_space<B: Backend>(module: &Module<B>, basek: usize, k: usize, rank: usize) -> usize
+    where
+        Module<B>: GLWETensorKeyEncryptSkFamily<B> + ScalarZnxAllocBytes + VecZnxAllocBytes,
+    {
+        GLWETensorKey::encrypt_sk_scratch_space(module, basek, k, rank)
+    }
+}
+
+impl<DataSelf: DataMut> GLWETensorKeyCompressed<DataSelf> {
+    pub fn encrypt_sk<DataSk: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        sk: &GLWESecret<DataSk>,
+        seed_xa: [u8; 32],
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch<B>,
+    ) where
+        Module<B>: GLWETensorKeyEncryptSkFamily<B>
+            + ScalarZnxAllocBytes
+            + VecZnxSwithcDegree
+            + VecZnxAllocBytes
+            + VecZnxAddScalarInplace,
+        Scratch<B>:
+            ScratchAvailable + TakeVecZnxDft<B> + TakeVecZnxBig<B> + TakeGLWESecretExec<B> + TakeScalarZnx<B> + TakeVecZnx<B>,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), sk.rank());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(sk.n(), module.n());
+        }
+
+        let rank: usize = self.rank();
+
+        let (mut sk_dft_prep, scratch1) = scratch.take_glwe_secret_exec(module, rank);
+        sk_dft_prep.prepare(module, &sk);
+
+        let (mut sk_dft, scratch2) = scratch1.take_vec_znx_dft(module, rank, 1);
+
+        (0..rank).for_each(|i| {
+            module.vec_znx_dft_from_vec_znx(1, 0, &mut sk_dft, i, &sk.data.as_vec_znx(), i);
+        });
+
+        let (mut sk_ij_big, scratch3) = scratch2.take_vec_znx_big(module, 1, 1);
+        let (mut sk_ij, scratch4) = scratch3.take_glwe_secret(module, 1);
+        let (mut sk_ij_dft, scratch5) = scratch4.take_vec_znx_dft(module, 1, 1);
+
+        let mut source_xa: Source = Source::new(seed_xa);
+
+        (0..rank).for_each(|i| {
+            (i..rank).for_each(|j| {
+                module.svp_apply(&mut sk_ij_dft, 0, &sk_dft_prep.data, j, &sk_dft, i);
+
+                module.vec_znx_dft_to_vec_znx_big_tmp_a(&mut sk_ij_big, 0, &mut sk_ij_dft, 0);
+                module.vec_znx_big_normalize(
+                    self.basek(),
+                    &mut sk_ij.data.as_vec_znx_mut(),
+                    0,
+                    &sk_ij_big,
+                    0,
+                    scratch5,
+                );
+
+                let (seed_xa_tmp, _) = source_xa.branch();
+
+                self.at_mut(i, j)
+                    .encrypt_sk(module, &sk_ij, sk, seed_xa_tmp, source_xe, sigma, scratch5);
+            });
+        })
+    }
+}

@@ -1,227 +0,0 @@
-use backend::hal::{
-    api::{MatZnxAlloc, MatZnxAllocBytes},
-    layouts::{Backend, Data, DataMut, DataRef, MatZnx, Module, ReaderFrom, Scratch, VmpPMat, WriterTo},
-};
-
-use crate::{GGLWECiphertext, GGLWECiphertextExec, GGLWEExecLayoutFamily, GLWECiphertext, Infos};
-
-#[derive(PartialEq, Eq)]
-pub struct GLWESwitchingKey<D: Data> {
-    pub(crate) key: GGLWECiphertext<D>,
-    pub(crate) sk_in_n: usize,  // Degree of sk_in
-    pub(crate) sk_out_n: usize, // Degree of sk_out
-}
-
-impl GLWESwitchingKey<Vec<u8>> {
-    pub fn alloc<B: Backend>(
-        module: &Module<B>,
-        basek: usize,
-        k: usize,
-        rows: usize,
-        digits: usize,
-        rank_in: usize,
-        rank_out: usize,
-    ) -> Self
-    where
-        Module<B>: MatZnxAlloc,
-    {
-        GLWESwitchingKey {
-            key: GGLWECiphertext::alloc(module, basek, k, rows, digits, rank_in, rank_out),
-            sk_in_n: 0,
-            sk_out_n: 0,
-        }
-    }
-
-    pub fn bytes_of<B: Backend>(
-        module: &Module<B>,
-        basek: usize,
-        k: usize,
-        rows: usize,
-        digits: usize,
-        rank_in: usize,
-        rank_out: usize,
-    ) -> usize
-    where
-        Module<B>: MatZnxAllocBytes,
-    {
-        GGLWECiphertext::<Vec<u8>>::bytes_of(module, basek, k, rows, digits, rank_in, rank_out)
-    }
-}
-
-impl<D: Data> Infos for GLWESwitchingKey<D> {
-    type Inner = MatZnx<D>;
-
-    fn inner(&self) -> &Self::Inner {
-        self.key.inner()
-    }
-
-    fn basek(&self) -> usize {
-        self.key.basek()
-    }
-
-    fn k(&self) -> usize {
-        self.key.k()
-    }
-}
-
-impl<D: Data> GLWESwitchingKey<D> {
-    pub fn rank(&self) -> usize {
-        self.key.data.cols_out() - 1
-    }
-
-    pub fn rank_in(&self) -> usize {
-        self.key.data.cols_in()
-    }
-
-    pub fn rank_out(&self) -> usize {
-        self.key.data.cols_out() - 1
-    }
-
-    pub fn digits(&self) -> usize {
-        self.key.digits()
-    }
-
-    pub fn sk_degree_in(&self) -> usize {
-        self.sk_in_n
-    }
-
-    pub fn sk_degree_out(&self) -> usize {
-        self.sk_out_n
-    }
-}
-
-impl<D: DataRef> GLWESwitchingKey<D> {
-    pub fn at(&self, row: usize, col: usize) -> GLWECiphertext<&[u8]> {
-        self.key.at(row, col)
-    }
-}
-
-impl<D: DataMut> GLWESwitchingKey<D> {
-    pub fn at_mut(&mut self, row: usize, col: usize) -> GLWECiphertext<&mut [u8]> {
-        self.key.at_mut(row, col)
-    }
-}
-
-use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
-
-impl<D: DataMut> ReaderFrom for GLWESwitchingKey<D> {
-    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
-        self.sk_in_n = reader.read_u64::<LittleEndian>()? as usize;
-        self.sk_out_n = reader.read_u64::<LittleEndian>()? as usize;
-        self.key.read_from(reader)
-    }
-}
-
-impl<D: DataRef> WriterTo for GLWESwitchingKey<D> {
-    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
-        writer.write_u64::<LittleEndian>(self.sk_in_n as u64)?;
-        writer.write_u64::<LittleEndian>(self.sk_out_n as u64)?;
-        self.key.write_to(writer)
-    }
-}
-
-#[derive(PartialEq, Eq)]
-pub struct GLWESwitchingKeyExec<D: Data, B: Backend> {
-    pub(crate) key: GGLWECiphertextExec<D, B>,
-    pub(crate) sk_in_n: usize,  // Degree of sk_in
-    pub(crate) sk_out_n: usize, // Degree of sk_out
-}
-
-impl<B: Backend> GLWESwitchingKeyExec<Vec<u8>, B> {
-    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank_in: usize, rank_out: usize) -> Self
-    where
-        Module<B>: GGLWEExecLayoutFamily<B>,
-    {
-        GLWESwitchingKeyExec::<Vec<u8>, B> {
-            key: GGLWECiphertextExec::alloc(module, basek, k, rows, digits, rank_in, rank_out),
-            sk_in_n: 0,
-            sk_out_n: 0,
-        }
-    }
-
-    pub fn bytes_of(
-        module: &Module<B>,
-        basek: usize,
-        k: usize,
-        rows: usize,
-        digits: usize,
-        rank_in: usize,
-        rank_out: usize,
-    ) -> usize
-    where
-        Module<B>: GGLWEExecLayoutFamily<B>,
-    {
-        GGLWECiphertextExec::bytes_of(module, basek, k, rows, digits, rank_in, rank_out)
-    }
-
-    pub fn from<DataOther: DataRef>(module: &Module<B>, other: &GLWESwitchingKey<DataOther>, scratch: &mut Scratch<B>) -> Self
-    where
-        Module<B>: GGLWEExecLayoutFamily<B>,
-    {
-        let mut ksk_exec: GLWESwitchingKeyExec<Vec<u8>, B> = Self::alloc(
-            module,
-            other.basek(),
-            other.k(),
-            other.rows(),
-            other.digits(),
-            other.rank_in(),
-            other.rank_out(),
-        );
-        ksk_exec.prepare(module, other, scratch);
-        ksk_exec
-    }
-}
-
-impl<D: Data, B: Backend> Infos for GLWESwitchingKeyExec<D, B> {
-    type Inner = VmpPMat<D, B>;
-
-    fn inner(&self) -> &Self::Inner {
-        self.key.inner()
-    }
-
-    fn basek(&self) -> usize {
-        self.key.basek()
-    }
-
-    fn k(&self) -> usize {
-        self.key.k()
-    }
-}
-
-impl<D: Data, B: Backend> GLWESwitchingKeyExec<D, B> {
-    pub fn rank(&self) -> usize {
-        self.key.data.cols_out() - 1
-    }
-
-    pub fn rank_in(&self) -> usize {
-        self.key.data.cols_in()
-    }
-
-    pub fn rank_out(&self) -> usize {
-        self.key.data.cols_out() - 1
-    }
-
-    pub fn digits(&self) -> usize {
-        self.key.digits()
-    }
-
-    pub fn sk_degree_in(&self) -> usize {
-        self.sk_in_n
-    }
-
-    pub fn sk_degree_out(&self) -> usize {
-        self.sk_out_n
-    }
-}
-
-impl<D: DataMut, B: Backend> GLWESwitchingKeyExec<D, B> {
-    pub fn prepare<DataOther>(&mut self, module: &Module<B>, other: &GLWESwitchingKey<DataOther>, scratch: &mut Scratch<B>)
-    where
-        DataOther: DataRef,
-        Module<B>: GGLWEExecLayoutFamily<B>,
-    {
-        self.key.prepare(module, &other.key, scratch);
-        self.sk_in_n = other.sk_in_n;
-        self.sk_out_n = other.sk_out_n;
-    }
-}

@@ -1,9 +1,10 @@
 use backend::hal::{
     api::{MatZnxAlloc, MatZnxAllocBytes, VmpPMatAlloc, VmpPMatAllocBytes, VmpPMatPrepare},
-    layouts::{Backend, Data, DataMut, DataRef, MatZnx, Module, ReaderFrom, Scratch, VmpPMat, WriterTo},
+    layouts::{Backend, Data, DataMut, DataRef, MatZnx, Module, ReaderFrom, WriterTo},
 };
 
 use crate::{GLWECiphertext, Infos};
+use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
 
 pub trait GGLWEExecLayoutFamily<B: Backend> = VmpPMatAlloc<B> + VmpPMatAllocBytes + VmpPMatPrepare<B>;
 
@@ -138,8 +139,6 @@ self.data.cols_out() - 1
     }
 }
 
-use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
-
 impl<D: DataMut> ReaderFrom for GGLWECiphertext<D> {
     fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
         self.k = reader.read_u64::<LittleEndian>()? as usize;
@@ -159,43 +158,33 @@ }
 }
 
 #[derive(PartialEq, Eq)]
-pub struct GGLWECiphertextExec<D: Data, B: Backend> {
-    pub(crate) data: VmpPMat<D, B>,
-    pub(crate) basek: usize,
-    pub(crate) k: usize,
-    pub(crate) digits: usize,
+pub struct GLWESwitchingKey<D: Data> {
+    pub(crate) key: GGLWECiphertext<D>,
+    pub(crate) sk_in_n: usize,  // Degree of sk_in
+    pub(crate) sk_out_n: usize, // Degree of sk_out
 }
 
-impl<B: Backend> GGLWECiphertextExec<Vec<u8>, B> {
-    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank_in: usize, rank_out: usize) -> Self
+impl GLWESwitchingKey<Vec<u8>> {
+    pub fn alloc<B: Backend>(
+        module: &Module<B>,
+        basek: usize,
+        k: usize,
+        rows: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> Self
     where
-        Module<B>: GGLWEExecLayoutFamily<B>,
+        Module<B>: MatZnxAlloc,
     {
-        let size: usize = k.div_ceil(basek);
-        debug_assert!(
-            size > digits,
-            "invalid gglwe: ceil(k/basek): {} <= digits: {}",
-            size,
-            digits
-        );
-
-        assert!(
-            rows * digits <= size,
-            "invalid gglwe: rows: {} * digits:{} > ceil(k/basek): {}",
-            rows,
-            digits,
-            size
-        );
-
-        Self {
-            data: module.vmp_pmat_alloc(rows, rank_in, rank_out + 1, size),
-            basek: basek,
-            k,
-            digits,
+        GLWESwitchingKey {
+            key: GGLWECiphertext::alloc(module, basek, k, rows, digits, rank_in, rank_out),
+            sk_in_n: 0,
+            sk_out_n: 0,
         }
     }
 
-    pub fn bytes_of(
+    pub fn bytes_of<B: Backend>(
         module: &Module<B>,
         basek: usize,
         k: usize,
@@ -205,71 +194,278 @@ rank_in: usize,
         rank_out: usize,
     ) -> usize
     where
-        Module<B>: GGLWEExecLayoutFamily<B>,
+        Module<B>: MatZnxAllocBytes,
     {
-        let size: usize = k.div_ceil(basek);
-        debug_assert!(
-            size > digits,
-            "invalid gglwe: ceil(k/basek): {} <= digits: {}",
-            size,
-            digits
-        );
+        GGLWECiphertext::<Vec<u8>>::bytes_of(module, basek, k, rows, digits, rank_in, rank_out)
+    }
+}
 
-        assert!(
-            rows * digits <= size,
-            "invalid gglwe: rows: {} * digits:{} > ceil(k/basek): {}",
-            rows,
-            digits,
-            size
-        );
+impl<D: Data> Infos for GLWESwitchingKey<D> {
+    type Inner = MatZnx<D>;
 
-        module.vmp_pmat_alloc_bytes(rows, rank_in, rank_out + 1, rows)
+    fn inner(&self) -> &Self::Inner {
+        self.key.inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.key.basek()
+    }
+
+    fn k(&self) -> usize {
+        self.key.k()
+    }
+}
+
+impl<D: Data> GLWESwitchingKey<D> {
+    pub fn rank(&self) -> usize {
+        self.key.data.cols_out() - 1
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.key.data.cols_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.key.data.cols_out() - 1
+    }
+
+    pub fn digits(&self) -> usize {
+        self.key.digits()
+    }
+
+    pub fn sk_degree_in(&self) -> usize {
+        self.sk_in_n
+    }
+
+    pub fn sk_degree_out(&self) -> usize {
+        self.sk_out_n
+    }
+}
+
+impl<D: DataRef> GLWESwitchingKey<D> {
+    pub fn at(&self, row: usize, col: usize) -> GLWECiphertext<&[u8]> {
+        self.key.at(row, col)
+    }
+}
+
+impl<D: DataMut> GLWESwitchingKey<D> {
+    pub fn at_mut(&mut self, row: usize, col: usize) -> GLWECiphertext<&mut [u8]> {
+        self.key.at_mut(row, col)
     }
 }
 
-impl<D: Data, B: Backend> Infos for GGLWECiphertextExec<D, B> {
-    type Inner = VmpPMat<D, B>;
+impl<D: DataMut> ReaderFrom for GLWESwitchingKey<D> {
+    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
+        self.sk_in_n = reader.read_u64::<LittleEndian>()? as usize;
+        self.sk_out_n = reader.read_u64::<LittleEndian>()? as usize;
+        self.key.read_from(reader)
+    }
+}
+
+impl<D: DataRef> WriterTo for GLWESwitchingKey<D> {
+    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
+        writer.write_u64::<LittleEndian>(self.sk_in_n as u64)?;
+        writer.write_u64::<LittleEndian>(self.sk_out_n as u64)?;
+        self.key.write_to(writer)
+    }
+}
+
+#[derive(PartialEq, Eq)]
+pub struct AutomorphismKey<D: Data> {
+    pub(crate) key: GLWESwitchingKey<D>,
+    pub(crate) p: i64,
+}
+
+impl AutomorphismKey<Vec<u8>> {
+    pub fn alloc<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
+    where
+        Module<B>: MatZnxAlloc,
+    {
+        AutomorphismKey {
+            key: GLWESwitchingKey::alloc(module, basek, k, rows, digits, rank, rank),
+            p: 0,
+        }
+    }
+
+    pub fn bytes_of<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
+    where
+        Module<B>: MatZnxAllocBytes,
+    {
+        GLWESwitchingKey::<Vec<u8>>::bytes_of(module, basek, k, rows, digits, rank, rank)
+    }
+}
+
+impl<D: Data> Infos for AutomorphismKey<D> {
+    type Inner = MatZnx<D>;
 
     fn inner(&self) -> &Self::Inner {
-        &self.data
+        &self.key.inner()
     }
 
     fn basek(&self) -> usize {
-        self.basek
+        self.key.basek()
     }
 
     fn k(&self) -> usize {
-        self.k
+        self.key.k()
     }
 }
 
-impl<D: Data, B: Backend> GGLWECiphertextExec<D, B> {
-    pub fn rank(&self) -> usize {
-        self.data.cols_out() - 1
+impl<D: Data> AutomorphismKey<D> {
+    pub fn p(&self) -> i64 {
+        self.p
     }
 
     pub fn digits(&self) -> usize {
-        self.digits
+        self.key.digits()
+    }
+
+    pub fn rank(&self) -> usize {
+        self.key.rank()
     }
 
     pub fn rank_in(&self) -> usize {
-        self.data.cols_in()
+        self.key.rank_in()
     }
 
     pub fn rank_out(&self) -> usize {
-        self.data.cols_out() - 1
+        self.key.rank_out()
+    }
+}
+
+impl<D: DataRef> AutomorphismKey<D> {
+    pub fn at(&self, row: usize, col: usize) -> GLWECiphertext<&[u8]> {
+        self.key.at(row, col)
+    }
+}
+
+impl<D: DataMut> AutomorphismKey<D> {
+    pub fn at_mut(&mut self, row: usize, col: usize) -> GLWECiphertext<&mut [u8]> {
+        self.key.at_mut(row, col)
+    }
+}
+
+impl<D: DataMut> ReaderFrom for AutomorphismKey<D> {
+    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
+        self.p = reader.read_u64::<LittleEndian>()? as i64;
+        self.key.read_from(reader)
+    }
+}
+
+impl<D: DataRef> WriterTo for AutomorphismKey<D> {
+    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
+        writer.write_u64::<LittleEndian>(self.p as u64)?;
+        self.key.write_to(writer)
     }
 }
 
-impl<D: DataMut, B: Backend> GGLWECiphertextExec<D, B> {
-    pub fn prepare<DataOther>(&mut self, module: &Module<B>, other: &GGLWECiphertext<DataOther>, scratch: &mut Scratch<B>)
+#[derive(PartialEq, Eq)]
+pub struct GLWETensorKey<D: Data> {
+    pub(crate) keys: Vec<GLWESwitchingKey<D>>,
+}
+
+impl GLWETensorKey<Vec<u8>> {
+    pub fn alloc<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
+    where
+        Module<B>: MatZnxAlloc,
+    {
+        let mut keys: Vec<GLWESwitchingKey<Vec<u8>>> = Vec::new();
+        let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
+        (0..pairs).for_each(|_| {
+            keys.push(GLWESwitchingKey::alloc(
+                module, basek, k, rows, digits, 1, rank,
+            ));
+        });
+        Self { keys: keys }
+    }
+
+    pub fn bytes_of<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
     where
-        DataOther: DataRef,
-        Module<B>: GGLWEExecLayoutFamily<B>,
+        Module<B>: MatZnxAllocBytes,
     {
-        module.vmp_prepare(&mut self.data, &other.data, scratch);
-        self.basek = other.basek;
-        self.k = other.k;
-        self.digits = other.digits;
+        let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
+        pairs * GLWESwitchingKey::<Vec<u8>>::bytes_of(module, basek, k, rows, digits, 1, rank)
+    }
+}
+
+impl<D: Data> Infos for GLWETensorKey<D> {
+    type Inner = MatZnx<D>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.keys[0].inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.keys[0].basek()
+    }
+
+    fn k(&self) -> usize {
+        self.keys[0].k()
+    }
+}
+
+impl<D: Data> GLWETensorKey<D> {
+    pub fn rank(&self) -> usize {
+        self.keys[0].rank()
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.keys[0].rank_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.keys[0].rank_out()
+    }
+
+    pub fn digits(&self) -> usize {
+        self.keys[0].digits()
+    }
+}
+
+impl<D: DataMut> GLWETensorKey<D> {
+    // Returns a mutable reference to GLWESwitchingKey_{s}(s[i] * s[j])
+    pub fn at_mut(&mut self, mut i: usize, mut j: usize) -> &mut GLWESwitchingKey<D> {
+        if i > j {
+            std::mem::swap(&mut i, &mut j);
+        };
+        let rank: usize = self.rank();
+        &mut self.keys[i * rank + j - (i * (i + 1) / 2)]
+    }
+}
+
+impl<D: DataRef> GLWETensorKey<D> {
+    // Returns a reference to GLWESwitchingKey_{s}(s[i] * s[j])
+    pub fn at(&self, mut i: usize, mut j: usize) -> &GLWESwitchingKey<D> {
+        if i > j {
+            std::mem::swap(&mut i, &mut j);
+        };
+        let rank: usize = self.rank();
+        &self.keys[i * rank + j - (i * (i + 1) / 2)]
+    }
+}
+
+impl<D: DataMut> ReaderFrom for GLWETensorKey<D> {
+    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
+        let len: usize = reader.read_u64::<LittleEndian>()? as usize;
+        if self.keys.len() != len {
+            return Err(std::io::Error::new(
+                std::io::ErrorKind::InvalidData,
+                format!("self.keys.len()={} != read len={}", self.keys.len(), len),
+            ));
+        }
+        for key in &mut self.keys {
+            key.read_from(reader)?;
+        }
+        Ok(())
+    }
+}
+
+impl<D: DataRef> WriterTo for GLWETensorKey<D> {
+    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
+        writer.write_u64::<LittleEndian>(self.keys.len() as u64)?;
+        for key in &self.keys {
+            key.write_to(writer)?;
+        }
+        Ok(())
     }
 }

