@@ -49,9 +49,9 @@ checksum = "79296716171880943b8470b5f8d03aa55eb2e645a4874bdbb28adb49162e012c"
 
 [[package]]
 name = "bytemuck"
-version = "1.23.2"
+version = "1.24.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3995eaeebcdf32f91f980d360f78732ddc061097ab4e39991ae7a6ace9194677"
+checksum = "1fbdf580320f38b612e485521afda1ee26d10cc9884efaaa750d383e13e3c5f4"
 
 [[package]]
 name = "byteorder"
@@ -353,7 +353,7 @@ ]
 
 [[package]]
 name = "poulpy-backend"
-version = "0.2.0"
+version = "0.3.1"
 dependencies = [
  "byteorder",
  "cmake",
@@ -370,8 +370,9 @@ ]
 
 [[package]]
 name = "poulpy-core"
-version = "0.2.0"
+version = "0.3.1"
 dependencies = [
+ "bytemuck",
  "byteorder",
  "criterion",
  "itertools 0.14.0",
@@ -383,7 +384,7 @@ ]
 
 [[package]]
 name = "poulpy-hal"
-version = "0.2.0"
+version = "0.3.1"
 dependencies = [
  "bytemuck",
  "byteorder",
@@ -400,7 +401,7 @@ ]
 
 [[package]]
 name = "poulpy-schemes"
-version = "0.2.0"
+version = "0.3.0"
 dependencies = [
  "byteorder",
  "criterion",
@@ -534,9 +535,9 @@ checksum = "2b15c43186be67a4fd63bee50d0303afffcef381492ebe2c5d87f324e1b8815c"
 
 [[package]]
 name = "rug"
-version = "1.27.0"
+version = "1.28.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4207e8d668e5b8eb574bda8322088ccd0d7782d3d03c7e8d562e82ed82bdcbc3"
+checksum = "58ad2e973fe3c3214251a840a621812a4f40468da814b1a3d6947d433c2af11f"
 dependencies = [
  "az",
  "gmp-mpfr-sys",

@@ -7,8 +7,8 @@ poulpy-hal = {path = "poulpy-hal"}
 poulpy-core = {path = "poulpy-core"}
 poulpy-backend = {path = "poulpy-backend"}
 poulpy-schemes = {path = "poulpy-schemes"}
-rug = "1.27"
-rand = "0.9.1"
+rug = "1.28.0"
+rand = "0.9.2"
 rand_chacha = "0.9.0"
 rand_core = "0.9.3"
 rand_distr = "0.5.1"
@@ -16,4 +16,5 @@ itertools = "0.14.0"
 criterion = "0.7.0"
 byteorder = "1.5.0"
 zstd = "0.13.3"
-once_cell = "1.21.3"+once_cell = "1.21.3"
+bytemuck = "1.24.0"

@@ -1,6 +1,6 @@
 [package]
 name = "poulpy-backend"
-version = "0.2.0"
+version = "0.3.1"
 edition = "2024"
 license = "Apache-2.0"
 readme = "README.md"

@@ -1,5 +1,6 @@
 use poulpy_hal::{
-    api::ModuleNew, backend_test_suite, cross_backend_test_suite, layouts::Module, test_suite::convolution::test_convolution,
+    api::ModuleNew, backend_test_suite, cross_backend_test_suite, layouts::Module,
+    test_suite::convolution::test_bivariate_tensoring,
 };
 
 use crate::FFT64Avx;
@@ -123,5 +124,5 @@
 #[test]
 fn test_convolution_fft64_avx() {
     let module: Module<FFT64Avx> = Module::<FFT64Avx>::new(64);
-    test_convolution(&module);
+    test_bivariate_tensoring(&module);
 }

@@ -14,7 +14,7 @@ VecZnxMulXpMinusOneInplaceTmpBytesImpl, VecZnxNegateImpl, VecZnxNegateInplaceImpl, VecZnxNormalizeImpl,
         VecZnxNormalizeInplaceImpl, VecZnxNormalizeTmpBytesImpl, VecZnxRotateImpl, VecZnxRotateInplaceImpl,
         VecZnxRotateInplaceTmpBytesImpl, VecZnxRshImpl, VecZnxRshInplaceImpl, VecZnxRshTmpBytesImpl, VecZnxSplitRingImpl,
         VecZnxSplitRingTmpBytesImpl, VecZnxSubImpl, VecZnxSubInplaceImpl, VecZnxSubNegateInplaceImpl, VecZnxSubScalarImpl,
-        VecZnxSubScalarInplaceImpl, VecZnxSwitchRingImpl,
+        VecZnxSubScalarInplaceImpl, VecZnxSwitchRingImpl, VecZnxZeroImpl,
     },
     reference::vec_znx::{
         vec_znx_add, vec_znx_add_inplace, vec_znx_add_normal_ref, vec_znx_add_scalar, vec_znx_add_scalar_inplace,
@@ -25,12 +25,21 @@ vec_znx_mul_xp_minus_one_inplace_tmp_bytes, vec_znx_negate, vec_znx_negate_inplace, vec_znx_normalize,
         vec_znx_normalize_inplace, vec_znx_normalize_tmp_bytes, vec_znx_rotate, vec_znx_rotate_inplace,
         vec_znx_rotate_inplace_tmp_bytes, vec_znx_rsh, vec_znx_rsh_inplace, vec_znx_rsh_tmp_bytes, vec_znx_split_ring,
         vec_znx_split_ring_tmp_bytes, vec_znx_sub, vec_znx_sub_inplace, vec_znx_sub_negate_inplace, vec_znx_sub_scalar,
-        vec_znx_sub_scalar_inplace, vec_znx_switch_ring,
+        vec_znx_sub_scalar_inplace, vec_znx_switch_ring, vec_znx_zero,
     },
     source::Source,
 };
 
 use crate::cpu_fft64_avx::FFT64Avx;
+
+unsafe impl VecZnxZeroImpl<Self> for FFT64Avx {
+    fn vec_znx_zero_impl<R>(_module: &Module<Self>, res: &mut R, res_col: usize)
+    where
+        R: VecZnxToMut,
+    {
+        vec_znx_zero::<_, FFT64Avx>(res, res_col);
+    }
+}
 
 unsafe impl VecZnxNormalizeTmpBytesImpl<Self> for FFT64Avx {
     fn vec_znx_normalize_tmp_bytes_impl(module: &Module<Self>) -> usize {

@@ -194,10 +194,10 @@ }
 }
 
 unsafe impl VecZnxDftZeroImpl<Self> for FFT64Avx {
-    fn vec_znx_dft_zero_impl<R>(_module: &Module<Self>, res: &mut R)
+    fn vec_znx_dft_zero_impl<R>(_module: &Module<Self>, res: &mut R, res_col: usize)
     where
         R: VecZnxDftToMut<Self>,
     {
-        vec_znx_dft_zero(res);
+        vec_znx_dft_zero(res, res_col);
     }
 }

@@ -1,9 +1,9 @@
-use poulpy_hal::{api::ModuleNew, layouts::Module, test_suite::convolution::test_convolution};
+use poulpy_hal::{api::ModuleNew, layouts::Module, test_suite::convolution::test_bivariate_tensoring};
 
 use crate::FFT64Ref;
 
 #[test]
 fn test_convolution_fft64_ref() {
-    let module: Module<FFT64Ref> = Module::<FFT64Ref>::new(64);
-    test_convolution(&module);
+    let module: Module<FFT64Ref> = Module::<FFT64Ref>::new(8);
+    test_bivariate_tensoring(&module);
 }

@@ -14,7 +14,7 @@ VecZnxMulXpMinusOneInplaceTmpBytesImpl, VecZnxNegateImpl, VecZnxNegateInplaceImpl, VecZnxNormalizeImpl,
         VecZnxNormalizeInplaceImpl, VecZnxNormalizeTmpBytesImpl, VecZnxRotateImpl, VecZnxRotateInplaceImpl,
         VecZnxRotateInplaceTmpBytesImpl, VecZnxRshImpl, VecZnxRshInplaceImpl, VecZnxRshTmpBytesImpl, VecZnxSplitRingImpl,
         VecZnxSplitRingTmpBytesImpl, VecZnxSubImpl, VecZnxSubInplaceImpl, VecZnxSubNegateInplaceImpl, VecZnxSubScalarImpl,
-        VecZnxSubScalarInplaceImpl, VecZnxSwitchRingImpl,
+        VecZnxSubScalarInplaceImpl, VecZnxSwitchRingImpl, VecZnxZeroImpl,
     },
     reference::vec_znx::{
         vec_znx_add, vec_znx_add_inplace, vec_znx_add_normal_ref, vec_znx_add_scalar, vec_znx_add_scalar_inplace,
@@ -25,12 +25,21 @@ vec_znx_mul_xp_minus_one_inplace_tmp_bytes, vec_znx_negate, vec_znx_negate_inplace, vec_znx_normalize,
         vec_znx_normalize_inplace, vec_znx_normalize_tmp_bytes, vec_znx_rotate, vec_znx_rotate_inplace,
         vec_znx_rotate_inplace_tmp_bytes, vec_znx_rsh, vec_znx_rsh_inplace, vec_znx_rsh_tmp_bytes, vec_znx_split_ring,
         vec_znx_split_ring_tmp_bytes, vec_znx_sub, vec_znx_sub_inplace, vec_znx_sub_negate_inplace, vec_znx_sub_scalar,
-        vec_znx_sub_scalar_inplace, vec_znx_switch_ring,
+        vec_znx_sub_scalar_inplace, vec_znx_switch_ring, vec_znx_zero,
     },
     source::Source,
 };
 
 use crate::cpu_fft64_ref::FFT64Ref;
+
+unsafe impl VecZnxZeroImpl<Self> for FFT64Ref {
+    fn vec_znx_zero_impl<R>(_module: &Module<Self>, res: &mut R, res_col: usize)
+    where
+        R: VecZnxToMut,
+    {
+        vec_znx_zero::<_, FFT64Ref>(res, res_col);
+    }
+}
 
 unsafe impl VecZnxNormalizeTmpBytesImpl<Self> for FFT64Ref {
     fn vec_znx_normalize_tmp_bytes_impl(module: &Module<Self>) -> usize {

@@ -194,10 +194,10 @@ }
 }
 
 unsafe impl VecZnxDftZeroImpl<Self> for FFT64Ref {
-    fn vec_znx_dft_zero_impl<R>(_module: &Module<Self>, res: &mut R)
+    fn vec_znx_dft_zero_impl<R>(_module: &Module<Self>, res: &mut R, res_col: usize)
     where
         R: VecZnxDftToMut<Self>,
     {
-        vec_znx_dft_zero(res);
+        vec_znx_dft_zero(res, res_col);
     }
 }

@@ -15,7 +15,7 @@ VecZnxMulXpMinusOneInplaceTmpBytesImpl, VecZnxNegateImpl, VecZnxNegateInplaceImpl, VecZnxNormalizeImpl,
         VecZnxNormalizeInplaceImpl, VecZnxNormalizeTmpBytesImpl, VecZnxRotateImpl, VecZnxRotateInplaceImpl,
         VecZnxRotateInplaceTmpBytesImpl, VecZnxRshImpl, VecZnxRshInplaceImpl, VecZnxRshTmpBytesImpl, VecZnxSplitRingImpl,
         VecZnxSplitRingTmpBytesImpl, VecZnxSubImpl, VecZnxSubInplaceImpl, VecZnxSubNegateInplaceImpl, VecZnxSubScalarImpl,
-        VecZnxSubScalarInplaceImpl, VecZnxSwitchRingImpl,
+        VecZnxSubScalarInplaceImpl, VecZnxSwitchRingImpl, VecZnxZeroImpl,
     },
     reference::{
         vec_znx::{
@@ -23,7 +23,7 @@ vec_znx_add_normal_ref, vec_znx_automorphism_inplace_tmp_bytes, vec_znx_copy, vec_znx_fill_normal_ref,
             vec_znx_fill_uniform_ref, vec_znx_lsh, vec_znx_lsh_inplace, vec_znx_lsh_tmp_bytes, vec_znx_merge_rings,
             vec_znx_merge_rings_tmp_bytes, vec_znx_mul_xp_minus_one_inplace_tmp_bytes, vec_znx_normalize_tmp_bytes,
             vec_znx_rotate_inplace_tmp_bytes, vec_znx_rsh, vec_znx_rsh_inplace, vec_znx_rsh_tmp_bytes, vec_znx_split_ring,
-            vec_znx_split_ring_tmp_bytes, vec_znx_switch_ring,
+            vec_znx_split_ring_tmp_bytes, vec_znx_switch_ring, vec_znx_zero,
         },
         znx::{znx_copy_ref, znx_zero_ref},
     },
@@ -34,6 +34,15 @@ use crate::cpu_spqlios::{
     FFT64Spqlios,
     ffi::{module::module_info_t, vec_znx, znx},
 };
+
+unsafe impl VecZnxZeroImpl<Self> for FFT64Spqlios {
+    fn vec_znx_zero_impl<R>(_module: &Module<Self>, res: &mut R, res_col: usize)
+    where
+        R: VecZnxToMut,
+    {
+        vec_znx_zero::<_, FFT64Spqlios>(res, res_col);
+    }
+}
 
 unsafe impl VecZnxNormalizeTmpBytesImpl<Self> for FFT64Spqlios {
     fn vec_znx_normalize_tmp_bytes_impl(module: &Module<Self>) -> usize {

@@ -12,7 +12,7 @@ },
     reference::{
         fft64::{
             reim::{ReimCopy, ReimZero, reim_copy_ref, reim_negate_inplace_ref, reim_negate_ref, reim_zero_ref},
-            vec_znx_dft::vec_znx_dft_copy,
+            vec_znx_dft::{vec_znx_dft_copy, vec_znx_dft_zero},
         },
         znx::znx_zero_ref,
     },
@@ -426,10 +426,10 @@ }
 }
 
 unsafe impl VecZnxDftZeroImpl<Self> for FFT64Spqlios {
-    fn vec_znx_dft_zero_impl<R>(_module: &Module<Self>, res: &mut R)
+    fn vec_znx_dft_zero_impl<R>(_module: &Module<Self>, res: &mut R, res_col: usize)
     where
         R: VecZnxDftToMut<Self>,
     {
-        res.to_mut().data.fill(0);
+        vec_znx_dft_zero(res, res_col);
     }
 }

@@ -1,6 +1,6 @@
 [package]
 name = "poulpy-core"
-version = "0.2.0"
+version = "0.3.1"
 edition = "2024"
 license = "Apache-2.0"
 description = "A backend agnostic crate implementing RLWE-based encryption & arithmetic."
@@ -15,6 +15,7 @@ poulpy-hal = {workspace = true}
 poulpy-backend = {workspace = true}
 itertools = {workspace = true}
 byteorder = {workspace = true}
+bytemuck = {workspace = true}
 once_cell = {workspace = true}
 
 [[bench]]

@@ -1,11 +1,10 @@
 use poulpy_hal::{
-    api::VecZnxAutomorphism,
-    layouts::{Backend, DataMut, GaloisElement, Module, Scratch},
+    api::{VecZnxAutomorphism, VecZnxAutomorphismInplace},
+    layouts::{Backend, CyclotomicOrder, DataMut, GaloisElement, Module, Scratch},
 };
 
 use crate::{
-    ScratchTakeCore,
-    automorphism::glwe_ct::GLWEAutomorphism,
+    GLWEKeyswitch, ScratchTakeCore,
     layouts::{
         GGLWE, GGLWEInfos, GGLWEPreparedToRef, GGLWEToMut, GGLWEToRef, GLWE, GLWEAutomorphismKey, GetGaloisElement,
         SetGaloisElement,
@@ -45,14 +44,10 @@ module.glwe_automorphism_key_automorphism_inplace(self, key, scratch);
     }
 }
 
-impl<BE: Backend> GLWEAutomorphismKeyAutomorphism<BE> for Module<BE> where
-    Self: GaloisElement + GLWEAutomorphism<BE> + VecZnxAutomorphism
-{
-}
-
-pub trait GLWEAutomorphismKeyAutomorphism<BE: Backend>
+impl<BE: Backend> GLWEAutomorphismKeyAutomorphism<BE> for Module<BE>
 where
-    Self: GaloisElement + GLWEAutomorphism<BE> + VecZnxAutomorphism,
+    Self: GaloisElement + GLWEKeyswitch<BE> + VecZnxAutomorphism + VecZnxAutomorphismInplace<BE> + CyclotomicOrder,
+    Scratch<BE>: ScratchTakeCore<BE>,
 {
     fn glwe_automorphism_key_automorphism_tmp_bytes<R, A, K>(&self, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
     where
@@ -68,7 +63,6 @@ where
         R: GGLWEToMut + SetGaloisElement + GGLWEInfos,
         A: GGLWEToRef + GetGaloisElement + GGLWEInfos,
         K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
-        Scratch<BE>: ScratchTakeCore<BE>,
     {
         assert!(
             res.dnum().as_u32() <= a.dnum().as_u32(),
@@ -163,3 +157,22 @@
         res.set_p((res.p() * key.p()) % self.cyclotomic_order());
     }
 }
+
+pub trait GLWEAutomorphismKeyAutomorphism<BE: Backend> {
+    fn glwe_automorphism_key_automorphism_tmp_bytes<R, A, K>(&self, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
+    where
+        R: GGLWEInfos,
+        A: GGLWEInfos,
+        K: GGLWEInfos;
+
+    fn glwe_automorphism_key_automorphism<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GGLWEToMut + SetGaloisElement + GGLWEInfos,
+        A: GGLWEToRef + GetGaloisElement + GGLWEInfos,
+        K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos;
+
+    fn glwe_automorphism_key_automorphism_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GGLWEToMut + SetGaloisElement + GetGaloisElement + GGLWEInfos,
+        K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos;
+}

@@ -7,8 +7,8 @@ use crate::{
     GGSWExpandRows, ScratchTakeCore,
     automorphism::glwe_ct::GLWEAutomorphism,
     layouts::{
-        GGLWEInfos, GGLWEPreparedToRef, GGSW, GGSWInfos, GGSWToMut, GGSWToRef, GetGaloisElement,
-        prepared::{GLWETensorKeyPrepared, GLWETensorKeyPreparedToRef},
+        GGLWEInfos, GGLWEPreparedToRef, GGLWEToGGSWKeyPrepared, GGLWEToGGSWKeyPreparedToRef, GGSW, GGSWInfos, GGSWToMut,
+        GGSWToRef, GetGaloisElement,
     },
 };
 
@@ -36,7 +36,7 @@ pub fn automorphism<A, K, T, M, BE: Backend>(&mut self, module: &M, a: &A, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
         A: GGSWToRef,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
-        T: GLWETensorKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
         M: GGSWAutomorphism<BE>,
     {
@@ -46,7 +46,7 @@
     pub fn automorphism_inplace<K, T, M, BE: Backend>(&mut self, module: &M, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
-        T: GLWETensorKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
         M: GGSWAutomorphism<BE>,
     {
@@ -67,11 +67,8 @@ A: GGSWInfos,
         K: GGLWEInfos,
         T: GGLWEInfos,
     {
-        let out_size: usize = res_infos.size();
-        let ci_dft: usize = self.bytes_of_vec_znx_dft((key_infos.rank_out() + 1).into(), out_size);
-        let ks_internal: usize = self.glwe_automorphism_tmp_bytes(res_infos, a_infos, key_infos);
-        let expand: usize = self.ggsw_expand_rows_tmp_bytes(res_infos, tsk_infos);
-        ci_dft + (ks_internal.max(expand))
+        self.glwe_automorphism_tmp_bytes(res_infos, a_infos, key_infos)
+            .max(self.ggsw_expand_rows_tmp_bytes(res_infos, tsk_infos))
     }
 
     fn ggsw_automorphism<R, A, K, T>(&self, res: &mut R, a: &A, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
@@ -79,12 +76,12 @@ where
         R: GGSWToMut,
         A: GGSWToRef,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
-        T: GLWETensorKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
         let a: &GGSW<&[u8]> = &a.to_ref();
-        let tsk: &GLWETensorKeyPrepared<&[u8], BE> = &tsk.to_ref();
+        let tsk: &GGLWEToGGSWKeyPrepared<&[u8], BE> = &tsk.to_ref();
 
         assert_eq!(res.dsize(), a.dsize());
         assert!(res.dnum() <= a.dnum());
@@ -104,11 +101,11 @@ fn ggsw_automorphism_inplace<R, K, T>(&self, res: &mut R, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
         R: GGSWToMut,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
-        T: GLWETensorKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
-        let tsk: &GLWETensorKeyPrepared<&[u8], BE> = &tsk.to_ref();
+        let tsk: &GGLWEToGGSWKeyPrepared<&[u8], BE> = &tsk.to_ref();
 
         // Keyswitch the j-th row of the col 0
         for row in 0..res.dnum().as_usize() {

@@ -1,13 +1,13 @@
 use poulpy_hal::{
     api::{
-        ScratchTakeBasic, VecZnxAutomorphismInplace, VecZnxBigAutomorphismInplace, VecZnxBigSubSmallInplace,
-        VecZnxBigSubSmallNegateInplace,
+        ScratchTakeBasic, VecZnxAutomorphismInplace, VecZnxBigAddSmallInplace, VecZnxBigAutomorphismInplace, VecZnxBigNormalize,
+        VecZnxBigSubSmallInplace, VecZnxBigSubSmallNegateInplace, VecZnxNormalize,
     },
     layouts::{Backend, DataMut, Module, Scratch, VecZnxBig},
 };
 
 use crate::{
-    GLWEKeyswitch, ScratchTakeCore, keyswitch_internal,
+    GLWEKeySwitchInternal, GLWEKeyswitch, ScratchTakeCore,
     layouts::{GGLWEInfos, GGLWEPreparedToRef, GLWE, GLWEInfos, GLWEToMut, GLWEToRef, GetGaloisElement, LWEInfos},
 };
 
@@ -101,13 +101,71 @@ module.glwe_automorphism_sub_negate_inplace(self, key, scratch);
     }
 }
 
-pub trait GLWEAutomorphism<BE: Backend>
+pub trait GLWEAutomorphism<BE: Backend> {
+    fn glwe_automorphism_tmp_bytes<R, A, K>(&self, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
+    where
+        R: GLWEInfos,
+        A: GLWEInfos,
+        K: GGLWEInfos;
+
+    fn glwe_automorphism<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
+
+    fn glwe_automorphism_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
+
+    fn glwe_automorphism_add<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
+
+    fn glwe_automorphism_add_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
+
+    fn glwe_automorphism_sub<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
+
+    fn glwe_automorphism_sub_negate<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
+
+    fn glwe_automorphism_sub_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
+
+    fn glwe_automorphism_sub_negate_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
+}
+
+impl<BE: Backend> GLWEAutomorphism<BE> for Module<BE>
 where
-    Self: GLWEKeyswitch<BE>
+    Self: Sized
+        + GLWEKeyswitch<BE>
+        + GLWEKeySwitchInternal<BE>
+        + VecZnxNormalize<BE>
         + VecZnxAutomorphismInplace<BE>
         + VecZnxBigAutomorphismInplace<BE>
         + VecZnxBigSubSmallInplace<BE>
-        + VecZnxBigSubSmallNegateInplace<BE>,
+        + VecZnxBigSubSmallNegateInplace<BE>
+        + VecZnxBigAddSmallInplace<BE>
+        + VecZnxBigNormalize<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
 {
     fn glwe_automorphism_tmp_bytes<R, A, K>(&self, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
     where
@@ -160,7 +218,7 @@ let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         let a: &GLWE<&[u8]> = &a.to_ref();
 
         let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // TODO: optimise size
-        let mut res_big: VecZnxBig<_, BE> = keyswitch_internal(self, res_dft, a, key, scratch_1);
+        let mut res_big: VecZnxBig<_, BE> = self.glwe_keyswitch_internal(res_dft, a, key, scratch_1);
 
         for i in 0..res.rank().as_usize() + 1 {
             self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_1);
@@ -186,7 +244,7 @@ {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
 
         let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // TODO: optimise size
-        let mut res_big: VecZnxBig<_, BE> = keyswitch_internal(self, res_dft, res, key, scratch_1);
+        let mut res_big: VecZnxBig<_, BE> = self.glwe_keyswitch_internal(res_dft, res, key, scratch_1);
 
         for i in 0..res.rank().as_usize() + 1 {
             self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_1);
@@ -214,7 +272,7 @@ let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         let a: &GLWE<&[u8]> = &a.to_ref();
 
         let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // TODO: optimise size
-        let mut res_big: VecZnxBig<_, BE> = keyswitch_internal(self, res_dft, a, key, scratch_1);
+        let mut res_big: VecZnxBig<_, BE> = self.glwe_keyswitch_internal(res_dft, a, key, scratch_1);
 
         for i in 0..res.rank().as_usize() + 1 {
             self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_1);
@@ -242,7 +300,7 @@ let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         let a: &GLWE<&[u8]> = &a.to_ref();
 
         let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // TODO: optimise size
-        let mut res_big: VecZnxBig<_, BE> = keyswitch_internal(self, res_dft, a, key, scratch_1);
+        let mut res_big: VecZnxBig<_, BE> = self.glwe_keyswitch_internal(res_dft, a, key, scratch_1);
 
         for i in 0..res.rank().as_usize() + 1 {
             self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_1);
@@ -268,7 +326,7 @@ {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
 
         let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // TODO: optimise size
-        let mut res_big: VecZnxBig<_, BE> = keyswitch_internal(self, res_dft, res, key, scratch_1);
+        let mut res_big: VecZnxBig<_, BE> = self.glwe_keyswitch_internal(res_dft, res, key, scratch_1);
 
         for i in 0..res.rank().as_usize() + 1 {
             self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_1);
@@ -294,7 +352,7 @@ {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
 
         let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // TODO: optimise size
-        let mut res_big: VecZnxBig<_, BE> = keyswitch_internal(self, res_dft, res, key, scratch_1);
+        let mut res_big: VecZnxBig<_, BE> = self.glwe_keyswitch_internal(res_dft, res, key, scratch_1);
 
         for i in 0..res.rank().as_usize() + 1 {
             self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_1);
@@ -311,12 +369,3 @@ );
         }
     }
 }
-
-impl<BE: Backend> GLWEAutomorphism<BE> for Module<BE> where
-    Self: GLWEKeyswitch<BE>
-        + VecZnxAutomorphismInplace<BE>
-        + VecZnxBigAutomorphismInplace<BE>
-        + VecZnxBigSubSmallInplace<BE>
-        + VecZnxBigSubSmallNegateInplace<BE>
-{
-}

@@ -1,17 +1,16 @@
 use poulpy_hal::{
     api::{
-        ModuleN, ScratchAvailable, ScratchTakeBasic, VecZnxBigBytesOf, VecZnxBigNormalize, VecZnxDftAddInplace, VecZnxDftApply,
-        VecZnxDftBytesOf, VecZnxDftCopy, VecZnxIdftApplyTmpA, VecZnxNormalize, VecZnxNormalizeTmpBytes, VmpApplyDftToDft,
-        VmpApplyDftToDftAdd, VmpApplyDftToDftTmpBytes,
+        ScratchAvailable, ScratchTakeBasic, VecZnxBigAddSmallInplace, VecZnxBigBytesOf, VecZnxBigNormalize,
+        VecZnxBigNormalizeTmpBytes, VecZnxDftApply, VecZnxDftBytesOf, VecZnxIdftApplyConsume, VecZnxNormalize,
     },
-    layouts::{Backend, DataMut, Module, Scratch, VmpPMat, ZnxInfos},
+    layouts::{Backend, DataMut, Module, Scratch, VecZnxBig},
 };
 
 use crate::{
-    GLWECopy, ScratchTakeCore,
+    GGLWEProduct, GLWECopy, ScratchTakeCore,
     layouts::{
-        GGLWE, GGLWEInfos, GGLWEToRef, GGSW, GGSWInfos, GGSWToMut, GLWEInfos, LWEInfos,
-        prepared::{GLWETensorKeyPrepared, GLWETensorKeyPreparedToRef},
+        GGLWE, GGLWEInfos, GGLWEToGGSWKeyPrepared, GGLWEToGGSWKeyPreparedToRef, GGLWEToRef, GGSW, GGSWInfos, GGSWToMut, GLWE,
+        GLWEInfos, LWEInfos,
     },
 };
 
@@ -31,7 +30,7 @@ pub fn from_gglwe<G, M, T, BE: Backend>(&mut self, module: &M, gglwe: &G, tsk: &T, scratch: &mut Scratch<BE>)
     where
         M: GGSWFromGGLWE<BE>,
         G: GGLWEToRef,
-        T: GLWETensorKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         module.ggsw_from_gglwe(self, gglwe, tsk, scratch);
@@ -54,12 +53,12 @@ fn ggsw_from_gglwe<R, A, T>(&self, res: &mut R, a: &A, tsk: &T, scratch: &mut Scratch<BE>)
     where
         R: GGSWToMut,
         A: GGLWEToRef,
-        T: GLWETensorKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
         let a: &GGLWE<&[u8]> = &a.to_ref();
-        let tsk: &GLWETensorKeyPrepared<&[u8], BE> = &tsk.to_ref();
+        let tsk: &GGLWEToGGSWKeyPrepared<&[u8], BE> = &tsk.to_ref();
 
         assert_eq!(res.rank(), a.rank_out());
         assert_eq!(res.dnum(), a.dnum());
@@ -85,177 +84,140 @@ fn ggsw_from_gglwe<R, A, T>(&self, res: &mut R, a: &A, tsk: &T, scratch: &mut Scratch<BE>)
     where
         R: GGSWToMut,
         A: GGLWEToRef,
-        T: GLWETensorKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>;
 }
 
-impl<BE: Backend> GGSWExpandRows<BE> for Module<BE> where
-    Self: Sized
-        + ModuleN
-        + VecZnxDftBytesOf
-        + VmpApplyDftToDftTmpBytes
-        + VecZnxBigBytesOf
-        + VecZnxNormalizeTmpBytes
-        + VecZnxDftBytesOf
-        + VmpApplyDftToDftTmpBytes
-        + VecZnxBigBytesOf
-        + VecZnxNormalizeTmpBytes
-        + VecZnxDftApply<BE>
-        + VecZnxDftCopy<BE>
-        + VmpApplyDftToDft<BE>
-        + VmpApplyDftToDftAdd<BE>
-        + VecZnxDftAddInplace<BE>
-        + VecZnxBigNormalize<BE>
-        + VecZnxIdftApplyTmpA<BE>
-        + VecZnxNormalize<BE>
-{
+pub trait GGSWExpandRows<BE: Backend> {
+    fn ggsw_expand_rows_tmp_bytes<R, A>(&self, res_infos: &R, tsk_infos: &A) -> usize
+    where
+        R: GGSWInfos,
+        A: GGLWEInfos;
+
+    fn ggsw_expand_row<R, T>(&self, res: &mut R, tsk: &T, scratch: &mut Scratch<BE>)
+    where
+        R: GGSWToMut,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>;
 }
 
-pub trait GGSWExpandRows<BE: Backend>
+impl<BE: Backend> GGSWExpandRows<BE> for Module<BE>
 where
-    Self: Sized
-        + ModuleN
-        + VecZnxDftBytesOf
-        + VmpApplyDftToDftTmpBytes
+    Self: GGLWEProduct<BE>
+        + VecZnxBigNormalize<BE>
+        + VecZnxBigNormalizeTmpBytes
         + VecZnxBigBytesOf
-        + VecZnxNormalizeTmpBytes
+        + VecZnxDftBytesOf
         + VecZnxDftApply<BE>
-        + VecZnxDftCopy<BE>
-        + VmpApplyDftToDft<BE>
-        + VmpApplyDftToDftAdd<BE>
-        + VecZnxDftAddInplace<BE>
-        + VecZnxBigNormalize<BE>
-        + VecZnxIdftApplyTmpA<BE>
-        + VecZnxNormalize<BE>,
+        + VecZnxNormalize<BE>
+        + VecZnxBigAddSmallInplace<BE>
+        + VecZnxIdftApplyConsume<BE>,
 {
     fn ggsw_expand_rows_tmp_bytes<R, A>(&self, res_infos: &R, tsk_infos: &A) -> usize
     where
         R: GGSWInfos,
         A: GGLWEInfos,
     {
-        let tsk_size: usize = tsk_infos.k().div_ceil(tsk_infos.base2k()) as usize;
-        let size_in: usize = res_infos
-            .k()
-            .div_ceil(tsk_infos.base2k())
-            .div_ceil(tsk_infos.dsize().into()) as usize;
+        let base2k_in: usize = res_infos.base2k().into();
+        let base2k_tsk: usize = tsk_infos.base2k().into();
+
+        let rank: usize = res_infos.rank().into();
+        let cols: usize = rank + 1;
 
-        let tmp_dft_i: usize = self.bytes_of_vec_znx_dft((tsk_infos.rank_out() + 1).into(), tsk_size);
-        let tmp_a: usize = self.bytes_of_vec_znx_dft(1, size_in);
-        let vmp: usize = self.vmp_apply_dft_to_dft_tmp_bytes(
-            tsk_size,
-            size_in,
-            size_in,
-            (tsk_infos.rank_in()).into(),  // Verify if rank+1
-            (tsk_infos.rank_out()).into(), // Verify if rank+1
-            tsk_size,
-        );
-        let tmp_idft: usize = self.bytes_of_vec_znx_big(1, tsk_size);
-        let norm: usize = self.vec_znx_normalize_tmp_bytes();
+        let res_size = res_infos.size();
+        let a_size: usize = (res_infos.size() * base2k_in).div_ceil(base2k_tsk);
 
-        tmp_dft_i + ((tmp_a + vmp) | (tmp_idft + norm))
+        let a_dft = self.bytes_of_vec_znx_dft(cols - 1, a_size);
+        let res_dft = self.bytes_of_vec_znx_dft(cols, a_size);
+        let gglwe_prod: usize = self.gglwe_product_dft_tmp_bytes(res_size, a_size, tsk_infos);
+        let normalize = self.vec_znx_big_normalize_tmp_bytes();
+
+        (a_dft + res_dft + gglwe_prod).max(normalize)
     }
 
     fn ggsw_expand_row<R, T>(&self, res: &mut R, tsk: &T, scratch: &mut Scratch<BE>)
     where
         R: GGSWToMut,
-        T: GLWETensorKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
-        let tsk: &GLWETensorKeyPrepared<&[u8], BE> = &tsk.to_ref();
+        let tsk: &GGLWEToGGSWKeyPrepared<&[u8], BE> = &tsk.to_ref();
 
-        let basek_in: usize = res.base2k().into();
-        let basek_tsk: usize = tsk.base2k().into();
+        let base2k_in: usize = res.base2k().into();
+        let base2k_tsk: usize = tsk.base2k().into();
 
         assert!(scratch.available() >= self.ggsw_expand_rows_tmp_bytes(res, tsk));
 
         let rank: usize = res.rank().into();
         let cols: usize = rank + 1;
 
-        let a_size: usize = (res.size() * basek_in).div_ceil(basek_tsk);
+        let a_size: usize = (res.size() * base2k_in).div_ceil(base2k_tsk);
 
         // Keyswitch the j-th row of the col 0
-        for row_i in 0..res.dnum().into() {
-            let a = &res.at(row_i, 0).data;
+        for row in 0..res.dnum().as_usize() {
+            let (mut a_dft, scratch_1) = scratch.take_vec_znx_dft(self, cols - 1, a_size);
 
-            // Pre-compute DFT of (a0, a1, a2)
-            let (mut ci_dft, scratch_1) = scratch.take_vec_znx_dft(self, cols, a_size);
+            {
+                let glwe_mi_1: &GLWE<&[u8]> = &res.at(row, 0);
 
-            if basek_in == basek_tsk {
-                for i in 0..cols {
-                    self.vec_znx_dft_apply(1, 0, &mut ci_dft, i, a, i);
-                }
-            } else {
-                let (mut a_conv, scratch_2) = scratch_1.take_vec_znx(self.n(), 1, a_size);
-                for i in 0..cols {
-                    self.vec_znx_normalize(basek_tsk, &mut a_conv, 0, basek_in, a, i, scratch_2);
-                    self.vec_znx_dft_apply(1, 0, &mut ci_dft, i, &a_conv, 0);
+                if base2k_in == base2k_tsk {
+                    for col_i in 0..cols - 1 {
+                        self.vec_znx_dft_apply(1, 0, &mut a_dft, col_i, glwe_mi_1.data(), col_i + 1);
+                    }
+                } else {
+                    let (mut a_conv, scratch_2) = scratch_1.take_vec_znx(self.n(), 1, a_size);
+                    for i in 0..cols - 1 {
+                        self.vec_znx_normalize(
+                            base2k_tsk,
+                            &mut a_conv,
+                            0,
+                            base2k_in,
+                            glwe_mi_1.data(),
+                            i + 1,
+                            scratch_2,
+                        );
+                        self.vec_znx_dft_apply(1, 0, &mut a_dft, i, &a_conv, 0);
+                    }
                 }
             }
 
