@@ -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);

@@ -1,74 +1,91 @@
 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, ZnxInfos, 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();
-
-                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();
+        println!("col: {res_col} {}", pt_want.to_ref().cols());
+        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)
     }
 }

@@ -30,7 +30,8 @@ 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,
@@ -92,7 +93,8 @@ 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,

@@ -5,11 +5,11 @@ source::Source,
 };
 
 use crate::{
-    GLWEAutomorphismKeyAutomorphism, GLWEAutomorphismKeyEncryptSk, GLWEDecrypt, ScratchTakeCore,
+    GGLWENoise, GLWEAutomorphismKeyAutomorphism, GLWEAutomorphismKeyEncryptSk, ScratchTakeCore,
     encryption::SIGMA,
     layouts::{
-        GGLWEInfos, GLWEAutomorphismKey, GLWEAutomorphismKeyLayout, GLWEAutomorphismKeyPreparedFactory, GLWEPlaintext,
-        GLWESecret, GLWESecretPreparedFactory, LWEInfos,
+        GGLWEInfos, GLWEAutomorphismKey, GLWEAutomorphismKeyLayout, GLWEAutomorphismKeyPreparedFactory, GLWEInfos, GLWESecret,
+        GLWESecretPreparedFactory,
         prepared::{GLWEAutomorphismKeyPrepared, GLWESecretPrepared},
     },
     var_noise_gglwe_product_v2,
@@ -25,7 +25,7 @@ + VecZnxAutomorphism
         + GaloisElement
         + VecZnxSubScalarInplace
         + GLWESecretPreparedFactory<BE>
-        + GLWEDecrypt<BE>,
+        + GGLWENoise<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
@@ -132,8 +132,6 @@ &auto_key_apply_prepared,
                 scratch.borrow(),
             );
 
-            let mut pt_out: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&auto_key_out_infos);
-
             let mut sk_auto: GLWESecret<Vec<u8>> = GLWESecret::alloc_from_infos(&auto_key_out_infos);
             sk_auto.fill_zero(); // Necessary to avoid panic of unfilled sk
             for i in 0..rank {
@@ -149,40 +147,33 @@
             let mut sk_auto_dft: GLWESecretPrepared<Vec<u8>, BE> = GLWESecretPrepared::alloc_from_infos(module, &sk_auto);
             sk_auto_dft.prepare(module, &sk_auto);
 
-            for col_i in 0..auto_key_out.rank_in().into() {
-                for row_i in 0..auto_key_out.dnum().into() {
-                    auto_key_out
-                        .at(row_i, col_i)
-                        .decrypt(module, &mut pt_out, &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_out.data,
-                        0,
-                        (dsize_in - 1) + row_i * dsize_in,
-                        &sk.data,
-                        col_i,
-                    );
-
-                    let noise_have: f64 = pt_out.data.stats(pt_out.base2k().into(), 0).std().log2();
-                    let max_noise: f64 = var_noise_gglwe_product_v2(
-                        module.n() as f64,
-                        k_ksk,
-                        dnum_ksk,
-                        dsize,
-                        base2k_key,
-                        0.5,
-                        0.5,
-                        0f64,
-                        SIGMA * SIGMA,
-                        0f64,
-                        rank as f64,
-                    )
-                    .sqrt()
-                    .log2();
+            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 < max_noise + 0.5,
-                        "{noise_have} {}",
+                        "{noise_have} > {}",
                         max_noise + 0.5
                     );
                 }
@@ -201,7 +192,7 @@ + VecZnxAutomorphism
         + GaloisElement
         + VecZnxSubScalarInplace
         + GLWESecretPreparedFactory<BE>
-        + GLWEDecrypt<BE>,
+        + GGLWENoise<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchAvailable + ScratchTakeCore<BE>,
 {
@@ -284,8 +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
 
@@ -302,43 +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(pt.base2k().into(), 0).std().log2();
-                    let max_noise: f64 = var_noise_gglwe_product_v2(
-                        module.n() as f64,
-                        k_ksk,
-                        dnum_ksk,
-                        dsize,
-                        base2k_key,
-                        0.5,
-                        0.5,
-                        0f64,
-                        SIGMA * SIGMA,
-                        0f64,
-                        rank as f64,
-                    )
-                    .sqrt()
-                    .log2();
+            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 < max_noise + 0.5,
                         "{noise_have} {}",
                         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,
@@ -169,7 +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)
+                    )
+                }
+            }
         }
     }
 }
@@ -307,10 +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}",
+                    )
+                }
+            }
         }
     }
 }

