diff --git a/poulpy-core/src/automorphism/mod.rs b/poulpy-core/src/automorphism/mod.rs
index 1cd7bea..fd10f33 100644
--- a/poulpy-core/src/automorphism/mod.rs
+++ b/poulpy-core/src/automorphism/mod.rs
@@ -4,4 +4,4 @@ mod glwe_ct;
 
 pub use gglwe_atk::*;
 pub use ggsw_ct::*;
-pub use glwe_ct::*;
\ No newline at end of file
+pub use glwe_ct::*;
diff --git a/poulpy-core/src/conversion/gglwe_to_ggsw.rs b/poulpy-core/src/conversion/gglwe_to_ggsw.rs
index a7b86fa..24d02bd 100644
--- a/poulpy-core/src/conversion/gglwe_to_ggsw.rs
+++ b/poulpy-core/src/conversion/gglwe_to_ggsw.rs
@@ -1,19 +1,18 @@
 use poulpy_hal::{
     api::{
-        ModuleN, ScratchAvailable, ScratchTakeBasic, VecZnxBigBytesOf, VecZnxBigNormalize, VecZnxCopy, VecZnxDftAddInplace,
-        VecZnxDftApply, VecZnxDftBytesOf, VecZnxDftCopy, VecZnxIdftApplyTmpA, VecZnxNormalize, VecZnxNormalizeTmpBytes,
-        VmpApplyDftToDft, VmpApplyDftToDftAdd, VmpApplyDftToDftTmpBytes,
+        ModuleN, ScratchAvailable, ScratchTakeBasic, VecZnxBigBytesOf, VecZnxBigNormalize, VecZnxDftAddInplace, VecZnxDftApply,
+        VecZnxDftBytesOf, VecZnxDftCopy, VecZnxIdftApplyTmpA, VecZnxNormalize, VecZnxNormalizeTmpBytes, VmpApplyDftToDft,
+        VmpApplyDftToDftAdd, VmpApplyDftToDftTmpBytes,
     },
     layouts::{Backend, DataMut, Module, Scratch, VmpPMat, ZnxInfos},
 };
 
 use crate::{
-    ScratchTakeCore,
+    GLWECopy, ScratchTakeCore,
     layouts::{
         GGLWE, GGLWEInfos, GGLWEToRef, GGSW, GGSWInfos, GGSWToMut, GLWEInfos, LWEInfos,
         prepared::{TensorKeyPrepared, TensorKeyPreparedToRef},
     },
-    operations::GLWEOperations,
 };
 
 impl GGLWE<Vec<u8>> {
@@ -39,11 +38,11 @@ impl<D: DataMut> GGSW<D> {
     }
 }
 
-impl<BE: Backend> GGSWFromGGLWE<BE> for Module<BE> where Self: GGSWExpandRows<BE> + VecZnxCopy {}
+impl<BE: Backend> GGSWFromGGLWE<BE> for Module<BE> where Self: GGSWExpandRows<BE> + GLWECopy {}
 
 pub trait GGSWFromGGLWE<BE: Backend>
 where
-    Self: GGSWExpandRows<BE> + VecZnxCopy,
+    Self: GGSWExpandRows<BE> + GLWECopy,
 {
     fn ggsw_from_gglwe_tmp_bytes<R, A>(&self, res_infos: &R, tsk_infos: &A) -> usize
     where
@@ -71,7 +70,7 @@ where
         assert_eq!(tsk.n(), self.n() as u32);
 
         for row in 0..res.dnum().into() {
-            res.at_mut(row, 0).copy(self, &a.at(row, 0));
+            self.glwe_copy(&mut res.at_mut(row, 0), &a.at(row, 0));
         }
 
         self.ggsw_expand_row(res, tsk, scratch);
diff --git a/poulpy-core/src/glwe_packing.rs b/poulpy-core/src/glwe_packing.rs
index 129de7e..6fbdb1d 100644
--- a/poulpy-core/src/glwe_packing.rs
+++ b/poulpy-core/src/glwe_packing.rs
@@ -1,14 +1,13 @@
 use std::collections::HashMap;
 
 use poulpy_hal::{
-    api::{
-        ModuleLogN, ModuleN, ScratchAvailable, VecZnxAddInplace, VecZnxAutomorphismInplace, VecZnxBigAddSmallInplace, VecZnxBigAutomorphismInplace, VecZnxBigNormalize, VecZnxBigNormalizeTmpBytes, VecZnxBigSubSmallNegateInplace, VecZnxCopy, VecZnxDftApply, VecZnxDftBytesOf, VecZnxDftCopy, VecZnxIdftApplyConsume, VecZnxIdftApplyTmpA, VecZnxNegateInplace, VecZnxNormalize, VecZnxNormalizeInplace, VecZnxNormalizeTmpBytes, VecZnxRotate, VecZnxRotateInplace, VecZnxRshInplace, VecZnxSub, VecZnxSubInplace, VecZnxSwitchRing, VmpApplyDftToDft, VmpApplyDftToDftAdd, VmpApplyDftToDftTmpBytes
-    },
+    api::{ModuleLogN, VecZnxCopy, VecZnxRotateInplace},
     layouts::{Backend, DataMut, DataRef, GaloisElement, Module, Scratch},
 };
 
 use crate::{
-    layouts::{prepared::{AutomorphismKeyPrepared, AutomorphismKeyPreparedToRef}, GGLWEInfos, GLWEAlloc, GLWEInfos, GLWEToRef, LWEInfos, GLWE}, GLWEAutomorphism, GLWEOperations, ScratchTakeCore
+    GLWEAutomorphism, ScratchTakeCore,
+    layouts::{GGLWEInfos, GLWE, GLWEAlloc, GLWEInfos, GLWEToMut, GLWEToRef, LWEInfos, prepared::AutomorphismKeyPreparedToRef},
 };
 
