@@ -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 {}

@@ -53,10 +53,10 @@ Self: TakeSliceImpl<Self> + VecZnxNormalizeTmpBytesImpl<Self>,
 {
     fn vec_znx_normalize_impl<R, A>(
         module: &Module<Self>,
-        res_basek: usize,
+        res_base2k: usize,
         res: &mut R,
         res_col: usize,
-        a_basek: usize,
+        a_base2k: usize,
         a: &A,
         a_col: usize,
         scratch: &mut Scratch<Self>,
@@ -65,7 +65,7 @@ R: VecZnxToMut,
         A: VecZnxToRef,
     {
         let (carry, _) = scratch.take_slice(module.vec_znx_normalize_tmp_bytes() / size_of::<i64>());
-        vec_znx_normalize::<R, A, Self>(res_basek, res, res_col, a_basek, a, a_col, carry);
+        vec_znx_normalize::<R, A, Self>(res_base2k, res, res_col, a_base2k, a, a_col, carry);
     }
 }
 

@@ -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);
-    }
-}

@@ -68,7 +68,6 @@ pub fn znx_extract_digit_addmul_avx(base2k: usize, lsh: usize, res: &mut [i64], src: &mut [i64]) {
     #[cfg(debug_assertions)]
     {
         assert_eq!(res.len(), src.len());
-        assert!(lsh < base2k);
     }
 
     use std::arch::x86_64::{

@@ -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>> {
@@ -27,7 +27,7 @@ impl<DataSelf: DataMut> GLWE<DataSelf> {
     pub fn automorphism<M, A, K, BE: Backend>(&mut self, module: &M, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
         M: GLWEAutomorphism<BE>,
-        A: GLWEToRef,
+        A: GLWEToRef + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
@@ -37,7 +37,7 @@
     pub fn automorphism_add<M, A, K, BE: Backend>(&mut self, module: &M, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
         M: GLWEAutomorphism<BE>,
-        A: GLWEToRef,
+        A: GLWEToRef + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
@@ -47,7 +47,7 @@
     pub fn automorphism_sub<M, A, K, BE: Backend>(&mut self, module: &M, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
         M: GLWEAutomorphism<BE>,
-        A: GLWEToRef,
+        A: GLWEToRef + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
@@ -57,7 +57,7 @@
     pub fn automorphism_sub_negate<M, A, K, BE: Backend>(&mut self, module: &M, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
         M: GLWEAutomorphism<BE>,
-        A: GLWEToRef,
+        A: GLWEToRef + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
@@ -110,46 +110,46 @@ K: GGLWEInfos;
 
     fn glwe_automorphism<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
-        A: GLWEToRef,
+        R: GLWEToMut + GLWEInfos,
+        A: GLWEToRef + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
 
     fn glwe_automorphism_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
+        R: GLWEToMut + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
 
     fn glwe_automorphism_add<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
-        A: GLWEToRef,
+        R: GLWEToMut + GLWEInfos,
+        A: GLWEToRef + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
 
     fn glwe_automorphism_add_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
+        R: GLWEToMut + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
 
     fn glwe_automorphism_sub<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
-        A: GLWEToRef,
+        R: GLWEToMut + GLWEInfos,
+        A: GLWEToRef + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
 
     fn glwe_automorphism_sub_negate<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
-        A: GLWEToRef,
+        R: GLWEToMut + GLWEInfos,
+        A: GLWEToRef + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
 
     fn glwe_automorphism_sub_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
+        R: GLWEToMut + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
 
     fn glwe_automorphism_sub_negate_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
+        R: GLWEToMut + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos;
 }
 
@@ -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
@@ -178,8 +179,8 @@ }
 
     fn glwe_automorphism<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
-        A: GLWEToRef,
+        R: GLWEToMut + GLWEInfos,
+        A: GLWEToRef + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
@@ -194,7 +195,7 @@ }
 
     fn glwe_automorphism_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
+        R: GLWEToMut + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
@@ -209,30 +210,58 @@ }
 
     fn glwe_automorphism_add<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
-        A: GLWEToRef,
+        R: GLWEToMut + GLWEInfos,
+        A: GLWEToRef + GLWEInfos,
         K: GetGaloisElement + GGLWEPreparedToRef<BE> + GGLWEInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         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>)
@@ -242,23 +271,50 @@ 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_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>)
@@ -324,23 +436,50 @@ 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_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>)
@@ -351,21 +490,48 @@ 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));
     }

@@ -143,20 +143,21 @@
             let mut source_xa = Source::new(seed);
 
             let (mut tmp_pt, scrach_1) = scratch.take_glwe_plaintext(res);
-            for col_i in 0..rank_in {
-                for d_i in 0..dnum {
+
+            for col_j in 0..rank_in {
+                for row_i in 0..dnum {
                     // Adds the scalar_znx_pt to the i-th limb of the vec_znx_pt
                     tmp_pt.data.zero(); // zeroes for next iteration
-                    self.vec_znx_add_scalar_inplace(&mut tmp_pt.data, 0, (dsize - 1) + d_i * dsize, pt, col_i);
+                    self.vec_znx_add_scalar_inplace(&mut tmp_pt.data, 0, (dsize - 1) + row_i * dsize, pt, col_j);
                     self.vec_znx_normalize_inplace(base2k, &mut tmp_pt.data, 0, scrach_1);
 
                     let (seed, mut source_xa_tmp) = source_xa.branch();
-                    seeds[col_i * dnum + d_i] = seed;
+                    seeds[row_i * rank_in + col_j] = seed;
 
                     self.glwe_encrypt_sk_internal(
                         res.base2k().into(),
                         res.k().into(),
-                        &mut res.at_mut(d_i, col_i).data,
+                        &mut res.at_mut(row_i, col_j).data,
                         cols,
                         true,
                         Some((&tmp_pt, 0)),

@@ -105,8 +105,6 @@
         {
             let res: &mut GGSWCompressed<&mut [u8]> = &mut res.to_mut();
 
-            println!("res.seed: {:?}", res.seed);
-
             let (mut tmp_pt, scratch_1) = scratch.take_glwe_plaintext(res);
 
             let mut source = Source::new(seed_xa);

@@ -516,8 +516,6 @@
                 // ct[i] = uniform (+ pt)
                 self.vec_znx_fill_uniform(base2k, ct, col_ct, source_xa);
 
-                // println!("vec_znx_fill_uniform: {}", ct);
-
                 let (mut ci_dft, scratch_3) = scratch_2.take_vec_znx_dft(self, 1, size);
 
                 // ci = ct[i] - pt

@@ -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();

@@ -1,10 +1,10 @@
 use poulpy_hal::{
     api::{
-        ModuleN, ScratchTakeBasic, VecZnxBigAddSmallInplace, VecZnxBigNormalize, VecZnxBigNormalizeTmpBytes, VecZnxDftApply,
-        VecZnxDftBytesOf, VecZnxIdftApplyConsume, VecZnxNormalize, VecZnxNormalizeTmpBytes, VmpApplyDftToDft,
+        ModuleN, ScratchAvailable, ScratchTakeBasic, VecZnxBigAddSmallInplace, VecZnxBigNormalize, VecZnxBigNormalizeTmpBytes,
+        VecZnxDftApply, VecZnxDftBytesOf, VecZnxIdftApplyConsume, VecZnxNormalize, VecZnxNormalizeTmpBytes, VmpApplyDftToDft,
         VmpApplyDftToDftAdd, VmpApplyDftToDftTmpBytes,
     },
-    layouts::{Backend, DataMut, DataViewMut, Module, Scratch, VecZnx, VecZnxBig, VecZnxDft},
+    layouts::{Backend, DataMut, DataViewMut, Module, Scratch, VecZnxBig, VecZnxDft},
 };
 
 use crate::{
@@ -30,7 +30,7 @@
 impl<DataSelf: DataMut> GLWE<DataSelf> {
     pub fn external_product<A, B, M, BE: Backend>(&mut self, module: &M, a: &A, b: &B, scratch: &mut Scratch<BE>)
     where
-        A: GLWEToRef,
+        A: GLWEToRef + GLWEInfos,
         B: GGSWPreparedToRef<BE> + GGSWInfos,
         M: GLWEExternalProduct<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
@@ -57,20 +57,14 @@ B: GGSWInfos;
 
     fn glwe_external_product_inplace<R, D>(&self, res: &mut R, a: &D, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
+        R: GLWEToMut + GLWEInfos,
         D: GGSWPreparedToRef<BE> + GGSWInfos,
         Scratch<BE>: ScratchTakeCore<BE>;
 
     fn glwe_external_product<R, A, D>(&self, res: &mut R, lhs: &A, rhs: &D, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
-        A: GLWEToRef,
-        D: GGSWPreparedToRef<BE> + GGSWInfos,
-        Scratch<BE>: ScratchTakeCore<BE>;
-    fn glwe_external_product_add<R, A, D>(&self, res: &mut R, lhs: &A, rhs: &D, scratch: &mut Scratch<BE>)
-    where
-        R: GLWEToMut,
-        A: GLWEToRef,
+        R: GLWEToMut + GLWEInfos,
+        A: GLWEToRef + GLWEInfos,
         D: GGSWPreparedToRef<BE> + GGSWInfos,
         Scratch<BE>: ScratchTakeCore<BE>;
 }
@@ -84,48 +78,63 @@ + VecZnxBigNormalizeTmpBytes
         + VecZnxBigAddSmallInplace<BE>
         + GLWENormalize<BE>,
 {
-    fn glwe_external_product_tmp_bytes<R, A, B>(&self, res_infos: &R, a_infos: &A, b_infos: &B) -> usize
+    fn glwe_external_product_tmp_bytes<R, A, B>(&self, res: &R, a: &A, ggsw: &B) -> usize
     where
         R: GLWEInfos,
         A: GLWEInfos,
         B: GGSWInfos,
     {
-        let res_dft: usize = self.bytes_of_vec_znx_dft((b_infos.rank() + 1).into(), b_infos.size());
-        res_dft
-            + self
-                .glwe_external_product_internal_tmp_bytes(res_infos, a_infos, b_infos)
-                .max(self.vec_znx_big_normalize_tmp_bytes())
+        let cols: usize = res.rank().as_usize() + 1;
+        let size: usize = if a.base2k() != ggsw.base2k() {
+            let a_conv_infos = &GLWELayout {
+                n: a.n(),
+                base2k: ggsw.base2k(),
+                k: a.k(),
+                rank: a.rank(),
+            };
+            self.glwe_external_product_internal_tmp_bytes(res, a_conv_infos, ggsw) + GLWE::bytes_of_from_infos(a_conv_infos)
+        } else {
+            self.glwe_external_product_internal_tmp_bytes(res, a, ggsw)
+        };
+
+        size.max(self.vec_znx_big_normalize_tmp_bytes()) + self.bytes_of_vec_znx_dft(cols, ggsw.size())
     }
 
-    fn glwe_external_product_inplace<R, D>(&self, res: &mut R, a: &D, scratch: &mut Scratch<BE>)
+    fn glwe_external_product_inplace<R, D>(&self, res: &mut R, ggsw: &D, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
+        R: GLWEToMut + GLWEInfos,
         D: GGSWPreparedToRef<BE> + GGSWInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
-        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
-        let rhs: &GGSWPrepared<&[u8], BE> = &a.to_ref();
+        assert_eq!(ggsw.rank(), res.rank());
+        assert_eq!(ggsw.n(), res.n());
+        assert!(scratch.available() >= self.glwe_external_product_tmp_bytes(res, res, ggsw));
 
-        let basek_in: usize = res.base2k().into();
-        let basek_ggsw: usize = rhs.base2k().into();
+        let base2k_res: usize = res.base2k().as_usize();
+        let base2k_ggsw: usize = ggsw.base2k().as_usize();
 
-        #[cfg(debug_assertions)]
-        {
-            use poulpy_hal::api::ScratchAvailable;
+        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), ggsw.size()); // Todo optimise
 
-            assert_eq!(rhs.rank(), res.rank());
-            assert_eq!(rhs.n(), res.n());
-            assert!(scratch.available() >= self.glwe_external_product_tmp_bytes(res, res, rhs));
-        }
+        let res_big: VecZnxBig<&mut [u8], BE> = if base2k_res != base2k_ggsw {
+            let (mut res_conv, scratch_2) = scratch_1.take_glwe(&GLWELayout {
+                n: res.n(),
+                base2k: ggsw.base2k(),
+                k: res.k(),
+                rank: res.rank(),
+            });
+            self.glwe_normalize(&mut res_conv, res, scratch_2);
+            self.glwe_external_product_internal(res_dft, &res_conv, ggsw, scratch_2)
+        } else {
+            self.glwe_external_product_internal(res_dft, res, ggsw, scratch_1)
+        };
 
-        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), a.size()); // Todo optimise
-        let res_big = self.glwe_external_product_internal(res_dft, res, a, scratch_1);
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         for j in 0..(res.rank() + 1).into() {
             self.vec_znx_big_normalize(
-                basek_in,
-                &mut res.data,
+                base2k_res,
+                res.data_mut(),
                 j,
-                basek_ggsw,
+                base2k_ggsw,
                 &res_big,
                 j,
                 scratch_1,
@@ -133,121 +142,51 @@ );
         }
     }
 
-    fn glwe_external_product<R, A, D>(&self, res: &mut R, lhs: &A, rhs: &D, scratch: &mut Scratch<BE>)
+    fn glwe_external_product<R, A, G>(&self, res: &mut R, a: &A, ggsw: &G, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
-        A: GLWEToRef,
-        D: GGSWPreparedToRef<BE>,
+        R: GLWEToMut + GLWEInfos,
+        A: GLWEToRef + GLWEInfos,
+        G: GGSWPreparedToRef<BE> + GGSWInfos,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
-        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
-        let lhs: &GLWE<&[u8]> = &lhs.to_ref();
-
-        let rhs: &GGSWPrepared<&[u8], BE> = &rhs.to_ref();
-
-        let basek_ggsw: usize = rhs.base2k().into();
-        let basek_out: usize = res.base2k().into();
+        assert_eq!(ggsw.rank(), a.rank());
+        assert_eq!(ggsw.rank(), res.rank());
+        assert_eq!(ggsw.n(), res.n());
+        assert_eq!(a.n(), res.n());
+        assert!(scratch.available() >= self.glwe_external_product_tmp_bytes(res, a, ggsw));
 
-        #[cfg(debug_assertions)]
-        {
-            use poulpy_hal::api::ScratchAvailable;
+        let base2k_a: usize = a.base2k().into();
+        let base2k_ggsw: usize = ggsw.base2k().into();
+        let base2k_res: usize = res.base2k().into();
 
-            assert_eq!(rhs.rank(), lhs.rank());
-            assert_eq!(rhs.rank(), res.rank());
-            assert_eq!(rhs.n(), res.n());
-            assert_eq!(lhs.n(), res.n());
-            assert!(scratch.available() >= self.glwe_external_product_tmp_bytes(res, lhs, rhs));
-        }
+        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), ggsw.size()); // Todo optimise
 
-        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), rhs.size()); // Todo optimise
-        let res_big = self.glwe_external_product_internal(res_dft, lhs, rhs, scratch_1);
+        let res_big: VecZnxBig<&mut [u8], BE> = if base2k_a != base2k_ggsw {
+            let (mut a_conv, scratch_2) = scratch_1.take_glwe(&GLWELayout {
+                n: a.n(),
+                base2k: ggsw.base2k(),
+                k: a.k(),
+                rank: a.rank(),
+            });
+            self.glwe_normalize(&mut a_conv, a, scratch_2);
+            self.glwe_external_product_internal(res_dft, &a_conv, ggsw, scratch_2)
+        } else {
+            self.glwe_external_product_internal(res_dft, a, ggsw, scratch_1)
+        };
 
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         for j in 0..(res.rank() + 1).into() {
             self.vec_znx_big_normalize(
-                basek_out,
-                &mut res.data,
+                base2k_res,
+                res.data_mut(),
                 j,
-                basek_ggsw,
+                base2k_ggsw,
                 &res_big,
                 j,
                 scratch_1,
             );
         }
     }
-
-    fn glwe_external_product_add<R, A, D>(&self, res: &mut R, a: &A, key: &D, scratch: &mut Scratch<BE>)
-    where
-        R: GLWEToMut,
-        A: GLWEToRef,
-        D: GGSWPreparedToRef<BE>,
-        Scratch<BE>: ScratchTakeCore<BE>,
-    {
-        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
-        let a: &GLWE<&[u8]> = &a.to_ref();
-        let key: &GGSWPrepared<&[u8], BE> = &key.to_ref();
-
-        assert_eq!(a.base2k(), res.base2k());
-
-        let res_base2k: usize = res.base2k().into();
-        let key_base2k: usize = key.base2k().into();
-
-        #[cfg(debug_assertions)]
-        {
-            use poulpy_hal::api::ScratchAvailable;
-
-            assert_eq!(key.rank(), a.rank());
-            assert_eq!(key.rank(), res.rank());
-            assert_eq!(key.n(), res.n());
-            assert_eq!(a.n(), res.n());
-            assert!(scratch.available() >= self.glwe_external_product_tmp_bytes(res, a, key));
-        }
-
-        if res_base2k == key_base2k {
-            let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // Todo optimise
-            let mut res_big = self.glwe_external_product_internal(res_dft, a, key, scratch_1);
-            for j in 0..(res.rank() + 1).into() {
-                self.vec_znx_big_add_small_inplace(&mut res_big, j, res.data(), j);
-                self.vec_znx_big_normalize(
-                    res_base2k,
-                    &mut res.data,
-                    j,
-                    key_base2k,
-                    &res_big,
-                    j,
-                    scratch_1,
-                );
-            }
-        } else {
-            let (mut a_conv, scratch_1) = scratch.take_glwe(&GLWELayout {
-                n: a.n(),
-                base2k: key.base2k(),
-                k: a.k(),
-                rank: a.rank(),
-            });
-            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 a_conv, a, scratch_2);
-            self.glwe_normalize(&mut res_conv, res, scratch_2);
-            let (res_dft, scratch_2) = scratch_2.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // Todo optimise
-            let mut res_big = self.glwe_external_product_internal(res_dft, &a_conv, key, scratch_2);
-            for j in 0..(res.rank() + 1).into() {
-                self.vec_znx_big_add_small_inplace(&mut res_big, j, res_conv.data(), j);
-                self.vec_znx_big_normalize(
-                    res_base2k,
-                    &mut res.data,
-                    j,
-                    key_base2k,
-                    &res_big,
-                    j,
-                    scratch_2,
-                );
-            }
-        }
-    }
 }
 
 pub trait GLWEExternalProductInternal<BE: Backend> {
@@ -309,12 +248,7 @@ ggsw_size,
         );
         let normalize_big: usize = self.vec_znx_normalize_tmp_bytes();
 
-        if a_infos.base2k() == b_infos.base2k() {
-            a_dft + (vmp | normalize_big)
-        } else {
-            let normalize_conv: usize = VecZnx::bytes_of(self.n(), (b_infos.rank() + 1).into(), in_size);
-            (a_dft + normalize_conv + (self.vec_znx_normalize_tmp_bytes() | vmp)) | normalize_big
-        }
+        a_dft + vmp.max(normalize_big)
     }
 
     fn glwe_external_product_internal<DR, A, G>(
@@ -333,69 +267,36 @@ {
         let a: &GLWE<&[u8]> = &a.to_ref();
         let ggsw: &GGSWPrepared<&[u8], BE> = &ggsw.to_ref();
 