@@ -135,7 +135,13 @@
             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_out, max_noise + 1.0);
+            assert!(
+                ct_out
+                    .noise(module, &pt_out, &sk_prepared, scratch.borrow())
+                    .std()
+                    .log2()
+                    <= max_noise + 1.0
+            )
         }
     }
 }
@@ -249,7 +255,12 @@ .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
+            )
         }
     }
 }

@@ -56,14 +56,14 @@ 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(GLWE::decrypt_tmp_bytes(module, &glwe_infos_out)),
+                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_in);
+            let pt_out: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&glwe_infos_out);
 
             ct_in.encrypt_sk(
                 module,
@@ -87,12 +87,13 @@ ct_out
                 .data()
                 .decode_vec_float(ct_out.base2k().into(), 0, &mut data_conv);
 
-            ct_out.assert_noise(
-                module,
-                &sk_prep,
-                &pt_out,
-                -(ct_out.k().as_u32() as f64) + SIGMA.log2() + 0.5,
-            );
+            assert!(
+                ct_out
+                    .noise(module, &pt_out, &sk_prep, scratch.borrow())
+                    .std()
+                    .log2()
+                    <= -(ct_out.k().as_u32() as f64) + SIGMA.log2() + 0.50
+            )
         }
     }
 }

@@ -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 +174,31 @@
             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;
+
+            println!("rank: {rank} dsize: {dsize} dnum: {dnum}");
+            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
+                    );
+                }
+            }
         }
     }
 }

@@ -9,8 +9,8 @@ GGLWEEncryptSk, GGLWEKeyswitch, GLWESwitchingKeyCompressedEncryptSk, GLWESwitchingKeyEncryptSk, ScratchTakeCore,
     decryption::GLWEDecrypt,
     encryption::SIGMA,
     layouts::{
-        GGLWELayout, GLWESecret, GLWESecretPreparedFactory, GLWESwitchingKey, GLWESwitchingKeyCompressed,
-        GLWESwitchingKeyDecompress,
+        GGLWEInfos, GGLWELayout, GLWESecret, GLWESecretPreparedFactory, GLWESwitchingKey, GLWESwitchingKeyCompressed,
+        GLWESwitchingKeyDecompress, LWEInfos,
         prepared::{GGLWEPreparedFactory, GLWESecretPrepared},
     },
     noise::GGLWENoise,
@@ -74,8 +74,30 @@ &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
+                        );
+                    }
+                }
             }
         }
     }
@@ -148,8 +170,30 @@
                 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
+                        );
+                    }
+                }
             }
         }
     }

@@ -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,
     },
 };
 
@@ -79,7 +80,17 @@ 0,
                 );
             }
 
-            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
+                    )
+                }
+            }
         }
     }
 }
@@ -134,9 +145,32 @@ key.decompress(module, &key_compressed);
 
         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>,
 {
@@ -110,14 +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);
@@ -142,24 +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>,
 {
@@ -176,14 +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);
@@ -200,9 +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);
     }
 }
 
@@ -211,7 +208,7 @@ where
     Module<BE>: GLWEEncryptPk<BE>
         + GLWEPublicKeyPreparedFactory<BE>
         + GLWEPublicKeyGenerate<BE>
-        + GLWEDecrypt<BE>
+        + GLWENoise<BE>
         + GLWESecretPreparedFactory<BE>
         + VecZnxFillUniform
         + GLWESub,
@@ -232,7 +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]);
@@ -240,8 +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);
@@ -266,17 +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 +9,9 @@ GGLWENoise, GLWETensorKeyCompressedEncryptSk, GLWETensorKeyEncryptSk, ScratchTakeCore,
     decryption::GLWEDecrypt,
     encryption::SIGMA,
     layouts::{
-        Dsize, GGLWEDecompress, GLWESecret, GLWESecretPreparedFactory, GLWESecretTensor, GLWESecretTensorFactory, GLWETensorKey,
-        GLWETensorKeyCompressed, GLWETensorKeyLayout, prepared::GLWESecretPrepared,
+        Dsize, GGLWEDecompress, GGLWEInfos, GLWEInfos, GLWESecret, GLWESecretPreparedFactory, GLWESecretTensor,
+        GLWESecretTensorFactory, GLWETensorKey, GLWETensorKeyCompressed, GLWETensorKeyLayout, LWEInfos,
+        prepared::GLWESecretPrepared,
     },
 };
 
@@ -67,7 +68,27 @@
         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().as_usize() + 1 {
+                assert!(
+                    tensor_key
+                        .0
+                        .noise(
+                            module,
+                            row,
+                            col,
+                            &sk_tensor.data,
+                            &sk_prepared,
+                            scratch.borrow()
+                        )
+                        .std()
+                        .log2()
+                        <= max_noise
+                )
+            }
+        }
     }
 }
 