@@ -0,0 +1,535 @@
+use backend::hal::{
+    api::{MatZnxAlloc, MatZnxAllocBytes, VecZnxCopy, VecZnxFillUniform},
+    layouts::{Backend, Data, DataMut, DataRef, MatZnx, Module, ReaderFrom, WriterTo},
+};
+
+use crate::{AutomorphismKey, GGLWECiphertext, GLWECiphertextCompressed, GLWESwitchingKey, GLWETensorKey, Infos};
+use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
+
+#[derive(PartialEq, Eq)]
+pub struct GGLWECiphertextCompressed<D: Data> {
+    pub(crate) data: MatZnx<D>,
+    pub(crate) basek: usize,
+    pub(crate) k: usize,
+    pub(crate) rank_out: usize,
+    pub(crate) digits: usize,
+    pub(crate) seed: Vec<[u8; 32]>,
+}
+
+impl GGLWECiphertextCompressed<Vec<u8>> {
+    pub fn alloc<B: Backend>(
+        module: &Module<B>,
+        basek: usize,
+        k: usize,
+        rows: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> Self
+    where
+        Module<B>: MatZnxAlloc,
+    {
+        let size: usize = k.div_ceil(basek);
+        debug_assert!(
+            size > digits,
+            "invalid gglwe: ceil(k/basek): {} <= digits: {}",
+            size,
+            digits
+        );
+
+        assert!(
+            rows * digits <= size,
+            "invalid gglwe: rows: {} * digits:{} > ceil(k/basek): {}",
+            rows,
+            digits,
+            size
+        );
+
+        Self {
+            data: module.mat_znx_alloc(rows, rank_in, 1, size),
+            basek: basek,
+            k,
+            rank_out,
+            digits,
+            seed: vec![[0u8; 32]; rows * rank_in],
+        }
+    }
+
+    pub fn bytes_of<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank_in: usize) -> usize
+    where
+        Module<B>: MatZnxAllocBytes,
+    {
+        let size: usize = k.div_ceil(basek);
+        debug_assert!(
+            size > digits,
+            "invalid gglwe: ceil(k/basek): {} <= digits: {}",
+            size,
+            digits
+        );
+
+        assert!(
+            rows * digits <= size,
+            "invalid gglwe: rows: {} * digits:{} > ceil(k/basek): {}",
+            rows,
+            digits,
+            size
+        );
+
+        module.mat_znx_alloc_bytes(rows, rank_in, 1, rows)
+    }
+}
+
+impl<D: Data> Infos for GGLWECiphertextCompressed<D> {
+    type Inner = MatZnx<D>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.data
+    }
+
+    fn basek(&self) -> usize {
+        self.basek
+    }
+
+    fn k(&self) -> usize {
+        self.k
+    }
+}
+
+impl<D: Data> GGLWECiphertextCompressed<D> {
+    pub fn rank(&self) -> usize {
+        self.rank_out
+    }
+
+    pub fn digits(&self) -> usize {
+        self.digits
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.data.cols_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.rank_out
+    }
+}
+
+impl<D: DataRef> GGLWECiphertextCompressed<D> {
+    pub(crate) fn at(&self, row: usize, col: usize) -> GLWECiphertextCompressed<&[u8]> {
+        GLWECiphertextCompressed {
+            data: self.data.at(row, col),
+            basek: self.basek,
+            k: self.k,
+            rank: self.rank_out,
+            seed: self.seed[self.rank_in() * row + col],
+        }
+    }
+}
+
+impl<D: DataMut> GGLWECiphertextCompressed<D> {
+    pub(crate) fn at_mut(&mut self, row: usize, col: usize) -> GLWECiphertextCompressed<&mut [u8]> {
+        let rank_in: usize = self.rank_in();
+        GLWECiphertextCompressed {
+            data: self.data.at_mut(row, col),
+            basek: self.basek,
+            k: self.k,
+            rank: self.rank_out,
+            seed: self.seed[rank_in * row + col], // Warning: value is copied and not borrow mut
+        }
+    }
+}
+
+impl<D: DataMut> ReaderFrom for GGLWECiphertextCompressed<D> {
+    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
+        self.k = reader.read_u64::<LittleEndian>()? as usize;
+        self.basek = reader.read_u64::<LittleEndian>()? as usize;
+        self.digits = reader.read_u64::<LittleEndian>()? as usize;
+        self.rank_out = reader.read_u64::<LittleEndian>()? as usize;
+        let seed_len = reader.read_u64::<LittleEndian>()? as usize;
+        if seed_len != self.seed.len() {
+        } else {
+            for s in &mut self.seed {
+                reader.read_exact(s)?;
+            }
+        }
+        self.data.read_from(reader)
+    }
+}
+
+impl<D: DataRef> WriterTo for GGLWECiphertextCompressed<D> {
+    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
+        writer.write_u64::<LittleEndian>(self.k as u64)?;
+        writer.write_u64::<LittleEndian>(self.basek as u64)?;
+        writer.write_u64::<LittleEndian>(self.digits as u64)?;
+        writer.write_u64::<LittleEndian>(self.rank_out as u64)?;
+        writer.write_u64::<LittleEndian>(self.seed.len() as u64)?;
+        for s in &self.seed {
+            writer.write_all(s)?;
+        }
+        self.data.write_to(writer)
+    }
+}
+
+impl<D: DataMut> GGLWECiphertext<D> {
+    pub fn decompress<DataOther: DataRef, B: Backend>(&mut self, module: &Module<B>, other: &GGLWECiphertextCompressed<DataOther>)
+    where
+        Module<B>: VecZnxFillUniform + VecZnxCopy,
+    {
+        #[cfg(debug_assertions)]
+        {
+            use backend::hal::api::ZnxInfos;
+
+            assert_eq!(
+                self.n(),
+                other.data.n(),
+                "invalid receiver: self.n()={} != other.n()={}",
+                self.n(),
+                other.data.n()
+            );
+            assert_eq!(
+                self.size(),
+                other.size(),
+                "invalid receiver: self.size()={} != other.size()={}",
+                self.size(),
+                other.size()
+            );
+            assert_eq!(
+                self.rank_in(),
+                other.rank_in(),
+                "invalid receiver: self.rank_in()={} != other.rank_in()={}",
+                self.rank_in(),
+                other.rank_in()
+            );
+            assert_eq!(
+                self.rank_out(),
+                other.rank_out(),
+                "invalid receiver: self.rank_out()={} != other.rank_out()={}",
+                self.rank_out(),
+                other.rank_out()
+            );
+
+            assert_eq!(
+                self.rows(),
+                other.rows(),
+                "invalid receiver: self.rows()={} != other.rows()={}",
+                self.rows(),
+                other.rows()
+            );
+        }
+
+        let rank_in: usize = self.rank_in();
+        let rows: usize = self.rows();
+
+        (0..rank_in).for_each(|col_i| {
+            (0..rows).for_each(|row_i| {
+                self.at_mut(row_i, col_i)
+                    .decompress(module, &other.at(row_i, col_i));
+            });
+        });
+    }
+}
+
+#[derive(PartialEq, Eq)]
+pub struct GLWESwitchingKeyCompressed<D: Data> {
+    pub(crate) key: GGLWECiphertextCompressed<D>,
+    pub(crate) sk_in_n: usize,  // Degree of sk_in
+    pub(crate) sk_out_n: usize, // Degree of sk_out
+}
+
+impl<D: Data> Infos for GLWESwitchingKeyCompressed<D> {
+    type Inner = MatZnx<D>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.key.inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.key.basek()
+    }
+
+    fn k(&self) -> usize {
+        self.key.k()
+    }
+}
+
+impl<D: Data> GLWESwitchingKeyCompressed<D> {
+    pub fn rank(&self) -> usize {
+        self.key.rank()
+    }
+
+    pub fn digits(&self) -> usize {
+        self.key.digits()
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.key.rank_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.key.rank_out()
+    }
+}
+
+impl GLWESwitchingKeyCompressed<Vec<u8>> {
+    pub fn alloc<B: Backend>(
+        module: &Module<B>,
+        basek: usize,
+        k: usize,
+        rows: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> Self
+    where
+        Module<B>: MatZnxAlloc,
+    {
+        GLWESwitchingKeyCompressed {
+            key: GGLWECiphertextCompressed::alloc(module, basek, k, rows, digits, rank_in, rank_out),
+            sk_in_n: 0,
+            sk_out_n: 0,
+        }
+    }
+
+    pub fn bytes_of<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank_in: usize) -> usize
+    where
+        Module<B>: MatZnxAllocBytes,
+    {
+        GGLWECiphertextCompressed::<Vec<u8>>::bytes_of(module, basek, k, rows, digits, rank_in)
+    }
+}
+
+impl<D: DataMut> ReaderFrom for GLWESwitchingKeyCompressed<D> {
+    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
+        self.sk_in_n = reader.read_u64::<LittleEndian>()? as usize;
+        self.sk_out_n = reader.read_u64::<LittleEndian>()? as usize;
+        self.key.read_from(reader)
+    }
+}
+
+impl<D: DataRef> WriterTo for GLWESwitchingKeyCompressed<D> {
+    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
+        writer.write_u64::<LittleEndian>(self.sk_in_n as u64)?;
+        writer.write_u64::<LittleEndian>(self.sk_out_n as u64)?;
+        self.key.write_to(writer)
+    }
+}
+
+impl<D: DataMut> GLWESwitchingKey<D> {
+    pub fn decompress<DataOther: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        other: &GLWESwitchingKeyCompressed<DataOther>,
+    ) where
+        Module<B>: VecZnxFillUniform + VecZnxCopy,
+    {
+        self.key.decompress(module, &other.key);
+        self.sk_in_n = other.sk_in_n;
+        self.sk_out_n = other.sk_out_n;
+    }
+}
+
+#[derive(PartialEq, Eq)]
+pub struct AutomorphismKeyCompressed<D: Data> {
+    pub(crate) key: GLWESwitchingKeyCompressed<D>,
+    pub(crate) p: i64,
+}
+
+impl AutomorphismKeyCompressed<Vec<u8>> {
+    pub fn alloc<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
+    where
+        Module<B>: MatZnxAlloc,
+    {
+        AutomorphismKeyCompressed {
+            key: GLWESwitchingKeyCompressed::alloc(module, basek, k, rows, digits, rank, rank),
+            p: 0,
+        }
+    }
+
+    pub fn bytes_of<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
+    where
+        Module<B>: MatZnxAllocBytes,
+    {
+        GLWESwitchingKeyCompressed::<Vec<u8>>::bytes_of(module, basek, k, rows, digits, rank)
+    }
+}
+
+impl<D: Data> Infos for AutomorphismKeyCompressed<D> {
+    type Inner = MatZnx<D>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.key.inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.key.basek()
+    }
+
+    fn k(&self) -> usize {
+        self.key.k()
+    }
+}
+
+impl<D: Data> AutomorphismKeyCompressed<D> {
+    pub fn rank(&self) -> usize {
+        self.key.rank()
+    }
+
+    pub fn digits(&self) -> usize {
+        self.key.digits()
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.key.rank_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.key.rank_out()
+    }
+}
+
+impl<D: DataMut> ReaderFrom for AutomorphismKeyCompressed<D> {
+    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
+        self.p = reader.read_u64::<LittleEndian>()? as i64;
+        self.key.read_from(reader)
+    }
+}
+
+impl<D: DataRef> WriterTo for AutomorphismKeyCompressed<D> {
+    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
+        writer.write_u64::<LittleEndian>(self.p as u64)?;
+        self.key.write_to(writer)
+    }
+}
+
+impl<D: DataMut> AutomorphismKey<D> {
+    pub fn decompress<DataOther: DataRef, B: Backend>(&mut self, module: &Module<B>, other: &AutomorphismKeyCompressed<DataOther>)
+    where
+        Module<B>: VecZnxFillUniform + VecZnxCopy,
+    {
+        self.key.decompress(module, &other.key);
+        self.p = other.p;
+    }
+}
+
+#[derive(PartialEq, Eq)]
+pub struct GLWETensorKeyCompressed<D: Data> {
+    pub(crate) keys: Vec<GLWESwitchingKeyCompressed<D>>,
+}
+
+impl GLWETensorKeyCompressed<Vec<u8>> {
+    pub fn alloc<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
+    where
+        Module<B>: MatZnxAlloc,
+    {
+        let mut keys: Vec<GLWESwitchingKeyCompressed<Vec<u8>>> = Vec::new();
+        let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
+        (0..pairs).for_each(|_| {
+            keys.push(GLWESwitchingKeyCompressed::alloc(
+                module, basek, k, rows, digits, 1, rank,
+            ));
+        });
+        Self { keys: keys }
+    }
+
+    pub fn bytes_of<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
+    where
+        Module<B>: MatZnxAllocBytes,
+    {
+        let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
+        pairs * GLWESwitchingKeyCompressed::<Vec<u8>>::bytes_of(module, basek, k, rows, digits, 1)
+    }
+}
+
+impl<D: Data> Infos for GLWETensorKeyCompressed<D> {
+    type Inner = MatZnx<D>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.keys[0].inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.keys[0].basek()
+    }
+
+    fn k(&self) -> usize {
+        self.keys[0].k()
+    }
+}
+
+impl<D: Data> GLWETensorKeyCompressed<D> {
+    pub fn rank(&self) -> usize {
+        self.keys[0].rank()
+    }
+
+    pub fn digits(&self) -> usize {
+        self.keys[0].digits()
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.keys[0].rank_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.keys[0].rank_out()
+    }
+}
+
+impl<D: DataMut> ReaderFrom for GLWETensorKeyCompressed<D> {
+    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
+        let len: usize = reader.read_u64::<LittleEndian>()? as usize;
+        if self.keys.len() != len {
+            return Err(std::io::Error::new(
+                std::io::ErrorKind::InvalidData,
+                format!("self.keys.len()={} != read len={}", self.keys.len(), len),
+            ));
+        }
+        for key in &mut self.keys {
+            key.read_from(reader)?;
+        }
+        Ok(())
+    }
+}
+
+impl<D: DataRef> WriterTo for GLWETensorKeyCompressed<D> {
+    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
+        writer.write_u64::<LittleEndian>(self.keys.len() as u64)?;
+        for key in &self.keys {
+            key.write_to(writer)?;
+        }
+        Ok(())
+    }
+}
+
+impl<D: DataMut> GLWETensorKeyCompressed<D> {
+    pub(crate) fn at_mut(&mut self, mut i: usize, mut j: usize) -> &mut GLWESwitchingKeyCompressed<D> {
+        if i > j {
+            std::mem::swap(&mut i, &mut j);
+        };
+        let rank: usize = self.rank();
+        &mut self.keys[i * rank + j - (i * (i + 1) / 2)]
+    }
+}
+
+impl<D: DataMut> GLWETensorKey<D> {
+    pub fn decompress<DataOther: DataRef, B: Backend>(&mut self, module: &Module<B>, other: &GLWETensorKeyCompressed<DataOther>)
+    where
+        Module<B>: VecZnxFillUniform + VecZnxCopy,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(
+                self.keys.len(),
+                other.keys.len(),
+                "invalid receiver: self.keys.len()={} != other.keys.len()={}",
+                self.keys.len(),
+                other.keys.len()
+            );
+        }
+
+        self.keys
+            .iter_mut()
+            .zip(other.keys.iter())
+            .for_each(|(a, b)| {
+                a.decompress(module, b);
+            });
+    }
+}

@@ -0,0 +1,422 @@
+use backend::hal::{
+    api::{VmpPMatAlloc, VmpPMatAllocBytes, VmpPMatPrepare},
+    layouts::{Backend, Data, DataMut, DataRef, Module, Scratch, VmpPMat},
+};
+
+use crate::{AutomorphismKey, GGLWECiphertext, GGLWEExecLayoutFamily, GLWESwitchingKey, GLWETensorKey, Infos};
+
+#[derive(PartialEq, Eq)]
+pub struct GGLWECiphertextExec<D: Data, B: Backend> {
+    pub(crate) data: VmpPMat<D, B>,
+    pub(crate) basek: usize,
+    pub(crate) k: usize,
+    pub(crate) digits: usize,
+}
+
+impl<B: Backend> GGLWECiphertextExec<Vec<u8>, B> {
+    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank_in: usize, rank_out: usize) -> Self
+    where
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        let size: usize = k.div_ceil(basek);
+        debug_assert!(
+            size > digits,
+            "invalid gglwe: ceil(k/basek): {} <= digits: {}",
+            size,
+            digits
+        );
+
+        assert!(
+            rows * digits <= size,
+            "invalid gglwe: rows: {} * digits:{} > ceil(k/basek): {}",
+            rows,
+            digits,
+            size
+        );
+
+        Self {
+            data: module.vmp_pmat_alloc(rows, rank_in, rank_out + 1, size),
+            basek: basek,
+            k,
+            digits,
+        }
+    }
+
+    pub fn bytes_of(
+        module: &Module<B>,
+        basek: usize,
+        k: usize,
+        rows: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> usize
+    where
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        let size: usize = k.div_ceil(basek);
+        debug_assert!(
+            size > digits,
+            "invalid gglwe: ceil(k/basek): {} <= digits: {}",
+            size,
+            digits
+        );
+
+        assert!(
+            rows * digits <= size,
+            "invalid gglwe: rows: {} * digits:{} > ceil(k/basek): {}",
+            rows,
+            digits,
+            size
+        );
+
+        module.vmp_pmat_alloc_bytes(rows, rank_in, rank_out + 1, rows)
+    }
+}
+
+impl<D: Data, B: Backend> Infos for GGLWECiphertextExec<D, B> {
+    type Inner = VmpPMat<D, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.data
+    }
+
+    fn basek(&self) -> usize {
+        self.basek
+    }
+
+    fn k(&self) -> usize {
+        self.k
+    }
+}
+
+impl<D: Data, B: Backend> GGLWECiphertextExec<D, B> {
+    pub fn rank(&self) -> usize {
+        self.data.cols_out() - 1
+    }
+
+    pub fn digits(&self) -> usize {
+        self.digits
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.data.cols_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.data.cols_out() - 1
+    }
+}
+
+impl<D: DataMut, B: Backend> GGLWECiphertextExec<D, B> {
+    pub fn prepare<DataOther>(&mut self, module: &Module<B>, other: &GGLWECiphertext<DataOther>, scratch: &mut Scratch<B>)
+    where
+        DataOther: DataRef,
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        module.vmp_prepare(&mut self.data, &other.data, scratch);
+        self.basek = other.basek;
+        self.k = other.k;
+        self.digits = other.digits;
+    }
+}
+
+#[derive(PartialEq, Eq)]
+pub struct GLWESwitchingKeyExec<D: Data, B: Backend> {
+    pub(crate) key: GGLWECiphertextExec<D, B>,
+    pub(crate) sk_in_n: usize,  // Degree of sk_in
+    pub(crate) sk_out_n: usize, // Degree of sk_out
+}
+
+impl<B: Backend> GLWESwitchingKeyExec<Vec<u8>, B> {
+    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank_in: usize, rank_out: usize) -> Self
+    where
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        GLWESwitchingKeyExec::<Vec<u8>, B> {
+            key: GGLWECiphertextExec::alloc(module, basek, k, rows, digits, rank_in, rank_out),
+            sk_in_n: 0,
+            sk_out_n: 0,
+        }
+    }
+
+    pub fn bytes_of(
+        module: &Module<B>,
+        basek: usize,
+        k: usize,
+        rows: usize,
+        digits: usize,
+        rank_in: usize,
+        rank_out: usize,
+    ) -> usize
+    where
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        GGLWECiphertextExec::bytes_of(module, basek, k, rows, digits, rank_in, rank_out)
+    }
+
+    pub fn from<DataOther: DataRef>(module: &Module<B>, other: &GLWESwitchingKey<DataOther>, scratch: &mut Scratch<B>) -> Self
+    where
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        let mut ksk_exec: GLWESwitchingKeyExec<Vec<u8>, B> = Self::alloc(
+            module,
+            other.basek(),
+            other.k(),
+            other.rows(),
+            other.digits(),
+            other.rank_in(),
+            other.rank_out(),
+        );
+        ksk_exec.prepare(module, other, scratch);
+        ksk_exec
+    }
+}
+
+impl<D: Data, B: Backend> Infos for GLWESwitchingKeyExec<D, B> {
+    type Inner = VmpPMat<D, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        self.key.inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.key.basek()
+    }
+
+    fn k(&self) -> usize {
+        self.key.k()
+    }
+}
+
+impl<D: Data, B: Backend> GLWESwitchingKeyExec<D, B> {
+    pub fn rank(&self) -> usize {
+        self.key.data.cols_out() - 1
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.key.data.cols_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.key.data.cols_out() - 1
+    }
+
+    pub fn digits(&self) -> usize {
+        self.key.digits()
+    }
+
+    pub fn sk_degree_in(&self) -> usize {
+        self.sk_in_n
+    }
+
+    pub fn sk_degree_out(&self) -> usize {
+        self.sk_out_n
+    }
+}
+
+impl<D: DataMut, B: Backend> GLWESwitchingKeyExec<D, B> {
+    pub fn prepare<DataOther>(&mut self, module: &Module<B>, other: &GLWESwitchingKey<DataOther>, scratch: &mut Scratch<B>)
+    where
+        DataOther: DataRef,
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        self.key.prepare(module, &other.key, scratch);
+        self.sk_in_n = other.sk_in_n;
+        self.sk_out_n = other.sk_out_n;
+    }
+}
+
+#[derive(PartialEq, Eq)]
+pub struct AutomorphismKeyExec<D: Data, B: Backend> {
+    pub(crate) key: GLWESwitchingKeyExec<D, B>,
+    pub(crate) p: i64,
+}
+
+impl<B: Backend> AutomorphismKeyExec<Vec<u8>, B> {
+    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
+    where
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        AutomorphismKeyExec::<Vec<u8>, B> {
+            key: GLWESwitchingKeyExec::alloc(module, basek, k, rows, digits, rank, rank),
+            p: 0,
+        }
+    }
+
+    pub fn bytes_of(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
+    where
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        GLWESwitchingKeyExec::<Vec<u8>, B>::bytes_of(module, basek, k, rows, digits, rank, rank)
+    }
+
+    pub fn from<DataOther: DataRef>(module: &Module<B>, other: &AutomorphismKey<DataOther>, scratch: &mut Scratch<B>) -> Self
+    where
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        let mut atk_exec: AutomorphismKeyExec<Vec<u8>, B> = Self::alloc(
+            module,
+            other.basek(),
+            other.k(),
+            other.rows(),
+            other.digits(),
+            other.rank(),
+        );
+        atk_exec.prepare(module, other, scratch);
+        atk_exec
+    }
+}
+
+impl<D: DataMut, B: Backend> AutomorphismKeyExec<D, B> {
+    pub fn prepare<DataOther>(&mut self, module: &Module<B>, other: &AutomorphismKey<DataOther>, scratch: &mut Scratch<B>)
+    where
+        DataOther: DataRef,
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        self.key.prepare(module, &other.key, scratch);
+        self.p = other.p;
+    }
+}
+
+impl<D: Data, B: Backend> Infos for AutomorphismKeyExec<D, B> {
+    type Inner = VmpPMat<D, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.key.inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.key.basek()
+    }
+
+    fn k(&self) -> usize {
+        self.key.k()
+    }
+}
+
+impl<D: Data, B: Backend> AutomorphismKeyExec<D, B> {
+    pub fn p(&self) -> i64 {
+        self.p
+    }
+
+    pub fn digits(&self) -> usize {
+        self.key.digits()
+    }
+
+    pub fn rank(&self) -> usize {
+        self.key.rank()
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.key.rank_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.key.rank_out()
+    }
+}
+
+#[derive(PartialEq, Eq)]
+pub struct GLWETensorKeyExec<D: Data, B: Backend> {
+    pub(crate) keys: Vec<GLWESwitchingKeyExec<D, B>>,
+}
+
+impl<B: Backend> GLWETensorKeyExec<Vec<u8>, B> {
+    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
+    where
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        let mut keys: Vec<GLWESwitchingKeyExec<Vec<u8>, B>> = Vec::new();
+        let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
+        (0..pairs).for_each(|_| {
+            keys.push(GLWESwitchingKeyExec::alloc(
+                module, basek, k, rows, digits, 1, rank,
+            ));
+        });
+        Self { keys }
+    }
+
+    pub fn bytes_of(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
+    where
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
+        pairs * GLWESwitchingKeyExec::<Vec<u8>, B>::bytes_of(module, basek, k, rows, digits, 1, rank)
+    }
+}
+
+impl<D: Data, B: Backend> Infos for GLWETensorKeyExec<D, B> {
+    type Inner = VmpPMat<D, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.keys[0].inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.keys[0].basek()
+    }
+
+    fn k(&self) -> usize {
+        self.keys[0].k()
+    }
+}
+
+impl<D: Data, B: Backend> GLWETensorKeyExec<D, B> {
+    pub fn rank(&self) -> usize {
+        self.keys[0].rank()
+    }
+
+    pub fn rank_in(&self) -> usize {
+        self.keys[0].rank_in()
+    }
+
+    pub fn rank_out(&self) -> usize {
+        self.keys[0].rank_out()
+    }
+
+    pub fn digits(&self) -> usize {
+        self.keys[0].digits()
+    }
+}
+
+impl<D: DataMut, B: Backend> GLWETensorKeyExec<D, B> {
+    // Returns a mutable reference to GLWESwitchingKey_{s}(s[i] * s[j])
+    pub fn at_mut(&mut self, mut i: usize, mut j: usize) -> &mut GLWESwitchingKeyExec<D, B> {
+        if i > j {
+            std::mem::swap(&mut i, &mut j);
+        };
+        let rank: usize = self.rank();
+        &mut self.keys[i * rank + j - (i * (i + 1) / 2)]
+    }
+}
+
+impl<D: DataRef, B: Backend> GLWETensorKeyExec<D, B> {
+    // Returns a reference to GLWESwitchingKey_{s}(s[i] * s[j])
+    pub fn at(&self, mut i: usize, mut j: usize) -> &GLWESwitchingKeyExec<D, B> {
+        if i > j {
+            std::mem::swap(&mut i, &mut j);
+        };
+        let rank: usize = self.rank();
+        &self.keys[i * rank + j - (i * (i + 1) / 2)]
+    }
+}
+
+impl<D: DataMut, B: Backend> GLWETensorKeyExec<D, B> {
+    pub fn prepare<DataOther>(&mut self, module: &Module<B>, other: &GLWETensorKey<DataOther>, scratch: &mut Scratch<B>)
+    where
+        DataOther: DataRef,
+        Module<B>: GGLWEExecLayoutFamily<B>,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.keys.len(), other.keys.len());
+        }
+        self.keys
+            .iter_mut()
+            .zip(other.keys.iter())
+            .for_each(|(a, b)| {
+                a.prepare(module, b, scratch);
+            });
+    }
+}

