@@ -1,5 +1,5 @@
 use itertools::izip;
-use poulpy_backend::cpu_spqlios::FFT64Spqlios;
+use poulpy_backend::cpu_fft64_ref::FFT64Ref;
 use poulpy_hal::{
     api::{
         ModuleNew, ScratchOwnedAlloc, ScratchOwnedBorrow, SvpApplyDftToDftInplace, SvpPPolAlloc, SvpPrepare, VecZnxAddNormal,
@@ -16,9 +16,9 @@ let base2k: usize = 18;
     let ct_size: usize = 3;
     let msg_size: usize = 2;
     let log_scale: usize = msg_size * base2k - 5;
-    let module: Module<FFT64Spqlios> = Module::<FFT64Spqlios>::new(n as u64);
+    let module: Module<FFT64Ref> = Module::<FFT64Ref>::new(n as u64);
 
-    let mut scratch: ScratchOwned<FFT64Spqlios> = ScratchOwned::<FFT64Spqlios>::alloc(module.vec_znx_big_normalize_tmp_bytes());
+    let mut scratch: ScratchOwned<FFT64Ref> = ScratchOwned::<FFT64Ref>::alloc(module.vec_znx_big_normalize_tmp_bytes());
 
     let seed: [u8; 32] = [0; 32];
     let mut source: Source = Source::new(seed);
@@ -28,7 +28,7 @@ let mut s: ScalarZnx<Vec<u8>> = ScalarZnx::alloc(module.n(), 1);
     s.fill_ternary_prob(0, 0.5, &mut source);
 
     // Buffer to store s in the DFT domain
-    let mut s_dft: SvpPPol<Vec<u8>, FFT64Spqlios> = module.svp_ppol_alloc(s.cols());
+    let mut s_dft: SvpPPol<Vec<u8>, FFT64Ref> = module.svp_ppol_alloc(s.cols());
 
     // s_dft <- DFT(s)
     module.svp_prepare(&mut s_dft, 0, &s, 0);
@@ -43,7 +43,7 @@
     // Fill the second column with random values: ct = (0, a)
     module.vec_znx_fill_uniform(base2k, &mut ct, 1, &mut source);
 
-    let mut buf_dft: VecZnxDft<Vec<u8>, FFT64Spqlios> = module.vec_znx_dft_alloc(1, ct_size);
+    let mut buf_dft: VecZnxDft<Vec<u8>, FFT64Ref> = module.vec_znx_dft_alloc(1, ct_size);
 
     module.vec_znx_dft_apply(1, 0, &mut buf_dft, 0, &ct, 1);
 
@@ -58,7 +58,7 @@
     // Alias scratch space (VecZnxDft<B> is always at least as big as VecZnxBig<B>)
 
     // BIG(ct[1] * s) <- IDFT(DFT(ct[1] * s)) (not normalized)
-    let mut buf_big: VecZnxBig<Vec<u8>, FFT64Spqlios> = module.vec_znx_big_alloc(1, ct_size);
+    let mut buf_big: VecZnxBig<Vec<u8>, FFT64Ref> = module.vec_znx_big_alloc(1, ct_size);
     module.vec_znx_idft_apply_tmpa(&mut buf_big, 0, &mut buf_dft, 0);
 
     // Creates a plaintext: VecZnx with 1 column

@@ -7,7 +7,6 @@ mod vec_znx;
 mod vec_znx_big;
 mod vec_znx_dft;
 mod vmp;
-mod zn;
 mod znx_avx;
 
 pub struct FFT64Avx {}

@@ -1,73 +0,0 @@
-use poulpy_hal::{
-    api::TakeSlice,
-    layouts::{Scratch, ZnToMut},
-    oep::{TakeSliceImpl, ZnAddNormalImpl, ZnFillNormalImpl, ZnFillUniformImpl, ZnNormalizeInplaceImpl, ZnNormalizeTmpBytesImpl},
-    reference::zn::{zn_add_normal, zn_fill_normal, zn_fill_uniform, zn_normalize_inplace, zn_normalize_tmp_bytes},
-    source::Source,
-};
-
-use crate::cpu_fft64_avx::FFT64Avx;
-
-unsafe impl ZnNormalizeTmpBytesImpl<Self> for FFT64Avx {
-    fn zn_normalize_tmp_bytes_impl(n: usize) -> usize {
-        zn_normalize_tmp_bytes(n)
-    }
-}
-
-unsafe impl ZnNormalizeInplaceImpl<Self> for FFT64Avx
-where
-    Self: TakeSliceImpl<Self>,
-{
-    fn zn_normalize_inplace_impl<R>(n: usize, base2k: usize, res: &mut R, res_col: usize, scratch: &mut Scratch<Self>)
-    where
-        R: ZnToMut,
-    {
-        let (carry, _) = scratch.take_slice(n);
-        zn_normalize_inplace::<R, FFT64Avx>(n, base2k, res, res_col, carry);
-    }
-}
-
-unsafe impl ZnFillUniformImpl<Self> for FFT64Avx {
-    fn zn_fill_uniform_impl<R>(n: usize, base2k: usize, res: &mut R, res_col: usize, source: &mut Source)
-    where
-        R: ZnToMut,
-    {
-        zn_fill_uniform(n, base2k, res, res_col, source);
-    }
-}
-
-unsafe impl ZnFillNormalImpl<Self> for FFT64Avx {
-    #[allow(clippy::too_many_arguments)]
-    fn zn_fill_normal_impl<R>(
-        n: usize,
-        base2k: usize,
-        res: &mut R,
-        res_col: usize,
-        k: usize,
-        source: &mut Source,
-        sigma: f64,
-        bound: f64,
-    ) where
-        R: ZnToMut,
-    {
-        zn_fill_normal(n, base2k, res, res_col, k, source, sigma, bound);
-    }
-}
-
-unsafe impl ZnAddNormalImpl<Self> for FFT64Avx {
-    #[allow(clippy::too_many_arguments)]
-    fn zn_add_normal_impl<R>(
-        n: usize,
-        base2k: usize,
-        res: &mut R,
-        res_col: usize,
-        k: usize,
-        source: &mut Source,
-        sigma: f64,
-        bound: f64,
-    ) where
-        R: ZnToMut,
-    {
-        zn_add_normal(n, base2k, res, res_col, k, source, sigma, bound);
-    }
-}

@@ -6,7 +6,6 @@ mod vec_znx;
 mod vec_znx_big;
 mod vec_znx_dft;
 mod vmp;
-mod zn;
 mod znx;
 
 #[cfg(test)]

@@ -1,73 +0,0 @@
-use poulpy_hal::{
-    api::TakeSlice,
-    layouts::{Scratch, ZnToMut},
-    oep::{TakeSliceImpl, ZnAddNormalImpl, ZnFillNormalImpl, ZnFillUniformImpl, ZnNormalizeInplaceImpl, ZnNormalizeTmpBytesImpl},
-    reference::zn::{zn_add_normal, zn_fill_normal, zn_fill_uniform, zn_normalize_inplace, zn_normalize_tmp_bytes},
-    source::Source,
-};
-
-use crate::cpu_fft64_ref::FFT64Ref;
-
-unsafe impl ZnNormalizeTmpBytesImpl<Self> for FFT64Ref {
-    fn zn_normalize_tmp_bytes_impl(n: usize) -> usize {
-        zn_normalize_tmp_bytes(n)
-    }
-}
-
-unsafe impl ZnNormalizeInplaceImpl<Self> for FFT64Ref
-where
-    Self: TakeSliceImpl<Self>,
-{
-    fn zn_normalize_inplace_impl<R>(n: usize, base2k: usize, res: &mut R, res_col: usize, scratch: &mut Scratch<Self>)
-    where
-        R: ZnToMut,
-    {
-        let (carry, _) = scratch.take_slice(n);
-        zn_normalize_inplace::<R, FFT64Ref>(n, base2k, res, res_col, carry);
-    }
-}
-
-unsafe impl ZnFillUniformImpl<Self> for FFT64Ref {
-    fn zn_fill_uniform_impl<R>(n: usize, base2k: usize, res: &mut R, res_col: usize, source: &mut Source)
-    where
-        R: ZnToMut,
-    {
-        zn_fill_uniform(n, base2k, res, res_col, source);
-    }
-}
-
-unsafe impl ZnFillNormalImpl<Self> for FFT64Ref {
-    #[allow(clippy::too_many_arguments)]
-    fn zn_fill_normal_impl<R>(
-        n: usize,
-        base2k: usize,
-        res: &mut R,
-        res_col: usize,
-        k: usize,
-        source: &mut Source,
-        sigma: f64,
-        bound: f64,
-    ) where
-        R: ZnToMut,
-    {
-        zn_fill_normal(n, base2k, res, res_col, k, source, sigma, bound);
-    }
-}
-
-unsafe impl ZnAddNormalImpl<Self> for FFT64Ref {
-    #[allow(clippy::too_many_arguments)]
-    fn zn_add_normal_impl<R>(
-        n: usize,
-        base2k: usize,
-        res: &mut R,
-        res_col: usize,
-        k: usize,
-        source: &mut Source,
-        sigma: f64,
-        bound: f64,
-    ) where
-        R: ZnToMut,
-    {
-        zn_add_normal(n, base2k, res, res_col, k, source, sigma, bound);
-    }
-}

@@ -5,7 +5,6 @@ mod vec_znx;
 mod vec_znx_big;
 mod vec_znx_dft;
 mod vmp_pmat;
-mod zn;
 mod znx;
 
 pub struct FFT64Spqlios;

@@ -1,82 +0,0 @@
-use poulpy_hal::{
-    api::TakeSlice,
-    layouts::{Scratch, Zn, ZnToMut, ZnxInfos, ZnxSliceSize, ZnxView, ZnxViewMut},
-    oep::{TakeSliceImpl, ZnAddNormalImpl, ZnFillNormalImpl, ZnFillUniformImpl, ZnNormalizeInplaceImpl},
-    reference::zn::{zn_add_normal, zn_fill_normal, zn_fill_uniform},
-    source::Source,
-};
-
-use crate::cpu_spqlios::{FFT64Spqlios, ffi::zn64};
-
-unsafe impl ZnNormalizeInplaceImpl<Self> for FFT64Spqlios
-where
-    Self: TakeSliceImpl<Self>,
-{
-    fn zn_normalize_inplace_impl<A>(n: usize, base2k: usize, a: &mut A, a_col: usize, scratch: &mut Scratch<Self>)
-    where
-        A: ZnToMut,
-    {
-        let mut a: Zn<&mut [u8]> = a.to_mut();
-
-        let (tmp_bytes, _) = scratch.take_slice(n * size_of::<i64>());
-
-        unsafe {
-            zn64::zn64_normalize_base2k_ref(
-                n as u64,
-                base2k as u64,
-                a.at_mut_ptr(a_col, 0),
-                a.size() as u64,
-                a.sl() as u64,
-                a.at_ptr(a_col, 0),
-                a.size() as u64,
-                a.sl() as u64,
-                tmp_bytes.as_mut_ptr(),
-            );
-        }
-    }
-}
-
-unsafe impl ZnFillUniformImpl<Self> for FFT64Spqlios {
-    fn zn_fill_uniform_impl<R>(n: usize, base2k: usize, res: &mut R, res_col: usize, source: &mut Source)
-    where
-        R: ZnToMut,
-    {
-        zn_fill_uniform(n, base2k, res, res_col, source);
-    }
-}
-
-unsafe impl ZnFillNormalImpl<Self> for FFT64Spqlios {
-    #[allow(clippy::too_many_arguments)]
-    fn zn_fill_normal_impl<R>(
-        n: usize,
-        base2k: usize,
-        res: &mut R,
-        res_col: usize,
-        k: usize,
-        source: &mut Source,
-        sigma: f64,
-        bound: f64,
-    ) where
-        R: ZnToMut,
-    {
-        zn_fill_normal(n, base2k, res, res_col, k, source, sigma, bound);
-    }
-}
-
-unsafe impl ZnAddNormalImpl<Self> for FFT64Spqlios {
-    #[allow(clippy::too_many_arguments)]
-    fn zn_add_normal_impl<R>(
-        n: usize,
-        base2k: usize,
-        res: &mut R,
-        res_col: usize,
-        k: usize,
-        source: &mut Source,
-        sigma: f64,
-        bound: f64,
-    ) where
-        R: ZnToMut,
-    {
-        zn_add_normal(n, base2k, res, res_col, k, source, sigma, bound);
-    }
-}

@@ -55,7 +55,11 @@ R: GGLWEInfos,
         A: GGLWEInfos,
         K: GGLWEInfos,
     {
-        self.glwe_keyswitch_tmp_bytes(res_infos, a_infos, key_infos)
+        if res_infos.glwe_layout() == a_infos.glwe_layout() {
+            self.glwe_keyswitch_tmp_bytes(res_infos, a_infos, key_infos)
+        } else {
+            self.glwe_keyswitch_tmp_bytes(res_infos, a_infos, key_infos) + GLWE::bytes_of_from_infos(a_infos)
+        }
     }
 
     fn glwe_automorphism_key_automorphism<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
@@ -79,11 +83,15 @@ res.dsize(),
             a.dsize()
         );
 
+        assert_eq!(res.base2k(), a.base2k());
+
         let cols_out: usize = (key.rank_out() + 1).into();
         let cols_in: usize = key.rank_in().into();
 
         let p: i64 = a.p();
         let p_inv: i64 = self.galois_element_inv(p);
+
+        let same_layout: bool = res.glwe_layout() == a.glwe_layout();
 
         {
             let res: &mut GGLWE<&mut [u8]> = &mut res.to_mut();
@@ -94,18 +102,30 @@ for col in 0..cols_in {
                     let mut res_tmp: GLWE<&mut [u8]> = res.at_mut(row, col);
                     let a_ct: GLWE<&[u8]> = a.at(row, col);
 
-                    // Reverts the automorphism X^{-k}: (-pi^{-1}_{k}(s)a + s, a) to (-sa + pi_{k}(s), a)
-                    for i in 0..cols_out {
-                        self.vec_znx_automorphism(p, res_tmp.data_mut(), i, &a_ct.data, i);
-                    }
+                    if same_layout {
+                        // Reverts the automorphism X^{-k}: (-pi^{-1}_{k}(s)a + s, a) to (-sa + pi_{k}(s), a)
+                        for i in 0..cols_out {
+                            self.vec_znx_automorphism(p, res_tmp.data_mut(), i, &a_ct.data, i);
+                        }
 
-                    // Key-switch (-sa + pi_{k}(s), a) to (-pi^{-1}_{k'}(s)a + pi_{k}(s), a)
-                    self.glwe_keyswitch_inplace(&mut res_tmp, key, scratch);
+                        // Key-switch (-sa + pi_{k}(s), a) to (-pi^{-1}_{k'}(s)a + pi_{k}(s), a)
+                        self.glwe_keyswitch_inplace(&mut res_tmp, key, scratch);
+                    } else {
+                        let (mut tmp_glwe, scratch_1) = scratch.take_glwe(a);
+
+                        // Reverts the automorphism X^{-k}: (-pi^{-1}_{k}(s)a + s, a) to (-sa + pi_{k}(s), a)
+                        for i in 0..cols_out {
+                            self.vec_znx_automorphism(p, tmp_glwe.data_mut(), i, &a_ct.data, i);
+                        }
+
+                        // Key-switch (-sa + pi_{k}(s), a) to (-pi^{-1}_{k'}(s)a + pi_{k}(s), a)
+                        self.glwe_keyswitch(&mut res_tmp, &tmp_glwe, key, scratch_1);
+                    }
 
                     // Applies back the automorphism X^{-k}: (-pi^{-1}_{k'}(s)a + pi_{k}(s), a) to (-pi^{-1}_{k'+k}(s)a + s, a)
-                    (0..cols_out).for_each(|i| {
+                    for i in 0..cols_out {
                         self.vec_znx_automorphism_inplace(p_inv, res_tmp.data_mut(), i, scratch);
-                    });
+                    }
                 }
             }
         }

@@ -34,9 +34,9 @@
 impl<D: DataMut> GGSW<D> {
     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,
+        A: GGSWToRef + GGSWInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
-        T: GGLWEToGGSWKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
         M: GGSWAutomorphism<BE>,
     {
@@ -73,19 +73,20 @@ }
 
     fn ggsw_automorphism<R, A, K, T>(&self, res: &mut R, a: &A, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
-        R: GGSWToMut,
-        A: GGSWToRef,
+        R: GGSWToMut + GGSWInfos,
+        A: GGSWToRef + GGSWInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
-        T: GGLWEToGGSWKeyPreparedToRef<BE>,
+        T: GGLWEToGGSWKeyPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
+        assert_eq!(res.dsize(), a.dsize());
+        assert_eq!(res.base2k(), a.base2k());
+        assert!(res.dnum() <= a.dnum());
+        assert!(scratch.available() >= self.ggsw_automorphism_tmp_bytes(res, a, key, tsk));
+
         let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
         let a: &GGSW<&[u8]> = &a.to_ref();
         let tsk: &GGLWEToGGSWKeyPrepared<&[u8], BE> = &tsk.to_ref();
-
-        assert_eq!(res.dsize(), a.dsize());
-        assert!(res.dnum() <= a.dnum());
-        assert!(scratch.available() >= self.ggsw_automorphism_tmp_bytes(res, a, key, tsk));
 
         // Keyswitch the j-th row of the col 0
         for row in 0..res.dnum().as_usize() {