@@ -124,6 +145,26 @@
         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().as_usize() + 1 {
+                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, GLWEInfos, GLWESecret, GLWESecretPreparedFactory, GLWESwitchingKey,
+        GLWESwitchingKeyLayout,
         prepared::{GGSWPrepared, GLWESecretPrepared},
     },
     noise::noise_ggsw_product,
@@ -159,9 +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
+                        )
+                    }
+                }
             }
         }
     }
@@ -300,9 +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,
@@ -146,7 +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)
+                    )
+                }
+            }
         }
     }
 }
@@ -271,7 +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)
+                    )
+                }
+            }
         }
     }
 }

@@ -145,7 +145,13 @@ k_in,
                 k_ggsw,
             );
 
-            glwe_out.assert_noise(module, &sk_prepared, &pt_out, max_noise + 0.5);
+            assert!(
+                glwe_out
+                    .noise(module, &pt_out, &sk_prepared, scratch.borrow())
+                    .std()
+                    .log2()
+                    <= max_noise + 1.0
+            )
         }
     }
 }
@@ -268,7 +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)
+    );
+}

@@ -8,7 +8,8 @@ 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,
@@ -154,9 +155,25 @@ )
                     .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
+                            )
+                        }
+                    }
                 }
             }
         }
@@ -284,9 +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},
     },
@@ -180,7 +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)
+                    )
+                }
+            }
         }
     }
 }
@@ -330,7 +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)
+                    )
+                }
+            }
         }
     }
 }

@@ -140,7 +140,13 @@ .log2();
 
                 module.glwe_normalize(&mut pt_out, &pt_in, scratch.borrow());
 
-                glwe_out.assert_noise(module, &sk_out_prepared, &pt_out, max_noise + 0.5);
+                assert!(
+                    glwe_out
+                        .noise(module, &pt_out, &sk_out_prepared, scratch.borrow())
+                        .std()
+                        .log2()
+                        <= max_noise + 1.0
+                )
             }
         }
     }
@@ -260,7 +266,13 @@ )
             .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
+            )
         }
     }
 }

@@ -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,

@@ -1,8 +1,8 @@
 use poulpy_core::{
     GLWENormalize,
     layouts::{
-        GGLWEToGGSWKeyLayout, GGSW, GGSWLayout, GLWE, GLWEAutomorphismKeyLayout, GLWELayout, GLWEPlaintext, GLWESecret, LWE,
-        LWELayout, LWEPlaintext, LWESecret,
+        GGLWEToGGSWKeyLayout, GGSW, GGSWInfos, GGSWLayout, GLWE, GLWEAutomorphismKeyLayout, GLWEInfos, GLWELayout, GLWEPlaintext,
+        GLWESecret, LWE, LWELayout, LWEPlaintext, LWESecret,
         prepared::{GGSWPrepared, GLWESecretPrepared},
     },
 };
@@ -212,7 +212,23 @@ let mut pt_ggsw: ScalarZnx<Vec<u8>> = ScalarZnx::alloc(n_glwe, 1);
     pt_ggsw.at_mut(0, 0)[0] = data;
 
     // Prints noise of GGSW(data)
-    res.print_noise(&module, &sk_glwe_prepared, &pt_ggsw);
+    for row in 0..res.dnum().as_usize() {
+        for col in 0..res.rank().as_usize() + 1 {
+            println!(
+                "row:{row} col:{col} -> {}",
+                res.noise(
+                    &module,
+                    row,
+                    col,
+                    &pt_ggsw,
+                    &sk_glwe_prepared,
+                    scratch.borrow()
+                )
+                .std()
+                .log2()
+            )
+        }
+    }
 
     // Tests RLWE(1) * GGSW(data)
 

@@ -146,7 +146,7 @@ for i in 0..T::BITS as usize {
             data_bits[T::bit_index(i) << log_gap] = want.bit(i) as i64
         }
         pt.encode_vec_i64(&data_bits, TorusPrecision(2));
-        self.bits.noise(module, sk, &pt, scratch_1)
+        self.bits.noise(module, &pt, sk, scratch_1)
     }
 
     pub fn decrypt<S, M, BE: Backend>(&self, module: &M, sk: &S, scratch: &mut Scratch<BE>) -> T

@@ -13,8 +13,8 @@ LWEFromGLWE, ScratchTakeCore,
     layouts::{GGSWInfos, GGSWPreparedFactory, GLWEInfos, LWEInfos},
 };
 