@@ -1,20 +1,16 @@
 mod automorphism;
-mod automorphism_key;
 mod encryption;
 mod external_product;
 mod keyswitch;
-mod keyswitch_key;
 mod layout;
+mod layouts_compressed;
+mod layouts_exec;
 mod noise;
-mod tensor_key;
 
-pub use automorphism_key::{AutomorphismKey, AutomorphismKeyExec};
-pub use encryption::{
-    AutomorphismKeyEncryptSkFamily, GGLWEEncryptSkFamily, GLWESwitchingKeyEncryptSkFamily, GLWETensorKeyEncryptSkFamily,
-};
-pub use keyswitch_key::{GLWESwitchingKey, GLWESwitchingKeyExec};
-pub use layout::{GGLWECiphertext, GGLWECiphertextExec, GGLWEExecLayoutFamily};
-pub use tensor_key::{GLWETensorKey, GLWETensorKeyExec};
+pub use encryption::*;
+pub use layout::*;
+pub use layouts_compressed::*;
+pub use layouts_exec::*;
 
 #[cfg(test)]
-mod test;
+mod tests;

@@ -1,223 +0,0 @@
-use backend::hal::{
-    api::{MatZnxAlloc, MatZnxAllocBytes},
-    layouts::{Backend, Data, DataMut, DataRef, MatZnx, Module, ReaderFrom, Scratch, VmpPMat, WriterTo},
-};
-
-use crate::{GGLWEExecLayoutFamily, GLWESwitchingKey, GLWESwitchingKeyExec, Infos};
-
-#[derive(PartialEq, Eq)]
-pub struct GLWETensorKey<D: Data> {
-    pub(crate) keys: Vec<GLWESwitchingKey<D>>,
-}
-
-impl GLWETensorKey<Vec<u8>> {
-    pub fn alloc<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
-    where
-        Module<B>: MatZnxAlloc,
-    {
-        let mut keys: Vec<GLWESwitchingKey<Vec<u8>>> = Vec::new();
-        let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
-        (0..pairs).for_each(|_| {
-            keys.push(GLWESwitchingKey::alloc(
-                module, basek, k, rows, digits, 1, rank,
-            ));
-        });
-        Self { keys: keys }
-    }
-
-    pub fn bytes_of<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
-    where
-        Module<B>: MatZnxAllocBytes,
-    {
-        let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
-        pairs * GLWESwitchingKey::<Vec<u8>>::bytes_of(module, basek, k, rows, digits, 1, rank)
-    }
-}
-
-impl<D: Data> Infos for GLWETensorKey<D> {
-    type Inner = MatZnx<D>;
-
-    fn inner(&self) -> &Self::Inner {
-        &self.keys[0].inner()
-    }
-
-    fn basek(&self) -> usize {
-        self.keys[0].basek()
-    }
-
-    fn k(&self) -> usize {
-        self.keys[0].k()
-    }
-}
-
-impl<D: Data> GLWETensorKey<D> {
-    pub fn rank(&self) -> usize {
-        self.keys[0].rank()
-    }
-
-    pub fn rank_in(&self) -> usize {
-        self.keys[0].rank_in()
-    }
-
-    pub fn rank_out(&self) -> usize {
-        self.keys[0].rank_out()
-    }
-
-    pub fn digits(&self) -> usize {
-        self.keys[0].digits()
-    }
-}
-
-impl<D: DataMut> GLWETensorKey<D> {
-    // Returns a mutable reference to GLWESwitchingKey_{s}(s[i] * s[j])
-    pub fn at_mut(&mut self, mut i: usize, mut j: usize) -> &mut GLWESwitchingKey<D> {
-        if i > j {
-            std::mem::swap(&mut i, &mut j);
-        };
-        let rank: usize = self.rank();
-        &mut self.keys[i * rank + j - (i * (i + 1) / 2)]
-    }
-}
-
-impl<D: DataRef> GLWETensorKey<D> {
-    // Returns a reference to GLWESwitchingKey_{s}(s[i] * s[j])
-    pub fn at(&self, mut i: usize, mut j: usize) -> &GLWESwitchingKey<D> {
-        if i > j {
-            std::mem::swap(&mut i, &mut j);
-        };
-        let rank: usize = self.rank();
-        &self.keys[i * rank + j - (i * (i + 1) / 2)]
-    }
-}
-
-use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
-
-impl<D: DataMut> ReaderFrom for GLWETensorKey<D> {
-    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
-        let len: usize = reader.read_u64::<LittleEndian>()? as usize;
-        if self.keys.len() != len {
-            return Err(std::io::Error::new(
-                std::io::ErrorKind::InvalidData,
-                format!("self.keys.len()={} != read len={}", self.keys.len(), len),
-            ));
-        }
-        for key in &mut self.keys {
-            key.read_from(reader)?;
-        }
-        Ok(())
-    }
-}
-
-impl<D: DataRef> WriterTo for GLWETensorKey<D> {
-    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
-        writer.write_u64::<LittleEndian>(self.keys.len() as u64)?;
-        for key in &self.keys {
-            key.write_to(writer)?;
-        }
-        Ok(())
-    }
-}
-
-#[derive(PartialEq, Eq)]
-pub struct GLWETensorKeyExec<D: Data, B: Backend> {
-    pub(crate) keys: Vec<GLWESwitchingKeyExec<D, B>>,
-}
-
-impl<B: Backend> GLWETensorKeyExec<Vec<u8>, B> {
-    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
-    where
-        Module<B>: GGLWEExecLayoutFamily<B>,
-    {
-        let mut keys: Vec<GLWESwitchingKeyExec<Vec<u8>, B>> = Vec::new();
-        let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
-        (0..pairs).for_each(|_| {
-            keys.push(GLWESwitchingKeyExec::alloc(
-                module, basek, k, rows, digits, 1, rank,
-            ));
-        });
-        Self { keys }
-    }
-
-    pub fn bytes_of(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
-    where
-        Module<B>: GGLWEExecLayoutFamily<B>,
-    {
-        let pairs: usize = (((rank + 1) * rank) >> 1).max(1);
-        pairs * GLWESwitchingKeyExec::<Vec<u8>, B>::bytes_of(module, basek, k, rows, digits, 1, rank)
-    }
-}
-
-impl<D: Data, B: Backend> Infos for GLWETensorKeyExec<D, B> {
-    type Inner = VmpPMat<D, B>;
-
-    fn inner(&self) -> &Self::Inner {
-        &self.keys[0].inner()
-    }
-
-    fn basek(&self) -> usize {
-        self.keys[0].basek()
-    }
-
-    fn k(&self) -> usize {
-        self.keys[0].k()
-    }
-}
-
-impl<D: Data, B: Backend> GLWETensorKeyExec<D, B> {
-    pub fn rank(&self) -> usize {
-        self.keys[0].rank()
-    }
-
-    pub fn rank_in(&self) -> usize {
-        self.keys[0].rank_in()
-    }
-
-    pub fn rank_out(&self) -> usize {
-        self.keys[0].rank_out()
-    }
-
-    pub fn digits(&self) -> usize {
-        self.keys[0].digits()
-    }
-}
-
-impl<D: DataMut, B: Backend> GLWETensorKeyExec<D, B> {
-    // Returns a mutable reference to GLWESwitchingKey_{s}(s[i] * s[j])
-    pub fn at_mut(&mut self, mut i: usize, mut j: usize) -> &mut GLWESwitchingKeyExec<D, B> {
-        if i > j {
-            std::mem::swap(&mut i, &mut j);
-        };
-        let rank: usize = self.rank();
-        &mut self.keys[i * rank + j - (i * (i + 1) / 2)]
-    }
-}
-
-impl<D: DataRef, B: Backend> GLWETensorKeyExec<D, B> {
-    // Returns a reference to GLWESwitchingKey_{s}(s[i] * s[j])
-    pub fn at(&self, mut i: usize, mut j: usize) -> &GLWESwitchingKeyExec<D, B> {
-        if i > j {
-            std::mem::swap(&mut i, &mut j);
-        };
-        let rank: usize = self.rank();
-        &self.keys[i * rank + j - (i * (i + 1) / 2)]
-    }
-}
-
-impl<D: DataMut, B: Backend> GLWETensorKeyExec<D, B> {
-    pub fn prepare<DataOther>(&mut self, module: &Module<B>, other: &GLWETensorKey<DataOther>, scratch: &mut Scratch<B>)
-    where
-        DataOther: DataRef,
-        Module<B>: GGLWEExecLayoutFamily<B>,
-    {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(self.keys.len(), other.keys.len());
-        }
-        self.keys
-            .iter_mut()
-            .zip(other.keys.iter())
-            .for_each(|(a, b)| {
-                a.prepare(module, b, scratch);
-            });
-    }
-}

@@ -1,286 +0,0 @@
-use backend::{
-    hal::{
-        api::{ModuleNew, ScalarZnxAutomorphism, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxStd, VecZnxSubScalarInplace},
-        layouts::{Module, ScratchOwned},
-    },
-    implementation::cpu_spqlios::FFT64,
-};
-use sampling::source::Source;
-
-use crate::{
-    AutomorphismKey, AutomorphismKeyExec, GLWEPlaintext, GLWESecret, GLWESecretExec, Infos, noise::log2_std_noise_gglwe_product,
-};
-
-#[test]
-fn automorphism() {
-    let log_n: usize = 8;
-    let basek: usize = 12;
-    let k_in: usize = 60;
-    let k_out: usize = 40;
-    let digits: usize = k_in.div_ceil(basek);
-    let sigma: f64 = 3.2;
-    (1..4).for_each(|rank| {
-        (2..digits + 1).for_each(|di| {
-            println!("test automorphism digits: {} rank: {}", di, rank);
-            let k_apply: usize = (digits + di) * basek;
-            test_automorphism(-1, 5, log_n, basek, di, k_in, k_out, k_apply, sigma, rank);
-        });
-    });
-}
-
-#[test]
-fn automorphism_inplace() {
-    let log_n: usize = 8;
-    let basek: usize = 12;
-    let k_in: usize = 60;
-    let digits: usize = k_in.div_ceil(basek);
-    let sigma: f64 = 3.2;
-    (1..4).for_each(|rank| {
-        (2..digits + 1).for_each(|di| {
-            println!("test automorphism digits: {} rank: {}", di, rank);
-            let k_apply: usize = (digits + di) * basek;
-            test_automorphism_inplace(-1, 5, log_n, basek, di, k_in, k_apply, sigma, rank);
-        });
-    });
-}
-
-fn test_automorphism(
-    p0: i64,
-    p1: i64,
-    log_n: usize,
-    basek: usize,
-    digits: usize,
-    k_in: usize,
-    k_out: usize,
-    k_apply: usize,
-    sigma: f64,
-    rank: usize,
-) {
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-
-    let digits_in: usize = 1;
-
-    let rows_in: usize = k_in / (basek * digits);
-    let rows_apply: usize = k_in.div_ceil(basek * digits);
-
-    let mut auto_key_in: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(&module, basek, k_in, rows_in, digits_in, rank);
-    let mut auto_key_out: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(&module, basek, k_out, rows_in, digits_in, rank);
-    let mut auto_key_apply: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(&module, basek, k_apply, rows_apply, digits, rank);
-
-    let mut source_xs: Source = Source::new([0u8; 32]);
-    let mut source_xe: Source = Source::new([0u8; 32]);
-    let mut source_xa: Source = Source::new([0u8; 32]);
-
-    let mut scratch: ScratchOwned<FFT64> = ScratchOwned::alloc(
-        AutomorphismKey::encrypt_sk_scratch_space(&module, basek, k_apply, rank)
-            | AutomorphismKey::automorphism_scratch_space(&module, basek, k_out, k_in, k_apply, digits, rank),
-    );
-
-    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(0.5, &mut source_xs);
-
-    // gglwe_{s1}(s0) = s0 -> s1
-    auto_key_in.encrypt_sk(
-        &module,
-        p0,
-        &sk,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    // gglwe_{s2}(s1) -> s1 -> s2
-    auto_key_apply.encrypt_sk(
-        &module,
-        p1,
-        &sk,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    let mut auto_key_apply_exec: AutomorphismKeyExec<Vec<u8>, FFT64> =
-        AutomorphismKeyExec::alloc(&module, basek, k_apply, rows_apply, digits, rank);
-
-    auto_key_apply_exec.prepare(&module, &auto_key_apply, scratch.borrow());
-
-    // gglwe_{s1}(s0) (x) gglwe_{s2}(s1) = gglwe_{s2}(s0)
-    auto_key_out.automorphism(
-        &module,
-        &auto_key_in,
-        &auto_key_apply_exec,
-        scratch.borrow(),
-    );
-
-    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
-
-    let mut sk_auto: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
-    sk_auto.fill_zero(); // Necessary to avoid panic of unfilled sk
-    (0..rank).for_each(|i| {
-        module.scalar_znx_automorphism(
-            module.galois_element_inv(p0 * p1),
-            &mut sk_auto.data,
-            i,
-            &sk.data,
-            i,
-        );
-    });
-
-    let sk_auto_dft: GLWESecretExec<Vec<u8>, FFT64> = GLWESecretExec::from(&module, &sk_auto);
-
-    (0..auto_key_out.rank_in()).for_each(|col_i| {
-        (0..auto_key_out.rows()).for_each(|row_i| {
-            auto_key_out
-                .at(row_i, col_i)
-                .decrypt(&module, &mut pt, &sk_auto_dft, scratch.borrow());
-
-            module.vec_znx_sub_scalar_inplace(
-                &mut pt.data,
-                0,
-                (digits_in - 1) + row_i * digits_in,
-                &sk.data,
-                col_i,
-            );
-
-            let noise_have: f64 = module.vec_znx_std(basek, &pt.data, 0).log2();
-            let noise_want: f64 = log2_std_noise_gglwe_product(
-                module.n() as f64,
-                basek * digits,
-                0.5,
-                0.5,
-                0f64,
-                sigma * sigma,
-                0f64,
-                rank as f64,
-                k_out,
-                k_apply,
-            );
-
-            assert!(
-                noise_have < noise_want + 0.5,
-                "{} {}",
-                noise_have,
-                noise_want
-            );
-        });
-    });
-}
-
-fn test_automorphism_inplace(
-    p0: i64,
-    p1: i64,
-    log_n: usize,
-    basek: usize,
-    digits: usize,
-    k_in: usize,
-    k_apply: usize,
-    sigma: f64,
-    rank: usize,
-) {
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-
-    let digits_in: usize = 1;
-
-    let rows_in: usize = k_in / (basek * digits);
-    let rows_apply: usize = k_in.div_ceil(basek * digits);
-
-    let mut auto_key: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(&module, basek, k_in, rows_in, digits_in, rank);
-    let mut auto_key_apply: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(&module, basek, k_apply, rows_apply, digits, rank);
-
-    let mut source_xs: Source = Source::new([0u8; 32]);
-    let mut source_xe: Source = Source::new([0u8; 32]);
-    let mut source_xa: Source = Source::new([0u8; 32]);
-
-    let mut scratch: ScratchOwned<FFT64> = ScratchOwned::alloc(
-        AutomorphismKey::encrypt_sk_scratch_space(&module, basek, k_apply, rank)
-            | AutomorphismKey::automorphism_inplace_scratch_space(&module, basek, k_in, k_apply, digits, rank),
-    );
-
-    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(0.5, &mut source_xs);
-
-    // gglwe_{s1}(s0) = s0 -> s1
-    auto_key.encrypt_sk(
-        &module,
-        p0,
-        &sk,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    // gglwe_{s2}(s1) -> s1 -> s2
-    auto_key_apply.encrypt_sk(
-        &module,
-        p1,
-        &sk,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    let mut auto_key_apply_exec: AutomorphismKeyExec<Vec<u8>, FFT64> =
-        AutomorphismKeyExec::alloc(&module, basek, k_apply, rows_apply, digits, rank);
-
-    auto_key_apply_exec.prepare(&module, &auto_key_apply, scratch.borrow());
-
-    // gglwe_{s1}(s0) (x) gglwe_{s2}(s1) = gglwe_{s2}(s0)
-    auto_key.automorphism_inplace(&module, &auto_key_apply_exec, scratch.borrow());
-
-    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
-
-    let mut sk_auto: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
-    sk_auto.fill_zero(); // Necessary to avoid panic of unfilled sk
-
-    (0..rank).for_each(|i| {
-        module.scalar_znx_automorphism(
-            module.galois_element_inv(p0 * p1),
-            &mut sk_auto.data,
-            i,
-            &sk.data,
-            i,
-        );
-    });
-
-    let sk_auto_dft: GLWESecretExec<Vec<u8>, FFT64> = GLWESecretExec::from(&module, &sk_auto);
-
-    (0..auto_key.rank_in()).for_each(|col_i| {
-        (0..auto_key.rows()).for_each(|row_i| {
-            auto_key
-                .at(row_i, col_i)
-                .decrypt(&module, &mut pt, &sk_auto_dft, scratch.borrow());
-            module.vec_znx_sub_scalar_inplace(
-                &mut pt.data,
-                0,
-                (digits_in - 1) + row_i * digits_in,
-                &sk.data,
-                col_i,
-            );
-
-            let noise_have: f64 = module.vec_znx_std(basek, &pt.data, 0).log2();
-            let noise_want: f64 = log2_std_noise_gglwe_product(
-                module.n() as f64,
-                basek * digits,
-                0.5,
-                0.5,
-                0f64,
-                sigma * sigma,
-                0f64,
-                rank as f64,
-                k_in,
-                k_apply,
-            );
-
-            assert!(
-                noise_have < noise_want + 0.5,
-                "{} {}",
-                noise_have,
-                noise_want
-            );
-        });
-    });
-}