@@ -7,8 +7,8 @@ layouts::{Backend, DataMut, Module, Scratch, VecZnxBig},
 };
 
 use crate::{
-    GLWEKeySwitchInternal, GLWEKeyswitch, ScratchTakeCore,
-    layouts::{GGLWEInfos, GGLWEPreparedToRef, GLWE, GLWEInfos, GLWEToMut, GLWEToRef, GetGaloisElement, LWEInfos},
+    GLWEKeySwitchInternal, GLWEKeyswitch, GLWENormalize, ScratchTakeCore,
+    layouts::{GGLWEInfos, GGLWEPreparedToRef, GLWE, GLWEInfos, GLWELayout, GLWEToMut, GLWEToRef, GetGaloisElement, LWEInfos},
 };
 
 impl GLWE<Vec<u8>> {
@@ -164,7 +164,8 @@ + VecZnxBigAutomorphismInplace<BE>
         + VecZnxBigSubSmallInplace<BE>
         + VecZnxBigSubSmallNegateInplace<BE>
         + VecZnxBigAddSmallInplace<BE>
-        + VecZnxBigNormalize<BE>,
+        + VecZnxBigNormalize<BE>
+        + GLWENormalize<BE>,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
     fn glwe_automorphism_tmp_bytes<R, A, K>(&self, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
@@ -217,22 +218,50 @@ {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         let a: &GLWE<&[u8]> = &a.to_ref();
 
+        let base2k_a: usize = a.base2k().into();
+        let base2k_key: usize = key.base2k().into();
+        let base2k_res: usize = res.base2k().into();
+
         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> = 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);
-            self.vec_znx_big_add_small_inplace(&mut res_big, i, a.data(), i);
-            self.vec_znx_big_normalize(
-                res.base2k().into(),
-                res.data_mut(),
-                i,
-                key.base2k().into(),
-                &res_big,
-                i,
-                scratch_1,
-            );
-        }
+        if base2k_a != base2k_key {
+            let (mut a_conv, scratch_2) = scratch_1.take_glwe(&GLWELayout {
+                n: a.n(),
+                base2k: key.base2k(),
+                k: a.k(),
+                rank: a.rank(),
+            });
+            self.glwe_normalize(&mut a_conv, a, scratch_2);
+            let mut res_big: VecZnxBig<&mut [u8], BE> = self.glwe_keyswitch_internal(res_dft, &a_conv, key, scratch_2);
+            for i in 0..res.rank().as_usize() + 1 {
+                self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_2);
+                self.vec_znx_big_add_small_inplace(&mut res_big, i, a_conv.data(), i);
+                self.vec_znx_big_normalize(
+                    base2k_res,
+                    res.data_mut(),
+                    i,
+                    base2k_key,
+                    &res_big,
+                    i,
+                    scratch_2,
+                );
+            }
+        } else {
+            let mut res_big: VecZnxBig<&mut [u8], 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);
+                self.vec_znx_big_add_small_inplace(&mut res_big, i, a.data(), i);
+                self.vec_znx_big_normalize(
+                    base2k_res,
+                    res.data_mut(),
+                    i,
+                    base2k_key,
+                    &res_big,
+                    i,
+                    scratch_1,
+                );
+            }
+        };
     }
 
     fn glwe_automorphism_add_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
@@ -243,22 +272,49 @@ Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
 
+        let base2k_key: usize = key.base2k().into();
+        let base2k_res: usize = res.base2k().into();
+
         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> = 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);
-            self.vec_znx_big_add_small_inplace(&mut res_big, i, res.data(), i);
-            self.vec_znx_big_normalize(
-                res.base2k().into(),
-                res.data_mut(),
-                i,
-                key.base2k().into(),
-                &res_big,
-                i,
-                scratch_1,
-            );
-        }
+        if base2k_res != base2k_key {
+            let (mut res_conv, scratch_2) = scratch_1.take_glwe(&GLWELayout {
+                n: res.n(),
+                base2k: key.base2k(),
+                k: res.k(),
+                rank: res.rank(),
+            });
+            self.glwe_normalize(&mut res_conv, res, scratch_2);
+            let mut res_big: VecZnxBig<&mut [u8], BE> = self.glwe_keyswitch_internal(res_dft, &res_conv, key, scratch_2);
+            for i in 0..res.rank().as_usize() + 1 {
+                self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_2);
+                self.vec_znx_big_add_small_inplace(&mut res_big, i, res_conv.data(), i);
+                self.vec_znx_big_normalize(
+                    base2k_res,
+                    res.data_mut(),
+                    i,
+                    base2k_key,
+                    &res_big,
+                    i,
+                    scratch_2,
+                );
+            }
+        } else {
+            let mut res_big: VecZnxBig<&mut [u8], 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);
+                self.vec_znx_big_add_small_inplace(&mut res_big, i, res.data(), i);
+                self.vec_znx_big_normalize(
+                    base2k_res,
+                    res.data_mut(),
+                    i,
+                    base2k_key,
+                    &res_big,
+                    i,
+                    scratch_1,
+                );
+            }
+        };
     }
 
     fn glwe_automorphism_sub<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
@@ -271,22 +327,50 @@ {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         let a: &GLWE<&[u8]> = &a.to_ref();
 
+        let base2k_a: usize = a.base2k().into();
+        let base2k_key: usize = key.base2k().into();
+        let base2k_res: usize = res.base2k().into();
+
         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> = 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);
-            self.vec_znx_big_sub_small_inplace(&mut res_big, i, a.data(), i);
-            self.vec_znx_big_normalize(
-                res.base2k().into(),
-                res.data_mut(),
-                i,
-                key.base2k().into(),
-                &res_big,
-                i,
-                scratch_1,
-            );
-        }
+        if base2k_a != base2k_key {
+            let (mut a_conv, scratch_2) = scratch_1.take_glwe(&GLWELayout {
+                n: a.n(),
+                base2k: key.base2k(),
+                k: a.k(),
+                rank: a.rank(),
+            });
+            self.glwe_normalize(&mut a_conv, a, scratch_2);
+            let mut res_big: VecZnxBig<&mut [u8], BE> = self.glwe_keyswitch_internal(res_dft, &a_conv, key, scratch_2);
+            for i in 0..res.rank().as_usize() + 1 {
+                self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_2);
+                self.vec_znx_big_sub_small_inplace(&mut res_big, i, a_conv.data(), i);
+                self.vec_znx_big_normalize(
+                    base2k_res,
+                    res.data_mut(),
+                    i,
+                    base2k_key,
+                    &res_big,
+                    i,
+                    scratch_2,
+                );
+            }
+        } else {
+            let mut res_big: VecZnxBig<&mut [u8], 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);
+                self.vec_znx_big_sub_small_inplace(&mut res_big, i, a.data(), i);
+                self.vec_znx_big_normalize(
+                    base2k_res,
+                    res.data_mut(),
+                    i,
+                    base2k_key,
+                    &res_big,
+                    i,
+                    scratch_1,
+                );
+            }
+        };
     }
 
     fn glwe_automorphism_sub_negate<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
@@ -299,22 +383,50 @@ {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         let a: &GLWE<&[u8]> = &a.to_ref();
 
+        let base2k_a: usize = a.base2k().into();
+        let base2k_key: usize = key.base2k().into();
+        let base2k_res: usize = res.base2k().into();
+
         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> = 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);
-            self.vec_znx_big_sub_small_negate_inplace(&mut res_big, i, a.data(), i);
-            self.vec_znx_big_normalize(
-                res.base2k().into(),
-                res.data_mut(),
-                i,
-                key.base2k().into(),
-                &res_big,
-                i,
-                scratch_1,
-            );
-        }
+        if base2k_a != base2k_key {
+            let (mut a_conv, scratch_2) = scratch_1.take_glwe(&GLWELayout {
+                n: a.n(),
+                base2k: key.base2k(),
+                k: a.k(),
+                rank: a.rank(),
+            });
+            self.glwe_normalize(&mut a_conv, a, scratch_2);
+            let mut res_big: VecZnxBig<&mut [u8], BE> = self.glwe_keyswitch_internal(res_dft, &a_conv, key, scratch_2);
+            for i in 0..res.rank().as_usize() + 1 {
+                self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_2);
+                self.vec_znx_big_sub_small_negate_inplace(&mut res_big, i, a_conv.data(), i);
+                self.vec_znx_big_normalize(
+                    base2k_res,
+                    res.data_mut(),
+                    i,
+                    base2k_key,
+                    &res_big,
+                    i,
+                    scratch_2,
+                );
+            }
+        } else {
+            let mut res_big: VecZnxBig<&mut [u8], 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);
+                self.vec_znx_big_sub_small_negate_inplace(&mut res_big, i, a.data(), i);
+                self.vec_znx_big_normalize(
+                    base2k_res,
+                    res.data_mut(),
+                    i,
+                    base2k_key,
+                    &res_big,
+                    i,
+                    scratch_1,
+                );
+            }
+        };
     }
 
     fn glwe_automorphism_sub_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
@@ -325,22 +437,49 @@ Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
 
+        let base2k_key: usize = key.base2k().into();
+        let base2k_res: usize = res.base2k().into();
+
         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> = 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);
-            self.vec_znx_big_sub_small_inplace(&mut res_big, i, res.data(), i);
-            self.vec_znx_big_normalize(
-                res.base2k().into(),
-                res.data_mut(),
-                i,
-                key.base2k().into(),
-                &res_big,
-                i,
-                scratch_1,
-            );
-        }
+        if base2k_res != base2k_key {
+            let (mut res_conv, scratch_2) = scratch_1.take_glwe(&GLWELayout {
+                n: res.n(),
+                base2k: key.base2k(),
+                k: res.k(),
+                rank: res.rank(),
+            });
+            self.glwe_normalize(&mut res_conv, res, scratch_2);
+            let mut res_big: VecZnxBig<&mut [u8], BE> = self.glwe_keyswitch_internal(res_dft, &res_conv, key, scratch_2);
+            for i in 0..res.rank().as_usize() + 1 {
+                self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_2);
+                self.vec_znx_big_sub_small_inplace(&mut res_big, i, res_conv.data(), i);
+                self.vec_znx_big_normalize(
+                    base2k_res,
+                    res.data_mut(),
+                    i,
+                    base2k_key,
+                    &res_big,
+                    i,
+                    scratch_2,
+                );
+            }
+        } else {
+            let mut res_big: VecZnxBig<&mut [u8], 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);
+                self.vec_znx_big_sub_small_inplace(&mut res_big, i, res.data(), i);
+                self.vec_znx_big_normalize(
+                    base2k_res,
+                    res.data_mut(),
+                    i,
+                    base2k_key,
+                    &res_big,
+                    i,
+                    scratch_1,
+                );
+            }
+        };
     }
 
     fn glwe_automorphism_sub_negate_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
@@ -350,22 +489,49 @@ K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+
+        let base2k_key: usize = key.base2k().into();
+        let base2k_res: usize = res.base2k().into();
 
         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> = 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);
-            self.vec_znx_big_sub_small_negate_inplace(&mut res_big, i, res.data(), i);
-            self.vec_znx_big_normalize(
-                res.base2k().into(),
-                res.data_mut(),
-                i,
-                key.base2k().into(),
-                &res_big,
-                i,
-                scratch_1,
-            );
-        }
+        if base2k_res != base2k_key {
+            let (mut res_conv, scratch_2) = scratch_1.take_glwe(&GLWELayout {
+                n: res.n(),
+                base2k: key.base2k(),
+                k: res.k(),
+                rank: res.rank(),
+            });
+            self.glwe_normalize(&mut res_conv, res, scratch_2);
+            let mut res_big: VecZnxBig<&mut [u8], BE> = self.glwe_keyswitch_internal(res_dft, &res_conv, key, scratch_2);
+            for i in 0..res.rank().as_usize() + 1 {
+                self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_2);
+                self.vec_znx_big_sub_small_negate_inplace(&mut res_big, i, res_conv.data(), i);
+                self.vec_znx_big_normalize(
+                    base2k_res,
+                    res.data_mut(),
+                    i,
+                    base2k_key,
+                    &res_big,
+                    i,
+                    scratch_2,
+                );
+            }
+        } else {
+            let mut res_big: VecZnxBig<&mut [u8], 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);
+                self.vec_znx_big_sub_small_negate_inplace(&mut res_big, i, res.data(), i);
+                self.vec_znx_big_normalize(
+                    base2k_res,
+                    res.data_mut(),
+                    i,
+                    base2k_key,
+                    &res_big,
+                    i,
+                    scratch_1,
+                );
+            }
+        };
     }
 }

@@ -1,9 +1,9 @@
 use poulpy_hal::{
     api::{
         ScratchAvailable, ScratchTakeBasic, VecZnxBigAddSmallInplace, VecZnxBigBytesOf, VecZnxBigNormalize,
-        VecZnxBigNormalizeTmpBytes, VecZnxDftApply, VecZnxDftBytesOf, VecZnxIdftApplyConsume, VecZnxNormalize,
+        VecZnxBigNormalizeTmpBytes, VecZnxCopy, VecZnxDftApply, VecZnxDftBytesOf, VecZnxIdftApplyConsume, VecZnxNormalize,
     },
-    layouts::{Backend, DataMut, Module, Scratch, VecZnxBig},
+    layouts::{Backend, DataMut, Module, Scratch, VecZnx, VecZnxBig, VecZnxDft, VecZnxDftToRef, VecZnxToRef},
 };
 
 use crate::{
@@ -65,6 +65,7 @@ assert_eq!(res.dnum(), a.dnum());
         assert_eq!(res.n(), self.n() as u32);
         assert_eq!(a.n(), self.n() as u32);
         assert_eq!(tsk.n(), self.n() as u32);
+        assert_eq!(res.base2k(), a.base2k());
 
         for row in 0..res.dnum().into() {
             self.glwe_copy(&mut res.at_mut(row, 0), &a.at(row, 0));
@@ -111,28 +112,29 @@ + VecZnxDftBytesOf
         + VecZnxDftApply<BE>
         + VecZnxNormalize<BE>
         + VecZnxBigAddSmallInplace<BE>
-        + VecZnxIdftApplyConsume<BE>,
+        + VecZnxIdftApplyConsume<BE>
+        + VecZnxCopy,
 {
     fn ggsw_expand_rows_tmp_bytes<R, A>(&self, res_infos: &R, tsk_infos: &A) -> usize
     where
         R: GGSWInfos,
         A: GGLWEInfos,
     {
-        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 res_size = res_infos.size();
-        let a_size: usize = (res_infos.size() * base2k_in).div_ceil(base2k_tsk);
+        let res_size: usize = res_infos.size();
+        let a_size: usize = res_infos.max_k().as_usize().div_ceil(base2k_tsk);
 
-        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 a_0: usize = VecZnx::bytes_of(self.n(), 1, a_size);
+        let a_dft: usize = self.bytes_of_vec_znx_dft(cols - 1, a_size);
+        let res_dft: usize = 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();
+        let normalize: usize = self.vec_znx_big_normalize_tmp_bytes();
 
-        (a_dft + res_dft + gglwe_prod).max(normalize)
+        (a_0 + a_dft + res_dft + gglwe_prod).max(normalize)
     }
 
     fn ggsw_expand_row<R, T>(&self, res: &mut R, tsk: &T, scratch: &mut Scratch<BE>)
@@ -144,7 +146,7 @@ {
         let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
         let tsk: &GGLWEToGGSWKeyPrepared<&[u8], BE> = &tsk.to_ref();
 
-        let base2k_in: usize = res.base2k().into();
+        let base2k_res: usize = res.base2k().into();
         let base2k_tsk: usize = tsk.base2k().into();
 
         assert!(scratch.available() >= self.ggsw_expand_rows_tmp_bytes(res, tsk));
@@ -152,96 +154,129 @@
         let rank: usize = res.rank().into();
         let cols: usize = rank + 1;
 
-        let a_size: usize = (res.size() * base2k_in).div_ceil(base2k_tsk);
+        let res_conv_size: usize = res.max_k().as_usize().div_ceil(base2k_tsk);
+
+        let (mut a_dft, scratch_1) = scratch.take_vec_znx_dft(self, cols - 1, res_conv_size);
+        let (mut a_0, scratch_2) = scratch_1.take_vec_znx(self.n(), 1, res_conv_size);
 
         // Keyswitch the j-th row of the col 0
         for row in 0..res.dnum().as_usize() {
-            let (mut a_dft, scratch_1) = scratch.take_vec_znx_dft(self, cols - 1, a_size);
-
-            {
-                let glwe_mi_1: &GLWE<&[u8]> = &res.at(row, 0);
+            let glwe_mi_1: &GLWE<&[u8]> = &res.at(row, 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);
-                    }
+            if base2k_res == 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);
                 }
+                self.vec_znx_copy(&mut a_0, 0, glwe_mi_1.data(), 0);
+            } else {
+                for i in 0..cols - 1 {
+                    self.vec_znx_normalize(
+                        base2k_tsk,
+                        &mut a_0,
+                        0,
+                        base2k_res,
+                        glwe_mi_1.data(),
+                        i + 1,
+                        scratch_2,
+                    );
+                    self.vec_znx_dft_apply(1, 0, &mut a_dft, i, &a_0, 0);
+                }
+                self.vec_znx_normalize(
+                    base2k_tsk,
+                    &mut a_0,
+                    0,
+                    base2k_res,
+                    glwe_mi_1.data(),
+                    0,
+                    scratch_2,
+                );
             }
 
-            // 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
+            ggsw_expand_rows_internal(self, row, res, &a_0, &a_dft, tsk, scratch_2)
+        }
+    }
+}
+
+fn ggsw_expand_rows_internal<M, R, C, A, T, BE: Backend>(
+    module: &M,
+    row: usize,
+    res: &mut R,
+    a_0: &C,
+    a_dft: &A,
+    tsk: &T,
+    scratch: &mut Scratch<BE>,
+) where
+    R: GGSWToMut,
+    C: VecZnxToRef,
+    A: VecZnxDftToRef<BE>,
+    M: GGLWEProduct<BE> + VecZnxIdftApplyConsume<BE> + VecZnxBigAddSmallInplace<BE> + VecZnxBigNormalize<BE>,
+    T: GGLWEToGGSWKeyPreparedToRef<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
+{
+    let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
+    let a_0: &VecZnx<&[u8]> = &a_0.to_ref();
+    let a_dft: &VecZnxDft<&[u8], BE> = &a_dft.to_ref();
+    let tsk: &GGLWEToGGSWKeyPrepared<&[u8], BE> = &tsk.to_ref();
+    let cols: usize = res.rank().as_usize() + 1;
+
+    // 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_1) = scratch.take_vec_znx_dft(module, cols, tsk.size()); // Todo optimise
 