 /// [GLWEPacker] enables only the fly GLWE packing
@@ -41,7 +40,7 @@ impl Accumulator {
     pub fn alloc<A, M>(module: &M, infos: &A) -> Self
     where
         A: GLWEInfos,
-        M: GLWEAlloc
+        M: GLWEAlloc,
     {
         Self {
             data: GLWE::alloc_from_infos(module, infos),
@@ -65,7 +64,7 @@ impl GLWEPacker {
     pub fn new<A, M>(module: &M, infos: &A, log_batch: usize) -> Self
     where
         A: GLWEInfos,
-        M: GLWEAlloc
+        M: GLWEAlloc,
     {
         let mut accumulators: Vec<Accumulator> = Vec::<Accumulator>::new();
         let log_n: usize = infos.n().log2();
@@ -109,13 +108,8 @@ impl GLWEPacker {
     /// * `a`: ciphertext to pack. Can optionally give None to pack a 0 ciphertext.
     /// * `auto_keys`: a [HashMap] containing the [AutomorphismKeyExec]s.
     /// * `scratch`: scratch space of size at least [Self::tmp_bytes].
-    pub fn add<A, K, M, BE: Backend>(
-        &mut self,
-        module: &M,
-        a: Option<&A>,
-        auto_keys: &HashMap<i64, K>,
-        scratch: &mut Scratch<B>,
-    ) where
+    pub fn add<A, K, M, BE: Backend>(&mut self, module: &M, a: Option<&A>, auto_keys: &HashMap<i64, K>, scratch: &mut Scratch<B>)
+    where
         A: GLWEToRef,
         K: AutomorphismKeyPreparedToRef<BE>,
         M: GLWEAutomorphism<BE>,
@@ -327,110 +321,69 @@ fn combine<B, M, K, BE: Backend>(
     }
 }
 
-/// Packs [x_0: GLWE(m_0), x_1: GLWE(m_1), ..., x_i: GLWE(m_i)]
-/// to [0: GLWE(m_0 * X^x_0 + m_1 * X^x_1 + ... + m_i * X^x_i)]
-pub fn glwe_packing<D: DataMut, ATK, B: Backend>(
-    module: &Module<B>,
-    cts: &mut HashMap<usize, &mut GLWE<D>>,
-    log_gap_out: usize,
-    auto_keys: &HashMap<i64, AutomorphismKeyPrepared<ATK, B>>,
-    scratch: &mut Scratch<B>,
-) where
-    ATK: DataRef,
-    Module<B>: VecZnxRotateInplace<B>
-        + VecZnxNormalizeInplace<B>
-        + VecZnxNormalizeTmpBytes
-        + VecZnxSwitchRing
-        + VecZnxBigAutomorphismInplace<B>
-        + VecZnxRshInplace<B>
-        + VecZnxDftCopy<B>
-        + VecZnxIdftApplyTmpA<B>
-        + VecZnxSub
-        + VecZnxAddInplace
-        + VecZnxNegateInplace
-        + VecZnxCopy
-        + VecZnxSubInplace
-        + VecZnxDftBytesOf
-        + VmpApplyDftToDftTmpBytes
-        + VecZnxBigNormalizeTmpBytes
-        + VmpApplyDftToDft<B>
-        + VmpApplyDftToDftAdd<B>
-        + VecZnxDftApply<B>
-        + VecZnxIdftApplyConsume<B>
-        + VecZnxBigAddSmallInplace<B>
-        + VecZnxBigNormalize<B>
-        + VecZnxAutomorphismInplace<B>
-        + VecZnxBigSubSmallNegateInplace<B>
-        + VecZnxRotate
-        + VecZnxNormalize<B>,
-    Scratch<B>: ScratchAvailable,
+pub trait GLWEPacking<BE: Backend>
+where
+    Self: GLWEAutomorphism<BE> + GaloisElement + ModuleLogN,
 {
-    #[cfg(debug_assertions)]
+    /// Packs [x_0: GLWE(m_0), x_1: GLWE(m_1), ..., x_i: GLWE(m_i)]
+    /// to [0: GLWE(m_0 * X^x_0 + m_1 * X^x_1 + ... + m_i * X^x_i)]
+    fn glwe_pack<R, K>(
+        &self,
+        cts: &mut HashMap<usize, &mut R>,
+        log_gap_out: usize,
+        keys: &HashMap<i64, K>,
+        scratch: &mut Scratch<BE>,
+    ) where
+        R: GLWEToMut,
+        K: AutomorphismKeyPreparedToRef<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        assert!(*cts.keys().max().unwrap() < module.n())
-    }
+        #[cfg(debug_assertions)]
+        {
+            assert!(*cts.keys().max().unwrap() < self.n())
+        }
 