@@ -1,138 +0,0 @@
-use backend::{
-    hal::{api::ModuleNew, layouts::Module},
-    implementation::cpu_spqlios::FFT64,
-};
-
-use crate::gglwe::test::gglwe_generic::{
-    test_encrypt_sk, test_external_product, test_external_product_inplace, test_keyswitch, test_keyswitch_inplace,
-};
-
-#[test]
-fn encrypt_sk() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    let basek: usize = 12;
-    let k_ksk: usize = 54;
-    let digits: usize = k_ksk / basek;
-    (1..4).for_each(|rank_in| {
-        (1..4).for_each(|rank_out| {
-            (1..digits + 1).for_each(|di| {
-                println!(
-                    "test encrypt_sk digits: {} ranks: ({} {})",
-                    di, rank_in, rank_out
-                );
-                test_encrypt_sk(&module, basek, k_ksk, di, rank_in, rank_out, 3.2);
-            });
-        });
-    });
-}
-
-#[test]
-fn keyswitch() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    let basek: usize = 12;
-    let k_in: usize = 60;
-    let digits: usize = k_in.div_ceil(basek);
-    (1..4).for_each(|rank_in_s0s1| {
-        (1..4).for_each(|rank_out_s0s1| {
-            (1..4).for_each(|rank_out_s1s2| {
-                (1..digits + 1).for_each(|di| {
-                    let k_ksk: usize = k_in + basek * di;
-                    println!(
-                        "test key_switch digits: {} ranks: ({},{},{})",
-                        di, rank_in_s0s1, rank_out_s0s1, rank_out_s1s2
-                    );
-                    let k_out: usize = k_ksk; // Better capture noise.
-                    test_keyswitch(
-                        &module,
-                        basek,
-                        k_out,
-                        k_in,
-                        k_ksk,
-                        di,
-                        rank_in_s0s1,
-                        rank_out_s0s1,
-                        rank_out_s1s2,
-                        3.2,
-                    );
-                })
-            })
-        });
-    });
-}
-
-#[test]
-fn keyswitch_inplace() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    let basek: usize = 12;
-    let k_ct: usize = 60;
-    let digits: usize = k_ct.div_ceil(basek);
-    (1..4).for_each(|rank_in_s0s1| {
-        (1..4).for_each(|rank_out_s0s1| {
-            (1..digits + 1).for_each(|di| {
-                let k_ksk: usize = k_ct + basek * di;
-                println!(
-                    "test key_switch_inplace digits: {} ranks: ({},{})",
-                    di, rank_in_s0s1, rank_out_s0s1
-                );
-                test_keyswitch_inplace(
-                    &module,
-                    basek,
-                    k_ct,
-                    k_ksk,
-                    di,
-                    rank_in_s0s1,
-                    rank_out_s0s1,
-                    3.2,
-                );
-            });
-        });
-    });
-}
-
-#[test]
-fn external_product() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    let basek: usize = 12;
-    let k_in: usize = 60;
-    let digits: usize = k_in.div_ceil(basek);
-    (1..4).for_each(|rank_in| {
-        (1..4).for_each(|rank_out| {
-            (1..digits + 1).for_each(|di| {
-                let k_ggsw: usize = k_in + basek * di;
-                println!(
-                    "test external_product digits: {} ranks: ({} {})",
-                    di, rank_in, rank_out
-                );
-                let k_out: usize = k_in; // Better capture noise.
-                test_external_product(
-                    &module, basek, k_out, k_in, k_ggsw, di, rank_in, rank_out, 3.2,
-                );
-            });
-        });
-    });
-}
-
-#[test]
-fn external_product_inplace() {
-    let log_n: usize = 5;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    let basek: usize = 12;
-    let k_ct: usize = 60;
-    let digits: usize = k_ct.div_ceil(basek);
-    (1..4).for_each(|rank_in| {
-        (1..4).for_each(|rank_out| {
-            (1..digits).for_each(|di| {
-                let k_ggsw: usize = k_ct + basek * di;
-                println!(
-                    "test external_product_inplace digits: {} ranks: ({} {})",
-                    di, rank_in, rank_out
-                );
-                test_external_product_inplace(&module, basek, k_ct, k_ggsw, di, rank_in, rank_out, 3.2);
-            });
-        });
-    });
-}

@@ -1,7 +1,8 @@
 use backend::hal::{
     api::{
         MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
-        VecZnxAlloc, VecZnxAllocBytes, VecZnxRotateInplace, VecZnxStd, VecZnxSubScalarInplace, VecZnxSwithcDegree, ZnxViewMut,
+        VecZnxAlloc, VecZnxAllocBytes, VecZnxCopy, VecZnxRotateInplace, VecZnxStd, VecZnxSubScalarInplace, VecZnxSwithcDegree,
+        ZnxViewMut,
     },
     layouts::{Backend, Module, ScalarZnx, ScalarZnxToMut, ScratchOwned},
     oep::{
@@ -13,7 +14,7 @@ use sampling::source::Source;
 
 use crate::{
     GGLWEEncryptSkFamily, GGLWEExecLayoutFamily, GGSWCiphertext, GGSWCiphertextExec, GGSWLayoutFamily, GLWEDecryptFamily,
-    GLWEExternalProductFamily, GLWEKeyswitchFamily, GLWESecret, GLWESecretExec, GLWESwitchingKey,
+    GLWEExternalProductFamily, GLWEKeyswitchFamily, GLWESecret, GLWESecretExec, GLWESwitchingKey, GLWESwitchingKeyCompressed,
     GLWESwitchingKeyEncryptSkFamily, GLWESwitchingKeyExec,
     noise::{log2_std_noise_gglwe_product, noise_ggsw_product},
 };
@@ -28,7 +29,8 @@ + VecZnxSwithcDegree
     + VecZnxAddScalarInplace
     + VecZnxStd
     + VecZnxAlloc
-    + VecZnxSubScalarInplace;
+    + VecZnxSubScalarInplace
+    + VecZnxCopy;
 
 pub(crate) trait TestScratchFamily<B: Backend> = TakeVecZnxDftImpl<B>
     + TakeVecZnxBigImpl<B>
@@ -42,7 +44,7 @@ + VecZnxDftAllocBytesImpl<B>
     + VecZnxBigAllocBytesImpl<B>
     + TakeSvpPPolImpl<B>;
 
-pub(crate) fn test_encrypt_sk<B: Backend>(
+pub(crate) fn test_gglwe_encrypt_sk<B: Backend>(
     module: &Module<B>,
     basek: usize,
     k_ksk: usize,
@@ -87,7 +89,57 @@ ksk.key
         .assert_noise(module, &sk_out_exec, &sk_in.data, sigma);
 }
 
-pub(crate) fn test_keyswitch<B: Backend>(
+pub(crate) fn test_gglwe_encrypt_sk_compressed<B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank_in: usize,
+    rank_out: usize,
+    sigma: f64,
+) where
+    Module<B>: TestModuleFamily<B>,
+    B: TestScratchFamily<B>,
+{
+    let rows: usize = (k_ksk - digits * basek) / (digits * basek);
+
+    let mut ksk_compressed: GLWESwitchingKeyCompressed<Vec<u8>> =
+        GLWESwitchingKeyCompressed::alloc(module, basek, k_ksk, rows, digits, rank_in, rank_out);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(GLWESwitchingKeyCompressed::encrypt_sk_scratch_space(
+        module, basek, k_ksk, rank_in, rank_out,
+    ));
+
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank_in);
+    sk_in.fill_ternary_prob(0.5, &mut source_xs);
+
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank_out);
+    sk_out.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_out_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk_out);
+
+    let seed_xa = [1u8; 32];
+
+    ksk_compressed.encrypt_sk(
+        module,
+        &sk_in,
+        &sk_out,
+        seed_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut ksk: GLWESwitchingKey<Vec<u8>> = GLWESwitchingKey::alloc(module, basek, k_ksk, rows, digits, rank_in, rank_out);
+    ksk.decompress(module, &ksk_compressed);
+
+    ksk.key
+        .assert_noise(module, &sk_out_exec, &sk_in.data, sigma);
+}
+
+pub(crate) fn test_gglwe_keyswitch<B: Backend>(
     module: &Module<B>,
     basek: usize,
     k_out: usize,
@@ -217,7 +269,7 @@ .key
         .assert_noise(module, &sk2_exec, &sk0.data, max_noise + 0.5);
 }
 
-pub(crate) fn test_keyswitch_inplace<B: Backend>(
+pub(crate) fn test_gglwe_keyswitch_inplace<B: Backend>(
     module: &Module<B>,
     basek: usize,
     k_ct: usize,
@@ -317,7 +369,7 @@ .key
         .assert_noise(module, &sk2_exec, &sk0.data, max_noise + 0.5);
 }
 
-pub(crate) fn test_external_product<B: Backend>(
+pub(crate) fn test_gglwe_external_product<B: Backend>(
     module: &Module<B>,
     basek: usize,
     k_out: usize,
@@ -400,7 +452,7 @@ // gglwe_(m) (x) RGSW_(X^k) = gglwe_(m * X^k)
     ct_gglwe_out.external_product(module, &ct_gglwe_in, &ct_rgsw_exec, scratch.borrow());
 
     (0..rank_in).for_each(|i| {
-        module.vec_znx_rotate_inplace(r as i64, &mut sk_in.data, i); // * X^{r}
+        module.vec_znx_rotate_inplace(r as i64, &mut sk_in.data.as_vec_znx_mut(), i); // * X^{r}
     });
 
     let var_gct_err_lhs: f64 = sigma * sigma;
@@ -429,7 +481,7 @@ .key
         .assert_noise(module, &sk_out_exec, &sk_in.data, max_noise + 0.5);
 }
 
-pub(crate) fn test_external_product_inplace<B: Backend>(
+pub(crate) fn test_gglwe_external_product_inplace<B: Backend>(
     module: &Module<B>,
     basek: usize,
     k_ct: usize,
@@ -510,7 +562,7 @@ // gglwe_(m) (x) RGSW_(X^k) = gglwe_(m * X^k)
     ct_gglwe.external_product_inplace(module, &ct_rgsw_exec, scratch.borrow());
 
     (0..rank_in).for_each(|i| {
-        module.vec_znx_rotate_inplace(r as i64, &mut sk_in.data, i); // * X^{r}
+        module.vec_znx_rotate_inplace(r as i64, &mut sk_in.data.as_vec_znx_mut(), i); // * X^{r}
     });
 
     let var_gct_err_lhs: f64 = sigma * sigma;

@@ -1,5 +0,0 @@
-mod automorphism_key;
-mod gglwe_fft64;
-mod gglwe_generic;
-mod tensor_key_fft64;
-mod tensor_key_generic;

@@ -1,16 +0,0 @@
-use backend::{
-    hal::{api::ModuleNew, layouts::Module},
-    implementation::cpu_spqlios::FFT64,
-};
-
-use crate::gglwe::test::tensor_key_generic::test_encrypt_sk;
-
-#[test]
-fn encrypt_sk() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    (1..4).for_each(|rank| {
-        println!("test encrypt_sk rank: {}", rank);
-        test_encrypt_sk(&module, 16, 54, 3.2, rank);
-    });
-}

@@ -1,113 +0,0 @@
-use backend::hal::{
-    api::{
-        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
-        VecZnxAlloc, VecZnxAllocBytes, VecZnxBigAlloc, VecZnxDftAlloc, VecZnxStd, VecZnxSubScalarInplace, VecZnxSwithcDegree,
-    },
-    layouts::{Backend, Module, ScratchOwned, VecZnxDft},
-    oep::{
-        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
-        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl, VecZnxBigAllocBytesImpl, VecZnxDftAllocBytesImpl,
-    },
-};
-use sampling::source::Source;
-
-use crate::{
-    GGLWEEncryptSkFamily, GGLWEExecLayoutFamily, GLWEDecryptFamily, GLWEPlaintext, GLWESecret, GLWESecretExec, GLWETensorKey,
-    GLWETensorKeyEncryptSkFamily, Infos,
-};
-
-pub(crate) trait TestModuleFamily<B: Backend> = GGLWEEncryptSkFamily<B>
-    + GLWEDecryptFamily<B>
-    + MatZnxAlloc
-    + ScalarZnxAlloc
-    + ScalarZnxAllocBytes
-    + VecZnxAllocBytes
-    + VecZnxSwithcDegree
-    + VecZnxAddScalarInplace
-    + VecZnxStd
-    + VecZnxAlloc
-    + VecZnxSubScalarInplace;
-
-pub(crate) trait TestScratchFamily<B: Backend> = TakeVecZnxDftImpl<B>
-    + TakeVecZnxBigImpl<B>
-    + TakeSvpPPolImpl<B>
-    + ScratchOwnedAllocImpl<B>
-    + ScratchOwnedBorrowImpl<B>
-    + ScratchAvailableImpl<B>
-    + TakeScalarZnxImpl<B>
-    + TakeVecZnxImpl<B>
-    + VecZnxDftAllocBytesImpl<B>
-    + VecZnxBigAllocBytesImpl<B>
-    + TakeSvpPPolImpl<B>;
-
-pub(crate) fn test_encrypt_sk<B: Backend>(module: &Module<B>, basek: usize, k: usize, sigma: f64, rank: usize)
-where
-    Module<B>: TestModuleFamily<B>
-        + GGLWEExecLayoutFamily<B>
-        + GLWETensorKeyEncryptSkFamily<B>
-        + GLWEDecryptFamily<B>
-        + VecZnxDftAlloc<B>
-        + VecZnxBigAlloc<B>,
-    B: TestScratchFamily<B>,
-{
-    let rows: usize = k / basek;
-
-    let mut tensor_key: GLWETensorKey<Vec<u8>> = GLWETensorKey::alloc(&module, basek, k, rows, 1, rank);
-
-    let mut source_xs: Source = Source::new([0u8; 32]);
-    let mut source_xe: Source = Source::new([0u8; 32]);
-    let mut source_xa: Source = Source::new([0u8; 32]);
-
-    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(GLWETensorKey::encrypt_sk_scratch_space(
-        module,
-        basek,
-        tensor_key.k(),
-        rank,
-    ));
-
-    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
-    sk.fill_ternary_prob(0.5, &mut source_xs);
-    let mut sk_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(&module, &sk);
-    sk_exec.prepare(module, &sk);
-
-    tensor_key.encrypt_sk(
-        module,
-        &sk,
-        &mut source_xa,
-        &mut source_xe,
-        sigma,
-        scratch.borrow(),
-    );
-
-    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k);
-
-    let mut sk_ij_dft = module.vec_znx_dft_alloc(1, 1);
-    let mut sk_ij_big = module.vec_znx_big_alloc(1, 1);
-    let mut sk_ij: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, 1);
-    let mut sk_dft: VecZnxDft<Vec<u8>, B> = module.vec_znx_dft_alloc(rank, 1);
-
-    (0..rank).for_each(|i| {
-        module.vec_znx_dft_from_vec_znx(1, 0, &mut sk_dft, i, &sk.data, i);
-    });
-
-    (0..rank).for_each(|i| {
-        (0..rank).for_each(|j| {
-            module.svp_apply(&mut sk_ij_dft, 0, &sk_exec.data, j, &sk_dft, i);
-            module.vec_znx_dft_to_vec_znx_big_tmp_a(&mut sk_ij_big, 0, &mut sk_ij_dft, 0);
-            module.vec_znx_big_normalize(basek, &mut sk_ij.data, 0, &sk_ij_big, 0, scratch.borrow());
-            (0..tensor_key.rank_in()).for_each(|col_i| {
-                (0..tensor_key.rows()).for_each(|row_i| {
-                    tensor_key
-                        .at(i, j)
-                        .at(row_i, col_i)
-                        .decrypt(&module, &mut pt, &sk_exec, scratch.borrow());
-
-                    module.vec_znx_sub_scalar_inplace(&mut pt.data, 0, row_i, &sk_ij.data, col_i);
-
-                    let std_pt: f64 = module.vec_znx_std(basek, &pt.data, 0) * (k as f64).exp2();
-                    assert!((sigma - std_pt).abs() <= 0.5, "{} {}", sigma, std_pt);
-                });
-            });
-        })
-    })
-}

@@ -0,0 +1,259 @@
+use backend::{
+    hal::{api::ModuleNew, layouts::Module},
+    implementation::cpu_spqlios::FFT64,
+};
+
+use crate::gglwe::tests::{
+    generics_automorphism_key::{
+        test_automorphisk_key_encrypt_sk, test_automorphisk_key_encrypt_sk_compressed, test_gglwe_automorphism,
+        test_gglwe_automorphism_inplace,
+    },
+    generics_gglwe::{
+        test_gglwe_encrypt_sk, test_gglwe_encrypt_sk_compressed, test_gglwe_external_product,
+        test_gglwe_external_product_inplace, test_gglwe_keyswitch, test_gglwe_keyswitch_inplace,
+    },
+    generics_tensor_key::{test_tensor_key_encrypt_sk, test_tensor_key_encrypt_sk_compressed},
+};
+
+#[test]
+fn gglwe_encrypt_sk() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_ksk: usize = 54;
+    let digits: usize = k_ksk / basek;
+    (1..4).for_each(|rank_in| {
+        (1..4).for_each(|rank_out| {
+            (1..digits + 1).for_each(|di| {
+                println!(
+                    "test gglwe_encrypt_sk digits: {} ranks: ({} {})",
+                    di, rank_in, rank_out
+                );
+                test_gglwe_encrypt_sk(&module, basek, k_ksk, di, rank_in, rank_out, 3.2);
+            });
+        });
+    });
+}
+
+#[test]
+fn gglwe_encrypt_sk_compressed() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_ksk: usize = 54;
+    let digits: usize = k_ksk / basek;
+    (1..4).for_each(|rank_in| {
+        (1..4).for_each(|rank_out| {
+            (1..digits + 1).for_each(|di| {
+                println!(
+                    "test gglwe_encrypt_sk_compressed digits: {} ranks: ({} {})",
+                    di, rank_in, rank_out
+                );
+                test_gglwe_encrypt_sk_compressed(&module, basek, k_ksk, di, rank_in, rank_out, 3.2);
+            });
+        });
+    });
+}
+
+#[test]
+fn gglwe_keyswitch() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_in: usize = 60;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank_in_s0s1| {
+        (1..4).for_each(|rank_out_s0s1| {
+            (1..4).for_each(|rank_out_s1s2| {
+                (1..digits + 1).for_each(|di| {
+                    let k_ksk: usize = k_in + basek * di;
+                    println!(
+                        "test gglwe_keyswitch digits: {} ranks: ({},{},{})",
+                        di, rank_in_s0s1, rank_out_s0s1, rank_out_s1s2
+                    );
+                    let k_out: usize = k_ksk; // Better capture noise.
+                    test_gglwe_keyswitch(
+                        &module,
+                        basek,
+                        k_out,
+                        k_in,
+                        k_ksk,
+                        di,
+                        rank_in_s0s1,
+                        rank_out_s0s1,
+                        rank_out_s1s2,
+                        3.2,
+                    );
+                })
+            })
+        });
+    });
+}
+
+#[test]
+fn gglwe_keyswitch_inplace() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_ct: usize = 60;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank_in_s0s1| {
+        (1..4).for_each(|rank_out_s0s1| {
+            (1..digits + 1).for_each(|di| {
+                let k_ksk: usize = k_ct + basek * di;
+                println!(
+                    "test gglwe_keyswitch_inplace digits: {} ranks: ({},{})",
+                    di, rank_in_s0s1, rank_out_s0s1
+                );
+                test_gglwe_keyswitch_inplace(
+                    &module,
+                    basek,
+                    k_ct,
+                    k_ksk,
+                    di,
+                    rank_in_s0s1,
+                    rank_out_s0s1,
+                    3.2,
+                );
+            });
+        });
+    });
+}
+
+#[test]
+fn gglwe_external_product() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_in: usize = 60;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank_in| {
+        (1..4).for_each(|rank_out| {
+            (1..digits + 1).for_each(|di| {
+                let k_ggsw: usize = k_in + basek * di;
+                println!(
+                    "test gglwe_external_product digits: {} ranks: ({} {})",
+                    di, rank_in, rank_out
+                );
+                let k_out: usize = k_in; // Better capture noise.
+                test_gglwe_external_product(
+                    &module, basek, k_out, k_in, k_ggsw, di, rank_in, rank_out, 3.2,
+                );
+            });
+        });
+    });
+}
+
+#[test]
+fn gglwe_external_product_inplace() {
+    let log_n: usize = 5;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_ct: usize = 60;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank_in| {
+        (1..4).for_each(|rank_out| {
+            (1..digits).for_each(|di| {
+                let k_ggsw: usize = k_ct + basek * di;
+                println!(
+                    "test gglwe_external_product_inplace digits: {} ranks: ({} {})",
+                    di, rank_in, rank_out
+                );
+                test_gglwe_external_product_inplace(&module, basek, k_ct, k_ggsw, di, rank_in, rank_out, 3.2);
+            });
+        });
+    });
+}
+
+#[test]
+fn automorphism_key_encrypt_sk() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k: usize = 60;
+    let digits: usize = k.div_ceil(basek) - 1;
+    let sigma: f64 = 3.2;
+    (1..4).for_each(|rank| {
+        (2..digits + 1).for_each(|di| {
+            println!(
+                "test automorphism key encrypt sk digits: {} rank: {}",
+                di, rank
+            );
+            test_automorphisk_key_encrypt_sk(&module, basek, k, di, rank, sigma);
+        });
+    });
+}
+
+#[test]
+fn automorphism_key_encrypt_sk_compressed() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k: usize = 60;
+    let digits: usize = k.div_ceil(basek) - 1;
+    let sigma: f64 = 3.2;
+    (1..4).for_each(|rank| {
+        (2..digits + 1).for_each(|di| {
+            println!(
+                "test automorphism key encrypt sk compressed digits: {} rank: {}",
+                di, rank
+            );
+            test_automorphisk_key_encrypt_sk_compressed(&module, basek, k, di, rank, sigma);
+        });
+    });
+}
+
+#[test]
+fn gglwe_automorphism() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_in: usize = 60;
+    let k_out: usize = 40;
+    let digits: usize = k_in.div_ceil(basek);
+    let sigma: f64 = 3.2;
+    (1..4).for_each(|rank| {
+        (2..digits + 1).for_each(|di| {
+            println!("test automorphism digits: {} rank: {}", di, rank);
+            let k_apply: usize = (digits + di) * basek;
+            test_gglwe_automorphism(&module, -1, 5, basek, di, k_in, k_out, k_apply, sigma, rank);
+        });
+    });
+}
+
+#[test]
+fn gglwe_automorphism_inplace() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_in: usize = 60;
+    let digits: usize = k_in.div_ceil(basek);
+    let sigma: f64 = 3.2;
+    (1..4).for_each(|rank| {
+        (2..digits + 1).for_each(|di| {
+            println!("test automorphism_inplace digits: {} rank: {}", di, rank);
+            let k_apply: usize = (digits + di) * basek;
+            test_gglwe_automorphism_inplace(&module, -1, 5, basek, di, k_in, k_apply, sigma, rank);
+        });
+    });
+}
+
+#[test]
+fn tensor_key_encrypt_sk() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    (1..4).for_each(|rank| {
+        println!("test encrypt_sk rank: {}", rank);
+        test_tensor_key_encrypt_sk(&module, 16, 54, 3.2, rank);
+    });
+}
+
+#[test]
+fn tensor_key_encrypt_sk_compressed() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    (1..4).for_each(|rank| {
+        println!("test encrypt_sk_compressed rank: {}", rank);
+        test_tensor_key_encrypt_sk_compressed(&module, 16, 54, 3.2, rank);
+    });
+}