-            for col_j in 1..cols {
-                // Example for rank 3:
-                //
-                // Note: M is a vector (m, Bm, B^2m, B^3m, ...), so each column is
-                // actually composed of that many dnum and we focus on a specific row here
-                // implicitely given ci_dft.
-                //
-                // # Input
-                //
-                // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0    , a1    , a2    )
-                // col 1: (0, 0, 0, 0)
-                // col 2: (0, 0, 0, 0)
-                // col 3: (0, 0, 0, 0)
+            // Example for rank 3:
+            //
+            // Note: M is a vector (m, Bm, B^2m, B^3m, ...), so each column is
+            // actually composed of that many dnum and we focus on a specific row here
+            // implicitely given ci_dft.
+            //
+            // # Input
+            //
+            // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0    , a1    , a2    )
+            // col 1: (0, 0, 0, 0)
+            // col 2: (0, 0, 0, 0)
+            // col 3: (0, 0, 0, 0)
+            //
+            // # Output
+            //
+            // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0       , a1       , a2       )
+            // col 1: (-(b0s0 + b1s1 + b2s2)       , b0 + M[i], b1       , b2       )
+            // col 2: (-(c0s0 + c1s1 + c2s2)       , c0       , c1 + M[i], c2       )
+            // col 3: (-(d0s0 + d1s1 + d2s2)       , d0       , d1       , d2 + M[i])
+            for col in 1..cols {
+                let (mut res_dft, scratch_2) = scratch_1.take_vec_znx_dft(self, cols, tsk.size()); // Todo optimise
+
+                // Performs a key-switch for each combination of s[i]*s[j], i.e. for a0, a1, a2
                 //
-                // # Output
+                // # Example for col=1
                 //
-                // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0       , a1       , a2       )
-                // col 1: (-(b0s0 + b1s1 + b2s2)       , b0 + M[i], b1       , b2       )
-                // col 2: (-(c0s0 + c1s1 + c2s2)       , c0       , c1 + M[i], c2       )
-                // col 3: (-(d0s0 + d1s1 + d2s2)       , d0       , d1       , d2 + M[i])
+                // a0 * (-(f0s0 + f1s1 + f1s2) + s0^2, f0, f1, f2) = (-(a0f0s0 + a0f1s1 + a0f1s2) + a0s0^2, a0f0, a0f1, a0f2)
+                // +
+                // a1 * (-(g0s0 + g1s1 + g1s2) + s0s1, g0, g1, g2) = (-(a1g0s0 + a1g1s1 + a1g1s2) + a1s0s1, a1g0, a1g1, a1g2)
+                // +
+                // a2 * (-(h0s0 + h1s1 + h1s2) + s0s2, h0, h1, h2) = (-(a2h0s0 + a2h1s1 + a2h1s2) + a2s0s2, a2h0, a2h1, a2h2)
+                // =
+                // (-(x0s0 + x1s1 + x2s2) + s0(a0s0 + a1s1 + a2s2), x0, x1, x2)
+                self.gglwe_product_dft(&mut res_dft, &a_dft, tsk.at(col - 1), scratch_2);
 
-                let dsize: usize = tsk.dsize().into();
-
-                let (mut tmp_dft_i, scratch_2) = scratch_1.take_vec_znx_dft(self, cols, tsk.size());
-                let (mut tmp_a, scratch_3) = scratch_2.take_vec_znx_dft(self, 1, ci_dft.size().div_ceil(dsize));
-
-                {
-                    // Performs a key-switch for each combination of s[i]*s[j], i.e. for a0, a1, a2
-                    //
-                    // # Example for col=1
-                    //
-                    // a0 * (-(f0s0 + f1s1 + f1s2) + s0^2, f0, f1, f2) = (-(a0f0s0 + a0f1s1 + a0f1s2) + a0s0^2, a0f0, a0f1, a0f2)
-                    // +
-                    // a1 * (-(g0s0 + g1s1 + g1s2) + s0s1, g0, g1, g2) = (-(a1g0s0 + a1g1s1 + a1g1s2) + a1s0s1, a1g0, a1g1, a1g2)
-                    // +
-                    // a2 * (-(h0s0 + h1s1 + h1s2) + s0s2, h0, h1, h2) = (-(a2h0s0 + a2h1s1 + a2h1s2) + a2s0s2, a2h0, a2h1, a2h2)
-                    // =
-                    // (-(x0s0 + x1s1 + x2s2) + s0(a0s0 + a1s1 + a2s2), x0, x1, x2)
-                    for col_i in 1..cols {
-                        let pmat: &VmpPMat<&[u8], BE> = &tsk.at(col_i - 1, col_j - 1).data; // Selects Enc(s[i]s[j])
-
-                        // Extracts a[i] and multipies with Enc(s[i]s[j])
-                        for di in 0..dsize {
-                            tmp_a.set_size((ci_dft.size() + di) / dsize);
-
-                            // Small optimization for dsize > 2
-                            // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
-                            // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(dsize-1) * B}.
-                            // As such we can ignore the last dsize-2 limbs safely of the sum of vmp products.
-                            // It is possible to further ignore the last dsize-1 limbs, but this introduce
-                            // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
-                            // noise is kept with respect to the ideal functionality.
-                            tmp_dft_i.set_size(tsk.size() - ((dsize - di) as isize - 2).max(0) as usize);
-
-                            self.vec_znx_dft_copy(dsize, dsize - 1 - di, &mut tmp_a, 0, &ci_dft, col_i);
-                            if di == 0 && col_i == 1 {
-                                self.vmp_apply_dft_to_dft(&mut tmp_dft_i, &tmp_a, pmat, scratch_3);
-                            } else {
-                                self.vmp_apply_dft_to_dft_add(&mut tmp_dft_i, &tmp_a, pmat, di, scratch_3);
-                            }
-                        }
-                    }
-                }
+                let mut res_big: VecZnxBig<&mut [u8], BE> = self.vec_znx_idft_apply_consume(res_dft);
 
                 // Adds -(sum a[i] * s[i]) + m)  on the i-th column of tmp_idft_i
                 //
@@ -266,18 +228,17 @@ // =
                 // (-(x0s0 + x1s1 + x2s2) + s0(a0s0 + a1s1 + a2s2), x0 -(a0s0 + a1s1 + a2s2) + M[i], x1, x2)
                 // =
                 // (-(x0s0 + x1s1 + x2s2), x0 + M[i], x1, x2)
-                self.vec_znx_dft_add_inplace(&mut tmp_dft_i, col_j, &ci_dft, 0);
-                let (mut tmp_idft, scratch_3) = scratch_2.take_vec_znx_big(self, 1, tsk.size());
-                for i in 0..cols {
-                    self.vec_znx_idft_apply_tmpa(&mut tmp_idft, 0, &mut tmp_dft_i, i);
+                self.vec_znx_big_add_small_inplace(&mut res_big, col, res.at(row, 0).data(), 0);
+
+                for j in 0..cols {
                     self.vec_znx_big_normalize(
-                        basek_in,
-                        &mut res.at_mut(row_i, col_j).data,
-                        i,
-                        basek_tsk,
-                        &tmp_idft,
-                        0,
-                        scratch_3,
+                        res.base2k().as_usize(),
+                        res.at_mut(row, col).data_mut(),
+                        j,
+                        tsk.base2k().as_usize(),
+                        &res_big,
+                        j,
+                        scratch_2,
                     );
                 }
             }

@@ -1,5 +1,5 @@
 use poulpy_hal::{
-    api::ScratchTakeBasic,
+    api::{ScratchTakeBasic, VecZnxNormalize, VecZnxNormalizeTmpBytes},
     layouts::{Backend, DataMut, Module, Scratch, VecZnx, ZnxView, ZnxViewMut, ZnxZero},
 };
 
@@ -8,11 +8,10 @@ GLWEKeyswitch, ScratchTakeCore,
     layouts::{GGLWEInfos, GGLWEPreparedToRef, GLWE, GLWEInfos, GLWELayout, GLWEToMut, LWE, LWEInfos, LWEToRef},
 };
 
-impl<BE: Backend> GLWEFromLWE<BE> for Module<BE> where Self: GLWEKeyswitch<BE> {}
-
-pub trait GLWEFromLWE<BE: Backend>
+impl<BE: Backend> GLWEFromLWE<BE> for Module<BE>
 where
-    Self: GLWEKeyswitch<BE>,
+    Self: GLWEKeyswitch<BE> + VecZnxNormalizeTmpBytes + VecZnxNormalize<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
 {
     fn glwe_from_lwe_tmp_bytes<R, A, K>(&self, glwe_infos: &R, lwe_infos: &A, key_infos: &K) -> usize
     where
@@ -41,7 +40,6 @@ where
         R: GLWEToMut,
         A: LWEToRef,
         K: GGLWEPreparedToRef<BE> + GGLWEInfos,
-        Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         let lwe: &LWE<&[u8]> = &lwe.to_ref();
@@ -103,6 +101,23 @@ }
 
         self.glwe_keyswitch(res, &glwe, ksk, scratch_1);
     }
+}
+
+pub trait GLWEFromLWE<BE: Backend>
+where
+    Self: GLWEKeyswitch<BE>,
+{
+    fn glwe_from_lwe_tmp_bytes<R, A, K>(&self, glwe_infos: &R, lwe_infos: &A, key_infos: &K) -> usize
+    where
+        R: GLWEInfos,
+        A: LWEInfos,
+        K: GGLWEInfos;
+
+    fn glwe_from_lwe<R, A, K>(&self, res: &mut R, lwe: &A, ksk: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        A: LWEToRef,
+        K: GGLWEPreparedToRef<BE> + GGLWEInfos;
 }
 
 impl GLWE<Vec<u8>> {

@@ -0,0 +1,124 @@
+use poulpy_hal::{
+    api::{ModuleN, ScratchTakeBasic, VecZnxCopy},
+    layouts::{Backend, DataMut, Module, Scratch},
+    source::Source,
+};
+
+use crate::{
+    GGLWECompressedEncryptSk, GetDistribution, ScratchTakeCore,
+    layouts::{
+        GGLWEInfos, GGLWEToGGSWKeyCompressed, GGLWEToGGSWKeyCompressedToMut, GLWEInfos, GLWESecret, GLWESecretTensor,
+        GLWESecretTensorFactory, GLWESecretToRef,
+        prepared::{GLWESecretPrepared, GLWESecretPreparedFactory},
+    },
+};
+
+impl GGLWEToGGSWKeyCompressed<Vec<u8>> {
+    pub fn encrypt_sk_tmp_bytes<M, A, BE: Backend>(module: &M, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+        M: GGLWEToGGSWKeyCompressedEncryptSk<BE>,
+    {
+        module.gglwe_to_ggsw_key_encrypt_sk_tmp_bytes(infos)
+    }
+}
+
+impl<DataSelf: DataMut> GGLWEToGGSWKeyCompressed<DataSelf> {
+    pub fn encrypt_sk<M, S, BE: Backend>(
+        &mut self,
+        module: &M,
+        sk: &S,
+        seed_xa: [u8; 32],
+        source_xe: &mut Source,
+        scratch: &mut Scratch<BE>,
+    ) where
+        M: GGLWEToGGSWKeyCompressedEncryptSk<BE>,
+        S: GLWESecretToRef + GetDistribution + GLWEInfos,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        module.gglwe_to_ggsw_key_encrypt_sk(self, sk, seed_xa, source_xe, scratch);
+    }
+}
+
+pub trait GGLWEToGGSWKeyCompressedEncryptSk<BE: Backend> {
+    fn gglwe_to_ggsw_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos;
+
+    fn gglwe_to_ggsw_key_encrypt_sk<R, S>(
+        &self,
+        res: &mut R,
+        sk: &S,
+        seed_xa: [u8; 32],
+        source_xe: &mut Source,
+        scratch: &mut Scratch<BE>,
+    ) where
+        R: GGLWEToGGSWKeyCompressedToMut + GGLWEInfos,
+        S: GLWESecretToRef + GetDistribution + GLWEInfos;
+}
+
+impl<BE: Backend> GGLWEToGGSWKeyCompressedEncryptSk<BE> for Module<BE>
+where
+    Self: ModuleN + GGLWECompressedEncryptSk<BE> + GLWESecretTensorFactory<BE> + GLWESecretPreparedFactory<BE> + VecZnxCopy,
+    Scratch<BE>: ScratchTakeCore<BE>,
+{
+    fn gglwe_to_ggsw_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+    {
+        let sk_prepared: usize = GLWESecretPrepared::bytes_of(self, infos.rank());
+        let sk_tensor: usize = GLWESecretTensor::bytes_of_from_infos(infos);
+        let gglwe_encrypt: usize = self.gglwe_compressed_encrypt_sk_tmp_bytes(infos);
+        let sk_ij = GLWESecret::bytes_of(self.n().into(), infos.rank());
+        (sk_prepared + sk_tensor + sk_ij) + gglwe_encrypt.max(self.glwe_secret_tensor_prepare_tmp_bytes(infos.rank()))
+    }
+
+    fn gglwe_to_ggsw_key_encrypt_sk<R, S>(
+        &self,
+        res: &mut R,
+        sk: &S,
+        seed_xa: [u8; 32],
+        source_xe: &mut Source,
+        scratch: &mut Scratch<BE>,
+    ) where
+        R: GGLWEToGGSWKeyCompressedToMut + GGLWEInfos,
+        S: GLWESecretToRef + GetDistribution + GLWEInfos,
+    {
+        assert_eq!(res.rank(), sk.rank());
+        assert_eq!(res.n(), sk.n());
+
+        let res: &mut GGLWEToGGSWKeyCompressed<&mut [u8]> = &mut res.to_mut();
+        let rank: usize = res.rank_out().as_usize();
+
+        let (mut sk_prepared, scratch_1) = scratch.take_glwe_secret_prepared(self, res.rank());
+        let (mut sk_tensor, scratch_2) = scratch_1.take_glwe_secret_tensor(self.n().into(), res.rank());
+        sk_prepared.prepare(self, sk);
+        sk_tensor.prepare(self, sk, scratch_2);
+
+        let (mut sk_ij, scratch_3) = scratch_2.take_scalar_znx(self.n(), rank);
+
+        let mut source_xa = Source::new(seed_xa);
+
+        for i in 0..rank {
+            for j in 0..rank {
+                self.vec_znx_copy(
+                    &mut sk_ij.as_vec_znx_mut(),
+                    j,
+                    &sk_tensor.at(i, j).as_vec_znx(),
+                    0,
+                );
+            }
+
+            let (seed_xa_tmp, _) = source_xa.branch();
+
+            res.at_mut(i).encrypt_sk(
+                self,
+                &sk_ij,
+                &sk_prepared,
+                seed_xa_tmp,
+                source_xe,
+                scratch_3,
+            );
+        }
+    }
+}

@@ -1,17 +1,15 @@
 use poulpy_hal::{
-    api::{
-        ModuleN, ScratchTakeBasic, SvpApplyDftToDft, SvpPPolBytesOf, SvpPrepare, VecZnxBigBytesOf, VecZnxBigNormalize,
-        VecZnxDftApply, VecZnxDftBytesOf, VecZnxIdftApplyTmpA,
-    },
+    api::ScratchTakeBasic,
     layouts::{Backend, DataMut, Module, Scratch},
     source::Source,
 };
 
 use crate::{
-    GGLWECompressedEncryptSk, GLWETensorKeyEncryptSk, GetDistribution, ScratchTakeCore,
+    GGLWECompressedEncryptSk, GetDistribution, ScratchTakeCore,
     layouts::{
-        GGLWEInfos, GLWEInfos, GLWESecret, GLWESecretPrepared, GLWESecretPreparedFactory, GLWESecretToRef,
-        GLWETensorKeyCompressedAtMut, LWEInfos, Rank, compressed::GLWETensorKeyCompressed,
+        GGLWECompressedSeedMut, GGLWECompressedToMut, GGLWEInfos, GGLWELayout, GLWEInfos, GLWESecretPrepared,
+        GLWESecretPreparedFactory, GLWESecretTensor, GLWESecretTensorFactory, GLWESecretToRef,
+        compressed::GLWETensorKeyCompressed,
     },
 };
 
@@ -34,7 +32,7 @@ seed_xa: [u8; 32],
         source_xe: &mut Source,
         scratch: &mut Scratch<BE>,
     ) where
-        S: GLWESecretToRef + GetDistribution,
+        S: GLWESecretToRef + GetDistribution + GLWEInfos,
         M: GLWETensorKeyCompressedEncryptSk<BE>,
     {
         module.glwe_tensor_key_compressed_encrypt_sk(self, sk, seed_xa, source_xe, scratch);
@@ -46,7 +44,7 @@ fn glwe_tensor_key_compressed_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
     where
         A: GGLWEInfos;
 
-    fn glwe_tensor_key_compressed_encrypt_sk<R, S, D>(
+    fn glwe_tensor_key_compressed_encrypt_sk<R, S>(
         &self,
         res: &mut R,
         sk: &S,
@@ -54,40 +52,38 @@ seed_xa: [u8; 32],
         source_xe: &mut Source,
         scratch: &mut Scratch<BE>,
     ) where
-        D: DataMut,
-        R: GLWETensorKeyCompressedAtMut<D> + GGLWEInfos,
-        S: GLWESecretToRef + GetDistribution;
+        R: GGLWECompressedToMut + GGLWEInfos + GGLWECompressedSeedMut,
+        S: GLWESecretToRef + GetDistribution + GLWEInfos;
 }
 
 impl<BE: Backend> GLWETensorKeyCompressedEncryptSk<BE> for Module<BE>
 where
-    Self: ModuleN
-        + GGLWECompressedEncryptSk<BE>
-        + GLWETensorKeyEncryptSk<BE>
-        + VecZnxDftApply<BE>
-        + SvpApplyDftToDft<BE>
-        + VecZnxIdftApplyTmpA<BE>
-        + VecZnxBigNormalize<BE>
-        + SvpPrepare<BE>
-        + SvpPPolBytesOf
-        + VecZnxDftBytesOf
-        + VecZnxBigBytesOf
-        + GLWESecretPreparedFactory<BE>,
+    Self: GGLWECompressedEncryptSk<BE> + GLWESecretPreparedFactory<BE> + GLWESecretTensorFactory<BE>,
     Scratch<BE>: ScratchTakeBasic + ScratchTakeCore<BE>,
 {
     fn glwe_tensor_key_compressed_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
     where
         A: GGLWEInfos,
     {
-        GLWESecretPrepared::bytes_of(self, infos.rank_out())
-            + self.bytes_of_vec_znx_dft(infos.rank_out().into(), 1)
-            + self.bytes_of_vec_znx_big(1, 1)
-            + self.bytes_of_vec_znx_dft(1, 1)
-            + GLWESecret::bytes_of(self.n().into(), Rank(1))
-            + self.gglwe_compressed_encrypt_sk_tmp_bytes(infos)
+        let sk_prepared: usize = GLWESecretPrepared::bytes_of(self, infos.rank_out());
+        let sk_tensor: usize = GLWESecretTensor::bytes_of_from_infos(infos);
+
+        let tensor_infos: GGLWELayout = GGLWELayout {
+            n: infos.n(),
+            base2k: infos.base2k(),
+            k: infos.k(),
+            rank_in: GLWESecretTensor::pairs(infos.rank().into()).into(),
+            rank_out: infos.rank_out(),
+            dnum: infos.dnum(),
+            dsize: infos.dsize(),
+        };
+
+        let gglwe_encrypt: usize = self.gglwe_compressed_encrypt_sk_tmp_bytes(&tensor_infos);
+
+        (sk_prepared + sk_tensor) + gglwe_encrypt.max(self.glwe_secret_tensor_prepare_tmp_bytes(infos.rank()))
     }
 
-    fn glwe_tensor_key_compressed_encrypt_sk<R, S, D>(
+    fn glwe_tensor_key_compressed_encrypt_sk<R, S>(
         &self,
         res: &mut R,
         sk: &S,
@@ -95,62 +91,24 @@ seed_xa: [u8; 32],
         source_xe: &mut Source,
         scratch: &mut Scratch<BE>,
     ) where
-        D: DataMut,
-        R: GGLWEInfos + GLWETensorKeyCompressedAtMut<D>,
-        S: GLWESecretToRef + GetDistribution,
+        R: GGLWEInfos + GGLWECompressedToMut + GGLWECompressedSeedMut,
+        S: GLWESecretToRef + GetDistribution + GLWEInfos,
     {
-        let (mut sk_dft_prep, scratch_1) = scratch.take_glwe_secret_prepared(self, res.rank());
-        sk_dft_prep.prepare(self, sk);
-
-        let sk: &GLWESecret<&[u8]> = &sk.to_ref();
-
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(res.rank_out(), sk.rank());
-            assert_eq!(res.n(), sk.n());
-        }
-
-        // let n: usize = sk.n().into();
-        let rank: usize = res.rank_out().into();
-
-        let (mut sk_dft, scratch_2) = scratch_1.take_vec_znx_dft(self, rank, 1);
-
-        for i in 0..rank {
-            self.vec_znx_dft_apply(1, 0, &mut sk_dft, i, &sk.data.as_vec_znx(), i);
-        }
-
-        let (mut sk_ij_big, scratch_3) = scratch_2.take_vec_znx_big(self, 1, 1);
-        let (mut sk_ij, scratch_4) = scratch_3.take_glwe_secret(self.n().into(), Rank(1));
-        let (mut sk_ij_dft, scratch_5) = scratch_4.take_vec_znx_dft(self, 1, 1);
-
-        let mut source_xa: Source = Source::new(seed_xa);
-
-        for i in 0..rank {
-            for j in i..rank {
-                self.svp_apply_dft_to_dft(&mut sk_ij_dft, 0, &sk_dft_prep.data, j, &sk_dft, i);
-
-                self.vec_znx_idft_apply_tmpa(&mut sk_ij_big, 0, &mut sk_ij_dft, 0);
-                self.vec_znx_big_normalize(
-                    res.base2k().into(),
-                    &mut sk_ij.data.as_vec_znx_mut(),
-                    0,
-                    res.base2k().into(),
-                    &sk_ij_big,
-                    0,
-                    scratch_5,
-                );
+        assert_eq!(res.rank_out(), sk.rank());
+        assert_eq!(res.n(), sk.n());
 
-                let (seed_xa_tmp, _) = source_xa.branch();
+        let (mut sk_prepared, scratch_1) = scratch.take_glwe_secret_prepared(self, res.rank());
+        let (mut sk_tensor, scratch_2) = scratch_1.take_glwe_secret_tensor(self.n().into(), res.rank());
+        sk_prepared.prepare(self, sk);
+        sk_tensor.prepare(self, sk, scratch_2);
 
-                self.gglwe_compressed_encrypt_sk(
-                    res.at_mut(i, j),
-                    &sk_ij.data,
-                    &sk_dft_prep,
-                    seed_xa_tmp,
-                    source_xe,
-                    scratch_5,
-                );
-            }
-        }
+        self.gglwe_compressed_encrypt_sk(
+            res,
+            &sk_tensor.data,
+            &sk_prepared,
+            seed_xa,
+            source_xe,
+            scratch_2,
+        );
     }
 }

@@ -1,4 +1,5 @@
 mod gglwe;
+mod gglwe_to_ggsw_key;
 mod ggsw;
 mod glwe_automorphism_key;
 mod glwe_ct;
@@ -6,6 +7,7 @@ mod glwe_switching_key;
 mod glwe_tensor_key;
 
 pub use gglwe::*;
+pub use gglwe_to_ggsw_key::*;
 pub use ggsw::*;
 pub use glwe_automorphism_key::*;
 pub use glwe_ct::*;

@@ -148,7 +148,7 @@ //
         // Example for ksk rank 2 to rank 3:
         //
         // (-(a0*s0 + a1*s1 + a2*s2) + s0', a0, a1, a2)
-        // (-(b0*s0 + b1*s1 + b2*s2) + s0', b0, b1, b2)
+        // (-(b0*s0 + b1*s1 + b2*s2) + s1', b0, b1, b2)
         //
         // Example ksk rank 2 to rank 1
         //

@@ -0,0 +1,112 @@
+use poulpy_hal::{
+    api::{ModuleN, ScratchTakeBasic, VecZnxCopy},
+    layouts::{Backend, DataMut, Module, Scratch},
+    source::Source,
+};
+
+use crate::{
+    GGLWEEncryptSk, GetDistribution, ScratchTakeCore,
+    layouts::{
+        GGLWEInfos, GGLWEToGGSWKey, GGLWEToGGSWKeyToMut, GLWEInfos, GLWESecret, GLWESecretTensor, GLWESecretTensorFactory,
+        GLWESecretToRef,
+        prepared::{GLWESecretPrepared, GLWESecretPreparedFactory},
+    },
+};
+
+impl GGLWEToGGSWKey<Vec<u8>> {
+    pub fn encrypt_sk_tmp_bytes<M, A, BE: Backend>(module: &M, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+        M: GGLWEToGGSWKeyEncryptSk<BE>,
+    {
+        module.gglwe_to_ggsw_key_encrypt_sk_tmp_bytes(infos)
+    }
+}
+
+impl<DataSelf: DataMut> GGLWEToGGSWKey<DataSelf> {
+    pub fn encrypt_sk<M, S, BE: Backend>(
+        &mut self,
+        module: &M,
+        sk: &S,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        scratch: &mut Scratch<BE>,
+    ) where
+        M: GGLWEToGGSWKeyEncryptSk<BE>,
+        S: GLWESecretToRef + GetDistribution + GLWEInfos,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        module.gglwe_to_ggsw_key_encrypt_sk(self, sk, source_xa, source_xe, scratch);
+    }
+}
+
+pub trait GGLWEToGGSWKeyEncryptSk<BE: Backend> {
+    fn gglwe_to_ggsw_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos;
+
+    fn gglwe_to_ggsw_key_encrypt_sk<R, S>(
+        &self,
+        res: &mut R,
+        sk: &S,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        scratch: &mut Scratch<BE>,
+    ) where
+        R: GGLWEToGGSWKeyToMut,
+        S: GLWESecretToRef + GetDistribution + GLWEInfos;
+}
+
+impl<BE: Backend> GGLWEToGGSWKeyEncryptSk<BE> for Module<BE>
+where
+    Self: ModuleN + GGLWEEncryptSk<BE> + GLWESecretTensorFactory<BE> + GLWESecretPreparedFactory<BE> + VecZnxCopy,
+    Scratch<BE>: ScratchTakeCore<BE>,
+{
+    fn gglwe_to_ggsw_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+    {
+        let sk_prepared: usize = GLWESecretPrepared::bytes_of(self, infos.rank());
+        let sk_tensor: usize = GLWESecretTensor::bytes_of_from_infos(infos);
+        let gglwe_encrypt: usize = self.gglwe_encrypt_sk_tmp_bytes(infos);
+        let sk_ij = GLWESecret::bytes_of(self.n().into(), infos.rank());
+        (sk_prepared + sk_tensor + sk_ij) + gglwe_encrypt.max(self.glwe_secret_tensor_prepare_tmp_bytes(infos.rank()))
+    }
+
+    fn gglwe_to_ggsw_key_encrypt_sk<R, S>(
+        &self,
+        res: &mut R,
+        sk: &S,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        scratch: &mut Scratch<BE>,
+    ) where
+        R: GGLWEToGGSWKeyToMut,
+        S: GLWESecretToRef + GetDistribution + GLWEInfos,
+    {
+        let res: &mut GGLWEToGGSWKey<&mut [u8]> = &mut res.to_mut();
+
+        let rank: usize = res.rank_out().as_usize();
+
+        let (mut sk_prepared, scratch_1) = scratch.take_glwe_secret_prepared(self, res.rank());
+        let (mut sk_tensor, scratch_2) = scratch_1.take_glwe_secret_tensor(self.n().into(), res.rank());
+        sk_prepared.prepare(self, sk);
+        sk_tensor.prepare(self, sk, scratch_2);
+
+        let (mut sk_ij, scratch_3) = scratch_2.take_scalar_znx(self.n(), rank);
+
+        for i in 0..rank {
+            for j in 0..rank {
+                self.vec_znx_copy(
+                    &mut sk_ij.as_vec_znx_mut(),
+                    j,
+                    &sk_tensor.at(i, j).as_vec_znx(),
+                    0,
+                );
+            }
+
+            res.at_mut(i)
+                .encrypt_sk(self, &sk_ij, &sk_prepared, source_xa, source_xe, scratch_3);
+        }
+    }
+}

@@ -1,8 +1,5 @@
 use poulpy_hal::{
-    api::{
-        ModuleN, ScratchTakeBasic, SvpApplyDftToDft, VecZnxBigBytesOf, VecZnxBigNormalize, VecZnxDftApply, VecZnxDftBytesOf,
-        VecZnxIdftApplyTmpA,
-    },
+    api::ModuleN,
     layouts::{Backend, DataMut, Module, Scratch},
     source::Source,
 };
@@ -10,7 +7,8 @@
 use crate::{
     GGLWEEncryptSk, GetDistribution, ScratchTakeCore,
     layouts::{
-        GGLWE, GGLWEInfos, GLWEInfos, GLWESecret, GLWESecretToRef, GLWETensorKey, GLWETensorKeyToMut, LWEInfos, Rank,
+        GGLWEInfos, GGLWELayout, GGLWEToMut, GLWEInfos, GLWESecretTensor, GLWESecretTensorFactory, GLWESecretToRef,
+        GLWETensorKey,
         prepared::{GLWESecretPrepared, GLWESecretPreparedFactory},
     },
 };
@@ -55,33 +53,35 @@ source_xa: &mut Source,
         source_xe: &mut Source,
         scratch: &mut Scratch<BE>,
     ) where
-        R: GLWETensorKeyToMut,
+        R: GGLWEToMut + GGLWEInfos,
         S: GLWESecretToRef + GetDistribution + GLWEInfos;
 }
 
 impl<BE: Backend> GLWETensorKeyEncryptSk<BE> for Module<BE>
 where
-    Self: ModuleN
-        + GGLWEEncryptSk<BE>
-        + VecZnxDftBytesOf
-        + VecZnxBigBytesOf
-        + GLWESecretPreparedFactory<BE>
-        + VecZnxDftApply<BE>
-        + SvpApplyDftToDft<BE>
-        + VecZnxIdftApplyTmpA<BE>
-        + VecZnxBigNormalize<BE>,
+    Self: ModuleN + GGLWEEncryptSk<BE> + GLWESecretPreparedFactory<BE> + GLWESecretTensorFactory<BE>,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
     fn glwe_tensor_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
     where
         A: GGLWEInfos,
     {
-        GLWESecretPrepared::bytes_of(self, infos.rank_out())
-            + self.bytes_of_vec_znx_dft(infos.rank_out().into(), 1)
-            + self.bytes_of_vec_znx_big(1, 1)
-            + self.bytes_of_vec_znx_dft(1, 1)
-            + GLWESecret::bytes_of(self.n().into(), Rank(1))
-            + GGLWE::encrypt_sk_tmp_bytes(self, infos)
+        let sk_prepared: usize = GLWESecretPrepared::bytes_of(self, infos.rank_out());
+        let sk_tensor: usize = GLWESecretTensor::bytes_of_from_infos(infos);
+
+        let tensor_infos: GGLWELayout = GGLWELayout {
+            n: infos.n(),
+            base2k: infos.base2k(),
+            k: infos.k(),
+            rank_in: GLWESecretTensor::pairs(infos.rank().into()).into(),
+            rank_out: infos.rank_out(),
+            dnum: infos.dnum(),
+            dsize: infos.dsize(),
+        };
+
+        let gglwe_encrypt: usize = self.gglwe_encrypt_sk_tmp_bytes(&tensor_infos);
+
+        (sk_prepared + sk_tensor) + gglwe_encrypt.max(self.glwe_secret_tensor_prepare_tmp_bytes(infos.rank()))
     }
 
     fn glwe_tensor_key_encrypt_sk<R, S>(
@@ -92,56 +92,24 @@ source_xa: &mut Source,
         source_xe: &mut Source,
         scratch: &mut Scratch<BE>,
     ) where
-        R: GLWETensorKeyToMut,
+        R: GGLWEToMut + GGLWEInfos,
         S: GLWESecretToRef + GetDistribution + GLWEInfos,
     {
-        let res: &mut GLWETensorKey<&mut [u8]> = &mut res.to_mut();
-
-        // let n: RingDegree = sk.n();
-        let rank: Rank = res.rank_out();
-
-        let (mut sk_prepared, scratch_1) = scratch.take_glwe_secret_prepared(self, sk.rank());
-        sk_prepared.prepare(self, sk);
-
-        let sk: &GLWESecret<&[u8]> = &sk.to_ref();
-
         assert_eq!(res.rank_out(), sk.rank());
         assert_eq!(res.n(), sk.n());
 
-        let (mut sk_dft, scratch_2) = scratch_1.take_vec_znx_dft(self, rank.into(), 1);
-
-        (0..rank.into()).for_each(|i| {
-            self.vec_znx_dft_apply(1, 0, &mut sk_dft, i, &sk.data.as_vec_znx(), i);
-        });
-
-        let (mut sk_ij_big, scratch_3) = scratch_2.take_vec_znx_big(self, 1, 1);
-        let (mut sk_ij, scratch_4) = scratch_3.take_glwe_secret(self.n().into(), Rank(1));
-        let (mut sk_ij_dft, scratch_5) = scratch_4.take_vec_znx_dft(self, 1, 1);
-
-        (0..rank.into()).for_each(|i| {
-            (i..rank.into()).for_each(|j| {
-                self.svp_apply_dft_to_dft(&mut sk_ij_dft, 0, &sk_prepared.data, j, &sk_dft, i);
-
-                self.vec_znx_idft_apply_tmpa(&mut sk_ij_big, 0, &mut sk_ij_dft, 0);
-                self.vec_znx_big_normalize(
-                    res.base2k().into(),
-                    &mut sk_ij.data.as_vec_znx_mut(),
-                    0,
-                    res.base2k().into(),
-                    &sk_ij_big,
-                    0,
-                    scratch_5,
-                );
+        let (mut sk_prepared, scratch_1) = scratch.take_glwe_secret_prepared(self, res.rank());
+        let (mut sk_tensor, scratch_2) = scratch_1.take_glwe_secret_tensor(self.n().into(), res.rank());
+        sk_prepared.prepare(self, sk);
+        sk_tensor.prepare(self, sk, scratch_2);
 
-                res.at_mut(i, j).encrypt_sk(
-                    self,
-                    &sk_ij.data,
-                    &sk_prepared,
-                    source_xa,
-                    source_xe,
-                    scratch_5,
-                );
-            });
-        })
+        self.gglwe_encrypt_sk(
+            res,
+            &sk_tensor.data,
+            &sk_prepared,
+            source_xa,
+            source_xe,
+            scratch_2,
+        );
     }
 }

@@ -7,23 +7,22 @@
 use crate::{
     GGLWEEncryptSk, ScratchTakeCore,
     layouts::{
-        GGLWE, GGLWEInfos, GGLWEToMut, GLWESecret, GLWESecretToRef, GLWEToLWESwitchingKey, LWEInfos, LWESecret, LWESecretToRef,
-        Rank,
+        GGLWE, GGLWEInfos, GGLWEToMut, GLWESecret, GLWESecretToRef, GLWEToLWEKey, LWEInfos, LWESecret, LWESecretToRef, Rank,
         prepared::{GLWESecretPrepared, GLWESecretPreparedFactory},
     },
 };
 
-impl GLWEToLWESwitchingKey<Vec<u8>> {
+impl GLWEToLWEKey<Vec<u8>> {
     pub fn encrypt_sk_tmp_bytes<M, A, BE: Backend>(module: &M, infos: &A) -> usize
     where
         A: GGLWEInfos,
         M: GLWEToLWESwitchingKeyEncryptSk<BE>,
     {
-        module.glwe_to_lwe_switching_key_encrypt_sk_tmp_bytes(infos)
+        module.glwe_to_lwe_key_encrypt_sk_tmp_bytes(infos)
     }
 }
 
-impl<D: DataMut> GLWEToLWESwitchingKey<D> {
+impl<D: DataMut> GLWEToLWEKey<D> {
     pub fn encrypt_sk<M, S1, S2, BE: Backend>(
         &mut self,
         module: &M,
@@ -38,16 +37,16 @@ S1: LWESecretToRef,
         S2: GLWESecretToRef,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
-        module.glwe_to_lwe_switching_key_encrypt_sk(self, sk_lwe, sk_glwe, source_xa, source_xe, scratch);
+        module.glwe_to_lwe_key_encrypt_sk(self, sk_lwe, sk_glwe, source_xa, source_xe, scratch);
     }
 }
 
 pub trait GLWEToLWESwitchingKeyEncryptSk<BE: Backend> {
-    fn glwe_to_lwe_switching_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
+    fn glwe_to_lwe_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
     where
         A: GGLWEInfos;
 
-    fn glwe_to_lwe_switching_key_encrypt_sk<R, S1, S2>(
+    fn glwe_to_lwe_key_encrypt_sk<R, S1, S2>(
         &self,
         res: &mut R,
         sk_lwe: &S1,
@@ -70,7 +69,7 @@ + VecZnxAutomorphismInplace<BE>
         + VecZnxAutomorphismInplaceTmpBytes,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
-    fn glwe_to_lwe_switching_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
+    fn glwe_to_lwe_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
     where
         A: GGLWEInfos,
     {
@@ -79,7 +78,7 @@ + GGLWE::encrypt_sk_tmp_bytes(self, infos)
                 .max(GLWESecret::bytes_of(self.n().into(), infos.rank_in()) + self.vec_znx_automorphism_inplace_tmp_bytes())
     }
 
-    fn glwe_to_lwe_switching_key_encrypt_sk<R, S1, S2>(
+    fn glwe_to_lwe_key_encrypt_sk<R, S1, S2>(
         &self,
         res: &mut R,
         sk_lwe: &S1,

@@ -8,21 +8,21 @@ use crate::{
     GGLWEEncryptSk, ScratchTakeCore,
     layouts::{
         GGLWE, GGLWEInfos, GGLWEToMut, GLWESecret, GLWESecretPreparedFactory, GLWESecretPreparedToRef, LWEInfos, LWESecret,
-        LWESecretToRef, LWEToGLWESwitchingKey, Rank,
+        LWESecretToRef, LWEToGLWEKey, Rank,
     },
 };
 
-impl LWEToGLWESwitchingKey<Vec<u8>> {
+impl LWEToGLWEKey<Vec<u8>> {
     pub fn encrypt_sk_tmp_bytes<M, A, BE: Backend>(module: &M, infos: &A) -> usize
     where
         A: GGLWEInfos,
         M: LWEToGLWESwitchingKeyEncryptSk<BE>,
     {
-        module.lwe_to_glwe_switching_key_encrypt_sk_tmp_bytes(infos)
+        module.lwe_to_glwe_key_encrypt_sk_tmp_bytes(infos)
     }
 }
 
-impl<D: DataMut> LWEToGLWESwitchingKey<D> {
+impl<D: DataMut> LWEToGLWEKey<D> {
     pub fn encrypt_sk<S1, S2, M, BE: Backend>(
         &mut self,
         module: &M,
@@ -37,16 +37,16 @@ S2: GLWESecretPreparedToRef<BE>,
         M: LWEToGLWESwitchingKeyEncryptSk<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
-        module.lwe_to_glwe_switching_key_encrypt_sk(self, sk_lwe, sk_glwe, source_xa, source_xe, scratch);
+        module.lwe_to_glwe_key_encrypt_sk(self, sk_lwe, sk_glwe, source_xa, source_xe, scratch);
     }
 }
 
 pub trait LWEToGLWESwitchingKeyEncryptSk<BE: Backend> {
-    fn lwe_to_glwe_switching_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
+    fn lwe_to_glwe_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
     where
         A: GGLWEInfos;
 