-    let log_n: usize = module.log_n();
+        let log_n: usize = self.log_n();
 
-    (0..log_n - log_gap_out).for_each(|i| {
-        let t: usize = (1 << log_n).min(1 << (log_n - 1 - i));
+        (0..log_n - log_gap_out).for_each(|i| {
+            let t: usize = (1 << log_n).min(1 << (log_n - 1 - i));
 
-        let auto_key: &AutomorphismKeyPrepared<ATK, B> = if i == 0 {
-            auto_keys.get(&-1).unwrap()
-        } else {
-            auto_keys.get(&module.galois_element(1 << (i - 1))).unwrap()
-        };
+            let key: &K = if i == 0 {
+                keys.get(&-1).unwrap()
+            } else {
+                keys.get(&self.galois_element(1 << (i - 1))).unwrap()
+            };
 
-        (0..t).for_each(|j| {
-            let mut a: Option<&mut GLWE<D>> = cts.remove(&j);
-            let mut b: Option<&mut GLWE<D>> = cts.remove(&(j + t));
+            (0..t).for_each(|j| {
+                let mut a: Option<&mut R> = cts.remove(&j);
+                let mut b: Option<&mut R> = cts.remove(&(j + t));
 
-            pack_internal(module, &mut a, &mut b, i, auto_key, scratch);
+                pack_internal(self, &mut a, &mut b, i, key, scratch);
 
-            if let Some(a) = a {
-                cts.insert(j, a);
-            } else if let Some(b) = b {
-                cts.insert(j, b);
-            }
+                if let Some(a) = a {
+                    cts.insert(j, a);
+                } else if let Some(b) = b {
+                    cts.insert(j, b);
+                }
+            });
         });
-    });
+    }
 }
 
 #[allow(clippy::too_many_arguments)]
-fn pack_internal<A: DataMut, D: DataMut, DataAK: DataRef, B: Backend>(
-    module: &Module<B>,
-    a: &mut Option<&mut GLWE<A>>,
-    b: &mut Option<&mut GLWE<D>>,
+fn pack_internal<M, A, B, K, BE: Backend>(
+    module: &M,
+    a: &mut Option<&mut A>,
+    b: &mut Option<&mut B>,
     i: usize,
-    auto_key: &AutomorphismKeyPrepared<DataAK, B>,
-    scratch: &mut Scratch<B>,
+    auto_key: &K,
+    scratch: &mut Scratch<BE>,
 ) where
-    Module<B>: VecZnxRotateInplace<B>
-        + VecZnxNormalizeInplace<B>
-        + VecZnxNormalizeTmpBytes
-        + VecZnxBigAutomorphismInplace<B>
-        + VecZnxRshInplace<B>
-        + VecZnxDftCopy<B>
-        + VecZnxIdftApplyTmpA<B>
-        + VecZnxSub
-        + VecZnxAddInplace
-        + VecZnxNegateInplace
-        + VecZnxCopy
-        + VecZnxSubInplace
-        + VecZnxDftBytesOf
-        + VmpApplyDftToDftTmpBytes
-        + VecZnxBigNormalizeTmpBytes
-        + VmpApplyDftToDft<B>
-        + VmpApplyDftToDftAdd<B>
-        + VecZnxDftApply<B>
-        + VecZnxIdftApplyConsume<B>
-        + VecZnxBigAddSmallInplace<B>
-        + VecZnxBigNormalize<B>
-        + VecZnxAutomorphismInplace<B>
-        + VecZnxBigSubSmallNegateInplace<B>
-        + VecZnxRotate
-        + VecZnxNormalize<B>,
-    Scratch<B>: ScratchAvailable,
+    M: GLWEAutomorphism<BE>,
+    A: GLWEToMut + GLWEInfos,
+    B: GLWEToMut + GLWEInfos,
+    K: AutomorphismKeyPreparedToRef<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
 {
     // Goal is to evaluate: a = a + b*X^t + phi(a - b*X^t))
     // We also use the identity: AUTO(a * X^t, g) = -X^t * AUTO(a, g)
@@ -446,7 +399,7 @@ fn pack_internal<A: DataMut, D: DataMut, DataAK: DataRef, B: Backend>(
         let t: i64 = 1 << (a.n().log2() - i - 1);
 
         if let Some(b) = b.as_deref_mut() {
-            let (mut tmp_b, scratch_1) = scratch.take_glwe_ct(a);
+            let (mut tmp_b, scratch_1) = scratch.take_glwe_ct(module, a);
 
             // a = a * X^-t
             a.rotate_inplace(module, -t, scratch_1);
diff --git a/poulpy-core/src/glwe_trace.rs b/poulpy-core/src/glwe_trace.rs
index 36aabb9..dc5582c 100644
--- a/poulpy-core/src/glwe_trace.rs
+++ b/poulpy-core/src/glwe_trace.rs
@@ -9,10 +9,7 @@ use poulpy_hal::{
     layouts::{Backend, DataMut, DataRef, Module, Scratch, VecZnx},
 };
 