@@ -0,0 +1,1 @@
+mod fft64;

@@ -0,0 +1,403 @@
+use backend::hal::{
+    api::{
+        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
+        VecZnxAlloc, VecZnxAllocBytes, VecZnxAutomorphism, VecZnxAutomorphismInplace, VecZnxCopy, VecZnxStd,
+        VecZnxSubScalarInplace, VecZnxSwithcDegree,
+    },
+    layouts::{Backend, Module, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
+    },
+};
+use sampling::source::Source;
+
+use crate::{
+    AutomorphismKey, AutomorphismKeyCompressed, AutomorphismKeyEncryptSkFamily, AutomorphismKeyExec, GGLWEExecLayoutFamily,
+    GLWEDecryptFamily, GLWEKeyswitchFamily, GLWEPlaintext, GLWESecret, GLWESecretExec, Infos,
+    noise::log2_std_noise_gglwe_product,
+};
+
+pub(crate) trait AutomorphismTestModuleFamily<B: Backend> = MatZnxAlloc
+    + AutomorphismKeyEncryptSkFamily<B>
+    + ScalarZnxAllocBytes
+    + VecZnxAllocBytes
+    + GLWEKeyswitchFamily<B>
+    + ScalarZnxAlloc
+    + VecZnxAutomorphism
+    + GGLWEExecLayoutFamily<B>
+    + VecZnxSwithcDegree
+    + VecZnxAddScalarInplace
+    + VecZnxAutomorphism
+    + VecZnxAutomorphismInplace
+    + VecZnxAlloc
+    + GLWEDecryptFamily<B>
+    + VecZnxSubScalarInplace
+    + VecZnxStd
+    + VecZnxCopy;
+pub(crate) trait AutomorphismTestScratchFamily<B: Backend> = ScratchOwnedAllocImpl<B>
+    + ScratchOwnedBorrowImpl<B>
+    + ScratchAvailableImpl<B>
+    + TakeScalarZnxImpl<B>
+    + TakeVecZnxDftImpl<B>
+    + TakeVecZnxImpl<B>
+    + TakeSvpPPolImpl<B>
+    + TakeVecZnxBigImpl<B>;
+
+pub(crate) fn test_automorphisk_key_encrypt_sk<B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) where
+    Module<B>: AutomorphismTestModuleFamily<B>,
+    B: AutomorphismTestScratchFamily<B>,
+{
+    let rows: usize = (k_ksk - digits * basek) / (digits * basek);
+
+    let mut atk: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(module, basek, k_ksk, rows, digits, rank);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(AutomorphismKey::encrypt_sk_scratch_space(
+        module, basek, k_ksk, rank,
+    ));
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+
+    let p = -5;
+
+    atk.encrypt_sk(
+        module,
+        p,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut sk_out: GLWESecret<Vec<u8>> = sk.clone();
+    (0..atk.rank()).for_each(|i| {
+        module.vec_znx_automorphism(
+            module.galois_element_inv(p),
+            &mut sk_out.data.as_vec_znx_mut(),
+            i,
+            &sk.data.as_vec_znx(),
+            i,
+        );
+    });
+    let sk_out_exec = GLWESecretExec::from(module, &sk_out);
+
+    atk.key
+        .key
+        .assert_noise(module, &sk_out_exec, &sk.data, sigma);
+}
+
+pub(crate) fn test_automorphisk_key_encrypt_sk_compressed<B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) where
+    Module<B>: AutomorphismTestModuleFamily<B>,
+    B: AutomorphismTestScratchFamily<B>,
+{
+    let rows: usize = (k_ksk - digits * basek) / (digits * basek);
+
+    let mut atk_compressed: AutomorphismKeyCompressed<Vec<u8>> =
+        AutomorphismKeyCompressed::alloc(module, basek, k_ksk, rows, digits, rank);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(AutomorphismKey::encrypt_sk_scratch_space(
+        module, basek, k_ksk, rank,
+    ));
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+
+    let p = -5;
+
+    let seed_xa: [u8; 32] = [1u8; 32];
+
+    atk_compressed.encrypt_sk(
+        module,
+        p,
+        &sk,
+        seed_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut sk_out: GLWESecret<Vec<u8>> = sk.clone();
+    (0..atk_compressed.rank()).for_each(|i| {
+        module.vec_znx_automorphism(
+            module.galois_element_inv(p),
+            &mut sk_out.data.as_vec_znx_mut(),
+            i,
+            &sk.data.as_vec_znx(),
+            i,
+        );
+    });
+    let sk_out_exec = GLWESecretExec::from(module, &sk_out);
+
+    let mut atk: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(module, basek, k_ksk, rows, digits, rank);
+    atk.decompress(module, &atk_compressed);
+
+    atk.key
+        .key
+        .assert_noise(module, &sk_out_exec, &sk.data, sigma);
+}
+
+pub(crate) fn test_gglwe_automorphism<B: Backend>(
+    module: &Module<B>,
+    p0: i64,
+    p1: i64,
+    basek: usize,
+    digits: usize,
+    k_in: usize,
+    k_out: usize,
+    k_apply: usize,
+    sigma: f64,
+    rank: usize,
+) where
+    Module<B>: AutomorphismTestModuleFamily<B>,
+    B: AutomorphismTestScratchFamily<B>,
+{
+    let digits_in: usize = 1;
+
+    let rows_in: usize = k_in / (basek * digits);
+    let rows_apply: usize = k_in.div_ceil(basek * digits);
+
+    let mut auto_key_in: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(&module, basek, k_in, rows_in, digits_in, rank);
+    let mut auto_key_out: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(&module, basek, k_out, rows_in, digits_in, rank);
+    let mut auto_key_apply: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(&module, basek, k_apply, rows_apply, digits, rank);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        AutomorphismKey::encrypt_sk_scratch_space(&module, basek, k_apply, rank)
+            | AutomorphismKey::automorphism_scratch_space(&module, basek, k_out, k_in, k_apply, digits, rank),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+
+    // gglwe_{s1}(s0) = s0 -> s1
+    auto_key_in.encrypt_sk(
+        &module,
+        p0,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    // gglwe_{s2}(s1) -> s1 -> s2
+    auto_key_apply.encrypt_sk(
+        &module,
+        p1,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut auto_key_apply_exec: AutomorphismKeyExec<Vec<u8>, B> =
+        AutomorphismKeyExec::alloc(&module, basek, k_apply, rows_apply, digits, rank);
+
+    auto_key_apply_exec.prepare(&module, &auto_key_apply, scratch.borrow());
+
+    // gglwe_{s1}(s0) (x) gglwe_{s2}(s1) = gglwe_{s2}(s0)
+    auto_key_out.automorphism(
+        &module,
+        &auto_key_in,
+        &auto_key_apply_exec,
+        scratch.borrow(),
+    );
+
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
+
+    let mut sk_auto: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_auto.fill_zero(); // Necessary to avoid panic of unfilled sk
+    (0..rank).for_each(|i| {
+        module.vec_znx_automorphism(
+            module.galois_element_inv(p0 * p1),
+            &mut sk_auto.data.as_vec_znx_mut(),
+            i,
+            &sk.data.as_vec_znx(),
+            i,
+        );
+    });
+
+    let sk_auto_dft: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(&module, &sk_auto);
+
+    (0..auto_key_out.rank_in()).for_each(|col_i| {
+        (0..auto_key_out.rows()).for_each(|row_i| {
+            auto_key_out
+                .at(row_i, col_i)
+                .decrypt(&module, &mut pt, &sk_auto_dft, scratch.borrow());
+
+            module.vec_znx_sub_scalar_inplace(
+                &mut pt.data,
+                0,
+                (digits_in - 1) + row_i * digits_in,
+                &sk.data,
+                col_i,
+            );
+
+            let noise_have: f64 = module.vec_znx_std(basek, &pt.data, 0).log2();
+            let noise_want: f64 = log2_std_noise_gglwe_product(
+                module.n() as f64,
+                basek * digits,
+                0.5,
+                0.5,
+                0f64,
+                sigma * sigma,
+                0f64,
+                rank as f64,
+                k_out,
+                k_apply,
+            );
+
+            assert!(
+                noise_have < noise_want + 0.5,
+                "{} {}",
+                noise_have,
+                noise_want
+            );
+        });
+    });
+}
+
+pub(crate) fn test_gglwe_automorphism_inplace<B: Backend>(
+    module: &Module<B>,
+    p0: i64,
+    p1: i64,
+    basek: usize,
+    digits: usize,
+    k_in: usize,
+    k_apply: usize,
+    sigma: f64,
+    rank: usize,
+) where
+    Module<B>: AutomorphismTestModuleFamily<B>,
+    B: AutomorphismTestScratchFamily<B>,
+{
+    let digits_in: usize = 1;
+
+    let rows_in: usize = k_in / (basek * digits);
+    let rows_apply: usize = k_in.div_ceil(basek * digits);
+
+    let mut auto_key: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(&module, basek, k_in, rows_in, digits_in, rank);
+    let mut auto_key_apply: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(&module, basek, k_apply, rows_apply, digits, rank);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        AutomorphismKey::encrypt_sk_scratch_space(&module, basek, k_apply, rank)
+            | AutomorphismKey::automorphism_inplace_scratch_space(&module, basek, k_in, k_apply, digits, rank),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+
+    // gglwe_{s1}(s0) = s0 -> s1
+    auto_key.encrypt_sk(
+        &module,
+        p0,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    // gglwe_{s2}(s1) -> s1 -> s2
+    auto_key_apply.encrypt_sk(
+        &module,
+        p1,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut auto_key_apply_exec: AutomorphismKeyExec<Vec<u8>, B> =
+        AutomorphismKeyExec::alloc(&module, basek, k_apply, rows_apply, digits, rank);
+
+    auto_key_apply_exec.prepare(&module, &auto_key_apply, scratch.borrow());
+
+    // gglwe_{s1}(s0) (x) gglwe_{s2}(s1) = gglwe_{s2}(s0)
+    auto_key.automorphism_inplace(&module, &auto_key_apply_exec, scratch.borrow());
+
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
+
+    let mut sk_auto: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk_auto.fill_zero(); // Necessary to avoid panic of unfilled sk
+
+    (0..rank).for_each(|i| {
+        module.vec_znx_automorphism(
+            module.galois_element_inv(p0 * p1),
+            &mut sk_auto.data.as_vec_znx_mut(),
+            i,
+            &sk.data.as_vec_znx(),
+            i,
+        );
+    });
+
+    let sk_auto_dft: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(&module, &sk_auto);
+
+    (0..auto_key.rank_in()).for_each(|col_i| {
+        (0..auto_key.rows()).for_each(|row_i| {
+            auto_key
+                .at(row_i, col_i)
+                .decrypt(&module, &mut pt, &sk_auto_dft, scratch.borrow());
+            module.vec_znx_sub_scalar_inplace(
+                &mut pt.data,
+                0,
+                (digits_in - 1) + row_i * digits_in,
+                &sk.data,
+                col_i,
+            );
+
+            let noise_have: f64 = module.vec_znx_std(basek, &pt.data, 0).log2();
+            let noise_want: f64 = log2_std_noise_gglwe_product(
+                module.n() as f64,
+                basek * digits,
+                0.5,
+                0.5,
+                0f64,
+                sigma * sigma,
+                0f64,
+                rank as f64,
+                k_in,
+                k_apply,
+            );
+
+            assert!(
+                noise_have < noise_want + 0.5,
+                "{} {}",
+                noise_have,
+                noise_want
+            );
+        });
+    });
+}

@@ -0,0 +1,211 @@
+use backend::hal::{
+    api::{
+        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
+        VecZnxAlloc, VecZnxAllocBytes, VecZnxBigAlloc, VecZnxCopy, VecZnxDftAlloc, VecZnxStd, VecZnxSubScalarInplace,
+        VecZnxSwithcDegree,
+    },
+    layouts::{Backend, Module, ScratchOwned, VecZnxDft},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl, VecZnxBigAllocBytesImpl, VecZnxDftAllocBytesImpl,
+    },
+};
+use sampling::source::Source;
+
+use crate::{
+    GGLWEEncryptSkFamily, GGLWEExecLayoutFamily, GLWEDecryptFamily, GLWEPlaintext, GLWESecret, GLWESecretExec, GLWETensorKey,
+    GLWETensorKeyCompressed, GLWETensorKeyEncryptSkFamily, Infos,
+};
+
+pub(crate) trait TestModuleFamily<B: Backend> = GGLWEEncryptSkFamily<B>
+    + GLWEDecryptFamily<B>
+    + MatZnxAlloc
+    + ScalarZnxAlloc
+    + ScalarZnxAllocBytes
+    + VecZnxAllocBytes
+    + VecZnxSwithcDegree
+    + VecZnxAddScalarInplace
+    + VecZnxStd
+    + VecZnxAlloc
+    + VecZnxSubScalarInplace;
+
+pub(crate) trait TestScratchFamily<B: Backend> = TakeVecZnxDftImpl<B>
+    + TakeVecZnxBigImpl<B>
+    + TakeSvpPPolImpl<B>
+    + ScratchOwnedAllocImpl<B>
+    + ScratchOwnedBorrowImpl<B>
+    + ScratchAvailableImpl<B>
+    + TakeScalarZnxImpl<B>
+    + TakeVecZnxImpl<B>
+    + VecZnxDftAllocBytesImpl<B>
+    + VecZnxBigAllocBytesImpl<B>
+    + TakeSvpPPolImpl<B>;
+
+pub(crate) fn test_tensor_key_encrypt_sk<B: Backend>(module: &Module<B>, basek: usize, k: usize, sigma: f64, rank: usize)
+where
+    Module<B>: TestModuleFamily<B>
+        + GGLWEExecLayoutFamily<B>
+        + GLWETensorKeyEncryptSkFamily<B>
+        + GLWEDecryptFamily<B>
+        + VecZnxDftAlloc<B>
+        + VecZnxBigAlloc<B>,
+    B: TestScratchFamily<B>,
+{
+    let rows: usize = k / basek;
+
+    let mut tensor_key: GLWETensorKey<Vec<u8>> = GLWETensorKey::alloc(&module, basek, k, rows, 1, rank);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(GLWETensorKey::encrypt_sk_scratch_space(
+        module,
+        basek,
+        tensor_key.k(),
+        rank,
+    ));
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let mut sk_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(&module, &sk);
+    sk_exec.prepare(module, &sk);
+
+    tensor_key.encrypt_sk(
+        module,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k);
+
+    let mut sk_ij_dft = module.vec_znx_dft_alloc(1, 1);
+    let mut sk_ij_big = module.vec_znx_big_alloc(1, 1);
+    let mut sk_ij: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, 1);
+    let mut sk_dft: VecZnxDft<Vec<u8>, B> = module.vec_znx_dft_alloc(rank, 1);
+
+    (0..rank).for_each(|i| {
+        module.vec_znx_dft_from_vec_znx(1, 0, &mut sk_dft, i, &sk.data.as_vec_znx(), i);
+    });
+
+    (0..rank).for_each(|i| {
+        (0..rank).for_each(|j| {
+            module.svp_apply(&mut sk_ij_dft, 0, &sk_exec.data, j, &sk_dft, i);
+            module.vec_znx_dft_to_vec_znx_big_tmp_a(&mut sk_ij_big, 0, &mut sk_ij_dft, 0);
+            module.vec_znx_big_normalize(
+                basek,
+                &mut sk_ij.data.as_vec_znx_mut(),
+                0,
+                &sk_ij_big,
+                0,
+                scratch.borrow(),
+            );
+            (0..tensor_key.rank_in()).for_each(|col_i| {
+                (0..tensor_key.rows()).for_each(|row_i| {
+                    tensor_key
+                        .at(i, j)
+                        .at(row_i, col_i)
+                        .decrypt(&module, &mut pt, &sk_exec, scratch.borrow());
+
+                    module.vec_znx_sub_scalar_inplace(&mut pt.data, 0, row_i, &sk_ij.data, col_i);
+
+                    let std_pt: f64 = module.vec_znx_std(basek, &pt.data, 0) * (k as f64).exp2();
+                    assert!((sigma - std_pt).abs() <= 0.5, "{} {}", sigma, std_pt);
+                });
+            });
+        })
+    })
+}
+
+pub(crate) fn test_tensor_key_encrypt_sk_compressed<B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    k: usize,
+    sigma: f64,
+    rank: usize,
+) where
+    Module<B>: TestModuleFamily<B>
+        + GGLWEExecLayoutFamily<B>
+        + GLWETensorKeyEncryptSkFamily<B>
+        + GLWEDecryptFamily<B>
+        + VecZnxDftAlloc<B>
+        + VecZnxBigAlloc<B>
+        + VecZnxCopy,
+    B: TestScratchFamily<B>,
+{
+    let rows: usize = k / basek;
+
+    let mut tensor_key_compressed: GLWETensorKeyCompressed<Vec<u8>> =
+        GLWETensorKeyCompressed::alloc(&module, basek, k, rows, 1, rank);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(GLWETensorKeyCompressed::encrypt_sk_scratch_space(
+        module,
+        basek,
+        tensor_key_compressed.k(),
+        rank,
+    ));
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let mut sk_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(&module, &sk);
+    sk_exec.prepare(module, &sk);
+
+    let seed_xa: [u8; 32] = [1u8; 32];
+
+    tensor_key_compressed.encrypt_sk(
+        module,
+        &sk,
+        seed_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut tensor_key: GLWETensorKey<Vec<u8>> = GLWETensorKey::alloc(&module, basek, k, rows, 1, rank);
+    tensor_key.decompress(module, &tensor_key_compressed);
+
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k);
+
+    let mut sk_ij_dft = module.vec_znx_dft_alloc(1, 1);
+    let mut sk_ij_big = module.vec_znx_big_alloc(1, 1);
+    let mut sk_ij: GLWESecret<Vec<u8>> = GLWESecret::alloc(&module, 1);
+    let mut sk_dft: VecZnxDft<Vec<u8>, B> = module.vec_znx_dft_alloc(rank, 1);
+
+    (0..rank).for_each(|i| {
+        module.vec_znx_dft_from_vec_znx(1, 0, &mut sk_dft, i, &sk.data.as_vec_znx(), i);
+    });
+
+    (0..rank).for_each(|i| {
+        (0..rank).for_each(|j| {
+            module.svp_apply(&mut sk_ij_dft, 0, &sk_exec.data, j, &sk_dft, i);
+            module.vec_znx_dft_to_vec_znx_big_tmp_a(&mut sk_ij_big, 0, &mut sk_ij_dft, 0);
+            module.vec_znx_big_normalize(
+                basek,
+                &mut sk_ij.data.as_vec_znx_mut(),
+                0,
+                &sk_ij_big,
+                0,
+                scratch.borrow(),
+            );
+            (0..tensor_key.rank_in()).for_each(|col_i| {
+                (0..tensor_key.rows()).for_each(|row_i| {
+                    tensor_key
+                        .at(i, j)
+                        .at(row_i, col_i)
+                        .decrypt(&module, &mut pt, &sk_exec, scratch.borrow());
+
+                    module.vec_znx_sub_scalar_inplace(&mut pt.data, 0, row_i, &sk_ij.data, col_i);
+
+                    let std_pt: f64 = module.vec_znx_std(basek, &pt.data, 0) * (k as f64).exp2();
+                    assert!((sigma - std_pt).abs() <= 0.5, "{} {}", sigma, std_pt);
+                });
+            });
+        })
+    })
+}

@@ -0,0 +1,4 @@
+mod cpu_spqlios;
+mod generics_automorphism_key;
+mod generics_gglwe;
+mod generics_tensor_key;

@@ -64,7 +64,7 @@
             (0..rank + 1).for_each(|col_j| {
                 // rlwe encrypt of vec_znx_pt into vec_znx_ct
 
-                self.at_mut(row_i, col_j).encrypt_sk_private(
+                self.at_mut(row_i, col_j).encrypt_sk_internal(
                     module,
                     Some((&tmp_pt, col_j)),
                     sk,