-    fn lwe_to_glwe_switching_key_encrypt_sk<R, S1, S2>(
+    fn lwe_to_glwe_key_encrypt_sk<R, S1, S2>(
         &self,
         res: &mut R,
         sk_lwe: &S1,
@@ -69,20 +69,20 @@ + GLWESecretPreparedFactory<BE>
         + VecZnxAutomorphismInplaceTmpBytes,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
-    fn lwe_to_glwe_switching_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
+    fn lwe_to_glwe_key_encrypt_sk_tmp_bytes<A>(&self, infos: &A) -> usize
     where
         A: GGLWEInfos,
     {
         debug_assert_eq!(
             infos.rank_in(),
             Rank(1),
-            "rank_in != 1 is not supported for LWEToGLWESwitchingKey"
+            "rank_in != 1 is not supported for LWEToGLWEKeyPrepared"
         );
         GLWESecret::bytes_of(self.n().into(), infos.rank_in())
             + GGLWE::encrypt_sk_tmp_bytes(self, infos).max(self.vec_znx_automorphism_inplace_tmp_bytes())
     }
 
-    fn lwe_to_glwe_switching_key_encrypt_sk<R, S1, S2>(
+    fn lwe_to_glwe_key_encrypt_sk<R, S1, S2>(
         &self,
         res: &mut R,
         sk_lwe: &S1,

@@ -1,28 +1,30 @@
 mod compressed;
 mod gglwe;
+mod gglwe_to_ggsw_key;
 mod ggsw;
 mod glwe;
 mod glwe_automorphism_key;
 mod glwe_public_key;
 mod glwe_switching_key;
 mod glwe_tensor_key;
-mod glwe_to_lwe_switching_key;
+mod glwe_to_lwe_key;
 mod lwe;
 mod lwe_switching_key;
-mod lwe_to_glwe_switching_key;
+mod lwe_to_glwe_key;
 
 pub use compressed::*;
 pub use gglwe::*;
+pub use gglwe_to_ggsw_key::*;
 pub use ggsw::*;
 pub use glwe::*;
 pub use glwe_automorphism_key::*;
 pub use glwe_public_key::*;
 pub use glwe_switching_key::*;
 pub use glwe_tensor_key::*;
-pub use glwe_to_lwe_switching_key::*;
+pub use glwe_to_lwe_key::*;
 pub use lwe::*;
 pub use lwe_switching_key::*;
-pub use lwe_to_glwe_switching_key::*;
+pub use lwe_to_glwe_key::*;
 
 pub const SIGMA: f64 = 3.2;
 pub(crate) const SIGMA_BOUND: f64 = 6.0 * SIGMA;

@@ -0,0 +1,388 @@
+use std::collections::HashMap;
+
+use poulpy_hal::{
+    api::ModuleLogN,
+    layouts::{Backend, GaloisElement, Module, Scratch},
+};
+
+use crate::{
+    GLWEAdd, GLWEAutomorphism, GLWECopy, GLWENormalize, GLWERotate, GLWEShift, GLWESub, ScratchTakeCore,
+    glwe_trace::GLWETrace,
+    layouts::{GGLWEInfos, GGLWEPreparedToRef, GLWE, GLWEInfos, GLWEToMut, GLWEToRef, GetGaloisElement, LWEInfos},
+};
+
+/// [GLWEPacker] enables only the fly GLWE packing
+/// with constant memory of Log(N) ciphertexts.
+/// Main difference with usual GLWE packing is that
+/// the output is bit-reversed.
+pub struct GLWEPacker {
+    accumulators: Vec<Accumulator>,
+    log_batch: usize,
+    counter: usize,
+}
+
+/// [Accumulator] stores intermediate packing result.
+/// There are Log(N) such accumulators in a [GLWEPacker].
+struct Accumulator {
+    data: GLWE<Vec<u8>>,
+    value: bool,   // Implicit flag for zero ciphertext
+    control: bool, // Can be combined with incoming value
+}
+
+impl Accumulator {
+    /// Allocates a new [Accumulator].
+    ///
+    /// #Arguments
+    ///
+    /// * `module`: static backend FFT tables.
+    /// * `base2k`: base 2 logarithm of the GLWE ciphertext in memory digit representation.
+    /// * `k`: base 2 precision of the GLWE ciphertext precision over the Torus.
+    /// * `rank`: rank of the GLWE ciphertext.
+    pub fn alloc<A>(infos: &A) -> Self
+    where
+        A: GLWEInfos,
+    {
+        Self {
+            data: GLWE::alloc_from_infos(infos),
+            value: false,
+            control: false,
+        }
+    }
+}
+
+impl GLWEPacker {
+    /// Instantiates a new [GLWEPacker].
+    ///
+    /// # Arguments
+    ///
+    /// * `log_batch`: packs coefficients which are multiples of X^{N/2^log_batch}.
+    ///   i.e. with `log_batch=0` only the constant coefficient is packed
+    ///   and N GLWE ciphertext can be packed. With `log_batch=2` all coefficients
+    ///   which are multiples of X^{N/4} are packed. Meaning that N/4 ciphertexts
+    ///   can be packed.
+    pub fn alloc<A>(infos: &A, log_batch: usize) -> Self
+    where
+        A: GLWEInfos,
+    {
+        let mut accumulators: Vec<Accumulator> = Vec::<Accumulator>::new();
+        let log_n: usize = infos.n().log2();
+        (0..log_n - log_batch).for_each(|_| accumulators.push(Accumulator::alloc(infos)));
+        GLWEPacker {
+            accumulators,
+            log_batch,
+            counter: 0,
+        }
+    }
+
+    /// Implicit reset of the internal state (to be called before a new packing procedure).
+    fn reset(&mut self) {
+        for i in 0..self.accumulators.len() {
+            self.accumulators[i].value = false;
+            self.accumulators[i].control = false;
+        }
+        self.counter = 0;
+    }
+
+    /// Number of scratch space bytes required to call [Self::add].
+    pub fn tmp_bytes<R, K, M, BE: Backend>(module: &M, res_infos: &R, key_infos: &K) -> usize
+    where
+        R: GLWEInfos,
+        K: GGLWEInfos,
+        M: GLWEPackerOps<BE>,
+    {
+        GLWE::bytes_of_from_infos(res_infos)
+            + module
+                .glwe_rsh_tmp_byte()
+                .max(module.glwe_automorphism_tmp_bytes(res_infos, res_infos, key_infos))
+    }
+
+    pub fn galois_elements<M, BE: Backend>(module: &M) -> Vec<i64>
+    where
+        M: GLWETrace<BE>,
+    {
+        module.glwe_trace_galois_elements()
+    }
+
+    /// Adds a GLWE ciphertext to the [GLWEPacker].
+    /// #Arguments
+    ///
+    /// * `module`: static backend FFT tables.
+    /// * `res`: space to append fully packed ciphertext. Only when the number
+    ///   of packed ciphertexts reaches N/2^log_batch is a result written.
+    /// * `a`: ciphertext to pack. Can optionally give None to pack a 0 ciphertext.
+    /// * `auto_keys`: a [HashMap] containing the [AutomorphismKeyExec]s.
+    /// * `scratch`: scratch space of size at least [Self::tmp_bytes].
+    pub fn add<A, K, M, BE: Backend>(&mut self, module: &M, a: Option<&A>, auto_keys: &HashMap<i64, K>, scratch: &mut Scratch<BE>)
+    where
+        A: GLWEToRef + GLWEInfos,
+        K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
+        M: GLWEPackerOps<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        assert!(
+            (self.counter as u32) < self.accumulators[0].data.n(),
+            "Packing limit of {} reached",
+            self.accumulators[0].data.n().0 as usize >> self.log_batch
+        );
+
+        module.packer_add(self, a, self.log_batch, auto_keys, scratch);
+        self.counter += 1 << self.log_batch;
+    }
+
+    /// Flush result to`res`.
+    pub fn flush<R, M, BE: Backend>(&mut self, module: &M, res: &mut R)
+    where
+        R: GLWEToMut,
+        M: GLWEPackerOps<BE>,
+    {
+        assert!(self.counter as u32 == self.accumulators[0].data.n());
+        // Copy result GLWE into res GLWE
+        module.glwe_copy(
+            res,
+            &self.accumulators[module.log_n() - self.log_batch - 1].data,
+        );
+
+        self.reset();
+    }
+}
+
+impl<BE: Backend> GLWEPackerOps<BE> for Module<BE> where
+    Self: Sized
+        + ModuleLogN
+        + GLWEAutomorphism<BE>
+        + GaloisElement
+        + GLWERotate<BE>
+        + GLWESub
+        + GLWEShift<BE>
+        + GLWEAdd
+        + GLWENormalize<BE>
+        + GLWECopy
+        + GLWEAutomorphism<BE>
+        + GaloisElement
+        + GLWERotate<BE>
+        + GLWESub
+        + GLWEShift<BE>
+        + GLWEAdd
+        + GLWENormalize<BE>
+{
+}
+
+pub trait GLWEPackerOps<BE: Backend>
+where
+    Self: Sized
+        + ModuleLogN
+        + GLWEAutomorphism<BE>
+        + GaloisElement
+        + GLWERotate<BE>
+        + GLWESub
+        + GLWEShift<BE>
+        + GLWEAdd
+        + GLWENormalize<BE>
+        + GLWECopy
+        + GLWEAutomorphism<BE>
+        + GaloisElement
+        + GLWERotate<BE>
+        + GLWESub
+        + GLWEShift<BE>
+        + GLWEAdd
+        + GLWENormalize<BE>,
+{
+    fn packer_add<A, K>(
+        &self,
+        packer: &mut GLWEPacker,
+        a: Option<&A>,
+        i: usize,
+        auto_keys: &HashMap<i64, K>,
+        scratch: &mut Scratch<BE>,
+    ) where
+        A: GLWEToRef + GLWEInfos,
+        K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        pack_core(self, a, &mut packer.accumulators, i, auto_keys, scratch)
+    }
+}
+
+fn pack_core<A, K, M, BE: Backend>(
+    module: &M,
+    a: Option<&A>,
+    accumulators: &mut [Accumulator],
+    i: usize,
+    auto_keys: &HashMap<i64, K>,
+    scratch: &mut Scratch<BE>,
+) where
+    A: GLWEToRef + GLWEInfos,
+    M: ModuleLogN
+        + GLWEAutomorphism<BE>
+        + GaloisElement
+        + GLWERotate<BE>
+        + GLWESub
+        + GLWEShift<BE>
+        + GLWEAdd
+        + GLWENormalize<BE>
+        + GLWECopy
+        + GLWEAutomorphism<BE>
+        + GaloisElement
+        + GLWERotate<BE>
+        + GLWESub
+        + GLWEShift<BE>
+        + GLWEAdd
+        + GLWENormalize<BE>,
+    K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
+    Scratch<BE>: ScratchTakeCore<BE>,
+{
+    let log_n: usize = module.log_n();
+
+    if i == log_n {
+        return;
+    }
+
+    // Isolate the first accumulator
+    let (acc_prev, acc_next) = accumulators.split_at_mut(1);
+
+    // Control = true accumlator is free to overide
+    if !acc_prev[0].control {
+        let acc_mut_ref: &mut Accumulator = &mut acc_prev[0]; // from split_at_mut
+
+        // No previous value -> copies and sets flags accordingly
+        if let Some(a_ref) = a {
+            module.glwe_copy(&mut acc_mut_ref.data, a_ref);
+            acc_mut_ref.value = true
+        } else {
+            acc_mut_ref.value = false
+        }
+        acc_mut_ref.control = true; // Able to be combined on next call
+    } else {
+        // Compresses acc_prev <- combine(acc_prev, a).
+        combine(module, &mut acc_prev[0], a, i, auto_keys, scratch);
+        acc_prev[0].control = false;
+
+        // Propagates to next accumulator
+        if acc_prev[0].value {
+            pack_core(
+                module,
+                Some(&acc_prev[0].data),
+                acc_next,
+                i + 1,
+                auto_keys,
+                scratch,
+            );
+        } else {
+            pack_core(
+                module,
+                None::<&GLWE<Vec<u8>>>,
+                acc_next,
+                i + 1,
+                auto_keys,
+                scratch,
+            );
+        }
+    }
+}
+
+fn combine<B, K, M, BE: Backend>(
+    module: &M,
+    acc: &mut Accumulator,
+    b: Option<&B>,
+    i: usize,
+    auto_keys: &HashMap<i64, K>,
+    scratch: &mut Scratch<BE>,
+) where
+    B: GLWEToRef + GLWEInfos,
+    B: GLWEToRef + GLWEInfos,
+    M: ModuleLogN
+        + GLWEAutomorphism<BE>
+        + GaloisElement
+        + GLWERotate<BE>
+        + GLWESub
+        + GLWEShift<BE>
+        + GLWEAdd
+        + GLWENormalize<BE>
+        + GLWECopy
+        + GLWEAutomorphism<BE>
+        + GaloisElement
+        + GLWERotate<BE>
+        + GLWESub
+        + GLWEShift<BE>
+        + GLWEAdd
+        + GLWENormalize<BE>,
+    K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
+    Scratch<BE>: ScratchTakeCore<BE>,
+{
+    let log_n: usize = acc.data.n().log2();
+    let a: &mut GLWE<Vec<u8>> = &mut acc.data;
+
+    let gal_el: i64 = if i == 0 {
+        -1
+    } else {
+        module.galois_element(1 << (i - 1))
+    };
+
+    let t: i64 = 1 << (log_n - i - 1);
+
+    // Goal is to evaluate: a = a + b*X^t + phi(a - b*X^t))
+    // We also use the identity: AUTO(a * X^t, g) = -X^t * AUTO(a, g)
+    // where t = 2^(log_n - i - 1) and g = 5^{2^(i - 1)}
+    // Different cases for wether a and/or b are zero.
+    //
+    // Implicite RSH without modulus switch, introduces extra I(X) * Q/2 on decryption.
+    // Necessary so that the scaling of the plaintext remains constant.
+    // It however is ok to do so here because coefficients are eventually
+    // either mapped to garbage or twice their value which vanishes I(X)
+    // since 2*(I(X) * Q/2) = I(X) * Q = 0 mod Q.
+    if acc.value {
+        if let Some(b) = b {
+            let (mut tmp_b, scratch_1) = scratch.take_glwe(a);
+
+            // a = a * X^-t
+            module.glwe_rotate_inplace(-t, a, scratch_1);
+
+            // tmp_b = a * X^-t - b
+            module.glwe_sub(&mut tmp_b, a, b);
+            module.glwe_rsh(1, &mut tmp_b, scratch_1);
+
+            // a = a * X^-t + b
+            module.glwe_add_inplace(a, b);
+            module.glwe_rsh(1, a, scratch_1);
+
+            module.glwe_normalize_inplace(&mut tmp_b, scratch_1);
+
+            // tmp_b = phi(a * X^-t - b)
+            if let Some(auto_key) = auto_keys.get(&gal_el) {
+                module.glwe_automorphism_inplace(&mut tmp_b, auto_key, scratch_1);
+            } else {
+                panic!("auto_key[{gal_el}] not found");
+            }
+
+            // a = a * X^-t + b - phi(a * X^-t - b)
+            module.glwe_sub_inplace(a, &tmp_b);
+            module.glwe_normalize_inplace(a, scratch_1);
+
+            // a = a + b * X^t - phi(a * X^-t - b) * X^t
+            //   = a + b * X^t - phi(a * X^-t - b) * - phi(X^t)
+            //   = a + b * X^t + phi(a - b * X^t)
+            module.glwe_rotate_inplace(t, a, scratch_1);
+        } else {
+            module.glwe_rsh(1, a, scratch);
+            // a = a + phi(a)
+            if let Some(auto_key) = auto_keys.get(&gal_el) {
+                module.glwe_automorphism_add_inplace(a, auto_key, scratch);
+            } else {
+                panic!("auto_key[{gal_el}] not found");
+            }
+        }
+    } else if let Some(b) = b {
+        let (mut tmp_b, scratch_1) = scratch.take_glwe(a);
+        module.glwe_rotate(t, &mut tmp_b, b);
+        module.glwe_rsh(1, &mut tmp_b, scratch_1);
+
+        // a = (b* X^t - phi(b* X^t))
+        if let Some(auto_key) = auto_keys.get(&gal_el) {
+            module.glwe_automorphism_sub_negate(a, &tmp_b, auto_key, scratch_1);
+        } else {
+            panic!("auto_key[{gal_el}] not found");
+        }
+
+        acc.value = true;
+    }
+}

@@ -7,166 +7,23 @@ };
 
 use crate::{
     GLWEAdd, GLWEAutomorphism, GLWECopy, GLWENormalize, GLWERotate, GLWEShift, GLWESub, ScratchTakeCore,
-    glwe_trace::GLWETrace,
-    layouts::{GGLWEInfos, GGLWEPreparedToRef, GLWE, GLWEInfos, GLWEToMut, GLWEToRef, GetGaloisElement, LWEInfos},
+    layouts::{GGLWEInfos, GGLWEPreparedToRef, GLWEInfos, GLWEToMut, GLWEToRef, GetGaloisElement},
 };
-
-/// [GLWEPacker] enables only the fly GLWE packing
-/// with constant memory of Log(N) ciphertexts.
-/// Main difference with usual GLWE packing is that
-/// the output is bit-reversed.
-pub struct GLWEPacker {
-    accumulators: Vec<Accumulator>,
-    log_batch: usize,
-    counter: usize,
-}
-
-/// [Accumulator] stores intermediate packing result.
-/// There are Log(N) such accumulators in a [GLWEPacker].
-struct Accumulator {
-    data: GLWE<Vec<u8>>,
-    value: bool,   // Implicit flag for zero ciphertext
-    control: bool, // Can be combined with incoming value
-}
-
-impl Accumulator {
-    /// Allocates a new [Accumulator].
-    ///
-    /// #Arguments
-    ///
-    /// * `module`: static backend FFT tables.
-    /// * `base2k`: base 2 logarithm of the GLWE ciphertext in memory digit representation.
-    /// * `k`: base 2 precision of the GLWE ciphertext precision over the Torus.
-    /// * `rank`: rank of the GLWE ciphertext.
-    pub fn alloc<A>(infos: &A) -> Self
-    where
-        A: GLWEInfos,
-    {
-        Self {
-            data: GLWE::alloc_from_infos(infos),
-            value: false,
-            control: false,
-        }
-    }
-}
-
-impl GLWEPacker {
-    /// Instantiates a new [GLWEPacker].
-    ///
-    /// # Arguments
-    ///
-    /// * `log_batch`: packs coefficients which are multiples of X^{N/2^log_batch}.
-    ///   i.e. with `log_batch=0` only the constant coefficient is packed
-    ///   and N GLWE ciphertext can be packed. With `log_batch=2` all coefficients
-    ///   which are multiples of X^{N/4} are packed. Meaning that N/4 ciphertexts
-    ///   can be packed.
-    pub fn alloc<A>(infos: &A, log_batch: usize) -> Self
-    where
-        A: GLWEInfos,
-    {
-        let mut accumulators: Vec<Accumulator> = Vec::<Accumulator>::new();
-        let log_n: usize = infos.n().log2();
-        (0..log_n - log_batch).for_each(|_| accumulators.push(Accumulator::alloc(infos)));
-        GLWEPacker {
-            accumulators,
-            log_batch,
-            counter: 0,
-        }
-    }
-
-    /// Implicit reset of the internal state (to be called before a new packing procedure).
-    fn reset(&mut self) {
-        for i in 0..self.accumulators.len() {
-            self.accumulators[i].value = false;
-            self.accumulators[i].control = false;
-        }
-        self.counter = 0;
-    }
-
-    /// Number of scratch space bytes required to call [Self::add].
-    pub fn tmp_bytes<R, K, M, BE: Backend>(module: &M, res_infos: &R, key_infos: &K) -> usize
-    where
-        R: GLWEInfos,
-        K: GGLWEInfos,
-        M: GLWEPacking<BE>,
-    {
-        GLWE::bytes_of_from_infos(res_infos)
-            + module
-                .glwe_rsh_tmp_byte()
-                .max(module.glwe_automorphism_tmp_bytes(res_infos, res_infos, key_infos))
-    }
-
-    pub fn galois_elements<M, BE: Backend>(module: &M) -> Vec<i64>
-    where
-        M: GLWETrace<BE>,
-    {
-        module.glwe_trace_galois_elements()
-    }
-
-    /// Adds a GLWE ciphertext to the [GLWEPacker].
-    /// #Arguments
-    ///
-    /// * `module`: static backend FFT tables.
-    /// * `res`: space to append fully packed ciphertext. Only when the number
-    ///   of packed ciphertexts reaches N/2^log_batch is a result written.
-    /// * `a`: ciphertext to pack. Can optionally give None to pack a 0 ciphertext.
-    /// * `auto_keys`: a [HashMap] containing the [AutomorphismKeyExec]s.
-    /// * `scratch`: scratch space of size at least [Self::tmp_bytes].
-    pub fn add<A, K, M, BE: Backend>(&mut self, module: &M, a: Option<&A>, auto_keys: &HashMap<i64, K>, scratch: &mut Scratch<BE>)
-    where
-        A: GLWEToRef + GLWEInfos,
-        K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
-        M: GLWEPacking<BE>,
-        Scratch<BE>: ScratchTakeCore<BE>,
-    {
-        assert!(
-            (self.counter as u32) < self.accumulators[0].data.n(),
-            "Packing limit of {} reached",
-            self.accumulators[0].data.n().0 as usize >> self.log_batch
-        );
-
-        pack_core(
-            module,
-            a,
-            &mut self.accumulators,
-            self.log_batch,
-            auto_keys,
-            scratch,
-        );
-        self.counter += 1 << self.log_batch;
-    }
-
-    /// Flush result to`res`.
-    pub fn flush<R, M, BE: Backend>(&mut self, module: &M, res: &mut R)
-    where
-        R: GLWEToMut,
-        M: GLWEPacking<BE>,
-    {
-        assert!(self.counter as u32 == self.accumulators[0].data.n());
-        // Copy result GLWE into res GLWE
-        module.glwe_copy(
-            res,
-            &self.accumulators[module.log_n() - self.log_batch - 1].data,
-        );
-
-        self.reset();
-    }
-}
-
-impl<BE: Backend> GLWEPacking<BE> for Module<BE> where
-    Self: GLWEAutomorphism<BE>
-        + GaloisElement
-        + ModuleLogN
-        + GLWERotate<BE>
-        + GLWESub
-        + GLWEShift<BE>
-        + GLWEAdd
-        + GLWENormalize<BE>
-        + GLWECopy
-{
+pub trait GLWEPacking<BE: Backend> {
+    /// Packs [x_0: GLWE(m_0), x_1: GLWE(m_1), ..., x_i: GLWE(m_i)]
+    /// to [0: GLWE(m_0 * X^x_0 + m_1 * X^x_1 + ... + m_i * X^x_i)]
+    fn glwe_pack<R, K>(
+        &self,
+        cts: &mut HashMap<usize, &mut R>,
+        log_gap_out: usize,
+        keys: &HashMap<i64, K>,
+        scratch: &mut Scratch<BE>,
+    ) where
+        R: GLWEToMut + GLWEToRef + GLWEInfos,
+        K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos;
 }
 
-pub trait GLWEPacking<BE: Backend>
+impl<BE: Backend> GLWEPacking<BE> for Module<BE>
 where
     Self: GLWEAutomorphism<BE>
         + GaloisElement
@@ -177,6 +34,7 @@ + GLWEShift<BE>
         + GLWEAdd
         + GLWENormalize<BE>
         + GLWECopy,
+    Scratch<BE>: ScratchTakeCore<BE>,
 {
     /// Packs [x_0: GLWE(m_0), x_1: GLWE(m_1), ..., x_i: GLWE(m_i)]
     /// to [0: GLWE(m_0 * X^x_0 + m_1 * X^x_1 + ... + m_i * X^x_i)]
@@ -189,7 +47,6 @@ scratch: &mut Scratch<BE>,
     ) where
         R: GLWEToMut + GLWEToRef + GLWEInfos,
         K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
-        Scratch<BE>: ScratchTakeCore<BE>,
     {
         #[cfg(debug_assertions)]
         {
@@ -220,169 +77,6 @@ cts.insert(j, b);
                 }
             }
         }
-    }
-}
-
-fn pack_core<A, K, M, BE: Backend>(
-    module: &M,
-    a: Option<&A>,
-    accumulators: &mut [Accumulator],
-    i: usize,
-    auto_keys: &HashMap<i64, K>,
-    scratch: &mut Scratch<BE>,
-) where
-    A: GLWEToRef + GLWEInfos,
-    K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
-    M: ModuleLogN
-        + GLWEAutomorphism<BE>
-        + GaloisElement
-        + GLWERotate<BE>
-        + GLWESub
-        + GLWEShift<BE>
-        + GLWEAdd
-        + GLWENormalize<BE>
-        + GLWECopy,
-    Scratch<BE>: ScratchTakeCore<BE>,
-{
-    let log_n: usize = module.log_n();
-
-    if i == log_n {
-        return;
-    }
-
-    // Isolate the first accumulator
-    let (acc_prev, acc_next) = accumulators.split_at_mut(1);
-
-    // Control = true accumlator is free to overide
-    if !acc_prev[0].control {
-        let acc_mut_ref: &mut Accumulator = &mut acc_prev[0]; // from split_at_mut
-
-        // No previous value -> copies and sets flags accordingly
-        if let Some(a_ref) = a {
-            module.glwe_copy(&mut acc_mut_ref.data, a_ref);
-            acc_mut_ref.value = true
-        } else {
-            acc_mut_ref.value = false
-        }
-        acc_mut_ref.control = true; // Able to be combined on next call
-    } else {
-        // Compresses acc_prev <- combine(acc_prev, a).
-        combine(module, &mut acc_prev[0], a, i, auto_keys, scratch);
-        acc_prev[0].control = false;
-
-        // Propagates to next accumulator
-        if acc_prev[0].value {
-            pack_core(
-                module,
-                Some(&acc_prev[0].data),
-                acc_next,
-                i + 1,
-                auto_keys,
-                scratch,
-            );
-        } else {
-            pack_core(
-                module,
-                None::<&GLWE<Vec<u8>>>,
-                acc_next,
-                i + 1,
-                auto_keys,
-                scratch,
-            );
-        }
-    }
-}
-
-/// [combine] merges two ciphertexts together.
-fn combine<B, M, K, BE: Backend>(
-    module: &M,
-    acc: &mut Accumulator,
-    b: Option<&B>,
-    i: usize,
-    auto_keys: &HashMap<i64, K>,
-    scratch: &mut Scratch<BE>,
-) where
-    B: GLWEToRef + GLWEInfos,
-    M: GLWEAutomorphism<BE> + GaloisElement + GLWERotate<BE> + GLWESub + GLWEShift<BE> + GLWEAdd + GLWENormalize<BE>,
-    B: GLWEToRef + GLWEInfos,
-    K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
-    Scratch<BE>: ScratchTakeCore<BE>,
-{
-    let log_n: usize = acc.data.n().log2();
-    let a: &mut GLWE<Vec<u8>> = &mut acc.data;
-
-    let gal_el: i64 = if i == 0 {
-        -1
-    } else {
-        module.galois_element(1 << (i - 1))
-    };
-
-    let t: i64 = 1 << (log_n - i - 1);
-
-    // Goal is to evaluate: a = a + b*X^t + phi(a - b*X^t))
-    // We also use the identity: AUTO(a * X^t, g) = -X^t * AUTO(a, g)
-    // where t = 2^(log_n - i - 1) and g = 5^{2^(i - 1)}
-    // Different cases for wether a and/or b are zero.
-    //
-    // Implicite RSH without modulus switch, introduces extra I(X) * Q/2 on decryption.
-    // Necessary so that the scaling of the plaintext remains constant.
-    // It however is ok to do so here because coefficients are eventually
-    // either mapped to garbage or twice their value which vanishes I(X)
-    // since 2*(I(X) * Q/2) = I(X) * Q = 0 mod Q.
-    if acc.value {
-        if let Some(b) = b {
-            let (mut tmp_b, scratch_1) = scratch.take_glwe(a);
-
-            // a = a * X^-t
-            module.glwe_rotate_inplace(-t, a, scratch_1);
-
-            // tmp_b = a * X^-t - b
-            module.glwe_sub(&mut tmp_b, a, b);
-            module.glwe_rsh(1, &mut tmp_b, scratch_1);
-
-            // a = a * X^-t + b
-            module.glwe_add_inplace(a, b);
-            module.glwe_rsh(1, a, scratch_1);
-
-            module.glwe_normalize_inplace(&mut tmp_b, scratch_1);
-
-            // tmp_b = phi(a * X^-t - b)
-            if let Some(auto_key) = auto_keys.get(&gal_el) {
-                module.glwe_automorphism_inplace(&mut tmp_b, auto_key, scratch_1);
-            } else {
-                panic!("auto_key[{gal_el}] not found");
-            }
-
-            // a = a * X^-t + b - phi(a * X^-t - b)
-            module.glwe_sub_inplace(a, &tmp_b);
-            module.glwe_normalize_inplace(a, scratch_1);
-
-            // a = a + b * X^t - phi(a * X^-t - b) * X^t
-            //   = a + b * X^t - phi(a * X^-t - b) * - phi(X^t)
-            //   = a + b * X^t + phi(a - b * X^t)
-            module.glwe_rotate_inplace(t, a, scratch_1);
-        } else {
-            module.glwe_rsh(1, a, scratch);
-            // a = a + phi(a)
-            if let Some(auto_key) = auto_keys.get(&gal_el) {
-                module.glwe_automorphism_add_inplace(a, auto_key, scratch);
-            } else {
-                panic!("auto_key[{gal_el}] not found");
-            }
-        }
-    } else if let Some(b) = b {
-        let (mut tmp_b, scratch_1) = scratch.take_glwe(a);
-        module.glwe_rotate(t, &mut tmp_b, b);
-        module.glwe_rsh(1, &mut tmp_b, scratch_1);
-
-        // a = (b* X^t - phi(b* X^t))
-        if let Some(auto_key) = auto_keys.get(&gal_el) {
-            module.glwe_automorphism_sub_negate(a, &tmp_b, auto_key, scratch_1);
-        } else {
-            panic!("auto_key[{gal_el}] not found");
-        }
-
-        acc.value = true;
     }
 }
 

@@ -1,8 +1,8 @@
 use std::collections::HashMap;
 
 use poulpy_hal::{
-    api::ModuleLogN,
-    layouts::{Backend, DataMut, GaloisElement, Module, Scratch, VecZnx, galois_element},
+    api::{ModuleLogN, VecZnxNormalize, VecZnxNormalizeTmpBytes},
+    layouts::{Backend, CyclotomicOrder, DataMut, GaloisElement, Module, Scratch, VecZnx, galois_element},
 };
 
 use crate::{
@@ -27,7 +27,7 @@ A: GLWEInfos,
         K: GGLWEInfos,
         M: GLWETrace<BE>,
     {
-        module.glwe_automorphism_tmp_bytes(res_infos, a_infos, key_infos)
+        module.glwe_trace_tmp_bytes(res_infos, a_infos, key_infos)
     }
 }
 
@@ -65,11 +65,6 @@ module.glwe_trace_inplace(self, start, end, keys, scratch);
     }
 }
 
-impl<BE: Backend> GLWETrace<BE> for Module<BE> where
-    Self: ModuleLogN + GaloisElement + GLWEAutomorphism<BE> + GLWEShift<BE> + GLWECopy
-{
-}
-
 #[inline(always)]
 pub fn trace_galois_elements(log_n: usize, cyclotomic_order: i64) -> Vec<i64> {
     (0..log_n)
@@ -83,9 +78,17 @@ })
         .collect()
 }
 
-pub trait GLWETrace<BE: Backend>
+impl<BE: Backend> GLWETrace<BE> for Module<BE>
 where
-    Self: ModuleLogN + GaloisElement + GLWEAutomorphism<BE> + GLWEShift<BE> + GLWECopy,
+    Self: ModuleLogN
+        + GaloisElement
+        + GLWEAutomorphism<BE>
+        + GLWEShift<BE>
+        + GLWECopy
+        + CyclotomicOrder
+        + VecZnxNormalizeTmpBytes
+        + VecZnxNormalize<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
 {
     fn glwe_trace_galois_elements(&self) -> Vec<i64> {
         trace_galois_elements(self.log_n(), self.cyclotomic_order())
@@ -115,7 +118,6 @@ where
         R: GLWEToMut,
         A: GLWEToRef,
         K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
-        Scratch<BE>: ScratchTakeCore<BE>,
     {
         self.glwe_copy(res, a);
         self.glwe_trace_inplace(res, start, end, keys, scratch);
@@ -125,7 +127,6 @@ fn glwe_trace_inplace<R, K>(&self, res: &mut R, start: usize, end: usize, keys: &HashMap<i64, K>, scratch: &mut Scratch<BE>)
     where
         R: GLWEToMut,
         K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
-        Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
 
@@ -212,3 +213,31 @@ }
         }
     }
 }
+
+pub trait GLWETrace<BE: Backend> {
+    fn glwe_trace_galois_elements(&self) -> Vec<i64>;
+
+    fn glwe_trace_tmp_bytes<R, A, K>(&self, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
+    where
+        R: GLWEInfos,
+        A: GLWEInfos,
+        K: GGLWEInfos;
+
+    fn glwe_trace<R, A, K>(
+        &self,
+        res: &mut R,
+        start: usize,
+        end: usize,
+        a: &A,
+        keys: &HashMap<i64, K>,
+        scratch: &mut Scratch<BE>,
+    ) where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos;
+
+    fn glwe_trace_inplace<R, K>(&self, res: &mut R, start: usize, end: usize, keys: &HashMap<i64, K>, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos;
+}

@@ -1,9 +1,9 @@
-use poulpy_hal::layouts::{Backend, DataMut, Module, Scratch, VecZnx};
+use poulpy_hal::layouts::{Backend, DataMut, Module, Scratch};
 
 use crate::{
     GGSWExpandRows, ScratchTakeCore,
     keyswitching::GLWEKeyswitch,
-    layouts::{GGLWEInfos, GGLWEPreparedToRef, GGSW, GGSWInfos, GGSWToMut, GGSWToRef, prepared::GLWETensorKeyPreparedToRef},
+    layouts::{GGLWEInfos, GGLWEPreparedToRef, GGLWEToGGSWKeyPreparedToRef, GGSW, GGSWInfos, GGSWToMut, GGSWToRef},
 };
 
 impl GGSW<Vec<u8>> {
@@ -30,7 +30,7 @@ pub fn keyswitch<M, A, K, T, BE: Backend>(&mut self, module: &M, a: &A, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
         A: GGSWToRef,
         K: GGLWEPreparedToRef<BE>,
-        T: GLWETensorKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
         M: GGSWKeyswitch<BE>,
     {
@@ -40,7 +40,7 @@
     pub fn keyswitch_inplace<M, K, T, BE: Backend>(&mut self, module: &M, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
         K: GGLWEPreparedToRef<BE>,
-        T: GLWETensorKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
         M: GGSWKeyswitch<BE>,
     {
@@ -48,9 +48,7 @@ module.ggsw_keyswitch_inplace(self, key, tsk, scratch);
     }
 }
 
-impl<BE: Backend> GGSWKeyswitch<BE> for Module<BE> where Self: GLWEKeyswitch<BE> + GGSWExpandRows<BE> {}
-
-pub trait GGSWKeyswitch<BE: Backend>
+impl<BE: Backend> GGSWKeyswitch<BE> for Module<BE>
 where
     Self: GLWEKeyswitch<BE> + GGSWExpandRows<BE>,
 {
@@ -65,25 +63,26 @@ assert_eq!(key_infos.rank_in(), key_infos.rank_out());
         assert_eq!(tsk_infos.rank_in(), tsk_infos.rank_out());
         assert_eq!(key_infos.rank_in(), tsk_infos.rank_in());
 
-        let rank: usize = key_infos.rank_out().into();
+        self.glwe_keyswitch_tmp_bytes(res_infos, a_infos, key_infos)
+            .max(self.ggsw_expand_rows_tmp_bytes(res_infos, tsk_infos))
+    }
 
-        let size_out: usize = res_infos.k().div_ceil(res_infos.base2k()) as usize;
-        let res_znx: usize = VecZnx::bytes_of(self.n(), rank + 1, size_out);
-        let ci_dft: usize = self.bytes_of_vec_znx_dft(rank + 1, size_out);
-        let ks: usize = self.glwe_keyswitch_tmp_bytes(res_infos, a_infos, key_infos);
-        let expand_rows: usize = self.ggsw_expand_rows_tmp_bytes(res_infos, tsk_infos);
-        let res_dft: usize = self.bytes_of_vec_znx_dft(rank + 1, size_out);
+    fn ggsw_keyswitch_inplace<R, K, T>(&self, res: &mut R, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
+    where
+        R: GGSWToMut,
+        K: GGLWEPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
 