-use crate::{
-    layouts::{Base2K, GGLWEInfos, GLWE, GLWEInfos, GLWELayout, LWEInfos, prepared::AutomorphismKeyPrepared},
-    operations::GLWEOperations,
-};
+use crate::layouts::{Base2K, GGLWEInfos, GLWE, GLWEInfos, GLWELayout, LWEInfos, prepared::AutomorphismKeyPrepared};
 
 impl GLWE<Vec<u8>> {
     pub fn trace_galois_elements<B: Backend>(module: &Module<B>) -> Vec<i64> {
diff --git a/poulpy-core/src/keyswitching/mod.rs b/poulpy-core/src/keyswitching/mod.rs
index 462e474..7071680 100644
--- a/poulpy-core/src/keyswitching/mod.rs
+++ b/poulpy-core/src/keyswitching/mod.rs
@@ -4,6 +4,6 @@ mod glwe_ct;
 mod lwe_ct;
 
 pub use gglwe_ct::*;
-//pub use gglwe_ct::*;
+// pub use gglwe_ct::*;
 pub use glwe_ct::*;
 pub use lwe_ct::*;
diff --git a/poulpy-core/src/lib.rs b/poulpy-core/src/lib.rs
index 49c39b0..2dcc77a 100644
--- a/poulpy-core/src/lib.rs
+++ b/poulpy-core/src/lib.rs
@@ -14,12 +14,12 @@ mod utils;
 
 pub use operations::*;
 pub mod layouts;
+pub use automorphism::*;
 pub use conversion::*;
 pub use dist::*;
 pub use external_product::*;
 pub use glwe_packing::*;
 pub use keyswitching::*;
-pub use automorphism::*;
 
 pub use encryption::SIGMA;
 
diff --git a/poulpy-core/src/operations/glwe.rs b/poulpy-core/src/operations/glwe.rs
index 021d10e..4ad713c 100644
--- a/poulpy-core/src/operations/glwe.rs
+++ b/poulpy-core/src/operations/glwe.rs
@@ -1,320 +1,292 @@
 use poulpy_hal::{
     api::{
-        VecZnxAdd, VecZnxAddInplace, VecZnxCopy, VecZnxMulXpMinusOne, VecZnxMulXpMinusOneInplace, VecZnxNegateInplace,
+        ModuleN, VecZnxAdd, VecZnxAddInplace, VecZnxCopy, VecZnxMulXpMinusOne, VecZnxMulXpMinusOneInplace, VecZnxNegateInplace,
         VecZnxNormalize, VecZnxNormalizeInplace, VecZnxRotate, VecZnxRotateInplace, VecZnxRshInplace, VecZnxSub,
         VecZnxSubInplace, VecZnxSubNegateInplace,
     },
-    layouts::{Backend, DataMut, Scratch, VecZnx, ZnxZero},
+    layouts::{Backend, Module, Scratch, VecZnx, ZnxZero},
 };
 
-use crate::layouts::{GLWE, GLWEInfos, GLWEPlaintext, GLWEToMut, GLWEToRef, LWEInfos, SetGLWEInfos, TorusPrecision};
+use crate::{
+    ScratchTakeCore,
+    layouts::{GLWE, GLWEInfos, GLWEToMut, GLWEToRef, LWEInfos, SetGLWEInfos, TorusPrecision},
+};
 
-impl<D> GLWEOperations for GLWEPlaintext<D>
+pub trait GLWEAdd
 where
-    D: DataMut,
-    GLWEPlaintext<D>: GLWEToMut + GLWEInfos,
+    Self: ModuleN + VecZnxAdd + VecZnxCopy + VecZnxAddInplace,
 {
+    fn glwe_add<R, A, B>(&self, res: &mut R, a: &A, b: &B)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        B: GLWEToRef,
+    {
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &mut GLWE<&[u8]> = &mut a.to_ref();
+        let b: &GLWE<&[u8]> = &b.to_ref();
+
+        assert_eq!(a.n(), self.n() as u32);
+        assert_eq!(b.n(), self.n() as u32);
+        assert_eq!(res.n(), self.n() as u32);
+        assert_eq!(a.base2k(), b.base2k());
+        assert!(res.rank() >= a.rank().max(b.rank()));
+
+        let min_col: usize = (a.rank().min(b.rank()) + 1).into();
+        let max_col: usize = (a.rank().max(b.rank() + 1)).into();
+        let self_col: usize = (res.rank() + 1).into();
+
+        (0..min_col).for_each(|i| {
+            self.vec_znx_add(res.data_mut(), i, a.data(), i, b.data(), i);
+        });
+
+        if a.rank() > b.rank() {
+            (min_col..max_col).for_each(|i| {
+                self.vec_znx_copy(res.data_mut(), i, a.data(), i);
+            });
+        } else {
+            (min_col..max_col).for_each(|i| {
+                self.vec_znx_copy(res.data_mut(), i, b.data(), i);
+            });
+        }
+
+        let size: usize = res.size();
+        (max_col..self_col).for_each(|i| {
+            (0..size).for_each(|j| {
+                res.data.zero_at(i, j);
+            });
+        });
+
+        res.set_base2k(a.base2k());
+        res.set_k(set_k_binary(res, a, b));
+    }
+
+    fn glwe_add_inplace<R, A>(&self, res: &mut R, a: &A)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+    {
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWE<&[u8]> = &a.to_ref();
+
+        assert_eq!(res.n(), self.n() as u32);
+        assert_eq!(a.n(), self.n() as u32);
+        assert_eq!(res.base2k(), a.base2k());
+        assert!(res.rank() >= a.rank());
+
+        (0..(a.rank() + 1).into()).for_each(|i| {
+            self.vec_znx_add_inplace(res.data_mut(), i, a.data(), i);
+        });
+
+        res.set_k(set_k_unary(res, a))
+    }
 }
 