@@ -1,6 +1,6 @@
 use backend::hal::{
     api::{MatZnxAlloc, MatZnxAllocBytes, VmpPMatAlloc, VmpPMatAllocBytes, VmpPMatPrepare},
-    layouts::{Backend, Data, DataMut, DataRef, MatZnx, Module, ReaderFrom, Scratch, VmpPMat, WriterTo},
+    layouts::{Backend, Data, DataMut, DataRef, MatZnx, Module, ReaderFrom, WriterTo},
 };
 
 use crate::{GLWECiphertext, Infos};
@@ -135,125 +135,3 @@ writer.write_u64::<LittleEndian>(self.digits as u64)?;
         self.data.write_to(writer)
     }
 }
-
-#[derive(PartialEq, Eq)]
-pub struct GGSWCiphertextExec<D: Data, B: Backend> {
-    pub(crate) data: VmpPMat<D, B>,
-    pub(crate) basek: usize,
-    pub(crate) k: usize,
-    pub(crate) digits: usize,
-}
-
-impl<B: Backend> GGSWCiphertextExec<Vec<u8>, B> {
-    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
-    where
-        Module<B>: GGSWLayoutFamily<B>,
-    {
-        let size: usize = k.div_ceil(basek);
-        debug_assert!(digits > 0, "invalid ggsw: `digits` == 0");
-
-        debug_assert!(
-            size > digits,
-            "invalid ggsw: ceil(k/basek): {} <= digits: {}",
-            size,
-            digits
-        );
-
-        assert!(
-            rows * digits <= size,
-            "invalid ggsw: rows: {} * digits:{} > ceil(k/basek): {}",
-            rows,
-            digits,
-            size
-        );
-
-        Self {
-            data: module.vmp_pmat_alloc(rows, rank + 1, rank + 1, k.div_ceil(basek)),
-            basek,
-            k: k,
-            digits,
-        }
-    }
-
-    pub fn bytes_of(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
-    where
-        Module<B>: GGSWLayoutFamily<B>,
-    {
-        let size: usize = k.div_ceil(basek);
-        debug_assert!(
-            size > digits,
-            "invalid ggsw: ceil(k/basek): {} <= digits: {}",
-            size,
-            digits
-        );
-
-        assert!(
-            rows * digits <= size,
-            "invalid ggsw: rows: {} * digits:{} > ceil(k/basek): {}",
-            rows,
-            digits,
-            size
-        );
-
-        module.vmp_pmat_alloc_bytes(rows, rank + 1, rank + 1, size)
-    }
-
-    pub fn from<DataOther: DataRef>(
-        module: &Module<B>,
-        other: &GGSWCiphertext<DataOther>,
-        scratch: &mut Scratch<B>,
-    ) -> GGSWCiphertextExec<Vec<u8>, B>
-    where
-        Module<B>: GGSWLayoutFamily<B>,
-    {
-        let mut ggsw_exec: GGSWCiphertextExec<Vec<u8>, B> = Self::alloc(
-            module,
-            other.basek(),
-            other.k(),
-            other.rows(),
-            other.digits(),
-            other.rank(),
-        );
-        ggsw_exec.prepare(module, other, scratch);
-        ggsw_exec
-    }
-}
-
-impl<D: Data, B: Backend> Infos for GGSWCiphertextExec<D, B> {
-    type Inner = VmpPMat<D, B>;
-
-    fn inner(&self) -> &Self::Inner {
-        &self.data
-    }
-
-    fn basek(&self) -> usize {
-        self.basek
-    }
-
-    fn k(&self) -> usize {
-        self.k
-    }
-}
-
-impl<D: Data, B: Backend> GGSWCiphertextExec<D, B> {
-    pub fn rank(&self) -> usize {
-        self.data.cols_out() - 1
-    }
-
-    pub fn digits(&self) -> usize {
-        self.digits
-    }
-}
-
-impl<DataSelf: DataMut, B: Backend> GGSWCiphertextExec<DataSelf, B> {
-    pub fn prepare<DataOther>(&mut self, module: &Module<B>, other: &GGSWCiphertext<DataOther>, scratch: &mut Scratch<B>)
-    where
-        DataOther: DataRef,
-        Module<B>: GGSWLayoutFamily<B>,
-    {
-        module.vmp_prepare(&mut self.data, &other.data, scratch);
-        self.k = other.k;
-        self.basek = other.basek;
-        self.digits = other.digits;
-    }
-}

@@ -0,0 +1,80 @@
+use backend::hal::{
+    api::{MatZnxAlloc, MatZnxAllocBytes, VecZnxCopy, VecZnxFillUniform},
+    layouts::{Backend, Data, DataMut, DataRef, MatZnx, Module, ReaderFrom, WriterTo},
+};
+
+use crate::{GGLWECiphertextCompressed, GGSWCiphertext, Infos};
+
+#[derive(PartialEq, Eq)]
+pub struct GGSWCiphertextCompressed<D: Data> {
+    pub(crate) data: GGLWECiphertextCompressed<D>,
+}
+
+impl GGSWCiphertextCompressed<Vec<u8>> {
+    pub fn alloc<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
+    where
+        Module<B>: MatZnxAlloc,
+    {
+        GGSWCiphertextCompressed {
+            data: GGLWECiphertextCompressed::alloc(module, basek, k, rows, digits, rank, rank),
+        }
+    }
+
+    pub fn bytes_of<B: Backend>(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
+    where
+        Module<B>: MatZnxAllocBytes,
+    {
+        GGLWECiphertextCompressed::bytes_of(module, basek, k, rows, digits, rank)
+    }
+}
+
+impl<D: Data> Infos for GGSWCiphertextCompressed<D> {
+    type Inner = MatZnx<D>;
+
+    fn inner(&self) -> &Self::Inner {
+        self.data.inner()
+    }
+
+    fn basek(&self) -> usize {
+        self.data.basek()
+    }
+
+    fn k(&self) -> usize {
+        self.data.k()
+    }
+}
+
+impl<D: Data> GGSWCiphertextCompressed<D> {
+    pub fn rank(&self) -> usize {
+        self.data.rank()
+    }
+
+    pub fn digits(&self) -> usize {
+        self.data.digits()
+    }
+}
+
+impl<D: DataMut> ReaderFrom for GGSWCiphertextCompressed<D> {
+    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
+        self.data.read_from(reader)
+    }
+}
+
+impl<D: DataRef> WriterTo for GGSWCiphertextCompressed<D> {
+    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
+        self.data.write_to(writer)
+    }
+}
+
+impl<D: DataMut> GGSWCiphertext<D> {
+    pub fn decompress<DataOther: DataRef, B: Backend>(&mut self, module: &Module<B>, other: &GGSWCiphertextCompressed<DataOther>)
+    where
+        Module<B>: VecZnxFillUniform + VecZnxCopy,
+    {
+        let rows = self.rows();
+        (0..rows).for_each(|row_i| {
+            self.at_mut(row_i, 0)
+                .decompress(module, &other.data.at(row_i, 0));
+        });
+    }
+}

@@ -0,0 +1,128 @@
+use backend::hal::{
+    api::{VmpPMatAlloc, VmpPMatAllocBytes, VmpPMatPrepare},
+    layouts::{Backend, Data, DataMut, DataRef, Module, Scratch, VmpPMat},
+};
+
+use crate::{GGSWCiphertext, GGSWLayoutFamily, Infos};
+
+#[derive(PartialEq, Eq)]
+pub struct GGSWCiphertextExec<D: Data, B: Backend> {
+    pub(crate) data: VmpPMat<D, B>,
+    pub(crate) basek: usize,
+    pub(crate) k: usize,
+    pub(crate) digits: usize,
+}
+
+impl<B: Backend> GGSWCiphertextExec<Vec<u8>, B> {
+    pub fn alloc(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> Self
+    where
+        Module<B>: GGSWLayoutFamily<B>,
+    {
+        let size: usize = k.div_ceil(basek);
+        debug_assert!(digits > 0, "invalid ggsw: `digits` == 0");
+
+        debug_assert!(
+            size > digits,
+            "invalid ggsw: ceil(k/basek): {} <= digits: {}",
+            size,
+            digits
+        );
+
+        assert!(
+            rows * digits <= size,
+            "invalid ggsw: rows: {} * digits:{} > ceil(k/basek): {}",
+            rows,
+            digits,
+            size
+        );
+
+        Self {
+            data: module.vmp_pmat_alloc(rows, rank + 1, rank + 1, k.div_ceil(basek)),
+            basek,
+            k: k,
+            digits,
+        }
+    }
+
+    pub fn bytes_of(module: &Module<B>, basek: usize, k: usize, rows: usize, digits: usize, rank: usize) -> usize
+    where
+        Module<B>: GGSWLayoutFamily<B>,
+    {
+        let size: usize = k.div_ceil(basek);
+        debug_assert!(
+            size > digits,
+            "invalid ggsw: ceil(k/basek): {} <= digits: {}",
+            size,
+            digits
+        );
+
+        assert!(
+            rows * digits <= size,
+            "invalid ggsw: rows: {} * digits:{} > ceil(k/basek): {}",
+            rows,
+            digits,
+            size
+        );
+
+        module.vmp_pmat_alloc_bytes(rows, rank + 1, rank + 1, size)
+    }
+
+    pub fn from<DataOther: DataRef>(
+        module: &Module<B>,
+        other: &GGSWCiphertext<DataOther>,
+        scratch: &mut Scratch<B>,
+    ) -> GGSWCiphertextExec<Vec<u8>, B>
+    where
+        Module<B>: GGSWLayoutFamily<B>,
+    {
+        let mut ggsw_exec: GGSWCiphertextExec<Vec<u8>, B> = Self::alloc(
+            module,
+            other.basek(),
+            other.k(),
+            other.rows(),
+            other.digits(),
+            other.rank(),
+        );
+        ggsw_exec.prepare(module, other, scratch);
+        ggsw_exec
+    }
+}
+
+impl<D: Data, B: Backend> Infos for GGSWCiphertextExec<D, B> {
+    type Inner = VmpPMat<D, B>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.data
+    }
+
+    fn basek(&self) -> usize {
+        self.basek
+    }
+
+    fn k(&self) -> usize {
+        self.k
+    }
+}
+
+impl<D: Data, B: Backend> GGSWCiphertextExec<D, B> {
+    pub fn rank(&self) -> usize {
+        self.data.cols_out() - 1
+    }
+
+    pub fn digits(&self) -> usize {
+        self.digits
+    }
+}
+
+impl<DataSelf: DataMut, B: Backend> GGSWCiphertextExec<DataSelf, B> {
+    pub fn prepare<DataOther>(&mut self, module: &Module<B>, other: &GGSWCiphertext<DataOther>, scratch: &mut Scratch<B>)
+    where
+        DataOther: DataRef,
+        Module<B>: GGSWLayoutFamily<B>,
+    {
+        module.vmp_prepare(&mut self.data, &other.data, scratch);
+        self.k = other.k;
+        self.basek = other.basek;
+        self.digits = other.digits;
+    }
+}

@@ -3,12 +3,16 @@ mod encryption;
 mod external_product;
 mod keyswitch;
 mod layout;
+mod layout_compressed;
+mod layout_exec;
 mod noise;
 
-pub use encryption::GGSWEncryptSkFamily;
-pub use keyswitch::GGSWKeySwitchFamily;
-pub use layout::{GGSWCiphertext, GGSWCiphertextExec, GGSWLayoutFamily};
-pub use noise::GGSWAssertNoiseFamily;
+pub use encryption::*;
+pub use keyswitch::*;
+pub use layout::*;
+pub use layout_compressed::*;
+pub use layout_exec::*;
+pub use noise::*;
 
 #[cfg(test)]
 mod test;

@@ -0,0 +1,1 @@
+mod fft64;

@@ -1,8 +1,8 @@
 use backend::hal::{
     api::{
-        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScalarZnxAutomorphism, ScalarZnxAutomorphismInplace, ScratchOwnedAlloc,
-        ScratchOwnedBorrow, VecZnxAddScalarInplace, VecZnxAlloc, VecZnxAllocBytes, VecZnxAutomorphismInplace,
-        VecZnxRotateInplace, VecZnxStd, VecZnxSubABInplace, VecZnxSwithcDegree, ZnxViewMut,
+        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
+        VecZnxAlloc, VecZnxAllocBytes, VecZnxAutomorphism, VecZnxAutomorphismInplace, VecZnxRotateInplace, VecZnxStd,
+        VecZnxSubABInplace, VecZnxSwithcDegree, ZnxViewMut,
     },
     layouts::{Backend, Module, ScalarZnx, ScalarZnxToMut, ScratchOwned},
     oep::{
@@ -321,8 +321,8 @@ + GLWETensorKeyEncryptSkFamily<B>
         + GGLWEExecLayoutFamily<B>
         + VecZnxSwithcDegree
         + VecZnxAutomorphismInplace
-        + ScalarZnxAutomorphismInplace
-        + ScalarZnxAutomorphism,
+        + VecZnxAutomorphismInplace
+        + VecZnxAutomorphism,
     B: TestScratchFamily<B>,
 {
     let rows: usize = k_in.div_ceil(basek * digits);
@@ -393,7 +393,7 @@ tsk_exec.prepare(module, &tensor_key, scratch.borrow());
 
     ct_out.automorphism(module, &ct_in, &auto_key_exec, &tsk_exec, scratch.borrow());
 
-    module.scalar_znx_automorphism_inplace(p, &mut pt_scalar, 0);
+    module.vec_znx_automorphism_inplace(p, &mut pt_scalar.as_vec_znx_mut(), 0);
 
     let max_noise = |col_j: usize| -> f64 {
         noise_ggsw_keyswitch(
@@ -433,8 +433,8 @@ + GLWETensorKeyEncryptSkFamily<B>
         + GGLWEExecLayoutFamily<B>
         + VecZnxSwithcDegree
         + VecZnxAutomorphismInplace
-        + ScalarZnxAutomorphismInplace
-        + ScalarZnxAutomorphism,
+        + VecZnxAutomorphism
+        + VecZnxAutomorphismInplace,
     B: TestScratchFamily<B>,
 {
     let rows: usize = k_ct.div_ceil(digits * basek);
@@ -501,7 +501,7 @@ tsk_exec.prepare(module, &tensor_key, scratch.borrow());
 
     ct.automorphism_inplace(module, &auto_key_exec, &tsk_exec, scratch.borrow());
 
-    module.scalar_znx_automorphism_inplace(p, &mut pt_scalar, 0);
+    module.vec_znx_automorphism_inplace(p, &mut pt_scalar.as_vec_znx_mut(), 0);
 
     let max_noise = |col_j: usize| -> f64 {
         noise_ggsw_keyswitch(
@@ -595,7 +595,7 @@ ct_rhs_exec.prepare(module, &ct_ggsw_rhs, scratch.borrow());
 
     ct_ggsw_lhs_out.external_product(module, &ct_ggsw_lhs_in, &ct_rhs_exec, scratch.borrow());
 
-    module.vec_znx_rotate_inplace(k as i64, &mut pt_ggsw_lhs, 0);
+    module.vec_znx_rotate_inplace(k as i64, &mut pt_ggsw_lhs.as_vec_znx_mut(), 0);
 
     let var_gct_err_lhs: f64 = sigma * sigma;
     let var_gct_err_rhs: f64 = 0f64;
@@ -695,7 +695,7 @@ ct_rhs_exec.prepare(module, &ct_ggsw_rhs, scratch.borrow());
 
     ct_ggsw_lhs.external_product_inplace(module, &ct_rhs_exec, scratch.borrow());
 
-    module.vec_znx_rotate_inplace(k as i64, &mut pt_ggsw_lhs, 0);
+    module.vec_znx_rotate_inplace(k as i64, &mut pt_ggsw_lhs.as_vec_znx_mut(), 0);
 
     let var_gct_err_lhs: f64 = sigma * sigma;
     let var_gct_err_rhs: f64 = 0f64;

@@ -1,2 +1,2 @@
+mod cpu_spqlios;
 mod generic_tests;
-mod test_fft64;

@@ -3,13 +3,17 @@ api::{
         ScalarZnxAllocBytes, ScratchAvailable, SvpApply, SvpApplyInplace, SvpPPolAllocBytes, SvpPrepare, TakeScalarZnx,
         TakeSvpPPol, TakeVecZnx, TakeVecZnxDft, VecZnxAddInplace, VecZnxAddNormal, VecZnxBigAddNormal, VecZnxBigAddSmallInplace,
         VecZnxBigAllocBytes, VecZnxBigNormalize, VecZnxDftAllocBytes, VecZnxDftFromVecZnx, VecZnxDftToVecZnxBigConsume,
-        VecZnxFillUniform, VecZnxNormalize, VecZnxNormalizeInplace, VecZnxNormalizeTmpBytes, VecZnxSubABInplace, ZnxZero,
+        VecZnxFillUniform, VecZnxNormalize, VecZnxNormalizeInplace, VecZnxNormalizeTmpBytes, VecZnxSubABInplace, ZnxInfos,
+        ZnxZero,
     },
-    layouts::{Backend, DataMut, DataRef, Module, Scratch, VecZnxBig},
+    layouts::{Backend, DataMut, DataRef, Module, Scratch, VecZnx, VecZnxBig},
 };
 use sampling::source::Source;
 
-use crate::{GLWECiphertext, GLWEPlaintext, GLWEPublicKeyExec, GLWESecretExec, Infos, SIX_SIGMA, dist::Distribution};
+use crate::{
+    GLWECiphertext, GLWECiphertextCompressed, GLWEPlaintext, GLWEPublicKeyExec, GLWESecretExec, Infos, SIX_SIGMA,
+    dist::Distribution,
+};
 
 pub trait GLWEEncryptSkFamily<B: Backend> = VecZnxDftAllocBytes
     + VecZnxBigNormalize<B>
@@ -71,7 +75,20 @@ ) where
         Module<B>: GLWEEncryptSkFamily<B>,
         Scratch<B>: TakeVecZnxDft<B> + ScratchAvailable + TakeVecZnx<B>,
     {
-        self.encrypt_sk_private(
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), sk.rank());
+            assert_eq!(sk.n(), self.n());
+            assert_eq!(pt.n(), self.n());
+            assert!(
+                scratch.available() >= GLWECiphertext::encrypt_sk_scratch_space(module, self.basek(), self.k()),
+                "scratch.available(): {} < GLWECiphertext::encrypt_sk_scratch_space: {}",
+                scratch.available(),
+                GLWECiphertext::encrypt_sk_scratch_space(module, self.basek(), self.k())
+            )
+        }
+
+        self.encrypt_sk_internal(
             module,
             Some((pt, 0)),
             sk,
@@ -94,7 +111,18 @@ ) where
         Module<B>: GLWEEncryptSkFamily<B>,
         Scratch<B>: TakeVecZnxDft<B> + ScratchAvailable + TakeVecZnx<B>,
     {
-        self.encrypt_sk_private(
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), sk.rank());
+            assert_eq!(sk.n(), self.n());
+            assert!(
+                scratch.available() >= GLWECiphertext::encrypt_sk_scratch_space(module, self.basek(), self.k()),
+                "scratch.available(): {} < GLWECiphertext::encrypt_sk_scratch_space: {}",
+                scratch.available(),
+                GLWECiphertext::encrypt_sk_scratch_space(module, self.basek(), self.k())
+            )
+        }
+        self.encrypt_sk_internal(
             module,
             None::<(&GLWEPlaintext<Vec<u8>>, usize)>,
             sk,
@@ -105,6 +133,34 @@ scratch,
         );
     }
 
+    pub(crate) fn encrypt_sk_internal<DataPt: DataRef, DataSk: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        pt: Option<(&GLWEPlaintext<DataPt>, usize)>,
+        sk: &GLWESecretExec<DataSk, B>,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch<B>,
+    ) where
+        Module<B>: GLWEEncryptSkFamily<B>,
+        Scratch<B>: TakeVecZnxDft<B> + ScratchAvailable + TakeVecZnx<B>,
+    {
+        encrypt_sk_internal(
+            module,
+            self.basek(),
+            self.k(),
+            &mut self.data,
+            false,
+            pt,
+            sk,
+            source_xa,
+            source_xe,
+            sigma,
+            scratch,
+        );
+    }
+
     pub fn encrypt_pk<DataPt: DataRef, DataPk: DataRef, B: Backend>(
         &mut self,
         module: &Module<B>,
@@ -118,7 +174,7 @@ ) where
         Module<B>: GLWEEncryptPkFamily<B>,
         Scratch<B>: TakeVecZnxDft<B> + TakeSvpPPol<B> + TakeScalarZnx<B>,
     {
-        self.encrypt_pk_private::<DataPt, DataPk, B>(
+        self.encrypt_pk_internal::<DataPt, DataPk, B>(
             module,
             Some((pt, 0)),
             pk,
@@ -141,7 +197,7 @@ ) where
         Module<B>: GLWEEncryptPkFamily<B>,
         Scratch<B>: TakeVecZnxDft<B> + TakeSvpPPol<B> + TakeScalarZnx<B>,
     {
-        self.encrypt_pk_private::<Vec<u8>, DataPk, B>(
+        self.encrypt_pk_internal::<Vec<u8>, DataPk, B>(
             module,
             None::<(&GLWEPlaintext<Vec<u8>>, usize)>,
             pk,
@@ -152,89 +208,7 @@ scratch,
         );
     }
 