-use poulpy_hal::api::ModuleN;
-use poulpy_hal::layouts::{Backend, Data, DataMut, DataRef, Module, Scratch};
+use poulpy_hal::api::{ModuleN, ScratchTakeBasic};
+use poulpy_hal::layouts::{Backend, Data, DataMut, DataRef, Module, Scratch, Stats};
 
 pub struct FheUintPreparedDebug<D: Data, T: UnsignedInteger> {
     pub(crate) bits: Vec<GGSW<D>>,
@@ -81,31 +81,28 @@ }
 }
 
 impl<D: DataRef, T: UnsignedInteger + ToBits> FheUintPreparedDebug<D, T> {
-    pub fn print_noise<S, M, BE: Backend>(&self, module: &M, sk: &S, want: T)
+    pub fn noise<S, M, BE: Backend>(
+        &self,
+        module: &M,
+        row: usize,
+        col: usize,
+        want: T,
+        sk: &S,
+        scratch: &mut Scratch<BE>,
+    ) -> Vec<Stats>
     where
         S: GLWESecretPreparedToRef<BE>,
         M: GGSWNoise<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
+        let mut stats = Vec::new();
         for (i, ggsw) in self.bits.iter().enumerate() {
-            use poulpy_hal::layouts::{ScalarZnx, ZnxViewMut};
-            let mut pt_want = ScalarZnx::alloc(self.n().into(), 1);
+            use poulpy_hal::layouts::ZnxViewMut;
+            let (mut pt_want, scratch_1) = scratch.take_scalar_znx(self.n().into(), 1);
             pt_want.at_mut(0, 0)[0] = want.bit(i) as i64;
-            ggsw.print_noise(module, sk, &pt_want);
+            stats.push(ggsw.noise(module, row, col, &pt_want, sk, scratch_1));
         }
-    }
-
-    pub fn assert_noise<S, M, F, BE: Backend>(&self, module: &M, sk: &S, want: T, max_noise: &F)
-    where
-        S: GLWESecretPreparedToRef<BE>,
-        M: GGSWNoise<BE>,
-        F: Fn(usize) -> f64,
-    {
-        for (i, ggsw) in self.bits.iter().enumerate() {
-            use poulpy_hal::layouts::{ScalarZnx, ZnxViewMut};
-            let mut pt_want = ScalarZnx::alloc(self.n().into(), 1);
-            pt_want.at_mut(0, 0)[0] = want.bit(i) as i64;
-            ggsw.assert_noise(module, sk, &pt_want, max_noise);
-        }
+        stats
     }
 }
 

@@ -1,8 +1,8 @@
 use poulpy_core::{
     GGSWEncryptSk, GGSWNoise, GLWEDecrypt, GLWEEncryptSk, SIGMA, ScratchTakeCore,
     layouts::{
-        Base2K, Dnum, Dsize, GGSW, GGSWLayout, GGSWPreparedFactory, GLWESecretPrepared, GLWESecretPreparedFactory, LWEInfos,
-        Rank, TorusPrecision,
+        Base2K, Dnum, Dsize, GGSW, GGSWInfos, GGSWLayout, GGSWPreparedFactory, GLWEInfos, GLWESecretPrepared,
+        GLWESecretPreparedFactory, LWEInfos, Rank, TorusPrecision,
     },
 };
 use poulpy_hal::{
@@ -131,9 +131,23 @@ scalar_want.raw_mut().copy_from_slice(scalar.raw());
 
             module.vec_znx_rotate_inplace(-rot, &mut scalar_want.as_vec_znx_mut(), 0, scratch.borrow());
 
-            // res.print_noise(&module, &sk_glwe_prep, &scalar_want);
-
-            res.assert_noise(module, sk_glwe_prep, &scalar_want, &max_noise);
+            for row in 0..res.dnum().as_usize() {
+                for col in 0..res.rank().as_usize() + 1 {
+                    assert!(
+                        res.noise(
+                            module,
+                            row,
+                            col,
+                            &scalar_want,
+                            sk_glwe_prep,
+                            scratch.borrow()
+                        )
+                        .std()
+                        .log2()
+                            <= max_noise(col)
+                    )
+                }
+            }
 
             bit_step += digit;
             bit_start += digit;

@@ -1,10 +1,10 @@
 use poulpy_core::{
     GGSWNoise, GLWEDecrypt, GLWEEncryptSk, GLWENoise, SIGMA, ScratchTakeCore,
-    layouts::{GGSWLayout, GLWELayout, GLWESecretPreparedFactory, LWEInfos, prepared::GLWESecretPrepared},
+    layouts::{GGSWInfos, GGSWLayout, GLWEInfos, GLWELayout, GLWESecretPreparedFactory, LWEInfos, prepared::GLWESecretPrepared},
 };
 use poulpy_hal::{
     api::{ModuleNew, ScratchOwnedAlloc, ScratchOwnedBorrow},
-    layouts::{Backend, Module, Scratch, ScratchOwned},
+    layouts::{Backend, Module, Scratch, ScratchOwned, Stats},
     source::Source,
 };
 use rand::RngCore;
@@ -81,7 +81,12 @@ }
         noise
     };
 