-impl<D: DataMut> GLWEOperations for GLWE<D> where GLWE<D>: GLWEToMut + GLWEInfos {}
+impl<BE: Backend> GLWEAdd for Module<BE> where Self: ModuleN + VecZnxAdd + VecZnxCopy + VecZnxAddInplace {}
 
-pub trait GLWEOperations: GLWEToMut + GLWEInfos + SetGLWEInfos + Sized {
-    fn add<A, B, M>(&mut self, module: &M, a: &A, b: &B)
+pub trait GLWESub
+where
+    Self: ModuleN + VecZnxSub + VecZnxCopy + VecZnxNegateInplace + VecZnxSubInplace + VecZnxSubNegateInplace,
+{
+    fn glwe_sub<R, A, B>(&self, res: &mut R, a: &A, b: &B)
     where
-        A: GLWEToRef + GLWEInfos,
-        B: GLWEToRef + GLWEInfos,
-        M: VecZnxAdd + VecZnxCopy,
+        R: GLWEToMut,
+        A: GLWEToRef,
+        B: GLWEToRef,
     {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(a.n(), self.n());
-            assert_eq!(b.n(), self.n());
-            assert_eq!(a.base2k(), b.base2k());
-            assert!(self.rank() >= a.rank().max(b.rank()));
-        }
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWE<&[u8]> = &a.to_ref();
+        let b: &GLWE<&[u8]> = &b.to_ref();
+
+        assert_eq!(a.n(), self.n() as u32);
+        assert_eq!(b.n(), self.n() as u32);
+        assert_eq!(a.base2k(), b.base2k());
+        assert!(res.rank() >= a.rank().max(b.rank()));
 
         let min_col: usize = (a.rank().min(b.rank()) + 1).into();
         let max_col: usize = (a.rank().max(b.rank() + 1)).into();
-        let self_col: usize = (self.rank() + 1).into();
-
-        let self_mut: &mut GLWE<&mut [u8]> = &mut self.to_mut();
-        let a_ref: &GLWE<&[u8]> = &a.to_ref();
-        let b_ref: &GLWE<&[u8]> = &b.to_ref();
+        let self_col: usize = (res.rank() + 1).into();
 
         (0..min_col).for_each(|i| {
-            module.vec_znx_add(&mut self_mut.data, i, &a_ref.data, i, &b_ref.data, i);
+            self.vec_znx_sub(res.data_mut(), i, a.data(), i, b.data(), i);
         });
 
         if a.rank() > b.rank() {
             (min_col..max_col).for_each(|i| {
-                module.vec_znx_copy(&mut self_mut.data, i, &a_ref.data, i);
+                self.vec_znx_copy(res.data_mut(), i, a.data(), i);
             });
         } else {
             (min_col..max_col).for_each(|i| {
-                module.vec_znx_copy(&mut self_mut.data, i, &b_ref.data, i);
+                self.vec_znx_copy(res.data_mut(), i, b.data(), i);
+                self.vec_znx_negate_inplace(res.data_mut(), i);
             });
         }
 
-        let size: usize = self_mut.size();
+        let size: usize = res.size();
         (max_col..self_col).for_each(|i| {
             (0..size).for_each(|j| {
-                self_mut.data.zero_at(i, j);
+                res.data.zero_at(i, j);
             });
         });
 
-        self.set_base2k(a.base2k());
-        self.set_k(set_k_binary(self, a, b));
+        res.set_base2k(a.base2k());
+        res.set_k(set_k_binary(res, a, b));
     }
 
-    fn add_inplace<A, M>(&mut self, module: &M, a: &A)
+    fn glwe_sub_inplace<R, A>(&self, res: &mut R, a: &A)
     where
-        A: GLWEToRef + GLWEInfos,
-        M: VecZnxAddInplace,
+        R: GLWEToMut,
+        A: GLWEToRef,
     {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(a.n(), self.n());
-            assert_eq!(self.base2k(), a.base2k());
-            assert!(self.rank() >= a.rank())
-        }
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWE<&[u8]> = &a.to_ref();
 