-        if a_infos.base2k() == tsk_infos.base2k() {
-            res_znx + ci_dft + (ks | expand_rows | res_dft)
-        } else {
-            let a_conv: usize = VecZnx::bytes_of(
-                self.n(),
-                1,
-                res_infos.k().div_ceil(tsk_infos.base2k()) as usize,
-            ) + self.vec_znx_normalize_tmp_bytes();
-            res_znx + ci_dft + (a_conv | ks | expand_rows | res_dft)
+        for row in 0..res.dnum().into() {
+            // Key-switch column 0, i.e.
+            // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0, a1, a2) -> (-(a0s0' + a1s1' + a2s2') + M[i], a0, a1, a2)
+            self.glwe_keyswitch_inplace(&mut res.at_mut(row, 0), key, scratch);
         }
+
+        self.ggsw_expand_row(res, tsk, scratch);
     }
 
     fn ggsw_keyswitch<R, A, K, T>(&self, res: &mut R, a: &A, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
@@ -91,7 +90,7 @@ where
         R: GGSWToMut,
         A: GGSWToRef,
         K: GGLWEPreparedToRef<BE>,
-        T: GLWETensorKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
@@ -108,22 +107,31 @@ }
 
         self.ggsw_expand_row(res, tsk, scratch);
     }
+}
+
+pub trait GGSWKeyswitch<BE: Backend>
+where
+    Self: GLWEKeyswitch<BE> + GGSWExpandRows<BE>,
+{
+    fn ggsw_keyswitch_tmp_bytes<R, A, K, T>(&self, res_infos: &R, a_infos: &A, key_infos: &K, tsk_infos: &T) -> usize
+    where
+        R: GGSWInfos,
+        A: GGSWInfos,
+        K: GGLWEInfos,
+        T: GGLWEInfos;
+
+    fn ggsw_keyswitch<R, A, K, T>(&self, res: &mut R, a: &A, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
+    where
+        R: GGSWToMut,
+        A: GGSWToRef,
+        K: GGLWEPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>;
 
     fn ggsw_keyswitch_inplace<R, K, T>(&self, res: &mut R, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
         R: GGSWToMut,
         K: GGLWEPreparedToRef<BE>,
-        T: GLWETensorKeyPreparedToRef<BE>,
-        Scratch<BE>: ScratchTakeCore<BE>,
-    {
-        let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
-
-        for row in 0..res.dnum().into() {
-            // Key-switch column 0, i.e.
-            // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0, a1, a2) -> (-(a0s0' + a1s1' + a2s2') + M[i], a0, a1, a2)
-            self.glwe_keyswitch_inplace(&mut res.at_mut(row, 0), key, scratch);
-        }
-
-        self.ggsw_expand_row(res, tsk, scratch);
-    }
+        T: GGLWEToGGSWKeyPreparedToRef<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>;
 }

@@ -1,10 +1,10 @@
 use poulpy_hal::{
     api::{
         ModuleN, ScratchAvailable, ScratchTakeBasic, VecZnxBigAddSmallInplace, VecZnxBigNormalize, VecZnxBigNormalizeTmpBytes,
-        VecZnxDftApply, VecZnxDftBytesOf, VecZnxIdftApplyConsume, VecZnxNormalize, VecZnxNormalizeTmpBytes, VmpApplyDftToDft,
-        VmpApplyDftToDftAdd, VmpApplyDftToDftTmpBytes,
+        VecZnxDftApply, VecZnxDftBytesOf, VecZnxDftCopy, VecZnxIdftApplyConsume, VecZnxNormalize, VecZnxNormalizeTmpBytes,
+        VmpApplyDftToDft, VmpApplyDftToDftAdd, VmpApplyDftToDftTmpBytes,
     },
-    layouts::{Backend, DataMut, DataViewMut, Module, Scratch, VecZnx, VecZnxBig, VecZnxDft, VmpPMat, ZnxInfos},
+    layouts::{Backend, DataMut, DataViewMut, Module, Scratch, VecZnx, VecZnxBig, VecZnxDft, VecZnxDftToRef, VmpPMat, ZnxInfos},
 };
 
 use crate::{
@@ -45,46 +45,10 @@ module.glwe_keyswitch_inplace(self, a, scratch);
     }
 }
 
-impl<BE: Backend> GLWEKeyswitch<BE> for Module<BE> where
-    Self: Sized
-        + ModuleN
-        + VecZnxDftBytesOf
-        + VmpApplyDftToDftTmpBytes
-        + VecZnxBigNormalizeTmpBytes
-        + VecZnxNormalizeTmpBytes
-        + VecZnxDftBytesOf
-        + VmpApplyDftToDftTmpBytes
-        + VecZnxBigNormalizeTmpBytes
-        + VmpApplyDftToDft<BE>
-        + VmpApplyDftToDftAdd<BE>
-        + VecZnxDftApply<BE>
-        + VecZnxIdftApplyConsume<BE>
-        + VecZnxBigAddSmallInplace<BE>
-        + VecZnxBigNormalize<BE>
-        + VecZnxNormalize<BE>
-        + VecZnxNormalizeTmpBytes
-{
-}
-
-pub trait GLWEKeyswitch<BE: Backend>
+impl<BE: Backend> GLWEKeyswitch<BE> for Module<BE>
 where
-    Self: Sized
-        + ModuleN
-        + VecZnxDftBytesOf
-        + VmpApplyDftToDftTmpBytes
-        + VecZnxBigNormalizeTmpBytes
-        + VecZnxNormalizeTmpBytes
-        + VecZnxDftBytesOf
-        + VmpApplyDftToDftTmpBytes
-        + VecZnxBigNormalizeTmpBytes
-        + VmpApplyDftToDft<BE>
-        + VmpApplyDftToDftAdd<BE>
-        + VecZnxDftApply<BE>
-        + VecZnxIdftApplyConsume<BE>
-        + VecZnxBigAddSmallInplace<BE>
-        + VecZnxBigNormalize<BE>
-        + VecZnxNormalize<BE>
-        + VecZnxNormalizeTmpBytes,
+    Self: Sized + GLWEKeySwitchInternal<BE> + VecZnxBigNormalizeTmpBytes + VecZnxBigNormalize<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
 {
     fn glwe_keyswitch_tmp_bytes<R, A, B>(&self, res_infos: &R, a_infos: &A, key_infos: &B) -> usize
     where
@@ -92,34 +56,10 @@ R: GLWEInfos,
         A: GLWEInfos,
         B: GGLWEInfos,
     {
-        let in_size: usize = a_infos
-            .k()
-            .div_ceil(key_infos.base2k())
-            .div_ceil(key_infos.dsize().into()) as usize;
-        let out_size: usize = res_infos.size();
-        let ksk_size: usize = key_infos.size();
-        let res_dft: usize = self.bytes_of_vec_znx_dft((key_infos.rank_out() + 1).into(), ksk_size); // TODO OPTIMIZE
-        let ai_dft: usize = self.bytes_of_vec_znx_dft((key_infos.rank_in()).into(), in_size);
-        let vmp: usize = self.vmp_apply_dft_to_dft_tmp_bytes(
-            out_size,
-            in_size,
-            in_size,
-            (key_infos.rank_in()).into(),
-            (key_infos.rank_out() + 1).into(),
-            ksk_size,
-        ) + self.bytes_of_vec_znx_dft((key_infos.rank_in()).into(), in_size);
-        let normalize_big: usize = self.vec_znx_big_normalize_tmp_bytes();
-        if a_infos.base2k() == key_infos.base2k() {
-            res_dft + ((ai_dft + vmp) | normalize_big)
-        } else if key_infos.dsize() == 1 {
-            // In this case, we only need one column, temporary, that we can drop once a_dft is computed.
-            let normalize_conv: usize = VecZnx::bytes_of(self.n(), 1, in_size) + self.vec_znx_normalize_tmp_bytes();
-            res_dft + (((ai_dft + normalize_conv) | vmp) | normalize_big)
-        } else {
-            // Since we stride over a to get a_dft when dsize > 1, we need to store the full columns of a with in the base conversion.
-            let normalize_conv: usize = VecZnx::bytes_of(self.n(), (key_infos.rank_in()).into(), in_size);
-            res_dft + ((ai_dft + normalize_conv + (self.vec_znx_normalize_tmp_bytes() | vmp)) | normalize_big)
-        }
+        let cols: usize = res_infos.rank().as_usize() + 1;
+        self.glwe_keyswitch_internal_tmp_bytes(res_infos, a_infos, key_infos)
+            .max(self.vec_znx_big_normalize_tmp_bytes())
+            + self.bytes_of_vec_znx_dft(cols, key_infos.size())
     }
 
     fn glwe_keyswitch<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
@@ -127,7 +67,6 @@ where
         R: GLWEToMut,
         A: GLWEToRef,
         K: GGLWEPreparedToRef<BE>,
-        Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         let a: &GLWE<&[u8]> = &a.to_ref();
@@ -164,8 +103,8 @@ let basek_out: usize = res.base2k().into();
         let base2k_out: usize = b.base2k().into();
 
         let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), b.size()); // Todo optimise
-        let res_big: VecZnxBig<&mut [u8], BE> = keyswitch_internal(self, res_dft, a, b, scratch_1);
-        (0..(res.rank() + 1).into()).for_each(|i| {
+        let res_big: VecZnxBig<&mut [u8], BE> = self.glwe_keyswitch_internal(res_dft, a, b, scratch_1);
+        for i in 0..(res.rank() + 1).into() {
             self.vec_znx_big_normalize(
                 basek_out,
                 &mut res.data,
@@ -175,37 +114,36 @@ &res_big,
                 i,
                 scratch_1,
             );
-        })
+        }
     }
 
     fn glwe_keyswitch_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
     where
         R: GLWEToMut,
         K: GGLWEPreparedToRef<BE>,
-        Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
-        let a: &GGLWEPrepared<&[u8], BE> = &key.to_ref();
+        let key: &GGLWEPrepared<&[u8], BE> = &key.to_ref();
 
         assert_eq!(
             res.rank(),
-            a.rank_in(),
+            key.rank_in(),
             "res.rank(): {} != a.rank_in(): {}",
             res.rank(),
-            a.rank_in()
+            key.rank_in()
         );
         assert_eq!(
             res.rank(),
-            a.rank_out(),
+            key.rank_out(),
             "res.rank(): {} != b.rank_out(): {}",
             res.rank(),
-            a.rank_out()
+            key.rank_out()
         );
 
         assert_eq!(res.n(), self.n() as u32);
-        assert_eq!(a.n(), self.n() as u32);
+        assert_eq!(key.n(), self.n() as u32);
 
-        let scrach_needed: usize = self.glwe_keyswitch_tmp_bytes(res, res, a);
+        let scrach_needed: usize = self.glwe_keyswitch_tmp_bytes(res, res, key);
 
         assert!(
             scratch.available() >= scrach_needed,
@@ -214,11 +152,11 @@ scratch.available(),
         );
 
         let base2k_in: usize = res.base2k().into();
-        let base2k_out: usize = a.base2k().into();
+        let base2k_out: usize = key.base2k().into();
 
-        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), a.size()); // Todo optimise
-        let res_big: VecZnxBig<&mut [u8], BE> = keyswitch_internal(self, res_dft, res, a, scratch_1);
-        (0..(res.rank() + 1).into()).for_each(|i| {
+        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // Todo optimise
+        let res_big: VecZnxBig<&mut [u8], BE> = self.glwe_keyswitch_internal(res_dft, res, key, scratch_1);
+        for i in 0..(res.rank() + 1).into() {
             self.vec_znx_big_normalize(
                 base2k_in,
                 &mut res.data,
@@ -228,143 +166,235 @@ &res_big,
                 i,
                 scratch_1,
             );
-        })
+        }
     }
 }
 
-impl GLWE<Vec<u8>> {}
+pub trait GLWEKeyswitch<BE: Backend> {
+    fn glwe_keyswitch_tmp_bytes<R, A, B>(&self, res_infos: &R, a_infos: &A, key_infos: &B) -> usize
+    where
+        R: GLWEInfos,
+        A: GLWEInfos,
+        B: GGLWEInfos;
 
-impl<DataSelf: DataMut> GLWE<DataSelf> {}
+    fn glwe_keyswitch<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        K: GGLWEPreparedToRef<BE>;
 
-pub(crate) fn keyswitch_internal<BE: Backend, M, DR, A, K>(
-    module: &M,
-    mut res: VecZnxDft<DR, BE>,
-    a: &A,
-    key: &K,
-    scratch: &mut Scratch<BE>,
-) -> VecZnxBig<DR, BE>
+    fn glwe_keyswitch_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        K: GGLWEPreparedToRef<BE>;
+}
+
+impl<BE: Backend> GLWEKeySwitchInternal<BE> for Module<BE> where
+    Self: GGLWEProduct<BE>
+        + VecZnxDftApply<BE>
+        + VecZnxNormalize<BE>
+        + VecZnxIdftApplyConsume<BE>
+        + VecZnxBigAddSmallInplace<BE>
+        + VecZnxNormalizeTmpBytes
+{
+}
+
+pub(crate) trait GLWEKeySwitchInternal<BE: Backend>
 where
-    DR: DataMut,
-    A: GLWEToRef,
-    K: GGLWEPreparedToRef<BE>,
-    M: ModuleN
-        + VecZnxDftBytesOf
-        + VmpApplyDftToDftTmpBytes
-        + VecZnxBigNormalizeTmpBytes
-        + VmpApplyDftToDftTmpBytes
-        + VmpApplyDftToDft<BE>
-        + VmpApplyDftToDftAdd<BE>
+    Self: GGLWEProduct<BE>
         + VecZnxDftApply<BE>
+        + VecZnxNormalize<BE>
         + VecZnxIdftApplyConsume<BE>
         + VecZnxBigAddSmallInplace<BE>
-        + VecZnxBigNormalize<BE>
-        + VecZnxNormalize<BE>,
-    Scratch<BE>: ScratchTakeCore<BE>,
+        + VecZnxNormalizeTmpBytes,
 {
-    let a: &GLWE<&[u8]> = &a.to_ref();
-    let key: &GGLWEPrepared<&[u8], BE> = &key.to_ref();
+    fn glwe_keyswitch_internal_tmp_bytes<R, A, K>(&self, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
+    where
+        R: GLWEInfos,
+        A: GLWEInfos,
+        K: GGLWEInfos,
+    {
+        let cols: usize = (a_infos.rank() + 1).into();
+        let a_size: usize = a_infos.size();
 
-    let base2k_in: usize = a.base2k().into();
-    let base2k_out: usize = key.base2k().into();
-    let cols: usize = (a.rank() + 1).into();
-    let a_size: usize = (a.size() * base2k_in).div_ceil(base2k_out);
-    let pmat: &VmpPMat<&[u8], BE> = &key.data;
+        let a_conv = if a_infos.base2k() == key_infos.base2k() {
+            0
+        } else {
+            VecZnx::bytes_of(self.n(), 1, a_size) + self.vec_znx_normalize_tmp_bytes()
+        };
 
-    if key.dsize() == 1 {
-        let (mut ai_dft, scratch_1) = scratch.take_vec_znx_dft(module, cols - 1, a.size());
+        self.gglwe_product_dft_tmp_bytes(res_infos.size(), a_size, key_infos) + self.bytes_of_vec_znx_dft(cols, a_size) + a_conv
+    }
+
+    fn glwe_keyswitch_internal<DR, A, K>(
+        &self,
+        mut res: VecZnxDft<DR, BE>,
+        a: &A,
+        key: &K,
+        scratch: &mut Scratch<BE>,
+    ) -> VecZnxBig<DR, BE>
+    where
+        DR: DataMut,
+        A: GLWEToRef,
+        K: GGLWEPreparedToRef<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        let a: &GLWE<&[u8]> = &a.to_ref();
+        let key: &GGLWEPrepared<&[u8], BE> = &key.to_ref();
+
+        let base2k_in: usize = a.base2k().into();
+        let base2k_out: usize = key.base2k().into();
+        let cols: usize = (a.rank() + 1).into();
+        let a_size: usize = (a.size() * base2k_in).div_ceil(base2k_out);
+
+        let (mut a_dft, scratch_1) = scratch.take_vec_znx_dft(self, cols - 1, a_size);
 
         if base2k_in == base2k_out {
-            (0..cols - 1).for_each(|col_i| {
-                module.vec_znx_dft_apply(1, 0, &mut ai_dft, col_i, a.data(), col_i + 1);
-            });
+            for col_i in 0..cols - 1 {
+                self.vec_znx_dft_apply(1, 0, &mut a_dft, col_i, a.data(), col_i + 1);
+            }
         } else {
-            let (mut a_conv, scratch_2) = scratch_1.take_vec_znx(module.n(), 1, a_size);
-            (0..cols - 1).for_each(|col_i| {
-                module.vec_znx_normalize(
+            let (mut a_conv, scratch_2) = scratch_1.take_vec_znx(self.n(), 1, a_size);
+            for i in 0..cols - 1 {
+                self.vec_znx_normalize(
                     base2k_out,
                     &mut a_conv,
                     0,
                     base2k_in,
                     a.data(),
-                    col_i + 1,
+                    i + 1,
                     scratch_2,
                 );
-                module.vec_znx_dft_apply(1, 0, &mut ai_dft, col_i, &a_conv, 0);
-            });
+                self.vec_znx_dft_apply(1, 0, &mut a_dft, i, &a_conv, 0);
+            }
         }
 
-        module.vmp_apply_dft_to_dft(&mut res, &ai_dft, pmat, scratch_1);
-    } else {
-        let dsize: usize = key.dsize().into();
+        self.gglwe_product_dft(&mut res, &a_dft, key, scratch_1);
 
-        let (mut ai_dft, scratch_1) = scratch.take_vec_znx_dft(module, cols - 1, a_size.div_ceil(dsize));
-        ai_dft.data_mut().fill(0);
+        let mut res_big: VecZnxBig<DR, BE> = self.vec_znx_idft_apply_consume(res);
+        self.vec_znx_big_add_small_inplace(&mut res_big, 0, a.data(), 0);
+        res_big
+    }
+}
 
-        if base2k_in == base2k_out {
-            for di in 0..dsize {
-                ai_dft.set_size((a_size + di) / dsize);
+impl<BE: Backend> GGLWEProduct<BE> for Module<BE> where
+    Self: Sized
+        + ModuleN
+        + VecZnxDftBytesOf
+        + VmpApplyDftToDftTmpBytes
+        + VmpApplyDftToDft<BE>
+        + VmpApplyDftToDftAdd<BE>
+        + VecZnxDftCopy<BE>
+{
+}
 
-                // Small optimization for dsize > 2
-                // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
-                // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(dsize-1) * B}.
-                // As such we can ignore the last dsize-2 limbs safely of the sum of vmp products.
-                // It is possible to further ignore the last dsize-1 limbs, but this introduce
-                // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
-                // noise is kept with respect to the ideal functionality.
-                res.set_size(pmat.size() - ((dsize - di) as isize - 2).max(0) as usize);
+pub(crate) trait GGLWEProduct<BE: Backend>
+where
+    Self: Sized
+        + ModuleN
+        + VecZnxDftBytesOf
+        + VmpApplyDftToDftTmpBytes
+        + VmpApplyDftToDft<BE>
+        + VmpApplyDftToDftAdd<BE>
+        + VecZnxDftCopy<BE>,
+{
+    fn gglwe_product_dft_tmp_bytes<K>(&self, res_size: usize, a_size: usize, key_infos: &K) -> usize
+    where
+        K: GGLWEInfos,
+    {
+        let dsize: usize = key_infos.dsize().as_usize();
 
-                for j in 0..cols - 1 {
-                    module.vec_znx_dft_apply(dsize, dsize - di - 1, &mut ai_dft, j, a.data(), j + 1);
-                }
+        if dsize == 1 {
+            self.vmp_apply_dft_to_dft_tmp_bytes(
+                res_size,
+                a_size,
+                key_infos.dnum().into(),
+                (key_infos.rank_in()).into(),
+                (key_infos.rank_out() + 1).into(),
+                key_infos.size(),
+            )
+        } else {
+            let dnum: usize = key_infos.dnum().into();
+            let a_size: usize = a_size.div_ceil(dsize).min(dnum);
+            let ai_dft: usize = self.bytes_of_vec_znx_dft(key_infos.rank_in().into(), a_size);
 
-                if di == 0 {
-                    module.vmp_apply_dft_to_dft(&mut res, &ai_dft, pmat, scratch_1);
-                } else {
-                    module.vmp_apply_dft_to_dft_add(&mut res, &ai_dft, pmat, di, scratch_1);
-                }
-            }
+            let vmp: usize = self.vmp_apply_dft_to_dft_tmp_bytes(
+                res_size,
+                a_size,
+                dnum,
+                (key_infos.rank_in()).into(),
+                (key_infos.rank_out() + 1).into(),
+                key_infos.size(),
+            );
+
+            ai_dft + vmp
+        }
+    }
+
+    fn gglwe_product_dft<DR, A, K>(&self, res: &mut VecZnxDft<DR, BE>, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        DR: DataMut,
+        A: VecZnxDftToRef<BE>,
+        K: GGLWEPreparedToRef<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        let a: &VecZnxDft<&[u8], BE> = &a.to_ref();
+        let key: &GGLWEPrepared<&[u8], BE> = &key.to_ref();
+
+        let cols: usize = a.cols();
+        let a_size: usize = a.size();
+        let pmat: &VmpPMat<&[u8], BE> = &key.data;
+
+        // If dsize == 1, then the digit decomposition is equal to Base2K and we can simply
+        // can the vmp API.
+        if key.dsize() == 1 {
+            self.vmp_apply_dft_to_dft(res, a, pmat, scratch);
+        // If dsize != 1, then the digit decomposition is k * Base2K with k > 1.
+        // As such we need to perform a bivariate polynomial convolution in (X, Y) / (X^{N}+1) with Y = 2^-K
+        // (instead of yn univariate one in X).
+        //
+        // Since the basis in Y is small (in practice degree 6-7 max), we perform it naiveley.
+        // To do so, we group the different limbs of ai_dft by their respective degree in Y
+        // which are multiples of the current digit.
+        // For example if dsize = 3, with ai_dft = [a0, a1, a2, a3, a4, a5, a6],
+        // we group them as [[a0, a3, a5], [a1, a4, a6], [a2, a5, 0]]
+        // and evaluate sum(a_di * pmat * 2^{di*Base2k})
         } else {
-            let (mut a_conv, scratch_2) = scratch_1.take_vec_znx(module.n(), cols - 1, a_size);
-            for j in 0..cols - 1 {
-                module.vec_znx_normalize(
-                    base2k_out,
-                    &mut a_conv,
-                    j,
-                    base2k_in,
-                    a.data(),
-                    j + 1,
-                    scratch_2,
-                );
-            }
+            let dsize: usize = key.dsize().into();
+            let dnum: usize = key.dnum().into();
+
+            // We bound ai_dft size by the number of rows of the matrix
+            let (mut ai_dft, scratch_1) = scratch.take_vec_znx_dft(self, cols, a_size.div_ceil(dsize).min(dnum));
+            ai_dft.data_mut().fill(0);
 
             for di in 0..dsize {
-                ai_dft.set_size((a_size + di) / dsize);
+                // Sets ai_dft size according to the current digit (if dsize does not divides a_size),
+                // bounded by the number of rows (digits) in the prepared matrix.
+                ai_dft.set_size(((a_size + di) / dsize).min(dnum));
 
                 // Small optimization for dsize > 2
-                // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
-                // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(dsize-1) * B}.
+                // VMP produce some error e, and since we aggregate vmp * 2^{di * Base2k}, then
+                // we also aggregate ei * 2^{di * Base2k}, with the largest error being ei * 2^{(dsize-1) * Base2k}.
                 // As such we can ignore the last dsize-2 limbs safely of the sum of vmp products.
                 // It is possible to further ignore the last dsize-1 limbs, but this introduce
                 // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
                 // noise is kept with respect to the ideal functionality.
                 res.set_size(pmat.size() - ((dsize - di) as isize - 2).max(0) as usize);
 
-                for j in 0..cols - 1 {
-                    module.vec_znx_dft_apply(dsize, dsize - di - 1, &mut ai_dft, j, &a_conv, j);
+                for j in 0..cols {
+                    self.vec_znx_dft_copy(dsize, dsize - di - 1, &mut ai_dft, j, a, j);
                 }
 
                 if di == 0 {
-                    module.vmp_apply_dft_to_dft(&mut res, &ai_dft, pmat, scratch_2);
+                    // res = pmat * ai_dft
+                    self.vmp_apply_dft_to_dft(res, &ai_dft, pmat, scratch_1);
                 } else {
-                    module.vmp_apply_dft_to_dft_add(&mut res, &ai_dft, pmat, di, scratch_2);
+                    // res = (pmat * ai_dft) * 2^{di * Base2k}
+                    self.vmp_apply_dft_to_dft_add(res, &ai_dft, pmat, di, scratch_1);
                 }
             }
-        }
 
-        res.set_size(res.max_size());
+            res.set_size(res.max_size());
+        }
     }
-
-    let mut res_big: VecZnxBig<DR, BE> = module.vec_znx_idft_apply_consume(res);
-    module.vec_znx_big_add_small_inplace(&mut res_big, 0, a.data(), 0);
-    res_big
 }

@@ -0,0 +1,237 @@
+use poulpy_hal::{
+    layouts::{Data, DataMut, DataRef, FillUniform, ReaderFrom, WriterTo},
+    source::Source,
+};
+
+use crate::layouts::{
+    Base2K, Degree, Dnum, Dsize, GGLWECompressed, GGLWECompressedToMut, GGLWECompressedToRef, GGLWEDecompress, GGLWEInfos,
+    GGLWEToGGSWKey, GGLWEToGGSWKeyToMut, GLWEInfos, LWEInfos, Rank, TorusPrecision,
+};
+use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
+
+use std::fmt;
+
+#[derive(PartialEq, Eq, Clone)]
+pub struct GGLWEToGGSWKeyCompressed<D: Data> {
+    pub(crate) keys: Vec<GGLWECompressed<D>>,
+}
+
+impl<D: Data> LWEInfos for GGLWEToGGSWKeyCompressed<D> {
+    fn n(&self) -> Degree {
+        self.keys[0].n()
+    }
+
+    fn base2k(&self) -> Base2K {
+        self.keys[0].base2k()
+    }
+
+    fn k(&self) -> TorusPrecision {
+        self.keys[0].k()
+    }
+
+    fn size(&self) -> usize {
+        self.keys[0].size()
+    }
+}
+
+impl<D: Data> GLWEInfos for GGLWEToGGSWKeyCompressed<D> {
+    fn rank(&self) -> Rank {
+        self.keys[0].rank_out()
+    }
+}
+
+impl<D: Data> GGLWEInfos for GGLWEToGGSWKeyCompressed<D> {
+    fn rank_in(&self) -> Rank {
+        self.rank_out()
+    }
+
+    fn rank_out(&self) -> Rank {
+        self.keys[0].rank_out()
+    }
+
+    fn dsize(&self) -> Dsize {
+        self.keys[0].dsize()
+    }
+
+    fn dnum(&self) -> Dnum {
+        self.keys[0].dnum()
+    }
+}
+
+impl<D: DataRef> fmt::Debug for GGLWEToGGSWKeyCompressed<D> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "{self}")
+    }
+}
+
+impl<D: DataMut> FillUniform for GGLWEToGGSWKeyCompressed<D> {
+    fn fill_uniform(&mut self, log_bound: usize, source: &mut Source) {
+        self.keys
+            .iter_mut()
+            .for_each(|key: &mut GGLWECompressed<D>| key.fill_uniform(log_bound, source))
+    }
+}
+
+impl<D: DataRef> fmt::Display for GGLWEToGGSWKeyCompressed<D> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        writeln!(f, "(GGLWEToGGSWKeyCompressed)",)?;
+        for (i, key) in self.keys.iter().enumerate() {
+            write!(f, "{i}: {key}")?;
+        }
+        Ok(())
+    }
+}
+
+impl GGLWEToGGSWKeyCompressed<Vec<u8>> {
+    pub fn alloc_from_infos<A>(infos: &A) -> Self
+    where
+        A: GGLWEInfos,
+    {
+        assert_eq!(
+            infos.rank_in(),
+            infos.rank_out(),
+            "rank_in != rank_out is not supported for GGLWEToGGSWKeyCompressed"
+        );
+        Self::alloc(
+            infos.n(),
+            infos.base2k(),
+            infos.k(),
+            infos.rank(),
+            infos.dnum(),
+            infos.dsize(),
+        )
+    }
+
+    pub fn alloc(n: Degree, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> Self {
+        GGLWEToGGSWKeyCompressed {
+            keys: (0..rank.as_usize())
+                .map(|_| GGLWECompressed::alloc(n, base2k, k, rank, rank, dnum, dsize))
+                .collect(),
+        }
+    }
+
+    pub fn bytes_of_from_infos<A>(infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+    {
+        assert_eq!(
+            infos.rank_in(),
+            infos.rank_out(),
+            "rank_in != rank_out is not supported for GGLWEToGGSWKeyCompressed"
+        );
+        Self::bytes_of(
+            infos.n(),
+            infos.base2k(),
+            infos.k(),
+            infos.rank(),
+            infos.dnum(),
+            infos.dsize(),
+        )
+    }
+
+    pub fn bytes_of(n: Degree, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> usize {
+        rank.as_usize() * GGLWECompressed::bytes_of(n, base2k, k, rank, dnum, dsize)
+    }
+}
+
+impl<D: DataMut> GGLWEToGGSWKeyCompressed<D> {
+    // Returns a mutable reference to GGLWE_{s}([s[i]*s[0], s[i]*s[1], ..., s[i]*s[rank]])
+    pub fn at_mut(&mut self, i: usize) -> &mut GGLWECompressed<D> {
+        assert!((i as u32) < self.rank());
+        &mut self.keys[i]
+    }
+}
+
+impl<D: DataRef> GGLWEToGGSWKeyCompressed<D> {
+    // Returns a reference to GGLWE_{s}(s[i] * s[j])
+    pub fn at(&self, i: usize) -> &GGLWECompressed<D> {
+        assert!((i as u32) < self.rank());
+        &self.keys[i]
+    }
+}
+
+impl<D: DataMut> ReaderFrom for GGLWEToGGSWKeyCompressed<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 GGLWEToGGSWKeyCompressed<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(())
+    }
+}
+
+pub trait GGLWEToGGSWKeyDecompress
+where
+    Self: GGLWEDecompress,
+{
+    fn decompress_gglwe_to_ggsw_key<R, O>(&self, res: &mut R, other: &O)
+    where
+        R: GGLWEToGGSWKeyToMut,
+        O: GGLWEToGGSWKeyCompressedToRef,
+    {
+        let res: &mut GGLWEToGGSWKey<&mut [u8]> = &mut res.to_mut();
+        let other: &GGLWEToGGSWKeyCompressed<&[u8]> = &other.to_ref();
+
+        assert_eq!(res.keys.len(), other.keys.len());
+
+        for (a, b) in res.keys.iter_mut().zip(other.keys.iter()) {
+            self.decompress_gglwe(a, b);
+        }
+    }
+}
+
+impl<D: DataMut> GGLWEToGGSWKey<D> {
+    pub fn decompress<O, M>(&mut self, module: &M, other: &O)
+    where
+        M: GGLWEToGGSWKeyDecompress,
+        O: GGLWEToGGSWKeyCompressedToRef,
+    {
+        module.decompress_gglwe_to_ggsw_key(self, other);
+    }
+}
+
+pub trait GGLWEToGGSWKeyCompressedToRef {
+    fn to_ref(&self) -> GGLWEToGGSWKeyCompressed<&[u8]>;
+}
+
+impl<D: DataRef> GGLWEToGGSWKeyCompressedToRef for GGLWEToGGSWKeyCompressed<D>
+where
+    GGLWECompressed<D>: GGLWECompressedToRef,
+{
+    fn to_ref(&self) -> GGLWEToGGSWKeyCompressed<&[u8]> {
+        GGLWEToGGSWKeyCompressed {
+            keys: self.keys.iter().map(|c| c.to_ref()).collect(),
+        }
+    }
+}
+
+pub trait GGLWEToGGSWKeyCompressedToMut {
+    fn to_mut(&mut self) -> GGLWEToGGSWKeyCompressed<&mut [u8]>;
+}
+
+impl<D: DataMut> GGLWEToGGSWKeyCompressedToMut for GGLWEToGGSWKeyCompressed<D>
+where
+    GGLWECompressed<D>: GGLWECompressedToMut,
+{
+    fn to_mut(&mut self) -> GGLWEToGGSWKeyCompressed<&mut [u8]> {
+        GGLWEToGGSWKeyCompressed {
+            keys: self.keys.iter_mut().map(|c| c.to_mut()).collect(),
+        }
+    }
+}

@@ -4,31 +4,34 @@ source::Source,
 };
 
 use crate::layouts::{
-    Base2K, Degree, Dnum, Dsize, GGLWECompressed, GGLWECompressedToMut, GGLWECompressedToRef, GGLWEDecompress, GGLWEInfos,
-    GLWEInfos, GLWETensorKey, GLWETensorKeyToMut, LWEInfos, Rank, TorusPrecision,
+    Base2K, Degree, Dnum, Dsize, GGLWECompressed, GGLWECompressedSeedMut, GGLWECompressedToMut, GGLWECompressedToRef,
+    GGLWEDecompress, GGLWEInfos, GGLWEToMut, GLWEInfos, GLWETensorKey, LWEInfos, Rank, TorusPrecision,
 };
-use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
 use std::fmt;
 
 #[derive(PartialEq, Eq, Clone)]
-pub struct GLWETensorKeyCompressed<D: Data> {
-    pub(crate) keys: Vec<GGLWECompressed<D>>,
+pub struct GLWETensorKeyCompressed<D: Data>(pub(crate) GGLWECompressed<D>);
+
+impl<D: DataMut> GGLWECompressedSeedMut for GLWETensorKeyCompressed<D> {
+    fn seed_mut(&mut self) -> &mut Vec<[u8; 32]> {
+        &mut self.0.seed
+    }
 }
 
 impl<D: Data> LWEInfos for GLWETensorKeyCompressed<D> {
     fn n(&self) -> Degree {
-        self.keys[0].n()
+        self.0.n()
     }
 
     fn base2k(&self) -> Base2K {
-        self.keys[0].base2k()
+        self.0.base2k()
     }
 
     fn k(&self) -> TorusPrecision {
-        self.keys[0].k()
+        self.0.k()
     }
     fn size(&self) -> usize {
-        self.keys[0].size()
+        self.0.size()
     }
 }
 impl<D: Data> GLWEInfos for GLWETensorKeyCompressed<D> {
@@ -43,15 +46,15 @@ self.rank_out()
     }
 
     fn rank_out(&self) -> Rank {
-        self.keys[0].rank_out()
+        self.0.rank_out()
     }
 
     fn dsize(&self) -> Dsize {
-        self.keys[0].dsize()
+        self.0.dsize()
     }
 
     fn dnum(&self) -> Dnum {
-        self.keys[0].dnum()
+        self.0.dnum()
     }
 }
 
@@ -63,18 +66,14 @@ }
 
 impl<D: DataMut> FillUniform for GLWETensorKeyCompressed<D> {
     fn fill_uniform(&mut self, log_bound: usize, source: &mut Source) {
-        self.keys
-            .iter_mut()
-            .for_each(|key: &mut GGLWECompressed<D>| key.fill_uniform(log_bound, source))
+        self.0.fill_uniform(log_bound, source);
     }
 }
 
 impl<D: DataRef> fmt::Display for GLWETensorKeyCompressed<D> {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         writeln!(f, "(GLWETensorKeyCompressed)",)?;
-        for (i, key) in self.keys.iter().enumerate() {
-            write!(f, "{i}: {key}")?;
-        }
+        write!(f, "{}", self.0)?;
         Ok(())
     }
 }
@@ -96,11 +95,15 @@ }
 
     pub fn alloc(n: Degree, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> Self {
         let pairs: u32 = (((rank.as_u32() + 1) * rank.as_u32()) >> 1).max(1);
-        GLWETensorKeyCompressed {
-            keys: (0..pairs)
-                .map(|_| GGLWECompressed::alloc(n, base2k, k, Rank(1), rank, dnum, dsize))
-                .collect(),
-        }
+        GLWETensorKeyCompressed(GGLWECompressed::alloc(
+            n,
+            base2k,
+            k,
+            Rank(pairs),
+            rank,
+            dnum,
+            dsize,
+        ))
     }
 
     pub fn bytes_of_from_infos<A>(infos: &A) -> usize
@@ -118,88 +121,35 @@ )
     }
 
     pub fn bytes_of(n: Degree, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> usize {
-        let pairs: usize = (((rank.0 + 1) * rank.0) >> 1).max(1) as usize;
-        pairs * GGLWECompressed::bytes_of(n, base2k, k, Rank(1), dnum, dsize)
+        let pairs: u32 = (((rank.as_u32() + 1) * rank.as_u32()) >> 1).max(1);
+        GGLWECompressed::bytes_of(n, base2k, k, Rank(pairs), dnum, dsize)
     }
 }
 
 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)?;
-        }
+        self.0.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)?;
-        }
+        self.0.write_to(writer)?;
         Ok(())
     }
 }
 
-pub trait GLWETensorKeyCompressedAtRef<D: DataRef> {
-    fn at(&self, i: usize, j: usize) -> &GGLWECompressed<D>;
-}
-
-impl<D: DataRef> GLWETensorKeyCompressedAtRef<D> for GLWETensorKeyCompressed<D> {
-    fn at(&self, mut i: usize, mut j: usize) -> &GGLWECompressed<D> {
-        if i > j {
-            std::mem::swap(&mut i, &mut j);
-        };
-        let rank: usize = self.rank_out().into();
-        &self.keys[i * rank + j - (i * (i + 1) / 2)]
-    }
-}
-
-pub trait GLWETensorKeyCompressedAtMut<D: DataMut> {
-    fn at_mut(&mut self, i: usize, j: usize) -> &mut GGLWECompressed<D>;
-}
-
-impl<D: DataMut> GLWETensorKeyCompressedAtMut<D> for GLWETensorKeyCompressed<D> {
-    fn at_mut(&mut self, mut i: usize, mut j: usize) -> &mut GGLWECompressed<D> {
-        if i > j {
-            std::mem::swap(&mut i, &mut j);
-        };
-        let rank: usize = self.rank_out().into();
-        &mut self.keys[i * rank + j - (i * (i + 1) / 2)]
-    }
-}
-
 pub trait GLWETensorKeyDecompress
 where
     Self: GGLWEDecompress,
 {
     fn decompress_tensor_key<R, O>(&self, res: &mut R, other: &O)
     where
-        R: GLWETensorKeyToMut,
-        O: GLWETensorKeyCompressedToRef,
+        R: GGLWEToMut,
+        O: GGLWECompressedToRef,
     {
-        let res: &mut GLWETensorKey<&mut [u8]> = &mut res.to_mut();
-        let other: &GLWETensorKeyCompressed<&[u8]> = &other.to_ref();
-
-        assert_eq!(
-            res.keys.len(),
-            other.keys.len(),
-            "invalid receiver: res.keys.len()={} != other.keys.len()={}",
-            res.keys.len(),
-            other.keys.len()
-        );
-
-        for (a, b) in res.keys.iter_mut().zip(other.keys.iter()) {
-            self.decompress_gglwe(a, b);
-        }
+        self.decompress_gglwe(res, other);
     }
 }
 