-                // 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)
-                self.gglwe_product_dft(&mut res_dft, &a_dft, tsk.at(col - 1), scratch_2);
+        // 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)
+        module.gglwe_product_dft(&mut res_dft, a_dft, tsk.at(col - 1), scratch_1);
 
-                let mut res_big: VecZnxBig<&mut [u8], BE> = self.vec_znx_idft_apply_consume(res_dft);
+        let mut res_big: VecZnxBig<&mut [u8], BE> = module.vec_znx_idft_apply_consume(res_dft);
 
-                // Adds -(sum a[i] * s[i]) + m)  on the i-th column of tmp_idft_i
-                //
-                // (-(x0s0 + x1s1 + x2s2) + a0s0s0 + a1s0s1 + a2s0s2, x0, x1, x2)
-                // +
-                // (0, -(a0s0 + a1s1 + a2s2) + M[i], 0, 0)
-                // =
-                // (-(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_big_add_small_inplace(&mut res_big, col, res.at(row, 0).data(), 0);
+        // Adds -(sum a[i] * s[i]) + m)  on the i-th column of tmp_idft_i
+        //
+        // (-(x0s0 + x1s1 + x2s2) + a0s0s0 + a1s0s1 + a2s0s2, x0, x1, x2)
+        // +
+        // (0, -(a0s0 + a1s1 + a2s2) + M[i], 0, 0)
+        // =
+        // (-(x0s0 + x1s1 + x2s2) + s0(a0s0 + a1s1 + a2s2), x0 -(a0s0 + a1s1 + a2s2) + M[i], x1, x2)
+        // =
+        // (-(x0s0 + x1s1 + x2s2), x0 + M[i], x1, x2)
+        module.vec_znx_big_add_small_inplace(&mut res_big, col, a_0, 0);
 
-                for j in 0..cols {
-                    self.vec_znx_big_normalize(
-                        res.base2k().as_usize(),
-                        res.at_mut(row, col).data_mut(),
-                        j,
-                        tsk.base2k().as_usize(),
-                        &res_big,
-                        j,
-                        scratch_2,
-                    );
-                }
-            }
+        for j in 0..cols {
+            module.vec_znx_big_normalize(
+                res.base2k().as_usize(),
+                res.at_mut(row, col).data_mut(),
+                j,
+                tsk.base2k().as_usize(),
+                &res_big,
+                j,
+                scratch_1,
+            );
         }
     }
 }

@@ -1,39 +1,44 @@
 use poulpy_hal::{
-    api::{ScratchOwnedAlloc, ScratchOwnedBorrow, ZnNormalizeInplace},
-    layouts::{Backend, DataMut, DataRef, Module, ScratchOwned, ZnxView, ZnxViewMut},
+    api::VecZnxNormalizeInplace,
+    layouts::{Backend, DataMut, DataRef, Module, Scratch, ZnxView, ZnxViewMut},
 };
 
-use crate::layouts::{LWE, LWEInfos, LWEPlaintext, LWEPlaintextToMut, LWESecret, LWESecretToRef, LWEToMut};
+use crate::{
+    ScratchTakeCore,
+    layouts::{LWE, LWEInfos, LWEPlaintext, LWEPlaintextToMut, LWESecret, LWESecretToRef, LWEToMut},
+};
 
 impl<DataSelf: DataRef + DataMut> LWE<DataSelf> {
-    pub fn decrypt<P, S, M, B: Backend>(&mut self, module: &M, pt: &mut P, sk: &S)
+    pub fn decrypt<P, S, M, BE: Backend>(&mut self, module: &M, pt: &mut P, sk: &S, scratch: &mut Scratch<BE>)
     where
         P: LWEPlaintextToMut,
         S: LWESecretToRef,
-        M: LWEDecrypt<B>,
+        M: LWEDecrypt<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        module.lwe_decrypt(self, pt, sk);
+        module.lwe_decrypt(self, pt, sk, scratch);
     }
 }
 
 pub trait LWEDecrypt<BE: Backend> {
-    fn lwe_decrypt<R, P, S>(&self, res: &mut R, pt: &mut P, sk: &S)
+    fn lwe_decrypt<R, P, S>(&self, res: &mut R, pt: &mut P, sk: &S, scratch: &mut Scratch<BE>)
     where
         R: LWEToMut,
         P: LWEPlaintextToMut,
-        S: LWESecretToRef;
+        S: LWESecretToRef,
+        Scratch<BE>: ScratchTakeCore<BE>;
 }
 
 impl<BE: Backend> LWEDecrypt<BE> for Module<BE>
 where
-    Self: Sized + ZnNormalizeInplace<BE>,
-    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+    Self: Sized + VecZnxNormalizeInplace<BE>,
 {
-    fn lwe_decrypt<R, P, S>(&self, res: &mut R, pt: &mut P, sk: &S)
+    fn lwe_decrypt<R, P, S>(&self, res: &mut R, pt: &mut P, sk: &S, scratch: &mut Scratch<BE>)
     where
         R: LWEToMut,
         P: LWEPlaintextToMut,
         S: LWESecretToRef,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut LWE<&mut [u8]> = &mut res.to_mut();
         let pt: &mut LWEPlaintext<&mut [u8]> = &mut pt.to_mut();
@@ -52,13 +57,7 @@ .zip(sk.data.at(0, 0))
                     .map(|(x, y)| x * y)
                     .sum::<i64>();
         });
-        self.zn_normalize_inplace(
-            1,
-            res.base2k().into(),
-            &mut pt.data,
-            0,
-            ScratchOwned::alloc(size_of::<i64>()).borrow(),
-        );
+        self.vec_znx_normalize_inplace(res.base2k().into(), &mut pt.data, 0, scratch);
         pt.base2k = res.base2k();
         pt.k = crate::layouts::TorusPrecision(res.k().0.min(pt.size() as u32 * res.base2k().0));
     }

@@ -1,43 +1,67 @@
 use poulpy_hal::{
-    api::{ScratchOwnedAlloc, ScratchOwnedBorrow, ZnAddNormal, ZnFillUniform, ZnNormalizeInplace},
-    layouts::{Backend, DataMut, Module, ScratchOwned, Zn, ZnxView, ZnxViewMut},
+    api::{VecZnxAddNormal, VecZnxFillUniform, VecZnxNormalizeInplace},
+    layouts::{Backend, DataMut, Module, Scratch, VecZnx, ZnxView, ZnxViewMut},
     source::Source,
 };
 
 use crate::{
+    ScratchTakeCore,
     encryption::{SIGMA, SIGMA_BOUND},
     layouts::{LWE, LWEInfos, LWEPlaintext, LWEPlaintextToRef, LWESecret, LWESecretToRef, LWEToMut},
 };
 
 impl<DataSelf: DataMut> LWE<DataSelf> {
-    pub fn encrypt_sk<P, S, M, BE: Backend>(&mut self, module: &M, pt: &P, sk: &S, source_xa: &mut Source, source_xe: &mut Source)
-    where
+    pub fn encrypt_sk<P, S, M, BE: Backend>(
+        &mut self,
+        module: &M,
+        pt: &P,
+        sk: &S,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        scratch: &mut Scratch<BE>,
+    ) where
         P: LWEPlaintextToRef,
         S: LWESecretToRef,
         M: LWEEncryptSk<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        module.lwe_encrypt_sk(self, pt, sk, source_xa, source_xe);
+        module.lwe_encrypt_sk(self, pt, sk, source_xa, source_xe, scratch);
     }
 }
 
 pub trait LWEEncryptSk<BE: Backend> {
-    fn lwe_encrypt_sk<R, P, S>(&self, res: &mut R, pt: &P, sk: &S, source_xa: &mut Source, source_xe: &mut Source)
-    where
+    fn lwe_encrypt_sk<R, P, S>(
+        &self,
+        res: &mut R,
+        pt: &P,
+        sk: &S,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        scratch: &mut Scratch<BE>,
+    ) where
         R: LWEToMut,
         P: LWEPlaintextToRef,
-        S: LWESecretToRef;
+        S: LWESecretToRef,
+        Scratch<BE>: ScratchTakeCore<BE>;
 }
 
 impl<BE: Backend> LWEEncryptSk<BE> for Module<BE>
 where
-    Self: Sized + ZnFillUniform + ZnAddNormal + ZnNormalizeInplace<BE>,
-    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+    Self: Sized + VecZnxFillUniform + VecZnxAddNormal + VecZnxNormalizeInplace<BE>,
 {
-    fn lwe_encrypt_sk<R, P, S>(&self, res: &mut R, pt: &P, sk: &S, source_xa: &mut Source, source_xe: &mut Source)
-    where
+    fn lwe_encrypt_sk<R, P, S>(
+        &self,
+        res: &mut R,
+        pt: &P,
+        sk: &S,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        scratch: &mut Scratch<BE>,
+    ) where
         R: LWEToMut,
         P: LWEPlaintextToRef,
         S: LWESecretToRef,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut LWE<&mut [u8]> = &mut res.to_mut();
         let pt: &LWEPlaintext<&[u8]> = &pt.to_ref();
@@ -51,11 +75,11 @@
         let base2k: usize = res.base2k().into();
         let k: usize = res.k().into();
 
-        self.zn_fill_uniform((res.n() + 1).into(), base2k, &mut res.data, 0, source_xa);
+        self.vec_znx_fill_uniform(base2k, &mut res.data, 0, source_xa);
 
-        let mut tmp_znx: Zn<Vec<u8>> = Zn::alloc(1, 1, res.size());
+        let mut tmp_znx: VecZnx<Vec<u8>> = VecZnx::alloc(1, 1, res.size());
 
-        let min_size = res.size().min(pt.size());
+        let min_size: usize = res.size().min(pt.size());
 
         (0..min_size).for_each(|i| {
             tmp_znx.at_mut(0, i)[0] = pt.data.at(0, i)[0]
@@ -74,24 +98,9 @@ .map(|(x, y)| x * y)
                 .sum::<i64>();
         });
 
-        self.zn_add_normal(
-            1,
-            base2k,
-            &mut res.data,
-            0,
-            k,
-            source_xe,
-            SIGMA,
-            SIGMA_BOUND,
-        );
+        self.vec_znx_add_normal(base2k, &mut tmp_znx, 0, k, source_xe, SIGMA, SIGMA_BOUND);
 
-        self.zn_normalize_inplace(
-            1,
-            base2k,
-            &mut tmp_znx,
-            0,
-            ScratchOwned::alloc(size_of::<i64>()).borrow(),
-        );
+        self.vec_znx_normalize_inplace(base2k, &mut tmp_znx, 0, scratch);
 
         (0..res.size()).for_each(|i| {
             res.data.at_mut(0, i)[0] = tmp_znx.at(0, i)[0];

@@ -30,8 +30,8 @@ impl<DataSelf: DataMut> GLWEAutomorphismKey<DataSelf> {
     pub fn external_product<A, B, M, BE: Backend>(&mut self, module: &M, a: &A, b: &B, scratch: &mut Scratch<BE>)
     where
         M: GGLWEExternalProduct<BE>,
-        A: GGLWEToRef,
-        B: GGSWPreparedToRef<BE>,
+        A: GGLWEToRef + GGLWEInfos,
+        B: GGSWPreparedToRef<BE> + GGSWInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         module.gglwe_external_product(self, a, b, scratch);
@@ -62,15 +62,11 @@ }
 
     fn gglwe_external_product<R, A, B>(&self, res: &mut R, a: &A, b: &B, scratch: &mut Scratch<BE>)
     where
-        R: GGLWEToMut,
-        A: GGLWEToRef,
-        B: GGSWPreparedToRef<BE>,
+        R: GGLWEToMut + GGLWEInfos,
+        A: GGLWEToRef + GGLWEInfos,
+        B: GGSWPreparedToRef<BE> + GGSWInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
-        let res: &mut GGLWE<&mut [u8]> = &mut res.to_mut();
-        let a: &GGLWE<&[u8]> = &a.to_ref();
-        let b: &GGSWPrepared<&[u8], BE> = &b.to_ref();
-
         assert_eq!(
             res.rank_in(),
             a.rank_in(),
@@ -92,6 +88,11 @@ "res output rank_out: {} != b rank: {}",
             res.rank_out(),
             b.rank()
         );
+        assert_eq!(res.base2k(), a.base2k());
+
+        let res: &mut GGLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GGLWE<&[u8]> = &a.to_ref();
+        let b: &GGSWPrepared<&[u8], BE> = &b.to_ref();
 
         for row in 0..res.dnum().into() {
             for col in 0..res.rank_in().into() {
@@ -149,8 +150,8 @@ impl<DataSelf: DataMut> GLWESwitchingKey<DataSelf> {
     pub fn external_product<A, B, M, BE: Backend>(&mut self, module: &M, a: &A, b: &B, scratch: &mut Scratch<BE>)
     where
         M: GGLWEExternalProduct<BE>,
-        A: GGLWEToRef,
-        B: GGSWPreparedToRef<BE>,
+        A: GGLWEToRef + GGLWEInfos,
+        B: GGSWPreparedToRef<BE> + GGSWInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         module.gglwe_external_product(self, a, b, scratch);

@@ -50,6 +50,8 @@ res.rank(),
             b.rank()
         );
 
+        assert_eq!(res.base2k(), a.base2k());
+
         assert!(scratch.available() >= self.ggsw_external_product_tmp_bytes(res, a, b));
 
         let min_dnum: usize = res.dnum().min(a.dnum()).into();

@@ -21,7 +21,7 @@
 impl<DataSelf: DataMut> GLWEAutomorphismKey<DataSelf> {
     pub fn keyswitch<A, B, M, BE: Backend>(&mut self, module: &M, a: &A, b: &B, scratch: &mut Scratch<BE>)
     where
-        A: GGLWEToRef + GGLWEToRef,
+        A: GGLWEToRef + GGLWEInfos,
         B: GGLWEPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
         M: GGLWEKeyswitch<BE>,
@@ -54,7 +54,7 @@
 impl<DataSelf: DataMut> GLWESwitchingKey<DataSelf> {
     pub fn keyswitch<A, B, M, BE: Backend>(&mut self, module: &M, a: &A, b: &B, scratch: &mut Scratch<BE>)
     where
-        A: GGLWEToRef,
+        A: GGLWEToRef + GGLWEInfos,
         B: GGLWEPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
         M: GGLWEKeyswitch<BE>,
@@ -87,7 +87,7 @@
 impl<DataSelf: DataMut> GGLWE<DataSelf> {
     pub fn keyswitch<A, B, M, BE: Backend>(&mut self, module: &M, a: &A, b: &B, scratch: &mut Scratch<BE>)
     where
-        A: GGLWEToRef,
+        A: GGLWEToRef + GGLWEInfos,
         B: GGLWEPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
         M: GGLWEKeyswitch<BE>,
@@ -122,14 +122,11 @@ }
 
     fn gglwe_keyswitch<R, A, B>(&self, res: &mut R, a: &A, b: &B, scratch: &mut Scratch<BE>)
     where
-        R: GGLWEToMut,
-        A: GGLWEToRef,
+        R: GGLWEToMut + GGLWEInfos,
+        A: GGLWEToRef + GGLWEInfos,
         B: GGLWEPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
-        let res: &mut GGLWE<&mut [u8]> = &mut res.to_mut();
-        let a: &GGLWE<&[u8]> = &a.to_ref();
-
         assert_eq!(
             res.rank_in(),
             a.rank_in(),
@@ -164,6 +161,10 @@ "res dsize: {} != a dsize: {}",
             res.dsize(),
             a.dsize()
         );
+        assert_eq!(res.base2k(), a.base2k());
+
+        let res: &mut GGLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GGLWE<&[u8]> = &a.to_ref();
 
         for row in 0..res.dnum().into() {
             for col in 0..res.rank_in().into() {

@@ -3,7 +3,7 @@
 use crate::{
     GGSWExpandRows, ScratchTakeCore,
     keyswitching::GLWEKeyswitch,
-    layouts::{GGLWEInfos, GGLWEPreparedToRef, GGLWEToGGSWKeyPreparedToRef, GGSW, GGSWInfos, GGSWToMut, GGSWToRef},
+    layouts::{GGLWEInfos, GGLWEPreparedToRef, GGLWEToGGSWKeyPreparedToRef, GGSW, GGSWInfos, GGSWToMut, GGSWToRef, LWEInfos},
 };
 
 impl GGSW<Vec<u8>> {
@@ -98,6 +98,7 @@ let a: &GGSW<&[u8]> = &a.to_ref();
 
         assert!(res.dnum() <= a.dnum());
         assert_eq!(res.dsize(), a.dsize());
+        assert_eq!(res.base2k(), a.base2k());
 
         for row in 0..a.dnum().into() {
             // Key-switch column 0, i.e.