-        let self_mut: &mut GLWE<&mut [u8]> = &mut self.to_mut();
-        let a_ref: &GLWE<&[u8]> = &a.to_ref();
+        assert_eq!(res.n(), self.n() as u32);
+        assert_eq!(a.n(), self.n() as u32);
+        assert_eq!(res.base2k(), a.base2k());
+        assert!(res.rank() >= a.rank());
 
         (0..(a.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_add_inplace(&mut self_mut.data, i, &a_ref.data, i);
+            self.vec_znx_sub_inplace(res.data_mut(), i, a.data(), i);
         });
 
-        self.set_k(set_k_unary(self, a))
+        res.set_k(set_k_unary(res, a))
     }
 
-    fn sub<A, B, M>(&mut self, module: &M, a: &A, b: &B)
+    fn glwe_sub_negate_inplace<R, A>(&self, res: &mut R, a: &A)
     where
-        A: GLWEToRef + GLWEInfos,
-        B: GLWEToRef + GLWEInfos,
-        M: VecZnxSub + VecZnxCopy + VecZnxNegateInplace,
+        R: GLWEToMut,
+        A: GLWEToRef,
     {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(a.n(), self.n());
-            assert_eq!(b.n(), self.n());
-            assert_eq!(a.base2k(), b.base2k());
-            assert!(self.rank() >= a.rank().max(b.rank()));
-        }
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWE<&[u8]> = &a.to_ref();
 
-        let min_col: usize = (a.rank().min(b.rank()) + 1).into();
-        let max_col: usize = (a.rank().max(b.rank() + 1)).into();
-        let self_col: usize = (self.rank() + 1).into();
-
-        let self_mut: &mut GLWE<&mut [u8]> = &mut self.to_mut();
-        let a_ref: &GLWE<&[u8]> = &a.to_ref();
-        let b_ref: &GLWE<&[u8]> = &b.to_ref();
-
-        (0..min_col).for_each(|i| {
-            module.vec_znx_sub(&mut self_mut.data, i, &a_ref.data, i, &b_ref.data, i);
-        });
-
-        if a.rank() > b.rank() {
-            (min_col..max_col).for_each(|i| {
-                module.vec_znx_copy(&mut self_mut.data, i, &a_ref.data, i);
-            });
-        } else {
-            (min_col..max_col).for_each(|i| {
-                module.vec_znx_copy(&mut self_mut.data, i, &b_ref.data, i);
-                module.vec_znx_negate_inplace(&mut self_mut.data, i);
-            });
-        }
-
-        let size: usize = self_mut.size();
-        (max_col..self_col).for_each(|i| {
-            (0..size).for_each(|j| {
-                self_mut.data.zero_at(i, j);
-            });
-        });
-
-        self.set_base2k(a.base2k());
-        self.set_k(set_k_binary(self, a, b));
-    }
-
-    fn sub_inplace_ab<A, M>(&mut self, module: &M, a: &A)
-    where
-        A: GLWEToRef + GLWEInfos,
-        M: VecZnxSubInplace,
-    {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(a.n(), self.n());
-            assert_eq!(self.base2k(), a.base2k());
-            assert!(self.rank() >= a.rank())
-        }
-
-        let self_mut: &mut GLWE<&mut [u8]> = &mut self.to_mut();
-        let a_ref: &GLWE<&[u8]> = &a.to_ref();
+        assert_eq!(res.n(), self.n() as u32);
+        assert_eq!(a.n(), self.n() as u32);
+        assert_eq!(res.base2k(), a.base2k());
+        assert!(res.rank() >= a.rank());
 
         (0..(a.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_sub_inplace(&mut self_mut.data, i, &a_ref.data, i);
+            self.vec_znx_sub_negate_inplace(res.data_mut(), i, a.data(), i);
         });
 
-        self.set_k(set_k_unary(self, a))
+        res.set_k(set_k_unary(res, a))
     }
+}
 
-    fn sub_inplace_ba<A, M>(&mut self, module: &M, a: &A)
+pub trait GLWERotate<BE: Backend>
+where
+    Self: ModuleN + VecZnxRotate + VecZnxRotateInplace<BE>,
+{
+    fn glwe_rotate<R, A>(&self, k: i64, res: &mut R, a: &A)
     where
-        A: GLWEToRef + GLWEInfos,
-        M: VecZnxSubNegateInplace,
+        R: GLWEToMut,
+        A: GLWEToRef,
     {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(a.n(), self.n());
-            assert_eq!(self.base2k(), a.base2k());
-            assert!(self.rank() >= a.rank())
-        }
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWE<&[u8]> = &a.to_ref();
 
-        let self_mut: &mut GLWE<&mut [u8]> = &mut self.to_mut();
-        let a_ref: &GLWE<&[u8]> = &a.to_ref();
+        assert_eq!(a.n(), self.n() as u32);
+        assert_eq!(res.rank(), a.rank());
 
         (0..(a.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_sub_negate_inplace(&mut self_mut.data, i, &a_ref.data, i);
+            self.vec_znx_rotate(k, res.data_mut(), i, a.data(), i);
         });
 
-        self.set_k(set_k_unary(self, a))
+        res.set_base2k(a.base2k());
+        res.set_k(set_k_unary(res, a))
     }
 
