@@ -1,198 +1,169 @@
 use poulpy_hal::{
-    api::{
-        ScratchAvailable, VecZnxAutomorphism, VecZnxAutomorphismInplace, VecZnxBigAddSmallInplace, VecZnxBigNormalize,
-        VecZnxBigNormalizeTmpBytes, VecZnxDftApply, VecZnxDftBytesOf, VecZnxIdftApplyConsume, VecZnxNormalize,
-        VecZnxNormalizeTmpBytes, VmpApplyDftToDft, VmpApplyDftToDftAdd, VmpApplyDftToDftTmpBytes,
-    },
-    layouts::{Backend, DataMut, DataRef, Module, Scratch, ZnxZero},
+    api::VecZnxAutomorphism,
+    layouts::{Backend, DataMut, GaloisElement, Module, Scratch},
 };
 
-use crate::layouts::{AutomorphismKey, GGLWEInfos, GLWE, prepared::AutomorphismKeyPrepared};
+use crate::{
+    ScratchTakeCore,
+    automorphism::glwe_ct::GLWEAutomorphism,
+    layouts::{
+        AutomorphismKey, AutomorphismKeyToMut, AutomorphismKeyToRef, GGLWEInfos, GLWE, GLWEInfos,
+        prepared::{
+            AutomorphismKeyPrepared, AutomorphismKeyPreparedToRef, GetAutomorphismGaloisElement, SetAutomorphismGaloisElement,
+        },
+    },
+};
 
 impl AutomorphismKey<Vec<u8>> {
-    pub fn automorphism_tmp_bytes<B: Backend, OUT, IN, KEY>(
-        module: &Module<B>,
-        out_infos: &OUT,
-        in_infos: &IN,
-        key_infos: &KEY,
-    ) -> usize
+    pub fn automorphism_tmp_bytes<R, A, K, M, BE: Backend>(module: &M, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
+    where
+        R: GGLWEInfos,
+        A: GGLWEInfos,
+        K: GGLWEInfos,
+        M: AutomorphismKeyAutomorphism<BE>,
+    {
+        module.automorphism_key_automorphism_tmp_bytes(res_infos, a_infos, key_infos)
+    }
+}
+
+impl<DataSelf: DataMut> AutomorphismKey<DataSelf> {
+    pub fn automorphism<A, K, M, BE: Backend>(&mut self, module: &M, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
-        OUT: GGLWEInfos,
-        IN: GGLWEInfos,
-        KEY: GGLWEInfos,
-        Module<B>: VecZnxDftBytesOf + VmpApplyDftToDftTmpBytes + VecZnxBigNormalizeTmpBytes + VecZnxNormalizeTmpBytes,
+        A: AutomorphismKeyToRef + GetAutomorphismGaloisElement,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+        M: AutomorphismKeyAutomorphism<BE>,
     {
-        GLWE::keyswitch_tmp_bytes(
-            module,
-            &out_infos.glwe_layout(),
-            &in_infos.glwe_layout(),
-            key_infos,
-        )
+        module.automorphism_key_automorphism(self, a, key, scratch);
     }
 
-    pub fn automorphism_inplace_tmp_bytes<B: Backend, OUT, KEY>(module: &Module<B>, out_infos: &OUT, key_infos: &KEY) -> usize
+    pub fn automorphism_inplace<K, M, BE: Backend>(&mut self, module: &M, key: &K, scratch: &mut Scratch<BE>)
     where
-        OUT: GGLWEInfos,
-        KEY: GGLWEInfos,
-        Module<B>: VecZnxDftBytesOf + VmpApplyDftToDftTmpBytes + VecZnxBigNormalizeTmpBytes + VecZnxNormalizeTmpBytes,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+        M: AutomorphismKeyAutomorphism<BE>,
     {
-        AutomorphismKey::automorphism_tmp_bytes(module, out_infos, out_infos, key_infos)
+        module.automorphism_key_automorphism_inplace(self, key, scratch);
     }
 }
 
-impl<DataSelf: DataMut> AutomorphismKey<DataSelf> {
-    pub fn automorphism<DataLhs: DataRef, DataRhs: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        lhs: &AutomorphismKey<DataLhs>,
-        rhs: &AutomorphismKeyPrepared<DataRhs, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxAutomorphism
-            + VecZnxAutomorphismInplace<B>
-            + VecZnxNormalize<B>
-            + VecZnxNormalizeTmpBytes,
-        Scratch<B>: ScratchAvailable,
+impl<BE: Backend> AutomorphismKeyAutomorphism<BE> for Module<BE> where
+    Self: GaloisElement + GLWEAutomorphism<BE> + VecZnxAutomorphism
+{
+}
+
+pub trait AutomorphismKeyAutomorphism<BE: Backend>
+where
+    Self: GaloisElement + GLWEAutomorphism<BE> + VecZnxAutomorphism,
+{
+    fn automorphism_key_automorphism_tmp_bytes<R, A, K>(&self, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
+    where
+        R: GGLWEInfos,
+        A: GGLWEInfos,
+        K: GGLWEInfos,
+    {
+        self.glwe_keyswitch_tmp_bytes(res_infos, a_infos, key_infos)
+    }
+
+    fn automorphism_key_automorphism<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: AutomorphismKeyToMut + SetAutomorphismGaloisElement,
+        A: AutomorphismKeyToRef + GetAutomorphismGaloisElement,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        #[cfg(debug_assertions)]
         {
-            use crate::layouts::LWEInfos;
+            let res: &mut AutomorphismKey<&mut [u8]> = &mut res.to_mut();
+            let a: &AutomorphismKey<&[u8]> = &a.to_ref();
+            let key: &AutomorphismKeyPrepared<&[u8], _> = &key.to_ref();
 
-            assert_eq!(
-                self.rank_in(),
-                lhs.rank_in(),
-                "ksk_out input rank: {} != ksk_in input rank: {}",
-                self.rank_in(),
-                lhs.rank_in()
+            assert!(
+                res.dnum().as_u32() <= a.dnum().as_u32(),
+                "res dnum: {} > a dnum: {}",
+                res.dnum(),
+                a.dnum()
             );
+
             assert_eq!(
-                self.rank_out(),
-                rhs.rank_in(),
-                "ksk_in output rank: {} != ksk_apply input rank: {}",
-                self.rank_out(),
-                rhs.rank_in()
+                res.dsize(),
+                a.dsize(),
+                "res dnum: {} != a dnum: {}",
+                res.dsize(),
+                a.dsize()
             );
-            assert_eq!(
-                self.rank_out(),
-                rhs.rank_out(),
-                "ksk_out output rank: {} != ksk_apply output rank: {}",
-                self.rank_out(),
-                rhs.rank_out()
-            );
-            assert!(
-                self.k() <= lhs.k(),
-                "output k={} cannot be greater than input k={}",
-                self.k(),
-                lhs.k()
-            )
-        }
 
-        let cols_out: usize = (rhs.rank_out() + 1).into();
+            let cols_out: usize = (key.rank_out() + 1).into();
 
-        let p: i64 = lhs.p();
-        let p_inv: i64 = module.galois_element_inv(p);
+            let p: i64 = a.p();
+            let p_inv: i64 = self.galois_element_inv(p);
 
-        (0..self.rank_in().into()).for_each(|col_i| {
-            (0..self.dnum().into()).for_each(|row_j| {
-                let mut res_ct: GLWE<&mut [u8]> = self.at_mut(row_j, col_i);
-                let lhs_ct: GLWE<&[u8]> = lhs.at(row_j, col_i);
+            for row in 0..res.dnum().as_usize() {
+                for col in 0..cols_out {
+                    let mut res_tmp: GLWE<&mut [u8]> = res.at_mut(row, col);
+                    let a_ct: GLWE<&[u8]> = a.at(row, col);
 