@@ -57,21 +57,19 @@ A: GLWEInfos,
         B: GGLWEInfos,
     {
         let cols: usize = res_infos.rank().as_usize() + 1;
-        let size: usize = 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());
-
-        if a_infos.base2k() != key_infos.base2k() {
-            size + GLWE::bytes_of_from_infos(&GLWELayout {
+        let size: usize = if a_infos.base2k() != key_infos.base2k() {
+            let a_conv_infos = &GLWELayout {
                 n: a_infos.n(),
                 base2k: key_infos.base2k(),
                 k: a_infos.k(),
                 rank: a_infos.rank(),
-            })
+            };
+            self.glwe_keyswitch_internal_tmp_bytes(res_infos, a_conv_infos, key_infos) + GLWE::bytes_of_from_infos(a_conv_infos)
         } else {
-            size
-        }
+            self.glwe_keyswitch_internal_tmp_bytes(res_infos, a_infos, key_infos)
+        };
+
+        size.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>)
@@ -256,7 +254,7 @@ K: GGLWEInfos,
     {
         let cols: usize = (a_infos.rank() + 1).into();
         let a_size: usize = a_infos.size();
-        self.gglwe_product_dft_tmp_bytes(res_infos.size(), a_size, key_infos) + self.bytes_of_vec_znx_dft(cols, a_size)
+        self.gglwe_product_dft_tmp_bytes(res_infos.size(), a_size, key_infos) + self.bytes_of_vec_znx_dft(cols - 1, a_size)
     }
 
     fn glwe_keyswitch_internal<DR, A, K>(

@@ -83,34 +83,30 @@ assert!(a.n().as_usize() <= self.n());
         assert_eq!(ksk.n(), self.n() as u32);
         assert!(scratch.available() >= self.lwe_keyswitch_tmp_bytes(res, a, ksk));
 
-        let max_k: TorusPrecision = res.k().max(a.k());
-
-        let a_size: usize = a.k().div_ceil(ksk.base2k()) as usize;
-
         let (mut glwe_in, scratch_1) = scratch.take_glwe(&GLWELayout {
             n: ksk.n(),
             base2k: a.base2k(),
-            k: max_k,
+            k: a.k(),
             rank: Rank(1),
         });
         glwe_in.data.zero();
 
-        let (mut glwe_out, scratch_1) = scratch_1.take_glwe(&GLWELayout {
-            n: ksk.n(),
-            base2k: res.base2k(),
-            k: max_k,
-            rank: Rank(1),
-        });
-
         let n_lwe: usize = a.n().into();
 
-        for i in 0..a_size {
+        for i in 0..a.size() {
             let data_lwe: &[i64] = a.data.at(0, i);
             glwe_in.data.at_mut(0, i)[0] = data_lwe[0];
             glwe_in.data.at_mut(1, i)[..n_lwe].copy_from_slice(&data_lwe[1..]);
         }
 
-        self.glwe_keyswitch(&mut glwe_out, &glwe_in, ksk, scratch_1);
+        let (mut glwe_out, scratch_2) = scratch_1.take_glwe(&GLWELayout {
+            n: ksk.n(),
+            base2k: res.base2k(),
+            k: res.k(),
+            rank: Rank(1),
+        });
+
+        self.glwe_keyswitch(&mut glwe_out, &glwe_in, ksk, scratch_2);
         self.lwe_sample_extract(res, &glwe_out);
     }
 }

@@ -1,10 +1,10 @@
 use std::fmt;
 
 use poulpy_hal::{
-    api::ZnFillUniform,
+    api::VecZnxFillUniform,
     layouts::{
-        Backend, Data, DataMut, DataRef, FillUniform, Module, ReaderFrom, WriterTo, Zn, ZnToMut, ZnToRef, ZnxInfos, ZnxView,
-        ZnxViewMut,
+        Backend, Data, DataMut, DataRef, FillUniform, Module, ReaderFrom, VecZnx, VecZnxToMut, VecZnxToRef, WriterTo, ZnxInfos,
+        ZnxView, ZnxViewMut,
     },
     source::Source,
 };
@@ -13,7 +13,7 @@ use crate::layouts::{Base2K, Degree, LWE, LWEInfos, LWEToMut, TorusPrecision};
 
 #[derive(PartialEq, Eq, Clone)]
 pub struct LWECompressed<D: Data> {
-    pub(crate) data: Zn<D>,
+    pub(crate) data: VecZnx<D>,
     pub(crate) k: TorusPrecision,
     pub(crate) base2k: Base2K,
     pub(crate) seed: [u8; 32],
@@ -72,7 +72,7 @@ }
 
     pub fn alloc(base2k: Base2K, k: TorusPrecision) -> Self {
         LWECompressed {
-            data: Zn::alloc(1, 1, k.0.div_ceil(base2k.0) as usize),
+            data: VecZnx::alloc(1, 1, k.0.div_ceil(base2k.0) as usize),
             k,
             base2k,
             seed: [0u8; 32],
@@ -87,7 +87,7 @@ Self::bytes_of(infos.base2k(), infos.k())
     }
 
     pub fn bytes_of(base2k: Base2K, k: TorusPrecision) -> usize {
-        Zn::bytes_of(1, 1, k.0.div_ceil(base2k.0) as usize)
+        VecZnx::bytes_of(1, 1, k.0.div_ceil(base2k.0) as usize)
     }
 }
 
@@ -113,7 +113,7 @@ }
 
 pub trait LWEDecompress
 where
-    Self: ZnFillUniform,
+    Self: VecZnxFillUniform,
 {
     fn decompress_lwe<R, O>(&self, res: &mut R, other: &O)
     where
@@ -126,20 +126,14 @@
         assert_eq!(res.lwe_layout(), other.lwe_layout());
 
         let mut source: Source = Source::new(other.seed);
-        self.zn_fill_uniform(
-            res.n().into(),
-            other.base2k().into(),
-            &mut res.data,
-            0,
-            &mut source,
-        );
+        self.vec_znx_fill_uniform(other.base2k().into(), &mut res.data, 0, &mut source);
         for i in 0..res.size() {
             res.data.at_mut(0, i)[0] = other.data.at(0, i)[0];
         }
     }
 }
 
-impl<B: Backend> LWEDecompress for Module<B> where Self: ZnFillUniform {}
+impl<B: Backend> LWEDecompress for Module<B> where Self: VecZnxFillUniform {}
 
 impl<D: DataMut> LWE<D> {
     pub fn decompress<O, M>(&mut self, module: &M, other: &O)

@@ -158,3 +158,15 @@ data: self.data.to_mut(),
         }
     }
 }
+
+impl<D: DataMut> GLWEPlaintext<D> {
+    pub fn data_mut(&mut self) -> &mut VecZnx<D> {
+        &mut self.data
+    }
+}
+
+impl<D: DataRef> GLWEPlaintext<D> {
+    pub fn data(&self) -> &VecZnx<D> {
+        &self.data
+    }
+}

@@ -1,7 +1,7 @@
 use std::fmt;
 
 use poulpy_hal::{
-    layouts::{Data, DataMut, DataRef, FillUniform, ReaderFrom, WriterTo, Zn, ZnToMut, ZnToRef, ZnxInfos},
+    layouts::{Data, DataMut, DataRef, FillUniform, ReaderFrom, VecZnx, VecZnxToMut, VecZnxToRef, WriterTo, ZnxInfos},
     source::Source,
 };
 
@@ -57,7 +57,7 @@ }
 }
 #[derive(PartialEq, Eq, Clone)]
 pub struct LWE<D: Data> {
-    pub(crate) data: Zn<D>,
+    pub(crate) data: VecZnx<D>,
     pub(crate) k: TorusPrecision,
     pub(crate) base2k: Base2K,
 }
@@ -90,13 +90,13 @@ }
 }
 
 impl<D: DataRef> LWE<D> {
-    pub fn data(&self) -> &Zn<D> {
+    pub fn data(&self) -> &VecZnx<D> {
         &self.data
     }
 }
 
 impl<D: DataMut> LWE<D> {
-    pub fn data_mut(&mut self) -> &Zn<D> {
+    pub fn data_mut(&mut self) -> &VecZnx<D> {
         &mut self.data
     }
 }
@@ -121,7 +121,7 @@ }
 
 impl<D: DataMut> FillUniform for LWE<D>
 where
-    Zn<D>: FillUniform,
+    VecZnx<D>: FillUniform,
 {
     fn fill_uniform(&mut self, log_bound: usize, source: &mut Source) {
         self.data.fill_uniform(log_bound, source);
@@ -138,7 +138,7 @@ }
 
     pub fn alloc(n: Degree, base2k: Base2K, k: TorusPrecision) -> Self {
         LWE {
-            data: Zn::alloc((n + 1).into(), 1, k.0.div_ceil(base2k.0) as usize),
+            data: VecZnx::alloc((n + 1).into(), 1, k.0.div_ceil(base2k.0) as usize),
             k,
             base2k,
         }
@@ -152,7 +152,7 @@ Self::bytes_of(infos.n(), infos.base2k(), infos.k())
     }
 
     pub fn bytes_of(n: Degree, base2k: Base2K, k: TorusPrecision) -> usize {
-        Zn::bytes_of((n + 1).into(), 1, k.0.div_ceil(base2k.0) as usize)
+        VecZnx::bytes_of((n + 1).into(), 1, k.0.div_ceil(base2k.0) as usize)
     }
 }
 

@@ -1,6 +1,6 @@
 use std::fmt;
 
-use poulpy_hal::layouts::{Data, DataMut, DataRef, Zn, ZnToMut, ZnToRef, ZnxInfos};
+use poulpy_hal::layouts::{Data, DataMut, DataRef, VecZnx, VecZnxToMut, VecZnxToRef, ZnxInfos};
 
 use crate::layouts::{Base2K, Degree, LWEInfos, TorusPrecision};
 
@@ -29,7 +29,7 @@ }
 }
 
 pub struct LWEPlaintext<D: Data> {
-    pub(crate) data: Zn<D>,
+    pub(crate) data: VecZnx<D>,
     pub(crate) k: TorusPrecision,
     pub(crate) base2k: Base2K,
 }
@@ -62,7 +62,7 @@ }
 
     pub fn alloc(base2k: Base2K, k: TorusPrecision) -> Self {
         LWEPlaintext {
-            data: Zn::alloc(1, 1, k.0.div_ceil(base2k.0) as usize),
+            data: VecZnx::alloc(1, 1, k.0.div_ceil(base2k.0) as usize),
             k,
             base2k,
         }
@@ -111,8 +111,14 @@ }
     }
 }
 
+impl<D: DataRef> LWEPlaintext<D> {
+    pub fn data(&self) -> &VecZnx<D> {
+        &self.data
+    }
+}
+
 impl<D: DataMut> LWEPlaintext<D> {
-    pub fn data_mut(&mut self) -> &mut Zn<D> {
+    pub fn data_mut(&mut self) -> &mut VecZnx<D> {
         &mut self.data
     }
 }

@@ -42,7 +42,7 @@ #[allow(clippy::too_many_arguments)]
 #[allow(dead_code)]
 pub(crate) fn var_noise_gglwe_product_v2(
     n: f64,
-    logq: usize,
+    k_ksk: usize,
     dnum: usize,
     dsize: usize,
     base2k: usize,
@@ -55,7 +55,7 @@ rank_in: f64,
 ) -> f64 {
     let base: f64 = ((dsize * base2k) as f64).exp2();
     let var_base: f64 = base * base / 12f64;
-    let scale: f64 = (logq as f64).exp2();
+    let scale: f64 = (k_ksk as f64).exp2();
 
     let mut noise: f64 = (dnum as f64) * n * var_base * (var_gct_err_lhs + var_xs * var_gct_err_rhs);
     noise += var_msg * var_a_err * var_base * n;

@@ -23,7 +23,7 @@ fn take_lwe<A>(&mut self, infos: &A) -> (LWE<&mut [u8]>, &mut Self)
     where
         A: LWEInfos,
     {
-        let (data, scratch) = self.take_zn(infos.n().into(), 1, infos.size());
+        let (data, scratch) = self.take_vec_znx(infos.n().into(), 1, infos.size());
         (
             LWE {
                 k: infos.k(),

@@ -9,10 +9,10 @@ GLWEAutomorphismKeyAutomorphism, GLWEAutomorphismKeyEncryptSk, GLWEDecrypt, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
         GGLWEInfos, GLWEAutomorphismKey, GLWEAutomorphismKeyLayout, GLWEAutomorphismKeyPreparedFactory, GLWEPlaintext,
-        GLWESecret, GLWESecretPreparedFactory,
+        GLWESecret, GLWESecretPreparedFactory, LWEInfos,
         prepared::{GLWEAutomorphismKeyPrepared, GLWESecretPrepared},
     },
-    noise::log2_std_noise_gglwe_product,
+    var_noise_gglwe_product_v2,
 };
 
 #[allow(clippy::too_many_arguments)]
@@ -29,26 +29,27 @@ + GLWEDecrypt<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_in: usize = 60;
-    let k_out: usize = 40;
-    let dsize: usize = k_in.div_ceil(base2k);
+    let base2k_in: usize = 17;
+    let base2k_key: usize = 13;
+    let base2k_out: usize = base2k_in; // MUST BE SAME
+    let k_in: usize = 102;
+    let max_dsize: usize = k_in.div_ceil(base2k_key);
     let p0: i64 = -1;
     let p1: i64 = -5;
     for rank in 1_usize..3 {
-        for di in 1..dsize + 1 {
-            let k_apply: usize = (dsize + di) * base2k;
+        for dsize in 1..max_dsize + 1 {
+            let k_ksk: usize = k_in + base2k_key * dsize;
+            let k_out: usize = k_ksk; // Better capture noise.
 
             let n: usize = module.n();
             let dsize_in: usize = 1;
 
-            let dnum_in: usize = k_in / (base2k * di);
-            let dnum_out: usize = k_out / (base2k * di);
-            let dnum_apply: usize = k_in.div_ceil(base2k * di);
+            let dnum_in: usize = k_in / base2k_in;
+            let dnum_ksk: usize = k_in.div_ceil(base2k_key * dsize);
 
             let auto_key_in_infos: GLWEAutomorphismKeyLayout = GLWEAutomorphismKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_in.into(),
                 k: k_in.into(),
                 dnum: dnum_in.into(),
                 dsize: dsize_in.into(),
@@ -57,19 +58,19 @@ };
 
             let auto_key_out_infos: GLWEAutomorphismKeyLayout = GLWEAutomorphismKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_out.into(),
                 k: k_out.into(),
-                dnum: dnum_out.into(),
+                dnum: dnum_in.into(),
                 dsize: dsize_in.into(),
                 rank: rank.into(),
             };
 
             let auto_key_apply_infos: GLWEAutomorphismKeyLayout = GLWEAutomorphismKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
-                k: k_apply.into(),
-                dnum: dnum_apply.into(),
-                dsize: di.into(),
+                base2k: base2k_key.into(),
+                k: k_ksk.into(),
+                dnum: dnum_ksk.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
@@ -83,13 +84,16 @@ let mut source_xa: Source = Source::new([0u8; 32]);
 
             let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
                 GLWEAutomorphismKey::encrypt_sk_tmp_bytes(module, &auto_key_in_infos)
-                    | GLWEAutomorphismKey::encrypt_sk_tmp_bytes(module, &auto_key_apply_infos)
-                    | GLWEAutomorphismKey::automorphism_tmp_bytes(
+                    .max(GLWEAutomorphismKey::encrypt_sk_tmp_bytes(
+                        module,
+                        &auto_key_apply_infos,
+                    ))
+                    .max(GLWEAutomorphismKey::automorphism_tmp_bytes(
                         module,
                         &auto_key_out_infos,
                         &auto_key_in_infos,
                         &auto_key_apply_infos,
-                    ),
+                    )),
             );
 
             let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc_from_infos(&auto_key_in);
@@ -128,7 +132,7 @@ &auto_key_apply_prepared,
                 scratch.borrow(),
             );
 
-            let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&auto_key_out_infos);
+            let mut pt_out: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&auto_key_out_infos);
 
             let mut sk_auto: GLWESecret<Vec<u8>> = GLWESecret::alloc_from_infos(&auto_key_out_infos);
             sk_auto.fill_zero(); // Necessary to avoid panic of unfilled sk
@@ -145,41 +149,44 @@
             let mut sk_auto_dft: GLWESecretPrepared<Vec<u8>, BE> = GLWESecretPrepared::alloc_from_infos(module, &sk_auto);
             sk_auto_dft.prepare(module, &sk_auto);
 
-            (0..auto_key_out.rank_in().into()).for_each(|col_i| {
-                (0..auto_key_out.dnum().into()).for_each(|row_i| {
+            for col_i in 0..auto_key_out.rank_in().into() {
+                for row_i in 0..auto_key_out.dnum().into() {
                     auto_key_out
                         .at(row_i, col_i)
-                        .decrypt(module, &mut pt, &sk_auto_dft, scratch.borrow());
+                        .decrypt(module, &mut pt_out, &sk_auto_dft, scratch.borrow());
 
                     module.vec_znx_sub_scalar_inplace(
-                        &mut pt.data,
+                        &mut pt_out.data,
                         0,
                         (dsize_in - 1) + row_i * dsize_in,
                         &sk.data,
                         col_i,
                     );
 
-                    let noise_have: f64 = pt.data.stats(base2k, 0).std().log2();
-                    let noise_want: f64 = log2_std_noise_gglwe_product(
-                        n as f64,
-                        base2k * di,
+                    let noise_have: f64 = pt_out.data.stats(pt_out.base2k().into(), 0).std().log2();
+                    let max_noise: f64 = var_noise_gglwe_product_v2(
+                        module.n() as f64,
+                        k_ksk,
+                        dnum_ksk,
+                        dsize,
+                        base2k_key,
                         0.5,
                         0.5,
                         0f64,
                         SIGMA * SIGMA,
                         0f64,
                         rank as f64,
-                        k_out,
-                        k_apply,
-                    );
+                    )
+                    .sqrt()
+                    .log2();
 
                     assert!(
-                        noise_have < noise_want + 0.5,
+                        noise_have < max_noise + 0.5,
                         "{noise_have} {}",
-                        noise_want + 0.5
+                        max_noise + 0.5
                     );
-                });
-            });
+                }
+            }
         }
     }
 }
@@ -198,25 +205,27 @@ + GLWEDecrypt<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_in: usize = 60;
-    let dsize: usize = k_in.div_ceil(base2k);
+    let base2k_out: usize = 17;
+    let base2k_key: usize = 13;
+    let k_out: usize = 102;
+    let max_dsize: usize = k_out.div_ceil(base2k_key);
+
     let p0: i64 = -1;
     let p1: i64 = -5;
     for rank in 1_usize..3 {
-        for di in 1..dsize + 1 {
-            let k_apply: usize = (dsize + di) * base2k;
+        for dsize in 1..max_dsize + 1 {
+            let k_ksk: usize = k_out + base2k_key * dsize;
 
             let n: usize = module.n();
             let dsize_in: usize = 1;
 