-    fn rotate<A, M>(&mut self, module: &M, k: i64, a: &A)
+    fn glwe_rotate_inplace<R>(&self, k: i64, res: &mut R, scratch: &mut Scratch<BE>)
     where
-        A: GLWEToRef + GLWEInfos,
-        M: VecZnxRotate,
+        R: GLWEToMut,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(a.n(), self.n());
-            assert_eq!(self.rank(), a.rank())
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+
+        (0..(res.rank() + 1).into()).for_each(|i| {
+            self.vec_znx_rotate_inplace(k, res.data_mut(), i, scratch);
+        });
+    }
+}
+
+pub trait GLWEMulXpMinusOne<BE: Backend>
+where
+    Self: ModuleN + VecZnxMulXpMinusOne + VecZnxMulXpMinusOneInplace<BE>,
+{
+    fn glwe_mul_xp_minus_one<R, A>(&self, k: i64, res: &mut R, a: &A)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+    {
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWE<&[u8]> = &a.to_ref();
+
+        assert_eq!(res.n(), self.n() as u32);
+        assert_eq!(a.n(), self.n() as u32);
+        assert_eq!(res.rank(), a.rank());
+
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_mul_xp_minus_one(k, res.data_mut(), i, a.data(), i);
         }
 
-        let self_mut: &mut GLWE<&mut [u8]> = &mut self.to_mut();
-        let a_ref: &GLWE<&[u8]> = &a.to_ref();
-
-        (0..(a.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_rotate(k, &mut self_mut.data, i, &a_ref.data, i);
-        });
-
-        self.set_base2k(a.base2k());
-        self.set_k(set_k_unary(self, a))
+        res.set_base2k(a.base2k());
+        res.set_k(set_k_unary(res, a))
     }
 
-    fn rotate_inplace<M, BE: Backend>(&mut self, module: &M, k: i64, scratch: &mut Scratch<BE>)
+    fn glwe_mul_xp_minus_one_inplace<R>(&self, k: i64, res: &mut R, scratch: &mut Scratch<BE>)
     where
-        M: VecZnxRotateInplace<BE>,
+        R: GLWEToMut,
     {
-        let self_mut: &mut GLWE<&mut [u8]> = &mut self.to_mut();
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
 
-        (0..(self_mut.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_rotate_inplace(k, &mut self_mut.data, i, scratch);
-        });
+        assert_eq!(res.n(), self.n() as u32);
+
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_mul_xp_minus_one_inplace(k, res.data_mut(), i, scratch);
+        }
     }
+}
 
-    fn mul_xp_minus_one<A, M>(&mut self, module: &M, k: i64, a: &A)
+pub trait GLWECopy
+where
+    Self: ModuleN + VecZnxCopy,
+{
+    fn glwe_copy<R, A>(&self, res: &mut R, a: &A)
     where
-        A: GLWEToRef + GLWEInfos,
-        M: VecZnxMulXpMinusOne,
+        R: GLWEToMut,
+        A: GLWEToRef,
     {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(a.n(), self.n());
-            assert_eq!(self.rank(), a.rank())
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWE<&[u8]> = &a.to_ref();
+
+        assert_eq!(res.n(), self.n() as u32);
+        assert_eq!(a.n(), self.n() as u32);
+        assert_eq!(res.rank(), a.rank());
+
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_copy(res.data_mut(), i, a.data(), i);
         }
 
-        let self_mut: &mut GLWE<&mut [u8]> = &mut self.to_mut();
-        let a_ref: &GLWE<&[u8]> = &a.to_ref();
-
-        (0..(a.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_mul_xp_minus_one(k, &mut self_mut.data, i, &a_ref.data, i);
-        });
-
-        self.set_base2k(a.base2k());
-        self.set_k(set_k_unary(self, a))
+        res.set_k(a.k().min(res.max_k()));
+        res.set_base2k(a.base2k());
     }
+}
 