-        let basek_in: usize = a.base2k().into();
-        let basek_ggsw: usize = ggsw.base2k().into();
+        assert_eq!(a.base2k(), ggsw.base2k());
 
         let cols: usize = (ggsw.rank() + 1).into();
         let dsize: usize = ggsw.dsize().into();
-        let a_size: usize = (a.size() * basek_in).div_ceil(basek_ggsw);
+        let a_size: usize = a.size();
 
         let (mut a_dft, scratch_1) = scratch.take_vec_znx_dft(self, cols, a_size.div_ceil(dsize));
         a_dft.data_mut().fill(0);
 
-        if basek_in == basek_ggsw {
-            for di in 0..dsize {
-                // (lhs.size() + di) / dsize = (a - (digit - di - 1)).div_ceil(dsize)
-                a_dft.set_size((a.size() + di) / dsize);
-
-                // Small optimization for dsize > 2
-                // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
-                // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(dsize-1) * B}.
-                // As such we can ignore the last dsize-2 limbs safely of the sum of vmp products.
-                // It is possible to further ignore the last dsize-1 limbs, but this introduce
-                // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
-                // noise is kept with respect to the ideal functionality.
-                res_dft.set_size(ggsw.size() - ((dsize - di) as isize - 2).max(0) as usize);
+        for di in 0..dsize {
+            // (lhs.size() + di) / dsize = (a - (digit - di - 1)).div_ceil(dsize)
+            a_dft.set_size((a.size() + di) / dsize);
 
-                for j in 0..cols {
-                    self.vec_znx_dft_apply(dsize, dsize - 1 - di, &mut a_dft, j, &a.data, j);
-                }
-
-                if di == 0 {
-                    self.vmp_apply_dft_to_dft(&mut res_dft, &a_dft, &ggsw.data, scratch_1);
-                } else {
-                    self.vmp_apply_dft_to_dft_add(&mut res_dft, &a_dft, &ggsw.data, di, scratch_1);
-                }
-            }
-        } else {
-            let (mut a_conv, scratch_3) = scratch_1.take_vec_znx(self.n(), cols, a_size);
+            // Small optimization for dsize > 2
+            // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
+            // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(dsize-1) * B}.
+            // As such we can ignore the last dsize-2 limbs safely of the sum of vmp products.
+            // It is possible to further ignore the last dsize-1 limbs, but this introduce
+            // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
+            // noise is kept with respect to the ideal functionality.
+            res_dft.set_size(ggsw.size() - ((dsize - di) as isize - 2).max(0) as usize);
 
             for j in 0..cols {
-                self.vec_znx_normalize(basek_ggsw, &mut a_conv, j, basek_in, &a.data, j, scratch_3);
+                self.vec_znx_dft_apply(dsize, dsize - 1 - di, &mut a_dft, j, &a.data, j);
             }
 
-            for di in 0..dsize {
-                // (lhs.size() + di) / dsize = (a - (digit - di - 1)).div_ceil(dsize)
-                a_dft.set_size((a.size() + di) / dsize);
-
-                // Small optimization for dsize > 2
-                // VMP produce some error e, and since we aggregate vmp * 2^{di * B}, then
-                // we also aggregate ei * 2^{di * B}, with the largest error being ei * 2^{(dsize-1) * B}.
-                // As such we can ignore the last dsize-2 limbs safely of the sum of vmp products.
-                // It is possible to further ignore the last dsize-1 limbs, but this introduce
-                // ~0.5 to 1 bit of additional noise, and thus not chosen here to ensure that the same
-                // noise is kept with respect to the ideal functionality.
-                res_dft.set_size(ggsw.size() - ((dsize - di) as isize - 2).max(0) as usize);
-
-                for j in 0..cols {
-                    self.vec_znx_dft_apply(dsize, dsize - 1 - di, &mut a_dft, j, &a.data, j);
-                }
-
-                if di == 0 {
-                    self.vmp_apply_dft_to_dft(&mut res_dft, &a_dft, &ggsw.data, scratch_1);
-                } else {
-                    self.vmp_apply_dft_to_dft_add(&mut res_dft, &a_dft, &ggsw.data, di, scratch_1);
-                }
+            if di == 0 {
+                self.vmp_apply_dft_to_dft(&mut res_dft, &a_dft, &ggsw.data, scratch_1);
+            } else {
+                self.vmp_apply_dft_to_dft_add(&mut res_dft, &a_dft, &ggsw.data, di, scratch_1);
             }
         }
 

@@ -132,17 +132,21 @@ self.counter += 1 << self.log_batch;
     }
 
     /// Flush result to`res`.
-    pub fn flush<R, M, BE: Backend>(&mut self, module: &M, res: &mut R)
+    pub fn flush<R, M, BE: Backend>(&mut self, module: &M, res: &mut R, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
+        R: GLWEToMut + GLWEInfos,
         M: GLWEPackerOps<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
         assert!(self.counter as u32 == self.accumulators[0].data.n());
-        // Copy result GLWE into res GLWE
-        module.glwe_copy(
-            res,
-            &self.accumulators[module.log_n() - self.log_batch - 1].data,
-        );
+
+        let out: &GLWE<Vec<u8>> = &self.accumulators[module.log_n() - self.log_batch - 1].data;
+
+        if out.base2k() == res.base2k() {
+            module.glwe_copy(res, out)
+        } else {
+            module.glwe_normalize(res, out, scratch);
+        }
 
         self.reset();
     }
@@ -244,7 +248,11 @@ let acc_mut_ref: &mut Accumulator = &mut acc_prev[0]; // from split_at_mut
 
         // No previous value -> copies and sets flags accordingly
         if let Some(a_ref) = a {
-            module.glwe_copy(&mut acc_mut_ref.data, a_ref);
+            if a_ref.base2k() == acc_mut_ref.data.base2k() {
+                module.glwe_copy(&mut acc_mut_ref.data, a_ref);
+            } else {
+                module.glwe_normalize(&mut acc_mut_ref.data, a_ref, scratch);
+            }
             acc_mut_ref.value = true
         } else {
             acc_mut_ref.value = false
@@ -331,30 +339,29 @@ // either mapped to garbage or twice their value which vanishes I(X)
     // since 2*(I(X) * Q/2) = I(X) * Q = 0 mod Q.
     if acc.value {
         if let Some(b) = b {
-            let (mut tmp_b, scratch_1) = scratch.take_glwe(a);
+            let (mut tmp, scratch_1) = scratch.take_glwe(a);
 
             // a = a * X^-t
             module.glwe_rotate_inplace(-t, a, scratch_1);
 
             // tmp_b = a * X^-t - b
-            module.glwe_sub(&mut tmp_b, a, b);
-            module.glwe_rsh(1, &mut tmp_b, scratch_1);
-
+            module.glwe_sub(&mut tmp, a, b);
+            module.glwe_rsh(1, &mut tmp, scratch_1);
             // a = a * X^-t + b
             module.glwe_add_inplace(a, b);
+
             module.glwe_rsh(1, a, scratch_1);
-
-            module.glwe_normalize_inplace(&mut tmp_b, scratch_1);
+            module.glwe_normalize_inplace(&mut tmp, scratch_1);
 
             // tmp_b = phi(a * X^-t - b)
             if let Some(auto_key) = auto_keys.get_automorphism_key(gal_el) {
-                module.glwe_automorphism_inplace(&mut tmp_b, auto_key, scratch_1);
+                module.glwe_automorphism_inplace(&mut tmp, auto_key, scratch_1);
             } else {
                 panic!("auto_key[{gal_el}] not found");
             }
 
             // a = a * X^-t + b - phi(a * X^-t - b)
-            module.glwe_sub_inplace(a, &tmp_b);
+            module.glwe_sub_inplace(a, &tmp);
             module.glwe_normalize_inplace(a, scratch_1);
 
             // a = a + b * X^t - phi(a * X^-t - b) * X^t

@@ -7,9 +7,16 @@ };
 
 use crate::{
     GLWEAdd, GLWEAutomorphism, GLWECopy, GLWENormalize, GLWERotate, GLWEShift, GLWESub, GLWETrace, ScratchTakeCore,
-    layouts::{GGLWEInfos, GGLWEPreparedToRef, GLWEAutomorphismKeyHelper, GLWEInfos, GLWEToMut, GetGaloisElement},
+    layouts::{GGLWEInfos, GGLWEPreparedToRef, GLWE, GLWEAutomorphismKeyHelper, GLWEInfos, GLWEToMut, GetGaloisElement},
 };
 pub trait GLWEPacking<BE: Backend> {
+    fn glwe_pack_galois_elements(&self) -> Vec<i64>;
+
+    fn glwe_pack_tmp_bytes<R, K>(&self, res: &R, key: &K) -> usize
+    where
+        R: GLWEInfos,
+        K: GGLWEInfos;
+
     /// Packs [x_0: GLWE(m_0), x_1: GLWE(m_1), ..., x_i: GLWE(m_i)]
     /// to [0: GLWE(m_0 * X^x_0 + m_1 * X^x_1 + ... + m_i * X^x_i)]
     fn glwe_pack<R, A, K, H>(
@@ -40,6 +47,22 @@ + GLWECopy
         + GLWETrace<BE>,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
+    fn glwe_pack_galois_elements(&self) -> Vec<i64> {
+        self.glwe_trace_galois_elements()
+    }
+
+    fn glwe_pack_tmp_bytes<R, K>(&self, res: &R, key: &K) -> usize
+    where
+        R: GLWEInfos,
+        K: GGLWEInfos,
+    {
+        self.glwe_rotate_tmp_bytes()
+            .max(self.glwe_rsh_tmp_byte())
+            .max(self.glwe_normalize_tmp_bytes())
+            .max(self.glwe_automorphism_tmp_bytes(res, res, key))
+            + GLWE::bytes_of_from_infos(res)
+    }
+
     /// Packs [x_0: GLWE(m_0), x_1: GLWE(m_1), ..., x_i: GLWE(m_i)]
     /// to [0: GLWE(m_0 * X^x_0 + m_1 * X^x_1 + ... + m_i * X^x_i)]
     fn glwe_pack<R, A, K, H>(

@@ -1,10 +1,10 @@
 use poulpy_hal::{
-    api::{ModuleLogN, VecZnxNormalize, VecZnxNormalizeTmpBytes},
+    api::{ModuleLogN, VecZnxNormalizeTmpBytes},
     layouts::{Backend, CyclotomicOrder, DataMut, GaloisElement, Module, Scratch, VecZnx, galois_element},
 };
 
 use crate::{
-    GLWEAutomorphism, GLWECopy, GLWEShift, ScratchTakeCore,
+    GLWEAutomorphism, GLWECopy, GLWENormalize, GLWEShift, ScratchTakeCore,
     layouts::{
         GGLWEInfos, GGLWELayout, GGLWEPreparedToRef, GLWE, GLWEAutomorphismKeyHelper, GLWEInfos, GLWELayout, GLWEToMut,
         GLWEToRef, GetGaloisElement, LWEInfos,
@@ -75,7 +75,7 @@ + GLWEShift<BE>
         + GLWECopy
         + CyclotomicOrder
         + VecZnxNormalizeTmpBytes
-        + VecZnxNormalize<BE>,
+        + GLWENormalize<BE>,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
     fn glwe_trace_galois_elements(&self) -> Vec<i64> {
@@ -114,15 +114,28 @@ A: GLWEToRef + GLWEInfos,
         K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
         H: GLWEAutomorphismKeyHelper<K, BE>,
     {
-        let (mut tmp, scratch_1) = if a.k() > res.k() {
-            scratch.take_glwe(a)
+        let atk_layout: &GGLWELayout = &keys.automorphism_key_infos();
+
+        let (mut tmp, scratch_1) = scratch.take_glwe(&GLWELayout {
+            n: res.n(),
+            base2k: atk_layout.base2k(),
+            k: a.k().max(res.k()),
+            rank: res.rank(),
+        });
+
+        if a.base2k() == atk_layout.base2k() {
+            self.glwe_copy(&mut tmp, a);
         } else {
-            scratch.take_glwe(res)
-        };
+            self.glwe_normalize(&mut tmp, a, scratch_1);
+        }
 
-        self.glwe_copy(&mut tmp, a);
         self.glwe_trace_inplace(&mut tmp, skip, keys, scratch_1);
-        self.glwe_copy(res, &tmp);
+
+        if res.base2k() == atk_layout.base2k() {
+            self.glwe_copy(res, &tmp);
+        } else {
+            self.glwe_normalize(res, &tmp, scratch_1);
+        }
     }
 
     fn glwe_trace_inplace<R, K, H>(&self, res: &mut R, skip: usize, keys: &H, scratch: &mut Scratch<BE>)
@@ -143,52 +156,15 @@ assert_eq!(ksk_infos.rank_in(), res.rank());
         assert_eq!(ksk_infos.rank_out(), res.rank());
 
         if res.base2k() != ksk_infos.base2k() {
-            let (mut self_conv, scratch_1) = scratch.take_glwe(&GLWELayout {
+            let (mut res_conv, scratch_1) = scratch.take_glwe(&GLWELayout {
                 n: self.n().into(),
                 base2k: ksk_infos.base2k(),
                 k: res.k(),
                 rank: res.rank(),
             });
-
-            for j in 0..(res.rank() + 1).into() {
-                self.vec_znx_normalize(
-                    ksk_infos.base2k().into(),
-                    &mut self_conv.data,
-                    j,
-                    res.base2k().into(),
-                    res.data(),
-                    j,
-                    scratch_1,
-                );
-            }
-
-            for i in skip..log_n {
-                self.glwe_rsh(1, &mut self_conv, scratch_1);
-
-                let p: i64 = if i == 0 {
-                    -1
-                } else {
-                    self.galois_element(1 << (i - 1))
-                };
-
-                if let Some(key) = keys.get_automorphism_key(p) {
-                    self.glwe_automorphism_add_inplace(&mut self_conv, key, scratch_1);
-                } else {
-                    panic!("keys[{p}] is empty")
-                }
-            }
-
-            for j in 0..(res.rank() + 1).into() {
-                self.vec_znx_normalize(
-                    res.base2k().into(),
-                    res.data_mut(),
-                    j,
-                    ksk_infos.base2k().into(),
-                    &self_conv.data,
-                    j,
-                    scratch_1,
-                );
-            }
+            self.glwe_normalize(&mut res_conv, res, scratch_1);
+            self.glwe_trace_inplace(&mut res_conv, skip, keys, scratch_1);
+            self.glwe_normalize(res, &res_conv, scratch_1);
         } else {
             for i in skip..log_n {
                 self.glwe_rsh(1, res, scratch);

@@ -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>> {
@@ -29,7 +29,7 @@ impl<D: DataMut> GGSW<D> {
     pub fn keyswitch<M, A, K, T, BE: Backend>(&mut self, module: &M, a: &A, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
         A: GGSWToRef,
-        K: GGLWEPreparedToRef<BE>,
+        K: GGLWEPreparedToRef<BE> + GGLWEInfos,
         T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
         M: GGSWKeyswitch<BE>,
@@ -39,7 +39,7 @@ }
 
     pub fn keyswitch_inplace<M, K, T, BE: Backend>(&mut self, module: &M, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
-        K: GGLWEPreparedToRef<BE>,
+        K: GGLWEPreparedToRef<BE> + GGLWEInfos,
         T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
         M: GGSWKeyswitch<BE>,
@@ -70,7 +70,7 @@
     fn ggsw_keyswitch_inplace<R, K, T>(&self, res: &mut R, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
         R: GGSWToMut,
-        K: GGLWEPreparedToRef<BE>,
+        K: GGLWEPreparedToRef<BE> + GGLWEInfos,
         T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
@@ -89,7 +89,7 @@ fn ggsw_keyswitch<R, A, K, T>(&self, res: &mut R, a: &A, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
         R: GGSWToMut,
         A: GGSWToRef,
-        K: GGLWEPreparedToRef<BE>,
+        K: GGLWEPreparedToRef<BE> + GGLWEInfos,
         T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
@@ -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.
@@ -124,14 +125,14 @@ fn ggsw_keyswitch<R, A, K, T>(&self, res: &mut R, a: &A, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
         R: GGSWToMut,
         A: GGSWToRef,
-        K: GGLWEPreparedToRef<BE>,
+        K: GGLWEPreparedToRef<BE> + GGLWEInfos,
         T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>;
 
     fn ggsw_keyswitch_inplace<R, K, T>(&self, res: &mut R, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
         R: GGSWToMut,
-        K: GGLWEPreparedToRef<BE>,
+        K: GGLWEPreparedToRef<BE> + GGLWEInfos,
         T: GGLWEToGGSWKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>;
 }

@@ -4,12 +4,12 @@ ModuleN, ScratchAvailable, ScratchTakeBasic, VecZnxBigAddSmallInplace, VecZnxBigNormalize, VecZnxBigNormalizeTmpBytes,
         VecZnxDftApply, VecZnxDftBytesOf, VecZnxDftCopy, VecZnxIdftApplyConsume, VecZnxNormalize, VecZnxNormalizeTmpBytes,
         VmpApplyDftToDft, VmpApplyDftToDftAdd, VmpApplyDftToDftTmpBytes,
     },
-    layouts::{Backend, DataMut, DataViewMut, Module, Scratch, VecZnx, VecZnxBig, VecZnxDft, VecZnxDftToRef, VmpPMat, ZnxInfos},
+    layouts::{Backend, DataMut, DataViewMut, Module, Scratch, VecZnxBig, VecZnxDft, VecZnxDftToRef, VmpPMat, ZnxInfos},
 };
 
 use crate::{
-    ScratchTakeCore,
-    layouts::{GGLWEInfos, GGLWEPrepared, GGLWEPreparedToRef, GLWE, GLWEInfos, GLWEToMut, GLWEToRef, LWEInfos},
+    GLWENormalize, ScratchTakeCore,
+    layouts::{GGLWEInfos, GGLWEPrepared, GGLWEPreparedToRef, GLWE, GLWEInfos, GLWELayout, GLWEToMut, GLWEToRef, LWEInfos},
 };
 
 impl GLWE<Vec<u8>> {
@@ -27,8 +27,8 @@
 impl<D: DataMut> GLWE<D> {
     pub fn keyswitch<A, B, M, BE: Backend>(&mut self, module: &M, a: &A, b: &B, scratch: &mut Scratch<BE>)
     where
-        A: GLWEToRef,
-        B: GGLWEPreparedToRef<BE>,
+        A: GLWEToRef + GLWEInfos,
+        B: GGLWEPreparedToRef<BE> + GGLWEInfos,
         M: GLWEKeyswitch<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
@@ -37,7 +37,7 @@ }
 
     pub fn keyswitch_inplace<A, M, BE: Backend>(&mut self, module: &M, a: &A, scratch: &mut Scratch<BE>)
     where
-        A: GGLWEPreparedToRef<BE>,
+        A: GGLWEPreparedToRef<BE> + GGLWEInfos,
         M: GLWEKeyswitch<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
@@ -47,7 +47,7 @@ }
 
 impl<BE: Backend> GLWEKeyswitch<BE> for Module<BE>
 where
-    Self: Sized + GLWEKeySwitchInternal<BE> + VecZnxBigNormalizeTmpBytes + VecZnxBigNormalize<BE>,
+    Self: Sized + GLWEKeySwitchInternal<BE> + VecZnxBigNormalizeTmpBytes + VecZnxBigNormalize<BE> + GLWENormalize<BE>,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
     fn glwe_keyswitch_tmp_bytes<R, A, B>(&self, res_infos: &R, a_infos: &A, key_infos: &B) -> usize
@@ -57,41 +57,47 @@ A: GLWEInfos,
         B: GGLWEInfos,
     {
         let cols: usize = res_infos.rank().as_usize() + 1;
-        self.glwe_keyswitch_internal_tmp_bytes(res_infos, a_infos, key_infos)
-            .max(self.vec_znx_big_normalize_tmp_bytes())
-            + self.bytes_of_vec_znx_dft(cols, key_infos.size())
+        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 {
+            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>)
     where
-        R: GLWEToMut,
-        A: GLWEToRef,
-        K: GGLWEPreparedToRef<BE>,
+        R: GLWEToMut + GLWEInfos,
+        A: GLWEToRef + GLWEInfos,
+        K: GGLWEPreparedToRef<BE> + GGLWEInfos,
     {
-        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
-        let a: &GLWE<&[u8]> = &a.to_ref();
-        let b: &GGLWEPrepared<&[u8], BE> = &key.to_ref();
-
         assert_eq!(
             a.rank(),
-            b.rank_in(),
+            key.rank_in(),
             "a.rank(): {} != b.rank_in(): {}",
             a.rank(),
-            b.rank_in()
+            key.rank_in()
         );
         assert_eq!(
             res.rank(),
-            b.rank_out(),
+            key.rank_out(),
             "res.rank(): {} != b.rank_out(): {}",
             res.rank(),
-            b.rank_out()
+            key.rank_out()
         );
 
         assert_eq!(res.n(), self.n() as u32);
         assert_eq!(a.n(), self.n() as u32);
-        assert_eq!(b.n(), self.n() as u32);
+        assert_eq!(key.n(), self.n() as u32);
 