-                // Reverts the automorphism X^{-k}: (-pi^{-1}_{k}(s)a + s, a) to (-sa + pi_{k}(s), a)
-                (0..cols_out).for_each(|i| {
-                    module.vec_znx_automorphism(lhs.p(), &mut res_ct.data, i, &lhs_ct.data, i);
-                });
+                    // Reverts the automorphism X^{-k}: (-pi^{-1}_{k}(s)a + s, a) to (-sa + pi_{k}(s), a)
+                    for i in 0..cols_out {
+                        self.vec_znx_automorphism(a.p(), res_tmp.data_mut(), i, &a_ct.data, i);
+                    }
 
-                // Key-switch (-sa + pi_{k}(s), a) to (-pi^{-1}_{k'}(s)a + pi_{k}(s), a)
-                res_ct.keyswitch_inplace(module, &rhs.key, scratch);
+                    // Key-switch (-sa + pi_{k}(s), a) to (-pi^{-1}_{k'}(s)a + pi_{k}(s), a)
+                    self.glwe_keyswitch_inplace(&mut res_tmp, &key.key, scratch);
 
-                // Applies back the automorphism X^{-k}: (-pi^{-1}_{k'}(s)a + pi_{k}(s), a) to (-pi^{-1}_{k'+k}(s)a + s, a)
-                (0..cols_out).for_each(|i| {
-                    module.vec_znx_automorphism_inplace(p_inv, &mut res_ct.data, i, scratch);
-                });
-            });
-        });
-
-        (self.dnum().min(lhs.dnum()).into()..self.dnum().into()).for_each(|row_i| {
-            (0..self.rank_in().into()).for_each(|col_j| {
-                self.at_mut(row_i, col_j).data.zero();
-            });
-        });
+                    // Applies back the automorphism X^{-k}: (-pi^{-1}_{k'}(s)a + pi_{k}(s), a) to (-pi^{-1}_{k'+k}(s)a + s, a)
+                    (0..cols_out).for_each(|i| {
+                        self.vec_znx_automorphism_inplace(p_inv, res_tmp.data_mut(), i, scratch);
+                    });
+                }
+            }
+        }
 
-        self.p = (lhs.p * rhs.p) % (module.cyclotomic_order() as i64);
+        res.set_p((a.p() * key.p()) % (self.cyclotomic_order() as i64));
     }
 
-    pub fn automorphism_inplace<DataRhs: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        rhs: &AutomorphismKeyPrepared<DataRhs, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxAutomorphism
-            + VecZnxAutomorphismInplace<B>
-            + VecZnxNormalize<B>
-            + VecZnxNormalizeTmpBytes,
-        Scratch<B>: ScratchAvailable,
+    fn automorphism_key_automorphism_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: AutomorphismKeyToMut + SetAutomorphismGaloisElement + GetAutomorphismGaloisElement,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        #[cfg(debug_assertions)]
         {
+            let res: &mut AutomorphismKey<&mut [u8]> = &mut res.to_mut();
+            let key: &AutomorphismKeyPrepared<&[u8], _> = &key.to_ref();
+
             assert_eq!(
-                self.rank_out(),
-                rhs.rank_in(),
-                "ksk_in output rank: {} != ksk_apply input rank: {}",
-                self.rank_out(),
-                rhs.rank_in()
+                res.rank(),
+                key.rank(),
+                "key rank: {} != key rank: {}",
+                res.rank(),
+                key.rank()
             );
-            assert_eq!(
-                self.rank_out(),
-                rhs.rank_out(),
-                "ksk_out output rank: {} != ksk_apply output rank: {}",
-                self.rank_out(),
-                rhs.rank_out()
-            );
-        }
 
-        let cols_out: usize = (rhs.rank_out() + 1).into();
+            let cols_out: usize = (key.rank_out() + 1).into();
 
-        let p: i64 = self.p();
-        let p_inv = module.galois_element_inv(p);
+            let p: i64 = res.p();
+            let p_inv: i64 = self.galois_element_inv(p);
 
-        (0..self.rank_in().into()).for_each(|col_i| {
-            (0..self.dnum().into()).for_each(|row_j| {
-                let mut res_ct: GLWE<&mut [u8]> = self.at_mut(row_j, col_i);
+            for row in 0..res.dnum().as_usize() {
+                for col in 0..cols_out {
+                    let mut res_tmp: GLWE<&mut [u8]> = res.at_mut(row, col);
 
-                // Reverts the automorphism X^{-k}: (-pi^{-1}_{k}(s)a + s, a) to (-sa + pi_{k}(s), a)
-                (0..cols_out).for_each(|i| {
-                    module.vec_znx_automorphism_inplace(p_inv, &mut res_ct.data, i, scratch);
-                });
+                    // Reverts the automorphism X^{-k}: (-pi^{-1}_{k}(s)a + s, a) to (-sa + pi_{k}(s), a)
+                    for i in 0..cols_out {
+                        self.vec_znx_automorphism_inplace(p_inv, res_tmp.data_mut(), i, scratch);
+                    }
 
-                // Key-switch (-sa + pi_{k}(s), a) to (-pi^{-1}_{k'}(s)a + pi_{k}(s), a)
-                res_ct.keyswitch_inplace(module, &rhs.key, scratch);
+                    // Key-switch (-sa + pi_{k}(s), a) to (-pi^{-1}_{k'}(s)a + pi_{k}(s), a)
+                    self.glwe_keyswitch_inplace(&mut res_tmp, &key.key, scratch);
 
-                // Applies back the automorphism X^{-k}: (-pi^{-1}_{k'}(s)a + pi_{k}(s), a) to (-pi^{-1}_{k'+k}(s)a + s, a)
-                (0..cols_out).for_each(|i| {
-                    module.vec_znx_automorphism_inplace(p_inv, &mut res_ct.data, i, scratch);
-                });
-            });
-        });
+                    // Applies back the automorphism X^{-k}: (-pi^{-1}_{k'}(s)a + pi_{k}(s), a) to (-pi^{-1}_{k'+k}(s)a + s, a)
+                    for i in 0..cols_out {
+                        self.vec_znx_automorphism_inplace(p_inv, res_tmp.data_mut(), i, scratch);
+                    }
+                }
+            }
+        }
 
-        self.p = (self.p * rhs.p) % (module.cyclotomic_order() as i64);
+        res.set_p((res.p() * key.p()) % (self.cyclotomic_order() as i64));
     }
 }

@@ -1,165 +1,127 @@
 use poulpy_hal::{
-    api::{
-        ScratchAvailable, VecZnxAutomorphismInplace, VecZnxBigAddSmallInplace, VecZnxBigBytesOf, VecZnxBigNormalize,
-        VecZnxBigNormalizeTmpBytes, VecZnxDftAddInplace, VecZnxDftApply, VecZnxDftBytesOf, VecZnxDftCopy, VecZnxIdftApplyConsume,
-        VecZnxIdftApplyTmpA, VecZnxNormalize, VecZnxNormalizeTmpBytes, VmpApplyDftToDft, VmpApplyDftToDftAdd,
-        VmpApplyDftToDftTmpBytes,
-    },
-    layouts::{Backend, DataMut, DataRef, Module, Scratch},
+    api::ScratchAvailable,
+    layouts::{Backend, DataMut, Module, Scratch},
 };
 