-    pub(crate) fn encrypt_sk_private<DataPt: DataRef, DataSk: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        pt: Option<(&GLWEPlaintext<DataPt>, usize)>,
-        sk: &GLWESecretExec<DataSk, B>,
-        source_xa: &mut Source,
-        source_xe: &mut Source,
-        sigma: f64,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: GLWEEncryptSkFamily<B>,
-        Scratch<B>: TakeVecZnxDft<B> + ScratchAvailable + TakeVecZnx<B>,
-    {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(self.rank(), sk.rank());
-            assert_eq!(sk.n(), module.n());
-            assert_eq!(self.n(), module.n());
-            if let Some((pt, col)) = pt {
-                assert_eq!(pt.n(), module.n());
-                assert!(col < self.rank() + 1);
-            }
-            assert!(
-                scratch.available() >= GLWECiphertext::encrypt_sk_scratch_space(module, self.basek(), self.k()),
-                "scratch.available(): {} < GLWECiphertext::encrypt_sk_scratch_space: {}",
-                scratch.available(),
-                GLWECiphertext::encrypt_sk_scratch_space(module, self.basek(), self.k())
-            )
-        }
-
-        let basek: usize = self.basek();
-        let k: usize = self.k();
-        let size: usize = self.size();
-        let cols: usize = self.rank() + 1;
-
-        let (mut c0, scratch_1) = scratch.take_vec_znx(module, 1, size);
-        c0.zero();
-
-        {
-            // c[i] = uniform
-            // c[0] -= c[i] * s[i],
-            (1..cols).for_each(|i| {
-                let (mut ci_dft, scratch_2) = scratch_1.take_vec_znx_dft(module, 1, size);
-
-                // c[i] = uniform
-                module.vec_znx_fill_uniform(basek, &mut self.data, i, k, source_xa);
-
-                // c[i] = norm(IDFT(DFT(c[i]) * DFT(s[i])))
-                module.vec_znx_dft_from_vec_znx(1, 0, &mut ci_dft, 0, &self.data, i);
-                module.svp_apply_inplace(&mut ci_dft, 0, &sk.data, i - 1);
-                let ci_big: VecZnxBig<&mut [u8], B> = module.vec_znx_dft_to_vec_znx_big_consume(ci_dft);
-
-                // use c[0] as buffer, which is overwritten later by the normalization step
-                module.vec_znx_big_normalize(basek, &mut self.data, 0, &ci_big, 0, scratch_2);
-
-                // c0_tmp = -c[i] * s[i] (use c[0] as buffer)
-                module.vec_znx_sub_ab_inplace(&mut c0, 0, &self.data, 0);
-
-                // c[i] += m if col = i
-                if let Some((pt, col)) = pt {
-                    if i == col {
-                        module.vec_znx_add_inplace(&mut self.data, i, &pt.data, 0);
-                        module.vec_znx_normalize_inplace(basek, &mut self.data, i, scratch_2);
-                    }
-                }
-            });
-        }
-
-        // c[0] += e
-        module.vec_znx_add_normal(basek, &mut c0, 0, k, source_xe, sigma, sigma * SIX_SIGMA);
-
-        // c[0] += m if col = 0
-        if let Some((pt, col)) = pt {
-            if col == 0 {
-                module.vec_znx_add_inplace(&mut c0, 0, &pt.data, 0);
-            }
-        }
-
-        // c[0] = norm(c[0])
-        module.vec_znx_normalize(basek, &mut self.data, 0, &c0, 0, scratch_1);
-    }
-
-    pub(crate) fn encrypt_pk_private<DataPt: DataRef, DataPk: DataRef, B: Backend>(
+    pub(crate) fn encrypt_pk_internal<DataPt: DataRef, DataPk: DataRef, B: Backend>(
         &mut self,
         module: &Module<B>,
         pt: Option<(&GLWEPlaintext<DataPt>, usize)>,
@@ -323,3 +297,158 @@ module.vec_znx_big_normalize(basek, &mut self.data, i, &ci_big, 0, scratch_2);
         });
     }
 }
+
+impl GLWECiphertextCompressed<Vec<u8>> {
+    pub fn encrypt_sk_scratch_space<B: Backend>(module: &Module<B>, basek: usize, k: usize) -> usize
+    where
+        Module<B>: GLWEEncryptSkFamily<B>,
+    {
+        GLWECiphertext::encrypt_sk_scratch_space(module, basek, k)
+    }
+}
+impl<D: DataMut> GLWECiphertextCompressed<D> {
+    pub fn encrypt_sk<DataPt: DataRef, DataSk: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        pt: &GLWEPlaintext<DataPt>,
+        sk: &GLWESecretExec<DataSk, B>,
+        seed_xa: [u8; 32],
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch<B>,
+    ) where
+        Module<B>: GLWEEncryptSkFamily<B>,
+        Scratch<B>: TakeVecZnxDft<B> + ScratchAvailable + TakeVecZnx<B>,
+    {
+        self.encrypt_sk_internal(
+            module,
+            Some((pt, 0)),
+            sk,
+            seed_xa,
+            source_xe,
+            sigma,
+            scratch,
+        );
+    }
+
+    pub(crate) fn encrypt_sk_internal<DataPt: DataRef, DataSk: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        pt: Option<(&GLWEPlaintext<DataPt>, usize)>,
+        sk: &GLWESecretExec<DataSk, B>,
+        seed_xa: [u8; 32],
+        source_xe: &mut Source,
+        sigma: f64,
+        scratch: &mut Scratch<B>,
+    ) where
+        Module<B>: GLWEEncryptSkFamily<B>,
+        Scratch<B>: TakeVecZnxDft<B> + ScratchAvailable + TakeVecZnx<B>,
+    {
+        let mut source_xa = Source::new(seed_xa);
+        encrypt_sk_internal(
+            module,
+            self.basek(),
+            self.k(),
+            &mut self.data,
+            true,
+            pt,
+            sk,
+            &mut source_xa,
+            source_xe,
+            sigma,
+            scratch,
+        );
+        self.seed = seed_xa;
+    }
+}
+
+pub(crate) fn encrypt_sk_internal<DataCt: DataMut, DataPt: DataRef, DataSk: DataRef, B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    k: usize,
+    ct: &mut VecZnx<DataCt>,
+    compressed: bool,
+    pt: Option<(&GLWEPlaintext<DataPt>, usize)>,
+    sk: &GLWESecretExec<DataSk, B>,
+    source_xa: &mut Source,
+    source_xe: &mut Source,
+    sigma: f64,
+    scratch: &mut Scratch<B>,
+) where
+    Module<B>: GLWEEncryptSkFamily<B>,
+    Scratch<B>: TakeVecZnxDft<B> + ScratchAvailable + TakeVecZnx<B>,
+{
+    #[cfg(debug_assertions)]
+    {
+        if compressed {
+            if let Some((_, col)) = pt {
+                assert_eq!(
+                    col, 0,
+                    "invalid plaintext: cannot put pt in col>0 if compressed encryption"
+                )
+            }
+            assert_eq!(
+                ct.cols(),
+                1,
+                "invalid ciphertext: compressed tag=true but #cols={} != 1",
+                ct.cols()
+            )
+        }
+    }
+
+    let size: usize = ct.size();
+    let cols: usize = ct.cols();
+
+    let (mut c0, scratch_1) = scratch.take_vec_znx(module, 1, size);
+    c0.zero();
+
+    {
+        // c[i] = uniform
+        // c[0] -= c[i] * s[i],
+        (1..cols).for_each(|i| {
+            let col_ct: usize;
+            if compressed {
+                col_ct = 0;
+            } else {
+                col_ct = i;
+            }
+
+            let (mut ci_dft, scratch_2) = scratch_1.take_vec_znx_dft(module, 1, size);
+
+            // c[i] = uniform
+            module.vec_znx_fill_uniform(basek, ct, col_ct, k, source_xa);
+
+            // c[i] = norm(IDFT(DFT(c[i]) * DFT(s[i])))
+            module.vec_znx_dft_from_vec_znx(1, 0, &mut ci_dft, 0, ct, col_ct);
+            module.svp_apply_inplace(&mut ci_dft, 0, &sk.data, i - 1);
+            let ci_big: VecZnxBig<&mut [u8], B> = module.vec_znx_dft_to_vec_znx_big_consume(ci_dft);
+
+            // use c[0] as buffer, which is overwritten later by the normalization step
+            module.vec_znx_big_normalize(basek, ct, 0, &ci_big, 0, scratch_2);
+
+            // c0_tmp = -c[i] * s[i] (use c[0] as buffer)
+            module.vec_znx_sub_ab_inplace(&mut c0, 0, ct, 0);
+
+            // c[i] += m if col = i
+            // note: case cannot happen if compressed = true
+            if let Some((pt, col)) = pt {
+                if i == col {
+                    module.vec_znx_add_inplace(ct, i, &pt.data, 0);
+                }
+            }
+        });
+    }
+
+    // c[0] += e
+    module.vec_znx_add_normal(basek, &mut c0, 0, k, source_xe, sigma, sigma * SIX_SIGMA);
+
+    // c[0] += m if col = 0
+    if let Some((pt, col)) = pt {
+        if col == 0 {
+            module.vec_znx_add_inplace(&mut c0, 0, &pt.data, 0);
+        }
+    }
+
+    // c[0] = norm(c[0])
+    module.vec_znx_normalize(basek, ct, 0, &c0, 0, scratch_1);
+}

@@ -1,15 +1,52 @@
+use std::fmt::Debug;
+
 use backend::hal::{
-    api::{VecZnxAlloc, VecZnxAllocBytes},
+    api::{FillUniform, VecZnxAlloc, VecZnxAllocBytes, VecZnxCopy, VecZnxFillUniform, ZnxInfos, ZnxZero},
     layouts::{Backend, Data, DataMut, DataRef, Module, ReaderFrom, VecZnx, VecZnxToMut, VecZnxToRef, WriterTo},
 };
+use sampling::source::Source;
 
 use crate::{GLWEOps, Infos, SetMetaData};
 
-#[derive(PartialEq, Eq)]
+#[derive(PartialEq, Eq, Clone)]
 pub struct GLWECiphertext<D: Data> {
     pub data: VecZnx<D>,
     pub basek: usize,
     pub k: usize,
+}
+
+impl<D: DataRef> Debug for GLWECiphertext<D> {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        write!(
+            f,
+            "GLWECiphertext: basek={} k={}: {}",
+            self.basek(),
+            self.k(),
+            self.data
+        )
+    }
+}
+
+impl<D: DataMut> ZnxZero for GLWECiphertext<D>
+where
+    VecZnx<D>: ZnxZero,
+{
+    fn zero(&mut self) {
+        self.data.zero()
+    }
+
+    fn zero_at(&mut self, i: usize, j: usize) {
+        self.data.zero_at(i, j);
+    }
+}
+
+impl<D: DataMut> FillUniform for GLWECiphertext<D>
+where
+    VecZnx<D>: FillUniform,
+{
+    fn fill_uniform(&mut self, source: &mut Source) {
+        self.data.fill_uniform(source);
+    }
 }
 
 impl GLWECiphertext<Vec<u8>> {
@@ -121,3 +158,165 @@ writer.write_u64::<LittleEndian>(self.basek as u64)?;
         self.data.write_to(writer)
     }
 }
+
+#[derive(PartialEq, Eq, Clone)]
+pub struct GLWECiphertextCompressed<D: Data> {
+    pub(crate) data: VecZnx<D>,
+    pub(crate) basek: usize,
+    pub(crate) k: usize,
+    pub(crate) rank: usize,
+    pub(crate) seed: [u8; 32],
+}
+
+impl<D: DataRef> Debug for GLWECiphertextCompressed<D> {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        write!(
+            f,
+            "GLWECiphertext: basek={} k={}: {}",
+            self.basek(),
+            self.k(),
+            self.data
+        )
+    }
+}
+
+impl<D: DataMut> ZnxZero for GLWECiphertextCompressed<D>
+where
+    VecZnx<D>: ZnxZero,
+{
+    fn zero(&mut self) {
+        self.data.zero()
+    }
+
+    fn zero_at(&mut self, i: usize, j: usize) {
+        self.data.zero_at(i, j);
+    }
+}
+
+impl<D: DataMut> FillUniform for GLWECiphertextCompressed<D>
+where
+    VecZnx<D>: FillUniform,
+{
+    fn fill_uniform(&mut self, source: &mut Source) {
+        self.data.fill_uniform(source);
+    }
+}
+
+impl<D: Data> Infos for GLWECiphertextCompressed<D> {
+    type Inner = VecZnx<D>;
+
+    fn inner(&self) -> &Self::Inner {
+        &self.data
+    }
+
+    fn basek(&self) -> usize {
+        self.basek
+    }
+
+    fn k(&self) -> usize {
+        self.k
+    }
+}
+
+impl<D: Data> GLWECiphertextCompressed<D> {
+    pub fn rank(&self) -> usize {
+        self.rank
+    }
+}
+
+impl GLWECiphertextCompressed<Vec<u8>> {
+    pub fn alloc<B: Backend>(module: &Module<B>, basek: usize, k: usize, rank: usize) -> Self
+    where
+        Module<B>: VecZnxAlloc,
+    {
+        Self {
+            data: module.vec_znx_alloc(1, k.div_ceil(basek)),
+            basek,
+            k,
+            rank,
+            seed: [0u8; 32],
+        }
+    }
+
+    pub fn bytes_of<B: Backend>(module: &Module<B>, basek: usize, k: usize) -> usize
+    where
+        Module<B>: VecZnxAllocBytes,
+    {
+        GLWECiphertext::bytes_of(module, basek, k, 1)
+    }
+}
+
+impl<D: DataMut> ReaderFrom for GLWECiphertextCompressed<D> {
+    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
+        self.k = reader.read_u64::<LittleEndian>()? as usize;
+        self.basek = reader.read_u64::<LittleEndian>()? as usize;
+        self.rank = reader.read_u64::<LittleEndian>()? as usize;
+        reader.read(&mut self.seed)?;
+        self.data.read_from(reader)
+    }
+}
+
+impl<D: DataRef> WriterTo for GLWECiphertextCompressed<D> {
+    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
+        writer.write_u64::<LittleEndian>(self.k as u64)?;
+        writer.write_u64::<LittleEndian>(self.basek as u64)?;
+        writer.write_u64::<LittleEndian>(self.rank as u64)?;
+        writer.write_all(&self.seed)?;
+        self.data.write_to(writer)
+    }
+}
+
+impl<D: DataMut> GLWECiphertext<D> {
+    pub fn decompress<DataOther, B: Backend>(&mut self, module: &Module<B>, other: &GLWECiphertextCompressed<DataOther>)
+    where
+        DataOther: DataRef,
+        Module<B>: VecZnxFillUniform + VecZnxCopy,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(
+                self.n(),
+                other.data.n(),
+                "invalid receiver: self.n()={} != other.n()={}",
+                self.n(),
+                other.data.n()
+            );
+            assert_eq!(
+                self.size(),
+                other.size(),
+                "invalid receiver: self.size()={} != other.size()={}",
+                self.size(),
+                other.size()
+            );
+            assert_eq!(
+                self.rank(),
+                other.rank(),
+                "invalid receiver: self.rank()={} != other.rank()={}",
+                self.rank(),
+                other.rank()
+            );
+            let mut source: Source = Source::new(other.seed);
+            self.decompress_internal(module, other, &mut source);
+        }
+    }
+
+    pub(crate) fn decompress_internal<DataOther, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        other: &GLWECiphertextCompressed<DataOther>,
+        source: &mut Source,
+    ) where
+        DataOther: DataRef,
+        Module<B>: VecZnxFillUniform + VecZnxCopy,
+    {
+        let k: usize = other.k;
+        let basek: usize = other.basek;
+        let cols: usize = other.cols();
+        module.vec_znx_copy(&mut self.data, 0, &other.data, 0);
+        (1..cols).for_each(|i| {
+            module.vec_znx_fill_uniform(basek, &mut self.data, i, k, source);
+        });
+        self.basek = basek;
+        self.k = k;
+    }
+}

@@ -12,6 +12,9 @@ mod public_key;
 mod secret;
 mod trace;
 
+#[cfg(test)]
+mod tests;
+
 pub use decryption::*;
 pub use encryption::*;
 pub use external_product::*;
@@ -22,6 +25,3 @@ pub use packing::*;
 pub use plaintext::*;
 pub use public_key::*;
 pub use secret::*;
-
-#[cfg(test)]
-mod test_fft64;

@@ -8,7 +8,7 @@ use crate::dist::Distribution;
 
 pub trait GLWESecretFamily<B: Backend> = SvpPrepare<B> + SvpPPolAllocBytes + SvpPPolAlloc<B>;
 
-#[derive(PartialEq, Eq)]
+#[derive(PartialEq, Eq, Clone)]
 pub struct GLWESecret<D: Data> {
     pub(crate) data: ScalarZnx<D>,
     pub(crate) dist: Distribution,

@@ -1,17 +1,14 @@
-use backend::{
-    hal::{
-        api::{
-            MatZnxAlloc, ModuleNew, ScalarZnxAlloc, ScalarZnxAllocBytes, ScalarZnxAutomorphism, ScratchOwnedAlloc,
-            ScratchOwnedBorrow, VecZnxAddScalarInplace, VecZnxAlloc, VecZnxAllocBytes, VecZnxAutomorphismInplace,
-            VecZnxFillUniform, VecZnxStd, VecZnxSwithcDegree,
-        },
-        layouts::{Backend, Module, ScratchOwned},
-        oep::{
-            ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
-            TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
-        },
+use backend::hal::{
+    api::{
+        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
+        VecZnxAlloc, VecZnxAllocBytes, VecZnxAutomorphism, VecZnxAutomorphismInplace, VecZnxFillUniform, VecZnxStd,
+        VecZnxSwithcDegree,
     },
-    implementation::cpu_spqlios::FFT64,
+    layouts::{Backend, Module, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
+    },
 };
 use sampling::source::Source;
 
@@ -21,39 +18,6 @@ GLWEDecryptFamily, GLWEKeyswitchFamily, GLWEPlaintext, GLWESecret, GLWESecretExec, Infos,
     noise::log2_std_noise_gglwe_product,
 };
 
-#[test]
-fn apply_inplace() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    let basek: usize = 12;
-    let k_ct: usize = 60;
-    let digits: usize = k_ct.div_ceil(basek);
-    (1..4).for_each(|rank| {
-        (1..digits + 1).for_each(|di| {
-            let k_ksk: usize = k_ct + basek * di;
-            println!("test automorphism_inplace digits: {} rank: {}", di, rank);
-            test_automorphism_inplace(&module, basek, -5, k_ct, k_ksk, di, rank, 3.2);
-        });
-    });
-}
-
-#[test]
-fn apply() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    let basek: usize = 12;
-    let k_in: usize = 60;
-    let digits: usize = k_in.div_ceil(basek);
-    (1..4).for_each(|rank| {
-        (1..digits + 1).for_each(|di| {
-            let k_ksk: usize = k_in + basek * di;
-            let k_out: usize = k_ksk; // Better capture noise.
-            println!("test automorphism digits: {} rank: {}", di, rank);
-            test_automorphism(&module, basek, -5, k_out, k_in, k_ksk, di, rank, 3.2);
-        })
-    });
-}
-
 pub(crate) trait AutomorphismTestModuleFamily<B: Backend> = AutomorphismKeyEncryptSkFamily<B>
     + GLWEDecryptFamily<B>
     + GGLWEExecLayoutFamily<B>
@@ -62,7 +26,7 @@ + MatZnxAlloc
     + VecZnxAlloc
     + ScalarZnxAllocBytes
     + VecZnxAllocBytes
-    + ScalarZnxAutomorphism
+    + VecZnxAutomorphism
     + VecZnxSwithcDegree
     + ScalarZnxAlloc
     + VecZnxAddScalarInplace
@@ -77,7 +41,7 @@ + ScratchAvailableImpl<B>
     + TakeScalarZnxImpl<B>
     + TakeVecZnxImpl<B>;
 
-fn test_automorphism<B: Backend>(
+pub(crate) fn test_automorphism<B: Backend>(
     module: &Module<B>,
     basek: usize,
     p: i64,
@@ -166,7 +130,7 @@
     ct_out.assert_noise(module, &sk_exec, &pt_want, max_noise + 1.0);
 }
 
-fn test_automorphism_inplace<B: Backend>(
+pub(crate) fn test_automorphism_inplace<B: Backend>(
     module: &Module<B>,
     basek: usize,
     p: i64,

@@ -1,54 +1,21 @@
-use backend::{
-    hal::{
-        api::{
-            ModuleNew, ScalarZnxAlloc, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAlloc, VecZnxDftAlloc, VecZnxFillUniform,
-            VecZnxStd, VecZnxSubABInplace,
-        },
-        layouts::{Backend, Module, ScratchOwned},
-        oep::{
-            ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
-            TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
-        },
+use backend::hal::{
+    api::{
+        ScalarZnxAlloc, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAlloc, VecZnxCopy, VecZnxDftAlloc, VecZnxFillUniform,
+        VecZnxStd, VecZnxSubABInplace,
     },
-    implementation::cpu_spqlios::FFT64,
+    layouts::{Backend, Module, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
+    },
 };
 use sampling::source::Source;
 
 use crate::{
-    GLWECiphertext, GLWEDecryptFamily, GLWEEncryptPkFamily, GLWEEncryptSkFamily, GLWEOps, GLWEPlaintext, GLWEPublicKey,
-    GLWEPublicKeyExec, GLWESecret, GLWESecretExec, GLWESecretFamily, Infos,
+    GLWECiphertext, GLWECiphertextCompressed, GLWEDecryptFamily, GLWEEncryptPkFamily, GLWEEncryptSkFamily, GLWEOps,
+    GLWEPlaintext, GLWEPublicKey, GLWEPublicKeyExec, GLWESecret, GLWESecretExec, GLWESecretFamily, Infos,
 };
 
-#[test]
-fn encrypt_sk() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    (1..4).for_each(|rank| {
-        println!("test encrypt_sk rank: {}", rank);
-        test_encrypt_sk(&module, 8, 54, 30, 3.2, rank);
-    });
-}
-
-#[test]
-fn encrypt_zero_sk() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    (1..4).for_each(|rank| {
-        println!("test encrypt_zero_sk rank: {}", rank);
-        test_encrypt_zero_sk(&module, 8, 64, 3.2, rank);
-    });
-}
-
-#[test]
-fn encrypt_pk() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    (1..4).for_each(|rank| {
-        println!("test encrypt_pk rank: {}", rank);
-        test_encrypt_pk(&module, 8, 64, 64, 3.2, rank)
-    });
-}
-
 pub(crate) trait EncryptionTestModuleFamily<B: Backend> =
     GLWEDecryptFamily<B> + GLWESecretFamily<B> + VecZnxAlloc + ScalarZnxAlloc + VecZnxStd;
 
@@ -61,7 +28,7 @@ + ScratchAvailableImpl<B>
     + TakeScalarZnxImpl<B>
     + TakeVecZnxImpl<B>;
 
-fn test_encrypt_sk<B: Backend>(module: &Module<B>, basek: usize, k_ct: usize, k_pt: usize, sigma: f64, rank: usize)
+pub(crate) fn test_encrypt_sk<B: Backend>(module: &Module<B>, basek: usize, k_ct: usize, k_pt: usize, sigma: f64, rank: usize)
 where
     Module<B>: EncryptionTestModuleFamily<B> + GLWEEncryptSkFamily<B>,
     B: EncryptionTestScratchFamily<B>,
@@ -105,7 +72,63 @@
     assert!(noise_have <= noise_want + 0.2);
 }
 
-fn test_encrypt_zero_sk<B: Backend>(module: &Module<B>, basek: usize, k_ct: usize, sigma: f64, rank: usize)
+pub(crate) fn test_encrypt_sk_compressed<B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    k_ct: usize,
+    k_pt: usize,
+    sigma: f64,
+    rank: usize,
+) where
+    Module<B>: EncryptionTestModuleFamily<B> + GLWEEncryptSkFamily<B> + VecZnxCopy,
+    B: EncryptionTestScratchFamily<B>,
+{
+    let mut ct_compressed: GLWECiphertextCompressed<Vec<u8>> = GLWECiphertextCompressed::alloc(module, basek, k_ct, rank);
+
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_pt);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_pt);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        GLWECiphertextCompressed::encrypt_sk_scratch_space(module, basek, k_ct)
+            | GLWECiphertext::decrypt_scratch_space(module, basek, k_ct),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk);
+
+    module.vec_znx_fill_uniform(basek, &mut pt_want.data, 0, k_pt, &mut source_xa);
+
+    let seed_xa: [u8; 32] = [1u8; 32];
+
+    ct_compressed.encrypt_sk(
+        module,
+        &pt_want,
+        &sk_exec,
+        seed_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_ct, rank);
+    ct.decompress(module, &ct_compressed);
+
+    ct.decrypt(module, &mut pt_have, &sk_exec, scratch.borrow());
+
+    pt_want.sub_inplace_ab(module, &pt_have);
+
+    let noise_have: f64 = module.vec_znx_std(basek, &pt_want.data, 0) * (ct.k() as f64).exp2();
+    let noise_want: f64 = sigma;
+
+    assert!(noise_have <= noise_want + 0.2);
+}
+
+pub(crate) fn test_encrypt_zero_sk<B: Backend>(module: &Module<B>, basek: usize, k_ct: usize, sigma: f64, rank: usize)
 where
     Module<B>: EncryptionTestModuleFamily<B> + GLWEEncryptSkFamily<B>,
     B: EncryptionTestScratchFamily<B>,
@@ -140,7 +163,7 @@
     assert!((sigma - module.vec_znx_std(basek, &pt.data, 0) * (k_ct as f64).exp2()) <= 0.2);
 }
 