-        let scrach_needed: usize = self.glwe_keyswitch_tmp_bytes(res, a, b);
+        let scrach_needed: usize = self.glwe_keyswitch_tmp_bytes(res, a, key);
 
         assert!(
             scratch.available() >= scrach_needed,
@@ -99,17 +105,32 @@ "scratch.available()={} < glwe_keyswitch_tmp_bytes={scrach_needed}",
             scratch.available(),
         );
 
-        let basek_out: usize = res.base2k().into();
-        let base2k_out: usize = b.base2k().into();
+        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
+
+        let res_big: VecZnxBig<&mut [u8], BE> = 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);
+            self.glwe_keyswitch_internal(res_dft, &a_conv, key, scratch_2)
+        } else {
+            self.glwe_keyswitch_internal(res_dft, a, key, scratch_1)
+        };
 
-        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), b.size()); // Todo optimise
-        let res_big: VecZnxBig<&mut [u8], BE> = self.glwe_keyswitch_internal(res_dft, a, b, scratch_1);
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         for i in 0..(res.rank() + 1).into() {
             self.vec_znx_big_normalize(
-                basek_out,
-                &mut res.data,
+                base2k_res,
+                res.data_mut(),
                 i,
-                base2k_out,
+                base2k_key,
                 &res_big,
                 i,
                 scratch_1,
@@ -119,12 +140,9 @@ }
 
     fn glwe_keyswitch_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
-        K: GGLWEPreparedToRef<BE>,
+        R: GLWEToMut + GLWEInfos,
+        K: GGLWEPreparedToRef<BE> + GGLWEInfos,
     {
-        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
-        let key: &GGLWEPrepared<&[u8], BE> = &key.to_ref();
-
         assert_eq!(
             res.rank(),
             key.rank_in(),
@@ -151,17 +169,32 @@ "scratch.available()={} < glwe_keyswitch_tmp_bytes={scrach_needed}",
             scratch.available(),
         );
 
-        let base2k_in: usize = res.base2k().into();
-        let base2k_out: usize = key.base2k().into();
+        let base2k_res: usize = res.base2k().as_usize();
+        let base2k_key: usize = key.base2k().as_usize();
 
         let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // Todo optimise
-        let res_big: VecZnxBig<&mut [u8], BE> = self.glwe_keyswitch_internal(res_dft, res, key, scratch_1);
+
+        let res_big: VecZnxBig<&mut [u8], BE> = 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);
+
+            self.glwe_keyswitch_internal(res_dft, &res_conv, key, scratch_2)
+        } else {
+            self.glwe_keyswitch_internal(res_dft, res, key, scratch_1)
+        };
+
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         for i in 0..(res.rank() + 1).into() {
             self.vec_znx_big_normalize(
-                base2k_in,
-                &mut res.data,
+                base2k_res,
+                res.data_mut(),
                 i,
-                base2k_out,
+                base2k_key,
                 &res_big,
                 i,
                 scratch_1,
@@ -179,14 +212,14 @@ B: GGLWEInfos;
 
     fn glwe_keyswitch<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
-        A: GLWEToRef,
-        K: GGLWEPreparedToRef<BE>;
+        R: GLWEToMut + GLWEInfos,
+        A: GLWEToRef + GLWEInfos,
+        K: GGLWEPreparedToRef<BE> + GGLWEInfos;
 
     fn glwe_keyswitch_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
     where
-        R: GLWEToMut,
-        K: GGLWEPreparedToRef<BE>;
+        R: GLWEToMut + GLWEInfos,
+        K: GGLWEPreparedToRef<BE> + GGLWEInfos;
 }
 
 impl<BE: Backend> GLWEKeySwitchInternal<BE> for Module<BE> where
@@ -216,14 +249,7 @@ K: GGLWEInfos,
     {
         let cols: usize = (a_infos.rank() + 1).into();
         let a_size: usize = a_infos.size();
-
-        let a_conv = if a_infos.base2k() == key_infos.base2k() {
-            0
-        } else {
-            VecZnx::bytes_of(self.n(), 1, a_size) + self.vec_znx_normalize_tmp_bytes()
-        };
-
-        self.gglwe_product_dft_tmp_bytes(res_infos.size(), a_size, key_infos) + self.bytes_of_vec_znx_dft(cols, a_size) + a_conv
+        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>(
@@ -241,36 +267,14 @@ Scratch<BE>: ScratchTakeCore<BE>,
     {
         let a: &GLWE<&[u8]> = &a.to_ref();
         let key: &GGLWEPrepared<&[u8], BE> = &key.to_ref();
-
-        let base2k_in: usize = a.base2k().into();
-        let base2k_out: usize = key.base2k().into();
+        assert_eq!(a.base2k(), key.base2k());
         let cols: usize = (a.rank() + 1).into();
-        let a_size: usize = (a.size() * base2k_in).div_ceil(base2k_out);
-
+        let a_size: usize = a.size();
         let (mut a_dft, scratch_1) = scratch.take_vec_znx_dft(self, cols - 1, a_size);
-
-        if base2k_in == base2k_out {
-            for col_i in 0..cols - 1 {
-                self.vec_znx_dft_apply(1, 0, &mut a_dft, col_i, a.data(), col_i + 1);
-            }
-        } else {
-            let (mut a_conv, scratch_2) = scratch_1.take_vec_znx(self.n(), 1, a_size);
-            for i in 0..cols - 1 {
-                self.vec_znx_normalize(
-                    base2k_out,
-                    &mut a_conv,
-                    0,
-                    base2k_in,
-                    a.data(),
-                    i + 1,
-                    scratch_2,
-                );
-                self.vec_znx_dft_apply(1, 0, &mut a_dft, i, &a_conv, 0);
-            }
+        for col_i in 0..cols - 1 {
+            self.vec_znx_dft_apply(1, 0, &mut a_dft, col_i, a.data(), col_i + 1);
         }
-
         self.gglwe_product_dft(&mut res, &a_dft, key, scratch_1);
-
         let mut res_big: VecZnxBig<DR, BE> = self.vec_znx_idft_apply_consume(res);
         self.vec_znx_big_add_small_inplace(&mut res_big, 0, a.data(), 0);
         res_big

@@ -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);
     }
 }

@@ -263,9 +263,8 @@ assert!(res.dnum() <= other.dnum());
 
         let rank_in: usize = res.rank_in().into();
         let dnum: usize = res.dnum().into();
-
-        for row_i in 0..dnum {
-            for col_i in 0..rank_in {
+        for col_i in 0..rank_in {
+            for row_i in 0..dnum {
                 self.decompress_glwe(&mut res.at_mut(row_i, col_i), &other.at(row_i, col_i));
             }
         }

@@ -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,
 };
 
@@ -15,7 +15,7 @@ (u64::BITS - (self.n().as_usize() as u64 - 1).leading_zeros()) as usize
     }
     fn k(&self) -> TorusPrecision;
     fn max_k(&self) -> TorusPrecision {
-        TorusPrecision(self.k().0 * self.size() as u32)
+        TorusPrecision(self.base2k().0 * self.size() as u32)
     }
     fn base2k(&self) -> Base2K;
     fn size(&self) -> usize {
@@ -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
     }
 }

@@ -1,76 +1,90 @@
 use poulpy_hal::{
-    api::{ScratchAvailable, ScratchOwnedAlloc, ScratchOwnedBorrow, ScratchTakeBasic, VecZnxFillUniform, VecZnxSubScalarInplace},
-    layouts::{Backend, DataRef, Module, ScalarZnxToRef, Scratch, ScratchOwned, ZnxZero},
+    api::VecZnxAddScalarInplace,
+    layouts::{Backend, DataRef, Module, ScalarZnxToRef, Scratch, Stats, ZnxZero},
 };
 
-use crate::decryption::GLWEDecrypt;
-use crate::layouts::{GGLWE, GGLWEInfos, GGLWEToRef, GLWEPlaintext, LWEInfos, prepared::GLWESecretPreparedToRef};
+use crate::{
+    GLWENoise,
+    layouts::{GGLWE, GGLWEInfos, GGLWEToRef, prepared::GLWESecretPreparedToRef},
+};
+use crate::{ScratchTakeCore, layouts::GLWEPlaintext};
 
 impl<D: DataRef> GGLWE<D> {
-    pub fn assert_noise<M, S, P, BE: Backend>(&self, module: &M, sk_prepared: &S, pt_want: &P, max_noise: f64)
+    pub fn noise<M, S, P, BE: Backend>(
+        &self,
+        module: &M,
+        row: usize,
+        col: usize,
+        pt_want: &P,
+        sk_prepared: &S,
+        scratch: &mut Scratch<BE>,
+    ) -> Stats
     where
         S: GLWESecretPreparedToRef<BE>,
         P: ScalarZnxToRef,
         M: GGLWENoise<BE>,
-        Scratch<BE>: ScratchTakeBasic,
     {
-        module.gglwe_assert_noise(self, sk_prepared, pt_want, max_noise);
+        module.gglwe_noise(self, row, col, pt_want, sk_prepared, scratch)
     }
 }
 
 pub trait GGLWENoise<BE: Backend> {
-    fn gglwe_assert_noise<R, S, P>(&self, res: &R, sk_prepared: &S, pt_want: &P, max_noise: f64)
+    fn gglwe_noise_tmp_bytes<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos;
+
+    fn gglwe_noise<R, S, P>(
+        &self,
+        res: &R,
+        res_row: usize,
+        res_col: usize,
+        pt_want: &P,
+        sk_prepared: &S,
+        scratch: &mut Scratch<BE>,
+    ) -> Stats
     where
         R: GGLWEToRef,
         S: GLWESecretPreparedToRef<BE>,
-        P: ScalarZnxToRef,
-        Scratch<BE>: ScratchTakeBasic;
+        P: ScalarZnxToRef;
 }
 
 impl<BE: Backend> GGLWENoise<BE> for Module<BE>
 where
-    Module<BE>: GLWEDecrypt<BE> + VecZnxFillUniform + VecZnxSubScalarInplace,
-    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
-    Scratch<BE>: ScratchAvailable + ScratchTakeBasic,
+    Module<BE>: VecZnxAddScalarInplace + GLWENoise<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
 {
-    fn gglwe_assert_noise<R, S, P>(&self, res: &R, sk_prepared: &S, pt_want: &P, max_noise: f64)
+    fn gglwe_noise_tmp_bytes<A>(&self, infos: &A) -> usize
+    where
+        A: GGLWEInfos,
+    {
+        GLWEPlaintext::bytes_of_from_infos(infos) + self.glwe_noise_tmp_bytes(infos)
+    }
+
+    fn gglwe_noise<R, S, P>(
+        &self,
+        res: &R,
+        res_row: usize,
+        res_col: usize,
+        pt_want: &P,
+        sk_prepared: &S,
+        scratch: &mut Scratch<BE>,
+    ) -> Stats
     where
         R: GGLWEToRef,
         S: GLWESecretPreparedToRef<BE>,
         P: ScalarZnxToRef,
-        ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
-        Scratch<BE>: ScratchAvailable + ScratchTakeBasic,
     {
         let res: &GGLWE<&[u8]> = &res.to_ref();
-
         let dsize: usize = res.dsize().into();
-        let base2k: usize = res.base2k().into();
-
-        let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(self.glwe_decrypt_tmp_bytes(res));
-        let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(res);
-
-        (0..res.rank_in().into()).for_each(|col_i| {
-            (0..res.dnum().into()).for_each(|row_i| {
-                self.glwe_decrypt(
-                    &res.at(row_i, col_i),
-                    &mut pt,
-                    sk_prepared,
-                    scratch.borrow(),
-                );
-
-                self.vec_znx_sub_scalar_inplace(&mut pt.data, 0, (dsize - 1) + row_i * dsize, pt_want, col_i);
-
-                let noise_have: f64 = pt.data.stats(base2k, 0).std().log2();
-
-                println!("noise_have: {noise_have}");
-
-                assert!(
-                    noise_have <= max_noise,
-                    "noise_have: {noise_have} > max_noise: {max_noise}"
-                );
-
-                pt.data.zero();
-            });
-        });
+        let (mut pt, scratch_1) = scratch.take_glwe_plaintext(res);
+        pt.data_mut().zero();
+        self.vec_znx_add_scalar_inplace(
+            &mut pt.data,
+            0,
+            (dsize - 1) + res_row * dsize,
+            pt_want,
+            res_col,
+        );
+        self.glwe_noise(&res.at(res_row, res_col), &pt, sk_prepared, scratch_1)
     }
 }

@@ -1,45 +1,49 @@
 use poulpy_hal::{
     api::{
-        ScratchOwnedAlloc, ScratchOwnedBorrow, ScratchTakeBasic, SvpApplyDftToDftInplace, VecZnxAddScalarInplace, VecZnxBigAlloc,
-        VecZnxBigNormalize, VecZnxDftAlloc, VecZnxDftApply, VecZnxIdftApplyTmpA, VecZnxNormalizeTmpBytes, VecZnxSubInplace,
+        ScratchTakeBasic, SvpApplyDftToDftInplace, VecZnxAddScalarInplace, VecZnxBigNormalize, VecZnxBigNormalizeTmpBytes,
+        VecZnxDftApply, VecZnxDftBytesOf, VecZnxIdftApplyConsume,
     },
-    layouts::{Backend, DataRef, Module, ScalarZnxToRef, Scratch, ScratchOwned, VecZnxBig, VecZnxDft, ZnxZero},
+    layouts::{Backend, DataRef, Module, ScalarZnxToRef, Scratch, Stats, ZnxZero},
 };
 
-use crate::decryption::GLWEDecrypt;
-use crate::layouts::prepared::GLWESecretPreparedToRef;
-use crate::layouts::{GGSW, GGSWInfos, GGSWToRef, GLWEInfos, GLWEPlaintext, LWEInfos, prepared::GLWESecretPrepared};
+use crate::layouts::{GGSW, GGSWInfos, GGSWToRef, LWEInfos, prepared::GLWESecretPrepared};
+use crate::{GLWENoise, layouts::prepared::GLWESecretPreparedToRef};
+use crate::{ScratchTakeCore, layouts::GLWEPlaintext};
 
 impl<D: DataRef> GGSW<D> {
-    pub fn assert_noise<M, BE: Backend, P, S, F>(&self, module: &M, sk_prepared: &S, pt_want: &P, max_noise: &F)
-    where
-        S: GLWESecretPreparedToRef<BE>,
-        P: ScalarZnxToRef,
-        M: GGSWNoise<BE>,
-        F: Fn(usize) -> f64,
-    {
-        module.ggsw_assert_noise(self, sk_prepared, pt_want, max_noise);
-    }
-
-    pub fn print_noise<M, BE: Backend, P, S>(&self, module: &M, sk_prepared: &S, pt_want: &P)
+    pub fn noise<M, BE: Backend, P, S>(
+        &self,
+        module: &M,
+        row: usize,
+        col: usize,
+        pt_want: &P,
+        sk_prepared: &S,
+        scratch: &mut Scratch<BE>,
+    ) -> Stats
     where
         S: GLWESecretPreparedToRef<BE>,
         P: ScalarZnxToRef,
         M: GGSWNoise<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        module.ggsw_print_noise(self, sk_prepared, pt_want);
+        module.ggsw_noise(self, row, col, pt_want, sk_prepared, scratch)
     }
 }
 
 pub trait GGSWNoise<BE: Backend> {
-    fn ggsw_assert_noise<R, S, P, F>(&self, res: &R, sk_prepared: &S, pt_want: &P, max_noise: &F)
+    fn ggsw_noise_tmp_bytes<A>(&self, infos: &A) -> usize
     where
-        R: GGSWToRef,
-        S: GLWESecretPreparedToRef<BE>,
-        P: ScalarZnxToRef,
-        F: Fn(usize) -> f64;
+        A: GGSWInfos;
 
-    fn ggsw_print_noise<R, S, P>(&self, res: &R, sk_prepared: &S, pt_want: &P)
+    fn ggsw_noise<R, S, P>(
+        &self,
+        res: &R,
+        res_row: usize,
+        res_col: usize,
+        pt_want: &P,
+        sk_prepared: &S,
+        scratch: &mut Scratch<BE>,
+    ) -> Stats
     where
         R: GGSWToRef,
         S: GLWESecretPreparedToRef<BE>,
@@ -48,79 +52,39 @@ }
 
 impl<BE: Backend> GGSWNoise<BE> for Module<BE>
 where
-    Module<BE>: GLWEDecrypt<BE>
-        + VecZnxDftAlloc<BE>
-        + VecZnxBigAlloc<BE>
-        + VecZnxAddScalarInplace
-        + VecZnxIdftApplyTmpA<BE>
-        + VecZnxSubInplace,
-    Scratch<BE>: ScratchTakeBasic,
-    ScratchOwned<BE>: ScratchOwnedBorrow<BE> + ScratchOwnedAlloc<BE>,
+    Module<BE>: VecZnxAddScalarInplace
+        + VecZnxDftApply<BE>
+        + SvpApplyDftToDftInplace<BE>
+        + VecZnxIdftApplyConsume<BE>
+        + VecZnxDftBytesOf
+        + VecZnxBigNormalize<BE>
+        + VecZnxBigNormalizeTmpBytes
+        + GLWENoise<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
 {
-    fn ggsw_assert_noise<R, S, P, F>(&self, res: &R, sk_prepared: &S, pt_want: &P, max_noise: &F)
+    fn ggsw_noise_tmp_bytes<A>(&self, infos: &A) -> usize
     where
-        R: GGSWToRef,
-        S: GLWESecretPreparedToRef<BE>,
-        P: ScalarZnxToRef,
-        F: Fn(usize) -> f64,
+        A: GGSWInfos,
     {
-        let res: &GGSW<&[u8]> = &res.to_ref();
-        let sk_prepared: &GLWESecretPrepared<&[u8], BE> = &sk_prepared.to_ref();
-
-        let base2k: usize = res.base2k().into();
-        let dsize: usize = res.dsize().into();
-
-        let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(res);
-        let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(res);
-        let mut pt_dft: VecZnxDft<Vec<u8>, BE> = self.vec_znx_dft_alloc(1, res.size());
-        let mut pt_big: VecZnxBig<Vec<u8>, BE> = self.vec_znx_big_alloc(1, res.size());
-
-        let mut scratch: ScratchOwned<BE> =
-            ScratchOwned::alloc(self.glwe_decrypt_tmp_bytes(res) | self.vec_znx_normalize_tmp_bytes());
-
-        (0..(res.rank() + 1).into()).for_each(|col_j| {
-            (0..res.dnum().into()).for_each(|row_i| {
-                self.vec_znx_add_scalar_inplace(&mut pt.data, 0, (dsize - 1) + row_i * dsize, pt_want, 0);
-
-                // mul with sk[col_j-1]
-                if col_j > 0 {
-                    self.vec_znx_dft_apply(1, 0, &mut pt_dft, 0, &pt.data, 0);
-                    self.svp_apply_dft_to_dft_inplace(&mut pt_dft, 0, &sk_prepared.data, col_j - 1);
-                    self.vec_znx_idft_apply_tmpa(&mut pt_big, 0, &mut pt_dft, 0);
-                    self.vec_znx_big_normalize(
-                        base2k,
-                        &mut pt.data,
-                        0,
-                        base2k,
-                        &pt_big,
-                        0,
-                        scratch.borrow(),
-                    );
-                }
-
-                self.glwe_decrypt(
-                    &res.at(row_i, col_j),
-                    &mut pt_have,
-                    sk_prepared,
-                    scratch.borrow(),
-                );
-
-                self.vec_znx_sub_inplace(&mut pt_have.data, 0, &pt.data, 0);
-
-                let std_pt: f64 = pt_have.data.stats(base2k, 0).std().log2();
-                let noise: f64 = max_noise(col_j);
-                assert!(std_pt <= noise, "{std_pt} > {noise}");
-
-                pt.data.zero();
-            });
-        });
+        GLWEPlaintext::bytes_of_from_infos(infos)
+            + (self.bytes_of_vec_znx_dft(1, infos.size()) + self.vec_znx_big_normalize_tmp_bytes())
+                .max(self.glwe_noise_tmp_bytes(infos))
     }
 