-use crate::layouts::{
-    GGLWEInfos, GGSW, GGSWInfos, GLWE,
-    prepared::{AutomorphismKeyPrepared, TensorKeyPrepared},
+use crate::{
+    GGSWExpandRows, ScratchTakeCore,
+    automorphism::glwe_ct::GLWEAutomorphism,
+    layouts::{
+        GGLWEInfos, GGSW, GGSWInfos, GGSWToMut, GGSWToRef, GLWEInfos, LWEInfos,
+        prepared::{AutomorphismKeyPrepared, AutomorphismKeyPreparedToRef, TensorKeyPrepared, TensorKeyPreparedToRef},
+    },
 };
 
 impl GGSW<Vec<u8>> {
-    pub fn automorphism_tmp_bytes<B: Backend, OUT, IN, KEY, TSK>(
-        module: &Module<B>,
-        out_infos: &OUT,
-        in_infos: &IN,
-        key_infos: &KEY,
-        tsk_infos: &TSK,
+    pub fn automorphism_tmp_bytes<R, A, K, T, M, BE: Backend>(
+        module: &M,
+        res_infos: &R,
+        a_infos: &A,
+        key_infos: &K,
+        tsk_infos: &T,
     ) -> usize
     where
-        OUT: GGSWInfos,
-        IN: GGSWInfos,
-        KEY: GGLWEInfos,
-        TSK: GGLWEInfos,
-        Module<B>:
-            VecZnxDftBytesOf + VmpApplyDftToDftTmpBytes + VecZnxBigBytesOf + VecZnxNormalizeTmpBytes + VecZnxBigNormalizeTmpBytes,
+        R: GGSWInfos,
+        A: GGSWInfos,
+        K: GGLWEInfos,
+        T: GGLWEInfos,
+        M: GGSWAutomorphism<BE>,
+    {
+        module.ggsw_automorphism_tmp_bytes(res_infos, a_infos, key_infos, tsk_infos)
+    }
+}
+
+impl<D: DataMut> GGSW<D> {
+    pub fn automorphism<A, K, T, M, BE: Backend>(&mut self, module: &M, a: &A, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
+    where
+        A: GGSWToRef,
+        K: AutomorphismKeyPreparedToRef<BE>,
+        T: TensorKeyPreparedToRef<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
+        M: GGSWAutomorphism<BE>,
     {
-        let out_size: usize = out_infos.size();
-        let ci_dft: usize = module.bytes_of_vec_znx_dft((key_infos.rank_out() + 1).into(), out_size);
-        let ks_internal: usize = GLWE::keyswitch_tmp_bytes(
-            module,
-            &out_infos.glwe_layout(),
-            &in_infos.glwe_layout(),
-            key_infos,
-        );
-        let expand: usize = GGSW::expand_row_tmp_bytes(module, out_infos, tsk_infos);
-        ci_dft + (ks_internal | expand)
+        module.ggsw_automorphism(self, a, key, tsk, scratch);
     }
 
-    pub fn automorphism_inplace_tmp_bytes<B: Backend, OUT, KEY, TSK>(
-        module: &Module<B>,
-        out_infos: &OUT,
-        key_infos: &KEY,
-        tsk_infos: &TSK,
-    ) -> usize
+    pub fn automorphism_inplace<K, T, M, BE: Backend>(&mut self, module: &M, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
     where
-        OUT: GGSWInfos,
-        KEY: GGLWEInfos,
-        TSK: GGLWEInfos,
-        Module<B>:
-            VecZnxDftBytesOf + VmpApplyDftToDftTmpBytes + VecZnxBigBytesOf + VecZnxNormalizeTmpBytes + VecZnxBigNormalizeTmpBytes,
+        K: AutomorphismKeyPreparedToRef<BE>,
+        T: TensorKeyPreparedToRef<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
+        M: GGSWAutomorphism<BE>,
     {
-        GGSW::automorphism_tmp_bytes(module, out_infos, out_infos, key_infos, tsk_infos)
+        module.ggsw_automorphism_inplace(self, key, tsk, scratch);
     }
 }
 
-impl<DataSelf: DataMut> GGSW<DataSelf> {
-    pub fn automorphism<DataLhs: DataRef, DataAk: DataRef, DataTsk: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        lhs: &GGSW<DataLhs>,
-        auto_key: &AutomorphismKeyPrepared<DataAk, B>,
-        tensor_key: &TensorKeyPrepared<DataTsk, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxAutomorphismInplace<B>
-            + VecZnxBigBytesOf
-            + VecZnxNormalizeTmpBytes
-            + VecZnxDftCopy<B>
-            + VecZnxDftAddInplace<B>
-            + VecZnxIdftApplyTmpA<B>
-            + VecZnxNormalize<B>,
-        Scratch<B>: ScratchAvailable,
+impl<BE: Backend> GGSWAutomorphism<BE> for Module<BE> where Self: GLWEAutomorphism<BE> + GGSWExpandRows<BE> {}
+
+pub trait GGSWAutomorphism<BE: Backend>
+where
+    Self: GLWEAutomorphism<BE> + GGSWExpandRows<BE>,
+{
+    fn ggsw_automorphism_tmp_bytes<R, A, K, T>(&self, res_infos: &R, a_infos: &A, key_infos: &K, tsk_infos: &T) -> usize
+    where
+        R: GGSWInfos,
+        A: GGSWInfos,
+        K: GGLWEInfos,
+        T: GGLWEInfos,
     {
-        #[cfg(debug_assertions)]
-        {
-            use crate::layouts::{GLWEInfos, LWEInfos};
+        let out_size: usize = res_infos.size();
+        let ci_dft: usize = self.bytes_of_vec_znx_dft((key_infos.rank_out() + 1).into(), out_size);
+        let ks_internal: usize = self.glwe_automorphism_tmp_bytes(res_infos, a_infos, key_infos);
+        let expand: usize = self.ggsw_expand_rows_tmp_bytes(res_infos, tsk_infos);
+        ci_dft + (ks_internal.max(expand))
+    }
 
-            assert_eq!(self.n(), module.n() as u32);
-            assert_eq!(lhs.n(), module.n() as u32);
-            assert_eq!(auto_key.n(), module.n() as u32);
-            assert_eq!(tensor_key.n(), module.n() as u32);
+    fn ggsw_automorphism<R, A, K, T>(&self, res: &mut R, a: &A, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
+    where
+        R: GGSWToMut,
+        A: GGSWToRef,
+        K: AutomorphismKeyPreparedToRef<BE>,
+        T: TensorKeyPreparedToRef<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
+        let a: &GGSW<&[u8]> = &a.to_ref();
+        let key: &AutomorphismKeyPrepared<&[u8], BE> = &key.to_ref();
+        let tsk: &TensorKeyPrepared<&[u8], BE> = &tsk.to_ref();
 
-            assert_eq!(
-                self.rank(),
-                lhs.rank(),
-                "ggsw_out rank: {} != ggsw_in rank: {}",
-                self.rank(),
-                lhs.rank()
-            );
-            assert_eq!(
-                self.rank(),
-                auto_key.rank_out(),
-                "ggsw_in rank: {} != auto_key rank: {}",
-                self.rank(),
-                auto_key.rank_out()
-            );
-            assert_eq!(
-                self.rank(),
-                tensor_key.rank_out(),
-                "ggsw_in rank: {} != tensor_key rank: {}",
-                self.rank(),
-                tensor_key.rank_out()
-            );
-            assert!(scratch.available() >= GGSW::automorphism_tmp_bytes(module, self, lhs, auto_key, tensor_key))
-        };
+        assert_eq!(res.ggsw_layout(), a.ggsw_layout());
+        assert_eq!(res.glwe_layout(), a.glwe_layout());
+        assert_eq!(res.lwe_layout(), a.lwe_layout());
+        assert!(scratch.available() >= self.ggsw_automorphism_tmp_bytes(res, a, key, tsk));
 
         // Keyswitch the j-th row of the col 0
-        (0..lhs.dnum().into()).for_each(|row_i| {
+        for row in 0..res.dnum().as_usize() {
             // Key-switch column 0, i.e.
             // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0, a1, a2) -> (-(a0pi^-1(s0) + a1pi^-1(s1) + a2pi^-1(s2)) + M[i], a0, a1, a2)
-            self.at_mut(row_i, 0)
-                .automorphism(module, &lhs.at(row_i, 0), auto_key, scratch);
-        });
-        self.expand_row(module, tensor_key, scratch);
+            self.glwe_automorphism(&mut res.at_mut(row, 0), &a.at(row, 0), key, scratch);
+        }
+
+        self.ggsw_expand_row(res, tsk, scratch);
     }
 