-fn test_encrypt_pk<B: Backend>(module: &Module<B>, basek: usize, k_ct: usize, k_pk: usize, sigma: f64, rank: usize)
+pub(crate) fn test_encrypt_pk<B: Backend>(module: &Module<B>, basek: usize, k_ct: usize, k_pk: usize, sigma: f64, rank: usize)
 where
     Module<B>: EncryptionTestModuleFamily<B>
         + GLWEEncryptPkFamily<B>

@@ -1,16 +1,13 @@
-use backend::{
-    hal::{
-        api::{
-            MatZnxAlloc, ModuleNew, ScalarZnxAlloc, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace, VecZnxAlloc,
-            VecZnxAllocBytes, VecZnxFillUniform, VecZnxRotateInplace, VecZnxStd, ZnxViewMut,
-        },
-        layouts::{Backend, Module, ScalarZnx, ScratchOwned},
-        oep::{
-            ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
-            TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
-        },
+use backend::hal::{
+    api::{
+        MatZnxAlloc, ScalarZnxAlloc, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace, VecZnxAlloc,
+        VecZnxAllocBytes, VecZnxFillUniform, VecZnxRotateInplace, VecZnxStd, ZnxViewMut,
     },
-    implementation::cpu_spqlios::FFT64,
+    layouts::{Backend, Module, ScalarZnx, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
+    },
 };
 use sampling::source::Source;
 
@@ -19,39 +16,6 @@ GGSWCiphertext, GGSWCiphertextExec, GGSWLayoutFamily, GLWECiphertext, GLWEDecryptFamily, GLWEEncryptSkFamily,
     GLWEExternalProductFamily, GLWEPlaintext, GLWESecret, GLWESecretExec, GLWESecretFamily, Infos, noise::noise_ggsw_product,
 };
 
-#[test]
-fn apply() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    let basek: usize = 12;
-    let k_in: usize = 45;
-    let digits: usize = k_in.div_ceil(basek);
-    (1..4).for_each(|rank| {
-        (1..digits + 1).for_each(|di| {
-            let k_ggsw: usize = k_in + basek * di;
-            let k_out: usize = k_ggsw; // Better capture noise
-            println!("test external_product digits: {} rank: {}", di, rank);
-            test_external_product(&module, basek, k_out, k_in, k_ggsw, di, rank, 3.2);
-        });
-    });
-}
-
-#[test]
-fn apply_inplace() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    let basek: usize = 12;
-    let k_ct: usize = 60;
-    let digits: usize = k_ct.div_ceil(basek);
-    (1..4).for_each(|rank| {
-        (1..digits + 1).for_each(|di| {
-            let k_ggsw: usize = k_ct + basek * di;
-            println!("test external_product digits: {} rank: {}", di, rank);
-            test_external_product_inplace(&module, basek, k_ct, k_ggsw, di, rank, 3.2);
-        });
-    });
-}
-
 pub(crate) trait ExternalProductTestModuleFamily<B: Backend> = GLWEEncryptSkFamily<B>
     + GLWEDecryptFamily<B>
     + GLWESecretFamily<B>
@@ -74,7 +38,7 @@ + ScratchAvailableImpl<B>
     + TakeScalarZnxImpl<B>
     + TakeVecZnxImpl<B>;
 
-fn test_external_product<B: Backend>(
+pub(crate) fn test_external_product<B: Backend>(
     module: &Module<B>,
     basek: usize,
     k_out: usize,
@@ -176,7 +140,7 @@
     ct_glwe_out.assert_noise(module, &sk_exec, &pt_want, max_noise + 0.5);
 }
 
-fn test_external_product_inplace<B: Backend>(
+pub(crate) fn test_external_product_inplace<B: Backend>(
     module: &Module<B>,
     basek: usize,
     k_ct: usize,

@@ -1,16 +1,13 @@
-use backend::{
-    hal::{
-        api::{
-            MatZnxAlloc, ModuleNew, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow,
-            VecZnxAddScalarInplace, VecZnxAlloc, VecZnxAllocBytes, VecZnxFillUniform, VecZnxStd, VecZnxSwithcDegree,
-        },
-        layouts::{Backend, Module, ScratchOwned},
-        oep::{
-            ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
-            TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
-        },
+use backend::hal::{
+    api::{
+        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
+        VecZnxAlloc, VecZnxAllocBytes, VecZnxFillUniform, VecZnxStd, VecZnxSwithcDegree,
     },
-    implementation::cpu_spqlios::FFT64,
+    layouts::{Backend, Module, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
+    },
 };
 use sampling::source::Source;
 
@@ -20,46 +17,6 @@ GLWESecretFamily, GLWESwitchingKey, GLWESwitchingKeyEncryptSkFamily, GLWESwitchingKeyExec, Infos,
     noise::log2_std_noise_gglwe_product,
 };
 
-#[test]
-fn apply() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    let basek: usize = 12;
-    let k_in: usize = 45;
-    let digits: usize = k_in.div_ceil(basek);
-    (1..4).for_each(|rank_in| {
-        (1..4).for_each(|rank_out| {
-            (1..digits + 1).for_each(|di| {
-                let k_ksk: usize = k_in + basek * di;
-                let k_out: usize = k_ksk; // better capture noise
-                println!(
-                    "test keyswitch digits: {} rank_in: {} rank_out: {}",
-                    di, rank_in, rank_out
-                );
-                test_keyswitch(
-                    &module, basek, k_out, k_in, k_ksk, di, rank_in, rank_out, 3.2,
-                );
-            })
-        });
-    });
-}
-
-#[test]
-fn apply_inplace() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    let basek: usize = 12;
-    let k_ct: usize = 45;
-    let digits: usize = k_ct.div_ceil(basek);
-    (1..4).for_each(|rank| {
-        (1..digits + 1).for_each(|di| {
-            let k_ksk: usize = k_ct + basek * di;
-            println!("test keyswitch_inplace digits: {} rank: {}", di, rank);
-            test_keyswitch_inplace(&module, basek, k_ct, k_ksk, di, rank, 3.2);
-        });
-    });
-}
-
 pub(crate) trait KeySwitchTestModuleFamily<B: Backend> = GLWESecretFamily<B>
     + GLWESwitchingKeyEncryptSkFamily<B>
     + GLWEKeyswitchFamily<B>
@@ -83,7 +40,7 @@ + ScratchAvailableImpl<B>
     + TakeScalarZnxImpl<B>
     + TakeVecZnxImpl<B>;
 
-fn test_keyswitch<B: Backend>(
+pub(crate) fn test_keyswitch<B: Backend>(
     module: &Module<B>,
     basek: usize,
     k_out: usize,
@@ -173,7 +130,7 @@
     ct_out.assert_noise(module, &sk_out_exec, &pt_want, max_noise + 0.5);
 }
 
-fn test_keyswitch_inplace<B: Backend>(
+pub(crate) fn test_keyswitch_inplace<B: Backend>(
     module: &Module<B>,
     basek: usize,
     k_ct: usize,

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

@@ -1,19 +1,16 @@
 use std::collections::HashMap;
 
-use backend::{
-    hal::{
-        api::{
-            MatZnxAlloc, ModuleNew, ScalarZnxAlloc, ScalarZnxAllocBytes, ScalarZnxAutomorphism, ScratchOwnedAlloc,
-            ScratchOwnedBorrow, VecZnxAddScalarInplace, VecZnxAlloc, VecZnxAllocBytes, VecZnxBigSubSmallBInplace,
-            VecZnxEncodeVeci64, VecZnxRotateInplace, VecZnxStd, VecZnxSwithcDegree,
-        },
-        layouts::{Backend, Module, ScratchOwned},
-        oep::{
-            ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
-            TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
-        },
+use backend::hal::{
+    api::{
+        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
+        VecZnxAlloc, VecZnxAllocBytes, VecZnxAutomorphism, VecZnxBigSubSmallBInplace, VecZnxEncodeVeci64, VecZnxRotateInplace,
+        VecZnxStd, VecZnxSwithcDegree,
     },
-    implementation::cpu_spqlios::FFT64,
+    layouts::{Backend, Module, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
+    },
 };
 use sampling::source::Source;
 
@@ -22,13 +19,6 @@ AutomorphismKey, AutomorphismKeyExec, GGLWEExecLayoutFamily, GLWECiphertext, GLWEDecryptFamily, GLWEKeyswitchFamily, GLWEOps,
     GLWEPacker, GLWEPackingFamily, GLWEPlaintext, GLWESecret, GLWESecretExec, GLWESecretFamily, GLWESwitchingKeyEncryptSkFamily,
 };
 
-#[test]
-fn trace() {
-    let log_n: usize = 5;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    test_packing(&module);
-}
-
 pub(crate) trait PackingTestModuleFamily<B: Backend> = GLWEPackingFamily<B>
     + GLWESecretFamily<B>
     + GLWESwitchingKeyEncryptSkFamily<B>
@@ -44,8 +34,8 @@ + VecZnxStd
     + VecZnxSwithcDegree
     + VecZnxAddScalarInplace
     + VecZnxEncodeVeci64
-    + ScalarZnxAutomorphism
     + VecZnxRotateInplace
+    + VecZnxAutomorphism
     + VecZnxBigSubSmallBInplace<B>;
 
 pub(crate) trait PackingTestScratchFamily<B: Backend> = TakeVecZnxDftImpl<B>

@@ -1,20 +1,17 @@
 use std::collections::HashMap;
 
-use backend::{
-    hal::{
-        api::{
-            MatZnxAlloc, ModuleNew, ScalarZnxAlloc, ScalarZnxAllocBytes, ScalarZnxAutomorphism, ScratchOwnedAlloc,
-            ScratchOwnedBorrow, VecZnxAddScalarInplace, VecZnxAlloc, VecZnxAllocBytes, VecZnxBigAutomorphismInplace,
-            VecZnxBigSubSmallBInplace, VecZnxCopy, VecZnxEncodeVeci64, VecZnxFillUniform, VecZnxNormalizeInplace,
-            VecZnxRotateInplace, VecZnxRshInplace, VecZnxStd, VecZnxSubABInplace, VecZnxSwithcDegree, ZnxView, ZnxViewMut,
-        },
-        layouts::{Backend, Module, ScratchOwned},
-        oep::{
-            ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
-            TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
-        },
+use backend::hal::{
+    api::{
+        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
+        VecZnxAlloc, VecZnxAllocBytes, VecZnxAutomorphism, VecZnxBigAutomorphismInplace, VecZnxBigSubSmallBInplace, VecZnxCopy,
+        VecZnxEncodeVeci64, VecZnxFillUniform, VecZnxNormalizeInplace, VecZnxRotateInplace, VecZnxRshInplace, VecZnxStd,
+        VecZnxSubABInplace, VecZnxSwithcDegree, ZnxView, ZnxViewMut,
+    },
+    layouts::{Backend, Module, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
     },
-    implementation::cpu_spqlios::FFT64,
 };
 use sampling::source::Source;
 
@@ -24,16 +21,6 @@ GLWEPlaintext, GLWESecret, GLWESecretExec, GLWESecretFamily, GLWESwitchingKeyEncryptSkFamily, Infos,
     noise::var_noise_gglwe_product,
 };
 
-#[test]
-fn apply_inplace() {
-    let log_n: usize = 8;
-    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
-    (1..4).for_each(|rank| {
-        println!("test trace_inplace rank: {}", rank);
-        test_trace_inplace(&module, 8, 54, 3.2, rank);
-    });
-}
-
 pub(crate) trait TraceTestModuleFamily<B: Backend> = GLWESecretFamily<B>
     + GLWESwitchingKeyEncryptSkFamily<B>
     + GLWEKeyswitchFamily<B>
@@ -48,11 +35,11 @@ + VecZnxStd
     + VecZnxSwithcDegree
     + VecZnxAddScalarInplace
     + VecZnxEncodeVeci64
-    + ScalarZnxAutomorphism
     + VecZnxRotateInplace
     + VecZnxBigSubSmallBInplace<B>
     + VecZnxBigAutomorphismInplace<B>
     + VecZnxCopy
+    + VecZnxAutomorphism
     + VecZnxRshInplace;
 
 pub(crate) trait TraceTestScratchFamily<B: Backend> = TakeVecZnxDftImpl<B>
@@ -64,7 +51,7 @@ + ScratchAvailableImpl<B>
     + TakeScalarZnxImpl<B>
     + TakeVecZnxImpl<B>;
 
-fn test_trace_inplace<B: Backend>(module: &Module<B>, basek: usize, k: usize, sigma: f64, rank: usize)
+pub(crate) fn test_trace_inplace<B: Backend>(module: &Module<B>, basek: usize, k: usize, sigma: f64, rank: usize)
 where
     Module<B>: TraceTestModuleFamily<B>,
     B: TraceTestScratchFamily<B>,

@@ -0,0 +1,191 @@
+use backend::{
+    hal::{api::ModuleNew, layouts::Module},
+    implementation::cpu_spqlios::FFT64,
+};
+
+use crate::glwe::tests::{
+    generic_automorphism::{test_automorphism, test_automorphism_inplace},
+    generic_encryption::{test_encrypt_pk, test_encrypt_sk, test_encrypt_sk_compressed, test_encrypt_zero_sk},
+    generic_external_product::{test_external_product, test_external_product_inplace},
+    generic_keyswitch::{test_keyswitch, test_keyswitch_inplace},
+    generic_serialization::{test_serialization, test_serialization_compressed},
+    packing::test_packing,
+    trace::test_trace_inplace,
+};
+
+#[test]
+fn encrypt_sk() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    (1..4).for_each(|rank| {
+        println!("test encrypt_sk rank: {}", rank);
+        test_encrypt_sk(&module, 8, 54, 30, 3.2, rank);
+    });
+}
+
+#[test]
+fn encrypt_sk_compressed() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    (1..4).for_each(|rank| {
+        println!("test encrypt_sk rank: {}", rank);
+        test_encrypt_sk_compressed(&module, 8, 54, 30, 3.2, rank);
+    });
+}
+
+#[test]
+fn encrypt_zero_sk() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    (1..4).for_each(|rank| {
+        println!("test encrypt_zero_sk rank: {}", rank);
+        test_encrypt_zero_sk(&module, 8, 64, 3.2, rank);
+    });
+}
+
+#[test]
+fn encrypt_pk() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    (1..4).for_each(|rank| {
+        println!("test encrypt_pk rank: {}", rank);
+        test_encrypt_pk(&module, 8, 64, 64, 3.2, rank)
+    });
+}
+
+#[test]
+fn apply() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_in: usize = 45;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank_in| {
+        (1..4).for_each(|rank_out| {
+            (1..digits + 1).for_each(|di| {
+                let k_ksk: usize = k_in + basek * di;
+                let k_out: usize = k_ksk; // better capture noise
+                println!(
+                    "test keyswitch digits: {} rank_in: {} rank_out: {}",
+                    di, rank_in, rank_out
+                );
+                test_keyswitch(
+                    &module, basek, k_out, k_in, k_ksk, di, rank_in, rank_out, 3.2,
+                );
+            })
+        });
+    });
+}
+
+#[test]
+fn apply_inplace() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_ct: usize = 45;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_ct + basek * di;
+            println!("test keyswitch_inplace digits: {} rank: {}", di, rank);
+            test_keyswitch_inplace(&module, basek, k_ct, k_ksk, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn automorphism_inplace() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_ct: usize = 60;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_ct + basek * di;
+            println!("test automorphism_inplace digits: {} rank: {}", di, rank);
+            test_automorphism_inplace(&module, basek, -5, k_ct, k_ksk, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn automorphism() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_in: usize = 60;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_in + basek * di;
+            let k_out: usize = k_ksk; // Better capture noise.
+            println!("test automorphism digits: {} rank: {}", di, rank);
+            test_automorphism(&module, basek, -5, k_out, k_in, k_ksk, di, rank, 3.2);
+        })
+    });
+}
+
+#[test]
+fn external_product() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_in: usize = 45;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ggsw: usize = k_in + basek * di;
+            let k_out: usize = k_ggsw; // Better capture noise
+            println!("test external_product digits: {} rank: {}", di, rank);
+            test_external_product(&module, basek, k_out, k_in, k_ggsw, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn external_product_inplace() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_ct: usize = 60;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ggsw: usize = k_ct + basek * di;
+            println!("test external_product digits: {} rank: {}", di, rank);
+            test_external_product_inplace(&module, basek, k_ct, k_ggsw, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn trace_inplace() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    (1..4).for_each(|rank| {
+        println!("test trace_inplace rank: {}", rank);
+        test_trace_inplace(&module, 8, 54, 3.2, rank);
+    });
+}
+
+#[test]
+fn packing() {
+    let log_n: usize = 5;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    test_packing(&module);
+}
+
+#[test]
+fn serialization() {
+    let log_n: usize = 5;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    test_serialization(&module);
+}
+
+#[test]
+fn serialization_compressed() {
+    let log_n: usize = 5;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    test_serialization_compressed(&module);
+}

@@ -0,0 +1,1 @@
+mod fft64;

@@ -0,0 +1,23 @@
+use backend::hal::{
+    api::VecZnxAlloc,
+    layouts::{Backend, Module},
+    tests::serialization::test_reader_writer_interface,
+};
+
+use crate::{GLWECiphertext, GLWECiphertextCompressed};
+
+pub(crate) fn test_serialization<B: Backend>(module: &Module<B>)
+where
+    Module<B>: VecZnxAlloc,
+{
+    let original: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, 12, 54, 3);
+    test_reader_writer_interface(original);
+}
+
+pub(crate) fn test_serialization_compressed<B: Backend>(module: &Module<B>)
+where
+    Module<B>: VecZnxAlloc,
+{
+    let original: GLWECiphertextCompressed<Vec<u8>> = GLWECiphertextCompressed::alloc(module, 12, 54, 3);
+    test_reader_writer_interface(original);
+}

@@ -0,0 +1,8 @@
+mod cpu_spqlios;
+mod generic_automorphism;
+mod generic_encryption;
+mod generic_external_product;
+mod generic_keyswitch;
+mod generic_serialization;
+mod packing;
+mod trace;

@@ -14,7 +14,7 @@
 impl LWECiphertext<Vec<u8>> {
     pub fn alloc(n: usize, basek: usize, k: usize) -> Self {
         Self {
-            data: VecZnx::new::<i64>(n + 1, 1, k.div_ceil(basek)),
+            data: VecZnx::alloc::<i64>(n + 1, 1, k.div_ceil(basek)),
             k: k,
             basek: basek,
         }

@@ -34,7 +34,7 @@ let k: usize = self.k();
 
         module.vec_znx_fill_uniform(basek, &mut self.data, 0, k, source_xa);
 
-        let mut tmp_znx: VecZnx<Vec<u8>> = VecZnx::<Vec<u8>>::new::<i64>(1, 1, self.size());
+        let mut tmp_znx: VecZnx<Vec<u8>> = VecZnx::<Vec<u8>>::alloc::<i64>(1, 1, self.size());
 
         let min_size = self.size().min(pt.size());
 

@@ -126,7 +126,7 @@
         let (mut sk_lwe_as_glwe, scratch1) = scratch.take_glwe_secret(module, 1);
         sk_lwe_as_glwe.data.zero();
         sk_lwe_as_glwe.data.at_mut(0, 0)[..sk_lwe.n()].copy_from_slice(sk_lwe.data.at(0, 0));
-        module.vec_znx_automorphism_inplace(-1, &mut sk_lwe_as_glwe.data, 0);
+        module.vec_znx_automorphism_inplace(-1, &mut sk_lwe_as_glwe.data.as_vec_znx_mut(), 0);
 
         self.0.encrypt_sk(
             module,
@@ -252,7 +252,7 @@
         let (mut sk_lwe_as_glwe, scratch1) = scratch.take_glwe_secret(module, 1);
         sk_lwe_as_glwe.data.at_mut(0, 0)[..sk_lwe.n()].copy_from_slice(sk_lwe.data.at(0, 0));
         sk_lwe_as_glwe.data.at_mut(0, 0)[sk_lwe.n()..].fill(0);
-        module.vec_znx_automorphism_inplace(-1, &mut sk_lwe_as_glwe.data, 0);
+        module.vec_znx_automorphism_inplace(-1, &mut sk_lwe_as_glwe.data.as_vec_znx_mut(), 0);
 
         self.0.encrypt_sk(
             module,
@@ -368,11 +368,11 @@ let (mut sk_out_glwe, scratch2) = scratch1.take_glwe_secret(module, 1);
 
         sk_out_glwe.data.at_mut(0, 0)[..sk_lwe_out.n()].copy_from_slice(sk_lwe_out.data.at(0, 0));
         sk_out_glwe.data.at_mut(0, 0)[sk_lwe_out.n()..].fill(0);
-        module.vec_znx_automorphism_inplace(-1, &mut sk_out_glwe.data, 0);
+        module.vec_znx_automorphism_inplace(-1, &mut sk_out_glwe.data.as_vec_znx_mut(), 0);
 
         sk_in_glwe.data.at_mut(0, 0)[..sk_lwe_in.n()].copy_from_slice(sk_lwe_in.data.at(0, 0));
         sk_in_glwe.data.at_mut(0, 0)[sk_lwe_in.n()..].fill(0);
-        module.vec_znx_automorphism_inplace(-1, &mut sk_in_glwe.data, 0);
+        module.vec_znx_automorphism_inplace(-1, &mut sk_in_glwe.data.as_vec_znx_mut(), 0);
 
         self.0.encrypt_sk(
             module,

@@ -11,7 +11,7 @@
 impl LWEPlaintext<Vec<u8>> {
     pub fn alloc(basek: usize, k: usize) -> Self {
         Self {
-            data: VecZnx::new::<i64>(1, 1, k.div_ceil(basek)),
+            data: VecZnx::alloc::<i64>(1, 1, k.div_ceil(basek)),
             k: k,
             basek: basek,
         }

@@ -14,7 +14,7 @@
 impl LWESecret<Vec<u8>> {
     pub fn alloc(n: usize) -> Self {
         Self {
-            data: ScalarZnx::new(n, 1),
+            data: ScalarZnx::alloc(n, 1),
             dist: Distribution::NONE,
         }
     }

@@ -14,11 +14,10 @@ source: ChaCha8Rng::from_seed(seed),
         }
     }
 
-    pub fn branch(&mut self) -> Self {
+    pub fn branch(&mut self) -> ([u8; 32], Self) {
         let mut seed = [0; 32];
         self.source.fill_bytes(&mut seed);
-
-        Source::new(seed)
+        (seed, Source::new(seed))
     }
 
     #[inline(always)]