-    fn ggsw_print_noise<R, S, P>(&self, res: &R, sk_prepared: &S, pt_want: &P)
+    fn ggsw_noise<R, S, P>(
+        &self,
+        res: &R,
+        res_row: usize,
+        res_col: usize,
+        pt_want: &P,
+        sk_prepared: &S,
+        scratch: &mut Scratch<BE>,
+    ) -> Stats
     where
         R: GGSWToRef,
         S: GLWESecretPreparedToRef<BE>,
         P: ScalarZnxToRef,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &GGSW<&[u8]> = &res.to_ref();
         let sk_prepared: &GLWESecretPrepared<&[u8], BE> = &sk_prepared.to_ref();
@@ -128,47 +92,19 @@
         let base2k: usize = res.base2k().into();
         let dsize: usize = res.dsize().into();
 
-        let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(res);
-        let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(res);
-        let mut pt_dft: VecZnxDft<Vec<u8>, BE> = self.vec_znx_dft_alloc(1, res.size());
-        let mut pt_big: VecZnxBig<Vec<u8>, BE> = self.vec_znx_big_alloc(1, res.size());
-
-        let mut scratch: ScratchOwned<BE> =
-            ScratchOwned::alloc(self.glwe_decrypt_tmp_bytes(res) | self.vec_znx_normalize_tmp_bytes());
-
-        for col_j in 0..(res.rank() + 1).into() {
-            for row_i in 0..res.dnum().into() {
-                self.vec_znx_add_scalar_inplace(&mut pt.data, 0, (dsize - 1) + row_i * dsize, pt_want, 0);
-
-                // mul with sk[col_j-1]
-                if col_j > 0 {
-                    self.vec_znx_dft_apply(1, 0, &mut pt_dft, 0, &pt.data, 0);
-                    self.svp_apply_dft_to_dft_inplace(&mut pt_dft, 0, &sk_prepared.data, col_j - 1);
-                    self.vec_znx_idft_apply_tmpa(&mut pt_big, 0, &mut pt_dft, 0);
-                    self.vec_znx_big_normalize(
-                        base2k,
-                        &mut pt.data,
-                        0,
-                        base2k,
-                        &pt_big,
-                        0,
-                        scratch.borrow(),
-                    );
-                }
-
-                self.glwe_decrypt(
-                    &res.at(row_i, col_j),
-                    &mut pt_have,
-                    sk_prepared,
-                    scratch.borrow(),
-                );
-
-                self.vec_znx_sub_inplace(&mut pt_have.data, 0, &pt.data, 0);
+        let (mut pt, scratch_1) = scratch.take_glwe_plaintext(res);
+        pt.data_mut().zero();
+        self.vec_znx_add_scalar_inplace(&mut pt.data, 0, (dsize - 1) + res_row * dsize, pt_want, 0);
 
-                let std_pt: f64 = pt_have.data.stats(base2k, 0).std().log2();
-                println!("col: {col_j} row: {row_i}: {std_pt}");
-                pt.data.zero();
-            }
+        // mul with sk[col_j-1]
+        if res_col > 0 {
+            let (mut pt_dft, scratch_2) = scratch_1.take_vec_znx_dft(self, 1, res.size());
+            self.vec_znx_dft_apply(1, 0, &mut pt_dft, 0, &pt.data, 0);
+            self.svp_apply_dft_to_dft_inplace(&mut pt_dft, 0, &sk_prepared.data, res_col - 1);
+            let pt_big = self.vec_znx_idft_apply_consume(pt_dft);
+            self.vec_znx_big_normalize(base2k, &mut pt.data, 0, base2k, &pt_big, 0, scratch_2);
         }
+
+        self.glwe_noise(&res.at(res_row, res_col), &pt, sk_prepared, scratch_1)
     }
 }

@@ -1,83 +1,61 @@
-use poulpy_hal::{
-    api::{ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxNormalizeInplace, VecZnxSubInplace},
-    layouts::{Backend, DataRef, Module, Scratch, ScratchOwned, Stats},
-};
+use poulpy_hal::layouts::{Backend, DataRef, Module, Scratch, Stats};
 
 use crate::{
-    ScratchTakeCore,
+    GLWENormalize, GLWESub, ScratchTakeCore,
     decryption::GLWEDecrypt,
-    layouts::{GLWE, GLWEPlaintext, GLWEPlaintextToRef, GLWEToRef, LWEInfos, prepared::GLWESecretPreparedToRef},
+    layouts::{GLWE, GLWEInfos, GLWEPlaintext, GLWEToRef, LWEInfos, prepared::GLWESecretPreparedToRef},
 };
 
 impl<D: DataRef> GLWE<D> {
-    pub fn noise<M, S, P, BE: Backend>(&self, module: &M, sk_prepared: &S, pt_want: &P, scratch: &mut Scratch<BE>) -> Stats
+    pub fn noise<M, P, S, BE: Backend>(&self, module: &M, pt_want: &P, sk_prepared: &S, scratch: &mut Scratch<BE>) -> Stats
     where
         M: GLWENoise<BE>,
+        P: GLWEToRef,
         S: GLWESecretPreparedToRef<BE>,
-        P: GLWEPlaintextToRef,
     {
-        module.glwe_noise(self, sk_prepared, pt_want, scratch)
-    }
-
-    pub fn assert_noise<M, BE: Backend, S, P>(&self, module: &M, sk_prepared: &S, pt_want: &P, max_noise: f64)
-    where
-        S: GLWESecretPreparedToRef<BE>,
-        P: GLWEPlaintextToRef,
-        M: GLWENoise<BE>,
-    {
-        module.glwe_assert_noise(self, sk_prepared, pt_want, max_noise);
+        module.glwe_noise(self, pt_want, sk_prepared, scratch)
     }
 }
 
 pub trait GLWENoise<BE: Backend> {
-    fn glwe_noise<R, S, P>(&self, res: &R, sk_prepared: &S, pt_want: &P, scratch: &mut Scratch<BE>) -> Stats
+    fn glwe_noise_tmp_bytes<A>(&self, infos: &A) -> usize
     where
-        R: GLWEToRef,
-        S: GLWESecretPreparedToRef<BE>,
-        P: GLWEPlaintextToRef;
+        A: GLWEInfos;
 
-    fn glwe_assert_noise<R, S, P>(&self, res: &R, sk_prepared: &S, pt_want: &P, max_noise: f64)
+    fn glwe_noise<R, P, S>(&self, res: &R, pt_want: &P, sk_prepared: &S, scratch: &mut Scratch<BE>) -> Stats
     where
-        R: GLWEToRef,
-        S: GLWESecretPreparedToRef<BE>,
-        P: GLWEPlaintextToRef;
+        R: GLWEToRef + GLWEInfos,
+        P: GLWEToRef,
+        S: GLWESecretPreparedToRef<BE>;
 }
 
 impl<BE: Backend> GLWENoise<BE> for Module<BE>
 where
-    Module<BE>: GLWEDecrypt<BE> + VecZnxSubInplace + VecZnxNormalizeInplace<BE>,
-    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+    Module<BE>: GLWEDecrypt<BE> + GLWESub + GLWENormalize<BE>,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
-    fn glwe_noise<R, S, P>(&self, res: &R, sk_prepared: &S, pt_want: &P, scratch: &mut Scratch<BE>) -> Stats
+    fn glwe_noise_tmp_bytes<A>(&self, infos: &A) -> usize
     where
-        R: GLWEToRef,
-        S: GLWESecretPreparedToRef<BE>,
-        P: GLWEPlaintextToRef,
+        A: GLWEInfos,
     {
-        let res_ref: &GLWE<&[u8]> = &res.to_ref();
-
-        let pt_want: &GLWEPlaintext<&[u8]> = &pt_want.to_ref();
-
-        let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(res_ref);
-        self.glwe_decrypt(res, &mut pt_have, sk_prepared, scratch);
-        self.vec_znx_sub_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
-        self.vec_znx_normalize_inplace(res_ref.base2k().into(), &mut pt_have.data, 0, scratch);
-        pt_have.data.stats(res_ref.base2k().into(), 0)
+        GLWEPlaintext::bytes_of_from_infos(infos)
+            + self
+                .glwe_normalize_tmp_bytes()
+                .max(self.glwe_decrypt_tmp_bytes(infos))
     }
 
-    fn glwe_assert_noise<R, S, P>(&self, res: &R, sk_prepared: &S, pt_want: &P, max_noise: f64)
+    fn glwe_noise<R, P, S>(&self, res: &R, pt_want: &P, sk_prepared: &S, scratch: &mut Scratch<BE>) -> Stats
     where
-        R: GLWEToRef,
+        R: GLWEToRef + GLWEInfos,
+        P: GLWEToRef,
         S: GLWESecretPreparedToRef<BE>,
-        P: GLWEPlaintextToRef,
     {
-        let res: &GLWE<&[u8]> = &res.to_ref();
-        let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(self.glwe_decrypt_tmp_bytes(res));
-        let noise_have: f64 = self
-            .glwe_noise(res, sk_prepared, pt_want, scratch.borrow())
-            .std()
-            .log2();
-        assert!(noise_have <= max_noise, "{noise_have} {max_noise}");
+        let (mut pt_have, scratch_1) = scratch.take_glwe_plaintext(res);
+        self.glwe_decrypt(res, &mut pt_have, sk_prepared, scratch_1);
+        // println!("pt_have: {pt_have}");
+        // println!("pt_want: {}", pt_want.to_ref());
+        self.glwe_sub_inplace(&mut pt_have, pt_want);
+        self.glwe_normalize_inplace(&mut pt_have, scratch_1);
+        pt_have.data.stats(pt_have.base2k().into(), 0)
     }
 }

@@ -40,6 +40,32 @@ }
 
 #[allow(clippy::too_many_arguments)]
 #[allow(dead_code)]
+pub(crate) fn var_noise_gglwe_product_v2(
+    n: f64,
+    k_ksk: usize,
+    dnum: usize,
+    dsize: usize,
+    base2k: usize,
+    var_xs: f64,
+    var_msg: f64,
+    var_a_err: f64,
+    var_gct_err_lhs: f64,
+    var_gct_err_rhs: f64,
+    rank_in: f64,
+) -> f64 {
+    let base: f64 = ((dsize * base2k) as f64).exp2();
+    let var_base: f64 = base * base / 12f64;
+    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;
+    noise *= rank_in;
+    noise /= scale * scale;
+    noise
+}
+
+#[allow(clippy::too_many_arguments)]
+#[allow(dead_code)]
 pub(crate) fn log2_std_noise_gglwe_product(
     n: f64,
     base2k: usize,

@@ -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(),

@@ -8,64 +8,6 @@ use poulpy_hal::backend_test_suite;
 
 #[cfg(test)]
 backend_test_suite!(
- mod cpu_spqlios,
- backend = poulpy_backend::cpu_spqlios::FFT64Spqlios,
- size = 1<<8,
- tests = {
- //GLWE Encryption
- glwe_encrypt_sk => crate::tests::test_suite::encryption::test_glwe_encrypt_sk,
- glwe_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_glwe_compressed_encrypt_sk,
- glwe_encrypt_zero_sk => crate::tests::test_suite::encryption::test_glwe_encrypt_zero_sk,
- glwe_encrypt_pk => crate::tests::test_suite::encryption::test_glwe_encrypt_pk,
-// GLWE Keyswitch
-glwe_keyswitch => crate::tests::test_suite::keyswitch::test_glwe_keyswitch,
-glwe_keyswitch_inplace => crate::tests::test_suite::keyswitch::test_glwe_keyswitch_inplace,
-// GLWE Automorphism
-glwe_automorphism => crate::tests::test_suite::automorphism::test_glwe_automorphism,
-glwe_automorphism_inplace => crate::tests::test_suite::automorphism::test_glwe_automorphism_inplace,
-// GLWE External Product
-glwe_external_product => crate::tests::test_suite::external_product::test_glwe_external_product,
-glwe_external_product_inplace => crate::tests::test_suite::external_product::test_glwe_external_product_inplace,
-// GLWE Trace
-glwe_trace_inplace => crate::tests::test_suite::test_glwe_trace_inplace,
-glwe_packing => crate::tests::test_suite::test_glwe_packer,
-// GGLWE Encryption
-gglwe_switching_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_switching_key_encrypt_sk,
-gglwe_switching_key_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_switching_key_compressed_encrypt_sk,
-gglwe_automorphism_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_automorphism_key_encrypt_sk,
-gglwe_automorphism_key_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_automorphism_key_compressed_encrypt_sk,
-gglwe_tensor_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_tensor_key_encrypt_sk,
-gglwe_tensor_key_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_tensor_key_compressed_encrypt_sk,
-gglwe_to_ggsw_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_to_ggsw_key_encrypt_sk,
-// GGLWE Keyswitching
-gglwe_switching_key_keyswitch => crate::tests::test_suite::keyswitch::test_gglwe_switching_key_keyswitch,
-gglwe_switching_key_keyswitch_inplace => crate::tests::test_suite::keyswitch::test_gglwe_switching_key_keyswitch_inplace,
-// GGLWE External Product
-gglwe_switching_key_external_product => crate::tests::test_suite::external_product::test_gglwe_switching_key_external_product,
-gglwe_switching_key_external_product_inplace => crate::tests::test_suite::external_product::test_gglwe_switching_key_external_product_inplace,
-// GGLWE Automorphism
-gglwe_automorphism_key_automorphism => crate::tests::test_suite::automorphism::test_gglwe_automorphism_key_automorphism,
-gglwe_automorphism_key_automorphism_inplace => crate::tests::test_suite::automorphism::test_gglwe_automorphism_key_automorphism_inplace,
-// GGSW Encryption
-ggsw_encrypt_sk => crate::tests::test_suite::encryption::test_ggsw_encrypt_sk,
-ggsw_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_ggsw_compressed_encrypt_sk,
-// GGSW Keyswitching
-ggsw_keyswitch => crate::tests::test_suite::keyswitch::test_ggsw_keyswitch,
-ggsw_keyswitch_inplace => crate::tests::test_suite::keyswitch::test_ggsw_keyswitch_inplace,
-// GGSW External Product
-ggsw_external_product => crate::tests::test_suite::external_product::test_ggsw_external_product,
-ggsw_external_product_inplace => crate::tests::test_suite::external_product::test_ggsw_external_product_inplace,
-// GGSW Automorphism
-ggsw_automorphism => crate::tests::test_suite::automorphism::test_ggsw_automorphism,
-ggsw_automorphism_inplace => crate::tests::test_suite::automorphism::test_ggsw_automorphism_inplace,
-// LWE
-lwe_keyswitch => crate::tests::test_suite::keyswitch::test_lwe_keyswitch,
-glwe_to_lwe => crate::tests::test_suite::test_glwe_to_lwe,
-lwe_to_glwe => crate::tests::test_suite::test_lwe_to_glwe,
-}
-);
-#[cfg(test)]
-backend_test_suite!(
  mod cpu_ref,
  backend = poulpy_backend::cpu_fft64_ref::FFT64Ref,
  size = 1<<8,
@@ -75,6 +17,8 @@ glwe_encrypt_sk => crate::tests::test_suite::encryption::test_glwe_encrypt_sk,
  glwe_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_glwe_compressed_encrypt_sk,
  glwe_encrypt_zero_sk => crate::tests::test_suite::encryption::test_glwe_encrypt_zero_sk,
  glwe_encrypt_pk => crate::tests::test_suite::encryption::test_glwe_encrypt_pk,
+// GLWE Base2k Conversion
+glwe_base2k_conv => crate::tests::test_suite::test_glwe_base2k_conversion,
 // GLWE Keyswitch
 glwe_keyswitch => crate::tests::test_suite::keyswitch::test_glwe_keyswitch,
 glwe_keyswitch_inplace => crate::tests::test_suite::keyswitch::test_glwe_keyswitch_inplace,
@@ -86,10 +30,12 @@ glwe_external_product => crate::tests::test_suite::external_product::test_glwe_external_product,
 glwe_external_product_inplace => crate::tests::test_suite::external_product::test_glwe_external_product_inplace,
 // GLWE Trace
 glwe_trace_inplace => crate::tests::test_suite::test_glwe_trace_inplace,
-glwe_packing => crate::tests::test_suite::test_glwe_packer,
+glwe_packing => crate::tests::test_suite::test_glwe_packing,
+glwe_packer => crate::tests::test_suite::test_glwe_packer,
 // GGLWE Encryption
 gglwe_switching_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_switching_key_encrypt_sk,
 gglwe_switching_key_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_switching_key_compressed_encrypt_sk,
+gglwe_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_compressed_encrypt_sk,
 gglwe_automorphism_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_automorphism_key_encrypt_sk,
 gglwe_automorphism_key_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_automorphism_key_compressed_encrypt_sk,
 gglwe_tensor_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_tensor_key_encrypt_sk,
@@ -135,6 +81,8 @@ glwe_encrypt_sk => crate::tests::test_suite::encryption::test_glwe_encrypt_sk,
  glwe_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_glwe_compressed_encrypt_sk,
  glwe_encrypt_zero_sk => crate::tests::test_suite::encryption::test_glwe_encrypt_zero_sk,
  glwe_encrypt_pk => crate::tests::test_suite::encryption::test_glwe_encrypt_pk,
+ // GLWE Base2k Conversion
+glwe_base2k_conv => crate::tests::test_suite::test_glwe_base2k_conversion,
 // GLWE Keyswitch
 glwe_keyswitch => crate::tests::test_suite::keyswitch::test_glwe_keyswitch,
 glwe_keyswitch_inplace => crate::tests::test_suite::keyswitch::test_glwe_keyswitch_inplace,
@@ -146,10 +94,12 @@ glwe_external_product => crate::tests::test_suite::external_product::test_glwe_external_product,
 glwe_external_product_inplace => crate::tests::test_suite::external_product::test_glwe_external_product_inplace,
 // GLWE Trace
 glwe_trace_inplace => crate::tests::test_suite::test_glwe_trace_inplace,
-glwe_packing => crate::tests::test_suite::test_glwe_packer,
+glwe_packing => crate::tests::test_suite::test_glwe_packing,
+glwe_packer => crate::tests::test_suite::test_glwe_packer,
 // GGLWE Encryption
 gglwe_switching_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_switching_key_encrypt_sk,
 gglwe_switching_key_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_switching_key_compressed_encrypt_sk,
+gglwe_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_compressed_encrypt_sk,
 gglwe_automorphism_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_automorphism_key_encrypt_sk,
 gglwe_automorphism_key_compressed_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_automorphism_key_compressed_encrypt_sk,
 gglwe_tensor_key_encrypt_sk => crate::tests::test_suite::encryption::test_gglwe_tensor_key_encrypt_sk,