-    pub fn automorphism_inplace<DataKsk: DataRef, DataTsk: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        auto_key: &AutomorphismKeyPrepared<DataKsk, B>,
-        tensor_key: &TensorKeyPrepared<DataTsk, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxAutomorphismInplace<B>
-            + VecZnxBigBytesOf
-            + VecZnxNormalizeTmpBytes
-            + VecZnxDftCopy<B>
-            + VecZnxDftAddInplace<B>
-            + VecZnxIdftApplyTmpA<B>
-            + VecZnxNormalize<B>,
-        Scratch<B>: ScratchAvailable,
+    fn ggsw_automorphism_inplace<R, K, T>(&self, res: &mut R, key: &K, tsk: &T, scratch: &mut Scratch<BE>)
+    where
+        R: GGSWToMut,
+        K: AutomorphismKeyPreparedToRef<BE>,
+        T: TensorKeyPreparedToRef<BE>,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
+        let res: &mut GGSW<&mut [u8]> = &mut res.to_mut();
+        let key: &AutomorphismKeyPrepared<&[u8], BE> = &key.to_ref();
+        let tsk: &TensorKeyPrepared<&[u8], BE> = &tsk.to_ref();
+
         // Keyswitch the j-th row of the col 0
-        (0..self.dnum().into()).for_each(|row_i| {
+        for row in 0..res.dnum().as_usize() {
             // Key-switch column 0, i.e.
             // col 0: (-(a0s0 + a1s1 + a2s2) + M[i], a0, a1, a2) -> (-(a0pi^-1(s0) + a1pi^-1(s1) + a2pi^-1(s2)) + M[i], a0, a1, a2)
-            self.at_mut(row_i, 0)
-                .automorphism_inplace(module, auto_key, scratch);
-        });
-        self.expand_row(module, tensor_key, scratch);
+            self.glwe_automorphism_inplace(&mut res.at_mut(row, 0), key, scratch);
+        }
+
+        self.ggsw_expand_row(res, tsk, scratch);
     }
 }
+
+impl<DataSelf: DataMut> GGSW<DataSelf> {}

@@ -1,345 +1,331 @@
 use poulpy_hal::{
     api::{
-        ScratchAvailable, VecZnxAutomorphismInplace, VecZnxBigAddSmallInplace, VecZnxBigAutomorphismInplace, VecZnxBigNormalize,
-        VecZnxBigNormalizeTmpBytes, VecZnxBigSubSmallInplace, VecZnxBigSubSmallNegateInplace, VecZnxDftApply, VecZnxDftBytesOf,
-        VecZnxIdftApplyConsume, VecZnxNormalize, VecZnxNormalizeTmpBytes, VmpApplyDftToDft, VmpApplyDftToDftAdd,
-        VmpApplyDftToDftTmpBytes,
+        ScratchTakeBasic, VecZnxAutomorphismInplace, VecZnxBigAutomorphismInplace, VecZnxBigSubSmallInplace,
+        VecZnxBigSubSmallNegateInplace,
     },
-    layouts::{Backend, DataMut, DataRef, Module, Scratch, VecZnxBig},
+    layouts::{Backend, DataMut, Module, Scratch, VecZnxBig},
 };
 
-use crate::layouts::{GGLWEInfos, GLWE, GLWEInfos, LWEInfos, prepared::AutomorphismKeyPrepared};
+use crate::{
+    GLWEKeyswitch, ScratchTakeCore, keyswitch_internal,
+    layouts::{
+        GGLWEInfos, GLWE, GLWEInfos, GLWEToMut, GLWEToRef, LWEInfos,
+        prepared::{AutomorphismKeyPrepared, AutomorphismKeyPreparedToRef, GetAutomorphismGaloisElement},
+    },
+};
 
 impl GLWE<Vec<u8>> {
-    pub fn automorphism_tmp_bytes<B: Backend, OUT, IN, KEY>(
-        module: &Module<B>,
-        out_infos: &OUT,
-        in_infos: &IN,
-        key_infos: &KEY,
-    ) -> usize
+    pub fn automorphism_tmp_bytes<M, R, A, K, BE: Backend>(module: &M, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
+    where
+        R: GLWEInfos,
+        A: GLWEInfos,
+        K: GGLWEInfos,
+        M: GLWEAutomorphism<BE>,
+    {
+        module.glwe_automorphism_tmp_bytes(res_infos, a_infos, key_infos)
+    }
+}
+
+impl<DataSelf: DataMut> GLWE<DataSelf> {
+    pub fn automorphism<M, A, K, BE: Backend>(&mut self, module: &M, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        M: GLWEAutomorphism<BE>,
+        A: GLWEToRef,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        module.glwe_automorphism(self, a, key, scratch);
+    }
+
+    pub fn automorphism_add<M, A, K, BE: Backend>(&mut self, module: &M, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
-        OUT: GLWEInfos,
-        IN: GLWEInfos,
-        KEY: GGLWEInfos,
-        Module<B>: VecZnxDftBytesOf + VmpApplyDftToDftTmpBytes + VecZnxBigNormalizeTmpBytes + VecZnxNormalizeTmpBytes,
+        M: GLWEAutomorphism<BE>,
+        A: GLWEToRef,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        Self::keyswitch_tmp_bytes(module, out_infos, in_infos, key_infos)
+        module.glwe_automorphism_add(self, a, key, scratch);
     }
 
-    pub fn automorphism_inplace_tmp_bytes<B: Backend, OUT, KEY>(module: &Module<B>, out_infos: &OUT, key_infos: &KEY) -> usize
+    pub fn automorphism_sub<M, A, K, BE: Backend>(&mut self, module: &M, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
-        OUT: GLWEInfos,
-        KEY: GGLWEInfos,
-        Module<B>: VecZnxDftBytesOf + VmpApplyDftToDftTmpBytes + VecZnxBigNormalizeTmpBytes + VecZnxNormalizeTmpBytes,
+        M: GLWEAutomorphism<BE>,
+        A: GLWEToRef,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        Self::keyswitch_inplace_tmp_bytes(module, out_infos, key_infos)
+        module.glwe_automorphism_sub(self, a, key, scratch);
+    }
+
+    pub fn glwe_automorphism_sub_negate<M, A, K, BE: Backend>(&mut self, module: &M, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        M: GLWEAutomorphism<BE>,
+        A: GLWEToRef,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        module.glwe_automorphism_sub_negate(self, a, key, scratch);
+    }
+
+    pub fn automorphism_inplace<M, K, BE: Backend>(&mut self, module: &M, key: &K, scratch: &mut Scratch<BE>)
+    where
+        M: GLWEAutomorphism<BE>,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        module.glwe_automorphism_inplace(self, key, scratch);
+    }
+
+    pub fn automorphism_add_inplace<M, K, BE: Backend>(&mut self, module: &M, key: &K, scratch: &mut Scratch<BE>)
+    where
+        M: GLWEAutomorphism<BE>,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        module.glwe_automorphism_add_inplace(self, key, scratch);
+    }
+
+    pub fn automorphism_sub_inplace<M, K, BE: Backend>(&mut self, module: &M, key: &K, scratch: &mut Scratch<BE>)
+    where
+        M: GLWEAutomorphism<BE>,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        module.glwe_automorphism_sub_inplace(self, key, scratch);
+    }
+
+    pub fn automorphism_sub_negate_inplace<M, K, BE: Backend>(&mut self, module: &M, key: &K, scratch: &mut Scratch<BE>)
+    where
+        M: GLWEAutomorphism<BE>,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        module.glwe_automorphism_sub_negate_inplace(self, key, scratch);
     }
 }
 