-            let dnum_in: usize = k_in / (base2k * di);
-            let dnum_apply: usize = k_in.div_ceil(base2k * di);
+            let dnum_in: usize = k_out / base2k_out;
+            let dnum_ksk: usize = k_out.div_ceil(base2k_key * dsize);
 
             let auto_key_layout: GLWEAutomorphismKeyLayout = GLWEAutomorphismKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
-                k: k_in.into(),
+                base2k: base2k_out.into(),
+                k: k_out.into(),
                 dnum: dnum_in.into(),
                 dsize: dsize_in.into(),
                 rank: rank.into(),
@@ -224,10 +233,10 @@ };
 
             let auto_key_apply_layout: GLWEAutomorphismKeyLayout = GLWEAutomorphismKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
-                k: k_apply.into(),
-                dnum: dnum_apply.into(),
-                dsize: di.into(),
+                base2k: base2k_key.into(),
+                k: k_ksk.into(),
+                dnum: dnum_ksk.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
@@ -306,24 +315,27 @@ &sk.data,
                         col_i,
                     );
 
-                    let noise_have: f64 = pt.data.stats(base2k, 0).std().log2();
-                    let noise_want: f64 = log2_std_noise_gglwe_product(
-                        n as f64,
-                        base2k * di,
+                    let noise_have: f64 = pt.data.stats(pt.base2k().into(), 0).std().log2();
+                    let max_noise: f64 = var_noise_gglwe_product_v2(
+                        module.n() as f64,
+                        k_ksk,
+                        dnum_ksk,
+                        dsize,
+                        base2k_key,
                         0.5,
                         0.5,
                         0f64,
                         SIGMA * SIGMA,
                         0f64,
                         rank as f64,
-                        k_in,
-                        k_apply,
-                    );
+                    )
+                    .sqrt()
+                    .log2();
 
                     assert!(
-                        noise_have < noise_want + 0.5,
+                        noise_have < max_noise + 0.5,
                         "{noise_have} {}",
-                        noise_want + 0.5
+                        max_noise + 0.5
                     );
                 });
             });

@@ -29,26 +29,28 @@ + GGSWNoise<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_in: usize = 54;
-    let dsize: usize = k_in.div_ceil(base2k);
+    let base2k_in: usize = 17;
+    let base2k_key: usize = 13;
+    let base2k_out: usize = base2k_in; // MUST BE SAME
+    let k_in: usize = 102;
+    let max_dsize: usize = k_in.div_ceil(base2k_key);
+
     let p: i64 = -5;
-
     for rank in 1_usize..3 {
-        for di in 1..dsize + 1 {
-            let k_ksk: usize = k_in + base2k * di;
+        for dsize in 1..max_dsize + 1 {
+            let k_ksk: usize = k_in + base2k_key * dsize;
             let k_tsk: usize = k_ksk;
             let k_out: usize = k_ksk; // Better capture noise.
 
             let n: usize = module.n();
-            let dnum: usize = k_in.div_ceil(base2k * di);
-            let dnum_in: usize = k_in.div_euclid(base2k * di);
+            let dnum_in: usize = k_in / base2k_in;
+            let dnum_ksk: usize = k_in.div_ceil(base2k_key * dsize);
 
             let dsize_in: usize = 1;
 
             let ggsw_in_layout: GGSWLayout = GGSWLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_in.into(),
                 k: k_in.into(),
                 dnum: dnum_in.into(),
                 dsize: dsize_in.into(),
@@ -57,7 +59,7 @@ };
 
             let ggsw_out_layout: GGSWLayout = GGSWLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_out.into(),
                 k: k_out.into(),
                 dnum: dnum_in.into(),
                 dsize: dsize_in.into(),
@@ -66,19 +68,19 @@ };
 
             let tsk_layout: GGLWEToGGSWKeyLayout = GGLWEToGGSWKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_tsk.into(),
-                dnum: dnum.into(),
-                dsize: di.into(),
+                dnum: dnum_ksk.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
             let auto_key_layout: GGLWEToGGSWKeyLayout = GGLWEToGGSWKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_ksk.into(),
-                dnum: dnum.into(),
-                dsize: di.into(),
+                dnum: dnum_ksk.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
@@ -154,7 +156,7 @@
             let max_noise = |col_j: usize| -> f64 {
                 noise_ggsw_keyswitch(
                     n as f64,
-                    base2k * di,
+                    base2k_key * dsize,
                     col_j,
                     var_xs,
                     0f64,
@@ -187,23 +189,25 @@ + GGSWNoise<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_out: usize = 54;
-    let dsize: usize = k_out.div_ceil(base2k);
+    let base2k_out: usize = 17;
+    let base2k_key: usize = 13;
+    let k_out: usize = 102;
+    let max_dsize: usize = k_out.div_ceil(base2k_key);
+
     let p: i64 = -1;
     for rank in 1_usize..3 {
-        for di in 1..dsize + 1 {
-            let k_ksk: usize = k_out + base2k * di;
+        for dsize in 1..max_dsize + 1 {
+            let k_ksk: usize = k_out + base2k_key * dsize;
             let k_tsk: usize = k_ksk;
 
             let n: usize = module.n();
-            let dnum: usize = k_out.div_ceil(di * base2k);
-            let dnum_in: usize = k_out.div_euclid(base2k * di);
+            let dnum_in: usize = k_out / base2k_out;
+            let dnum_ksk: usize = k_out.div_ceil(base2k_key * dsize);
             let dsize_in: usize = 1;
 
             let ggsw_out_layout: GGSWLayout = GGSWLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_out.into(),
                 k: k_out.into(),
                 dnum: dnum_in.into(),
                 dsize: dsize_in.into(),
@@ -212,19 +216,19 @@ };
 
             let tsk_layout: GGLWEToGGSWKeyLayout = GGLWEToGGSWKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_tsk.into(),
-                dnum: dnum.into(),
-                dsize: di.into(),
+                dnum: dnum_ksk.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
             let auto_key_layout: GGLWEToGGSWKeyLayout = GGLWEToGGSWKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_ksk.into(),
-                dnum: dnum.into(),
-                dsize: di.into(),
+                dnum: dnum_ksk.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
@@ -293,7 +297,7 @@
             let max_noise = |col_j: usize| -> f64 {
                 noise_ggsw_keyswitch(
                     n as f64,
-                    base2k * di,
+                    base2k_key * dsize,
                     col_j,
                     var_xs,
                     0f64,

@@ -5,14 +5,14 @@ source::Source,
 };
 
 use crate::{
-    GLWEAutomorphism, GLWEAutomorphismKeyEncryptSk, GLWEDecrypt, GLWEEncryptSk, GLWENoise, ScratchTakeCore,
+    GLWEAutomorphism, GLWEAutomorphismKeyEncryptSk, GLWEDecrypt, GLWEEncryptSk, GLWENoise, GLWENormalize, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
         GLWE, GLWEAutomorphismKey, GLWEAutomorphismKeyLayout, GLWEAutomorphismKeyPreparedFactory, GLWELayout, GLWEPlaintext,
         GLWESecret, GLWESecretPreparedFactory,
         prepared::{GLWEAutomorphismKeyPrepared, GLWESecretPrepared},
     },
-    noise::log2_std_noise_gglwe_product,
+    var_noise_gglwe_product_v2,
 };
 
 pub fn test_glwe_automorphism<BE: Backend>(module: &Module<BE>)
@@ -25,55 +25,59 @@ + GLWEAutomorphism<BE>
         + GLWEAutomorphismKeyEncryptSk<BE>
         + GLWEAutomorphismKeyPreparedFactory<BE>
         + GLWENoise<BE>
-        + VecZnxAutomorphismInplace<BE>,
+        + VecZnxAutomorphismInplace<BE>
+        + GLWENormalize<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_in: usize = 60;
-    let dsize: usize = k_in.div_ceil(base2k);
+    let base2k_in: usize = 17;
+    let base2k_key: usize = 13;
+    let base2k_out: usize = 15;
+    let k_in: usize = 102;
+    let max_dsize: usize = k_in.div_ceil(base2k_key);
     let p: i64 = -5;
     for rank in 1_usize..3 {
-        for di in 1..dsize + 1 {
-            let k_ksk: usize = k_in + base2k * di;
+        for dsize in 1..max_dsize + 1 {
+            let k_ksk: usize = k_in + base2k_key * dsize;
             let k_out: usize = k_ksk; // Better capture noise.
 
             let n: usize = module.n();
-            let dnum: usize = k_in.div_ceil(base2k * dsize);
+            let dnum: usize = k_in.div_ceil(base2k_key * dsize);
 
             let ct_in_infos: GLWELayout = GLWELayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_in.into(),
                 k: k_in.into(),
                 rank: rank.into(),
             };
 
             let ct_out_infos: GLWELayout = GLWELayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_out.into(),
                 k: k_out.into(),
                 rank: rank.into(),
             };
 
             let autokey_infos: GLWEAutomorphismKeyLayout = GLWEAutomorphismKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_out.into(),
                 rank: rank.into(),
                 dnum: dnum.into(),
-                dsize: di.into(),
+                dsize: dsize.into(),
             };
 
             let mut autokey: GLWEAutomorphismKey<Vec<u8>> = GLWEAutomorphismKey::alloc_from_infos(&autokey_infos);
             let mut ct_in: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&ct_in_infos);
             let mut ct_out: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&ct_out_infos);
-            let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&ct_out_infos);
+            let mut pt_in: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&ct_in_infos);
+            let mut pt_out: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&ct_out_infos);
 
             let mut source_xs: Source = Source::new([0u8; 32]);
             let mut source_xe: Source = Source::new([0u8; 32]);
             let mut source_xa: Source = Source::new([0u8; 32]);
 
-            module.vec_znx_fill_uniform(base2k, &mut pt_want.data, 0, &mut source_xa);
+            module.vec_znx_fill_uniform(base2k_in, &mut pt_in.data, 0, &mut source_xa);
 
             let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
                 GLWEAutomorphismKey::encrypt_sk_tmp_bytes(module, &autokey)
@@ -99,7 +103,7 @@ );
 
             ct_in.encrypt_sk(
                 module,
-                &pt_want,
+                &pt_in,
                 &sk_prepared,
                 &mut source_xa,
                 &mut source_xe,
@@ -112,22 +116,26 @@ autokey_prepared.prepare(module, &autokey, scratch.borrow());
 
             ct_out.automorphism(module, &ct_in, &autokey_prepared, scratch.borrow());
 
-            let max_noise: f64 = log2_std_noise_gglwe_product(
+            let max_noise: f64 = var_noise_gglwe_product_v2(
                 module.n() as f64,
-                base2k * dsize,
+                k_ksk,
+                dnum,
+                max_dsize,
+                base2k_key,
                 0.5,
                 0.5,
                 0f64,
                 SIGMA * SIGMA,
                 0f64,
                 rank as f64,
-                k_in,
-                k_ksk,
-            );
+            )
+            .sqrt()
+            .log2();
 
-            module.vec_znx_automorphism_inplace(p, &mut pt_want.data, 0, scratch.borrow());
+            module.glwe_normalize(&mut pt_out, &pt_in, scratch.borrow());
+            module.vec_znx_automorphism_inplace(p, &mut pt_out.data, 0, scratch.borrow());
 
-            ct_out.assert_noise(module, &sk_prepared, &pt_want, max_noise + 1.0);
+            ct_out.assert_noise(module, &sk_prepared, &pt_out, max_noise + 1.0);
         }
     }
 }
@@ -147,31 +155,33 @@ + VecZnxAutomorphismInplace<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_out: usize = 60;
-    let dsize: usize = k_out.div_ceil(base2k);
+    let base2k_out: usize = 17;
+    let base2k_key: usize = 13;
+    let k_out: usize = 102;
+    let max_dsize: usize = k_out.div_ceil(base2k_key);
+
     let p = -5;
     for rank in 1_usize..3 {
-        for di in 1..dsize + 1 {
-            let k_ksk: usize = k_out + base2k * di;
+        for dsize in 1..max_dsize + 1 {
+            let k_ksk: usize = k_out + base2k_key * dsize;
 
             let n: usize = module.n();
-            let dnum: usize = k_out.div_ceil(base2k * dsize);
+            let dnum: usize = k_out.div_ceil(base2k_key * dsize);
 
             let ct_out_infos: GLWELayout = GLWELayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_out.into(),
                 k: k_out.into(),
                 rank: rank.into(),
             };
 
             let autokey_infos: GLWEAutomorphismKeyLayout = GLWEAutomorphismKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_ksk.into(),
                 rank: rank.into(),
                 dnum: dnum.into(),
-                dsize: di.into(),
+                dsize: dsize.into(),
             };
 
             let mut autokey: GLWEAutomorphismKey<Vec<u8>> = GLWEAutomorphismKey::alloc_from_infos(&autokey_infos);
@@ -182,7 +192,7 @@ let mut source_xs: Source = Source::new([0u8; 32]);
             let mut source_xe: Source = Source::new([0u8; 32]);
             let mut source_xa: Source = Source::new([0u8; 32]);
 
-            module.vec_znx_fill_uniform(base2k, &mut pt_want.data, 0, &mut source_xa);
+            module.vec_znx_fill_uniform(base2k_out, &mut pt_want.data, 0, &mut source_xa);
 
             let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
                 GLWEAutomorphismKey::encrypt_sk_tmp_bytes(module, &autokey)
@@ -221,18 +231,21 @@ autokey_prepared.prepare(module, &autokey, scratch.borrow());
 
             ct.automorphism_inplace(module, &autokey_prepared, scratch.borrow());
 
-            let max_noise: f64 = log2_std_noise_gglwe_product(
+            let max_noise: f64 = var_noise_gglwe_product_v2(
                 module.n() as f64,
-                base2k * dsize,
+                k_ksk,
+                dnum,
+                dsize,
+                base2k_key,
                 0.5,
                 0.5,
                 0f64,
                 SIGMA * SIGMA,
                 0f64,
                 rank as f64,
-                k_out,
-                k_ksk,
-            );
+            )
+            .sqrt()
+            .log2();
 
             module.vec_znx_automorphism_inplace(p, &mut pt_want.data, 0, scratch.borrow());
 

@@ -1,5 +1,5 @@
 use poulpy_hal::{
-    api::{ScratchAvailable, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxFillUniform},
+    api::{ScratchAvailable, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxFillUniform, VecZnxNormalize},
     layouts::{Backend, FillUniform, Module, Scratch, ScratchOwned, ZnxView},
     source::Source,
 };
@@ -104,7 +104,8 @@ + LWEToGLWESwitchingKeyEncryptSk<BE>
         + GLWEDecrypt<BE>
         + GLWESecretPreparedFactory<BE>
         + LWEEncryptSk<BE>
-        + LWEToGLWEKeyPreparedFactory<BE>,
+        + LWEToGLWEKeyPreparedFactory<BE>
+        + VecZnxNormalize<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
@@ -120,23 +121,23 @@ let mut source_xe: Source = Source::new([0u8; 32]);
 
     let lwe_to_glwe_infos: LWEToGLWEKeyLayout = LWEToGLWEKeyLayout {
         n: n_glwe,
-        base2k: Base2K(17),
-        k: TorusPrecision(51),
+        base2k: Base2K(13),
+        k: TorusPrecision(92),
         dnum: Dnum(2),
         rank_out: rank,
     };
 
     let glwe_infos: GLWELayout = GLWELayout {
         n: n_glwe,
-        base2k: Base2K(17),
-        k: TorusPrecision(34),
+        base2k: Base2K(15),
+        k: TorusPrecision(75),
         rank,
     };
 
     let lwe_infos: LWELayout = LWELayout {
         n: n_lwe,
         base2k: Base2K(17),
-        k: TorusPrecision(34),
+        k: TorusPrecision(75),
     };
 
     let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
@@ -160,7 +161,14 @@ let mut lwe_pt: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc_from_infos(&lwe_infos);
     lwe_pt.encode_i64(data, k_lwe_pt);
 
     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);
+    lwe_ct.encrypt_sk(
+        module,
+        &lwe_pt,
+        &sk_lwe,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
 
     let mut ksk: LWEToGLWEKey<Vec<u8>> = LWEToGLWEKey::alloc_from_infos(&lwe_to_glwe_infos);
 
@@ -183,7 +191,19 @@
     let mut glwe_pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_infos);
     glwe_ct.decrypt(module, &mut glwe_pt, &sk_glwe_prepared, scratch.borrow());
 