-    fn mul_xp_minus_one_inplace<M, BE: Backend>(&mut self, module: &M, k: i64, scratch: &mut Scratch<BE>)
+pub trait GLWEShift<BE: Backend>
+where
+    Self: ModuleN + VecZnxRshInplace<BE>,
+{
+    fn glwe_rsh<R>(&self, k: usize, res: &mut R, scratch: &mut Scratch<BE>)
     where
-        M: VecZnxMulXpMinusOneInplace<BE>,
+        R: GLWEToMut,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        let self_mut: &mut GLWE<&mut [u8]> = &mut self.to_mut();
-
-        (0..(self_mut.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_mul_xp_minus_one_inplace(k, &mut self_mut.data, i, scratch);
-        });
-    }
-
-    fn copy<A, M>(&mut self, module: &M, a: &A)
-    where
-        A: GLWEToRef + GLWEInfos,
-        M: VecZnxCopy,
-    {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(self.n(), a.n());
-            assert_eq!(self.rank(), a.rank());
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let base2k: usize = res.base2k().into();
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_rsh_inplace(base2k, k, res.data_mut(), i, scratch);
         }
-
-        let self_mut: &mut GLWE<&mut [u8]> = &mut self.to_mut();
-        let a_ref: &GLWE<&[u8]> = &a.to_ref();
-
-        (0..(self_mut.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_copy(&mut self_mut.data, i, &a_ref.data, i);
-        });
-
-        self.set_k(a.k().min(self.max_k()));
-        self.set_base2k(a.base2k());
-    }
-
-    fn rsh<M, BE: Backend>(&mut self, module: &M, k: usize, scratch: &mut Scratch<BE>)
-    where
-        M: VecZnxRshInplace<BE>,
-    {
-        let base2k: usize = self.base2k().into();
-        (0..(self.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_rsh_inplace(base2k, k, &mut self.to_mut().data, i, scratch);
-        })
-    }
-
-    fn normalize<A, M, BE: Backend>(&mut self, module: &M, a: &A, scratch: &mut Scratch<BE>)
-    where
-        A: GLWEToRef + GLWEInfos,
-        M: VecZnxNormalize<BE>,
-    {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(self.n(), a.n());
-            assert_eq!(self.rank(), a.rank());
-        }
-
-        let self_mut: &mut GLWE<&mut [u8]> = &mut self.to_mut();
-        let a_ref: &GLWE<&[u8]> = &a.to_ref();
-
-        (0..(self_mut.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_normalize(
-                a.base2k().into(),
-                &mut self_mut.data,
-                i,
-                a.base2k().into(),
-                &a_ref.data,
-                i,
-                scratch,
-            );
-        });
-        self.set_base2k(a.base2k());
-        self.set_k(a.k().min(self.k()));
-    }
-
-    fn normalize_inplace<M, BE: Backend>(&mut self, module: &M, scratch: &mut Scratch<BE>)
-    where
-        M: VecZnxNormalizeInplace<BE>,
-    {
-        let self_mut: &mut GLWE<&mut [u8]> = &mut self.to_mut();
-        (0..(self_mut.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_normalize_inplace(self_mut.base2k().into(), &mut self_mut.data, i, scratch);
-        });
     }
 }
 
@@ -324,6 +296,50 @@ impl GLWE<Vec<u8>> {
     }
 }
 
+pub trait GLWENormalize<BE: Backend>
+where
+    Self: ModuleN + VecZnxNormalize<BE> + VecZnxNormalizeInplace<BE>,
+{
+    fn glwe_normalize<R, A>(&self, res: &mut R, a: &A, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWE<&[u8]> = &a.to_ref();
+
+        assert_eq!(res.n(), self.n() as u32);
+        assert_eq!(a.n(), self.n() as u32);
+        assert_eq!(res.rank(), a.rank());
+
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_normalize(
+                res.base2k().into(),
+                res.data_mut(),
+                i,
+                a.base2k().into(),
+                a.data(),
+                i,
+                scratch,
+            );
+        }
+
+        res.set_k(a.k().min(res.k()));
+    }
+
+    fn glwe_normalize_inplace<R>(&mut self, res: &mut R, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_normalize_inplace(res.base2k().into(), res.data_mut(), i, scratch);
+        }
+    }
+}
+
 // c = op(a, b)
 fn set_k_binary(c: &impl GLWEInfos, a: &impl GLWEInfos, b: &impl GLWEInfos) -> TorusPrecision {
     // If either operands is a ciphertext
diff --git a/poulpy-hal/src/api/module.rs b/poulpy-hal/src/api/module.rs
index c2e2f1c..a18af44 100644
--- a/poulpy-hal/src/api/module.rs
+++ b/poulpy-hal/src/api/module.rs
@@ -9,8 +9,11 @@ pub trait ModuleN {
     fn n(&self) -> usize;
 }
 
-pub trait ModuleLogN where Self: ModuleN{
-    fn log_n(&self) -> usize{
-        (u64::BITS - (self.n() as u64-1).leading_zeros()) as usize
+pub trait ModuleLogN
+where
+    Self: ModuleN,
+{
+    fn log_n(&self) -> usize {
+        (u64::BITS - (self.n() as u64 - 1).leading_zeros()) as usize
     }
-}
\ No newline at end of file
+}
diff --git a/poulpy-hal/src/layouts/module.rs b/poulpy-hal/src/layouts/module.rs
index ccefb3a..3382774 100644
--- a/poulpy-hal/src/layouts/module.rs
+++ b/poulpy-hal/src/layouts/module.rs
@@ -2,7 +2,10 @@ use std::{fmt::Display, marker::PhantomData, ptr::NonNull};
 
 use rand_distr::num_traits::Zero;
 
-use crate::{api::{ModuleLogN, ModuleN}, GALOISGENERATOR};
+use crate::{
+    GALOISGENERATOR,
+    api::{ModuleLogN, ModuleN},
+};
 
 #[allow(clippy::missing_safety_doc)]
 pub trait Backend: Sized {
@@ -86,7 +89,7 @@ where
     }
 }
 
-impl<BE: Backend> ModuleLogN for Module<BE> where Self: ModuleN{}
+impl<BE: Backend> ModuleLogN for Module<BE> where Self: ModuleN {}
 
 impl<BE: Backend> CyclotomicOrder for Module<BE> where Self: ModuleN {}