-impl<DataSelf: DataMut> GLWE<DataSelf> {
-    pub fn automorphism<DataLhs: DataRef, DataRhs: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        lhs: &GLWE<DataLhs>,
-        rhs: &AutomorphismKeyPrepared<DataRhs, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxAutomorphismInplace<B>
-            + VecZnxNormalize<B>
-            + VecZnxNormalizeTmpBytes,
-        Scratch<B>: ScratchAvailable,
+pub trait GLWEAutomorphism<BE: Backend>
+where
+    Self: GLWEKeyswitch<BE>
+        + VecZnxAutomorphismInplace<BE>
+        + VecZnxBigAutomorphismInplace<BE>
+        + VecZnxBigSubSmallInplace<BE>
+        + VecZnxBigSubSmallNegateInplace<BE>,
+{
+    fn glwe_automorphism_tmp_bytes<R, A, K>(&self, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
+    where
+        R: GLWEInfos,
+        A: GLWEInfos,
+        K: GGLWEInfos,
     {
-        self.keyswitch(module, lhs, &rhs.key, scratch);
-        (0..(self.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_automorphism_inplace(rhs.p(), &mut self.data, i, scratch);
-        })
+        self.glwe_keyswitch_tmp_bytes(res_infos, a_infos, key_infos)
     }
 
-    pub fn automorphism_inplace<DataRhs: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        rhs: &AutomorphismKeyPrepared<DataRhs, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxAutomorphismInplace<B>
-            + VecZnxNormalize<B>
-            + VecZnxNormalizeTmpBytes,
-        Scratch<B>: ScratchAvailable,
+    fn glwe_automorphism<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        self.keyswitch_inplace(module, &rhs.key, scratch);
-        (0..(self.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_automorphism_inplace(rhs.p(), &mut self.data, i, scratch);
-        })
+        self.glwe_keyswitch(res, a, &key.to_ref().key, scratch);
+
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_automorphism_inplace(key.p(), res.data_mut(), i, scratch);
+        }
     }
 
-    pub fn automorphism_add<DataLhs: DataRef, DataRhs: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        lhs: &GLWE<DataLhs>,
-        rhs: &AutomorphismKeyPrepared<DataRhs, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxBigAutomorphismInplace<B>
-            + VecZnxNormalizeTmpBytes
-            + VecZnxNormalize<B>,
-        Scratch<B>: ScratchAvailable,
+    fn glwe_automorphism_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        #[cfg(debug_assertions)]
-        {
-            self.assert_keyswitch(module, lhs, &rhs.key, scratch);
+        self.glwe_keyswitch_inplace(res, &key.to_ref().key, scratch);
+
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_automorphism_inplace(key.p(), res.data_mut(), i, scratch);
         }
-        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self.n().into(), (self.rank() + 1).into(), rhs.size()); // TODO: optimise size
-        let mut res_big: VecZnxBig<_, B> = lhs.keyswitch_internal(module, res_dft, &rhs.key, scratch_1);
-        (0..(self.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_big_automorphism_inplace(rhs.p(), &mut res_big, i, scratch_1);
-            module.vec_znx_big_add_small_inplace(&mut res_big, i, &lhs.data, i);
-            module.vec_znx_big_normalize(
-                self.base2k().into(),
-                &mut self.data,
+    }
+
+    fn glwe_automorphism_add<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWE<&[u8]> = &a.to_ref();
+        let key: &AutomorphismKeyPrepared<&[u8], BE> = &key.to_ref();
+
+        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // TODO: optimise size
+        let mut res_big: VecZnxBig<_, BE> = keyswitch_internal(self, res_dft, a, &key.key, scratch_1);
+
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_1);
+            self.vec_znx_big_add_small_inplace(&mut res_big, i, a.data(), i);
+            self.vec_znx_big_normalize(
+                res.base2k().into(),
+                res.data_mut(),
                 i,
-                rhs.base2k().into(),
+                key.base2k().into(),
                 &res_big,
                 i,
                 scratch_1,
             );
-        })
+        }
     }
 
-    pub fn automorphism_add_inplace<DataRhs: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        rhs: &AutomorphismKeyPrepared<DataRhs, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxBigAutomorphismInplace<B>
-            + VecZnxNormalizeTmpBytes
-            + VecZnxNormalize<B>,
-        Scratch<B>: ScratchAvailable,
+    fn glwe_automorphism_add_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        #[cfg(debug_assertions)]
-        {
-            self.assert_keyswitch_inplace(module, &rhs.key, scratch);
-        }
-        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self.n().into(), (self.rank() + 1).into(), rhs.size()); // TODO: optimise size
-        let mut res_big: VecZnxBig<_, B> = self.keyswitch_internal(module, res_dft, &rhs.key, scratch_1);
-        (0..(self.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_big_automorphism_inplace(rhs.p(), &mut res_big, i, scratch_1);
-            module.vec_znx_big_add_small_inplace(&mut res_big, i, &self.data, i);
-            module.vec_znx_big_normalize(
-                self.base2k().into(),
-                &mut self.data,
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let key: &AutomorphismKeyPrepared<&[u8], BE> = &key.to_ref();
+
+        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // TODO: optimise size
+        let mut res_big: VecZnxBig<_, BE> = keyswitch_internal(self, res_dft, res, &key.key, scratch_1);
+
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_1);
+            self.vec_znx_big_add_small_inplace(&mut res_big, i, res.data(), i);
+            self.vec_znx_big_normalize(
+                res.base2k().into(),
+                res.data_mut(),
                 i,
-                rhs.base2k().into(),
+                key.base2k().into(),
                 &res_big,
                 i,
                 scratch_1,
             );
-        })
+        }
     }
 
-    pub fn automorphism_sub_ab<DataLhs: DataRef, DataRhs: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        lhs: &GLWE<DataLhs>,
-        rhs: &AutomorphismKeyPrepared<DataRhs, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxBigAutomorphismInplace<B>
-            + VecZnxBigSubSmallInplace<B>
-            + VecZnxNormalizeTmpBytes
-            + VecZnxNormalize<B>,
-        Scratch<B>: ScratchAvailable,
+    fn glwe_automorphism_sub<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        #[cfg(debug_assertions)]
-        {
-            self.assert_keyswitch(module, lhs, &rhs.key, scratch);
-        }
-        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self.n().into(), (self.rank() + 1).into(), rhs.size()); // TODO: optimise size
-        let mut res_big: VecZnxBig<_, B> = lhs.keyswitch_internal(module, res_dft, &rhs.key, scratch_1);
-        (0..(self.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_big_automorphism_inplace(rhs.p(), &mut res_big, i, scratch_1);
-            module.vec_znx_big_sub_small_inplace(&mut res_big, i, &lhs.data, i);
-            module.vec_znx_big_normalize(
-                self.base2k().into(),
-                &mut self.data,
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWE<&[u8]> = &a.to_ref();
+        let key: &AutomorphismKeyPrepared<&[u8], BE> = &key.to_ref();
+
+        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // TODO: optimise size
+        let mut res_big: VecZnxBig<_, BE> = keyswitch_internal(self, res_dft, a, &key.key, scratch_1);
+
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_1);
+            self.vec_znx_big_sub_small_inplace(&mut res_big, i, a.data(), i);
+            self.vec_znx_big_normalize(
+                res.base2k().into(),
+                res.data_mut(),
                 i,
-                rhs.base2k().into(),
+                key.base2k().into(),
                 &res_big,
                 i,
                 scratch_1,
             );
-        })
+        }
     }
 