-    assert_eq!(glwe_pt.data.at(0, 0)[0], lwe_pt.data.at(0, 0)[0]);
+    let mut lwe_pt_conv = LWEPlaintext::alloc(glwe_pt.base2k(), lwe_pt.k());
+
+    module.vec_znx_normalize(
+        glwe_pt.base2k().as_usize(),
+        lwe_pt_conv.data_mut(),
+        0,
+        lwe_pt.base2k().as_usize(),
+        lwe_pt.data(),
+        0,
+        scratch.borrow(),
+    );
+
+    assert_eq!(glwe_pt.data.at(0, 0)[0], lwe_pt_conv.data.at(0, 0)[0]);
 }
 
 pub fn test_glwe_to_lwe<BE: Backend>(module: &Module<BE>)
@@ -196,7 +216,8 @@ + LWEFromGLWE<BE>
         + GLWEDecrypt<BE>
         + GLWESecretPreparedFactory<BE>
         + GLWEToLWESwitchingKeyEncryptSk<BE>
-        + GLWEToLWEKeyPreparedFactory<BE>,
+        + GLWEToLWEKeyPreparedFactory<BE>
+        + VecZnxNormalize<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
@@ -208,8 +229,8 @@ let k_lwe_pt: TorusPrecision = TorusPrecision(8);
 
     let glwe_to_lwe_infos: GLWEToLWEKeyLayout = GLWEToLWEKeyLayout {
         n: n_glwe,
-        base2k: Base2K(17),
-        k: TorusPrecision(51),
+        base2k: Base2K(13),
+        k: TorusPrecision(91),
         dnum: Dnum(2),
         rank_in: rank,
     };
@@ -217,14 +238,14 @@
     let glwe_infos: GLWELayout = GLWELayout {
         n: n_glwe,
         base2k: Base2K(17),
-        k: TorusPrecision(34),
+        k: TorusPrecision(72),
         rank,
     };
 
     let lwe_infos: LWELayout = LWELayout {
         n: n_lwe,
-        base2k: Base2K(17),
-        k: TorusPrecision(34),
+        base2k: Base2K(15),
+        k: TorusPrecision(72),
     };
 
     let mut source_xs: Source = Source::new([0u8; 32]);
@@ -284,7 +305,19 @@
     lwe_ct.from_glwe(module, &glwe_ct, a_idx, &ksk_prepared, scratch.borrow());
 
     let mut lwe_pt: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc_from_infos(&lwe_infos);
-    lwe_ct.decrypt(module, &mut lwe_pt, &sk_lwe);
+    lwe_ct.decrypt(module, &mut lwe_pt, &sk_lwe, scratch.borrow());
 
-    assert_eq!(glwe_pt.data.at(0, 0)[a_idx], lwe_pt.data.at(0, 0)[0]);
+    let mut glwe_pt_conv = GLWEPlaintext::alloc(glwe_ct.n(), lwe_pt.base2k(), lwe_pt.k());
+
+    module.vec_znx_normalize(
+        lwe_pt.base2k().as_usize(),
+        glwe_pt_conv.data_mut(),
+        0,
+        glwe_ct.base2k().as_usize(),
+        glwe_pt.data(),
+        0,
+        scratch.borrow(),
+    );
+
+    assert_eq!(glwe_pt_conv.data.at(0, 0)[a_idx], lwe_pt.data.at(0, 0)[0]);
 }

@@ -12,6 +12,7 @@ GLWESecret, GLWESecretPreparedFactory, GLWESwitchingKey, GLWESwitchingKeyLayout, GLWESwitchingKeyPreparedFactory,
         prepared::{GLWESecretPrepared, GLWESwitchingKeyPrepared},
     },
     noise::log2_std_noise_gglwe_product,
+    var_noise_gglwe_product_v2,
 };
 
 pub fn test_gglwe_switching_key_keyswitch<BE: Backend>(module: &Module<BE>)
@@ -24,27 +25,29 @@ + GGLWENoise<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_in: usize = 60;
-    let dsize: usize = k_in.div_ceil(base2k);
+    let base2k_in: usize = 17;
+    let base2k_key: usize = 13;
+    let base2k_out: usize = base2k_in; // MUST BE SAME
+    let k_in: usize = 102;
+    let max_dsize: usize = k_in.div_ceil(base2k_key);
 
-    for rank_in_s0s1 in 1_usize..3 {
+    for rank_in_s0s1 in 1_usize..2 {
         for rank_out_s0s1 in 1_usize..3 {
             for rank_out_s1s2 in 1_usize..3 {
-                for di in 1_usize..dsize + 1 {
-                    let k_ksk: usize = k_in + base2k * di;
+                for dsize in 1_usize..max_dsize + 1 {
+                    let k_ksk: usize = k_in + base2k_key * dsize;
                     let k_out: usize = k_ksk; // Better capture noise.
 
                     let n: usize = module.n();
-                    let dnum: usize = k_in / base2k;
-                    let dnum_apply: usize = k_in.div_ceil(base2k * di);
                     let dsize_in: usize = 1;
+                    let dnum_in: usize = k_in / base2k_in;
+                    let dnum_ksk: usize = k_in.div_ceil(base2k_key * dsize);
 
                     let gglwe_s0s1_infos: GLWESwitchingKeyLayout = GLWESwitchingKeyLayout {
                         n: n.into(),
-                        base2k: base2k.into(),
+                        base2k: base2k_in.into(),
                         k: k_in.into(),
-                        dnum: dnum.into(),
+                        dnum: dnum_in.into(),
                         dsize: dsize_in.into(),
                         rank_in: rank_in_s0s1.into(),
                         rank_out: rank_out_s0s1.into(),
@@ -52,19 +55,19 @@ };
 
                     let gglwe_s1s2_infos: GLWESwitchingKeyLayout = GLWESwitchingKeyLayout {
                         n: n.into(),
-                        base2k: base2k.into(),
+                        base2k: base2k_key.into(),
                         k: k_ksk.into(),
-                        dnum: dnum_apply.into(),
-                        dsize: di.into(),
+                        dnum: dnum_ksk.into(),
+                        dsize: dsize.into(),
                         rank_in: rank_out_s0s1.into(),
                         rank_out: rank_out_s1s2.into(),
                     };
 
                     let gglwe_s0s2_infos: GLWESwitchingKeyLayout = GLWESwitchingKeyLayout {
                         n: n.into(),
-                        base2k: base2k.into(),
+                        base2k: base2k_out.into(),
                         k: k_out.into(),
-                        dnum: dnum_apply.into(),
+                        dnum: dnum_in.into(),
                         dsize: dsize_in.into(),
                         rank_in: rank_in_s0s1.into(),
                         rank_out: rank_out_s1s2.into(),
@@ -85,8 +88,8 @@ | GLWESwitchingKey::encrypt_sk_tmp_bytes(module, &gglwe_s0s2_infos),
                     );
                     let mut scratch_apply: ScratchOwned<BE> = ScratchOwned::alloc(GLWESwitchingKey::keyswitch_tmp_bytes(
                         module,
-                        &gglwe_s0s1_infos,
                         &gglwe_s0s2_infos,
+                        &gglwe_s0s1_infos,
                         &gglwe_s1s2_infos,
                     ));
 
@@ -135,18 +138,21 @@ &gglwe_s1s2_prepared,
                         scratch_apply.borrow(),
                     );
 
-                    let max_noise: f64 = log2_std_noise_gglwe_product(
-                        n as f64,
-                        base2k * di,
+                    let max_noise: f64 = var_noise_gglwe_product_v2(
+                        module.n() as f64,
+                        k_ksk,
+                        dnum_ksk,
+                        dsize,
+                        base2k_key,
                         0.5,
                         0.5,
                         0f64,
                         SIGMA * SIGMA,
                         0f64,
                         rank_out_s0s1 as f64,
-                        k_in,
-                        k_ksk,
-                    );
+                    )
+                    .sqrt()
+                    .log2();
 
                     gglwe_s0s2
                         .key
@@ -168,23 +174,27 @@ + GLWESwitchingKeyPreparedFactory<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_out: usize = 60;
-    let dsize: usize = k_out.div_ceil(base2k);
+    let base2k_out: usize = 17;
+    let base2k_key: usize = 13;
+    let k_out: usize = 102;
+    let max_dsize: usize = k_out.div_ceil(base2k_key);
+
     for rank_in in 1_usize..3 {
         for rank_out in 1_usize..3 {
-            for di in 1_usize..dsize + 1 {
-                let k_ksk: usize = k_out + base2k * di;
+            for dsize in 1_usize..max_dsize + 1 {
+                let k_ksk: usize = k_out + base2k_key * dsize;
 
                 let n: usize = module.n();
-                let dnum: usize = k_out.div_ceil(base2k * di);
                 let dsize_in: usize = 1;
 
+                let dnum_in: usize = k_out / base2k_out;
+                let dnum_ksk: usize = k_out.div_ceil(base2k_key * dsize);
+
                 let gglwe_s0s1_infos: GLWESwitchingKeyLayout = GLWESwitchingKeyLayout {
                     n: n.into(),
-                    base2k: base2k.into(),
+                    base2k: base2k_out.into(),
                     k: k_out.into(),
-                    dnum: dnum.into(),
+                    dnum: dnum_in.into(),
                     dsize: dsize_in.into(),
                     rank_in: rank_in.into(),
                     rank_out: rank_out.into(),
@@ -192,10 +202,10 @@ };
 
                 let gglwe_s1s2_infos: GLWESwitchingKeyLayout = GLWESwitchingKeyLayout {
                     n: n.into(),
-                    base2k: base2k.into(),
+                    base2k: base2k_key.into(),
                     k: k_ksk.into(),
-                    dnum: dnum.into(),
-                    dsize: di.into(),
+                    dnum: dnum_ksk.into(),
+                    dsize: dsize.into(),
                     rank_in: rank_out.into(),
                     rank_out: rank_out.into(),
                 };
@@ -263,7 +273,7 @@ let gglwe_s0s2: GLWESwitchingKey<Vec<u8>> = gglwe_s0s1;
 
                 let max_noise: f64 = log2_std_noise_gglwe_product(
                     n as f64,
-                    base2k * di,
+                    base2k_key * dsize,
                     var_xs,
                     var_xs,
                     0f64,

@@ -30,53 +30,57 @@ + GGSWNoise<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_in: usize = 54;
-    let dsize: usize = k_in.div_ceil(base2k);
+    let base2k_in: usize = 17;
+    let base2k_key: usize = 13;
+    let base2k_out: usize = base2k_in; // MUST BE SAME
+    let k_in: usize = 102;
+    let max_dsize: usize = k_in.div_ceil(base2k_key);
+
     for rank in 1_usize..3 {
-        for di in 1..dsize + 1 {
-            let k_ksk: usize = k_in + base2k * di;
+        for dsize in 1..max_dsize + 1 {
+            let k_ksk: usize = k_in + base2k_key * dsize;
             let k_tsk: usize = k_ksk;
             let k_out: usize = k_ksk; // Better capture noise.
 
             let n: usize = module.n();
-            let dnum: usize = k_in.div_ceil(di * base2k);
+            let dnum_in: usize = k_in / base2k_in;
+            let dnum_ksk: usize = k_in.div_ceil(base2k_key * dsize);
 
             let dsize_in: usize = 1;
 
             let ggsw_in_infos: GGSWLayout = GGSWLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_in.into(),
                 k: k_in.into(),
-                dnum: dnum.into(),
+                dnum: dnum_in.into(),
                 dsize: dsize_in.into(),
                 rank: rank.into(),
             };
 
             let ggsw_out_infos: GGSWLayout = GGSWLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_out.into(),
                 k: k_out.into(),
-                dnum: dnum.into(),
+                dnum: dnum_in.into(),
                 dsize: dsize_in.into(),
                 rank: rank.into(),
             };
 
             let tsk_infos: GLWETensorKeyLayout = GLWETensorKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_tsk.into(),
-                dnum: dnum.into(),
-                dsize: di.into(),
+                dnum: dnum_ksk.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
             let ksk_apply_infos: GLWESwitchingKeyLayout = GLWESwitchingKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_ksk.into(),
-                dnum: dnum.into(),
-                dsize: di.into(),
+                dnum: dnum_ksk.into(),
+                dsize: dsize.into(),
                 rank_in: rank.into(),
                 rank_out: rank.into(),
             };
@@ -163,7 +167,7 @@
             let max_noise = |col_j: usize| -> f64 {
                 noise_ggsw_keyswitch(
                     n as f64,
-                    base2k * di,
+                    base2k_key * dsize,
                     col_j,
                     var_xs,
                     0f64,
@@ -195,43 +199,45 @@ + GGSWNoise<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_out: usize = 54;
-    let dsize: usize = k_out.div_ceil(base2k);
+    let base2k_out: usize = 17;
+    let base2k_key: usize = 13;
+    let k_out: usize = 102;
+    let max_dsize: usize = k_out.div_ceil(base2k_key);
+
     for rank in 1_usize..3 {
-        for di in 1..dsize + 1 {
-            let k_ksk: usize = k_out + base2k * di;
+        for dsize in 1..max_dsize + 1 {
+            let k_ksk: usize = k_out + base2k_key * dsize;
             let k_tsk: usize = k_ksk;
 
             let n: usize = module.n();
-            let dnum: usize = k_out.div_ceil(di * base2k);
-
+            let dnum_in: usize = k_out / base2k_out;
+            let dnum_ksk: usize = k_out.div_ceil(base2k_key * dsize);
             let dsize_in: usize = 1;
 
             let ggsw_out_infos: GGSWLayout = GGSWLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_out.into(),
                 k: k_out.into(),
-                dnum: dnum.into(),
+                dnum: dnum_in.into(),
                 dsize: dsize_in.into(),
                 rank: rank.into(),
             };
 
             let tsk_infos: GLWETensorKeyLayout = GLWETensorKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_tsk.into(),
-                dnum: dnum.into(),
-                dsize: di.into(),
+                dnum: dnum_ksk.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
             let ksk_apply_infos: GLWESwitchingKeyLayout = GLWESwitchingKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_ksk.into(),
-                dnum: dnum.into(),
-                dsize: di.into(),
+                dnum: dnum_ksk.into(),
+                dsize: dsize.into(),
                 rank_in: rank.into(),
                 rank_out: rank.into(),
             };
@@ -311,7 +317,7 @@
             let max_noise = |col_j: usize| -> f64 {
                 noise_ggsw_keyswitch(
                     n as f64,
-                    base2k * di,
+                    base2k_key * dsize,
                     col_j,
                     var_xs,
                     0f64,

@@ -12,7 +12,6 @@ GLWE, GLWELayout, GLWEPlaintext, GLWESecret, GLWESecretPreparedFactory, GLWESwitchingKey, GLWESwitchingKeyLayout,
         GLWESwitchingKeyPreparedFactory, LWEInfos,
         prepared::{GLWESecretPrepared, GLWESwitchingKeyPrepared},
     },
-    noise::log2_std_noise_gglwe_product,
     var_noise_gglwe_product_v2,
 };
 

@@ -1,5 +1,5 @@
 use poulpy_hal::{
-    api::{ScratchAvailable, ScratchOwnedAlloc, ScratchOwnedBorrow},
+    api::{ScratchAvailable, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxNormalize},
     layouts::{Backend, Module, Scratch, ScratchOwned, ZnxView},
     source::Source,
 };
@@ -14,21 +14,27 @@ };
 
 pub fn test_lwe_keyswitch<BE: Backend>(module: &Module<BE>)
 where
-    Module<BE>:
-        LWEKeySwitch<BE> + LWESwitchingKeyEncrypt<BE> + LWEEncryptSk<BE> + LWESwitchingKeyPreparedFactory<BE> + LWEDecrypt<BE>,
+    Module<BE>: LWEKeySwitch<BE>
+        + LWESwitchingKeyEncrypt<BE>
+        + LWEEncryptSk<BE>
+        + LWESwitchingKeyPreparedFactory<BE>
+        + LWEDecrypt<BE>
+        + VecZnxNormalize<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
     let n: usize = module.n();
-    let base2k: usize = 17;
+    let base2k_in: usize = 17;
+    let base2k_out: usize = 15;
+    let base2k_key: usize = 13;
 
-    let n_lwe_in: usize = 22;
-    let n_lwe_out: usize = 30;
-    let k_lwe_ct: usize = 2 * base2k;
+    let n_lwe_in: usize = module.n() >> 1;
+    let n_lwe_out: usize = module.n() >> 1;
+    let k_lwe_ct: usize = 102;
     let k_lwe_pt: usize = 8;
 
-    let k_ksk: usize = k_lwe_ct + base2k;
-    let dnum: usize = k_lwe_ct.div_ceil(base2k);
+    let k_ksk: usize = k_lwe_ct + base2k_key;
+    let dnum: usize = k_lwe_ct.div_ceil(base2k_key);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xa: Source = Source::new([0u8; 32]);
@@ -36,21 +42,21 @@ let mut source_xe: Source = Source::new([0u8; 32]);
 
     let key_apply_infos: LWESwitchingKeyLayout = LWESwitchingKeyLayout {
         n: n.into(),
-        base2k: base2k.into(),
+        base2k: base2k_key.into(),
         k: k_ksk.into(),
         dnum: dnum.into(),
     };
 
     let lwe_in_infos: LWELayout = LWELayout {
         n: n_lwe_in.into(),
-        base2k: base2k.into(),
+        base2k: base2k_in.into(),
         k: k_lwe_ct.into(),
     };
 
     let lwe_out_infos: LWELayout = LWELayout {
         n: n_lwe_out.into(),
         k: k_lwe_ct.into(),
-        base2k: base2k.into(),
+        base2k: base2k_out.into(),
     };
 
     let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
@@ -66,7 +72,7 @@ sk_lwe_out.fill_ternary_prob(0.5, &mut source_xs);
 
     let data: i64 = 17;
 
-    let mut lwe_pt_in: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc(base2k.into(), k_lwe_pt.into());
+    let mut lwe_pt_in: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc(base2k_in.into(), k_lwe_pt.into());
     lwe_pt_in.encode_i64(data, k_lwe_pt.into());
 
     let mut lwe_ct_in: LWE<Vec<u8>> = LWE::alloc_from_infos(&lwe_in_infos);
@@ -76,6 +82,7 @@ &lwe_pt_in,
         &sk_lwe_in,
         &mut source_xa,
         &mut source_xe,
+        scratch.borrow(),
     );
 
     let mut ksk: LWESwitchingKey<Vec<u8>> = LWESwitchingKey::alloc_from_infos(&key_apply_infos);
@@ -97,7 +104,18 @@
     lwe_ct_out.keyswitch(module, &lwe_ct_in, &ksk_prepared, scratch.borrow());
 
     let mut lwe_pt_out: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc_from_infos(&lwe_out_infos);
-    lwe_ct_out.decrypt(module, &mut lwe_pt_out, &sk_lwe_out);
+    lwe_ct_out.decrypt(module, &mut lwe_pt_out, &sk_lwe_out, scratch.borrow());
 