-    // c_enc_prep_debug.print_noise(module, sk_glwe_prep, value);
-
-    c_enc_prep_debug.assert_noise(module, sk_glwe_prep, value, &max_noise);
+    for row in 0..c_enc_prep_debug.dnum().as_usize() {
+        for col in 0..c_enc_prep_debug.rank().as_usize() + 1 {
+            let stats: Vec<Stats> = c_enc_prep_debug.noise(module, row, col, value, sk_glwe_prep, scratch.borrow());
+            for stat in &stats {
+                assert!(stat.std().log2() <= max_noise(col))
+            }
+        }
+    }
 }

@@ -2,14 +2,14 @@ use std::collections::HashMap;
 
 use poulpy_hal::{
     api::{ModuleLogN, ModuleN, ScratchAvailable, ScratchOwnedAlloc, ScratchOwnedBorrow},
-    layouts::{Backend, DataRef, Module, Scratch, ScratchOwned, ToOwnedDeep},
+    layouts::{Backend, DataRef, Module, Scratch, ScratchOwned},
 };
 
 use poulpy_core::{
-    GGSWFromGGLWE, GLWEDecrypt, GLWEPacking, GLWERotate, GLWETrace, ScratchTakeCore,
+    GGSWExpandRows, GGSWFromGGLWE, GLWECopy, GLWEDecrypt, GLWENormalize, GLWEPacking, GLWERotate, GLWETrace, ScratchTakeCore,
     layouts::{
         Dsize, GGLWE, GGLWEInfos, GGLWELayout, GGLWEPreparedToRef, GGSWInfos, GGSWToMut, GLWEAutomorphismKeyHelper, GLWEInfos,
-        GLWESecretPreparedFactory, GLWEToMut, GLWEToRef, GetGaloisElement, LWEInfos, LWEToRef, Rank,
+        GLWELayout, GLWESecretPreparedFactory, GLWEToMut, GLWEToRef, GetGaloisElement, LWEInfos, LWEToRef, Rank,
     },
 };
 
@@ -114,10 +114,12 @@ + LookupTableFactory
         + BlindRotationExecute<BRA, BE>
         + GLWETrace<BE>
         + GLWEPacking<BE>
-        + GGSWFromGGLWE<BE>
         + GLWESecretPreparedFactory<BE>
         + GLWEDecrypt<BE>
-        + GLWERotate<BE>,
+        + GLWERotate<BE>
+        + GLWENormalize<BE>
+        + GLWECopy
+        + GGSWExpandRows<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
@@ -240,7 +242,10 @@ + GGSWFromGGLWE<BE>
         + GLWESecretPreparedFactory<BE>
         + GLWEDecrypt<BE>
         + GLWERotate<BE>
-        + ModuleLogN,
+        + ModuleLogN
+        + GLWENormalize<BE>
+        + GLWECopy
+        + GGSWExpandRows<BE>,
     ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
@@ -248,27 +253,22 @@ let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
     let lwe: &LWE<&[u8]> = &lwe.to_ref();
 
     assert_eq!(res.n(), key.brk.n());
-    assert_eq!(lwe.base2k(), key.brk.base2k());
-    assert_eq!(res.base2k(), key.brk.base2k());
 
-    let n: usize = res.n().into();
-    let base2k: usize = res.base2k().into();
-    let dnum: usize = res.dnum().into();
-    let rank: usize = res.rank().into();
-    let k: usize = res.k().into();
+    let base2k_res: usize = res.base2k().as_usize();
+    let dnum_res: usize = res.dnum().into();
 
-    let alpha: usize = dnum.next_power_of_two();
+    let alpha: usize = dnum_res.next_power_of_two();
 
     let mut f: Vec<i64> = vec![0i64; (1 << log_domain) * alpha];
 
     if to_exponent {
-        (0..dnum).for_each(|i| {
-            f[i] = 1 << (base2k * (dnum - 1 - i));
+        (0..dnum_res).for_each(|i| {
+            f[i] = 1 << (base2k_res * (dnum_res - 1 - i));
         });
     } else {
         (0..1 << log_domain).for_each(|j| {
-            (0..dnum).for_each(|i| {
-                f[j * alpha + i] = j as i64 * (1 << (base2k * (dnum - 1 - i)));
+            (0..dnum_res).for_each(|i| {
+                f[j * alpha + i] = j as i64 * (1 << (base2k_res * (dnum_res - 1 - i)));
             });
         });
     }
@@ -276,65 +276,79 @@
     let lut_infos: LookUpTableLayout = LookUpTableLayout {
         n: module.n().into(),
         extension_factor,
-        k: (base2k * dnum).into(),
-        base2k: base2k.into(),
+        k: (base2k_res * dnum_res).into(),
+        base2k: key.brk.base2k(),
     };
 