-    pub fn automorphism_sub_inplace<DataRhs: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        rhs: &AutomorphismKeyPrepared<DataRhs, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxBigAutomorphismInplace<B>
-            + VecZnxBigSubSmallInplace<B>
-            + VecZnxNormalizeTmpBytes
-            + VecZnxNormalize<B>,
-        Scratch<B>: ScratchAvailable,
+    fn glwe_automorphism_sub_negate<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        #[cfg(debug_assertions)]
-        {
-            self.assert_keyswitch_inplace(module, &rhs.key, scratch);
-        }
-        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self.n().into(), (self.rank() + 1).into(), rhs.size()); // TODO: optimise size
-        let mut res_big: VecZnxBig<_, B> = self.keyswitch_internal(module, res_dft, &rhs.key, scratch_1);
-        (0..(self.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_big_automorphism_inplace(rhs.p(), &mut res_big, i, scratch_1);
-            module.vec_znx_big_sub_small_inplace(&mut res_big, i, &self.data, i);
-            module.vec_znx_big_normalize(
-                self.base2k().into(),
-                &mut self.data,
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let a: &GLWE<&[u8]> = &a.to_ref();
+        let key: &AutomorphismKeyPrepared<&[u8], BE> = &key.to_ref();
+
+        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // TODO: optimise size
+        let mut res_big: VecZnxBig<_, BE> = keyswitch_internal(self, res_dft, a, &key.key, scratch_1);
+
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_1);
+            self.vec_znx_big_sub_small_negate_inplace(&mut res_big, i, a.data(), i);
+            self.vec_znx_big_normalize(
+                res.base2k().into(),
+                res.data_mut(),
                 i,
-                rhs.base2k().into(),
+                key.base2k().into(),
                 &res_big,
                 i,
                 scratch_1,
             );
-        })
+        }
     }
 
-    pub fn automorphism_sub_negate<DataLhs: DataRef, DataRhs: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        lhs: &GLWE<DataLhs>,
-        rhs: &AutomorphismKeyPrepared<DataRhs, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxBigAutomorphismInplace<B>
-            + VecZnxBigSubSmallNegateInplace<B>
-            + VecZnxNormalizeTmpBytes
-            + VecZnxNormalize<B>,
-        Scratch<B>: ScratchAvailable,
+    fn glwe_automorphism_sub_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        #[cfg(debug_assertions)]
-        {
-            self.assert_keyswitch(module, lhs, &rhs.key, scratch);
-        }
-        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self.n().into(), (self.rank() + 1).into(), rhs.size()); // TODO: optimise size
-        let mut res_big: VecZnxBig<_, B> = lhs.keyswitch_internal(module, res_dft, &rhs.key, scratch_1);
-        (0..(self.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_big_automorphism_inplace(rhs.p(), &mut res_big, i, scratch_1);
-            module.vec_znx_big_sub_small_negate_inplace(&mut res_big, i, &lhs.data, i);
-            module.vec_znx_big_normalize(
-                self.base2k().into(),
-                &mut self.data,
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let key: &AutomorphismKeyPrepared<&[u8], BE> = &key.to_ref();
+
+        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // TODO: optimise size
+        let mut res_big: VecZnxBig<_, BE> = keyswitch_internal(self, res_dft, res, &key.key, scratch_1);
+
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_1);
+            self.vec_znx_big_sub_small_inplace(&mut res_big, i, res.data(), i);
+            self.vec_znx_big_normalize(
+                res.base2k().into(),
+                res.data_mut(),
                 i,
-                rhs.base2k().into(),
+                key.base2k().into(),
                 &res_big,
                 i,
                 scratch_1,
             );
-        })
+        }
     }
 
-    pub fn automorphism_sub_negate_inplace<DataRhs: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        rhs: &AutomorphismKeyPrepared<DataRhs, B>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxBigAutomorphismInplace<B>
-            + VecZnxBigSubSmallNegateInplace<B>
-            + VecZnxNormalizeTmpBytes
-            + VecZnxNormalize<B>,
-        Scratch<B>: ScratchAvailable,
+    fn glwe_automorphism_sub_negate_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        #[cfg(debug_assertions)]
-        {
-            self.assert_keyswitch_inplace(module, &rhs.key, scratch);
-        }
-        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self.n().into(), (self.rank() + 1).into(), rhs.size()); // TODO: optimise size
-        let mut res_big: VecZnxBig<_, B> = self.keyswitch_internal(module, res_dft, &rhs.key, scratch_1);
-        (0..(self.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_big_automorphism_inplace(rhs.p(), &mut res_big, i, scratch_1);
-            module.vec_znx_big_sub_small_negate_inplace(&mut res_big, i, &self.data, i);
-            module.vec_znx_big_normalize(
-                self.base2k().into(),
-                &mut self.data,
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+        let key: &AutomorphismKeyPrepared<&[u8], BE> = &key.to_ref();
+
+        let (res_dft, scratch_1) = scratch.take_vec_znx_dft(self, (res.rank() + 1).into(), key.size()); // TODO: optimise size
+        let mut res_big: VecZnxBig<_, BE> = keyswitch_internal(self, res_dft, res, &key.key, scratch_1);
+
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_big_automorphism_inplace(key.p(), &mut res_big, i, scratch_1);
+            self.vec_znx_big_sub_small_negate_inplace(&mut res_big, i, res.data(), i);
+            self.vec_znx_big_normalize(
+                res.base2k().into(),
+                res.data_mut(),
                 i,
-                rhs.base2k().into(),
+                key.base2k().into(),
                 &res_big,
                 i,
                 scratch_1,
             );
-        })
+        }
     }
 }
+
+impl<BE: Backend> GLWEAutomorphism<BE> for Module<BE> where
+    Self: GLWEKeyswitch<BE>
+        + VecZnxAutomorphismInplace<BE>
+        + VecZnxBigAutomorphismInplace<BE>
+        + VecZnxBigSubSmallInplace<BE>
+        + VecZnxBigSubSmallNegateInplace<BE>
+{
+}

@@ -1,3 +1,7 @@
 mod gglwe_atk;
 mod ggsw_ct;
 mod glwe_ct;
+
+pub use gglwe_atk::*;
+pub use ggsw_ct::*;
+pub use glwe_ct::*;

@@ -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 @@ module.ggsw_from_gglwe(self, gglwe, tsk, scratch);
     }
 }
 
-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 @@ assert_eq!(a.n(), self.n() as u32);
         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);

@@ -141,3 +141,18 @@ {
         module.gglwe_tensor_key_encrypt_sk(self, sk, seed_xa, source_xe, scratch);
     }
 }
+
+impl<DataSelf: DataMut> TensorKeyCompressed<DataSelf> {
+    pub fn encrypt_sk<DataSk: DataRef, B: Backend>(
+        &mut self,
+        module: &Module<B>,
+        sk: &GLWESecret<DataSk>,
+        seed_xa: [u8; 32],
+        source_xe: &mut Source,
+        scratch: &mut Scratch<B>,
+    ) where
+        Module<B>: GGLWETensorKeyCompressedEncryptSk<B>,
+    {
+        module.gglwe_tensor_key_encrypt_sk(self, sk, seed_xa, source_xe, scratch);
+    }
+}

@@ -6,6 +6,7 @@ VecZnxIdftApplyConsume, VecZnxNormalize, VecZnxNormalizeInplace, VecZnxNormalizeTmpBytes, VecZnxSub, VecZnxSubInplace,
         VecZnxSwitchRing,
     },
     layouts::{Backend, DataMut, Module, Scratch},
+    layouts::{Backend, DataMut, Module, Scratch},
     source::Source,
 };
 
@@ -16,6 +17,8 @@ AutomorphismKey, AutomorphismKeyToMut, GGLWEInfos, GLWEInfos, GLWESecret, GLWESecretToRef, GLWESwitchingKey, LWEInfos,
     },
 };
 
+impl AutomorphismKey<Vec<u8>> {
+    pub fn encrypt_sk_tmp_bytes<BE: Backend, A>(module: &Module<BE>, infos: &A) -> usize
 impl AutomorphismKey<Vec<u8>> {
     pub fn encrypt_sk_tmp_bytes<BE: Backend, A>(module: &Module<BE>, infos: &A) -> usize
     where
@@ -28,8 +31,10 @@ infos.rank_out(),
             "rank_in != rank_out is not supported for GGLWEAutomorphismKey"
         );
         GLWESwitchingKey::encrypt_sk_tmp_bytes(module, infos) + GLWESecret::bytes_of_from_infos(module, &infos.glwe_layout())
+        GLWESwitchingKey::encrypt_sk_tmp_bytes(module, infos) + GLWESecret::bytes_of_from_infos(module, &infos.glwe_layout())
     }
 