@@ -208,39 +158,27 @@
 impl<D: DataMut> GLWETensorKey<D> {
     pub fn decompress<O, M>(&mut self, module: &M, other: &O)
     where
-        O: GLWETensorKeyCompressedToRef,
+        O: GGLWECompressedToRef,
         M: GLWETensorKeyDecompress,
     {
         module.decompress_tensor_key(self, other);
     }
 }
 
-pub trait GLWETensorKeyCompressedToMut {
-    fn to_mut(&mut self) -> GLWETensorKeyCompressed<&mut [u8]>;
-}
-
-impl<D: DataMut> GLWETensorKeyCompressedToMut for GLWETensorKeyCompressed<D>
+impl<D: DataMut> GGLWECompressedToMut for GLWETensorKeyCompressed<D>
 where
     GGLWECompressed<D>: GGLWECompressedToMut,
 {
-    fn to_mut(&mut self) -> GLWETensorKeyCompressed<&mut [u8]> {
-        GLWETensorKeyCompressed {
-            keys: self.keys.iter_mut().map(|c| c.to_mut()).collect(),
-        }
+    fn to_mut(&mut self) -> GGLWECompressed<&mut [u8]> {
+        self.0.to_mut()
     }
 }
 
-pub trait GLWETensorKeyCompressedToRef {
-    fn to_ref(&self) -> GLWETensorKeyCompressed<&[u8]>;
-}
-
-impl<D: DataRef> GLWETensorKeyCompressedToRef for GLWETensorKeyCompressed<D>
+impl<D: DataRef> GGLWECompressedToRef for GLWETensorKeyCompressed<D>
 where
     GGLWECompressed<D>: GGLWECompressedToRef,
 {
-    fn to_ref(&self) -> GLWETensorKeyCompressed<&[u8]> {
-        GLWETensorKeyCompressed {
-            keys: self.keys.iter().map(|c| c.to_ref()).collect(),
-        }
+    fn to_ref(&self) -> GGLWECompressed<&[u8]> {
+        self.0.to_ref()
     }
 }

@@ -7,7 +7,7 @@ };
 
 use crate::layouts::{
     Base2K, Degree, Dnum, Dsize, GGLWECompressed, GGLWECompressedToMut, GGLWECompressedToRef, GGLWEInfos, GGLWEToMut, GLWEInfos,
-    GLWESwitchingKeyDegrees, GLWESwitchingKeyDegreesMut, GLWEToLWESwitchingKey, LWEInfos, Rank, TorusPrecision,
+    GLWESwitchingKeyDegrees, GLWESwitchingKeyDegreesMut, GLWEToLWEKey, LWEInfos, Rank, TorusPrecision,
     compressed::{GLWESwitchingKeyCompressed, GLWESwitchingKeyDecompress},
 };
 
@@ -147,7 +147,7 @@ pub trait GLWEToLWESwitchingKeyDecompress
 where
     Self: GLWESwitchingKeyDecompress,
 {
-    fn decompress_glwe_to_lwe_switching_key<R, O>(&self, res: &mut R, other: &O)
+    fn decompress_glwe_to_lwe_key<R, O>(&self, res: &mut R, other: &O)
     where
         R: GGLWEToMut + GLWESwitchingKeyDegreesMut,
         O: GGLWECompressedToRef + GLWESwitchingKeyDegrees,
@@ -158,13 +158,13 @@ }
 
 impl<B: Backend> GLWEToLWESwitchingKeyDecompress for Module<B> where Self: GLWESwitchingKeyDecompress {}
 
-impl<D: DataMut> GLWEToLWESwitchingKey<D> {
+impl<D: DataMut> GLWEToLWEKey<D> {
     pub fn decompress<O, M>(&mut self, module: &M, other: &O)
     where
         O: GGLWECompressedToRef + GLWESwitchingKeyDegrees,
         M: GLWEToLWESwitchingKeyDecompress,
     {
-        module.decompress_glwe_to_lwe_switching_key(self, other);
+        module.decompress_glwe_to_lwe_key(self, other);
     }
 }
 

@@ -5,15 +5,15 @@ };
 
 use crate::layouts::{
     Base2K, Degree, Dnum, Dsize, GGLWECompressed, GGLWECompressedToMut, GGLWECompressedToRef, GGLWEInfos, GGLWEToMut, GLWEInfos,
-    GLWESwitchingKeyDegrees, GLWESwitchingKeyDegreesMut, LWEInfos, LWEToGLWESwitchingKey, Rank, TorusPrecision,
+    GLWESwitchingKeyDegrees, GLWESwitchingKeyDegreesMut, LWEInfos, LWEToGLWEKey, Rank, TorusPrecision,
     compressed::{GLWESwitchingKeyCompressed, GLWESwitchingKeyDecompress},
 };
 use std::fmt;
 
 #[derive(PartialEq, Eq, Clone)]
-pub struct LWEToGLWESwitchingKeyCompressed<D: Data>(pub(crate) GLWESwitchingKeyCompressed<D>);
+pub struct LWEToGLWEKeyCompressed<D: Data>(pub(crate) GLWESwitchingKeyCompressed<D>);
 
-impl<D: Data> LWEInfos for LWEToGLWESwitchingKeyCompressed<D> {
+impl<D: Data> LWEInfos for LWEToGLWEKeyCompressed<D> {
     fn n(&self) -> Degree {
         self.0.n()
     }
@@ -29,13 +29,13 @@ fn size(&self) -> usize {
         self.0.size()
     }
 }
-impl<D: Data> GLWEInfos for LWEToGLWESwitchingKeyCompressed<D> {
+impl<D: Data> GLWEInfos for LWEToGLWEKeyCompressed<D> {
     fn rank(&self) -> Rank {
         self.rank_out()
     }
 }
 
-impl<D: Data> GGLWEInfos for LWEToGLWESwitchingKeyCompressed<D> {
+impl<D: Data> GGLWEInfos for LWEToGLWEKeyCompressed<D> {
     fn dsize(&self) -> Dsize {
         self.0.dsize()
     }
@@ -53,37 +53,37 @@ self.0.dnum()
     }
 }
 
-impl<D: DataRef> fmt::Debug for LWEToGLWESwitchingKeyCompressed<D> {
+impl<D: DataRef> fmt::Debug for LWEToGLWEKeyCompressed<D> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         write!(f, "{self}")
     }
 }
 
-impl<D: DataMut> FillUniform for LWEToGLWESwitchingKeyCompressed<D> {
+impl<D: DataMut> FillUniform for LWEToGLWEKeyCompressed<D> {
     fn fill_uniform(&mut self, log_bound: usize, source: &mut Source) {
         self.0.fill_uniform(log_bound, source);
     }
 }
 
-impl<D: DataRef> fmt::Display for LWEToGLWESwitchingKeyCompressed<D> {
+impl<D: DataRef> fmt::Display for LWEToGLWEKeyCompressed<D> {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         write!(f, "(LWEToGLWESwitchingKeyCompressed) {}", self.0)
     }
 }
 
-impl<D: DataMut> ReaderFrom for LWEToGLWESwitchingKeyCompressed<D> {
+impl<D: DataMut> ReaderFrom for LWEToGLWEKeyCompressed<D> {
     fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
         self.0.read_from(reader)
     }
 }
 
-impl<D: DataRef> WriterTo for LWEToGLWESwitchingKeyCompressed<D> {
+impl<D: DataRef> WriterTo for LWEToGLWEKeyCompressed<D> {
     fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
         self.0.write_to(writer)
     }
 }
 
-impl LWEToGLWESwitchingKeyCompressed<Vec<u8>> {
+impl LWEToGLWEKeyCompressed<Vec<u8>> {
     pub fn alloc_from_infos<A>(infos: &A) -> Self
     where
         A: GGLWEInfos,
@@ -108,7 +108,7 @@ )
     }
 
     pub fn alloc(n: Degree, base2k: Base2K, k: TorusPrecision, rank_out: Rank, dnum: Dnum) -> Self {
-        LWEToGLWESwitchingKeyCompressed(GLWESwitchingKeyCompressed::alloc(
+        LWEToGLWEKeyCompressed(GLWESwitchingKeyCompressed::alloc(
             n,
             base2k,
             k,
@@ -141,11 +141,11 @@ GLWESwitchingKeyCompressed::bytes_of(n, base2k, k, Rank(1), dnum, Dsize(1))
     }
 }
 
-pub trait LWEToGLWESwitchingKeyDecompress
+pub trait LWEToGLWEKeyDecompress
 where
     Self: GLWESwitchingKeyDecompress,
 {
-    fn decompress_lwe_to_glwe_switching_key<R, O>(&self, res: &mut R, other: &O)
+    fn decompress_lwe_to_glwe_key<R, O>(&self, res: &mut R, other: &O)
     where
         R: GGLWEToMut + GLWESwitchingKeyDegreesMut,
         O: GGLWECompressedToRef + GLWESwitchingKeyDegrees,
@@ -154,25 +154,25 @@ self.decompress_glwe_switching_key(res, other);
     }
 }
 
-impl<B: Backend> LWEToGLWESwitchingKeyDecompress for Module<B> where Self: GLWESwitchingKeyDecompress {}
+impl<B: Backend> LWEToGLWEKeyDecompress for Module<B> where Self: GLWESwitchingKeyDecompress {}
 
-impl<D: DataMut> LWEToGLWESwitchingKey<D> {
+impl<D: DataMut> LWEToGLWEKey<D> {
     pub fn decompress<O, M>(&mut self, module: &M, other: &O)
     where
         O: GGLWECompressedToRef + GLWESwitchingKeyDegrees,
-        M: LWEToGLWESwitchingKeyDecompress,
+        M: LWEToGLWEKeyDecompress,
     {
-        module.decompress_lwe_to_glwe_switching_key(self, other);
+        module.decompress_lwe_to_glwe_key(self, other);
     }
 }
 
-impl<D: DataRef> GGLWECompressedToRef for LWEToGLWESwitchingKeyCompressed<D> {
+impl<D: DataRef> GGLWECompressedToRef for LWEToGLWEKeyCompressed<D> {
     fn to_ref(&self) -> GGLWECompressed<&[u8]> {
         self.0.to_ref()
     }
 }
 
-impl<D: DataMut> GGLWECompressedToMut for LWEToGLWESwitchingKeyCompressed<D> {
+impl<D: DataMut> GGLWECompressedToMut for LWEToGLWEKeyCompressed<D> {
     fn to_mut(&mut self) -> GGLWECompressed<&mut [u8]> {
         self.0.to_mut()
     }

@@ -1,21 +1,23 @@
 mod gglwe;
+mod gglwe_to_ggsw_key;
 mod ggsw;
 mod glwe;
 mod glwe_automorphism_key;
 mod glwe_switching_key;
 mod glwe_tensor_key;
-mod glwe_to_lwe_switching_key;
+mod glwe_to_lwe_key;
 mod lwe;
 mod lwe_switching_key;
-mod lwe_to_glwe_switching_key;
+mod lwe_to_glwe_key;
 
 pub use gglwe::*;
+pub use gglwe_to_ggsw_key::*;
 pub use ggsw::*;
 pub use glwe::*;
 pub use glwe_automorphism_key::*;
 pub use glwe_switching_key::*;
 pub use glwe_tensor_key::*;
-pub use glwe_to_lwe_switching_key::*;
+pub use glwe_to_lwe_key::*;
 pub use lwe::*;
 pub use lwe_switching_key::*;
-pub use lwe_to_glwe_switching_key::*;
+pub use lwe_to_glwe_key::*;

@@ -0,0 +1,254 @@
+use poulpy_hal::{
+    layouts::{Data, DataMut, DataRef, FillUniform, ReaderFrom, WriterTo},
+    source::Source,
+};
+
+use crate::layouts::{
+    Base2K, Degree, Dnum, Dsize, GGLWE, GGLWEInfos, GGLWEToMut, GGLWEToRef, GLWEInfos, LWEInfos, Rank, TorusPrecision,
+};
+use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
+
+use std::fmt;
+
+#[derive(PartialEq, Eq, Copy, Clone, Debug)]
+pub struct GGLWEToGGSWKeyLayout {
+    pub n: Degree,
+    pub base2k: Base2K,
+    pub k: TorusPrecision,
+    pub rank: Rank,
+    pub dnum: Dnum,
+    pub dsize: Dsize,
+}
+
+#[derive(PartialEq, Eq, Clone)]
+pub struct GGLWEToGGSWKey<D: Data> {
+    pub(crate) keys: Vec<GGLWE<D>>,
+}
+
+impl<D: Data> LWEInfos for GGLWEToGGSWKey<D> {
+    fn n(&self) -> Degree {
+        self.keys[0].n()
+    }
+
+    fn base2k(&self) -> Base2K {
+        self.keys[0].base2k()
+    }
+
+    fn k(&self) -> TorusPrecision {
+        self.keys[0].k()
+    }
+
+    fn size(&self) -> usize {
+        self.keys[0].size()
+    }
+}
+
+impl<D: Data> GLWEInfos for GGLWEToGGSWKey<D> {
+    fn rank(&self) -> Rank {
+        self.keys[0].rank_out()
+    }
+}
+
+impl<D: Data> GGLWEInfos for GGLWEToGGSWKey<D> {
+    fn rank_in(&self) -> Rank {
+        self.rank_out()
+    }
+
+    fn rank_out(&self) -> Rank {
+        self.keys[0].rank_out()
+    }
+
+    fn dsize(&self) -> Dsize {
+        self.keys[0].dsize()
+    }
+
+    fn dnum(&self) -> Dnum {
+        self.keys[0].dnum()
+    }
+}
+
+impl LWEInfos for GGLWEToGGSWKeyLayout {
+    fn n(&self) -> Degree {
+        self.n
+    }
+
+    fn base2k(&self) -> Base2K {
+        self.base2k
+    }
+
+    fn k(&self) -> TorusPrecision {
+        self.k
+    }
+}
+
+impl GLWEInfos for GGLWEToGGSWKeyLayout {
+    fn rank(&self) -> Rank {
+        self.rank_out()
+    }
+}
+
+impl GGLWEInfos for GGLWEToGGSWKeyLayout {
+    fn rank_in(&self) -> Rank {
+        self.rank
+    }
+
+    fn dsize(&self) -> Dsize {
+        self.dsize
+    }
+
+    fn rank_out(&self) -> Rank {
+        self.rank
+    }
+
+    fn dnum(&self) -> Dnum {
+        self.dnum
+    }
+}
+
+impl<D: DataRef> fmt::Debug for GGLWEToGGSWKey<D> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "{self}")
+    }
+}
+
+impl<D: DataMut> FillUniform for GGLWEToGGSWKey<D> {
+    fn fill_uniform(&mut self, log_bound: usize, source: &mut Source) {
+        self.keys
+            .iter_mut()
+            .for_each(|key: &mut GGLWE<D>| key.fill_uniform(log_bound, source))
+    }
+}
+
+impl<D: DataRef> fmt::Display for GGLWEToGGSWKey<D> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        writeln!(f, "(GGLWEToGGSWKey)",)?;
+        for (i, key) in self.keys.iter().enumerate() {
+            write!(f, "{i}: {key}")?;
+        }
+        Ok(())
+    }
+}
+
+impl GGLWEToGGSWKey<Vec<u8>> {
+    pub fn alloc_from_infos<A>(infos: &A) -> Self
+    where
+        A: GGLWEInfos,
+    {
+        assert_eq!(
+            infos.rank_in(),
+            infos.rank_out(),
+            "rank_in != rank_out is not supported for GGLWEToGGSWKey"
+        );
+        Self::alloc(
+            infos.n(),
+            infos.base2k(),
+            infos.k(),
+            infos.rank(),
+            infos.dnum(),
+            infos.dsize(),
+        )
+    }
+
+    pub fn alloc(n: Degree, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> Self {
+        GGLWEToGGSWKey {
+            keys: (0..rank.as_usize())
+                .map(|_| GGLWE::alloc(n, base2k, k, rank, rank, dnum, dsize))
+                .collect(),
+        }
+    }
+
+    pub fn bytes_of_from_infos<A>(infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+    {
+        assert_eq!(
+            infos.rank_in(),
+            infos.rank_out(),
+            "rank_in != rank_out is not supported for GGLWEToGGSWKey"
+        );
+        Self::bytes_of(
+            infos.n(),
+            infos.base2k(),
+            infos.k(),
+            infos.rank(),
+            infos.dnum(),
+            infos.dsize(),
+        )
+    }
+
+    pub fn bytes_of(n: Degree, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> usize {
+        rank.as_usize() * GGLWE::bytes_of(n, base2k, k, rank, rank, dnum, dsize)
+    }
+}
+
+impl<D: DataMut> GGLWEToGGSWKey<D> {
+    // Returns a mutable reference to GGLWE_{s}([s[i]*s[0], s[i]*s[1], ..., s[i]*s[rank]])
+    pub fn at_mut(&mut self, i: usize) -> &mut GGLWE<D> {
+        assert!((i as u32) < self.rank());
+        &mut self.keys[i]
+    }
+}
+
+impl<D: DataRef> GGLWEToGGSWKey<D> {
+    // Returns a reference to GGLWE_{s}(s[i] * s[j])
+    pub fn at(&self, i: usize) -> &GGLWE<D> {
+        assert!((i as u32) < self.rank());
+        &self.keys[i]
+    }
+}
+
+impl<D: DataMut> ReaderFrom for GGLWEToGGSWKey<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 GGLWEToGGSWKey<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(())
+    }
+}
+
+pub trait GGLWEToGGSWKeyToRef {
+    fn to_ref(&self) -> GGLWEToGGSWKey<&[u8]>;
+}
+
+impl<D: DataRef> GGLWEToGGSWKeyToRef for GGLWEToGGSWKey<D>
+where
+    GGLWE<D>: GGLWEToRef,
+{
+    fn to_ref(&self) -> GGLWEToGGSWKey<&[u8]> {
+        GGLWEToGGSWKey {
+            keys: self.keys.iter().map(|c| c.to_ref()).collect(),
+        }
+    }
+}
+
+pub trait GGLWEToGGSWKeyToMut {
+    fn to_mut(&mut self) -> GGLWEToGGSWKey<&mut [u8]>;
+}
+
+impl<D: DataMut> GGLWEToGGSWKeyToMut for GGLWEToGGSWKey<D>
+where
+    GGLWE<D>: GGLWEToMut,
+{
+    fn to_mut(&mut self) -> GGLWEToGGSWKey<&mut [u8]> {
+        GGLWEToGGSWKey {
+            keys: self.keys.iter_mut().map(|c| c.to_mut()).collect(),
+        }
+    }
+}

@@ -0,0 +1,221 @@
+use poulpy_hal::{
+    api::{
+        ModuleN, ScratchTakeBasic, SvpApplyDftToDft, VecZnxBigBytesOf, VecZnxBigNormalize, VecZnxBigNormalizeTmpBytes,
+        VecZnxDftApply, VecZnxDftBytesOf, VecZnxIdftApplyTmpA,
+    },
+    layouts::{
+        Backend, Data, DataMut, DataRef, Module, ScalarZnx, ScalarZnxToMut, ScalarZnxToRef, Scratch, ZnxInfos, ZnxView,
+        ZnxViewMut,
+    },
+};
+
+use crate::{
+    ScratchTakeCore,
+    dist::Distribution,
+    layouts::{
+        Base2K, Degree, GLWEInfos, GLWESecret, GLWESecretPreparedFactory, GLWESecretToMut, GLWESecretToRef, LWEInfos, Rank,
+        TorusPrecision,
+    },
+};
+
+pub struct GLWESecretTensor<D: Data> {
+    pub(crate) data: ScalarZnx<D>,
+    pub(crate) rank: Rank,
+    pub(crate) dist: Distribution,
+}
+
+impl GLWESecretTensor<Vec<u8>> {
+    pub(crate) fn pairs(rank: usize) -> usize {
+        (((rank + 1) * rank) >> 1).max(1)
+    }
+}
+
+impl<D: Data> LWEInfos for GLWESecretTensor<D> {
+    fn base2k(&self) -> Base2K {
+        Base2K(0)
+    }
+
+    fn k(&self) -> TorusPrecision {
+        TorusPrecision(0)
+    }
+
+    fn n(&self) -> Degree {
+        Degree(self.data.n() as u32)
+    }
+
+    fn size(&self) -> usize {
+        1
+    }
+}
+
+impl<D: DataRef> GLWESecretTensor<D> {
+    pub fn at(&self, mut i: usize, mut j: usize) -> ScalarZnx<&[u8]> {
+        if i > j {
+            std::mem::swap(&mut i, &mut j);
+        };
+        let rank: usize = self.rank().into();
+        ScalarZnx {
+            data: bytemuck::cast_slice(self.data.at(i * rank + j - (i * (i + 1) / 2), 0)),
+            n: self.n().into(),
+            cols: 1,
+        }
+    }
+}
+
+impl<D: DataMut> GLWESecretTensor<D> {
+    pub fn at_mut(&mut self, mut i: usize, mut j: usize) -> ScalarZnx<&mut [u8]> {
+        if i > j {
+            std::mem::swap(&mut i, &mut j);
+        };
+        let rank: usize = self.rank().into();
+        ScalarZnx {
+            n: self.n().into(),
+            data: bytemuck::cast_slice_mut(self.data.at_mut(i * rank + j - (i * (i + 1) / 2), 0)),
+            cols: 1,
+        }
+    }
+}
+
+impl<D: Data> GLWEInfos for GLWESecretTensor<D> {
+    fn rank(&self) -> Rank {
+        self.rank
+    }
+}
+
+impl<D: DataRef> GLWESecretToRef for GLWESecretTensor<D> {
+    fn to_ref(&self) -> GLWESecret<&[u8]> {
+        GLWESecret {
+            data: self.data.to_ref(),
+            dist: self.dist,
+        }
+    }
+}
+
+impl<D: DataMut> GLWESecretToMut for GLWESecretTensor<D> {
+    fn to_mut(&mut self) -> GLWESecret<&mut [u8]> {
+        GLWESecret {
+            dist: self.dist,
+            data: self.data.to_mut(),
+        }
+    }
+}
+
+impl GLWESecretTensor<Vec<u8>> {
+    pub fn alloc_from_infos<A>(infos: &A) -> Self
+    where
+        A: GLWEInfos,
+    {
+        Self::alloc(infos.n(), infos.rank())
+    }
+
+    pub fn alloc(n: Degree, rank: Rank) -> Self {
+        GLWESecretTensor {
+            data: ScalarZnx::alloc(n.into(), Self::pairs(rank.into())),
+            rank,
+            dist: Distribution::NONE,
+        }
+    }
+
+    pub fn bytes_of_from_infos<A>(infos: &A) -> usize
+    where
+        A: GLWEInfos,
+    {
+        Self::bytes_of(infos.n(), Self::pairs(infos.rank().into()).into())
+    }
+
+    pub fn bytes_of(n: Degree, rank: Rank) -> usize {
+        ScalarZnx::bytes_of(n.into(), Self::pairs(rank.into()))
+    }
+}
+
+impl<D: DataMut> GLWESecretTensor<D> {
+    pub fn prepare<M, S, BE: Backend>(&mut self, module: &M, other: &S, scratch: &mut Scratch<BE>)
+    where
+        M: GLWESecretTensorFactory<BE>,
+        S: GLWESecretToRef + GLWEInfos,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        module.glwe_secret_tensor_prepare(self, other, scratch);
+    }
+}
+
+pub trait GLWESecretTensorFactory<BE: Backend> {
+    fn glwe_secret_tensor_prepare_tmp_bytes(&self, rank: Rank) -> usize;
+
+    fn glwe_secret_tensor_prepare<R, O>(&self, res: &mut R, other: &O, scratch: &mut Scratch<BE>)
+    where
+        R: GLWESecretToMut + GLWEInfos,
+        O: GLWESecretToRef + GLWEInfos;
+}
+
+impl<BE: Backend> GLWESecretTensorFactory<BE> for Module<BE>
+where
+    Self: ModuleN
+        + GLWESecretPreparedFactory<BE>
+        + VecZnxBigNormalize<BE>
+        + VecZnxDftApply<BE>
+        + SvpApplyDftToDft<BE>
+        + VecZnxIdftApplyTmpA<BE>
+        + VecZnxBigNormalize<BE>
+        + VecZnxDftBytesOf
+        + VecZnxBigBytesOf
+        + VecZnxBigNormalizeTmpBytes,
+    Scratch<BE>: ScratchTakeCore<BE>,
+{
+    fn glwe_secret_tensor_prepare_tmp_bytes(&self, rank: Rank) -> usize {
+        self.bytes_of_glwe_secret_prepared(rank)
+            + self.bytes_of_vec_znx_dft(rank.into(), 1)
+            + self.bytes_of_vec_znx_dft(1, 1)
+            + self.bytes_of_vec_znx_big(1, 1)
+            + self.vec_znx_big_normalize_tmp_bytes()
+    }
+
+    fn glwe_secret_tensor_prepare<R, A>(&self, res: &mut R, a: &A, scratch: &mut Scratch<BE>)
+    where
+        R: GLWESecretToMut + GLWEInfos,
+        A: GLWESecretToRef + GLWEInfos,
+    {
+        let res: &mut GLWESecret<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWESecret<&[u8]> = &a.to_ref();
+
+        println!("res.rank: {} a.rank: {}", res.rank(), a.rank());
+
+        assert_eq!(res.rank(), GLWESecretTensor::pairs(a.rank().into()) as u32);
+        assert_eq!(res.n(), self.n() as u32);
+        assert_eq!(a.n(), self.n() as u32);
+
+        let rank: usize = a.rank().into();
+
+        let (mut a_prepared, scratch_1) = scratch.take_glwe_secret_prepared(self, rank.into());
+        a_prepared.prepare(self, a);
+
+        let base2k: usize = 17;
+
+        let (mut a_dft, scratch_2) = scratch_1.take_vec_znx_dft(self, rank, 1);
+        for i in 0..rank {
+            self.vec_znx_dft_apply(1, 0, &mut a_dft, i, &a.data.as_vec_znx(), i);
+        }
+
+        let (mut a_ij_big, scratch_3) = scratch_2.take_vec_znx_big(self, 1, 1);
+        let (mut a_ij_dft, scratch_4) = scratch_3.take_vec_znx_dft(self, 1, 1);
+
+        // sk_tensor = sk (x) sk
+        // For example: (s0, s1) (x) (s0, s1) = (s0^2, s0s1, s1^2)
+        for i in 0..rank {
+            for j in i..rank {
+                let idx: usize = i * rank + j - (i * (i + 1) / 2);
+                self.svp_apply_dft_to_dft(&mut a_ij_dft, 0, &a_prepared.data, j, &a_dft, i);
+                self.vec_znx_idft_apply_tmpa(&mut a_ij_big, 0, &mut a_ij_dft, 0);
+                self.vec_znx_big_normalize(
+                    base2k,
+                    &mut res.data.as_vec_znx_mut(),
+                    idx,
+                    base2k,
+                    &a_ij_big,
+                    0,
+                    scratch_4,
+                );
+            }
+        }
+    }
+}

@@ -0,0 +1,146 @@
+use poulpy_hal::{
+    layouts::{Data, DataMut, DataRef, FillUniform, VecZnx, VecZnxToMut, VecZnxToRef, ZnxInfos},
+    source::Source,
+};
+
+use crate::layouts::{Base2K, Degree, GLWEInfos, LWEInfos, Rank, SetGLWEInfos, TorusPrecision};
+use std::fmt;
+
+#[derive(PartialEq, Eq, Clone)]
+pub struct GLWETensor<D: Data> {
+    pub(crate) data: VecZnx<D>,
+    pub(crate) base2k: Base2K,
+    pub(crate) rank: Rank,
+    pub(crate) k: TorusPrecision,
+}
+
+impl<D: DataMut> SetGLWEInfos for GLWETensor<D> {
+    fn set_base2k(&mut self, base2k: Base2K) {
+        self.base2k = base2k
+    }
+
+    fn set_k(&mut self, k: TorusPrecision) {
+        self.k = k
+    }
+}
+
+impl<D: DataRef> GLWETensor<D> {
+    pub fn data(&self) -> &VecZnx<D> {
+        &self.data
+    }
+}
+
+impl<D: DataMut> GLWETensor<D> {
+    pub fn data_mut(&mut self) -> &mut VecZnx<D> {
+        &mut self.data
+    }
+}
+
+impl<D: Data> LWEInfos for GLWETensor<D> {
+    fn base2k(&self) -> Base2K {
+        self.base2k
+    }
+
+    fn k(&self) -> TorusPrecision {
+        self.k
+    }
+
+    fn n(&self) -> Degree {
+        Degree(self.data.n() as u32)
+    }
+
+    fn size(&self) -> usize {
+        self.data.size()
+    }
+}
+
+impl<D: Data> GLWEInfos for GLWETensor<D> {
+    fn rank(&self) -> Rank {
+        self.rank
+    }
+}
+
+impl<D: DataRef> fmt::Debug for GLWETensor<D> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "{self}")
+    }
+}
+
+impl<D: DataRef> fmt::Display for GLWETensor<D> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        write!(
+            f,
+            "GLWETensor: base2k={} k={}: {}",
+            self.base2k().0,
+            self.k().0,
+            self.data
+        )
+    }
+}
+
+impl<D: DataMut> FillUniform for GLWETensor<D> {
+    fn fill_uniform(&mut self, log_bound: usize, source: &mut Source) {
+        self.data.fill_uniform(log_bound, source);
+    }
+}
+
+impl GLWETensor<Vec<u8>> {
+    pub fn alloc_from_infos<A>(infos: &A) -> Self
+    where
+        A: GLWEInfos,
+    {
+        Self::alloc(infos.n(), infos.base2k(), infos.k(), infos.rank())
+    }
+
+    pub fn alloc(n: Degree, base2k: Base2K, k: TorusPrecision, rank: Rank) -> Self {
+        let pairs: usize = (((rank + 1) * rank).as_usize() >> 1).max(1);
+        GLWETensor {
+            data: VecZnx::alloc(n.into(), pairs + 1, k.0.div_ceil(base2k.0) as usize),
+            base2k,
+            k,
+            rank,
+        }
+    }
+
+    pub fn bytes_of_from_infos<A>(infos: &A) -> usize
+    where
+        A: GLWEInfos,
+    {
+        Self::bytes_of(infos.n(), infos.base2k(), infos.k(), infos.rank())
+    }
+
+    pub fn bytes_of(n: Degree, base2k: Base2K, k: TorusPrecision, rank: Rank) -> usize {
+        let pairs: usize = (((rank + 1) * rank).as_usize() >> 1).max(1);
+        VecZnx::bytes_of(n.into(), pairs + 1, k.0.div_ceil(base2k.0) as usize)
+    }
+}
+
+pub trait GLWETensorToRef {
+    fn to_ref(&self) -> GLWETensor<&[u8]>;
+}
+
+impl<D: DataRef> GLWETensorToRef for GLWETensor<D> {
+    fn to_ref(&self) -> GLWETensor<&[u8]> {
+        GLWETensor {
+            k: self.k,
+            base2k: self.base2k,
+            data: self.data.to_ref(),
+            rank: self.rank,
+        }
+    }
+}
+
+pub trait GLWETensorToMut {
+    fn to_mut(&mut self) -> GLWETensor<&mut [u8]>;
+}
+
+impl<D: DataMut> GLWETensorToMut for GLWETensor<D> {
+    fn to_mut(&mut self) -> GLWETensor<&mut [u8]> {
+        GLWETensor {
+            k: self.k,
+            base2k: self.base2k,
+            rank: self.rank,
+            data: self.data.to_mut(),
+        }
+    }
+}

@@ -6,7 +6,6 @@
 use crate::layouts::{
     Base2K, Degree, Dnum, Dsize, GGLWE, GGLWEInfos, GGLWEToMut, GGLWEToRef, GLWEInfos, LWEInfos, Rank, TorusPrecision,
 };
-use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
 
 use std::fmt;
 
@@ -21,31 +20,29 @@ pub dsize: Dsize,
 }
 
 #[derive(PartialEq, Eq, Clone)]
-pub struct GLWETensorKey<D: Data> {
-    pub(crate) keys: Vec<GGLWE<D>>,
-}
+pub struct GLWETensorKey<D: Data>(pub(crate) GGLWE<D>);
 
 impl<D: Data> LWEInfos for GLWETensorKey<D> {
     fn n(&self) -> Degree {
-        self.keys[0].n()
+        self.0.n()
     }
 
     fn base2k(&self) -> Base2K {
-        self.keys[0].base2k()
+        self.0.base2k()
     }
 
     fn k(&self) -> TorusPrecision {
-        self.keys[0].k()
+        self.0.k()
     }
 
     fn size(&self) -> usize {
-        self.keys[0].size()
+        self.0.size()
     }
 }
 
 impl<D: Data> GLWEInfos for GLWETensorKey<D> {
     fn rank(&self) -> Rank {
-        self.keys[0].rank_out()
+        self.0.rank_out()
     }
 }
 
@@ -55,15 +52,15 @@ self.rank_out()
     }
 
     fn rank_out(&self) -> Rank {
-        self.keys[0].rank_out()
+        self.0.rank_out()
     }
 
     fn dsize(&self) -> Dsize {
-        self.keys[0].dsize()
+        self.0.dsize()
     }
 
     fn dnum(&self) -> Dnum {
-        self.keys[0].dnum()
+        self.0.dnum()
     }
 }
 
@@ -113,18 +110,14 @@ }
 
 impl<D: DataMut> FillUniform for GLWETensorKey<D> {
     fn fill_uniform(&mut self, log_bound: usize, source: &mut Source) {
-        self.keys
-            .iter_mut()
-            .for_each(|key: &mut GGLWE<D>| key.fill_uniform(log_bound, source))
+        self.0.fill_uniform(log_bound, source)
     }
 }
 
 impl<D: DataRef> fmt::Display for GLWETensorKey<D> {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         writeln!(f, "(GLWETensorKey)",)?;
-        for (i, key) in self.keys.iter().enumerate() {
-            write!(f, "{i}: {key}")?;
-        }
+        write!(f, "{}", self.0)?;
         Ok(())
     }
 }
@@ -151,11 +144,7 @@ }
 
     pub fn alloc(n: Degree, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> Self {
         let pairs: u32 = (((rank.0 + 1) * rank.0) >> 1).max(1);
-        GLWETensorKey {
-            keys: (0..pairs)
-                .map(|_| GGLWE::alloc(n, base2k, k, Rank(1), rank, dnum, dsize))
-                .collect(),
-        }
+        GLWETensorKey(GGLWE::alloc(n, base2k, k, Rank(pairs), rank, dnum, dsize))
     }
 
     pub fn bytes_of_from_infos<A>(infos: &A) -> usize
@@ -178,85 +167,39 @@ )
     }
 
     pub fn bytes_of(n: Degree, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> usize {
-        let pairs: usize = (((rank.0 + 1) * rank.0) >> 1).max(1) as usize;
-        pairs * GGLWE::bytes_of(n, base2k, k, Rank(1), rank, dnum, dsize)
-    }
-}
-
-impl<D: DataMut> GLWETensorKey<D> {
-    // Returns a mutable reference to GGLWE_{s}(s[i] * s[j])
-    pub fn at_mut(&mut self, mut i: usize, mut j: usize) -> &mut GGLWE<D> {
-        if i > j {
-            std::mem::swap(&mut i, &mut j);
-        };
-        let rank: usize = self.rank_out().into();
-        &mut self.keys[i * rank + j - (i * (i + 1) / 2)]
-    }
-}
-
-impl<D: DataRef> GLWETensorKey<D> {
-    // Returns a reference to GGLWE_{s}(s[i] * s[j])
-    pub fn at(&self, mut i: usize, mut j: usize) -> &GGLWE<D> {
-        if i > j {
-            std::mem::swap(&mut i, &mut j);
-        };
-        let rank: usize = self.rank_out().into();
-        &self.keys[i * rank + j - (i * (i + 1) / 2)]
+        let pairs: u32 = (((rank.0 + 1) * rank.0) >> 1).max(1);
+        GGLWE::bytes_of(n, base2k, k, Rank(pairs), rank, dnum, dsize)
     }
 }
 
 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)?;
-        }
+        self.0.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)?;
-        }
+        self.0.write_to(writer)?;
         Ok(())
     }
 }
 
-pub trait GLWETensorKeyToRef {
-    fn to_ref(&self) -> GLWETensorKey<&[u8]>;
-}
-
-impl<D: DataRef> GLWETensorKeyToRef for GLWETensorKey<D>
+impl<D: DataRef> GGLWEToRef for GLWETensorKey<D>
 where
     GGLWE<D>: GGLWEToRef,
 {
-    fn to_ref(&self) -> GLWETensorKey<&[u8]> {
-        GLWETensorKey {
-            keys: self.keys.iter().map(|c| c.to_ref()).collect(),
-        }
+    fn to_ref(&self) -> GGLWE<&[u8]> {
+        self.0.to_ref()
     }
 }
 
-pub trait GLWETensorKeyToMut {
-    fn to_mut(&mut self) -> GLWETensorKey<&mut [u8]>;
-}
-
-impl<D: DataMut> GLWETensorKeyToMut for GLWETensorKey<D>
+impl<D: DataMut> GGLWEToMut for GLWETensorKey<D>
 where
     GGLWE<D>: GGLWEToMut,
 {
-    fn to_mut(&mut self) -> GLWETensorKey<&mut [u8]> {
-        GLWETensorKey {
-            keys: self.keys.iter_mut().map(|c| c.to_mut()).collect(),
-        }
+    fn to_mut(&mut self) -> GGLWE<&mut [u8]> {
+        self.0.to_mut()
     }
 }