     // Lut precision, basically must be able to hold the decomposition power basis of the GGSW
     let mut lut: LookupTable = LookupTable::alloc(&lut_infos);
-    lut.set(module, &f, base2k * dnum);
+    lut.set(module, &f, base2k_res * dnum_res);
 
     if to_exponent {
         lut.set_rotation_direction(LookUpTableRotationDirection::Right);
     }
 
-    // TODO: separate GGSW k from output of blind rotation k
-    let (mut res_glwe, scratch_1) = scratch.take_glwe(res);
+    let glwe_brk_layout = &GLWELayout {
+        n: key.brk.n(),
+        base2k: key.brk.base2k(),
+        k: key.brk.k(),
+        rank: key.brk.rank(),
+    };
 
-    let gglwe_infos: GGLWELayout = GGLWELayout {
-        n: n.into(),
-        base2k: base2k.into(),
-        k: k.into(),
-        dnum: dnum.into(),
-        dsize: Dsize(1),
-        rank_in: rank.max(1).into(),
-        rank_out: rank.into(),
+    let atk_layout: &GGLWELayout = &key.atk.automorphism_key_infos();
+
+    let glwe_atk_layout: &GLWELayout = &GLWELayout {
+        n: glwe_brk_layout.n(),
+        base2k: atk_layout.base2k(),
+        k: glwe_brk_layout.k(),
+        rank: glwe_brk_layout.rank(),
     };
 
-    let (mut tmp_gglwe, scratch_2) = scratch_1.take_gglwe(&gglwe_infos);
+    let (mut res_glwe_atk_layout, scratch_1) = scratch.take_glwe(glwe_atk_layout);
+
+    // Execute blind rotation over BRK layout and returns result over ATK layout
+    {
+        let (mut res_glwe_brk_layout, scratch_2) = scratch_1.take_glwe(glwe_brk_layout);
+        key.brk
+            .execute(module, &mut res_glwe_brk_layout, lwe, &lut, scratch_2);
 
-    key.brk.execute(module, &mut res_glwe, lwe, &lut, scratch_2);
+        if res_glwe_brk_layout.base2k() == res_glwe_atk_layout.base2k() {
+            module.glwe_copy(&mut res_glwe_atk_layout, &res_glwe_brk_layout);
+        } else {
+            module.glwe_normalize(&mut res_glwe_atk_layout, &res_glwe_brk_layout, scratch_2);
+        }
+    }
 
     let gap: usize = 2 * lut.drift / lut.extension_factor();
 
     let log_gap_in: usize = (usize::BITS - (gap * alpha - 1).leading_zeros()) as _;
 
-    (0..dnum).for_each(|i| {
-        let mut tmp_glwe: GLWE<&mut [u8]> = tmp_gglwe.at_mut(i, 0);
+    for i in 0..dnum_res {
+        let mut res_row: GLWE<&mut [u8]> = res.at_mut(i, 0);
 
         if to_exponent {
             // Isolates i-th LUT and moves coefficients according to requested gap.
             post_process(
                 module,
-                &mut tmp_glwe,
-                &res_glwe,
+                &mut res_row,
+                &res_glwe_atk_layout,
                 log_gap_in,
                 log_gap_out,
                 log_domain,
                 &key.atk,
-                scratch_2,
+                scratch_1,
             );
         } else {
-            tmp_glwe.trace(module, 0, &res_glwe, &key.atk, scratch_2);
+            module.glwe_trace(&mut res_row, 0, &res_glwe_atk_layout, &key.atk, scratch_1);
         }
 
-        if i < dnum {
-            module.glwe_rotate_inplace(-(gap as i64), &mut res_glwe, scratch_2);
+        if i < dnum_res {
+            module.glwe_rotate_inplace(-(gap as i64), &mut res_glwe_atk_layout, scratch_1);
         }
-    });
+    }
 
     // Expands GGLWE to GGSW using GGLWE(s^2)
-    res.from_gglwe(module, &tmp_gglwe, &key.tsk, scratch_2);
+    module.ggsw_expand_row(res, &key.tsk, scratch);
 }
 