-    assert_eq!(lwe_pt_in.data.at(0, 0)[0], lwe_pt_out.data.at(0, 0)[0]);
+    let mut lwe_pt_want: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc_from_infos(&lwe_out_infos);
+    module.vec_znx_normalize(
+        base2k_out,
+        lwe_pt_want.data_mut(),
+        0,
+        base2k_in,
+        lwe_pt_in.data(),
+        0,
+        scratch.borrow(),
+    );
+
+    assert_eq!(lwe_pt_want.data.at(0, 0)[0], lwe_pt_out.data.at(0, 0)[0]);
 }

@@ -37,16 +37,20 @@
 impl<D: DataMut> LWEPlaintext<D> {
     pub fn encode_i64(&mut self, data: i64, k: TorusPrecision) {
         let base2k: usize = self.base2k().into();
-        self.data.encode_i64(base2k, k.into(), data);
+        self.data.encode_coeff_i64(base2k, 0, k.into(), 0, data);
     }
 }
 
 impl<D: DataRef> LWEPlaintext<D> {
     pub fn decode_i64(&self, k: TorusPrecision) -> i64 {
-        self.data.decode_i64(self.base2k().into(), k.into())
+        self.data
+            .decode_coeff_i64(self.base2k().into(), 0, k.into(), 0)
     }
 
     pub fn decode_float(&self) -> Float {
-        self.data.decode_float(self.base2k().into())
+        let mut out: [Float; 1] = [Float::new(self.k().as_u32())];
+        self.data
+            .decode_vec_float(self.base2k().into(), 0, &mut out);
+        out[0].clone()
     }
 }

@@ -6,7 +6,6 @@ mod vec_znx;
 mod vec_znx_big;
 mod vec_znx_dft;
 mod vmp_pmat;
-mod zn;
 
 pub use convolution::*;
 pub use module::*;
@@ -16,4 +15,3 @@ pub use vec_znx::*;
 pub use vec_znx_big::*;
 pub use vec_znx_dft::*;
 pub use vmp_pmat::*;
-pub use zn::*;

@@ -1,6 +1,6 @@
 use crate::{
     api::{ModuleN, SvpPPolBytesOf, VecZnxBigBytesOf, VecZnxDftBytesOf, VmpPMatBytesOf},
-    layouts::{Backend, MatZnx, ScalarZnx, Scratch, SvpPPol, VecZnx, VecZnxBig, VecZnxDft, VmpPMat, Zn},
+    layouts::{Backend, MatZnx, ScalarZnx, Scratch, SvpPPol, VecZnx, VecZnxBig, VecZnxDft, VmpPMat},
 };
 
 /// Allocates a new [crate::layouts::ScratchOwned] of `size` aligned bytes.
@@ -67,11 +67,6 @@ M: SvpPPolBytesOf + ModuleN,
     {
         let (take_slice, rem_slice) = self.take_slice(module.bytes_of_svp_ppol(cols));
         (SvpPPol::from_data(take_slice, module.n(), cols), rem_slice)
-    }
-
-    fn take_zn(&mut self, n: usize, cols: usize, size: usize) -> (Zn<&mut [u8]>, &mut Self) {
-        let (take_slice, rem_slice) = self.take_slice(Zn::bytes_of(n, cols, size));
-        (Zn::from_data(take_slice, n, cols, size), rem_slice)
     }
 
     fn take_vec_znx(&mut self, n: usize, cols: usize, size: usize) -> (VecZnx<&mut [u8]>, &mut Self) {

@@ -1,58 +0,0 @@
-use crate::{
-    layouts::{Backend, Scratch, ZnToMut},
-    reference::zn::zn_normalize_tmp_bytes,
-    source::Source,
-};
-
-pub trait ZnNormalizeTmpBytes {
-    fn zn_normalize_tmp_bytes(&self, n: usize) -> usize {
-        zn_normalize_tmp_bytes(n)
-    }
-}
-
-pub trait ZnNormalizeInplace<B: Backend> {
-    /// Normalizes the selected column of `a`.
-    fn zn_normalize_inplace<R>(&self, n: usize, base2k: usize, res: &mut R, res_col: usize, scratch: &mut Scratch<B>)
-    where
-        R: ZnToMut;
-}
-
-pub trait ZnFillUniform {
-    /// Fills the first `size` size with uniform values in \[-2^{base2k-1}, 2^{base2k-1}\]
-    fn zn_fill_uniform<R>(&self, n: usize, base2k: usize, res: &mut R, res_col: usize, source: &mut Source)
-    where
-        R: ZnToMut;
-}
-
-#[allow(clippy::too_many_arguments)]
-pub trait ZnFillNormal {
-    fn zn_fill_normal<R>(
-        &self,
-        n: usize,
-        base2k: usize,
-        res: &mut R,
-        res_col: usize,
-        k: usize,
-        source: &mut Source,
-        sigma: f64,
-        bound: f64,
-    ) where
-        R: ZnToMut;
-}
-
-#[allow(clippy::too_many_arguments)]
-pub trait ZnAddNormal {
-    /// Adds a discrete normal vector scaled by 2^{-k} with the provided standard deviation and bounded to \[-bound, bound\].
-    fn zn_add_normal<R>(
-        &self,
-        n: usize,
-        base2k: usize,
-        res: &mut R,
-        res_col: usize,
-        k: usize,
-        source: &mut Source,
-        sigma: f64,
-        bound: f64,
-    ) where
-        R: ZnToMut;
-}

@@ -5,4 +5,3 @@ mod vec_znx;
 mod vec_znx_big;
 mod vec_znx_dft;
 mod vmp_pmat;
-mod zn;

@@ -1,81 +0,0 @@
-use crate::{
-    api::{ZnAddNormal, ZnFillNormal, ZnFillUniform, ZnNormalizeInplace, ZnNormalizeTmpBytes},
-    layouts::{Backend, Module, Scratch, ZnToMut},
-    oep::{ZnAddNormalImpl, ZnFillNormalImpl, ZnFillUniformImpl, ZnNormalizeInplaceImpl, ZnNormalizeTmpBytesImpl},
-    source::Source,
-};
-
-impl<B> ZnNormalizeTmpBytes for Module<B>
-where
-    B: Backend + ZnNormalizeTmpBytesImpl<B>,
-{
-    fn zn_normalize_tmp_bytes(&self, n: usize) -> usize {
-        B::zn_normalize_tmp_bytes_impl(n)
-    }
-}
-
-impl<B> ZnNormalizeInplace<B> for Module<B>
-where
-    B: Backend + ZnNormalizeInplaceImpl<B>,
-{
-    fn zn_normalize_inplace<A>(&self, n: usize, base2k: usize, a: &mut A, a_col: usize, scratch: &mut Scratch<B>)
-    where
-        A: ZnToMut,
-    {
-        B::zn_normalize_inplace_impl(n, base2k, a, a_col, scratch)
-    }
-}
-
-impl<B> ZnFillUniform for Module<B>
-where
-    B: Backend + ZnFillUniformImpl<B>,
-{
-    fn zn_fill_uniform<R>(&self, n: usize, base2k: usize, res: &mut R, res_col: usize, source: &mut Source)
-    where
-        R: ZnToMut,
-    {
-        B::zn_fill_uniform_impl(n, base2k, res, res_col, source);
-    }
-}
-
-impl<B> ZnFillNormal for Module<B>
-where
-    B: Backend + ZnFillNormalImpl<B>,
-{
-    fn zn_fill_normal<R>(
-        &self,
-        n: usize,
-        base2k: usize,
-        res: &mut R,
-        res_col: usize,
-        k: usize,
-        source: &mut Source,
-        sigma: f64,
-        bound: f64,
-    ) where
-        R: ZnToMut,
-    {
-        B::zn_fill_normal_impl(n, base2k, res, res_col, k, source, sigma, bound);
-    }
-}
-
-impl<B> ZnAddNormal for Module<B>
-where
-    B: Backend + ZnAddNormalImpl<B>,
-{
-    fn zn_add_normal<R>(
-        &self,
-        n: usize,
-        base2k: usize,
-        res: &mut R,
-        res_col: usize,
-        k: usize,
-        source: &mut Source,
-        sigma: f64,
-        bound: f64,
-    ) where
-        R: ZnToMut,
-    {
-        B::zn_add_normal_impl(n, base2k, res, res_col, k, source, sigma, bound);
-    }
-}

@@ -2,7 +2,7 @@ use itertools::izip;
 use rug::{Assign, Float};
 
 use crate::{
-    layouts::{DataMut, DataRef, VecZnx, VecZnxToMut, VecZnxToRef, Zn, ZnToMut, ZnToRef, ZnxInfos, ZnxView, ZnxViewMut},
+    layouts::{DataMut, DataRef, VecZnx, VecZnxToMut, VecZnxToRef, ZnxInfos, ZnxView, ZnxViewMut},
     reference::znx::{
         ZnxNormalizeFinalStepInplace, ZnxNormalizeFirstStepInplace, ZnxNormalizeMiddleStepInplace, ZnxRef, ZnxZero,
         get_carry_i128, get_digit_i128, znx_zero_ref,
@@ -242,90 +242,6 @@ *y /= &base;
                 });
             }
         });
-    }
-}
-
-impl<D: DataMut> Zn<D> {
-    pub fn encode_i64(&mut self, base2k: usize, k: usize, data: i64) {
-        let size: usize = k.div_ceil(base2k);
-
-        #[cfg(debug_assertions)]
-        {
-            let a: Zn<&mut [u8]> = self.to_mut();
-            assert!(
-                size <= a.size(),
-                "invalid argument k.div_ceil(base2k)={} > a.size()={}",
-                size,
-                a.size()
-            );
-        }
-
-        let mut a: Zn<&mut [u8]> = self.to_mut();
-        let a_size = a.size();
-
-        for j in 0..a_size {
-            a.at_mut(0, j)[0] = 0
-        }
-
-        a.at_mut(0, size - 1)[0] = data;
-
-        let mut carry: Vec<i64> = vec![0i64; 1];
-        let k_rem: usize = (base2k - (k % base2k)) % base2k;
-
-        for j in (0..size).rev() {
-            let slice = &mut a.at_mut(0, j)[..1];
-
-            if j == size - 1 {
-                ZnxRef::znx_normalize_first_step_inplace(base2k, k_rem, slice, &mut carry);
-            } else if j == 0 {
-                ZnxRef::znx_normalize_final_step_inplace(base2k, k_rem, slice, &mut carry);
-            } else {
-                ZnxRef::znx_normalize_middle_step_inplace(base2k, k_rem, slice, &mut carry);
-            }
-        }
-    }
-}
-
-impl<D: DataRef> Zn<D> {
-    pub fn decode_i64(&self, base2k: usize, k: usize) -> i64 {
-        let a: Zn<&[u8]> = self.to_ref();
-        let size: usize = k.div_ceil(base2k);
-        let mut res: i64 = 0;
-        let rem: usize = base2k - (k % base2k);
-        (0..size).for_each(|j| {
-            let x: i64 = a.at(0, j)[0];
-            if j == size - 1 && rem != base2k {
-                let k_rem: usize = (base2k - rem) % base2k;
-                let scale: i64 = 1 << rem as i64;
-                res = (res << k_rem) + div_round(x, scale);
-            } else {
-                res = (res << base2k) + x;
-            }
-        });
-        res
-    }
-
-    pub fn decode_float(&self, base2k: usize) -> Float {
-        let a: Zn<&[u8]> = self.to_ref();
-        let size: usize = a.size();
-        let prec: u32 = (base2k * size) as u32;
-
-        // 2^{base2k}
-        let base: Float = Float::with_val(prec, (1 << base2k) as f64);
-        let mut res: Float = Float::with_val(prec, (1 << base2k) as f64);
-
-        // y[i] = sum x[j][i] * 2^{-base2k*j}
-        (0..size).for_each(|i| {
-            if i == 0 {
-                res.assign(a.at(0, size - i - 1)[0]);
-                res /= &base;
-            } else {
-                res += Float::with_val(prec, a.at(0, size - i - 1)[0]);
-                res /= &base;
-            }
-        });
-
-        res
     }
 }
 

@@ -10,7 +10,6 @@ mod vec_znx;
 mod vec_znx_big;
 mod vec_znx_dft;
 mod vmp_pmat;
-mod zn;
 mod znx_base;
 
 pub use mat_znx::*;
@@ -24,7 +23,6 @@ pub use vec_znx::*;
 pub use vec_znx_big::*;
 pub use vec_znx_dft::*;
 pub use vmp_pmat::*;
-pub use zn::*;
 pub use znx_base::*;
 
 pub trait Data = PartialEq + Eq + Sized + Default;

@@ -1,273 +0,0 @@
-use std::{
-    fmt,
-    hash::{DefaultHasher, Hasher},
-};
-
-use crate::{
-    alloc_aligned,
-    layouts::{
-        Data, DataMut, DataRef, DataView, DataViewMut, DigestU64, FillUniform, ReaderFrom, ToOwnedDeep, WriterTo, ZnxInfos,
-        ZnxSliceSize, ZnxView, ZnxViewMut, ZnxZero,
-    },
-    source::Source,
-};
-
-use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
-use rand::RngCore;
-
-#[repr(C)]
-#[derive(PartialEq, Eq, Clone, Copy, Hash)]
-pub struct Zn<D: Data> {
-    pub data: D,
-    pub n: usize,
-    pub cols: usize,
-    pub size: usize,
-    pub max_size: usize,
-}
-
-impl<D: DataRef> DigestU64 for Zn<D> {
-    fn digest_u64(&self) -> u64 {
-        let mut h: DefaultHasher = DefaultHasher::new();
-        h.write(self.data.as_ref());
-        h.write_usize(self.n);
-        h.write_usize(self.cols);
-        h.write_usize(self.size);
-        h.write_usize(self.max_size);
-        h.finish()
-    }
-}
-
-impl<D: DataRef> ToOwnedDeep for Zn<D> {
-    type Owned = Zn<Vec<u8>>;
-    fn to_owned_deep(&self) -> Self::Owned {
-        Zn {
-            data: self.data.as_ref().to_vec(),
-            n: self.n,
-            cols: self.cols,
-            size: self.size,
-            max_size: self.max_size,
-        }
-    }
-}
-
-impl<D: DataRef> fmt::Debug for Zn<D> {
-    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        write!(f, "{self}")
-    }
-}
-
-impl<D: Data> ZnxInfos for Zn<D> {
-    fn cols(&self) -> usize {
-        self.cols
-    }
-
-    fn rows(&self) -> usize {
-        1
-    }
-
-    fn n(&self) -> usize {
-        self.n
-    }
-
-    fn size(&self) -> usize {
-        self.size
-    }
-}
-
-impl<D: Data> ZnxSliceSize for Zn<D> {
-    fn sl(&self) -> usize {
-        self.n() * self.cols()
-    }
-}
-
-impl<D: Data> DataView for Zn<D> {
-    type D = D;
-    fn data(&self) -> &Self::D {
-        &self.data
-    }
-}
-
-impl<D: Data> DataViewMut for Zn<D> {
-    fn data_mut(&mut self) -> &mut Self::D {
-        &mut self.data
-    }
-}
-
-impl<D: DataRef> ZnxView for Zn<D> {
-    type Scalar = i64;
-}
-
-impl Zn<Vec<u8>> {
-    pub fn rsh_tmp_bytes(n: usize) -> usize {
-        n * std::mem::size_of::<i64>()
-    }
-}
-
-impl<D: DataMut> ZnxZero for Zn<D> {
-    fn zero(&mut self) {
-        self.raw_mut().fill(0)
-    }
-    fn zero_at(&mut self, i: usize, j: usize) {
-        self.at_mut(i, j).fill(0);
-    }
-}
-
-impl Zn<Vec<u8>> {
-    pub fn bytes_of(n: usize, cols: usize, size: usize) -> usize {
-        n * cols * size * size_of::<i64>()
-    }
-
-    pub fn alloc(n: usize, cols: usize, size: usize) -> Self {
-        let data: Vec<u8> = alloc_aligned::<u8>(Self::bytes_of(n, cols, size));
-        Self {
-            data,
-            n,
-            cols,
-            size,
-            max_size: size,
-        }
-    }
-
-    pub fn from_bytes<Scalar: Sized>(n: usize, cols: usize, size: usize, bytes: impl Into<Vec<u8>>) -> Self {
-        let data: Vec<u8> = bytes.into();
-        assert!(data.len() == Self::bytes_of(n, cols, size));
-        Self {
-            data,
-            n,
-            cols,
-            size,
-            max_size: size,
-        }
-    }
-}
-
-impl<D: Data> Zn<D> {
-    pub fn from_data(data: D, n: usize, cols: usize, size: usize) -> Self {
-        Self {
-            data,
-            n,
-            cols,
-            size,
-            max_size: size,
-        }
-    }
-}
-
-impl<D: DataRef> fmt::Display for Zn<D> {
-    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-        writeln!(
-            f,
-            "Zn(n={}, cols={}, size={})",
-            self.n, self.cols, self.size
-        )?;
-
-        for col in 0..self.cols {
-            writeln!(f, "Column {col}:")?;
-            for size in 0..self.size {
-                let coeffs = self.at(col, size);
-                write!(f, "  Size {size}: [")?;
-
-                let max_show = 100;
-                let show_count = coeffs.len().min(max_show);
-
-                for (i, &coeff) in coeffs.iter().take(show_count).enumerate() {
-                    if i > 0 {
-                        write!(f, ", ")?;
-                    }
-                    write!(f, "{coeff}")?;
-                }
-
-                if coeffs.len() > max_show {
-                    write!(f, ", ... ({} more)", coeffs.len() - max_show)?;
-                }
-
-                writeln!(f, "]")?;
-            }
-        }
-        Ok(())
-    }
-}
-
-impl<D: DataMut> FillUniform for Zn<D> {
-    fn fill_uniform(&mut self, log_bound: usize, source: &mut Source) {
-        match log_bound {
-            64 => source.fill_bytes(self.data.as_mut()),
-            0 => panic!("invalid log_bound, cannot be zero"),
-            _ => {
-                let mask: u64 = (1u64 << log_bound) - 1;
-                for x in self.raw_mut().iter_mut() {
-                    let r = source.next_u64() & mask;
-                    *x = ((r << (64 - log_bound)) as i64) >> (64 - log_bound);
-                }
-            }
-        }
-    }
-}
-
-pub type ZnOwned = Zn<Vec<u8>>;
-pub type ZnMut<'a> = Zn<&'a mut [u8]>;
-pub type ZnRef<'a> = Zn<&'a [u8]>;
-
-pub trait ZnToRef {
-    fn to_ref(&self) -> Zn<&[u8]>;
-}
-
-impl<D: DataRef> ZnToRef for Zn<D> {
-    fn to_ref(&self) -> Zn<&[u8]> {
-        Zn {
-            data: self.data.as_ref(),
-            n: self.n,
-            cols: self.cols,
-            size: self.size,
-            max_size: self.max_size,
-        }
-    }
-}
-
-pub trait ZnToMut {
-    fn to_mut(&mut self) -> Zn<&mut [u8]>;
-}
-
-impl<D: DataMut> ZnToMut for Zn<D> {
-    fn to_mut(&mut self) -> Zn<&mut [u8]> {
-        Zn {
-            data: self.data.as_mut(),
-            n: self.n,
-            cols: self.cols,
-            size: self.size,
-            max_size: self.max_size,
-        }
-    }
-}
-
-impl<D: DataMut> ReaderFrom for Zn<D> {
-    fn read_from<R: std::io::Read>(&mut self, reader: &mut R) -> std::io::Result<()> {
-        self.n = reader.read_u64::<LittleEndian>()? as usize;
-        self.cols = reader.read_u64::<LittleEndian>()? as usize;
-        self.size = reader.read_u64::<LittleEndian>()? as usize;
-        self.max_size = reader.read_u64::<LittleEndian>()? as usize;
-        let len: usize = reader.read_u64::<LittleEndian>()? as usize;
-        let buf: &mut [u8] = self.data.as_mut();
-        if buf.len() != len {
-            return Err(std::io::Error::new(
-                std::io::ErrorKind::UnexpectedEof,
-                format!("self.data.len()={} != read len={}", buf.len(), len),
-            ));
-        }
-        reader.read_exact(&mut buf[..len])?;
-        Ok(())
-    }
-}
-
-impl<D: DataRef> WriterTo for Zn<D> {
-    fn write_to<W: std::io::Write>(&self, writer: &mut W) -> std::io::Result<()> {
-        writer.write_u64::<LittleEndian>(self.n as u64)?;
-        writer.write_u64::<LittleEndian>(self.cols as u64)?;
-        writer.write_u64::<LittleEndian>(self.size as u64)?;
-        writer.write_u64::<LittleEndian>(self.max_size as u64)?;
-        let buf: &[u8] = self.data.as_ref();
-        writer.write_u64::<LittleEndian>(buf.len() as u64)?;
-        writer.write_all(buf)?;
-        Ok(())
-    }
-}