@@ -59,9 +59,9 @@ }
 
 /// A special [GLWESwitchingKey] required to for the conversion from [GLWE] to [LWE].
 #[derive(PartialEq, Eq, Clone)]
-pub struct GLWEToLWESwitchingKey<D: Data>(pub(crate) GLWESwitchingKey<D>);
+pub struct GLWEToLWEKey<D: Data>(pub(crate) GLWESwitchingKey<D>);
 
-impl<D: Data> LWEInfos for GLWEToLWESwitchingKey<D> {
+impl<D: Data> LWEInfos for GLWEToLWEKey<D> {
     fn base2k(&self) -> Base2K {
         self.0.base2k()
     }
@@ -79,12 +79,12 @@ self.0.size()
     }
 }
 
-impl<D: Data> GLWEInfos for GLWEToLWESwitchingKey<D> {
+impl<D: Data> GLWEInfos for GLWEToLWEKey<D> {
     fn rank(&self) -> Rank {
         self.rank_out()
     }
 }
-impl<D: Data> GGLWEInfos for GLWEToLWESwitchingKey<D> {
+impl<D: Data> GGLWEInfos for GLWEToLWEKey<D> {
     fn rank_in(&self) -> Rank {
         self.0.rank_in()
     }
@@ -102,37 +102,37 @@ self.0.dnum()
     }
 }
 
-impl<D: DataRef> fmt::Debug for GLWEToLWESwitchingKey<D> {
+impl<D: DataRef> fmt::Debug for GLWEToLWEKey<D> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         write!(f, "{self}")
     }
 }
 
-impl<D: DataMut> FillUniform for GLWEToLWESwitchingKey<D> {
+impl<D: DataMut> FillUniform for GLWEToLWEKey<D> {
     fn fill_uniform(&mut self, log_bound: usize, source: &mut Source) {
         self.0.fill_uniform(log_bound, source);
     }
 }
 
-impl<D: DataRef> fmt::Display for GLWEToLWESwitchingKey<D> {
+impl<D: DataRef> fmt::Display for GLWEToLWEKey<D> {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-        write!(f, "(GLWEToLWESwitchingKey) {}", self.0)
+        write!(f, "(GLWEToLWEKey) {}", self.0)
     }
 }
 
-impl<D: DataMut> ReaderFrom for GLWEToLWESwitchingKey<D> {
+impl<D: DataMut> ReaderFrom for GLWEToLWEKey<D> {
     fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
         self.0.read_from(reader)
     }
 }
 
-impl<D: DataRef> WriterTo for GLWEToLWESwitchingKey<D> {
+impl<D: DataRef> WriterTo for GLWEToLWEKey<D> {
     fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
         self.0.write_to(writer)
     }
 }
 
-impl GLWEToLWESwitchingKey<Vec<u8>> {
+impl GLWEToLWEKey<Vec<u8>> {
     pub fn alloc_from_infos<A>(infos: &A) -> Self
     where
         A: GGLWEInfos,
@@ -140,12 +140,12 @@ {
         assert_eq!(
             infos.rank_out().0,
             1,
-            "rank_out > 1 is not supported for GLWEToLWESwitchingKey"
+            "rank_out > 1 is not supported for GLWEToLWEKey"
         );
         assert_eq!(
             infos.dsize().0,
             1,
-            "dsize > 1 is not supported for GLWEToLWESwitchingKey"
+            "dsize > 1 is not supported for GLWEToLWEKey"
         );
         Self::alloc(
             infos.n(),
@@ -157,7 +157,7 @@ )
     }
 
     pub fn alloc(n: Degree, base2k: Base2K, k: TorusPrecision, rank_in: Rank, dnum: Dnum) -> Self {
-        GLWEToLWESwitchingKey(GLWESwitchingKey::alloc(
+        GLWEToLWEKey(GLWESwitchingKey::alloc(
             n,
             base2k,
             k,
@@ -196,19 +196,19 @@ GLWESwitchingKey::bytes_of(n, base2k, k, rank_in, Rank(1), dnum, Dsize(1))
     }
 }
 
-impl<D: DataRef> GGLWEToRef for GLWEToLWESwitchingKey<D> {
+impl<D: DataRef> GGLWEToRef for GLWEToLWEKey<D> {
     fn to_ref(&self) -> GGLWE<&[u8]> {
         self.0.to_ref()
     }
 }
 
-impl<D: DataMut> GGLWEToMut for GLWEToLWESwitchingKey<D> {
+impl<D: DataMut> GGLWEToMut for GLWEToLWEKey<D> {
     fn to_mut(&mut self) -> GGLWE<&mut [u8]> {
         self.0.to_mut()
     }
 }
 
-impl<D: DataMut> GLWESwitchingKeyDegreesMut for GLWEToLWESwitchingKey<D> {
+impl<D: DataMut> GLWESwitchingKeyDegreesMut for GLWEToLWEKey<D> {
     fn input_degree(&mut self) -> &mut Degree {
         &mut self.0.input_degree
     }
@@ -218,7 +218,7 @@ &mut self.0.output_degree
     }
 }
 
-impl<D: DataRef> GLWESwitchingKeyDegrees for GLWEToLWESwitchingKey<D> {
+impl<D: DataRef> GLWESwitchingKeyDegrees for GLWEToLWEKey<D> {
     fn input_degree(&self) -> &Degree {
         &self.0.input_degree
     }

@@ -11,7 +11,7 @@ GLWESwitchingKeyDegreesMut, LWEInfos, Rank, TorusPrecision,
 };
 
 #[derive(PartialEq, Eq, Copy, Clone, Debug)]
-pub struct LWEToGLWESwitchingKeyLayout {
+pub struct LWEToGLWEKeyLayout {
     pub n: Degree,
     pub base2k: Base2K,
     pub k: TorusPrecision,
@@ -19,7 +19,7 @@ pub rank_out: Rank,
     pub dnum: Dnum,
 }
 
-impl LWEInfos for LWEToGLWESwitchingKeyLayout {
+impl LWEInfos for LWEToGLWEKeyLayout {
     fn base2k(&self) -> Base2K {
         self.base2k
     }
@@ -33,13 +33,13 @@ self.n
     }
 }
 
-impl GLWEInfos for LWEToGLWESwitchingKeyLayout {
+impl GLWEInfos for LWEToGLWEKeyLayout {
     fn rank(&self) -> Rank {
         self.rank_out()
     }
 }
 
-impl GGLWEInfos for LWEToGLWESwitchingKeyLayout {
+impl GGLWEInfos for LWEToGLWEKeyLayout {
     fn rank_in(&self) -> Rank {
         Rank(1)
     }
@@ -58,9 +58,9 @@ }
 }
 
 #[derive(PartialEq, Eq, Clone)]
-pub struct LWEToGLWESwitchingKey<D: Data>(pub(crate) GLWESwitchingKey<D>);
+pub struct LWEToGLWEKey<D: Data>(pub(crate) GLWESwitchingKey<D>);
 
-impl<D: Data> LWEInfos for LWEToGLWESwitchingKey<D> {
+impl<D: Data> LWEInfos for LWEToGLWEKey<D> {
     fn base2k(&self) -> Base2K {
         self.0.base2k()
     }
@@ -78,12 +78,12 @@ self.0.size()
     }
 }
 
-impl<D: Data> GLWEInfos for LWEToGLWESwitchingKey<D> {
+impl<D: Data> GLWEInfos for LWEToGLWEKey<D> {
     fn rank(&self) -> Rank {
         self.rank_out()
     }
 }
-impl<D: Data> GGLWEInfos for LWEToGLWESwitchingKey<D> {
+impl<D: Data> GGLWEInfos for LWEToGLWEKey<D> {
     fn dsize(&self) -> Dsize {
         self.0.dsize()
     }
@@ -101,37 +101,37 @@ self.0.dnum()
     }
 }
 
-impl<D: DataRef> fmt::Debug for LWEToGLWESwitchingKey<D> {
+impl<D: DataRef> fmt::Debug for LWEToGLWEKey<D> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         write!(f, "{self}")
     }
 }
 
-impl<D: DataMut> FillUniform for LWEToGLWESwitchingKey<D> {
+impl<D: DataMut> FillUniform for LWEToGLWEKey<D> {
     fn fill_uniform(&mut self, log_bound: usize, source: &mut Source) {
         self.0.fill_uniform(log_bound, source);
     }
 }
 
-impl<D: DataRef> fmt::Display for LWEToGLWESwitchingKey<D> {
+impl<D: DataRef> fmt::Display for LWEToGLWEKey<D> {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-        write!(f, "(LWEToGLWESwitchingKey) {}", self.0)
+        write!(f, "(LWEToGLWEKey) {}", self.0)
     }
 }
 
-impl<D: DataMut> ReaderFrom for LWEToGLWESwitchingKey<D> {
+impl<D: DataMut> ReaderFrom for LWEToGLWEKey<D> {
     fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
         self.0.read_from(reader)
     }
 }
 
-impl<D: DataRef> WriterTo for LWEToGLWESwitchingKey<D> {
+impl<D: DataRef> WriterTo for LWEToGLWEKey<D> {
     fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
         self.0.write_to(writer)
     }
 }
 
-impl LWEToGLWESwitchingKey<Vec<u8>> {
+impl LWEToGLWEKey<Vec<u8>> {
     pub fn alloc_from_infos<A>(infos: &A) -> Self
     where
         A: GGLWEInfos,
@@ -139,12 +139,12 @@ {
         assert_eq!(
             infos.rank_in().0,
             1,
-            "rank_in > 1 is not supported for LWEToGLWESwitchingKey"
+            "rank_in > 1 is not supported for LWEToGLWEKey"
         );
         assert_eq!(
             infos.dsize().0,
             1,
-            "dsize > 1 is not supported for LWEToGLWESwitchingKey"
+            "dsize > 1 is not supported for LWEToGLWEKey"
         );
 
         Self::alloc(
@@ -157,7 +157,7 @@ )
     }
 
     pub fn alloc(n: Degree, base2k: Base2K, k: TorusPrecision, rank_out: Rank, dnum: Dnum) -> Self {
-        LWEToGLWESwitchingKey(GLWESwitchingKey::alloc(
+        LWEToGLWEKey(GLWESwitchingKey::alloc(
             n,
             base2k,
             k,
@@ -175,12 +175,12 @@ {
         assert_eq!(
             infos.rank_in().0,
             1,
-            "rank_in > 1 is not supported for LWEToGLWESwitchingKey"
+            "rank_in > 1 is not supported for LWEToGLWEKey"
         );
         assert_eq!(
             infos.dsize().0,
             1,
-            "dsize > 1 is not supported for LWEToGLWESwitchingKey"
+            "dsize > 1 is not supported for LWEToGLWEKey"
         );
         Self::bytes_of(
             infos.n(),
@@ -196,19 +196,19 @@ GLWESwitchingKey::bytes_of(n, base2k, k, Rank(1), rank_out, dnum, Dsize(1))
     }
 }
 
-impl<D: DataRef> GGLWEToRef for LWEToGLWESwitchingKey<D> {
+impl<D: DataRef> GGLWEToRef for LWEToGLWEKey<D> {
     fn to_ref(&self) -> GGLWE<&[u8]> {
         self.0.to_ref()
     }
 }
 
-impl<D: DataMut> GGLWEToMut for LWEToGLWESwitchingKey<D> {
+impl<D: DataMut> GGLWEToMut for LWEToGLWEKey<D> {
     fn to_mut(&mut self) -> GGLWE<&mut [u8]> {
         self.0.to_mut()
     }
 }
 
-impl<D: DataMut> GLWESwitchingKeyDegreesMut for LWEToGLWESwitchingKey<D> {
+impl<D: DataMut> GLWESwitchingKeyDegreesMut for LWEToGLWEKey<D> {
     fn input_degree(&mut self) -> &mut Degree {
         &mut self.0.input_degree
     }
@@ -218,7 +218,7 @@ &mut self.0.output_degree
     }
 }
 
-impl<D: DataRef> GLWESwitchingKeyDegrees for LWEToGLWESwitchingKey<D> {
+impl<D: DataRef> GLWESwitchingKeyDegrees for LWEToGLWEKey<D> {
     fn input_degree(&self) -> &Degree {
         &self.0.input_degree
     }

@@ -1,38 +1,44 @@
 mod gglwe;
+mod gglwe_to_ggsw_key;
 mod ggsw;
 mod glwe;
 mod glwe_automorphism_key;
 mod glwe_plaintext;
 mod glwe_public_key;
 mod glwe_secret;
+mod glwe_secret_tensor;
 mod glwe_switching_key;
+mod glwe_tensor;
 mod glwe_tensor_key;
-mod glwe_to_lwe_switching_key;
+mod glwe_to_lwe_key;
 mod lwe;
 mod lwe_plaintext;
 mod lwe_secret;
 mod lwe_switching_key;
-mod lwe_to_glwe_switching_key;
+mod lwe_to_glwe_key;
 
 pub mod compressed;
 pub mod prepared;
 
 pub use compressed::*;
 pub use gglwe::*;
+pub use gglwe_to_ggsw_key::*;
 pub use ggsw::*;
 pub use glwe::*;
 pub use glwe_automorphism_key::*;
 pub use glwe_plaintext::*;
 pub use glwe_public_key::*;
 pub use glwe_secret::*;
+pub use glwe_secret_tensor::*;
 pub use glwe_switching_key::*;
+pub use glwe_tensor::*;
 pub use glwe_tensor_key::*;
-pub use glwe_to_lwe_switching_key::*;
+pub use glwe_to_lwe_key::*;
 pub use lwe::*;
 pub use lwe_plaintext::*;
 pub use lwe_secret::*;
 pub use lwe_switching_key::*;
-pub use lwe_to_glwe_switching_key::*;
+pub use lwe_to_glwe_key::*;
 pub use prepared::*;
 
 use poulpy_hal::layouts::{Backend, Module};

@@ -0,0 +1,252 @@
+use poulpy_hal::layouts::{Backend, Data, DataMut, DataRef, Module, Scratch};
+
+use crate::layouts::{
+    Base2K, Degree, Dnum, Dsize, GGLWEInfos, GGLWEPrepared, GGLWEPreparedFactory, GGLWEPreparedToMut, GGLWEPreparedToRef,
+    GGLWEToGGSWKey, GGLWEToGGSWKeyToRef, GLWEInfos, LWEInfos, Rank, TorusPrecision,
+};
+
+pub struct GGLWEToGGSWKeyPrepared<D: Data, BE: Backend> {
+    pub(crate) keys: Vec<GGLWEPrepared<D, BE>>,
+}
+
+impl<D: Data, BE: Backend> LWEInfos for GGLWEToGGSWKeyPrepared<D, BE> {
+    fn n(&self) -> Degree {
+        self.keys[0].n()
+    }
+
+    fn base2k(&self) -> Base2K {
+        self.keys[0].base2k()
+    }
+
+    fn k(&self) -> TorusPrecision {
+        self.keys[0].k()
+    }
+
+    fn size(&self) -> usize {
+        self.keys[0].size()
+    }
+}
+
+impl<D: Data, BE: Backend> GLWEInfos for GGLWEToGGSWKeyPrepared<D, BE> {
+    fn rank(&self) -> Rank {
+        self.keys[0].rank_out()
+    }
+}
+
+impl<D: Data, BE: Backend> GGLWEInfos for GGLWEToGGSWKeyPrepared<D, BE> {
+    fn rank_in(&self) -> Rank {
+        self.rank_out()
+    }
+
+    fn rank_out(&self) -> Rank {
+        self.keys[0].rank_out()
+    }
+
+    fn dsize(&self) -> Dsize {
+        self.keys[0].dsize()
+    }
+
+    fn dnum(&self) -> Dnum {
+        self.keys[0].dnum()
+    }
+}
+
+pub trait GGLWEToGGSWKeyPreparedFactory<BE: Backend> {
+    fn alloc_gglwe_to_ggsw_key_prepared_from_infos<A>(&self, infos: &A) -> GGLWEToGGSWKeyPrepared<Vec<u8>, BE>
+    where
+        A: GGLWEInfos;
+
+    fn alloc_gglwe_to_ggsw_key_prepared(
+        &self,
+        base2k: Base2K,
+        k: TorusPrecision,
+        rank: Rank,
+        dnum: Dnum,
+        dsize: Dsize,
+    ) -> GGLWEToGGSWKeyPrepared<Vec<u8>, BE>;
+
+    fn bytes_of_gglwe_to_ggsw_from_infos<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos;
+
+    fn bytes_of_gglwe_to_ggsw(&self, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> usize;
+
+    fn prepare_gglwe_to_ggsw_key_tmp_bytes<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos;
+
+    fn prepare_gglwe_to_ggsw_key<R, O>(&self, res: &mut R, other: &O, scratch: &mut Scratch<BE>)
+    where
+        R: GGLWEToGGSWKeyPreparedToMut<BE>,
+        O: GGLWEToGGSWKeyToRef;
+}
+
+impl<BE: Backend> GGLWEToGGSWKeyPreparedFactory<BE> for Module<BE>
+where
+    Self: GGLWEPreparedFactory<BE>,
+{
+    fn alloc_gglwe_to_ggsw_key_prepared_from_infos<A>(&self, infos: &A) -> GGLWEToGGSWKeyPrepared<Vec<u8>, BE>
+    where
+        A: GGLWEInfos,
+    {
+        assert_eq!(
+            infos.rank_in(),
+            infos.rank_out(),
+            "rank_in != rank_out is not supported for GGLWEToGGSWKeyPrepared"
+        );
+        self.alloc_gglwe_to_ggsw_key_prepared(
+            infos.base2k(),
+            infos.k(),
+            infos.rank(),
+            infos.dnum(),
+            infos.dsize(),
+        )
+    }
+
+    fn alloc_gglwe_to_ggsw_key_prepared(
+        &self,
+        base2k: Base2K,
+        k: TorusPrecision,
+        rank: Rank,
+        dnum: Dnum,
+        dsize: Dsize,
+    ) -> GGLWEToGGSWKeyPrepared<Vec<u8>, BE> {
+        GGLWEToGGSWKeyPrepared {
+            keys: (0..rank.as_usize())
+                .map(|_| self.alloc_gglwe_prepared(base2k, k, rank, rank, dnum, dsize))
+                .collect(),
+        }
+    }
+
+    fn bytes_of_gglwe_to_ggsw_from_infos<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+    {
+        assert_eq!(
+            infos.rank_in(),
+            infos.rank_out(),
+            "rank_in != rank_out is not supported for GGLWEToGGSWKeyPrepared"
+        );
+        self.bytes_of_gglwe_to_ggsw(
+            infos.base2k(),
+            infos.k(),
+            infos.rank(),
+            infos.dnum(),
+            infos.dsize(),
+        )
+    }
+
+    fn bytes_of_gglwe_to_ggsw(&self, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> usize {
+        rank.as_usize() * self.bytes_of_gglwe_prepared(base2k, k, rank, rank, dnum, dsize)
+    }
+
+    fn prepare_gglwe_to_ggsw_key_tmp_bytes<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+    {
+        self.prepare_gglwe_tmp_bytes(infos)
+    }
+
+    fn prepare_gglwe_to_ggsw_key<R, O>(&self, res: &mut R, other: &O, scratch: &mut Scratch<BE>)
+    where
+        R: GGLWEToGGSWKeyPreparedToMut<BE>,
+        O: GGLWEToGGSWKeyToRef,
+    {
+        let res: &mut GGLWEToGGSWKeyPrepared<&mut [u8], BE> = &mut res.to_mut();
+        let other: &GGLWEToGGSWKey<&[u8]> = &other.to_ref();
+
+        assert_eq!(res.keys.len(), other.keys.len());
+
+        for (a, b) in res.keys.iter_mut().zip(other.keys.iter()) {
+            self.prepare_gglwe(a, b, scratch);
+        }
+    }
+}
+
+impl<BE: Backend> GGLWEToGGSWKeyPrepared<Vec<u8>, BE> {
+    pub fn alloc_from_infos<A, M>(module: &M, infos: &A) -> Self
+    where
+        A: GGLWEInfos,
+        M: GGLWEToGGSWKeyPreparedFactory<BE>,
+    {
+        module.alloc_gglwe_to_ggsw_key_prepared_from_infos(infos)
+    }
+
+    pub fn alloc<M>(module: &M, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> Self
+    where
+        M: GGLWEToGGSWKeyPreparedFactory<BE>,
+    {
+        module.alloc_gglwe_to_ggsw_key_prepared(base2k, k, rank, dnum, dsize)
+    }
+
+    pub fn bytes_of_from_infos<A, M>(module: &M, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+        M: GGLWEToGGSWKeyPreparedFactory<BE>,
+    {
+        module.bytes_of_gglwe_to_ggsw_from_infos(infos)
+    }
+
+    pub fn bytes_of<M>(module: &M, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> usize
+    where
+        M: GGLWEToGGSWKeyPreparedFactory<BE>,
+    {
+        module.bytes_of_gglwe_to_ggsw(base2k, k, rank, dnum, dsize)
+    }
+}
+
+impl<D: DataMut, BE: Backend> GGLWEToGGSWKeyPrepared<D, BE> {
+    pub fn prepare<M, O>(&mut self, module: &M, other: &O, scratch: &mut Scratch<BE>)
+    where
+        M: GGLWEToGGSWKeyPreparedFactory<BE>,
+        O: GGLWEToGGSWKeyToRef,
+    {
+        module.prepare_gglwe_to_ggsw_key(self, other, scratch);
+    }
+}
+
+impl<D: DataMut, BE: Backend> GGLWEToGGSWKeyPrepared<D, BE> {
+    // Returns a mutable reference to GGLWEPrepared_{s}([s[i]*s[0], s[i]*s[1], ..., s[i]*s[rank]])
+    pub fn at_mut(&mut self, i: usize) -> &mut GGLWEPrepared<D, BE> {
+        assert!((i as u32) < self.rank());
+        &mut self.keys[i]
+    }
+}
+
+impl<D: DataRef, BE: Backend> GGLWEToGGSWKeyPrepared<D, BE> {
+    // Returns a reference to GGLWEPrepared_{s}([s[i]*s[0], s[i]*s[1], ..., s[i]*s[rank]])
+    pub fn at(&self, i: usize) -> &GGLWEPrepared<D, BE> {
+        assert!((i as u32) < self.rank());
+        &self.keys[i]
+    }
+}
+
+pub trait GGLWEToGGSWKeyPreparedToRef<BE: Backend> {
+    fn to_ref(&self) -> GGLWEToGGSWKeyPrepared<&[u8], BE>;
+}
+
+impl<D: DataRef, BE: Backend> GGLWEToGGSWKeyPreparedToRef<BE> for GGLWEToGGSWKeyPrepared<D, BE>
+where
+    GGLWEPrepared<D, BE>: GGLWEPreparedToRef<BE>,
+{
+    fn to_ref(&self) -> GGLWEToGGSWKeyPrepared<&[u8], BE> {
+        GGLWEToGGSWKeyPrepared {
+            keys: self.keys.iter().map(|c| c.to_ref()).collect(),
+        }
+    }
+}
+
+pub trait GGLWEToGGSWKeyPreparedToMut<BE: Backend> {
+    fn to_mut(&mut self) -> GGLWEToGGSWKeyPrepared<&mut [u8], BE>;
+}
+
+impl<D: DataMut, BE: Backend> GGLWEToGGSWKeyPreparedToMut<BE> for GGLWEToGGSWKeyPrepared<D, BE>
+where
+    GGLWEPrepared<D, BE>: GGLWEPreparedToMut<BE>,
+{
+    fn to_mut(&mut self) -> GGLWEToGGSWKeyPrepared<&mut [u8], BE> {
+        GGLWEToGGSWKeyPrepared {
+            keys: self.keys.iter_mut().map(|c| c.to_mut()).collect(),
+        }
+    }
+}

@@ -109,7 +109,7 @@ infos.dsize(),
         )
     }
 
-    fn bytes_of_glwe_switching_key_prepared(
+    fn bytes_of_glwe_key_prepared(
         &self,
         base2k: Base2K,
         k: TorusPrecision,
@@ -125,7 +125,7 @@ fn bytes_of_glwe_switching_key_prepared_from_infos<A>(&self, infos: &A) -> usize
     where
         A: GGLWEInfos,
     {
-        self.bytes_of_glwe_switching_key_prepared(
+        self.bytes_of_glwe_key_prepared(
             infos.base2k(),
             infos.k(),
             infos.rank_in(),
@@ -199,7 +199,7 @@ ) -> usize
     where
         M: GLWESwitchingKeyPreparedFactory<B>,
     {
-        module.bytes_of_glwe_switching_key_prepared(base2k, k, rank_in, rank_out, dnum, dsize)
+        module.bytes_of_glwe_key_prepared(base2k, k, rank_in, rank_out, dnum, dsize)
     }
 }
 

@@ -2,29 +2,27 @@ use poulpy_hal::layouts::{Backend, Data, DataMut, DataRef, Module, Scratch};
 
 use crate::layouts::{
     Base2K, Degree, Dnum, Dsize, GGLWEInfos, GGLWEPrepared, GGLWEPreparedFactory, GGLWEPreparedToMut, GGLWEPreparedToRef,
-    GLWEInfos, GLWETensorKey, GLWETensorKeyToRef, LWEInfos, Rank, TorusPrecision,
+    GGLWEToRef, GLWEInfos, LWEInfos, Rank, TorusPrecision,
 };
 
 #[derive(PartialEq, Eq)]
-pub struct GLWETensorKeyPrepared<D: Data, B: Backend> {
-    pub(crate) keys: Vec<GGLWEPrepared<D, B>>,
-}
+pub struct GLWETensorKeyPrepared<D: Data, B: Backend>(pub(crate) GGLWEPrepared<D, B>);
 
 impl<D: Data, B: Backend> LWEInfos for GLWETensorKeyPrepared<D, B> {
     fn n(&self) -> Degree {
-        self.keys[0].n()
+        self.0.n()
     }
 
     fn base2k(&self) -> Base2K {
-        self.keys[0].base2k()
+        self.0.base2k()
     }
 
     fn k(&self) -> TorusPrecision {
-        self.keys[0].k()
+        self.0.k()
     }
 
     fn size(&self) -> usize {
-        self.keys[0].size()
+        self.0.size()
     }
 }
 
@@ -40,15 +38,15 @@ self.rank_out()
     }
 
     fn rank_out(&self) -> Rank {
-        self.keys[0].rank_out()
+        self.0.rank_out()
     }
 
     fn dsize(&self) -> Dsize {
-        self.keys[0].dsize()
+        self.0.dsize()
     }
 
     fn dnum(&self) -> Dnum {
-        self.keys[0].dnum()
+        self.0.dnum()
     }
 }
 
@@ -65,11 +63,7 @@ dsize: Dsize,
         rank: Rank,
     ) -> GLWETensorKeyPrepared<Vec<u8>, B> {
         let pairs: u32 = (((rank.as_u32() + 1) * rank.as_u32()) >> 1).max(1);
-        GLWETensorKeyPrepared {
-            keys: (0..pairs)
-                .map(|_| self.alloc_gglwe_prepared(base2k, k, Rank(1), rank, dnum, dsize))
-                .collect(),
-        }
+        GLWETensorKeyPrepared(self.alloc_gglwe_prepared(base2k, k, Rank(pairs), rank, dnum, dsize))
     }
 
     fn alloc_tensor_key_prepared_from_infos<A>(&self, infos: &A) -> GLWETensorKeyPrepared<Vec<u8>, B>
@@ -91,8 +85,8 @@ )
     }
 
     fn bytes_of_tensor_key_prepared(&self, base2k: Base2K, k: TorusPrecision, rank: Rank, dnum: Dnum, dsize: Dsize) -> usize {
-        let pairs: usize = (((rank.0 + 1) * rank.0) >> 1).max(1) as usize;
-        pairs * self.bytes_of_gglwe_prepared(base2k, k, Rank(1), rank, dnum, dsize)
+        let pairs: u32 = (((rank.as_u32() + 1) * rank.as_u32()) >> 1).max(1);
+        self.bytes_of_gglwe_prepared(base2k, k, Rank(pairs), rank, dnum, dsize)
     }
 
     fn bytes_of_tensor_key_prepared_from_infos<A>(&self, infos: &A) -> usize
@@ -117,17 +111,10 @@ }
 
     fn prepare_tensor_key<R, O>(&self, res: &mut R, other: &O, scratch: &mut Scratch<B>)
     where
-        R: GLWETensorKeyPreparedToMut<B>,
-        O: GLWETensorKeyToRef,
+        R: GGLWEPreparedToMut<B>,
+        O: GGLWEToRef,
     {
-        let mut res: GLWETensorKeyPrepared<&mut [u8], B> = res.to_mut();
-        let other: GLWETensorKey<&[u8]> = other.to_ref();
-
-        assert_eq!(res.keys.len(), other.keys.len());
-
-        for (a, b) in res.keys.iter_mut().zip(other.keys.iter()) {
-            self.prepare_gglwe(a, b, scratch);
-        }
+        self.prepare_gglwe(res, other, scratch);
     }
 }
 
@@ -165,28 +152,6 @@ module.bytes_of_tensor_key_prepared(base2k, k, rank, dnum, dsize)
     }
 }
 
-impl<D: DataMut, B: Backend> GLWETensorKeyPrepared<D, B> {
-    // Returns a mutable reference to GGLWE_{s}(s[i] * s[j])
-    pub fn at_mut(&mut self, mut i: usize, mut j: usize) -> &mut GGLWEPrepared<D, B> {
-        if i > j {
-            std::mem::swap(&mut i, &mut j);
-        };
-        let rank: usize = self.rank_out().into();
-        &mut self.keys[i * rank + j - (i * (i + 1) / 2)]
-    }
-}
-
-impl<D: DataRef, B: Backend> GLWETensorKeyPrepared<D, B> {
-    // Returns a reference to GGLWE_{s}(s[i] * s[j])
-    pub fn at(&self, mut i: usize, mut j: usize) -> &GGLWEPrepared<D, B> {
-        if i > j {
-            std::mem::swap(&mut i, &mut j);
-        };
-        let rank: usize = self.rank_out().into();
-        &self.keys[i * rank + j - (i * (i + 1) / 2)]
-    }
-}
-
 impl<B: Backend> GLWETensorKeyPrepared<Vec<u8>, B> {
     pub fn prepare_tmp_bytes<A, M>(&self, module: &M, infos: &A) -> usize
     where
@@ -200,39 +165,27 @@
 impl<D: DataMut, B: Backend> GLWETensorKeyPrepared<D, B> {
     pub fn prepare<O, M>(&mut self, module: &M, other: &O, scratch: &mut Scratch<B>)
     where
-        O: GLWETensorKeyToRef,
+        O: GGLWEToRef,
         M: GLWETensorKeyPreparedFactory<B>,
     {
         module.prepare_tensor_key(self, other, scratch);
     }
 }
 
-pub trait GLWETensorKeyPreparedToMut<B: Backend> {
-    fn to_mut(&mut self) -> GLWETensorKeyPrepared<&mut [u8], B>;
-}
-
-impl<D: DataMut, B: Backend> GLWETensorKeyPreparedToMut<B> for GLWETensorKeyPrepared<D, B>
+impl<D: DataMut, B: Backend> GGLWEPreparedToMut<B> for GLWETensorKeyPrepared<D, B>
 where
     GGLWEPrepared<D, B>: GGLWEPreparedToMut<B>,
 {
-    fn to_mut(&mut self) -> GLWETensorKeyPrepared<&mut [u8], B> {
-        GLWETensorKeyPrepared {
-            keys: self.keys.iter_mut().map(|c| c.to_mut()).collect(),
-        }
+    fn to_mut(&mut self) -> GGLWEPrepared<&mut [u8], B> {
+        self.0.to_mut()
     }
 }
 
-pub trait GLWETensorKeyPreparedToRef<B: Backend> {
-    fn to_ref(&self) -> GLWETensorKeyPrepared<&[u8], B>;
-}
-
-impl<D: DataRef, B: Backend> GLWETensorKeyPreparedToRef<B> for GLWETensorKeyPrepared<D, B>
+impl<D: DataRef, B: Backend> GGLWEPreparedToRef<B> for GLWETensorKeyPrepared<D, B>
 where
     GGLWEPrepared<D, B>: GGLWEPreparedToRef<B>,
 {
-    fn to_ref(&self) -> GLWETensorKeyPrepared<&[u8], B> {
-        GLWETensorKeyPrepared {
-            keys: self.keys.iter().map(|c| c.to_ref()).collect(),
-        }
+    fn to_ref(&self) -> GGLWEPrepared<&[u8], B> {
+        self.0.to_ref()
     }
 }

@@ -0,0 +1,211 @@
+use poulpy_hal::layouts::{Backend, Data, DataMut, DataRef, Module, Scratch};
+
+use crate::layouts::{
+    Base2K, Degree, Dnum, Dsize, GGLWEInfos, GGLWEPrepared, GGLWEPreparedToMut, GGLWEPreparedToRef, GGLWEToRef, GLWEInfos,
+    GLWESwitchingKeyDegrees, GLWESwitchingKeyDegreesMut, LWEInfos, Rank, TorusPrecision,
+    prepared::{GLWESwitchingKeyPrepared, GLWESwitchingKeyPreparedFactory},
+};
+
+#[derive(PartialEq, Eq)]
+pub struct GLWEToLWEKeyPrepared<D: Data, B: Backend>(pub(crate) GLWESwitchingKeyPrepared<D, B>);
+
+impl<D: Data, B: Backend> LWEInfos for GLWEToLWEKeyPrepared<D, B> {
+    fn base2k(&self) -> Base2K {
+        self.0.base2k()
+    }
+
+    fn k(&self) -> TorusPrecision {
+        self.0.k()
+    }
+
+    fn n(&self) -> Degree {
+        self.0.n()
+    }
+
+    fn size(&self) -> usize {
+        self.0.size()
+    }
+}
+
+impl<D: Data, B: Backend> GLWEInfos for GLWEToLWEKeyPrepared<D, B> {
+    fn rank(&self) -> Rank {
+        self.rank_out()
+    }
+}
+
+impl<D: Data, B: Backend> GGLWEInfos for GLWEToLWEKeyPrepared<D, B> {
+    fn rank_in(&self) -> Rank {
+        self.0.rank_in()
+    }
+
+    fn dsize(&self) -> Dsize {
+        self.0.dsize()
+    }
+
+    fn rank_out(&self) -> Rank {
+        self.0.rank_out()
+    }
+
+    fn dnum(&self) -> Dnum {
+        self.0.dnum()
+    }
+}
+
+pub trait GLWEToLWEKeyPreparedFactory<B: Backend>
+where
+    Self: GLWESwitchingKeyPreparedFactory<B>,
+{
+    fn alloc_glwe_to_lwe_key_prepared(
+        &self,
+        base2k: Base2K,
+        k: TorusPrecision,
+        rank_in: Rank,
+        dnum: Dnum,
+    ) -> GLWEToLWEKeyPrepared<Vec<u8>, B> {
+        GLWEToLWEKeyPrepared(self.alloc_glwe_switching_key_prepared(base2k, k, rank_in, Rank(1), dnum, Dsize(1)))
+    }
+    fn alloc_glwe_to_lwe_key_prepared_from_infos<A>(&self, infos: &A) -> GLWEToLWEKeyPrepared<Vec<u8>, B>
+    where
+        A: GGLWEInfos,
+    {
+        debug_assert_eq!(
+            infos.rank_out().0,
+            1,
+            "rank_out > 1 is not supported for GLWEToLWEKeyPrepared"
+        );
+        debug_assert_eq!(
+            infos.dsize().0,
+            1,
+            "dsize > 1 is not supported for GLWEToLWEKeyPrepared"
+        );
+        self.alloc_glwe_to_lwe_key_prepared(infos.base2k(), infos.k(), infos.rank_in(), infos.dnum())
+    }
+
+    fn bytes_of_glwe_to_lwe_key_prepared(&self, base2k: Base2K, k: TorusPrecision, rank_in: Rank, dnum: Dnum) -> usize {
+        self.bytes_of_glwe_key_prepared(base2k, k, rank_in, Rank(1), dnum, Dsize(1))
+    }
+
+    fn bytes_of_glwe_to_lwe_key_prepared_from_infos<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+    {
+        debug_assert_eq!(
+            infos.rank_out().0,
+            1,
+            "rank_out > 1 is not supported for GLWEToLWEKeyPrepared"
+        );
+        debug_assert_eq!(
+            infos.dsize().0,
+            1,
+            "dsize > 1 is not supported for GLWEToLWEKeyPrepared"
+        );
+        self.bytes_of_glwe_to_lwe_key_prepared(infos.base2k(), infos.k(), infos.rank_in(), infos.dnum())
+    }
+
+    fn prepare_glwe_to_lwe_key_tmp_bytes<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+    {
+        self.prepare_glwe_switching_key_tmp_bytes(infos)
+    }
+
+    fn prepare_glwe_to_lwe_key<R, O>(&self, res: &mut R, other: &O, scratch: &mut Scratch<B>)
+    where
+        R: GGLWEPreparedToMut<B> + GLWESwitchingKeyDegreesMut,
+        O: GGLWEToRef + GLWESwitchingKeyDegrees,
+    {
+        self.prepare_glwe_switching(res, other, scratch);
+    }
+}
+
+impl<B: Backend> GLWEToLWEKeyPreparedFactory<B> for Module<B> where Self: GLWESwitchingKeyPreparedFactory<B> {}
+
+impl<B: Backend> GLWEToLWEKeyPrepared<Vec<u8>, B> {
+    pub fn alloc_from_infos<A, M>(module: &M, infos: &A) -> Self
+    where
+        A: GGLWEInfos,
+        M: GLWEToLWEKeyPreparedFactory<B>,
+    {
+        module.alloc_glwe_to_lwe_key_prepared_from_infos(infos)
+    }
+
+    pub fn alloc<M>(module: &M, base2k: Base2K, k: TorusPrecision, rank_in: Rank, dnum: Dnum) -> Self
+    where
+        M: GLWEToLWEKeyPreparedFactory<B>,
+    {
+        module.alloc_glwe_to_lwe_key_prepared(base2k, k, rank_in, dnum)
+    }
+
+    pub fn bytes_of_from_infos<A, M>(module: &M, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+        M: GLWEToLWEKeyPreparedFactory<B>,
+    {
+        module.bytes_of_glwe_to_lwe_key_prepared_from_infos(infos)
+    }
+
+    pub fn bytes_of<M>(module: &M, base2k: Base2K, k: TorusPrecision, rank_in: Rank, dnum: Dnum) -> usize
+    where
+        M: GLWEToLWEKeyPreparedFactory<B>,
+    {
+        module.bytes_of_glwe_to_lwe_key_prepared(base2k, k, rank_in, dnum)
+    }
+}
+
+impl<B: Backend> GLWEToLWEKeyPrepared<Vec<u8>, B> {
+    pub fn prepare_tmp_bytes<A, M>(&self, module: &M, infos: &A)
+    where
+        A: GGLWEInfos,
+        M: GLWEToLWEKeyPreparedFactory<B>,
+    {
+        module.prepare_glwe_to_lwe_key_tmp_bytes(infos);
+    }
+}
+
+impl<D: DataMut, B: Backend> GLWEToLWEKeyPrepared<D, B> {
+    pub fn prepare<O, M>(&mut self, module: &M, other: &O, scratch: &mut Scratch<B>)
+    where
+        O: GGLWEToRef + GLWESwitchingKeyDegrees,
+        M: GLWEToLWEKeyPreparedFactory<B>,
+    {
+        module.prepare_glwe_to_lwe_key(self, other, scratch);
+    }
+}
+
+impl<D: DataRef, B: Backend> GGLWEPreparedToRef<B> for GLWEToLWEKeyPrepared<D, B>
+where
+    GLWESwitchingKeyPrepared<D, B>: GGLWEPreparedToRef<B>,
+{
+    fn to_ref(&self) -> GGLWEPrepared<&[u8], B> {
+        self.0.to_ref()
+    }
+}
+
+impl<D: DataMut, B: Backend> GGLWEPreparedToMut<B> for GLWEToLWEKeyPrepared<D, B>
+where
+    GLWESwitchingKeyPrepared<D, B>: GGLWEPreparedToRef<B>,
+{
+    fn to_mut(&mut self) -> GGLWEPrepared<&mut [u8], B> {
+        self.0.to_mut()
+    }
+}
+
+impl<D: DataMut, B: Backend> GLWESwitchingKeyDegreesMut for GLWEToLWEKeyPrepared<D, B> {
+    fn input_degree(&mut self) -> &mut Degree {
+        &mut self.0.input_degree
+    }
+
+    fn output_degree(&mut self) -> &mut Degree {
+        &mut self.0.output_degree
+    }
+}
+
+impl<D: DataRef, B: Backend> GLWESwitchingKeyDegrees for GLWEToLWEKeyPrepared<D, B> {
+    fn input_degree(&self) -> &Degree {
+        &self.0.input_degree
+    }
+
+    fn output_degree(&self) -> &Degree {
+        &self.0.output_degree
+    }
+}