@@ -5,14 +5,14 @@ source::Source,
 };
 
 use crate::{
-    GLWEAutomorphismKeyAutomorphism, GLWEAutomorphismKeyEncryptSk, GLWEDecrypt, ScratchTakeCore,
+    GGLWENoise, GLWEAutomorphismKeyAutomorphism, GLWEAutomorphismKeyEncryptSk, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
-        GGLWEInfos, GLWEAutomorphismKey, GLWEAutomorphismKeyLayout, GLWEAutomorphismKeyPreparedFactory, GLWEPlaintext,
-        GLWESecret, GLWESecretPreparedFactory,
+        GGLWEInfos, GLWEAutomorphismKey, GLWEAutomorphismKeyLayout, GLWEAutomorphismKeyPreparedFactory, GLWEInfos, GLWESecret,
+        GLWESecretPreparedFactory,
         prepared::{GLWEAutomorphismKeyPrepared, GLWESecretPrepared},
     },
-    noise::log2_std_noise_gglwe_product,
+    var_noise_gglwe_product_v2,
 };
 
 #[allow(clippy::too_many_arguments)]
@@ -25,30 +25,31 @@ + VecZnxAutomorphism
         + GaloisElement
         + VecZnxSubScalarInplace
         + GLWESecretPreparedFactory<BE>
-        + GLWEDecrypt<BE>,
+        + GGLWENoise<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);
@@ -128,8 +132,6 @@ &auto_key_apply_prepared,
                 scratch.borrow(),
             );
 
-            let mut pt: 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
             for i in 0..rank {
@@ -145,41 +147,37 @@
             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| {
-                    auto_key_out
-                        .at(row_i, col_i)
-                        .decrypt(module, &mut pt, &sk_auto_dft, scratch.borrow());
+            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,
+            )
+            .sqrt()
+            .log2();
 
-                    module.vec_znx_sub_scalar_inplace(
-                        &mut pt.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,
-                        0.5,
-                        0.5,
-                        0f64,
-                        SIGMA * SIGMA,
-                        0f64,
-                        rank as f64,
-                        k_out,
-                        k_apply,
-                    );
+            for row in 0..auto_key_out.dnum().as_usize() {
+                for col in 0..auto_key_out.rank().as_usize() {
+                    let noise_have = auto_key_out
+                        .key
+                        .noise(module, row, col, &sk.data, &sk_auto_dft, scratch.borrow())
+                        .std()
+                        .log2();
 
                     assert!(
-                        noise_have < noise_want + 0.5,
-                        "{noise_have} {}",
-                        noise_want + 0.5
+                        noise_have < max_noise + 0.5,
+                        "{noise_have} > {}",
+                        max_noise + 0.5
                     );
-                });
-            });
+                }
+            }
         }
     }
 }
@@ -194,29 +192,31 @@ + VecZnxAutomorphism
         + GaloisElement
         + VecZnxSubScalarInplace
         + GLWESecretPreparedFactory<BE>
-        + GLWEDecrypt<BE>,
+        + 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_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 +224,10 @@ };
 
             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(),
             };
 
@@ -275,8 +275,6 @@
             // gglwe_{s1}(s0) (x) gglwe_{s2}(s1) = gglwe_{s2}(s0)
             auto_key.automorphism_inplace(module, &auto_key_apply_prepared, scratch.borrow());
 
-            let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&auto_key);
-
             let mut sk_auto: GLWESecret<Vec<u8>> = GLWESecret::alloc_from_infos(&auto_key);
             sk_auto.fill_zero(); // Necessary to avoid panic of unfilled sk
 
@@ -293,40 +291,37 @@
             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.rank_in().into()).for_each(|col_i| {
-                (0..auto_key.dnum().into()).for_each(|row_i| {
-                    auto_key
-                        .at(row_i, col_i)
-                        .decrypt(module, &mut pt, &sk_auto_dft, scratch.borrow());
-                    module.vec_znx_sub_scalar_inplace(
-                        &mut pt.data,
-                        0,
-                        (dsize_in - 1) + row_i * dsize_in,
-                        &sk.data,
-                        col_i,
-                    );
+            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,
+            )
+            .sqrt()
+            .log2();
 
-                    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,
-                        0.5,
-                        0.5,
-                        0f64,
-                        SIGMA * SIGMA,
-                        0f64,
-                        rank as f64,
-                        k_in,
-                        k_apply,
-                    );
+            for row in 0..auto_key.dnum().as_usize() {
+                for col in 0..auto_key.rank().as_usize() {
+                    let noise_have = auto_key
+                        .key
+                        .noise(module, row, col, &sk.data, &sk_auto_dft, scratch.borrow())
+                        .std()
+                        .log2();
 
                     assert!(
-                        noise_have < noise_want + 0.5,
+                        noise_have < max_noise + 0.5,
                         "{noise_have} {}",
-                        noise_want + 0.5
+                        max_noise + 0.5
                     );
-                });
-            });
+                }
+            }
         }
     }
 }

@@ -8,8 +8,8 @@ use crate::{
     GGLWEToGGSWKeyEncryptSk, GGSWAutomorphism, GGSWEncryptSk, GGSWNoise, GLWEAutomorphismKeyEncryptSk, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
-        GGLWEToGGSWKey, GGLWEToGGSWKeyLayout, GGLWEToGGSWKeyPreparedFactory, GGSW, GGSWLayout, GLWEAutomorphismKey,
-        GLWEAutomorphismKeyPreparedFactory, GLWESecret, GLWESecretPreparedFactory,
+        GGLWEToGGSWKey, GGLWEToGGSWKeyLayout, GGLWEToGGSWKeyPreparedFactory, GGSW, GGSWInfos, GGSWLayout, GLWEAutomorphismKey,
+        GLWEAutomorphismKeyPreparedFactory, GLWEInfos, GLWESecret, GLWESecretPreparedFactory,
         prepared::{GGLWEToGGSWKeyPrepared, GLWEAutomorphismKeyPrepared, GLWESecretPrepared},
     },
     noise::noise_ggsw_keyswitch,
@@ -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,
@@ -167,7 +169,17 @@ k_tsk,
                 ) + 0.5
             };
 
-            ct_out.assert_noise(module, &sk_prepared, &pt_scalar, &max_noise);
+            for row in 0..ct_out.dnum().as_usize() {
+                for col in 0..ct_out.rank().as_usize() + 1 {
+                    assert!(
+                        ct_out
+                            .noise(module, row, col, &pt_scalar, &sk_prepared, scratch.borrow())
+                            .std()
+                            .log2()
+                            <= max_noise(col)
+                    )
+                }
+            }
         }
     }
 }
@@ -187,23 +199,25 @@ + 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 +226,19 @@ };
 
             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 +307,7 @@
             let max_noise = |col_j: usize| -> f64 {
                 noise_ggsw_keyswitch(
                     n as f64,
-                    base2k * di,
+                    base2k_key * dsize,
                     col_j,
                     var_xs,
                     0f64,
@@ -303,10 +317,22 @@ rank as f64,
                     k_out,
                     k_ksk,
                     k_tsk,
-                ) + 0.5
+                ) + 4.0
             };
 
-            ct.assert_noise(module, &sk_prepared, &pt_scalar, &max_noise);
+            for row in 0..ct.dnum().as_usize() {
+                for col in 0..ct.rank().as_usize() + 1 {
+                    let noise_have: f64 = ct
+                        .noise(module, row, col, &pt_scalar, &sk_prepared, scratch.borrow())
+                        .std()
+                        .log2();
+                    let noise_max: f64 = max_noise(col);
+                    assert!(
+                        noise_have <= noise_max,
+                        "noise_have:{noise_have} > noise_max:{noise_max}",
+                    )
+                }
+            }
         }
     }
 }

@@ -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 +116,32 @@ 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);
+            assert!(
+                ct_out
+                    .noise(module, &pt_out, &sk_prepared, scratch.borrow())
+                    .std()
+                    .log2()
+                    <= max_noise + 1.0
+            )
         }
     }
 }
@@ -147,31 +161,33 @@ + 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 p = -5;
+    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 = -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 +198,7 @@ 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)
@@ -221,22 +237,30 @@ 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());
 
-            ct.assert_noise(module, &sk_prepared, &pt_want, max_noise + 1.0);
+            assert!(
+                ct.noise(module, &pt_want, &sk_prepared, scratch.borrow())
+                    .std()
+                    .log2()
+                    <= max_noise + 1.0
+            )
         }
     }
 }

@@ -1,20 +1,103 @@
 use poulpy_hal::{
-    api::{ScratchAvailable, ScratchOwnedAlloc, ScratchOwnedBorrow},
-    layouts::{Backend, Module, Scratch, ScratchOwned, ZnxView},
+    api::{ScratchAvailable, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxFillUniform, VecZnxNormalize},
+    layouts::{Backend, FillUniform, Module, Scratch, ScratchOwned, ZnxView},
     source::Source,
 };
+use rug::Float;
 
 use crate::{
-    GLWEDecrypt, GLWEEncryptSk, GLWEFromLWE, GLWEToLWESwitchingKeyEncryptSk, LWEDecrypt, LWEEncryptSk, LWEFromGLWE,
-    LWEToGLWESwitchingKeyEncryptSk, ScratchTakeCore,
+    GLWEDecrypt, GLWEEncryptSk, GLWEFromLWE, GLWENoise, GLWENormalize, GLWEToLWESwitchingKeyEncryptSk, LWEDecrypt, LWEEncryptSk,
+    LWEFromGLWE, LWEToGLWESwitchingKeyEncryptSk, SIGMA, ScratchTakeCore,
     layouts::{
         Base2K, Degree, Dnum, GLWE, GLWELayout, GLWEPlaintext, GLWESecret, GLWESecretPreparedFactory, GLWEToLWEKey,
-        GLWEToLWEKeyLayout, GLWEToLWEKeyPrepared, GLWEToLWEKeyPreparedFactory, LWE, LWELayout, LWEPlaintext, LWESecret,
+        GLWEToLWEKeyLayout, GLWEToLWEKeyPrepared, GLWEToLWEKeyPreparedFactory, LWE, LWEInfos, LWELayout, LWEPlaintext, LWESecret,
         LWEToGLWEKey, LWEToGLWEKeyLayout, LWEToGLWEKeyPrepared, LWEToGLWEKeyPreparedFactory, Rank, TorusPrecision,
         prepared::GLWESecretPrepared,
     },
 };
 
+pub fn test_glwe_base2k_conversion<BE: Backend>(module: &Module<BE>)
+where
+    Module<BE>: GLWEEncryptSk<BE>
+        + GLWEDecrypt<BE>
+        + GLWENormalize<BE>
+        + VecZnxFillUniform
+        + GLWESecretPreparedFactory<BE>
+        + GLWENoise<BE>,
+    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+    Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
+{
+    let n_glwe: Degree = Degree(module.n() as u32);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+
+    for rank in 1_usize..3 {
+        for bases in [[12, 8], [8, 12]] {
+            let glwe_infos_in: GLWELayout = GLWELayout {
+                n: n_glwe,
+                base2k: Base2K(bases[0]),
+                k: TorusPrecision(34),
+                rank: Rank(rank as u32),
+            };
+
+            let glwe_infos_out: GLWELayout = GLWELayout {
+                n: n_glwe,
+                base2k: Base2K(bases[1]),
+                k: TorusPrecision(34),
+                rank: Rank(rank as u32),
+            };
+
+            let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module.n().into(), rank.into());
+            sk.fill_ternary_prob(0.5, &mut source_xs);
+
+            let mut sk_prep: GLWESecretPrepared<Vec<u8>, BE> = GLWESecretPrepared::alloc_from_infos(module, &sk);
+            sk_prep.prepare(module, &sk);
+
+            let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
+                GLWE::encrypt_sk_tmp_bytes(module, &glwe_infos_in).max(module.glwe_noise_tmp_bytes(&glwe_infos_out)),
+            );
+
+            let mut ct_in: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_infos_in);
+            let mut ct_out: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_infos_out);
+
+            let pt_in: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_infos_in);
+            let pt_out: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_infos_out);
+
+            ct_in.encrypt_sk(
+                module,
+                &pt_in,
+                &sk_prep,
+                &mut source_xa,
+                &mut source_xe,
+                scratch.borrow(),
+            );
+
+            let mut data: Vec<Float> = (0..module.n()).map(|_| Float::with_val(128, 0)).collect();
+            ct_in
+                .data()
+                .decode_vec_float(ct_in.base2k().into(), 0, &mut data);
+
+            ct_out.fill_uniform(ct_out.base2k().into(), &mut source_xa);
+            module.glwe_normalize(&mut ct_out, &ct_in, scratch.borrow());
+
+            let mut data_conv: Vec<Float> = (0..module.n()).map(|_| Float::with_val(128, 0)).collect();
+            ct_out
+                .data()
+                .decode_vec_float(ct_out.base2k().into(), 0, &mut data_conv);
+
+            assert!(
+                ct_out
+                    .noise(module, &pt_out, &sk_prep, scratch.borrow())
+                    .std()
+                    .log2()
+                    <= -(ct_out.k().as_u32() as f64) + SIGMA.log2() + 0.50
+            )
+        }
+    }
+}
+
 pub fn test_lwe_to_glwe<BE: Backend>(module: &Module<BE>)
 where
     Module<BE>: GLWEFromLWE<BE>
@@ -22,7 +105,8 @@ + 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>,
 {
@@ -38,23 +122,23 @@ 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(
@@ -78,7 +162,14 @@ 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);
 
@@ -101,7 +192,19 @@
     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>)
@@ -114,7 +217,8 @@ + 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>,
 {
@@ -126,8 +230,8 @@ 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,
     };
@@ -135,14 +239,14 @@
     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]);
@@ -170,8 +274,6 @@ let mut data: Vec<i64> = vec![0i64; module.n()];
     data[a_idx] = 17;
     let mut glwe_pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_infos);
     glwe_pt.encode_vec_i64(&data, k_lwe_pt);
-
-    println!("glwe_pt: {glwe_pt}");
 
     let mut glwe_ct: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_infos);
     glwe_ct.encrypt_sk(
@@ -202,7 +304,19 @@
     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());
+
+    let mut glwe_pt_conv = GLWEPlaintext::alloc(glwe_ct.n(), lwe_pt.base2k(), lwe_pt.k());
 
-    assert_eq!(glwe_pt.data.at(0, 0)[a_idx], lwe_pt.data.at(0, 0)[0]);
+    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]);
 }

@@ -9,8 +9,8 @@ GGLWEKeyswitch, GLWEAutomorphismKeyCompressedEncryptSk, GLWEAutomorphismKeyEncryptSk, GLWESwitchingKeyCompressedEncryptSk,
     GLWESwitchingKeyEncryptSk, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
-        GLWEAutomorphismKey, GLWEAutomorphismKeyDecompress, GLWEAutomorphismKeyLayout, GLWEInfos, GLWESecret,
-        GLWESecretPreparedFactory, GLWESwitchingKeyDecompress, compressed::GLWEAutomorphismKeyCompressed,
+        GGLWEInfos, GLWEAutomorphismKey, GLWEAutomorphismKeyDecompress, GLWEAutomorphismKeyLayout, GLWEInfos, GLWESecret,
+        GLWESecretPreparedFactory, GLWESwitchingKeyDecompress, LWEInfos, compressed::GLWEAutomorphismKeyCompressed,
         prepared::GLWESecretPrepared,
     },
     noise::GGLWENoise,
@@ -84,8 +84,26 @@ });
             let mut sk_out_prepared: GLWESecretPrepared<Vec<u8>, BE> = GLWESecretPrepared::alloc(module, sk_out.rank());
             sk_out_prepared.prepare(module, &sk_out);
 
-            atk.key
-                .assert_noise(module, &sk_out_prepared, &sk.data, SIGMA);
+            let max_noise: f64 = SIGMA.log2() - (atk.k().as_usize() as f64) + 0.5;
+
+            for row in 0..atk.dnum().as_usize() {
+                for col in 0..atk.rank().as_usize() {
+                    assert!(
+                        atk.key
+                            .noise(
+                                module,
+                                row,
+                                col,
+                                &sk.data,
+                                &sk_out_prepared,
+                                scratch.borrow()
+                            )
+                            .std()
+                            .log2()
+                            <= max_noise
+                    )
+                }
+            }
         }
     }
 }
@@ -106,18 +124,18 @@ Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
     let base2k: usize = 12;
     let k_ksk: usize = 60;
-    let dsize: usize = k_ksk.div_ceil(base2k) - 1;
-    for rank in 1_usize..3 {
-        for di in 1..dsize + 1 {
+    let max_dsize: usize = k_ksk.div_ceil(base2k) - 1;
+    for rank in 2_usize..3 {
+        for dsize in 1..max_dsize + 1 {
             let n: usize = module.n();
-            let dnum: usize = (k_ksk - di * base2k) / (di * base2k);
+            let dnum: usize = (k_ksk - dsize * base2k) / (dsize * base2k);
 
             let atk_infos: GLWEAutomorphismKeyLayout = GLWEAutomorphismKeyLayout {
                 n: n.into(),
                 base2k: base2k.into(),
                 k: k_ksk.into(),
                 dnum: dnum.into(),
-                dsize: di.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
@@ -134,7 +152,7 @@
             let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc_from_infos(&atk_infos);
             sk.fill_ternary_prob(0.5, &mut source_xs);
 
-            let p = -5;
+            let p: i64 = -5;
 
             let seed_xa: [u8; 32] = [1u8; 32];
 
@@ -156,8 +174,30 @@
             let mut atk: GLWEAutomorphismKey<Vec<u8>> = GLWEAutomorphismKey::alloc_from_infos(&atk_infos);
             atk.decompress(module, &atk_compressed);
 
-            atk.key
-                .assert_noise(module, &sk_out_prepared, &sk.data, SIGMA);
+            let max_noise: f64 = SIGMA.log2() - (atk.k().as_usize() as f64) + 0.5;
+
+            for row in 0..atk.dnum().as_usize() {
+                for col in 0..atk.rank().as_usize() {
+                    let noise_have = atk
+                        .key
+                        .noise(
+                            module,
+                            row,
+                            col,
+                            &sk.data,
+                            &sk_out_prepared,
+                            scratch.borrow(),
+                        )
+                        .std()
+                        .log2();
+
+                    assert!(
+                        noise_have < max_noise + 0.5,
+                        "row:{row} col:{col} noise_have:{noise_have} > max_noise:{}",
+                        max_noise + 0.5
+                    );
+                }
+            }
         }
     }
 }

@@ -5,12 +5,13 @@ source::Source,
 };
 
 use crate::{
-    GGLWEEncryptSk, GGLWEKeyswitch, GLWESwitchingKeyCompressedEncryptSk, GLWESwitchingKeyEncryptSk, ScratchTakeCore,
+    GGLWECompressedEncryptSk, GGLWEEncryptSk, GGLWEKeyswitch, GLWESwitchingKeyCompressedEncryptSk, GLWESwitchingKeyEncryptSk,
+    ScratchTakeCore,
     decryption::GLWEDecrypt,
     encryption::SIGMA,
     layouts::{
-        GGLWELayout, GLWESecret, GLWESecretPreparedFactory, GLWESwitchingKey, GLWESwitchingKeyCompressed,
-        GLWESwitchingKeyDecompress,
+        GGLWE, GGLWECompressed, GGLWEInfos, GGLWELayout, GLWESecret, GLWESecretPreparedFactory, GLWESwitchingKey,
+        GLWESwitchingKeyCompressed, GLWESwitchingKeyDecompress, LWEInfos,
         prepared::{GGLWEPreparedFactory, GLWESecretPrepared},
     },
     noise::GGLWENoise,
@@ -74,8 +75,30 @@ &mut source_xe,
                     scratch.borrow(),
                 );
 