 #[allow(clippy::too_many_arguments)]
@@ -348,47 +362,48 @@ log_domain: usize,
     auto_keys: &H,
     scratch: &mut Scratch<BE>,
 ) where
-    R: GLWEToMut,
-    A: GLWEToRef,
+    R: GLWEToMut + GLWEInfos,
+    A: GLWEToRef + GLWEInfos,
     H: GLWEAutomorphismKeyHelper<K, BE>,
     K: GGLWEPreparedToRef<BE> + GetGaloisElement + GGLWEInfos,
-    M: ModuleLogN + GLWETrace<BE> + GLWEPacking<BE> + GLWERotate<BE>,
+    M: ModuleLogN + GLWETrace<BE> + GLWEPacking<BE> + GLWERotate<BE> + GLWECopy,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
-    let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
-    let a: &GLWE<&[u8]> = &a.to_ref();
-
-    let mut cts: HashMap<usize, &mut GLWE<Vec<u8>>> = HashMap::new();
-
-    // First partial trace, vanishes all coefficients which are not multiples of gap_in
-    // [1, 1, 1, 1, 0, 0, 0, ..., 0, 0, -1, -1, -1, -1] -> [1, 0, 0, 0, 0, 0, 0, ..., 0, 0, 0, 0, 0, 0]
-    res.trace(
-        module,
-        module.log_n() - log_gap_in + 1,
-        a,
-        auto_keys,
-        scratch,
-    );
-
     // TODO: optimize with packing and final partial trace
     // If gap_out < gap_in, then we need to repack, i.e. reduce the cap between coefficients.
     if log_gap_in != log_gap_out {
+        let (mut a_trace, scratch_1) = scratch.take_glwe(a);
+
+        // First partial trace, vanishes all coefficients which are not multiples of gap_in
+        // [1, 1, 1, 1, 0, 0, 0, ..., 0, 0, -1, -1, -1, -1] -> [1, 0, 0, 0, 0, 0, 0, ..., 0, 0, 0, 0, 0, 0]
+        module.glwe_trace(
+            &mut a_trace,
+            module.log_n() - log_gap_in + 1,
+            a,
+            auto_keys,
+            scratch_1,
+        );
+
         let steps: usize = 1 << log_domain;
 
         // TODO: from Scratch
-        let mut cts_vec: Vec<GLWE<Vec<u8>>> = Vec::new();
+        let (mut cts_vec, scratch_2) = scratch_1.take_glwe_slice(steps, a);
 
         for i in 0..steps {
             if i != 0 {
-                module.glwe_rotate_inplace(-(1 << log_gap_in), res, scratch);
+                module.glwe_rotate_inplace(-(1 << log_gap_in), &mut a_trace, scratch_2);
             }
-            cts_vec.push(res.to_owned_deep());
+
+            module.glwe_copy(&mut cts_vec[i], &a_trace);
         }
 
+        let mut cts: HashMap<usize, &mut GLWE<&mut [u8]>> = HashMap::new();
         for (i, ct) in cts_vec.iter_mut().enumerate().take(steps) {
             cts.insert(i * (1 << log_gap_out), ct);
         }
 
-        module.glwe_pack(res, cts, log_gap_out, auto_keys, scratch);
+        module.glwe_pack(res, cts, log_gap_out, auto_keys, scratch_2);
+    } else {
+        module.glwe_trace(res, module.log_n() - log_gap_in + 1, a, auto_keys, scratch);
     }
 }

@@ -17,8 +17,8 @@
 use poulpy_core::{
     GGSWNoise, GLWEDecrypt, GLWEEncryptSk, GLWEExternalProduct, LWEEncryptSk, ScratchTakeCore,
     layouts::{
-        Dsize, GGLWEToGGSWKeyLayout, GGSWLayout, GGSWPreparedFactory, GLWEAutomorphismKeyLayout, GLWESecretPreparedFactory,
-        LWELayout,
+        Dsize, GGLWEToGGSWKeyLayout, GGSWInfos, GGSWLayout, GGSWPreparedFactory, GLWEAutomorphismKeyLayout, GLWEInfos,
+        GLWESecretPreparedFactory, LWELayout,
     },
 };
 
@@ -186,8 +186,23 @@ 0,
         scratch.borrow(),
     );
 
-    res.print_noise(module, &sk_glwe_prepared, &pt_ggsw);
-
+    for row in 0..res.dnum().as_usize() {
+        for col in 0..res.rank().as_usize() + 1 {
+            println!(
+                "row:{row} col:{col} -> {}",
+                res.noise(
+                    module,
+                    row,
+                    col,
+                    &pt_ggsw,
+                    &sk_glwe_prepared,
+                    scratch.borrow()
+                )
+                .std()
+                .log2()
+            )
+        }
+    }
     let mut ct_glwe: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&ggsw_infos);
     let mut pt_glwe: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&ggsw_infos);
     pt_glwe.data.at_mut(0, 0)[0] = 1 << (base2k - 2);
@@ -234,7 +249,10 @@ ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
     let n_glwe: usize = module.n();
-    let base2k: usize = 14;
+    let base2k_res: usize = 14;
+    let base2k_brk: usize = 13;
+    let base2k_tsk: usize = 12;
+    let base2k_atk: usize = 11;
     let extension_factor: usize = 1;
     let rank: usize = 1;
 