@@ -1,211 +0,0 @@
-use poulpy_hal::layouts::{Backend, Data, DataMut, DataRef, Module, Scratch};
-
-use crate::layouts::{
-    Base2K, Degree, Dnum, Dsize, GGLWEInfos, GGLWEPrepared, GGLWEPreparedToMut, GGLWEPreparedToRef, GGLWEToRef, GLWEInfos,
-    GLWESwitchingKeyDegrees, GLWESwitchingKeyDegreesMut, LWEInfos, Rank, TorusPrecision,
-    prepared::{GLWESwitchingKeyPrepared, GLWESwitchingKeyPreparedFactory},
-};
-
-#[derive(PartialEq, Eq)]
-pub struct GLWEToLWESwitchingKeyPrepared<D: Data, B: Backend>(pub(crate) GLWESwitchingKeyPrepared<D, B>);
-
-impl<D: Data, B: Backend> LWEInfos for GLWEToLWESwitchingKeyPrepared<D, B> {
-    fn base2k(&self) -> Base2K {
-        self.0.base2k()
-    }
-
-    fn k(&self) -> TorusPrecision {
-        self.0.k()
-    }
-
-    fn n(&self) -> Degree {
-        self.0.n()
-    }
-
-    fn size(&self) -> usize {
-        self.0.size()
-    }
-}
-
-impl<D: Data, B: Backend> GLWEInfos for GLWEToLWESwitchingKeyPrepared<D, B> {
-    fn rank(&self) -> Rank {
-        self.rank_out()
-    }
-}
-
-impl<D: Data, B: Backend> GGLWEInfos for GLWEToLWESwitchingKeyPrepared<D, B> {
-    fn rank_in(&self) -> Rank {
-        self.0.rank_in()
-    }
-
-    fn dsize(&self) -> Dsize {
-        self.0.dsize()
-    }
-
-    fn rank_out(&self) -> Rank {
-        self.0.rank_out()
-    }
-
-    fn dnum(&self) -> Dnum {
-        self.0.dnum()
-    }
-}
-
-pub trait GLWEToLWESwitchingKeyPreparedFactory<B: Backend>
-where
-    Self: GLWESwitchingKeyPreparedFactory<B>,
-{
-    fn alloc_glwe_to_lwe_switching_key_prepared(
-        &self,
-        base2k: Base2K,
-        k: TorusPrecision,
-        rank_in: Rank,
-        dnum: Dnum,
-    ) -> GLWEToLWESwitchingKeyPrepared<Vec<u8>, B> {
-        GLWEToLWESwitchingKeyPrepared(self.alloc_glwe_switching_key_prepared(base2k, k, rank_in, Rank(1), dnum, Dsize(1)))
-    }
-    fn alloc_glwe_to_lwe_switching_key_prepared_from_infos<A>(&self, infos: &A) -> GLWEToLWESwitchingKeyPrepared<Vec<u8>, B>
-    where
-        A: GGLWEInfos,
-    {
-        debug_assert_eq!(
-            infos.rank_out().0,
-            1,
-            "rank_out > 1 is not supported for GLWEToLWESwitchingKeyPrepared"
-        );
-        debug_assert_eq!(
-            infos.dsize().0,
-            1,
-            "dsize > 1 is not supported for GLWEToLWESwitchingKeyPrepared"
-        );
-        self.alloc_glwe_to_lwe_switching_key_prepared(infos.base2k(), infos.k(), infos.rank_in(), infos.dnum())
-    }
-
-    fn bytes_of_glwe_to_lwe_switching_key_prepared(&self, base2k: Base2K, k: TorusPrecision, rank_in: Rank, dnum: Dnum) -> usize {
-        self.bytes_of_glwe_switching_key_prepared(base2k, k, rank_in, Rank(1), dnum, Dsize(1))
-    }
-
-    fn bytes_of_glwe_to_lwe_switching_key_prepared_from_infos<A>(&self, infos: &A) -> usize
-    where
-        A: GGLWEInfos,
-    {
-        debug_assert_eq!(
-            infos.rank_out().0,
-            1,
-            "rank_out > 1 is not supported for GLWEToLWESwitchingKeyPrepared"
-        );
-        debug_assert_eq!(
-            infos.dsize().0,
-            1,
-            "dsize > 1 is not supported for GLWEToLWESwitchingKeyPrepared"
-        );
-        self.bytes_of_glwe_to_lwe_switching_key_prepared(infos.base2k(), infos.k(), infos.rank_in(), infos.dnum())
-    }
-
-    fn prepare_glwe_to_lwe_switching_key_tmp_bytes<A>(&self, infos: &A) -> usize
-    where
-        A: GGLWEInfos,
-    {
-        self.prepare_glwe_switching_key_tmp_bytes(infos)
-    }
-
-    fn prepare_glwe_to_lwe_switching_key<R, O>(&self, res: &mut R, other: &O, scratch: &mut Scratch<B>)
-    where
-        R: GGLWEPreparedToMut<B> + GLWESwitchingKeyDegreesMut,
-        O: GGLWEToRef + GLWESwitchingKeyDegrees,
-    {
-        self.prepare_glwe_switching(res, other, scratch);
-    }
-}
-
-impl<B: Backend> GLWEToLWESwitchingKeyPreparedFactory<B> for Module<B> where Self: GLWESwitchingKeyPreparedFactory<B> {}
-
-impl<B: Backend> GLWEToLWESwitchingKeyPrepared<Vec<u8>, B> {
-    pub fn alloc_from_infos<A, M>(module: &M, infos: &A) -> Self
-    where
-        A: GGLWEInfos,
-        M: GLWEToLWESwitchingKeyPreparedFactory<B>,
-    {
-        module.alloc_glwe_to_lwe_switching_key_prepared_from_infos(infos)
-    }
-
-    pub fn alloc<M>(module: &M, base2k: Base2K, k: TorusPrecision, rank_in: Rank, dnum: Dnum) -> Self
-    where
-        M: GLWEToLWESwitchingKeyPreparedFactory<B>,
-    {
-        module.alloc_glwe_to_lwe_switching_key_prepared(base2k, k, rank_in, dnum)
-    }
-
-    pub fn bytes_of_from_infos<A, M>(module: &M, infos: &A) -> usize
-    where
-        A: GGLWEInfos,
-        M: GLWEToLWESwitchingKeyPreparedFactory<B>,
-    {
-        module.bytes_of_glwe_to_lwe_switching_key_prepared_from_infos(infos)
-    }
-
-    pub fn bytes_of<M>(module: &M, base2k: Base2K, k: TorusPrecision, rank_in: Rank, dnum: Dnum) -> usize
-    where
-        M: GLWEToLWESwitchingKeyPreparedFactory<B>,
-    {
-        module.bytes_of_glwe_to_lwe_switching_key_prepared(base2k, k, rank_in, dnum)
-    }
-}
-
-impl<B: Backend> GLWEToLWESwitchingKeyPrepared<Vec<u8>, B> {
-    pub fn prepare_tmp_bytes<A, M>(&self, module: &M, infos: &A)
-    where
-        A: GGLWEInfos,
-        M: GLWEToLWESwitchingKeyPreparedFactory<B>,
-    {
-        module.prepare_glwe_to_lwe_switching_key_tmp_bytes(infos);
-    }
-}
-
-impl<D: DataMut, B: Backend> GLWEToLWESwitchingKeyPrepared<D, B> {
-    pub fn prepare<O, M>(&mut self, module: &M, other: &O, scratch: &mut Scratch<B>)
-    where
-        O: GGLWEToRef + GLWESwitchingKeyDegrees,
-        M: GLWEToLWESwitchingKeyPreparedFactory<B>,
-    {
-        module.prepare_glwe_to_lwe_switching_key(self, other, scratch);
-    }
-}
-
-impl<D: DataRef, B: Backend> GGLWEPreparedToRef<B> for GLWEToLWESwitchingKeyPrepared<D, B>
-where
-    GLWESwitchingKeyPrepared<D, B>: GGLWEPreparedToRef<B>,
-{
-    fn to_ref(&self) -> GGLWEPrepared<&[u8], B> {
-        self.0.to_ref()
-    }
-}
-
-impl<D: DataMut, B: Backend> GGLWEPreparedToMut<B> for GLWEToLWESwitchingKeyPrepared<D, B>
-where
-    GLWESwitchingKeyPrepared<D, B>: GGLWEPreparedToRef<B>,
-{
-    fn to_mut(&mut self) -> GGLWEPrepared<&mut [u8], B> {
-        self.0.to_mut()
-    }
-}
-
-impl<D: DataMut, B: Backend> GLWESwitchingKeyDegreesMut for GLWEToLWESwitchingKeyPrepared<D, B> {
-    fn input_degree(&mut self) -> &mut Degree {
-        &mut self.0.input_degree
-    }
-
-    fn output_degree(&mut self) -> &mut Degree {
-        &mut self.0.output_degree
-    }
-}
-
-impl<D: DataRef, B: Backend> GLWESwitchingKeyDegrees for GLWEToLWESwitchingKeyPrepared<D, B> {
-    fn input_degree(&self) -> &Degree {
-        &self.0.input_degree
-    }
-
-    fn output_degree(&self) -> &Degree {
-        &self.0.output_degree
-    }
-}

@@ -86,7 +86,7 @@ self.alloc_lwe_switching_key_prepared(infos.base2k(), infos.k(), infos.dnum())
     }
 
     fn bytes_of_lwe_switching_key_prepared(&self, base2k: Base2K, k: TorusPrecision, dnum: Dnum) -> usize {
-        self.bytes_of_glwe_switching_key_prepared(base2k, k, Rank(1), Rank(1), dnum, Dsize(1))
+        self.bytes_of_glwe_key_prepared(base2k, k, Rank(1), Rank(1), dnum, Dsize(1))
     }
 
     fn bytes_of_lwe_switching_key_prepared_from_infos<A>(&self, infos: &A) -> usize

@@ -0,0 +1,202 @@
+use poulpy_hal::layouts::{Backend, Data, DataMut, DataRef, Module, Scratch};
+
+use crate::layouts::{
+    Base2K, Degree, Dnum, Dsize, GGLWEInfos, GGLWEPrepared, GGLWEPreparedToMut, GGLWEPreparedToRef, GGLWEToRef, GLWEInfos,
+    GLWESwitchingKeyDegrees, GLWESwitchingKeyDegreesMut, LWEInfos, Rank, TorusPrecision,
+    prepared::{GLWESwitchingKeyPrepared, GLWESwitchingKeyPreparedFactory},
+};
+
+/// A special [GLWESwitchingKey] required to for the conversion from [LWE] to [GLWE].
+#[derive(PartialEq, Eq)]
+pub struct LWEToGLWEKeyPrepared<D: Data, B: Backend>(pub(crate) GLWESwitchingKeyPrepared<D, B>);
+
+impl<D: Data, B: Backend> LWEInfos for LWEToGLWEKeyPrepared<D, B> {
+    fn base2k(&self) -> Base2K {
+        self.0.base2k()
+    }
+
+    fn k(&self) -> TorusPrecision {
+        self.0.k()
+    }
+
+    fn n(&self) -> Degree {
+        self.0.n()
+    }
+
+    fn size(&self) -> usize {
+        self.0.size()
+    }
+}
+
+impl<D: Data, B: Backend> GLWEInfos for LWEToGLWEKeyPrepared<D, B> {
+    fn rank(&self) -> Rank {
+        self.rank_out()
+    }
+}
+
+impl<D: Data, B: Backend> GGLWEInfos for LWEToGLWEKeyPrepared<D, B> {
+    fn dsize(&self) -> Dsize {
+        self.0.dsize()
+    }
+
+    fn rank_in(&self) -> Rank {
+        self.0.rank_in()
+    }
+
+    fn rank_out(&self) -> Rank {
+        self.0.rank_out()
+    }
+
+    fn dnum(&self) -> Dnum {
+        self.0.dnum()
+    }
+}
+
+pub trait LWEToGLWEKeyPreparedFactory<B: Backend>
+where
+    Self: GLWESwitchingKeyPreparedFactory<B>,
+{
+    fn alloc_lwe_to_glwe_key_prepared(
+        &self,
+        base2k: Base2K,
+        k: TorusPrecision,
+        rank_out: Rank,
+        dnum: Dnum,
+    ) -> LWEToGLWEKeyPrepared<Vec<u8>, B> {
+        LWEToGLWEKeyPrepared(self.alloc_glwe_switching_key_prepared(base2k, k, Rank(1), rank_out, dnum, Dsize(1)))
+    }
+    fn alloc_lwe_to_glwe_key_prepared_from_infos<A>(&self, infos: &A) -> LWEToGLWEKeyPrepared<Vec<u8>, B>
+    where
+        A: GGLWEInfos,
+    {
+        debug_assert_eq!(
+            infos.rank_in().0,
+            1,
+            "rank_in > 1 is not supported for LWEToGLWEKey"
+        );
+        debug_assert_eq!(
+            infos.dsize().0,
+            1,
+            "dsize > 1 is not supported for LWEToGLWEKey"
+        );
+        self.alloc_lwe_to_glwe_key_prepared(infos.base2k(), infos.k(), infos.rank_out(), infos.dnum())
+    }
+
+    fn bytes_of_lwe_to_glwe_key_prepared(&self, base2k: Base2K, k: TorusPrecision, rank_out: Rank, dnum: Dnum) -> usize {
+        self.bytes_of_glwe_key_prepared(base2k, k, Rank(1), rank_out, dnum, Dsize(1))
+    }
+
+    fn bytes_of_lwe_to_glwe_key_prepared_from_infos<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+    {
+        debug_assert_eq!(
+            infos.rank_in().0,
+            1,
+            "rank_in > 1 is not supported for LWEToGLWEKey"
+        );
+        debug_assert_eq!(
+            infos.dsize().0,
+            1,
+            "dsize > 1 is not supported for LWEToGLWEKey"
+        );
+        self.bytes_of_lwe_to_glwe_key_prepared(infos.base2k(), infos.k(), infos.rank_out(), infos.dnum())
+    }
+
+    fn prepare_lwe_to_glwe_key_tmp_bytes<A>(&self, infos: &A)
+    where
+        A: GGLWEInfos,
+    {
+        self.prepare_glwe_switching_key_tmp_bytes(infos);
+    }
+
+    fn prepare_lwe_to_glwe_key<R, O>(&self, res: &mut R, other: &O, scratch: &mut Scratch<B>)
+    where
+        R: GGLWEPreparedToMut<B> + GLWESwitchingKeyDegreesMut,
+        O: GGLWEToRef + GLWESwitchingKeyDegrees,
+    {
+        self.prepare_glwe_switching(res, other, scratch);
+    }
+}
+
+impl<B: Backend> LWEToGLWEKeyPreparedFactory<B> for Module<B> where Self: GLWESwitchingKeyPreparedFactory<B> {}
+
+impl<B: Backend> LWEToGLWEKeyPrepared<Vec<u8>, B> {
+    pub fn alloc_from_infos<A, M>(module: &M, infos: &A) -> Self
+    where
+        A: GGLWEInfos,
+        M: LWEToGLWEKeyPreparedFactory<B>,
+    {
+        module.alloc_lwe_to_glwe_key_prepared_from_infos(infos)
+    }
+
+    pub fn alloc<M>(module: &M, base2k: Base2K, k: TorusPrecision, rank_out: Rank, dnum: Dnum) -> Self
+    where
+        M: LWEToGLWEKeyPreparedFactory<B>,
+    {
+        module.alloc_lwe_to_glwe_key_prepared(base2k, k, rank_out, dnum)
+    }
+
+    pub fn bytes_of_from_infos<A, M>(module: &M, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+        M: LWEToGLWEKeyPreparedFactory<B>,
+    {
+        module.bytes_of_lwe_to_glwe_key_prepared_from_infos(infos)
+    }
+
+    pub fn bytes_of<M>(module: &M, base2k: Base2K, k: TorusPrecision, rank_out: Rank, dnum: Dnum) -> usize
+    where
+        M: LWEToGLWEKeyPreparedFactory<B>,
+    {
+        module.bytes_of_lwe_to_glwe_key_prepared(base2k, k, rank_out, dnum)
+    }
+}
+
+impl<B: Backend> LWEToGLWEKeyPrepared<Vec<u8>, B> {
+    pub fn prepare_tmp_bytes<A, M>(&self, module: &M, infos: &A)
+    where
+        A: GGLWEInfos,
+        M: LWEToGLWEKeyPreparedFactory<B>,
+    {
+        module.prepare_lwe_to_glwe_key_tmp_bytes(infos);
+    }
+}
+
+impl<D: DataMut, B: Backend> LWEToGLWEKeyPrepared<D, B> {
+    pub fn prepare<O, M>(&mut self, module: &M, other: &O, scratch: &mut Scratch<B>)
+    where
+        O: GGLWEToRef + GLWESwitchingKeyDegrees,
+        M: LWEToGLWEKeyPreparedFactory<B>,
+    {
+        module.prepare_lwe_to_glwe_key(self, other, scratch);
+    }
+}
+
+impl<D: DataRef, B: Backend> GGLWEPreparedToRef<B> for LWEToGLWEKeyPrepared<D, B>
+where
+    GLWESwitchingKeyPrepared<D, B>: GGLWEPreparedToRef<B>,
+{
+    fn to_ref(&self) -> GGLWEPrepared<&[u8], B> {
+        self.0.to_ref()
+    }
+}
+
+impl<D: DataMut, B: Backend> GGLWEPreparedToMut<B> for LWEToGLWEKeyPrepared<D, B>
+where
+    GLWESwitchingKeyPrepared<D, B>: GGLWEPreparedToMut<B>,
+{
+    fn to_mut(&mut self) -> GGLWEPrepared<&mut [u8], B> {
+        self.0.to_mut()
+    }
+}
+
+impl<D: DataMut, B: Backend> GLWESwitchingKeyDegreesMut for LWEToGLWEKeyPrepared<D, B> {
+    fn input_degree(&mut self) -> &mut Degree {
+        &mut self.0.input_degree
+    }
+
+    fn output_degree(&mut self) -> &mut Degree {
+        &mut self.0.output_degree
+    }
+}

@@ -1,208 +0,0 @@
-use poulpy_hal::layouts::{Backend, Data, DataMut, DataRef, Module, Scratch};
-
-use crate::layouts::{
-    Base2K, Degree, Dnum, Dsize, GGLWEInfos, GGLWEPrepared, GGLWEPreparedToMut, GGLWEPreparedToRef, GGLWEToRef, GLWEInfos,
-    GLWESwitchingKeyDegrees, GLWESwitchingKeyDegreesMut, LWEInfos, Rank, TorusPrecision,
-    prepared::{GLWESwitchingKeyPrepared, GLWESwitchingKeyPreparedFactory},
-};
-
-/// A special [GLWESwitchingKey] required to for the conversion from [LWE] to [GLWE].
-#[derive(PartialEq, Eq)]
-pub struct LWEToGLWESwitchingKeyPrepared<D: Data, B: Backend>(pub(crate) GLWESwitchingKeyPrepared<D, B>);
-
-impl<D: Data, B: Backend> LWEInfos for LWEToGLWESwitchingKeyPrepared<D, B> {
-    fn base2k(&self) -> Base2K {
-        self.0.base2k()
-    }
-
-    fn k(&self) -> TorusPrecision {
-        self.0.k()
-    }
-
-    fn n(&self) -> Degree {
-        self.0.n()
-    }
-
-    fn size(&self) -> usize {
-        self.0.size()
-    }
-}
-
-impl<D: Data, B: Backend> GLWEInfos for LWEToGLWESwitchingKeyPrepared<D, B> {
-    fn rank(&self) -> Rank {
-        self.rank_out()
-    }
-}
-
-impl<D: Data, B: Backend> GGLWEInfos for LWEToGLWESwitchingKeyPrepared<D, B> {
-    fn dsize(&self) -> Dsize {
-        self.0.dsize()
-    }
-
-    fn rank_in(&self) -> Rank {
-        self.0.rank_in()
-    }
-
-    fn rank_out(&self) -> Rank {
-        self.0.rank_out()
-    }
-
-    fn dnum(&self) -> Dnum {
-        self.0.dnum()
-    }
-}
-
-pub trait LWEToGLWESwitchingKeyPreparedFactory<B: Backend>
-where
-    Self: GLWESwitchingKeyPreparedFactory<B>,
-{
-    fn alloc_lwe_to_glwe_switching_key_prepared(
-        &self,
-        base2k: Base2K,
-        k: TorusPrecision,
-        rank_out: Rank,
-        dnum: Dnum,
-    ) -> LWEToGLWESwitchingKeyPrepared<Vec<u8>, B> {
-        LWEToGLWESwitchingKeyPrepared(self.alloc_glwe_switching_key_prepared(base2k, k, Rank(1), rank_out, dnum, Dsize(1)))
-    }
-    fn alloc_lwe_to_glwe_switching_key_prepared_from_infos<A>(&self, infos: &A) -> LWEToGLWESwitchingKeyPrepared<Vec<u8>, B>
-    where
-        A: GGLWEInfos,
-    {
-        debug_assert_eq!(
-            infos.rank_in().0,
-            1,
-            "rank_in > 1 is not supported for LWEToGLWESwitchingKey"
-        );
-        debug_assert_eq!(
-            infos.dsize().0,
-            1,
-            "dsize > 1 is not supported for LWEToGLWESwitchingKey"
-        );
-        self.alloc_lwe_to_glwe_switching_key_prepared(infos.base2k(), infos.k(), infos.rank_out(), infos.dnum())
-    }
-
-    fn bytes_of_lwe_to_glwe_switching_key_prepared(
-        &self,
-        base2k: Base2K,
-        k: TorusPrecision,
-        rank_out: Rank,
-        dnum: Dnum,
-    ) -> usize {
-        self.bytes_of_glwe_switching_key_prepared(base2k, k, Rank(1), rank_out, dnum, Dsize(1))
-    }
-
-    fn bytes_of_lwe_to_glwe_switching_key_prepared_from_infos<A>(&self, infos: &A) -> usize
-    where
-        A: GGLWEInfos,
-    {
-        debug_assert_eq!(
-            infos.rank_in().0,
-            1,
-            "rank_in > 1 is not supported for LWEToGLWESwitchingKey"
-        );
-        debug_assert_eq!(
-            infos.dsize().0,
-            1,
-            "dsize > 1 is not supported for LWEToGLWESwitchingKey"
-        );
-        self.bytes_of_lwe_to_glwe_switching_key_prepared(infos.base2k(), infos.k(), infos.rank_out(), infos.dnum())
-    }
-
-    fn prepare_lwe_to_glwe_switching_key_tmp_bytes<A>(&self, infos: &A)
-    where
-        A: GGLWEInfos,
-    {
-        self.prepare_glwe_switching_key_tmp_bytes(infos);
-    }
-
-    fn prepare_lwe_to_glwe_switching_key<R, O>(&self, res: &mut R, other: &O, scratch: &mut Scratch<B>)
-    where
-        R: GGLWEPreparedToMut<B> + GLWESwitchingKeyDegreesMut,
-        O: GGLWEToRef + GLWESwitchingKeyDegrees,
-    {
-        self.prepare_glwe_switching(res, other, scratch);
-    }
-}
-
-impl<B: Backend> LWEToGLWESwitchingKeyPreparedFactory<B> for Module<B> where Self: GLWESwitchingKeyPreparedFactory<B> {}
-
-impl<B: Backend> LWEToGLWESwitchingKeyPrepared<Vec<u8>, B> {
-    pub fn alloc_from_infos<A, M>(module: &M, infos: &A) -> Self
-    where
-        A: GGLWEInfos,
-        M: LWEToGLWESwitchingKeyPreparedFactory<B>,
-    {
-        module.alloc_lwe_to_glwe_switching_key_prepared_from_infos(infos)
-    }
-
-    pub fn alloc<M>(module: &M, base2k: Base2K, k: TorusPrecision, rank_out: Rank, dnum: Dnum) -> Self
-    where
-        M: LWEToGLWESwitchingKeyPreparedFactory<B>,
-    {
-        module.alloc_lwe_to_glwe_switching_key_prepared(base2k, k, rank_out, dnum)
-    }
-
-    pub fn bytes_of_from_infos<A, M>(module: &M, infos: &A) -> usize
-    where
-        A: GGLWEInfos,
-        M: LWEToGLWESwitchingKeyPreparedFactory<B>,
-    {
-        module.bytes_of_lwe_to_glwe_switching_key_prepared_from_infos(infos)
-    }
-
-    pub fn bytes_of<M>(module: &M, base2k: Base2K, k: TorusPrecision, rank_out: Rank, dnum: Dnum) -> usize
-    where
-        M: LWEToGLWESwitchingKeyPreparedFactory<B>,
-    {
-        module.bytes_of_lwe_to_glwe_switching_key_prepared(base2k, k, rank_out, dnum)
-    }
-}
-
-impl<B: Backend> LWEToGLWESwitchingKeyPrepared<Vec<u8>, B> {
-    pub fn prepare_tmp_bytes<A, M>(&self, module: &M, infos: &A)
-    where
-        A: GGLWEInfos,
-        M: LWEToGLWESwitchingKeyPreparedFactory<B>,
-    {
-        module.prepare_lwe_to_glwe_switching_key_tmp_bytes(infos);
-    }
-}
-
-impl<D: DataMut, B: Backend> LWEToGLWESwitchingKeyPrepared<D, B> {
-    pub fn prepare<O, M>(&mut self, module: &M, other: &O, scratch: &mut Scratch<B>)
-    where
-        O: GGLWEToRef + GLWESwitchingKeyDegrees,
-        M: LWEToGLWESwitchingKeyPreparedFactory<B>,
-    {
-        module.prepare_lwe_to_glwe_switching_key(self, other, scratch);
-    }
-}
-
-impl<D: DataRef, B: Backend> GGLWEPreparedToRef<B> for LWEToGLWESwitchingKeyPrepared<D, B>
-where
-    GLWESwitchingKeyPrepared<D, B>: GGLWEPreparedToRef<B>,
-{
-    fn to_ref(&self) -> GGLWEPrepared<&[u8], B> {
-        self.0.to_ref()
-    }
-}
-
-impl<D: DataMut, B: Backend> GGLWEPreparedToMut<B> for LWEToGLWESwitchingKeyPrepared<D, B>
-where
-    GLWESwitchingKeyPrepared<D, B>: GGLWEPreparedToMut<B>,
-{
-    fn to_mut(&mut self) -> GGLWEPrepared<&mut [u8], B> {
-        self.0.to_mut()
-    }
-}
-
-impl<D: DataMut, B: Backend> GLWESwitchingKeyDegreesMut for LWEToGLWESwitchingKeyPrepared<D, B> {
-    fn input_degree(&mut self) -> &mut Degree {
-        &mut self.0.input_degree
-    }
-
-    fn output_degree(&mut self) -> &mut Degree {
-        &mut self.0.output_degree
-    }
-}

@@ -1,4 +1,5 @@
 mod gglwe;
+mod gglwe_to_ggsw_key;
 mod ggsw;
 mod glwe;
 mod glwe_automorphism_key;
@@ -6,11 +7,12 @@ mod glwe_public_key;
 mod glwe_secret;
 mod glwe_switching_key;
 mod glwe_tensor_key;
-mod glwe_to_lwe_switching_key;
+mod glwe_to_lwe_key;
 mod lwe_switching_key;
-mod lwe_to_glwe_switching_key;
+mod lwe_to_glwe_key;
 
 pub use gglwe::*;
+pub use gglwe_to_ggsw_key::*;
 pub use ggsw::*;
 pub use glwe::*;
 pub use glwe_automorphism_key::*;
@@ -18,6 +20,6 @@ pub use glwe_public_key::*;
 pub use glwe_secret::*;
 pub use glwe_switching_key::*;
 pub use glwe_tensor_key::*;
-pub use glwe_to_lwe_switching_key::*;
+pub use glwe_to_lwe_key::*;
 pub use lwe_switching_key::*;
-pub use lwe_to_glwe_switching_key::*;
+pub use lwe_to_glwe_key::*;

@@ -4,6 +4,7 @@ mod decryption;
 mod dist;
 mod encryption;
 mod external_product;
+mod glwe_packer;
 mod glwe_packing;
 mod glwe_trace;
 mod keyswitching;
@@ -20,6 +21,7 @@ pub use decryption::*;
 pub use dist::*;
 pub use encryption::*;
 pub use external_product::*;
+pub use glwe_packer::*;
 pub use glwe_packing::*;
 pub use glwe_trace::*;
 pub use keyswitching::*;

@@ -62,7 +62,7 @@ self.vec_znx_sub_scalar_inplace(&mut pt.data, 0, (dsize - 1) + row_i * dsize, pt_want, col_i);
 
                 let noise_have: f64 = pt.data.std(base2k, 0).log2();
 
-                // println!("noise_have: {noise_have}");
+                println!("noise_have: {noise_have}");
 
                 assert!(
                     noise_have <= max_noise,

@@ -162,6 +162,7 @@ &mut pt_have,
                     sk_prepared,
                     scratch.borrow(),
                 );
+
                 self.vec_znx_sub_inplace(&mut pt_have.data, 0, &pt.data, 0);
 
                 let std_pt: f64 = pt_have.data.std(base2k, 0).log2();

@@ -0,0 +1,55 @@
+use poulpy_hal::layouts::{Backend, Module, Scratch};
+
+use crate::{
+    GLWERotate, ScratchTakeCore,
+    layouts::{GGSW, GGSWInfos, GGSWToMut, GGSWToRef, GLWEInfos},
+};
+
+impl<BE: Backend> GGSWRotate<BE> for Module<BE> where Module<BE>: GLWERotate<BE> {}
+
+pub trait GGSWRotate<BE: Backend>
+where
+    Self: GLWERotate<BE>,
+{
+    fn ggsw_rotate_tmp_bytes(&self) -> usize {
+        self.glwe_rotate_tmp_bytes()
+    }
+
+    fn ggsw_rotate<R, A>(&self, k: i64, res: &mut R, a: &A)
+    where
+        R: GGSWToMut,
+        A: GGSWToRef,
+    {
+        let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
+        let a: &GGSW<&[u8]> = &a.to_ref();
+
+        assert!(res.dnum() <= a.dnum());
+        assert_eq!(res.dsize(), a.dsize());
+        assert_eq!(res.rank(), a.rank());
+        let rows: usize = res.dnum().into();
+        let cols: usize = (res.rank() + 1).into();
+
+        for row in 0..rows {
+            for col in 0..cols {
+                self.glwe_rotate(k, &mut res.at_mut(row, col), &a.at(row, col));
+            }
+        }
+    }
+
+    fn ggsw_rotate_inplace<R>(&self, k: i64, res: &mut R, scratch: &mut Scratch<BE>)
+    where
+        R: GGSWToMut,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
+
+        let rows: usize = res.dnum().into();
+        let cols: usize = (res.rank() + 1).into();
+
+        for row in 0..rows {
+            for col in 0..cols {
+                self.glwe_rotate_inplace(k, &mut res.at_mut(row, col), scratch);
+            }
+        }
+    }
+}

@@ -1,20 +1,85 @@
 use poulpy_hal::{
     api::{
-        ModuleN, VecZnxAdd, VecZnxAddInplace, VecZnxCopy, VecZnxMulXpMinusOne, VecZnxMulXpMinusOneInplace, VecZnxNegateInplace,
-        VecZnxNormalize, VecZnxNormalizeInplace, VecZnxRotate, VecZnxRotateInplace, VecZnxRshInplace, VecZnxSub,
-        VecZnxSubInplace, VecZnxSubNegateInplace,
+        BivariateTensoring, ModuleN, ScratchTakeBasic, VecZnxAdd, VecZnxAddInplace, VecZnxBigNormalize, VecZnxCopy,
+        VecZnxIdftApplyConsume, VecZnxMulXpMinusOne, VecZnxMulXpMinusOneInplace, VecZnxNegate, VecZnxNormalize,
+        VecZnxNormalizeInplace, VecZnxRotate, VecZnxRotateInplace, VecZnxRshInplace, VecZnxSub, VecZnxSubInplace,
+        VecZnxSubNegateInplace, VecZnxZero,
     },
-    layouts::{Backend, Module, Scratch, VecZnx, ZnxZero},
+    layouts::{Backend, Module, Scratch, VecZnx, VecZnxBig, ZnxInfos},
+    reference::vec_znx::vec_znx_rotate_inplace_tmp_bytes,
 };
 
 use crate::{
     ScratchTakeCore,
-    layouts::{GLWE, GLWEInfos, GLWEToMut, GLWEToRef, LWEInfos, SetGLWEInfos, TorusPrecision},
+    layouts::{
+        GLWE, GLWEInfos, GLWEPrepared, GLWEPreparedToRef, GLWETensor, GLWETensorToMut, GLWEToMut, GLWEToRef, LWEInfos,
+        TorusPrecision,
+    },
 };
 
+pub trait GLWETensoring<BE: Backend>
+where
+    Self: BivariateTensoring<BE> + VecZnxIdftApplyConsume<BE> + VecZnxBigNormalize<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
+{
+    /// res = (a (x) b) * 2^{k * a_base2k}
+    ///
+    /// # Requires
+    /// * a.base2k() == b.base2k()
+    /// * res.cols() >= a.cols() + b.cols() - 1
+    ///
+    /// # Behavior
+    /// * res precision is truncated to res.max_k().min(a.max_k() + b.max_k() + k * a_base2k)
+    fn glwe_tensor<R, A, B>(&self, k: i64, res: &mut R, a: &A, b: &B, scratch: &mut Scratch<BE>)
+    where
+        R: GLWETensorToMut,
+        A: GLWEToRef,
+        B: GLWEPreparedToRef<BE>,
+    {
+        let res: &mut GLWETensor<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWE<&[u8]> = &a.to_ref();
+        let b: &GLWEPrepared<&[u8], BE> = &b.to_ref();
+
+        assert_eq!(a.base2k(), b.base2k());
+        assert_eq!(a.rank(), res.rank());
+
+        let res_cols: usize = res.data.cols();
+
+        // Get tmp buffer of min precision between a_prec * b_prec and res_prec
+        let (mut res_dft, scratch_1) = scratch.take_vec_znx_dft(self, res_cols, res.max_k().div_ceil(a.base2k()) as usize);
+
+        // DFT(res) = DFT(a) (x) DFT(b)
+        self.bivariate_tensoring(k, &mut res_dft, &a.data, &b.data, scratch_1);
+
+        // res = IDFT(res)
+        let res_big: VecZnxBig<&mut [u8], BE> = self.vec_znx_idft_apply_consume(res_dft);
+
+        // Normalize and switches basis if required
+        for res_col in 0..res_cols {
+            self.vec_znx_big_normalize(
+                res.base2k().into(),
+                &mut res.data,
+                res_col,
+                a.base2k().into(),
+                &res_big,
+                res_col,
+                scratch_1,
+            );
+        }
+    }
+
+    // fn glwe_relinearize<R, A, T>(&self, res: &mut R, a: &A, tsk: &T, scratch: &mut Scratch<BE>)
+    // where
+    // R: GLWEToRef,
+    // A: GLWETensorToRef,
+    // T: GLWETensorKeyPreparedToRef<BE>,
+    // {
+    // }
+}
+
 pub trait GLWEAdd
 where
-    Self: ModuleN + VecZnxAdd + VecZnxCopy + VecZnxAddInplace,
+    Self: ModuleN + VecZnxAdd + VecZnxCopy + VecZnxAddInplace + VecZnxZero,
 {
     fn glwe_add<R, A, B>(&self, res: &mut R, a: &A, b: &B)
     where
@@ -30,35 +95,38 @@ assert_eq!(a.n(), self.n() as u32);
         assert_eq!(b.n(), self.n() as u32);
         assert_eq!(res.n(), self.n() as u32);
         assert_eq!(a.base2k(), b.base2k());
-        assert!(res.rank() >= a.rank().max(b.rank()));
+        assert_eq!(res.base2k(), b.base2k());
+
+        if a.rank() == 0 {
+            assert_eq!(res.rank(), b.rank());
+        } else if b.rank() == 0 {
+            assert_eq!(res.rank(), a.rank());
+        } else {
+            assert_eq!(res.rank(), a.rank());
+            assert_eq!(res.rank(), b.rank());
+        }
 
         let min_col: usize = (a.rank().min(b.rank()) + 1).into();
         let max_col: usize = (a.rank().max(b.rank() + 1)).into();
         let self_col: usize = (res.rank() + 1).into();
 