-                ksk.key
-                    .assert_noise(module, &sk_out_prepared, &sk_in.data, SIGMA);
+                let max_noise: f64 = SIGMA.log2() - (ksk.k().as_usize() as f64) + 0.5;
+
+                for row in 0..ksk.dnum().as_usize() {
+                    for col in 0..ksk.rank_in().as_usize() {
+                        let noise_have = ksk
+                            .key
+                            .noise(
+                                module,
+                                row,
+                                col,
+                                &sk_in.data,
+                                &sk_out_prepared,
+                                scratch.borrow(),
+                            )
+                            .std()
+                            .log2();
+
+                        assert!(
+                            noise_have < max_noise + 0.5,
+                            "row:{row} col:{col} noise_have:{noise_have} > max_noise:{}",
+                            max_noise + 0.5
+                        );
+                    }
+                }
             }
         }
     }
@@ -99,18 +122,18 @@ {
     let n: usize = module.n();
     let base2k: usize = 12;
     let k_ksk: usize = 54;
-    let dsize: usize = k_ksk / base2k;
+    let max_dsize: usize = k_ksk / base2k;
     for rank_in in 1_usize..3 {
         for rank_out in 1_usize..3 {
-            for di in 1_usize..dsize + 1 {
-                let dnum: usize = (k_ksk - di * base2k) / (di * base2k);
+            for dsize in 1_usize..max_dsize {
+                let dnum: usize = (k_ksk - dsize * base2k) / (dsize * base2k);
 
                 let gglwe_infos: GGLWELayout = GGLWELayout {
                     n: n.into(),
                     base2k: base2k.into(),
                     k: k_ksk.into(),
                     dnum: dnum.into(),
-                    dsize: di.into(),
+                    dsize: dsize.into(),
                     rank_in: rank_in.into(),
                     rank_out: rank_out.into(),
                 };
@@ -148,8 +171,122 @@
                 let mut ksk: GLWESwitchingKey<Vec<u8>> = GLWESwitchingKey::alloc_from_infos(&gglwe_infos);
                 ksk.decompress(module, &ksk_compressed);
 
-                ksk.key
-                    .assert_noise(module, &sk_out_prepared, &sk_in.data, SIGMA);
+                let max_noise: f64 = SIGMA.log2() - (ksk.k().as_usize() as f64) + 0.5;
+
+                for row in 0..ksk.dnum().as_usize() {
+                    for col in 0..ksk.rank_in().as_usize() {
+                        let noise_have = ksk
+                            .key
+                            .noise(
+                                module,
+                                row,
+                                col,
+                                &sk_in.data,
+                                &sk_out_prepared,
+                                scratch.borrow(),
+                            )
+                            .std()
+                            .log2();
+
+                        assert!(
+                            noise_have < max_noise + 0.5,
+                            "row:{row} col:{col} noise_have:{noise_have} > max_noise:{}",
+                            max_noise + 0.5
+                        );
+                    }
+                }
+            }
+        }
+    }
+}
+
+pub fn test_gglwe_compressed_encrypt_sk<BE: Backend>(module: &Module<BE>)
+where
+    Module<BE>: GGLWEEncryptSk<BE>
+        + GGLWEPreparedFactory<BE>
+        + GGLWEKeyswitch<BE>
+        + GLWEDecrypt<BE>
+        + GLWESecretPreparedFactory<BE>
+        + GLWESwitchingKeyEncryptSk<BE>
+        + GGLWECompressedEncryptSk<BE>
+        + GLWESwitchingKeyDecompress
+        + GGLWENoise<BE>
+        + VecZnxFillUniform,
+    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+    Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
+{
+    let n: usize = module.n();
+    let base2k: usize = 12;
+    let k_ksk: usize = 54;
+    let max_dsize: usize = k_ksk / base2k;
+    for rank_in in 1_usize..3 {
+        for rank_out in 1_usize..3 {
+            for dsize in 1_usize..max_dsize + 1 {
+                let dnum: usize = (k_ksk - dsize * base2k) / (dsize * base2k);
+
+                let gglwe_infos: GGLWELayout = GGLWELayout {
+                    n: n.into(),
+                    base2k: base2k.into(),
+                    k: k_ksk.into(),
+                    dnum: dnum.into(),
+                    dsize: dsize.into(),
+                    rank_in: rank_in.into(),
+                    rank_out: rank_out.into(),
+                };
+
+                let mut ksk_compressed: GGLWECompressed<Vec<u8>> = GGLWECompressed::alloc_from_infos(&gglwe_infos);
+
+                let mut source_xs: Source = Source::new([0u8; 32]);
+                let mut source_xe: Source = Source::new([0u8; 32]);
+
+                let mut scratch: ScratchOwned<BE> =
+                    ScratchOwned::alloc(GGLWECompressed::encrypt_sk_tmp_bytes(module, &gglwe_infos));
+
+                let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(n.into(), rank_in.into());
+                sk_in.fill_ternary_prob(0.5, &mut source_xs);
+
+                let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(n.into(), rank_out.into());
+                sk_out.fill_ternary_prob(0.5, &mut source_xs);
+                let mut sk_out_prepared: GLWESecretPrepared<Vec<u8>, BE> = GLWESecretPrepared::alloc(module, rank_out.into());
+                sk_out_prepared.prepare(module, &sk_out);
+
+                let seed_xa = [1u8; 32];
+
+                ksk_compressed.encrypt_sk(
+                    module,
+                    &sk_in.data,
+                    &sk_out_prepared,
+                    seed_xa,
+                    &mut source_xe,
+                    scratch.borrow(),
+                );
+
+                let mut ksk: GGLWE<Vec<u8>> = GGLWE::alloc_from_infos(&gglwe_infos);
+                ksk.decompress(module, &ksk_compressed);
+
+                let max_noise: f64 = SIGMA.log2() - (ksk.k().as_usize() as f64) + 0.5;
+
+                for row in 0..ksk.dnum().as_usize() {
+                    for col in 0..ksk.rank_in().as_usize() {
+                        let noise_have = ksk
+                            .noise(
+                                module,
+                                row,
+                                col,
+                                &sk_in.data,
+                                &sk_out_prepared,
+                                scratch.borrow(),
+                            )
+                            .std()
+                            .log2();
+
+                        assert!(
+                            noise_have < max_noise + 0.5,
+                            "row:{row} col:{col} noise_have:{noise_have} > max_noise:{}",
+                            max_noise + 0.5
+                        );
+                    }
+                }
             }
         }
     }

@@ -9,8 +9,9 @@ GGLWENoise, GGLWEToGGSWKeyCompressedEncryptSk, GGLWEToGGSWKeyEncryptSk, ScratchTakeCore,
     decryption::GLWEDecrypt,
     encryption::SIGMA,
     layouts::{
-        Dsize, GGLWEDecompress, GGLWEToGGSWKey, GGLWEToGGSWKeyCompressed, GGLWEToGGSWKeyDecompress, GGLWEToGGSWKeyLayout,
-        GLWESecret, GLWESecretPreparedFactory, GLWESecretTensor, GLWESecretTensorFactory, LWEInfos, prepared::GLWESecretPrepared,
+        Dsize, GGLWE, GGLWEDecompress, GGLWEInfos, GGLWEToGGSWKey, GGLWEToGGSWKeyCompressed, GGLWEToGGSWKeyDecompress,
+        GGLWEToGGSWKeyLayout, GLWESecret, GLWESecretPreparedFactory, GLWESecretTensor, GLWESecretTensorFactory, LWEInfos,
+        prepared::GLWESecretPrepared,
     },
 };
 
@@ -79,9 +80,17 @@ 0,
                 );
             }
 
-            println!("pt_want: {}", pt_want.as_vec_znx());
-
-            module.gglwe_assert_noise(key.at(i), &sk_prepared, &pt_want, max_noise);
+            let ksk: &GGLWE<Vec<u8>> = key.at(i);
+            for row in 0..ksk.dnum().as_usize() {
+                for col in 0..ksk.rank_in().as_usize() {
+                    assert!(
+                        ksk.noise(module, row, col, &pt_want, &sk_prepared, scratch.borrow())
+                            .std()
+                            .log2()
+                            <= max_noise
+                    )
+                }
+            }
         }
     }
 }
@@ -137,8 +146,31 @@
         let mut sk_tensor: GLWESecretTensor<Vec<u8>> = GLWESecretTensor::alloc_from_infos(&sk);
         sk_tensor.prepare(module, &sk, scratch.borrow());
 
+        let max_noise = SIGMA.log2() + 0.5 - (key.k().as_u32() as f64);
+
+        let mut pt_want: ScalarZnx<Vec<u8>> = ScalarZnx::alloc(module.n(), rank);
+
         for i in 0..rank {
-            module.gglwe_assert_noise(key.at(i), &sk_prepared, &sk_tensor.data, SIGMA + 0.5);
+            for j in 0..rank {
+                module.vec_znx_copy(
+                    &mut pt_want.as_vec_znx_mut(),
+                    j,
+                    &sk_tensor.at(i, j).as_vec_znx(),
+                    0,
+                );
+            }
+
+            let ksk: &GGLWE<Vec<u8>> = key.at(i);
+            for row in 0..ksk.dnum().as_usize() {
+                for col in 0..ksk.rank_in().as_usize() {
+                    assert!(
+                        ksk.noise(module, row, col, &pt_want, &sk_prepared, scratch.borrow())
+                            .std()
+                            .log2()
+                            <= max_noise
+                    )
+                }
+            }
         }
     }
 }

@@ -8,8 +8,8 @@ use crate::{
     GGSWCompressedEncryptSk, GGSWEncryptSk, GGSWNoise, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
-        GGSW, GGSWDecompress, GGSWLayout, GLWESecret, GLWESecretPreparedFactory, compressed::GGSWCompressed,
-        prepared::GLWESecretPrepared,
+        GGSW, GGSWDecompress, GGSWInfos, GGSWLayout, GLWEInfos, GLWESecret, GLWESecretPreparedFactory,
+        compressed::GGSWCompressed, prepared::GLWESecretPrepared,
     },
 };
 
@@ -65,7 +65,16 @@ );
 
             let noise_f = |_col_i: usize| -(k as f64) + SIGMA.log2() + 0.5;
 
-            ct.assert_noise(module, &sk_prepared, &pt_scalar, &noise_f);
+            for row in 0..ct.dnum().as_usize() {
+                for col in 0..ct.rank().as_usize() + 1 {
+                    assert!(
+                        ct.noise(module, row, col, &pt_scalar, &sk_prepared, scratch.borrow())
+                            .std()
+                            .log2()
+                            <= noise_f(col)
+                    )
+                }
+            }
         }
     }
 }
@@ -126,7 +135,16 @@
             let mut ct: GGSW<Vec<u8>> = GGSW::alloc_from_infos(&ggsw_infos);
             ct.decompress(module, &ct_compressed);
 
-            ct.assert_noise(module, &sk_prepared, &pt_scalar, &noise_f);
+            for row in 0..ct.dnum().as_usize() {
+                for col in 0..ct.rank().as_usize() + 1 {
+                    assert!(
+                        ct.noise(module, row, col, &pt_scalar, &sk_prepared, scratch.borrow())
+                            .std()
+                            .log2()
+                            <= noise_f(col)
+                    )
+                }
+            }
         }
     }
 }

@@ -5,8 +5,7 @@ source::Source,
 };
 
 use crate::{
-    GLWECompressedEncryptSk, GLWEEncryptPk, GLWEEncryptSk, GLWEPublicKeyGenerate, GLWESub, ScratchTakeCore,
-    decryption::GLWEDecrypt,
+    GLWECompressedEncryptSk, GLWEEncryptPk, GLWEEncryptSk, GLWENoise, GLWEPublicKeyGenerate, GLWESub, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
         GLWE, GLWELayout, GLWEPlaintext, GLWEPlaintextLayout, GLWEPublicKey, GLWEPublicKeyPreparedFactory, GLWESecret,
@@ -18,7 +17,7 @@ };
 
 pub fn test_glwe_encrypt_sk<BE: Backend>(module: &Module<BE>)
 where
-    Module<BE>: GLWEEncryptSk<BE> + GLWEDecrypt<BE> + GLWESecretPreparedFactory<BE> + VecZnxFillUniform + GLWESub,
+    Module<BE>: GLWEEncryptSk<BE> + GLWENoise<BE> + GLWESecretPreparedFactory<BE> + VecZnxFillUniform + GLWESub,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
@@ -44,14 +43,13 @@ };
 
         let mut ct: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_infos);
         let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&pt_infos);
-        let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&pt_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]);
 
         let mut scratch: ScratchOwned<BE> =
-            ScratchOwned::alloc(GLWE::encrypt_sk_tmp_bytes(module, &glwe_infos) | GLWE::decrypt_tmp_bytes(module, &glwe_infos));
+            ScratchOwned::alloc(GLWE::encrypt_sk_tmp_bytes(module, &glwe_infos).max(module.glwe_noise_tmp_bytes(&glwe_infos)));
 
         let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc_from_infos(&glwe_infos);
         sk.fill_ternary_prob(0.5, &mut source_xs);
@@ -70,12 +68,11 @@ &mut source_xe,
             scratch.borrow(),
         );
 
-        ct.decrypt(module, &mut pt_have, &sk_prepared, scratch.borrow());
-
-        module.glwe_sub_inplace(&mut pt_want, &pt_have);
-
-        let noise_have: f64 = pt_want.data.stats(base2k, 0).std() * (ct.k().as_u32() as f64).exp2();
-        let noise_want: f64 = SIGMA;
+        let noise_have: f64 = ct
+            .noise(module, &pt_want, &sk_prepared, scratch.borrow())
+            .std()
+            .log2();
+        let noise_want: f64 = SIGMA.log2() - (ct.k().as_usize() as f64) + 0.5;
 
         assert!(noise_have <= noise_want + 0.2);
     }
@@ -83,7 +80,7 @@ }
 
 pub fn test_glwe_compressed_encrypt_sk<BE: Backend>(module: &Module<BE>)
 where
-    Module<BE>: GLWECompressedEncryptSk<BE> + GLWEDecrypt<BE> + GLWESecretPreparedFactory<BE> + VecZnxFillUniform + GLWESub,
+    Module<BE>: GLWECompressedEncryptSk<BE> + GLWENoise<BE> + GLWESecretPreparedFactory<BE> + VecZnxFillUniform + GLWESub,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
@@ -92,7 +89,6 @@ let k_ct: usize = 54;
     let k_pt: usize = 30;
 
     for rank in 1_usize..3 {
-        // println!("rank: {}", rank);
         let n: usize = module.n();
 
         let glwe_infos: GLWELayout = GLWELayout {
@@ -111,14 +107,13 @@
         let mut ct_compressed: GLWECompressed<Vec<u8>> = GLWECompressed::alloc_from_infos(&glwe_infos);
 
         let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&pt_infos);
-        let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&pt_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]);
 
         let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
-            GLWECompressed::encrypt_sk_tmp_bytes(module, &glwe_infos) | GLWE::decrypt_tmp_bytes(module, &glwe_infos),
+            GLWECompressed::encrypt_sk_tmp_bytes(module, &glwe_infos).max(module.glwe_noise_tmp_bytes(&glwe_infos)),
         );
 
         let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc_from_infos(&glwe_infos);
@@ -143,24 +138,18 @@
         let mut ct: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_infos);
         ct.decompress(module, &ct_compressed);
 
-        ct.decrypt(module, &mut pt_have, &sk_prepared, scratch.borrow());
-
-        module.glwe_sub_inplace(&mut pt_want, &pt_have);
-
-        let noise_have: f64 = pt_want.data.stats(base2k, 0).std() * (ct.k().as_u32() as f64).exp2();
-        let noise_want: f64 = SIGMA;
-
-        assert!(
-            noise_have <= noise_want + 0.2,
-            "{noise_have} <= {}",
-            noise_want + 0.2
-        );
+        let noise_have: f64 = ct
+            .noise(module, &pt_want, &sk_prepared, scratch.borrow())
+            .std()
+            .log2();
+        let noise_want: f64 = SIGMA.log2() - (ct.k().as_usize() as f64) + 0.5;
+        assert!(noise_have <= noise_want + 0.2);
     }
 }
 
 pub fn test_glwe_encrypt_zero_sk<BE: Backend>(module: &Module<BE>)
 where
-    Module<BE>: GLWEEncryptSk<BE> + GLWEDecrypt<BE> + GLWESecretPreparedFactory<BE> + VecZnxFillUniform + GLWESub,
+    Module<BE>: GLWEEncryptSk<BE> + GLWENoise<BE> + GLWESecretPreparedFactory<BE> + VecZnxFillUniform + GLWESub,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
@@ -177,14 +166,17 @@ k: k_ct.into(),
             rank: rank.into(),
         };
 
-        let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_infos);
+        let pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_infos);
 
         let mut source_xs: Source = Source::new([0u8; 32]);
         let mut source_xe: Source = Source::new([1u8; 32]);
         let mut source_xa: Source = Source::new([0u8; 32]);
 
-        let mut scratch: ScratchOwned<BE> =
-            ScratchOwned::alloc(GLWE::decrypt_tmp_bytes(module, &glwe_infos) | GLWE::encrypt_sk_tmp_bytes(module, &glwe_infos));
+        let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
+            module
+                .glwe_noise_tmp_bytes(&glwe_infos)
+                .max(GLWE::encrypt_sk_tmp_bytes(module, &glwe_infos)),
+        );
 
         let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc_from_infos(&glwe_infos);
         sk.fill_ternary_prob(0.5, &mut source_xs);
@@ -201,9 +193,13 @@ &mut source_xa,
             &mut source_xe,
             scratch.borrow(),
         );
-        ct.decrypt(module, &mut pt, &sk_prepared, scratch.borrow());
 
-        assert!((SIGMA - pt.data.stats(base2k, 0).std() * (k_ct as f64).exp2()) <= 0.2);
+        let noise_have: f64 = ct
+            .noise(module, &pt, &sk_prepared, scratch.borrow())
+            .std()
+            .log2();
+        let noise_want: f64 = SIGMA.log2() - (ct.k().as_usize() as f64) + 0.5;
+        assert!(noise_have <= noise_want + 0.2);
     }
 }
 
@@ -212,7 +208,7 @@ where
     Module<BE>: GLWEEncryptPk<BE>
         + GLWEPublicKeyPreparedFactory<BE>
         + GLWEPublicKeyGenerate<BE>
-        + GLWEDecrypt<BE>
+        + GLWENoise<BE>
         + GLWESecretPreparedFactory<BE>
         + VecZnxFillUniform
         + GLWESub,
@@ -233,7 +229,6 @@ rank: rank.into(),
         };
 
         let mut ct: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_infos);
-        let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_infos);
         let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_infos);
 
         let mut source_xs: Source = Source::new([0u8; 32]);
@@ -241,8 +236,11 @@ let mut source_xe: Source = Source::new([0u8; 32]);
         let mut source_xa: Source = Source::new([0u8; 32]);
         let mut source_xu: Source = Source::new([0u8; 32]);
 