@@ -243,36 +261,36 @@ let k_lwe_pt: usize = 1;
     let k_lwe_ct: usize = 13;
     let block_size: usize = 7;
 
-    let k_brk: usize = 5 * base2k;
+    let k_ggsw_res: usize = 4 * base2k_res;
+    let rows_ggsw_res: usize = 3;
+
+    let k_brk: usize = k_ggsw_res + base2k_brk;
     let rows_brk: usize = 3;
 
-    let k_atk: usize = 5 * base2k;
+    let k_atk: usize = k_ggsw_res + base2k_tsk;
     let rows_atk: usize = 4;
 
-    let k_tsk: usize = 5 * base2k;
+    let k_tsk: usize = k_ggsw_res + base2k_atk;
     let rows_tsk: usize = 4;
 
-    let k_ggsw_res: usize = 4 * base2k;
-    let rows_ggsw_res: usize = 3;
-
     let lwe_infos: LWELayout = LWELayout {
         n: n_lwe.into(),
         k: k_lwe_ct.into(),
-        base2k: base2k.into(),
+        base2k: base2k_brk.into(),
     };
 
     let cbt_infos: CircuitBootstrappingKeyLayout = CircuitBootstrappingKeyLayout {
         layout_brk: BlindRotationKeyLayout {
             n_glwe: n_glwe.into(),
             n_lwe: n_lwe.into(),
-            base2k: base2k.into(),
+            base2k: base2k_brk.into(),
             k: k_brk.into(),
             dnum: rows_brk.into(),
             rank: rank.into(),
         },
         layout_atk: GLWEAutomorphismKeyLayout {
             n: n_glwe.into(),
-            base2k: base2k.into(),
+            base2k: base2k_atk.into(),
             k: k_atk.into(),
             dnum: rows_atk.into(),
             rank: rank.into(),
@@ -280,7 +298,7 @@ dsize: Dsize(1),
         },
         layout_tsk: GGLWEToGGSWKeyLayout {
             n: n_glwe.into(),
-            base2k: base2k.into(),
+            base2k: base2k_tsk.into(),
             k: k_tsk.into(),
             dnum: rows_tsk.into(),
             dsize: Dsize(1),
@@ -290,7 +308,7 @@ };
 
     let ggsw_infos: GGSWLayout = GGSWLayout {
         n: n_glwe.into(),
-        base2k: base2k.into(),
+        base2k: base2k_res.into(),
         k: k_ggsw_res.into(),
         dnum: rows_ggsw_res.into(),
         dsize: Dsize(1),
@@ -314,7 +332,7 @@ sk_glwe_prepared.prepare(module, &sk_glwe);
 
     let data: i64 = 1;
 
-    let mut pt_lwe: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc(base2k.into(), k_lwe_pt.into());
+    let mut pt_lwe: LWEPlaintext<Vec<u8>> = LWEPlaintext::alloc(base2k_res.into(), k_lwe_pt.into());
     pt_lwe.encode_i64(data, (k_lwe_pt + 1).into());
 
     println!("pt_lwe: {pt_lwe}");
@@ -365,11 +383,27 @@ // X^{data * 2^log_gap_out}
     let mut pt_ggsw: ScalarZnx<Vec<u8>> = ScalarZnx::alloc(n_glwe, 1);
     pt_ggsw.at_mut(0, 0)[0] = data;
 
-    res.print_noise(module, &sk_glwe_prepared, &pt_ggsw);
+    for row in 0..res.dnum().as_usize() {
+        for col in 0..res.rank().as_usize() + 1 {
+            println!(
+                "row:{row} col:{col} -> {}",
+                res.noise(
+                    module,
+                    row,
+                    col,
+                    &pt_ggsw,
+                    &sk_glwe_prepared,
+                    scratch.borrow()
+                )
+                .std()
+                .log2()
+            )
+        }
+    }
 
     let mut ct_glwe: GLWE<Vec<u8>> = GLWE::alloc_from_infos(&ggsw_infos);
     let mut pt_glwe: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc_from_infos(&ggsw_infos);
-    pt_glwe.data.at_mut(0, 0)[0] = 1 << (base2k - k_lwe_pt - 1);
+    pt_glwe.data.at_mut(0, 0)[0] = 1 << (base2k_res - k_lwe_pt - 1);
 
     ct_glwe.encrypt_sk(
         module,
@@ -391,5 +425,6 @@
     // Parameters are set such that the first limb should be noiseless.
     let mut pt_want: Vec<i64> = vec![0i64; module.n()];
     pt_want[0] = pt_glwe.data.at(0, 0)[0] * data;
+    println!("pt_res: {pt_res}");
     assert_eq!(pt_res.data.at(0, 0), pt_want);
 }