-        (0..min_col).for_each(|i| {
+        for i in 0..min_col {
             self.vec_znx_add(res.data_mut(), i, a.data(), i, b.data(), i);
-        });
+        }
 
         if a.rank() > b.rank() {
-            (min_col..max_col).for_each(|i| {
+            for i in min_col..max_col {
                 self.vec_znx_copy(res.data_mut(), i, a.data(), i);
-            });
+            }
         } else {
-            (min_col..max_col).for_each(|i| {
+            for i in min_col..max_col {
                 self.vec_znx_copy(res.data_mut(), i, b.data(), i);
-            });
+            }
         }
 
-        let size: usize = res.size();
-        (max_col..self_col).for_each(|i| {
-            (0..size).for_each(|j| {
-                res.data.zero_at(i, j);
-            });
-        });
-
-        res.set_base2k(a.base2k());
-        res.set_k(set_k_binary(res, a, b));
+        for i in max_col..self_col {
+            self.vec_znx_zero(res.data_mut(), i);
+        }
     }
 
     fn glwe_add_inplace<R, A>(&self, res: &mut R, a: &A)
@@ -74,24 +142,22 @@ assert_eq!(a.n(), self.n() as u32);
         assert_eq!(res.base2k(), a.base2k());
         assert!(res.rank() >= a.rank());
 
-        (0..(a.rank() + 1).into()).for_each(|i| {
+        for i in 0..(a.rank() + 1).into() {
             self.vec_znx_add_inplace(res.data_mut(), i, a.data(), i);
-        });
-
-        res.set_k(set_k_unary(res, a))
+        }
     }
 }
 
-impl<BE: Backend> GLWEAdd for Module<BE> where Self: ModuleN + VecZnxAdd + VecZnxCopy + VecZnxAddInplace {}
+impl<BE: Backend> GLWEAdd for Module<BE> where Self: ModuleN + VecZnxAdd + VecZnxCopy + VecZnxAddInplace + VecZnxZero {}
 
 impl<BE: Backend> GLWESub for Module<BE> where
-    Self: ModuleN + VecZnxSub + VecZnxCopy + VecZnxNegateInplace + VecZnxSubInplace + VecZnxSubNegateInplace
+    Self: ModuleN + VecZnxSub + VecZnxCopy + VecZnxNegate + VecZnxZero + VecZnxSubInplace + VecZnxSubNegateInplace
 {
 }
 
 pub trait GLWESub
 where
-    Self: ModuleN + VecZnxSub + VecZnxCopy + VecZnxNegateInplace + VecZnxSubInplace + VecZnxSubNegateInplace,
+    Self: ModuleN + VecZnxSub + VecZnxCopy + VecZnxNegate + VecZnxZero + VecZnxSubInplace + VecZnxSubNegateInplace,
 {
     fn glwe_sub<R, A, B>(&self, res: &mut R, a: &A, b: &B)
     where
@@ -105,37 +171,40 @@ let b: &GLWE<&[u8]> = &b.to_ref();
 
         assert_eq!(a.n(), self.n() as u32);
         assert_eq!(b.n(), self.n() as u32);
-        assert_eq!(a.base2k(), b.base2k());
-        assert!(res.rank() >= a.rank().max(b.rank()));
+        assert_eq!(res.n(), self.n() as u32);
+        assert_eq!(a.base2k(), res.base2k());
+        assert_eq!(b.base2k(), res.base2k());
+
+        if a.rank() == 0 {
+            assert_eq!(res.rank(), b.rank());
+        } else if b.rank() == 0 {
+            assert_eq!(res.rank(), a.rank());
+        } else {
+            assert_eq!(res.rank(), a.rank());
+            assert_eq!(res.rank(), b.rank());
+        }
 
         let min_col: usize = (a.rank().min(b.rank()) + 1).into();
         let max_col: usize = (a.rank().max(b.rank() + 1)).into();
         let self_col: usize = (res.rank() + 1).into();
 
-        (0..min_col).for_each(|i| {
+        for i in 0..min_col {
             self.vec_znx_sub(res.data_mut(), i, a.data(), i, b.data(), i);
-        });
+        }
 
         if a.rank() > b.rank() {
-            (min_col..max_col).for_each(|i| {
+            for i in min_col..max_col {
                 self.vec_znx_copy(res.data_mut(), i, a.data(), i);
-            });
+            }
         } else {
-            (min_col..max_col).for_each(|i| {
-                self.vec_znx_copy(res.data_mut(), i, b.data(), i);
-                self.vec_znx_negate_inplace(res.data_mut(), i);
-            });
+            for i in min_col..max_col {
+                self.vec_znx_negate(res.data_mut(), i, b.data(), i);
+            }
         }
 
-        let size: usize = res.size();
-        (max_col..self_col).for_each(|i| {
-            (0..size).for_each(|j| {
-                res.data.zero_at(i, j);
-            });
-        });
-
-        res.set_base2k(a.base2k());
-        res.set_k(set_k_binary(res, a, b));
+        for i in max_col..self_col {
+            self.vec_znx_zero(res.data_mut(), i);
+        }
     }
 
     fn glwe_sub_inplace<R, A>(&self, res: &mut R, a: &A)
@@ -149,13 +218,11 @@
         assert_eq!(res.n(), self.n() as u32);
         assert_eq!(a.n(), self.n() as u32);
         assert_eq!(res.base2k(), a.base2k());
-        assert!(res.rank() >= a.rank());
+        assert!(res.rank() == a.rank() || a.rank() == 0);
 
-        (0..(a.rank() + 1).into()).for_each(|i| {
+        for i in 0..(a.rank() + 1).into() {
             self.vec_znx_sub_inplace(res.data_mut(), i, a.data(), i);
-        });
-
-        res.set_k(set_k_unary(res, a))
+        }
     }
 
     fn glwe_sub_negate_inplace<R, A>(&self, res: &mut R, a: &A)
@@ -169,22 +236,24 @@
         assert_eq!(res.n(), self.n() as u32);
         assert_eq!(a.n(), self.n() as u32);
         assert_eq!(res.base2k(), a.base2k());
-        assert!(res.rank() >= a.rank());
+        assert!(res.rank() == a.rank() || a.rank() == 0);
 
-        (0..(a.rank() + 1).into()).for_each(|i| {
+        for i in 0..(a.rank() + 1).into() {
             self.vec_znx_sub_negate_inplace(res.data_mut(), i, a.data(), i);
-        });
-
-        res.set_k(set_k_unary(res, a))
+        }
     }
 }
 
-impl<BE: Backend> GLWERotate<BE> for Module<BE> where Self: ModuleN + VecZnxRotate + VecZnxRotateInplace<BE> {}
+impl<BE: Backend> GLWERotate<BE> for Module<BE> where Self: ModuleN + VecZnxRotate + VecZnxRotateInplace<BE> + VecZnxZero {}
 
 pub trait GLWERotate<BE: Backend>
 where
-    Self: ModuleN + VecZnxRotate + VecZnxRotateInplace<BE>,
+    Self: ModuleN + VecZnxRotate + VecZnxRotateInplace<BE> + VecZnxZero,
 {
+    fn glwe_rotate_tmp_bytes(&self) -> usize {
+        vec_znx_rotate_inplace_tmp_bytes(self.n())
+    }
+
     fn glwe_rotate<R, A>(&self, k: i64, res: &mut R, a: &A)
     where
         R: GLWEToMut,
@@ -194,14 +263,18 @@ let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         let a: &GLWE<&[u8]> = &a.to_ref();
 
         assert_eq!(a.n(), self.n() as u32);
-        assert_eq!(res.rank(), a.rank());
+        assert_eq!(res.n(), self.n() as u32);
+        assert!(res.rank() == a.rank() || a.rank() == 0);
 
-        (0..(a.rank() + 1).into()).for_each(|i| {
-            self.vec_znx_rotate(k, res.data_mut(), i, a.data(), i);
-        });
+        let res_cols = (res.rank() + 1).into();
+        let a_cols = (a.rank() + 1).into();
 
-        res.set_base2k(a.base2k());
-        res.set_k(set_k_unary(res, a))
+        for i in 0..a_cols {
+            self.vec_znx_rotate(k, res.data_mut(), i, a.data(), i);
+        }
+        for i in a_cols..res_cols {
+            self.vec_znx_zero(res.data_mut(), i);
+        }
     }
 
     fn glwe_rotate_inplace<R>(&self, k: i64, res: &mut R, scratch: &mut Scratch<BE>)
@@ -211,9 +284,9 @@ Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
 
-        (0..(res.rank() + 1).into()).for_each(|i| {
+        for i in 0..(res.rank() + 1).into() {
             self.vec_znx_rotate_inplace(k, res.data_mut(), i, scratch);
-        });
+        }
     }
 }
 
@@ -238,9 +311,6 @@
         for i in 0..res.rank().as_usize() + 1 {
             self.vec_znx_mul_xp_minus_one(k, res.data_mut(), i, a.data(), i);
         }
-
-        res.set_base2k(a.base2k());
-        res.set_k(set_k_unary(res, a))
     }
 
     fn glwe_mul_xp_minus_one_inplace<R>(&self, k: i64, res: &mut R, scratch: &mut Scratch<BE>)
@@ -257,11 +327,11 @@ }
     }
 }
 
-impl<BE: Backend> GLWECopy for Module<BE> where Self: ModuleN + VecZnxCopy {}
+impl<BE: Backend> GLWECopy for Module<BE> where Self: ModuleN + VecZnxCopy + VecZnxZero {}
 
 pub trait GLWECopy
 where
-    Self: ModuleN + VecZnxCopy,
+    Self: ModuleN + VecZnxCopy + VecZnxZero,
 {
     fn glwe_copy<R, A>(&self, res: &mut R, a: &A)
     where
@@ -273,14 +343,17 @@ let a: &GLWE<&[u8]> = &a.to_ref();
 
         assert_eq!(res.n(), self.n() as u32);
         assert_eq!(a.n(), self.n() as u32);
-        assert_eq!(res.rank(), a.rank());
+        assert!(res.rank() == a.rank() || a.rank() == 0);
+
+        let min_rank: usize = res.rank().min(a.rank()).as_usize() + 1;
 
-        for i in 0..res.rank().as_usize() + 1 {
+        for i in 0..min_rank {
             self.vec_znx_copy(res.data_mut(), i, a.data(), i);
         }
 
-        res.set_k(a.k().min(res.max_k()));
-        res.set_base2k(a.base2k());
+        for i in min_rank..(res.rank() + 1).into() {
+            self.vec_znx_zero(res.data_mut(), i);
+        }
     }
 }
 
@@ -346,8 +419,6 @@ i,
                 scratch,
             );
         }
-
-        res.set_k(a.k().min(res.k()));
     }
 
     fn glwe_normalize_inplace<R>(&self, res: &mut R, scratch: &mut Scratch<BE>)
@@ -362,6 +433,7 @@ }
     }
 }
 
+#[allow(dead_code)]
 // c = op(a, b)
 fn set_k_binary(c: &impl GLWEInfos, a: &impl GLWEInfos, b: &impl GLWEInfos) -> TorusPrecision {
     // If either operands is a ciphertext
@@ -383,6 +455,7 @@ c.k()
     }
 }
 
+#[allow(dead_code)]
 // a = op(a, b)
 fn set_k_unary(a: &impl GLWEInfos, b: &impl GLWEInfos) -> TorusPrecision {
     if a.rank() != 0 || b.rank() != 0 {

@@ -1,3 +1,5 @@
+mod ggsw;
 mod glwe;
 
+pub use ggsw::*;
 pub use glwe::*;

@@ -7,7 +7,7 @@ use crate::{
     dist::Distribution,
     layouts::{
         Degree, GGLWE, GGLWEInfos, GGLWELayout, GGSW, GGSWInfos, GLWE, GLWEAutomorphismKey, GLWEInfos, GLWEPlaintext,
-        GLWEPrepared, GLWEPublicKey, GLWESecret, GLWESwitchingKey, GLWETensorKey, Rank,
+        GLWEPrepared, GLWEPublicKey, GLWESecret, GLWESecretTensor, GLWESwitchingKey, GLWETensorKey, Rank,
         prepared::{
             GGLWEPrepared, GGSWPrepared, GLWEAutomorphismKeyPrepared, GLWEPublicKeyPrepared, GLWESecretPrepared,
             GLWESwitchingKeyPrepared, GLWETensorKeyPrepared,
@@ -232,6 +232,18 @@ scratch,
         )
     }
 
+    fn take_glwe_secret_tensor(&mut self, n: Degree, rank: Rank) -> (GLWESecretTensor<&mut [u8]>, &mut Self) {
+        let (data, scratch) = self.take_scalar_znx(n.into(), GLWESecretTensor::pairs(rank.into()));
+        (
+            GLWESecretTensor {
+                data,
+                rank,
+                dist: Distribution::NONE,
+            },
+            scratch,
+        )
+    }
+
     fn take_glwe_secret_prepared<M>(&mut self, module: &M, rank: Rank) -> (GLWESecretPrepared<&mut [u8], B>, &mut Self)
     where
         M: ModuleN + SvpPPolBytesOf,
@@ -313,25 +325,12 @@ infos.rank_in(),
             infos.rank_out(),
             "rank_in != rank_out is not supported for GLWETensorKey"
         );
-        let mut keys: Vec<GGLWE<&mut [u8]>> = Vec::new();
-        let pairs: usize = (((infos.rank_out().0 + 1) * infos.rank_out().0) >> 1).max(1) as usize;
 
-        let mut scratch: &mut Self = self;
-
+        let pairs: u32 = (((infos.rank_out().0 + 1) * infos.rank_out().0) >> 1).max(1);
         let mut ksk_infos: GGLWELayout = infos.gglwe_layout();
-        ksk_infos.rank_in = Rank(1);
-
-        if pairs != 0 {
-            let (gglwe, s) = scratch.take_gglwe(&ksk_infos);
-            scratch = s;
-            keys.push(gglwe);
-        }
-        for _ in 1..pairs {
-            let (gglwe, s) = scratch.take_gglwe(&ksk_infos);
-            scratch = s;
-            keys.push(gglwe);
-        }
-        (GLWETensorKey { keys }, scratch)
+        ksk_infos.rank_in = Rank(pairs);
+        let (data, scratch) = self.take_gglwe(infos);
+        (GLWETensorKey(data), scratch)
     }
 
     fn take_glwe_tensor_key_prepared<A, M>(&mut self, module: &M, infos: &A) -> (GLWETensorKeyPrepared<&mut [u8], B>, &mut Self)
@@ -346,25 +345,11 @@ infos.rank_out(),
             "rank_in != rank_out is not supported for GGLWETensorKeyPrepared"
         );
 
-        let mut keys: Vec<GGLWEPrepared<&mut [u8], B>> = Vec::new();
-        let pairs: usize = (((infos.rank_out().0 + 1) * infos.rank_out().0) >> 1).max(1) as usize;
-
-        let mut scratch: &mut Self = self;
-
+        let pairs: u32 = (((infos.rank_out().0 + 1) * infos.rank_out().0) >> 1).max(1);
         let mut ksk_infos: GGLWELayout = infos.gglwe_layout();
-        ksk_infos.rank_in = Rank(1);
-
-        if pairs != 0 {
-            let (gglwe, s) = scratch.take_gglwe_prepared(module, &ksk_infos);
-            scratch = s;
-            keys.push(gglwe);
-        }
-        for _ in 1..pairs {
-            let (gglwe, s) = scratch.take_gglwe_prepared(module, &ksk_infos);
-            scratch = s;
-            keys.push(gglwe);
-        }
-        (GLWETensorKeyPrepared { keys }, scratch)
+        ksk_infos.rank_in = Rank(pairs);
+        let (data, scratch) = self.take_gglwe_prepared(module, infos);
+        (GLWETensorKeyPrepared(data), scratch)
     }
 }
 

@@ -36,6 +36,7 @@ gglwe_automorphism_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_automorphism_key_encrypt_sk,
 gglwe_automorphism_key_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_automorphism_key_compressed_encrypt_sk,
 gglwe_tensor_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_tensor_key_encrypt_sk,
 gglwe_tensor_key_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_tensor_key_compressed_encrypt_sk,
+gglwe_to_ggsw_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_to_ggsw_key_encrypt_sk,
 // GGLWE Keyswitching
 gglwe_switching_key_keyswitch => crate::tests::test_suite::keyswitch::test_gglwe_switching_key_keyswitch,
 gglwe_switching_key_keyswitch_inplace => crate::tests::test_suite::keyswitch::test_gglwe_switching_key_keyswitch_inplace,
@@ -75,7 +76,7 @@ glwe_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_glwe_compressed_encrypt_sk,
  glwe_encrypt_zero_sk => crate::tests::test_suite::encryption::test_glwe_encrypt_zero_sk,
  glwe_encrypt_pk => crate::tests::test_suite::encryption::test_glwe_encrypt_pk,
 // GLWE Keyswitch
-    glwe_keyswitch => crate::tests::test_suite::keyswitch::test_glwe_keyswitch,
+glwe_keyswitch => crate::tests::test_suite::keyswitch::test_glwe_keyswitch,
 glwe_keyswitch_inplace => crate::tests::test_suite::keyswitch::test_glwe_keyswitch_inplace,
 // GLWE Automorphism
 glwe_automorphism => crate::tests::test_suite::automorphism::test_glwe_automorphism,
@@ -93,6 +94,7 @@ gglwe_automorphism_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_automorphism_key_encrypt_sk,
 gglwe_automorphism_key_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_automorphism_key_compressed_encrypt_sk,
 gglwe_tensor_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_tensor_key_encrypt_sk,
 gglwe_tensor_key_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_tensor_key_compressed_encrypt_sk,
+gglwe_to_ggsw_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_to_ggsw_key_encrypt_sk,
 // GGLWE Keyswitching
 gglwe_switching_key_keyswitch => crate::tests::test_suite::keyswitch::test_gglwe_switching_key_keyswitch,
 gglwe_switching_key_keyswitch_inplace => crate::tests::test_suite::keyswitch::test_gglwe_switching_key_keyswitch_inplace,

@@ -1,12 +1,12 @@
 use poulpy_hal::test_suite::serialization::test_reader_writer_interface;
 
 use crate::layouts::{
-    Base2K, Degree, Dnum, Dsize, GGLWE, GGSW, GLWE, GLWEAutomorphismKey, GLWESwitchingKey, GLWETensorKey, GLWEToLWESwitchingKey,
-    LWE, LWESwitchingKey, LWEToGLWESwitchingKey, Rank, TorusPrecision,
+    Base2K, Degree, Dnum, Dsize, GGLWE, GGSW, GLWE, GLWEAutomorphismKey, GLWESwitchingKey, GLWETensorKey, GLWEToLWEKey, LWE,
+    LWESwitchingKey, LWEToGLWEKey, Rank, TorusPrecision,
     compressed::{
         GGLWECompressed, GGSWCompressed, GLWEAutomorphismKeyCompressed, GLWECompressed, GLWESwitchingKeyCompressed,
         GLWETensorKeyCompressed, GLWEToLWESwitchingKeyCompressed, LWECompressed, LWESwitchingKeyCompressed,
-        LWEToGLWESwitchingKeyCompressed,
+        LWEToGLWEKeyCompressed,
     },
 };
 
@@ -93,28 +93,27 @@ test_reader_writer_interface(original);
 }
 
 #[test]
-fn glwe_to_lwe_switching_key_serialization() {
-    let original: GLWEToLWESwitchingKey<Vec<u8>> = GLWEToLWESwitchingKey::alloc(N_GLWE, BASE2K, K, RANK, DNUM);
+fn glwe_to_lwe_key_serialization() {
+    let original: GLWEToLWEKey<Vec<u8>> = GLWEToLWEKey::alloc(N_GLWE, BASE2K, K, RANK, DNUM);
     test_reader_writer_interface(original);
 }
 
 #[test]
-fn glwe_to_lwe_switching_key_compressed_serialization() {
+fn glwe_to_lwe_key_compressed_serialization() {
     let original: GLWEToLWESwitchingKeyCompressed<Vec<u8>> =
         GLWEToLWESwitchingKeyCompressed::alloc(N_GLWE, BASE2K, K, RANK, DNUM);
     test_reader_writer_interface(original);
 }
 
 #[test]
-fn lwe_to_glwe_switching_key_serialization() {
-    let original: LWEToGLWESwitchingKey<Vec<u8>> = LWEToGLWESwitchingKey::alloc(N_GLWE, BASE2K, K, RANK, DNUM);
+fn lwe_to_glwe_key_serialization() {
+    let original: LWEToGLWEKey<Vec<u8>> = LWEToGLWEKey::alloc(N_GLWE, BASE2K, K, RANK, DNUM);
     test_reader_writer_interface(original);
 }
 
 #[test]
-fn lwe_to_glwe_switching_key_compressed_serialization() {
-    let original: LWEToGLWESwitchingKeyCompressed<Vec<u8>> =
-        LWEToGLWESwitchingKeyCompressed::alloc(N_GLWE, BASE2K, K, RANK, DNUM);
+fn lwe_to_glwe_key_compressed_serialization() {
+    let original: LWEToGLWEKeyCompressed<Vec<u8>> = LWEToGLWEKeyCompressed::alloc(N_GLWE, BASE2K, K, RANK, DNUM);
     test_reader_writer_interface(original);
 }
 

@@ -5,12 +5,12 @@ source::Source,
 };
 
 use crate::{
-    GGSWAutomorphism, GGSWEncryptSk, GGSWNoise, GLWEAutomorphismKeyEncryptSk, GLWETensorKeyEncryptSk, ScratchTakeCore,
+    GGLWEToGGSWKeyEncryptSk, GGSWAutomorphism, GGSWEncryptSk, GGSWNoise, GLWEAutomorphismKeyEncryptSk, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
-        GGSW, GGSWLayout, GLWEAutomorphismKey, GLWEAutomorphismKeyPreparedFactory, GLWESecret, GLWESecretPreparedFactory,
-        GLWETensorKey, GLWETensorKeyLayout, GLWETensorKeyPreparedFactory,
-        prepared::{GLWEAutomorphismKeyPrepared, GLWESecretPrepared, GLWETensorKeyPrepared},
+        GGLWEToGGSWKey, GGLWEToGGSWKeyLayout, GGLWEToGGSWKeyPreparedFactory, GGSW, GGSWLayout, GLWEAutomorphismKey,
+        GLWEAutomorphismKeyPreparedFactory, GLWESecret, GLWESecretPreparedFactory,
+        prepared::{GGLWEToGGSWKeyPrepared, GLWEAutomorphismKeyPrepared, GLWESecretPrepared},
     },
     noise::noise_ggsw_keyswitch,
 };
@@ -21,8 +21,8 @@ Module<BE>: GGSWEncryptSk<BE>
         + GLWEAutomorphismKeyEncryptSk<BE>
         + GLWEAutomorphismKeyPreparedFactory<BE>
         + GGSWAutomorphism<BE>
-        + GLWETensorKeyPreparedFactory<BE>
-        + GLWETensorKeyEncryptSk<BE>
+        + GGLWEToGGSWKeyPreparedFactory<BE>
+        + GGLWEToGGSWKeyEncryptSk<BE>
         + GLWESecretPreparedFactory<BE>
         + VecZnxAutomorphismInplace<BE>
         + GGSWNoise<BE>,
@@ -64,7 +64,7 @@ dsize: dsize_in.into(),
                 rank: rank.into(),
             };
 
-            let tensor_key_layout: GLWETensorKeyLayout = GLWETensorKeyLayout {
+            let tsk_layout: GGLWEToGGSWKeyLayout = GGLWEToGGSWKeyLayout {
                 n: n.into(),
                 base2k: base2k.into(),
                 k: k_tsk.into(),
@@ -73,7 +73,7 @@ dsize: di.into(),
                 rank: rank.into(),
             };
 
-            let auto_key_layout: GLWETensorKeyLayout = GLWETensorKeyLayout {
+            let auto_key_layout: GGLWEToGGSWKeyLayout = GGLWEToGGSWKeyLayout {
                 n: n.into(),
                 base2k: base2k.into(),
                 k: k_ksk.into(),
@@ -84,7 +84,7 @@ };
 
             let mut ct_in: GGSW<Vec<u8>> = GGSW::alloc_from_infos(&ggsw_in_layout);
             let mut ct_out: GGSW<Vec<u8>> = GGSW::alloc_from_infos(&ggsw_out_layout);
-            let mut tensor_key: GLWETensorKey<Vec<u8>> = GLWETensorKey::alloc_from_infos(&tensor_key_layout);
+            let mut tsk: GGLWEToGGSWKey<Vec<u8>> = GGLWEToGGSWKey::alloc_from_infos(&tsk_layout);
             let mut auto_key: GLWEAutomorphismKey<Vec<u8>> = GLWEAutomorphismKey::alloc_from_infos(&auto_key_layout);
             let mut pt_scalar: ScalarZnx<Vec<u8>> = ScalarZnx::alloc(n, 1);
 
@@ -95,8 +95,8 @@
             let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
                 GGSW::encrypt_sk_tmp_bytes(module, &ct_in)
                     | GLWEAutomorphismKey::encrypt_sk_tmp_bytes(module, &auto_key)
-                    | GLWETensorKey::encrypt_sk_tmp_bytes(module, &tensor_key)
-                    | GGSW::automorphism_tmp_bytes(module, &ct_out, &ct_in, &auto_key, &tensor_key),
+                    | GGLWEToGGSWKey::encrypt_sk_tmp_bytes(module, &tsk)
+                    | GGSW::automorphism_tmp_bytes(module, &ct_out, &ct_in, &auto_key, &tsk),
             );
 
             let var_xs: f64 = 0.5;
@@ -115,7 +115,7 @@ &mut source_xa,
                 &mut source_xe,
                 scratch.borrow(),
             );
-            tensor_key.encrypt_sk(
+            tsk.encrypt_sk(
                 module,
                 &sk,
                 &mut source_xa,
@@ -138,9 +138,8 @@ let mut auto_key_prepared: GLWEAutomorphismKeyPrepared<Vec<u8>, BE> =
                 GLWEAutomorphismKeyPrepared::alloc_from_infos(module, &auto_key_layout);
             auto_key_prepared.prepare(module, &auto_key, scratch.borrow());
 
-            let mut tsk_prepared: GLWETensorKeyPrepared<Vec<u8>, BE> =
-                GLWETensorKeyPrepared::alloc_from_infos(module, &tensor_key_layout);
-            tsk_prepared.prepare(module, &tensor_key, scratch.borrow());
+            let mut tsk_prepared: GGLWEToGGSWKeyPrepared<Vec<u8>, BE> = GGLWEToGGSWKeyPrepared::alloc_from_infos(module, &tsk);
+            tsk_prepared.prepare(module, &tsk, scratch.borrow());
 
             ct_out.automorphism(
                 module,
@@ -180,8 +179,8 @@ Module<BE>: GGSWEncryptSk<BE>
         + GLWEAutomorphismKeyEncryptSk<BE>
         + GLWEAutomorphismKeyPreparedFactory<BE>
         + GGSWAutomorphism<BE>
-        + GLWETensorKeyPreparedFactory<BE>
-        + GLWETensorKeyEncryptSk<BE>
+        + GGLWEToGGSWKeyPreparedFactory<BE>
+        + GGLWEToGGSWKeyEncryptSk<BE>
         + GLWESecretPreparedFactory<BE>
         + VecZnxAutomorphismInplace<BE>
         + GGSWNoise<BE>,
@@ -211,7 +210,7 @@ dsize: dsize_in.into(),
                 rank: rank.into(),
             };
 
-            let tensor_key_layout: GLWETensorKeyLayout = GLWETensorKeyLayout {
+            let tsk_layout: GGLWEToGGSWKeyLayout = GGLWEToGGSWKeyLayout {
                 n: n.into(),
                 base2k: base2k.into(),
                 k: k_tsk.into(),
@@ -220,7 +219,7 @@ dsize: di.into(),
                 rank: rank.into(),
             };
 
-            let auto_key_layout: GLWETensorKeyLayout = GLWETensorKeyLayout {
+            let auto_key_layout: GGLWEToGGSWKeyLayout = GGLWEToGGSWKeyLayout {
                 n: n.into(),
                 base2k: base2k.into(),
                 k: k_ksk.into(),
@@ -230,7 +229,7 @@ rank: rank.into(),
             };
 
             let mut ct: GGSW<Vec<u8>> = GGSW::alloc_from_infos(&ggsw_out_layout);
-            let mut tensor_key: GLWETensorKey<Vec<u8>> = GLWETensorKey::alloc_from_infos(&tensor_key_layout);
+            let mut tsk: GGLWEToGGSWKey<Vec<u8>> = GGLWEToGGSWKey::alloc_from_infos(&tsk_layout);
             let mut auto_key: GLWEAutomorphismKey<Vec<u8>> = GLWEAutomorphismKey::alloc_from_infos(&auto_key_layout);
             let mut pt_scalar: ScalarZnx<Vec<u8>> = ScalarZnx::alloc(n, 1);
 
@@ -241,8 +240,8 @@
             let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
                 GGSW::encrypt_sk_tmp_bytes(module, &ct)
                     | GLWEAutomorphismKey::encrypt_sk_tmp_bytes(module, &auto_key)
-                    | GLWETensorKey::encrypt_sk_tmp_bytes(module, &tensor_key)
-                    | GGSW::automorphism_tmp_bytes(module, &ct, &ct, &auto_key, &tensor_key),
+                    | GGLWEToGGSWKey::encrypt_sk_tmp_bytes(module, &tsk)
+                    | GGSW::automorphism_tmp_bytes(module, &ct, &ct, &auto_key, &tsk),
             );
 
             let var_xs: f64 = 0.5;
@@ -261,7 +260,7 @@ &mut source_xa,
                 &mut source_xe,
                 scratch.borrow(),
             );
-            tensor_key.encrypt_sk(
+            tsk.encrypt_sk(
                 module,
                 &sk,
                 &mut source_xa,
@@ -284,9 +283,8 @@ let mut auto_key_prepared: GLWEAutomorphismKeyPrepared<Vec<u8>, BE> =
                 GLWEAutomorphismKeyPrepared::alloc_from_infos(module, &auto_key_layout);
             auto_key_prepared.prepare(module, &auto_key, scratch.borrow());
 
-            let mut tsk_prepared: GLWETensorKeyPrepared<Vec<u8>, BE> =
-                GLWETensorKeyPrepared::alloc_from_infos(module, &tensor_key_layout);
-            tsk_prepared.prepare(module, &tensor_key, scratch.borrow());
+            let mut tsk_prepared: GGLWEToGGSWKeyPrepared<Vec<u8>, BE> = GGLWEToGGSWKeyPrepared::alloc_from_infos(module, &tsk);
+            tsk_prepared.prepare(module, &tsk, scratch.borrow());
 
             ct.automorphism_inplace(module, &auto_key_prepared, &tsk_prepared, scratch.borrow());
 

@@ -8,10 +8,10 @@ use crate::{
     GLWEDecrypt, GLWEEncryptSk, GLWEFromLWE, GLWEToLWESwitchingKeyEncryptSk, LWEDecrypt, LWEEncryptSk,
     LWEToGLWESwitchingKeyEncryptSk, ScratchTakeCore,
     layouts::{
-        Base2K, Degree, Dnum, GLWE, GLWELayout, GLWEPlaintext, GLWESecret, GLWESecretPreparedFactory, GLWEToLWEKeyLayout,
-        GLWEToLWESwitchingKey, GLWEToLWESwitchingKeyPreparedFactory, LWE, LWELayout, LWEPlaintext, LWESecret,
-        LWEToGLWESwitchingKey, LWEToGLWESwitchingKeyLayout, LWEToGLWESwitchingKeyPreparedFactory, Rank, TorusPrecision,
-        prepared::{GLWESecretPrepared, GLWEToLWESwitchingKeyPrepared, LWEToGLWESwitchingKeyPrepared},
+        Base2K, Degree, Dnum, GLWE, GLWELayout, GLWEPlaintext, GLWESecret, GLWESecretPreparedFactory, GLWEToLWEKey,
+        GLWEToLWEKeyLayout, GLWEToLWEKeyPrepared, GLWEToLWEKeyPreparedFactory, LWE, LWELayout, LWEPlaintext, LWESecret,
+        LWEToGLWEKey, LWEToGLWEKeyLayout, LWEToGLWEKeyPrepared, LWEToGLWEKeyPreparedFactory, Rank, TorusPrecision,
+        prepared::GLWESecretPrepared,
     },
 };
 
@@ -22,7 +22,7 @@ + LWEToGLWESwitchingKeyEncryptSk<BE>
         + GLWEDecrypt<BE>
         + GLWESecretPreparedFactory<BE>
         + LWEEncryptSk<BE>
-        + LWEToGLWESwitchingKeyPreparedFactory<BE>,
+        + LWEToGLWEKeyPreparedFactory<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
@@ -36,7 +36,7 @@ let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xa: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
 
-    let lwe_to_glwe_infos: LWEToGLWESwitchingKeyLayout = LWEToGLWESwitchingKeyLayout {
+    let lwe_to_glwe_infos: LWEToGLWEKeyLayout = LWEToGLWEKeyLayout {
         n: n_glwe,
         base2k: Base2K(17),
         k: TorusPrecision(51),
@@ -58,7 +58,7 @@ k: TorusPrecision(34),
     };
 
     let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
-        LWEToGLWESwitchingKey::encrypt_sk_tmp_bytes(module, &lwe_to_glwe_infos)
+        LWEToGLWEKey::encrypt_sk_tmp_bytes(module, &lwe_to_glwe_infos)
             | GLWE::from_lwe_tmp_bytes(module, &glwe_infos, &lwe_infos, &lwe_to_glwe_infos)
             | GLWE::decrypt_tmp_bytes(module, &glwe_infos),
     );
@@ -80,7 +80,7 @@
     let mut lwe_ct: LWE<Vec<u8>> = LWE::alloc_from_infos(&lwe_infos);
     lwe_ct.encrypt_sk(module, &lwe_pt, &sk_lwe, &mut source_xa, &mut source_xe);
 
-    let mut ksk: LWEToGLWESwitchingKey<Vec<u8>> = LWEToGLWESwitchingKey::alloc_from_infos(&lwe_to_glwe_infos);
+    let mut ksk: LWEToGLWEKey<Vec<u8>> = LWEToGLWEKey::alloc_from_infos(&lwe_to_glwe_infos);
 
     ksk.encrypt_sk(
         module,
@@ -93,8 +93,7 @@ );
 
     let mut glwe_ct: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_infos);
 
-    let mut ksk_prepared: LWEToGLWESwitchingKeyPrepared<Vec<u8>, BE> =
-        LWEToGLWESwitchingKeyPrepared::alloc_from_infos(module, &ksk);
+    let mut ksk_prepared: LWEToGLWEKeyPrepared<Vec<u8>, BE> = LWEToGLWEKeyPrepared::alloc_from_infos(module, &ksk);
     ksk_prepared.prepare(module, &ksk, scratch.borrow());
 
     glwe_ct.from_lwe(module, &lwe_ct, &ksk_prepared, scratch.borrow());
@@ -114,7 +113,7 @@ + LWEDecrypt<BE>
         + GLWEDecrypt<BE>
         + GLWESecretPreparedFactory<BE>
         + GLWEToLWESwitchingKeyEncryptSk<BE>
-        + GLWEToLWESwitchingKeyPreparedFactory<BE>,
+        + GLWEToLWEKeyPreparedFactory<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
@@ -150,7 +149,7 @@ let mut source_xa: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
 
     let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
-        GLWEToLWESwitchingKey::encrypt_sk_tmp_bytes(module, &glwe_to_lwe_infos)
+        GLWEToLWEKey::encrypt_sk_tmp_bytes(module, &glwe_to_lwe_infos)
             | LWE::from_glwe_tmp_bytes(module, &lwe_infos, &glwe_infos, &glwe_to_lwe_infos)
             | GLWE::decrypt_tmp_bytes(module, &glwe_infos),
     );
@@ -178,7 +177,7 @@ &mut source_xe,
         scratch.borrow(),
     );
 
-    let mut ksk: GLWEToLWESwitchingKey<Vec<u8>> = GLWEToLWESwitchingKey::alloc_from_infos(&glwe_to_lwe_infos);
+    let mut ksk: GLWEToLWEKey<Vec<u8>> = GLWEToLWEKey::alloc_from_infos(&glwe_to_lwe_infos);
 
     ksk.encrypt_sk(
         module,
@@ -191,8 +190,7 @@ );
 
     let mut lwe_ct: LWE<Vec<u8>> = LWE::alloc_from_infos(&lwe_infos);
 
-    let mut ksk_prepared: GLWEToLWESwitchingKeyPrepared<Vec<u8>, BE> =
-        GLWEToLWESwitchingKeyPrepared::alloc_from_infos(module, &ksk);
+    let mut ksk_prepared: GLWEToLWEKeyPrepared<Vec<u8>, BE> = GLWEToLWEKeyPrepared::alloc_from_infos(module, &ksk);
     ksk_prepared.prepare(module, &ksk, scratch.borrow());
 
     lwe_ct.from_glwe(module, &glwe_ct, &ksk_prepared, scratch.borrow());