-        let mut scratch: ScratchOwned<BE> =
-            ScratchOwned::alloc(GLWE::decrypt_tmp_bytes(module, &glwe_infos) | GLWE::encrypt_pk_tmp_bytes(module, &glwe_infos));
+        let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
+            module
+                .glwe_noise_tmp_bytes(&glwe_infos)
+                .max(GLWE::encrypt_pk_tmp_bytes(module, &glwe_infos)),
+        );
 
         let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc_from_infos(&glwe_infos);
         sk.fill_ternary_prob(0.5, &mut source_xs);
@@ -267,17 +265,11 @@ &mut source_xe,
             scratch.borrow(),
         );
 
-        ct.decrypt(module, &mut pt_have, &sk_prepared, scratch.borrow());
-
-        module.glwe_sub_inplace(&mut pt_want, &pt_have);
-
-        let noise_have: f64 = pt_want.data.stats(base2k, 0).std().log2();
+        let noise_have: f64 = ct
+            .noise(module, &pt_want, &sk_prepared, scratch.borrow())
+            .std()
+            .log2();
         let noise_want: f64 = ((((rank as f64) + 1.0) * n as f64 * 0.5 * SIGMA * SIGMA).sqrt()).log2() - (k_ct as f64);
-
-        assert!(
-            noise_have <= noise_want + 0.2,
-            "{noise_have} <= {}",
-            noise_want + 0.2
-        );
+        assert!(noise_have <= noise_want + 0.2);
     }
 }

@@ -9,8 +9,8 @@ GGLWENoise, GLWETensorKeyCompressedEncryptSk, GLWETensorKeyEncryptSk, ScratchTakeCore,
     decryption::GLWEDecrypt,
     encryption::SIGMA,
     layouts::{
-        Dsize, GGLWEDecompress, GLWESecret, GLWESecretPreparedFactory, GLWESecretTensor, GLWESecretTensorFactory, GLWETensorKey,
-        GLWETensorKeyCompressed, GLWETensorKeyLayout, prepared::GLWESecretPrepared,
+        Dsize, GGLWEDecompress, GGLWEInfos, GLWESecret, GLWESecretPreparedFactory, GLWESecretTensor, GLWESecretTensorFactory,
+        GLWETensorKey, GLWETensorKeyCompressed, GLWETensorKeyLayout, LWEInfos, prepared::GLWESecretPrepared,
     },
 };
 
@@ -67,7 +67,27 @@
         let mut sk_tensor: GLWESecretTensor<Vec<u8>> = GLWESecretTensor::alloc_from_infos(&sk);
         sk_tensor.prepare(module, &sk, scratch.borrow());
 
-        module.gglwe_assert_noise(&tensor_key, &sk_prepared, &sk_tensor.data, SIGMA + 0.5);
+        let max_noise: f64 = SIGMA.log2() - (tensor_key.k().as_usize() as f64) + 0.5;
+
+        for row in 0..tensor_key.dnum().as_usize() {
+            for col in 0..tensor_key.rank_in().as_usize() {
+                assert!(
+                    tensor_key
+                        .0
+                        .noise(
+                            module,
+                            row,
+                            col,
+                            &sk_tensor.data,
+                            &sk_prepared,
+                            scratch.borrow()
+                        )
+                        .std()
+                        .log2()
+                        <= max_noise
+                )
+            }
+        }
     }
 }
 
@@ -124,6 +144,26 @@
         let mut sk_tensor: GLWESecretTensor<Vec<u8>> = GLWESecretTensor::alloc_from_infos(&sk);
         sk_tensor.prepare(module, &sk, scratch.borrow());
 
-        module.gglwe_assert_noise(&tensor_key, &sk_prepared, &sk_tensor.data, SIGMA + 0.5);
+        let max_noise: f64 = SIGMA.log2() - (tensor_key.k().as_usize() as f64) + 0.5;
+
+        for row in 0..tensor_key.dnum().as_usize() {
+            for col in 0..tensor_key.rank_in().as_usize() {
+                assert!(
+                    tensor_key
+                        .0
+                        .noise(
+                            module,
+                            row,
+                            col,
+                            &sk_tensor.data,
+                            &sk_prepared,
+                            scratch.borrow()
+                        )
+                        .std()
+                        .log2()
+                        <= max_noise
+                )
+            }
+        }
     }
 }

@@ -8,7 +8,8 @@ use crate::{
     GGLWEExternalProduct, GGLWENoise, GGSWEncryptSk, GLWESwitchingKeyEncryptSk, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
-        GGSW, GGSWLayout, GGSWPreparedFactory, GLWESecret, GLWESecretPreparedFactory, GLWESwitchingKey, GLWESwitchingKeyLayout,
+        GGLWEInfos, GGSW, GGSWLayout, GGSWPreparedFactory, GLWESecret, GLWESecretPreparedFactory, GLWESwitchingKey,
+        GLWESwitchingKeyLayout,
         prepared::{GGSWPrepared, GLWESecretPrepared},
     },
     noise::noise_ggsw_product,
@@ -27,24 +28,28 @@ + 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 in 1_usize..3 {
         for rank_out in 1_usize..3 {
-            for di in 1_usize..dsize + 1 {
-                let k_ggsw: usize = k_in + base2k * di;
+            for dsize in 1_usize..max_dsize + 1 {
+                let k_ggsw: usize = k_in + base2k_key * dsize;
                 let k_out: usize = k_in; // Better capture noise.
 
                 let n: usize = module.n();
-                let dnum: usize = k_in.div_ceil(base2k * di);
+                let dnum_in: usize = k_in / base2k_in;
+                let dnum: usize = k_in.div_ceil(base2k_key * dsize);
                 let dsize_in: usize = 1;
 
                 let gglwe_in_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.into(),
                     rank_out: rank_out.into(),
@@ -52,9 +57,9 @@ };
 
                 let gglwe_out_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(),
@@ -62,10 +67,10 @@ };
 
                 let ggsw_infos: GGSWLayout = GGSWLayout {
                     n: n.into(),
-                    base2k: base2k.into(),
+                    base2k: base2k_key.into(),
                     k: k_ggsw.into(),
                     dnum: dnum.into(),
-                    dsize: di.into(),
+                    dsize: dsize.into(),
                     rank: rank_out.into(),
                 };
 
@@ -143,7 +148,7 @@ let var_a1_err: f64 = 1f64 / 12f64;
 
                 let max_noise: f64 = noise_ggsw_product(
                     n as f64,
-                    base2k * di,
+                    base2k_key * dsize,
                     var_xs,
                     var_msg,
                     var_a0_err,
@@ -155,9 +160,25 @@ k_in,
                     k_ggsw,
                 );
 
-                ct_gglwe_out
-                    .key
-                    .assert_noise(module, &sk_out_prepared, &sk_in.data, max_noise + 0.5);
+                for row in 0..ct_gglwe_out.dnum().as_usize() {
+                    for col in 0..ct_gglwe_out.rank_in().as_usize() {
+                        assert!(
+                            ct_gglwe_out
+                                .key
+                                .noise(
+                                    module,
+                                    row,
+                                    col,
+                                    &sk_in.data,
+                                    &sk_out_prepared,
+                                    scratch.borrow()
+                                )
+                                .std()
+                                .log2()
+                                <= max_noise + 0.5
+                        )
+                    }
+                }
             }
         }
     }
@@ -176,24 +197,27 @@ + GGLWENoise<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_ggsw: usize = k_out + base2k * di;
+            for dsize in 1_usize..max_dsize + 1 {
+                let k_ggsw: usize = k_out + base2k_key * dsize;
 
                 let n: usize = module.n();
-                let dnum: usize = k_out.div_ceil(base2k * di);
+                let dnum_in: usize = k_out / base2k_out;
+                let dnum: usize = k_out.div_ceil(base2k_key * dsize);
 
                 let dsize_in: usize = 1;
 
                 let gglwe_out_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(),
@@ -201,10 +225,10 @@ };
 
                 let ggsw_infos: GGSWLayout = GGSWLayout {
                     n: n.into(),
-                    base2k: base2k.into(),
+                    base2k: base2k_key.into(),
                     k: k_ggsw.into(),
                     dnum: dnum.into(),
-                    dsize: di.into(),
+                    dsize: dsize.into(),
                     rank: rank_out.into(),
                 };
 
@@ -281,7 +305,7 @@ let var_a1_err: f64 = 1f64 / 12f64;
 
                 let max_noise: f64 = noise_ggsw_product(
                     n as f64,
-                    base2k * di,
+                    base2k_key * dsize,
                     var_xs,
                     var_msg,
                     var_a0_err,
@@ -293,9 +317,25 @@ k_out,
                     k_ggsw,
                 );
 
-                ct_gglwe
-                    .key
-                    .assert_noise(module, &sk_out_prepared, &sk_in.data, max_noise + 0.5);
+                for row in 0..ct_gglwe.dnum().as_usize() {
+                    for col in 0..ct_gglwe.rank_in().as_usize() {
+                        assert!(
+                            ct_gglwe
+                                .key
+                                .noise(
+                                    module,
+                                    row,
+                                    col,
+                                    &sk_in.data,
+                                    &sk_out_prepared,
+                                    scratch.borrow()
+                                )
+                                .std()
+                                .log2()
+                                <= max_noise + 0.5
+                        )
+                    }
+                }
             }
         }
     }

@@ -8,7 +8,7 @@ use crate::{
     GGSWEncryptSk, GGSWExternalProduct, GGSWNoise, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
-        GGSW, GGSWLayout, GGSWPreparedFactory, GLWESecret, GLWESecretPreparedFactory,
+        GGSW, GGSWInfos, GGSWLayout, GGSWPreparedFactory, GLWEInfos, GLWESecret, GLWESecretPreparedFactory,
         prepared::{GGSWPrepared, GLWESecretPrepared},
     },
     noise::noise_ggsw_product,
@@ -26,23 +26,26 @@ + GGSWNoise<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 1_usize..3 {
-        for di in 1..dsize + 1 {
-            let k_apply: usize = k_in + base2k * di;
+        for dsize in 1..max_dsize + 1 {
+            let k_apply: usize = k_in + base2k_key * dsize;
 
             let k_out: usize = k_in; // 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: usize = k_in.div_ceil(base2k_key * dsize);
+            let dnum_in: usize = k_in / base2k_in;
             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_in.into(),
                 dsize: dsize_in.into(),
@@ -51,7 +54,7 @@ };
 
             let ggsw_out_infos: GGSWLayout = GGSWLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_out.into(),
                 k: k_out.into(),
                 dnum: dnum_in.into(),
                 dsize: dsize_in.into(),
@@ -60,10 +63,10 @@ };
 
             let ggsw_apply_infos: GGSWLayout = GGSWLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_apply.into(),
                 dnum: dnum.into(),
-                dsize: di.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
@@ -130,7 +133,7 @@
             let max_noise = |_col_j: usize| -> f64 {
                 noise_ggsw_product(
                     n as f64,
-                    base2k * di,
+                    base2k_key * dsize,
                     0.5,
                     var_msg,
                     var_a0_err,
@@ -143,7 +146,17 @@ k_apply,
                 ) + 0.5
             };
 
-            ggsw_out.assert_noise(module, &sk_prepared, &pt_in, &max_noise);
+            for row in 0..ggsw_out.dnum().as_usize() {
+                for col in 0..ggsw_out.rank().as_usize() + 1 {
+                    assert!(
+                        ggsw_out
+                            .noise(module, row, col, &pt_in, &sk_prepared, scratch.borrow())
+                            .std()
+                            .log2()
+                            <= max_noise(col)
+                    )
+                }
+            }
         }
     }
 }
@@ -160,21 +173,23 @@ + GGSWNoise<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 1_usize..3 {
-        for di in 1..dsize + 1 {
-            let k_apply: usize = k_out + base2k * di;
+        for dsize in 1..max_dsize + 1 {
+            let k_apply: usize = k_out + base2k_key * dsize;
 
             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: usize = k_out.div_ceil(dsize * base2k_key);
+            let dnum_in: usize = k_out / base2k_out;
             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_in.into(),
                 dsize: dsize_in.into(),
@@ -183,10 +198,10 @@ };
 
             let ggsw_apply_infos: GGSWLayout = GGSWLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_apply.into(),
                 dnum: dnum.into(),
-                dsize: di.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
@@ -253,7 +268,7 @@
             let max_noise = |_col_j: usize| -> f64 {
                 noise_ggsw_product(
                     n as f64,
-                    base2k * di,
+                    base2k_key * dsize,
                     0.5,
                     var_msg,
                     var_a0_err,
@@ -266,7 +281,17 @@ k_apply,
                 ) + 0.5
             };
 
-            ggsw_out.assert_noise(module, &sk_prepared, &pt_in, &max_noise);
+            for row in 0..ggsw_out.dnum().as_usize() {
+                for col in 0..ggsw_out.rank().as_usize() + 1 {
+                    assert!(
+                        ggsw_out
+                            .noise(module, row, col, &pt_in, &sk_prepared, scratch.borrow())
+                            .std()
+                            .log2()
+                            <= max_noise(col)
+                    )
+                }
+            }
         }
     }
 }

@@ -5,7 +5,7 @@ source::Source,
 };
 
 use crate::{
-    GGSWEncryptSk, GLWEEncryptSk, GLWEExternalProduct, GLWENoise, ScratchTakeCore,
+    GGSWEncryptSk, GLWEEncryptSk, GLWEExternalProduct, GLWENoise, GLWENormalize, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
         GGSW, GGSWLayout, GGSWPreparedFactory, GLWE, GLWELayout, GLWEPlaintext, GLWESecret, GLWESecretPreparedFactory,
@@ -24,41 +24,44 @@ + GLWEExternalProduct<BE>
         + GLWEEncryptSk<BE>
         + GLWENoise<BE>
         + VecZnxRotateInplace<BE>
-        + GLWESecretPreparedFactory<BE>,
+        + GLWESecretPreparedFactory<BE>
+        + GLWENormalize<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_in: usize = 45;
-    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);
     for rank in 1_usize..3 {
-        for di in 1..dsize + 1 {
-            let k_ggsw: usize = k_in + base2k * di;
+        for dsize in 1..max_dsize + 1 {
+            let k_ggsw: usize = k_in + base2k_key * dsize;
             let k_out: usize = k_ggsw; // Better capture noise
 
             let n: usize = module.n();
-            let dnum: usize = k_in.div_ceil(base2k * dsize);
+            let dnum: usize = k_in.div_ceil(k_ggsw * dsize);
 
             let glwe_in_infos: GLWELayout = GLWELayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_in.into(),
                 k: k_in.into(),
                 rank: rank.into(),
             };
 
             let glwe_out_infos: GLWELayout = GLWELayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_out.into(),
                 k: k_out.into(),
                 rank: rank.into(),
             };
 
             let ggsw_apply_infos: GGSWLayout = GGSWLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_ggsw.into(),
                 dnum: dnum.into(),
-                dsize: di.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
@@ -66,16 +69,17 @@ let mut ggsw_apply: GGSW<Vec<u8>> = GGSW::alloc_from_infos(&ggsw_apply_infos);
             let mut glwe_in: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_in_infos);
             let mut glwe_out: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_out_infos);
             let mut pt_ggsw: ScalarZnx<Vec<u8>> = ScalarZnx::alloc(n, 1);
-            let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_in_infos);
+            let mut pt_in: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_in_infos);
+            let mut pt_out: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_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]);
 
             // Random input plaintext
-            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);
 
-            pt_want.data.at_mut(0, 0)[1] = 1;
+            pt_in.data.at_mut(0, 0)[1] = 1;
 
             let k: usize = 1;
 
@@ -104,7 +108,7 @@ );
 
             glwe_in.encrypt_sk(
                 module,
-                &pt_want,
+                &pt_in,
                 &sk_prepared,
                 &mut source_xa,
                 &mut source_xe,
@@ -116,7 +120,9 @@ ct_ggsw_prepared.prepare(module, &ggsw_apply, scratch.borrow());
 
             glwe_out.external_product(module, &glwe_in, &ct_ggsw_prepared, scratch.borrow());
 
-            module.vec_znx_rotate_inplace(k as i64, &mut pt_want.data, 0, scratch.borrow());
+            module.vec_znx_rotate_inplace(k as i64, &mut pt_in.data, 0, scratch.borrow());
+
+            module.glwe_normalize(&mut pt_out, &pt_in, scratch.borrow());
 
             let var_gct_err_lhs: f64 = SIGMA * SIGMA;
             let var_gct_err_rhs: f64 = 0f64;
@@ -127,7 +133,7 @@ let var_a1_err: f64 = 1f64 / 12f64;
 
             let max_noise: f64 = noise_ggsw_product(
                 n as f64,
-                base2k * dsize,
+                base2k_key * max_dsize,
                 0.5,
                 var_msg,
                 var_a0_err,
@@ -139,7 +145,13 @@ k_in,
                 k_ggsw,
             );
 
-            glwe_out.assert_noise(module, &sk_prepared, &pt_want, max_noise + 0.5);
+            assert!(
+                glwe_out
+                    .noise(module, &pt_out, &sk_prepared, scratch.borrow())
+                    .std()
+                    .log2()
+                    <= max_noise + 1.0
+            )
         }
     }
 }
@@ -158,29 +170,31 @@ + GLWESecretPreparedFactory<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 1_usize..3 {
-        for di in 1..dsize + 1 {
-            let k_ggsw: usize = k_out + base2k * di;
+        for dsize in 1..max_dsize + 1 {
+            let k_ggsw: 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_out * max_dsize);
 
             let glwe_out_infos: GLWELayout = GLWELayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_out.into(),
                 k: k_out.into(),
                 rank: rank.into(),
             };
 
             let ggsw_apply_infos: GGSWLayout = GGSWLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_ggsw.into(),
                 dnum: dnum.into(),
-                dsize: di.into(),
+                dsize: dsize.into(),
                 rank: rank.into(),
             };
 
@@ -194,7 +208,7 @@ let mut source_xe: Source = Source::new([0u8; 32]);
             let mut source_xa: Source = Source::new([0u8; 32]);
 
             // Random input plaintext
-            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);
 
             pt_want.data.at_mut(0, 0)[1] = 1;
 
@@ -248,7 +262,7 @@ let var_a1_err: f64 = 1f64 / 12f64;
 
             let max_noise: f64 = noise_ggsw_product(
                 n as f64,
-                base2k * dsize,
+                base2k_key * max_dsize,
                 0.5,
                 var_msg,
                 var_a0_err,
@@ -260,7 +274,13 @@ k_out,
                 k_ggsw,
             );
 
-            glwe_out.assert_noise(module, &sk_prepared, &pt_want, max_noise + 0.5);
+            assert!(
+                glwe_out
+                    .noise(module, &pt_want, &sk_prepared, scratch.borrow())
+                    .std()
+                    .log2()
+                    <= max_noise + 1.0
+            )
         }
     }
 }

@@ -33,25 +33,26 @@ let mut source_xe: Source = Source::new([0u8; 32]);
     let mut source_xa: Source = Source::new([0u8; 32]);
 
     let n: usize = module.n();
-    let base2k: usize = 18;
+    let base2k_out: usize = 15;
+    let base2k_key: usize = 10;
     let k_ct: usize = 36;
     let pt_k: usize = 18;
     let rank: usize = 3;
     let dsize: usize = 1;
-    let k_ksk: usize = k_ct + base2k * dsize;
+    let k_ksk: usize = k_ct + base2k_key * dsize;
 