+    pub fn encrypt_pk_tmp_bytes<BE: Backend, A>(module: &Module<BE>, _infos: &A) -> usize
     pub fn encrypt_pk_tmp_bytes<BE: Backend, A>(module: &Module<BE>, _infos: &A) -> usize
     where
         A: GGLWEInfos,
@@ -40,6 +45,7 @@ _infos.rank_out(),
             "rank_in != rank_out is not supported for GGLWEAutomorphismKey"
         );
         GLWESwitchingKey::encrypt_pk_tmp_bytes(module, _infos)
+        GLWESwitchingKey::encrypt_pk_tmp_bytes(module, _infos)
     }
 }
 
@@ -62,12 +68,34 @@ where
     Self: AutomorphismKeyToMut,
 {
     pub fn encrypt_sk<S, BE: Backend>(
+pub trait GGLWEAutomorphismKeyEncryptSk<BE: Backend> {
+    fn gglwe_automorphism_key_encrypt_sk<A, B>(
+        &self,
+        res: &mut A,
+        p: i64,
+        sk: &B,
+        source_xa: &mut Source,
+        source_xe: &mut Source,
+        scratch: &mut Scratch<BE>,
+    ) where
+        A: AutomorphismKeyToMut,
+        B: GLWESecretToRef;
+}
+
+impl<DM: DataMut> AutomorphismKey<DM>
+where
+    Self: AutomorphismKeyToMut,
+{
+    pub fn encrypt_sk<S, BE: Backend>(
         &mut self,
+        module: &Module<BE>,
         module: &Module<BE>,
         p: i64,
         sk: &S,
+        sk: &S,
         source_xa: &mut Source,
         source_xe: &mut Source,
+        scratch: &mut Scratch<BE>,
         scratch: &mut Scratch<BE>,
     ) where
         S: GLWESecretToRef,
@@ -124,10 +152,16 @@
             assert_eq!(res.n(), sk.n());
             assert_eq!(res.rank_out(), res.rank_in());
             assert_eq!(sk.rank(), res.rank_out());
+            assert_eq!(res.n(), sk.n());
+            assert_eq!(res.rank_out(), res.rank_in());
+            assert_eq!(sk.rank(), res.rank_out());
             assert!(
                 scratch.available() >= AutomorphismKey::encrypt_sk_tmp_bytes(self, res),
                 "scratch.available(): {} < AutomorphismKey::encrypt_sk_tmp_bytes: {:?}",
+                scratch.available() >= AutomorphismKey::encrypt_sk_tmp_bytes(self, res),
+                "scratch.available(): {} < AutomorphismKey::encrypt_sk_tmp_bytes: {:?}",
                 scratch.available(),
+                AutomorphismKey::encrypt_sk_tmp_bytes(self, res)
                 AutomorphismKey::encrypt_sk_tmp_bytes(self, res)
             )
         }
@@ -138,6 +172,9 @@ {
             (0..res.rank_out().into()).for_each(|i| {
                 self.vec_znx_automorphism(
                     self.galois_element_inv(p),
+            (0..res.rank_out().into()).for_each(|i| {
+                self.vec_znx_automorphism(
+                    self.galois_element_inv(p),
                     &mut sk_out.data.as_vec_znx_mut(),
                     i,
                     &sk.data.as_vec_znx(),
@@ -148,7 +185,10 @@ }
 
         res.key
             .encrypt_sk(self, sk, &sk_out, source_xa, source_xe, scratch_1);
+        res.key
+            .encrypt_sk(self, sk, &sk_out, source_xa, source_xe, scratch_1);
 
+        res.p = p;
         res.p = p;
     }
 }

@@ -1,19 +1,16 @@
 use std::collections::HashMap;
 
 use poulpy_hal::{
-    api::{
-        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,
-    },
-    layouts::{Backend, DataMut, DataRef, Module, Scratch},
+    api::{ModuleLogN, VecZnxCopy, VecZnxRotateInplace},
+    layouts::{Backend, DataMut, DataRef, GaloisElement, Module, Scratch},
 };
 
 use crate::{
-    GLWEOperations,
-    layouts::{GGLWEInfos, GLWE, GLWEInfos, LWEInfos, prepared::AutomorphismKeyPrepared},
+    GLWEAdd, GLWEAutomorphism, GLWENormalize, GLWERotate, GLWEShift, GLWESub, ScratchTakeCore,
+    layouts::{
+        GGLWEInfos, GLWE, GLWEAlloc, GLWEInfos, GLWEToMut, GLWEToRef, LWEInfos,
+        prepared::{AutomorphismKeyPreparedToRef, GetAutomorphismGaloisElement},
+    },
 };
 
 /// [GLWEPacker] enables only the fly GLWE packing
@@ -43,9 +40,10 @@ /// * `module`: static backend FFT tables.
     /// * `base2k`: base 2 logarithm of the GLWE ciphertext in memory digit representation.
     /// * `k`: base 2 precision of the GLWE ciphertext precision over the Torus.
     /// * `rank`: rank of the GLWE ciphertext.
-    pub fn alloc<A, B: Backend>(module: &Module<B>, infos: &A) -> Self
+    pub fn alloc<A, M>(module: &M, infos: &A) -> Self
     where
         A: GLWEInfos,
+        M: GLWEAlloc,
     {
         Self {
             data: GLWE::alloc_from_infos(module, infos),
@@ -66,9 +64,10 @@ ///   i.e. with `log_batch=0` only the constant coefficient is packed
     ///   and N GLWE ciphertext can be packed. With `log_batch=2` all coefficients
     ///   which are multiples of X^{N/4} are packed. Meaning that N/4 ciphertexts
     ///   can be packed.
-    pub fn new<A, B: Backend>(module: Module<B>, infos: &A, log_batch: usize) -> Self
+    pub fn new<A, M>(module: &M, infos: &A, log_batch: usize) -> Self
     where
         A: GLWEInfos,
+        M: GLWEAlloc,
     {
         let mut accumulators: Vec<Accumulator> = Vec::<Accumulator>::new();
         let log_n: usize = infos.n().log2();
@@ -90,13 +89,13 @@ self.counter = 0;
     }
 
     /// Number of scratch space bytes required to call [Self::add].
-    pub fn tmp_bytes<B: Backend, OUT, KEY>(module: &Module<B>, out_infos: &OUT, key_infos: &KEY) -> usize
+    pub fn tmp_bytes<R, K, M, BE: Backend>(module: &M, res_infos: &R, key_infos: &K) -> usize
     where
-        OUT: GLWEInfos,
-        KEY: GGLWEInfos,
-        Module<B>: VecZnxDftBytesOf + VmpApplyDftToDftTmpBytes + VecZnxBigNormalizeTmpBytes + VecZnxNormalizeTmpBytes,
+        R: GLWEInfos,
+        K: GGLWEInfos,
+        M: GLWEAlloc + GLWEAutomorphism<BE>,
     {
-        pack_core_tmp_bytes(module, out_infos, key_infos)
+        pack_core_tmp_bytes(module, res_infos, key_infos)
     }
 
     pub fn galois_elements<B: Backend>(module: &Module<B>) -> Vec<i64> {
@@ -112,37 +111,12 @@ ///   of packed ciphertexts reaches N/2^log_batch is a result written.
     /// * `a`: ciphertext to pack. Can optionally give None to pack a 0 ciphertext.
     /// * `auto_keys`: a [HashMap] containing the [AutomorphismKeyExec]s.
     /// * `scratch`: scratch space of size at least [Self::tmp_bytes].
-    pub fn add<DataA: DataRef, DataAK: DataRef, B: Backend>(
-        &mut self,
-        module: &Module<B>,
-        a: Option<&GLWE<DataA>>,
-        auto_keys: &HashMap<i64, AutomorphismKeyPrepared<DataAK, B>>,
-        scratch: &mut Scratch<B>,
-    ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxCopy
-            + VecZnxRotateInplace<B>
-            + VecZnxSub
-            + VecZnxNegateInplace
-            + VecZnxRshInplace<B>
-            + VecZnxAddInplace
-            + VecZnxNormalizeInplace<B>
-            + VecZnxSubInplace
-            + VecZnxRotate
-            + VecZnxAutomorphismInplace<B>
-            + VecZnxBigSubSmallNegateInplace<B>
-            + VecZnxBigAutomorphismInplace<B>
-            + VecZnxNormalize<B>
-            + VecZnxNormalizeTmpBytes,
-        Scratch<B>: ScratchAvailable,
+    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>,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
         assert!(
             (self.counter as u32) < self.accumulators[0].data.n(),
@@ -177,47 +151,27 @@ self.reset();
     }
 }
 