@@ -5,7 +5,6 @@ mod vec_znx;
 mod vec_znx_big;
 mod vec_znx_dft;
 mod vmp_pmat;
-mod zn;
 
 pub use module::*;
 pub use scratch::*;
@@ -14,4 +13,3 @@ pub use vec_znx::*;
 pub use vec_znx_big::*;
 pub use vec_znx_dft::*;
 pub use vmp_pmat::*;
-pub use zn::*;

@@ -1,70 +0,0 @@
-use crate::{
-    layouts::{Backend, Scratch, ZnToMut},
-    source::Source,
-};
-
-/// # THIS TRAIT IS AN OPEN EXTENSION POINT (unsafe)
-/// * See [poulpy-backend/src/cpu_fft64_ref/zn.rs](https://github.com/phantomzone-org/poulpy/blob/main/poulpy-backend/src/cpu_fft64_ref/zn.rs) for reference implementation.
-/// * See [crate::api::ZnNormalizeTmpBytes] for corresponding public API.
-/// # Safety [crate::doc::backend_safety] for safety contract.
-pub unsafe trait ZnNormalizeTmpBytesImpl<B: Backend> {
-    fn zn_normalize_tmp_bytes_impl(n: usize) -> usize;
-}
-
-/// # THIS TRAIT IS AN OPEN EXTENSION POINT (unsafe)
-/// * See [poulpy-backend/src/cpu_fft64_ref/zn.rs](https://github.com/phantomzone-org/poulpy/blob/main/poulpy-backend/src/cpu_fft64_ref/zn.rs) for reference implementation.
-/// * See [crate::api::ZnNormalizeInplace] for corresponding public API.
-/// # Safety [crate::doc::backend_safety] for safety contract.
-pub unsafe trait ZnNormalizeInplaceImpl<B: Backend> {
-    fn zn_normalize_inplace_impl<R>(n: usize, base2k: usize, res: &mut R, res_col: usize, scratch: &mut Scratch<B>)
-    where
-        R: ZnToMut;
-}
-
-/// # THIS TRAIT IS AN OPEN EXTENSION POINT (unsafe)
-/// * See [poulpy-backend/src/cpu_fft64_ref/zn.rs](https://github.com/phantomzone-org/poulpy/blob/main/poulpy-backend/src/cpu_fft64_ref/zn.rs) for reference implementation.
-/// * See [crate::api::ZnFillUniform] for corresponding public API.
-/// # Safety [crate::doc::backend_safety] for safety contract.
-pub unsafe trait ZnFillUniformImpl<B: Backend> {
-    fn zn_fill_uniform_impl<R>(n: usize, base2k: usize, res: &mut R, res_col: usize, source: &mut Source)
-    where
-        R: ZnToMut;
-}
-
-#[allow(clippy::too_many_arguments)]
-/// # THIS TRAIT IS AN OPEN EXTENSION POINT (unsafe)
-/// * See [poulpy-backend/src/cpu_fft64_ref/zn.rs](https://github.com/phantomzone-org/poulpy/blob/main/poulpy-backend/src/cpu_fft64_ref/zn.rs) for reference implementation.
-/// * See [crate::api::ZnFillNormal] for corresponding public API.
-/// # Safety [crate::doc::backend_safety] for safety contract.
-pub unsafe trait ZnFillNormalImpl<B: Backend> {
-    fn zn_fill_normal_impl<R>(
-        n: usize,
-        base2k: usize,
-        res: &mut R,
-        res_col: usize,
-        k: usize,
-        source: &mut Source,
-        sigma: f64,
-        bound: f64,
-    ) where
-        R: ZnToMut;
-}
-
-#[allow(clippy::too_many_arguments)]
-/// # THIS TRAIT IS AN OPEN EXTENSION POINT (unsafe)
-/// * See [poulpy-backend/src/cpu_fft64_ref/zn.rs](https://github.com/phantomzone-org/poulpy/blob/main/poulpy-backend/src/cpu_fft64_ref/zn.rs) for reference implementation.
-/// * See [crate::api::ZnAddNormal] for corresponding public API.
-/// # Safety [crate::doc::backend_safety] for safety contract.
-pub unsafe trait ZnAddNormalImpl<B: Backend> {
-    fn zn_add_normal_impl<R>(
-        n: usize,
-        base2k: usize,
-        res: &mut R,
-        res_col: usize,
-        k: usize,
-        source: &mut Source,
-        sigma: f64,
-        bound: f64,
-    ) where
-        R: ZnToMut;
-}

@@ -1,4 +1,3 @@
 pub mod fft64;
 pub mod vec_znx;
-pub mod zn;
 pub mod znx;

@@ -53,6 +53,8 @@ let n: usize = res.n();
     let res_size: usize = res.size();
     let a_size: usize = a.size();
 
+    let carry = &mut carry[..2 * n];
+
     if res_base2k == a_base2k {
         if a_size > res_size {
             for j in (res_size..a_size).rev() {

@@ -1,5 +0,0 @@
-mod normalization;
-mod sampling;
-
-pub use normalization::*;
-pub use sampling::*;

@@ -1,72 +0,0 @@
-use crate::{
-    api::{ScratchOwnedAlloc, ScratchOwnedBorrow, ZnNormalizeInplace, ZnNormalizeTmpBytes},
-    layouts::{Backend, Module, ScratchOwned, Zn, ZnToMut, ZnxInfos, ZnxView, ZnxViewMut},
-    reference::znx::{ZnxNormalizeFinalStepInplace, ZnxNormalizeFirstStepInplace, ZnxNormalizeMiddleStepInplace, ZnxRef},
-    source::Source,
-};
-
-pub fn zn_normalize_tmp_bytes(n: usize) -> usize {
-    n * size_of::<i64>()
-}
-
-pub fn zn_normalize_inplace<R, ARI>(n: usize, base2k: usize, res: &mut R, res_col: usize, carry: &mut [i64])
-where
-    R: ZnToMut,
-    ARI: ZnxNormalizeFirstStepInplace + ZnxNormalizeFinalStepInplace + ZnxNormalizeMiddleStepInplace,
-{
-    let mut res: Zn<&mut [u8]> = res.to_mut();
-
-    #[cfg(debug_assertions)]
-    {
-        assert_eq!(carry.len(), res.n());
-    }
-
-    let res_size: usize = res.size();
-
-    for j in (0..res_size).rev() {
-        let out = &mut res.at_mut(res_col, j)[..n];
-
-        if j == res_size - 1 {
-            ARI::znx_normalize_first_step_inplace(base2k, 0, out, carry);
-        } else if j == 0 {
-            ARI::znx_normalize_final_step_inplace(base2k, 0, out, carry);
-        } else {
-            ARI::znx_normalize_middle_step_inplace(base2k, 0, out, carry);
-        }
-    }
-}
-
-pub fn test_zn_normalize_inplace<B: Backend>(module: &Module<B>)
-where
-    Module<B>: ZnNormalizeInplace<B> + ZnNormalizeTmpBytes,
-    ScratchOwned<B>: ScratchOwnedAlloc<B> + ScratchOwnedBorrow<B>,
-{
-    let mut source: Source = Source::new([0u8; 32]);
-    let cols: usize = 2;
-    let base2k: usize = 12;
-
-    let n = 33;
-
-    let mut carry: Vec<i64> = vec![0i64; zn_normalize_tmp_bytes(n)];
-
-    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(module.zn_normalize_tmp_bytes(module.n()));
-
-    for res_size in [1, 2, 6, 11] {
-        let mut res_0: Zn<Vec<u8>> = Zn::alloc(n, cols, res_size);
-        let mut res_1: Zn<Vec<u8>> = Zn::alloc(n, cols, res_size);
-
-        res_0
-            .raw_mut()
-            .iter_mut()
-            .for_each(|x| *x = source.next_i32() as i64);
-        res_1.raw_mut().copy_from_slice(res_0.raw());
-
-        // Reference
-        for i in 0..cols {
-            zn_normalize_inplace::<_, ZnxRef>(n, base2k, &mut res_0, i, &mut carry);
-            module.zn_normalize_inplace(n, base2k, &mut res_1, i, scratch.borrow());
-        }
-
-        assert_eq!(res_0.raw(), res_1.raw());
-    }
-}

@@ -1,75 +0,0 @@
-use crate::{
-    layouts::{Zn, ZnToMut, ZnxInfos, ZnxViewMut},
-    reference::znx::{znx_add_normal_f64_ref, znx_fill_normal_f64_ref, znx_fill_uniform_ref},
-    source::Source,
-};
-
-pub fn zn_fill_uniform<R>(n: usize, base2k: usize, res: &mut R, res_col: usize, source: &mut Source)
-where
-    R: ZnToMut,
-{
-    let mut res: Zn<&mut [u8]> = res.to_mut();
-    for j in 0..res.size() {
-        znx_fill_uniform_ref(base2k, &mut res.at_mut(res_col, j)[..n], source)
-    }
-}
-
-#[allow(clippy::too_many_arguments)]
-pub fn zn_fill_normal<R>(
-    n: usize,
-    base2k: usize,
-    res: &mut R,
-    res_col: usize,
-    k: usize,
-    source: &mut Source,
-    sigma: f64,
-    bound: f64,
-) where
-    R: ZnToMut,
-{
-    let mut res: Zn<&mut [u8]> = res.to_mut();
-    assert!(
-        (bound.log2().ceil() as i64) < 64,
-        "invalid bound: ceil(log2(bound))={} > 63",
-        (bound.log2().ceil() as i64)
-    );
-
-    let limb: usize = k.div_ceil(base2k) - 1;
-    let scale: f64 = (1 << ((limb + 1) * base2k - k)) as f64;
-    znx_fill_normal_f64_ref(
-        &mut res.at_mut(res_col, limb)[..n],
-        sigma * scale,
-        bound * scale,
-        source,
-    )
-}
-
-#[allow(clippy::too_many_arguments)]
-pub fn zn_add_normal<R>(
-    n: usize,
-    base2k: usize,
-    res: &mut R,
-    res_col: usize,
-    k: usize,
-    source: &mut Source,
-    sigma: f64,
-    bound: f64,
-) where
-    R: ZnToMut,
-{
-    let mut res: Zn<&mut [u8]> = res.to_mut();
-    assert!(
-        (bound.log2().ceil() as i64) < 64,
-        "invalid bound: ceil(log2(bound))={} > 63",
-        (bound.log2().ceil() as i64)
-    );
-
-    let limb: usize = k.div_ceil(base2k) - 1;
-    let scale: f64 = (1 << ((limb + 1) * base2k - k)) as f64;
-    znx_add_normal_f64_ref(
-        &mut res.at_mut(res_col, limb)[..n],
-        sigma * scale,
-        bound * scale,
-        source,
-    )
-}

@@ -2,7 +2,7 @@ use poulpy_core::{
     GLWENormalize,
     layouts::{
         GGLWEToGGSWKeyLayout, GGSW, GGSWLayout, GLWE, GLWEAutomorphismKeyLayout, GLWELayout, GLWEPlaintext, GLWESecret, LWE,
-        LWEInfos, LWELayout, LWEPlaintext, LWESecret,
+        LWELayout, LWEPlaintext, LWESecret,
         prepared::{GGSWPrepared, GLWESecretPrepared},
     },
 };
@@ -15,7 +15,7 @@ #[cfg(not(any(target_arch = "x86_64", target_arch = "x86")))]
 use poulpy_backend::FFT64Ref as BackendImpl;
 
 use poulpy_hal::{
-    api::{ModuleNew, ScratchOwnedAlloc, ScratchOwnedBorrow, ZnNormalizeInplace},
+    api::{ModuleNew, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxNormalizeInplace},
     layouts::{Module, ScalarZnx, ScratchOwned, ZnxView, ZnxViewMut},
     source::Source,
 };
@@ -155,20 +155,21 @@ // LWE plaintext(data * 2^{- (k_lwe_pt - 1)})
     pt_lwe.encode_i64(data, (k_lwe_pt + 1).into()); // +1 for padding bit
 
     // Normalize plaintext to nicely print coefficients
-    module.zn_normalize_inplace(
-        pt_lwe.n().into(),
-        base2k,
-        pt_lwe.data_mut(),
-        0,
-        scratch.borrow(),
-    );
+    module.vec_znx_normalize_inplace(base2k, pt_lwe.data_mut(), 0, scratch.borrow());
     println!("pt_lwe: {pt_lwe}");
 
     // LWE ciphertext
     let mut ct_lwe: LWE<Vec<u8>> = LWE::alloc_from_infos(&lwe_infos);
 
     // Encrypt LWE Plaintext
-    ct_lwe.encrypt_sk(&module, &pt_lwe, &sk_lwe, &mut source_xa, &mut source_xe);
+    ct_lwe.encrypt_sk(
+        &module,
+        &pt_lwe,
+        &sk_lwe,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
 
     let now: Instant = Instant::now();
 

@@ -111,7 +111,14 @@ let x: i64 = 15 % (message_modulus as i64);
 
     pt_lwe.encode_i64(x, (log_message_modulus + 1).into());
 
-    lwe.encrypt_sk(module, &pt_lwe, &sk_lwe, &mut source_xa, &mut source_xe);
+    lwe.encrypt_sk(
+        module,
+        &pt_lwe,
+        &sk_lwe,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
 
     let f = |x: i64| -> i64 { 2 * x + 1 };
 

@@ -132,7 +132,14 @@
     println!("pt_lwe: {pt_lwe}");
 
     let mut ct_lwe: LWE<Vec<u8>> = LWE::alloc_from_infos(&lwe_infos);
-    ct_lwe.encrypt_sk(module, &pt_lwe, &sk_lwe, &mut source_xa, &mut source_xe);
+    ct_lwe.encrypt_sk(
+        module,
+        &pt_lwe,
+        &sk_lwe,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
 
     let now: Instant = Instant::now();
     let mut cbt_key: CircuitBootstrappingKey<Vec<u8>, BRA> = CircuitBootstrappingKey::alloc_from_infos(&cbt_infos);
@@ -313,7 +320,14 @@
     println!("pt_lwe: {pt_lwe}");
 
     let mut ct_lwe: LWE<Vec<u8>> = LWE::alloc_from_infos(&lwe_infos);
-    ct_lwe.encrypt_sk(module, &pt_lwe, &sk_lwe, &mut source_xa, &mut source_xe);
+    ct_lwe.encrypt_sk(
+        module,
+        &pt_lwe,
+        &sk_lwe,
+        &mut source_xa,
+        &mut source_xe,
+        scratch.borrow(),
+    );
 
     let now: Instant = Instant::now();
     let mut cbt_key: CircuitBootstrappingKey<Vec<u8>, BRA> = CircuitBootstrappingKey::alloc_from_infos(&cbt_infos);