-    let dnum: usize = k_ct.div_ceil(base2k * dsize);
+    let dnum: usize = k_ct.div_ceil(base2k_key * dsize);
 
     let glwe_out_infos: GLWELayout = GLWELayout {
         n: n.into(),
-        base2k: base2k.into(),
+        base2k: base2k_out.into(),
         k: k_ct.into(),
         rank: rank.into(),
     };
 
     let key_infos: GLWEAutomorphismKeyLayout = GLWEAutomorphismKeyLayout {
         n: n.into(),
-        base2k: base2k.into(),
+        base2k: base2k_key.into(),
         k: k_ksk.into(),
         rank: rank.into(),
         dsize: dsize.into(),
@@ -134,7 +135,7 @@ }
     });
 
     let mut res: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_out_infos);
-    packer.flush(module, &mut res);
+    packer.flush(module, &mut res, scratch.borrow());
 
     let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_out_infos);
     let mut data: Vec<i64> = vec![0i64; n];
@@ -153,7 +154,7 @@
     let noise_have: f64 = pt.stats().std().log2();
 
     assert!(
-        noise_have < -((k_ct - base2k) as f64),
+        noise_have < -((k_ct - base2k_out) as f64),
         "noise: {noise_have}"
     );
 }

@@ -0,0 +1,148 @@
+use std::collections::HashMap;
+
+use itertools::Itertools;
+use poulpy_hal::{
+    api::{ScratchAvailable, ScratchOwnedAlloc, ScratchOwnedBorrow},
+    layouts::{Backend, Module, Scratch, ScratchOwned},
+    source::Source,
+};
+
+use crate::{
+    GLWEAutomorphismKeyEncryptSk, GLWEDecrypt, GLWEEncryptSk, GLWENoise, GLWEPacking, GLWERotate, GLWESub, ScratchTakeCore,
+    layouts::{
+        GLWE, GLWEAutomorphismKey, GLWEAutomorphismKeyLayout, GLWEAutomorphismKeyPreparedFactory, GLWELayout, GLWEPlaintext,
+        GLWESecret, GLWESecretPreparedFactory,
+        prepared::{GLWEAutomorphismKeyPrepared, GLWESecretPrepared},
+    },
+};
+
+pub fn test_glwe_packing<BE: Backend>(module: &Module<BE>)
+where
+    Module<BE>: GLWEEncryptSk<BE>
+        + GLWEAutomorphismKeyEncryptSk<BE>
+        + GLWEAutomorphismKeyPreparedFactory<BE>
+        + GLWEPacking<BE>
+        + GLWESecretPreparedFactory<BE>
+        + GLWESub
+        + GLWEDecrypt<BE>
+        + GLWERotate<BE>
+        + GLWENoise<BE>,
+    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+    Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
+{
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let n: usize = module.n();
+    let base2k_out: usize = 15;
+    let base2k_key: usize = 10;
+    let k_ct: usize = 36;
+    let pt_k: usize = base2k_out;
+    let rank: usize = 3;
+    let dsize: usize = 1;
+    let k_ksk: usize = k_ct + base2k_key * dsize;
+
+    let dnum: usize = k_ct.div_ceil(base2k_key * dsize);
+
+    let glwe_out_infos: GLWELayout = GLWELayout {
+        n: n.into(),
+        base2k: base2k_out.into(),
+        k: k_ct.into(),
+        rank: rank.into(),
+    };
+
+    let key_infos: GLWEAutomorphismKeyLayout = GLWEAutomorphismKeyLayout {
+        n: n.into(),
+        base2k: base2k_key.into(),
+        k: k_ksk.into(),
+        rank: rank.into(),
+        dsize: dsize.into(),
+        dnum: dnum.into(),
+    };
+
+    let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
+        GLWE::encrypt_sk_tmp_bytes(module, &glwe_out_infos)
+            .max(GLWEAutomorphismKey::encrypt_sk_tmp_bytes(
+                module, &key_infos,
+            ))
+            .max(module.glwe_pack_tmp_bytes(&glwe_out_infos, &key_infos)),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc_from_infos(&glwe_out_infos);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+
+    let mut sk_prep: GLWESecretPrepared<Vec<u8>, BE> = GLWESecretPrepared::alloc_from_infos(module, &sk);
+    sk_prep.prepare(module, &sk);
+
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_out_infos);
+    let mut data: Vec<i64> = vec![0i64; n];
+    data.iter_mut().enumerate().for_each(|(i, x)| {
+        *x = i as i64;
+    });
+
+    pt.encode_vec_i64(&data, pt_k.into());
+
+    let gal_els: Vec<i64> = module.glwe_pack_galois_elements();
+
+    let mut auto_keys: HashMap<i64, GLWEAutomorphismKeyPrepared<Vec<u8>, BE>> = HashMap::new();
+    let mut tmp: GLWEAutomorphismKey<Vec<u8>> = GLWEAutomorphismKey::alloc_from_infos(&key_infos);
+    gal_els.iter().for_each(|gal_el| {
+        tmp.encrypt_sk(
+            module,
+            *gal_el,
+            &sk,
+            &mut source_xa,
+            &mut source_xe,
+            scratch.borrow(),
+        );
+        let mut atk_prepared: GLWEAutomorphismKeyPrepared<Vec<u8>, BE> =
+            GLWEAutomorphismKeyPrepared::alloc_from_infos(module, &tmp);
+        atk_prepared.prepare(module, &tmp, scratch.borrow());
+        auto_keys.insert(*gal_el, atk_prepared);
+    });
+
+    let mut cts = (0..n)
+        .step_by(5)
+        .map(|_| {
+            let mut ct = GLWE::alloc_from_infos(&glwe_out_infos);
+            ct.encrypt_sk(
+                module,
+                &pt,
+                &sk_prep,
+                &mut source_xa,
+                &mut source_xe,
+                scratch.borrow(),
+            );
+            module.glwe_rotate_inplace(-5, &mut pt, scratch.borrow()); // X^-batch * pt
+            ct
+        })
+        .collect_vec();
+
+    let mut cts_map: HashMap<usize, &mut GLWE<Vec<u8>>> = HashMap::new();
+
+    for (i, ct) in cts.iter_mut().enumerate() {
+        cts_map.insert(5 * i, ct);
+    }
+
+    let mut res: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_out_infos);
+
+    module.glwe_pack(&mut res, cts_map, 0, &auto_keys, scratch.borrow());
+
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_out_infos);
+    let mut data: Vec<i64> = vec![0i64; n];
+    data.iter_mut().enumerate().for_each(|(i, x)| {
+        if i.is_multiple_of(5) {
+            *x = i as i64;
+        }
+    });
+
+    pt_want.encode_vec_i64(&data, pt_k.into());
+
+    assert!(
+        res.noise(module, &pt_want, &sk_prep, scratch.borrow())
+            .std()
+            .log2()
+            <= ((k_ct - base2k_out) as f64)
+    );
+}

@@ -8,10 +8,12 @@ use crate::{
     GGLWEKeyswitch, GGLWENoise, GLWESwitchingKeyEncryptSk, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
-        GLWESecret, GLWESecretPreparedFactory, GLWESwitchingKey, GLWESwitchingKeyLayout, GLWESwitchingKeyPreparedFactory,
+        GGLWEInfos, 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 +26,29 @@ + 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 +56,19 @@ };
 
                     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 +89,8 @@ | 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,
                     ));
 
@@ -135,22 +139,41 @@ &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
-                        .assert_noise(module, &sk2_prepared, &sk0.data, max_noise + 0.5);
+                    for row in 0..gglwe_s0s2.dnum().as_usize() {
+                        for col in 0..gglwe_s0s2.rank_in().as_usize() {
+                            assert!(
+                                gglwe_s0s2
+                                    .key
+                                    .noise(
+                                        module,
+                                        row,
+                                        col,
+                                        &sk0.data,
+                                        &sk2_prepared,
+                                        scratch_apply.borrow()
+                                    )
+                                    .std()
+                                    .log2()
+                                    <= max_noise + 0.5
+                            )
+                        }
+                    }
                 }
             }
         }
@@ -168,23 +191,27 @@ + 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 +219,10 @@ };
 
                 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 +290,7 @@ 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,
@@ -274,9 +301,25 @@ k_out,
                     k_ksk,
                 );
 
-                gglwe_s0s2
-                    .key
-                    .assert_noise(module, &sk2_prepared, &sk0.data, max_noise + 0.5);
+                for row in 0..gglwe_s0s2.dnum().as_usize() {
+                    for col in 0..gglwe_s0s2.rank_in().as_usize() {
+                        assert!(
+                            gglwe_s0s2
+                                .key
+                                .noise(
+                                    module,
+                                    row,
+                                    col,
+                                    &sk0.data,
+                                    &sk2_prepared,
+                                    scratch_apply.borrow()
+                                )
+                                .std()
+                                .log2()
+                                <= max_noise + 0.5
+                        )
+                    }
+                }
             }
         }
     }

@@ -8,8 +8,8 @@ use crate::{
     GGLWEToGGSWKeyEncryptSk, GGSWEncryptSk, GGSWKeyswitch, GGSWNoise, GLWESwitchingKeyEncryptSk, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
-        GGLWEToGGSWKey, GGLWEToGGSWKeyPrepared, GGLWEToGGSWKeyPreparedFactory, GGSW, GGSWLayout, GLWESecret,
-        GLWESecretPreparedFactory, GLWESwitchingKey, GLWESwitchingKeyLayout, GLWESwitchingKeyPreparedFactory,
+        GGLWEToGGSWKey, GGLWEToGGSWKeyPrepared, GGLWEToGGSWKeyPreparedFactory, GGSW, GGSWInfos, GGSWLayout, GLWEInfos,
+        GLWESecret, GLWESecretPreparedFactory, GLWESwitchingKey, GLWESwitchingKeyLayout, GLWESwitchingKeyPreparedFactory,
         GLWETensorKeyLayout,
         prepared::{GLWESecretPrepared, GLWESwitchingKeyPrepared},
     },
@@ -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,
@@ -176,7 +180,24 @@ k_tsk,
                 ) + 0.5
             };
 
-            ggsw_out.assert_noise(module, &sk_out_prepared, &pt_scalar, &max_noise);
+            for row in 0..ggsw_out.dnum().as_usize() {
+                for col in 0..ggsw_out.rank().as_usize() + 1 {
+                    assert!(
+                        ggsw_out
+                            .noise(
+                                module,
+                                row,
+                                col,
+                                &pt_scalar,
+                                &sk_out_prepared,
+                                scratch.borrow()
+                            )
+                            .std()
+                            .log2()
+                            <= max_noise(col)
+                    )
+                }
+            }
         }
     }
 }
@@ -195,43 +216,45 @@ + 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 +334,7 @@
             let max_noise = |col_j: usize| -> f64 {
                 noise_ggsw_keyswitch(
                     n as f64,
-                    base2k * di,
+                    base2k_key * dsize,
                     col_j,
                     var_xs,
                     0f64,
@@ -324,7 +347,24 @@ k_tsk,
                 ) + 0.5
             };
 
-            ggsw_out.assert_noise(module, &sk_out_prepared, &pt_scalar, &max_noise);
+            for row in 0..ggsw_out.dnum().as_usize() {
+                for col in 0..ggsw_out.rank().as_usize() + 1 {
+                    assert!(
+                        ggsw_out
+                            .noise(
+                                module,
+                                row,
+                                col,
+                                &pt_scalar,
+                                &sk_out_prepared,
+                                scratch.borrow()
+                            )
+                            .std()
+                            .log2()
+                            <= max_noise(col)
+                    )
+                }
+            }
         }
     }
 }

@@ -5,14 +5,14 @@ source::Source,
 };
 
 use crate::{
-    GLWEEncryptSk, GLWEKeyswitch, GLWENoise, GLWESwitchingKeyEncryptSk, ScratchTakeCore,
+    GLWEEncryptSk, GLWEKeyswitch, GLWENoise, GLWENormalize, GLWESwitchingKeyEncryptSk, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
         GLWE, GLWELayout, GLWEPlaintext, GLWESecret, GLWESecretPreparedFactory, GLWESwitchingKey, GLWESwitchingKeyLayout,
-        GLWESwitchingKeyPreparedFactory,
+        GLWESwitchingKeyPreparedFactory, LWEInfos,
         prepared::{GLWESecretPrepared, GLWESwitchingKeyPrepared},
     },
-    noise::log2_std_noise_gglwe_product,
+    var_noise_gglwe_product_v2,
 };
 
 #[allow(clippy::too_many_arguments)]
@@ -24,43 +24,46 @@ + GLWEEncryptSk<BE>
         + GLWEKeyswitch<BE>
         + GLWESecretPreparedFactory<BE>
         + GLWESwitchingKeyPreparedFactory<BE>
-        + GLWENoise<BE>,
+        + GLWENoise<BE>
+        + GLWENormalize<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_in: usize = 45;
-    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);
 
     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_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.div_ceil(base2k * dsize);
+                let dnum: usize = k_in.div_ceil(base2k_key * dsize);
 
                 let glwe_in_infos: GLWELayout = GLWELayout {
                     n: n.into(),
-                    base2k: base2k.into(),
+                    base2k: base2k_in.into(),
                     k: k_in.into(),
                     rank: rank_in.into(),
                 };
 
                 let glwe_out_infos: GLWELayout = GLWELayout {
                     n: n.into(),
-                    base2k: base2k.into(),
+                    base2k: base2k_out.into(),
                     k: k_out.into(),
                     rank: rank_out.into(),
                 };
 
                 let ksk: GLWESwitchingKeyLayout = GLWESwitchingKeyLayout {
                     n: n.into(),
-                    base2k: base2k.into(),
+                    base2k: base2k_key.into(),
                     k: k_ksk.into(),
                     dnum: dnum.into(),
-                    dsize: di.into(),
+                    dsize: dsize.into(),
                     rank_in: rank_in.into(),
                     rank_out: rank_out.into(),
                 };
@@ -68,13 +71,14 @@
                 let mut ksk: GLWESwitchingKey<Vec<u8>> = GLWESwitchingKey::alloc_from_infos(&ksk);
                 let mut glwe_in: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_in_infos);
                 let mut glwe_out: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&glwe_out_infos);
-                let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_in_infos);
+                let mut pt_in: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_in_infos);
+                let mut pt_out: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_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(pt_in.base2k().into(), &mut pt_in.data, 0, &mut source_xa);
 
                 let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
                     GLWESwitchingKey::encrypt_sk_tmp_bytes(module, &ksk)
@@ -105,7 +109,7 @@ );
 
                 glwe_in.encrypt_sk(
                     module,
-                    &pt_want,
+                    &pt_in,
                     &sk_in_prepared,
                     &mut source_xa,
                     &mut source_xe,
@@ -118,20 +122,31 @@ ksk_prepared.prepare(module, &ksk, scratch.borrow());
 
                 glwe_out.keyswitch(module, &glwe_in, &ksk_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_in as f64,
-                    k_in,
-                    k_ksk,
-                );
+                )
+                .sqrt()
+                .log2();
+
+                module.glwe_normalize(&mut pt_out, &pt_in, scratch.borrow());
 
-                glwe_out.assert_noise(module, &sk_out_prepared, &pt_want, max_noise + 0.5);
+                assert!(
+                    glwe_out
+                        .noise(module, &pt_out, &sk_out_prepared, scratch.borrow())
+                        .std()
+                        .log2()
+                        <= max_noise + 1.0
+                )
             }
         }
     }
@@ -149,30 +164,31 @@ + GLWENoise<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 12;
-    let k_out: usize = 45;
-    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 n: usize = module.n();
-            let dnum: usize = k_out.div_ceil(base2k * dsize);
-
+            let dnum: usize = k_out.div_ceil(base2k_key * dsize);
             let glwe_out_infos: GLWELayout = GLWELayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_out.into(),
                 k: k_out.into(),
                 rank: rank.into(),
             };
 
             let ksk_infos: GLWESwitchingKeyLayout = GLWESwitchingKeyLayout {
                 n: n.into(),
-                base2k: base2k.into(),
+                base2k: base2k_key.into(),
                 k: k_ksk.into(),
                 dnum: dnum.into(),
-                dsize: di.into(),
+                dsize: dsize.into(),
                 rank_in: rank.into(),
                 rank_out: rank.into(),
             };
@@ -185,7 +201,12 @@ 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(
+                pt_want.base2k().into(),
+                &mut pt_want.data,
+                0,
+                &mut source_xa,
+            );
 
             let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(
                 GLWESwitchingKey::encrypt_sk_tmp_bytes(module, &ksk_infos)
@@ -229,20 +250,29 @@ ksk_prepared.prepare(module, &ksk, scratch.borrow());
 
             glwe_out.keyswitch_inplace(module, &ksk_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();
 
-            glwe_out.assert_noise(module, &sk_out_prepared, &pt_want, max_noise + 0.5);
+            assert!(
+                glwe_out
+                    .noise(module, &pt_want, &sk_out_prepared, scratch.borrow())
+                    .std()
+                    .log2()
+                    <= max_noise + 1.0
+            )
         }
     }
 }

@@ -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]);
 }

@@ -5,8 +5,10 @@ pub mod keyswitch;
 
 mod conversion;
 mod glwe_packer;
+mod glwe_packing;
 mod trace;
 
 pub use conversion::*;
 pub use glwe_packer::*;
+pub use glwe_packing::*;
 pub use trace::*;

@@ -32,26 +32,27 @@ + VecZnxNormalizeInplace<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
-    let base2k: usize = 8;
+    let base2k_out: usize = 15;
+    let base2k_key: usize = 10;
     let k: usize = 54;
 
     for rank in 1_usize..3 {
         let n: usize = module.n();
-        let k_autokey: usize = k + base2k;
+        let k_autokey: usize = k + base2k_key;
 
         let dsize: usize = 1;
-        let dnum: usize = k.div_ceil(base2k * dsize);
+        let dnum: usize = k.div_ceil(base2k_key * dsize);
 
         let glwe_out_infos: GLWELayout = GLWELayout {
             n: n.into(),
-            base2k: base2k.into(),
+            base2k: base2k_out.into(),
             k: k.into(),
             rank: rank.into(),
         };
 
         let key_infos: GLWEAutomorphismKeyLayout = GLWEAutomorphismKeyLayout {
             n: n.into(),
-            base2k: base2k.into(),
+            base2k: base2k_key.into(),
             k: k_autokey.into(),
             rank: rank.into(),
             dsize: dsize.into(),
@@ -85,7 +86,7 @@ data_want
             .iter_mut()
             .for_each(|x| *x = source_xa.next_i64() & 0xFF);
 
-        module.vec_znx_fill_uniform(base2k, &mut pt_have.data, 0, &mut source_xa);
+        module.vec_znx_fill_uniform(base2k_out, &mut pt_have.data, 0, &mut source_xa);
 
         glwe_out.encrypt_sk(
             module,
@@ -121,13 +122,18 @@
         glwe_out.decrypt(module, &mut pt_have, &sk_dft, scratch.borrow());
 
         module.vec_znx_sub_inplace(&mut pt_want.data, 0, &pt_have.data, 0);
-        module.vec_znx_normalize_inplace(base2k, &mut pt_want.data, 0, scratch.borrow());
+        module.vec_znx_normalize_inplace(
+            pt_want.base2k().as_usize(),
+            &mut pt_want.data,
+            0,
+            scratch.borrow(),
+        );
 
         let noise_have: f64 = pt_want.stats().std().log2();
 
         let mut noise_want: f64 = var_noise_gglwe_product(
             n as f64,
-            base2k,
+            base2k_key * dsize,
             0.5,
             0.5,
             1.0 / 12.0,

@@ -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;

@@ -32,7 +32,7 @@ let mut max: Float = Float::with_val(prec, 0);
 
         data.iter().for_each(|x| {
             avg.add_assign_round(x, Round::Nearest);
-            max.max_mut(&Float::with_val(53, x.abs_ref()));
+            max.max_mut(&Float::with_val(prec, x.abs_ref()));
         });
         avg.div_assign_round(Float::with_val(prec, data.len()), Round::Nearest);
         data.iter_mut().for_each(|x| {

@@ -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(())
-    }
-}