-fn pack_core_tmp_bytes<B: Backend, OUT, KEY>(module: &Module<B>, out_infos: &OUT, key_infos: &KEY) -> usize
+fn pack_core_tmp_bytes<R, K, M, BE: Backend>(module: &M, res_infos: &R, key_infos: &K) -> usize
 where
-    OUT: GLWEInfos,
-    KEY: GGLWEInfos,
-    Module<B>: VecZnxDftBytesOf + VmpApplyDftToDftTmpBytes + VecZnxBigNormalizeTmpBytes + VecZnxNormalizeTmpBytes,
+    R: GLWEInfos,
+    K: GGLWEInfos,
+    M: GLWEAlloc + GLWEAutomorphism<BE>,
 {
-    combine_tmp_bytes(module, out_infos, key_infos)
+    combine_tmp_bytes(module, res_infos, key_infos)
 }
 
-fn pack_core<D: DataRef, DataAK: DataRef, B: Backend>(
-    module: &Module<B>,
-    a: Option<&GLWE<D>>,
+fn pack_core<A, K, M, BE: Backend>(
+    module: &M,
+    a: Option<&A>,
     accumulators: &mut [Accumulator],
     i: usize,
-    auto_keys: &HashMap<i64, AutomorphismKeyPrepared<DataAK, B>>,
-    scratch: &mut Scratch<B>,
+    auto_keys: &HashMap<i64, K>,
+    scratch: &mut Scratch<BE>,
 ) where
-    Module<B>: VecZnxDftBytesOf
-        + VmpApplyDftToDftTmpBytes
-        + VecZnxBigNormalizeTmpBytes
-        + VmpApplyDftToDft<B>
-        + VmpApplyDftToDftAdd<B>
-        + VecZnxDftApply<B>
-        + VecZnxIdftApplyConsume<B>
-        + VecZnxBigAddSmallInplace<B>
-        + VecZnxBigNormalize<B>
-        + VecZnxCopy
-        + VecZnxRotateInplace<B>
-        + VecZnxSub
-        + VecZnxNegateInplace
-        + VecZnxRshInplace<B>
-        + VecZnxAddInplace
-        + VecZnxNormalizeInplace<B>
-        + VecZnxSubInplace
-        + VecZnxRotate
-        + VecZnxAutomorphismInplace<B>
-        + VecZnxBigSubSmallNegateInplace<B>
-        + VecZnxBigAutomorphismInplace<B>
-        + VecZnxNormalize<B>
-        + VecZnxNormalizeTmpBytes,
-    Scratch<B>: ScratchAvailable,
+    A: GLWEToRef + GLWEInfos,
+    K: AutomorphismKeyPreparedToRef<BE>,
+    M: GLWEAutomorphism<BE> + ModuleLogN + VecZnxCopy,
+    Scratch<BE>: ScratchTakeCore<BE>,
 {
     let log_n: usize = module.log_n();
 
@@ -268,49 +222,29 @@ }
     }
 }
 
-fn combine_tmp_bytes<B: Backend, OUT, KEY>(module: &Module<B>, out_infos: &OUT, key_infos: &KEY) -> usize
+fn combine_tmp_bytes<R, K, M, BE: Backend>(module: &M, res_infos: &R, key_infos: &K) -> usize
 where
-    OUT: GLWEInfos,
-    KEY: GGLWEInfos,
-    Module<B>: VecZnxDftBytesOf + VmpApplyDftToDftTmpBytes + VecZnxBigNormalizeTmpBytes + VecZnxNormalizeTmpBytes,
+    R: GLWEInfos,
+    K: GGLWEInfos,
+    M: GLWEAlloc + GLWEAutomorphism<BE>,
 {
-    GLWE::bytes_of_from_infos(module, out_infos)
-        + (GLWE::rsh_tmp_bytes(module.n()) | GLWE::automorphism_inplace_tmp_bytes(module, out_infos, key_infos))
+    GLWE::bytes_of_from_infos(module, res_infos)
+        + (GLWE::rsh_tmp_bytes(module.n()) | module.glwe_automorphism_tmp_bytes(res_infos, res_infos, key_infos))
 }
 
 /// [combine] merges two ciphertexts together.
-fn combine<D: DataRef, DataAK: DataRef, B: Backend>(
-    module: &Module<B>,
+fn combine<B, M, K, BE: Backend>(
+    module: &M,
     acc: &mut Accumulator,
-    b: Option<&GLWE<D>>,
+    b: Option<&B>,
     i: usize,
-    auto_keys: &HashMap<i64, AutomorphismKeyPrepared<DataAK, B>>,
-    scratch: &mut Scratch<B>,
+    auto_keys: &HashMap<i64, K>,
+    scratch: &mut Scratch<BE>,
 ) where
-    Module<B>: VecZnxDftBytesOf
-        + VmpApplyDftToDftTmpBytes
-        + VecZnxBigNormalizeTmpBytes
-        + VmpApplyDftToDft<B>
-        + VmpApplyDftToDftAdd<B>
-        + VecZnxDftApply<B>
-        + VecZnxIdftApplyConsume<B>
-        + VecZnxBigAddSmallInplace<B>
-        + VecZnxBigNormalize<B>
-        + VecZnxCopy
-        + VecZnxRotateInplace<B>
-        + VecZnxSub
-        + VecZnxNegateInplace
-        + VecZnxRshInplace<B>
-        + VecZnxAddInplace
-        + VecZnxNormalizeInplace<B>
-        + VecZnxSubInplace
-        + VecZnxRotate
-        + VecZnxAutomorphismInplace<B>
-        + VecZnxBigSubSmallNegateInplace<B>
-        + VecZnxBigAutomorphismInplace<B>
-        + VecZnxNormalize<B>
-        + VecZnxNormalizeTmpBytes,
-    Scratch<B>: ScratchAvailable,
+    B: GLWEToRef + GLWEInfos,
+    K: AutomorphismKeyPreparedToRef<BE>,
+    M: GLWEAutomorphism<BE> + GaloisElement + VecZnxRotateInplace<BE>,
+    Scratch<BE>: ScratchTakeCore<BE>,
 {
     let log_n: usize = acc.data.n().log2();
     let a: &mut GLWE<Vec<u8>> = &mut acc.data;
@@ -335,7 +269,7 @@ // 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_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);
@@ -390,110 +324,76 @@ acc.value = true;
     }
 }
 
-/// 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
+        + GLWERotate<BE>
+        + GLWESub
+        + GLWEShift<BE>
+        + GLWEAdd
+        + GLWENormalize<BE>,
 {
-    #[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 + GLWEToRef + GLWEInfos,
+        K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+        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));
+        for i in 0..(log_n - log_gap_out){
+            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));
+            for j in 0..t{
+                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> + GLWERotate<BE> + GLWESub + GLWEShift<BE> + GLWEAdd + GLWENormalize<BE>,
+    A: GLWEToMut + GLWEToRef + GLWEInfos,
+    B: GLWEToMut + GLWEToRef + GLWEInfos,
+    K: AutomorphismKeyPreparedToRef<BE> + GetAutomorphismGaloisElement,
+    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)
@@ -509,45 +409,45 @@ if let Some(a) = a.as_deref_mut() {
         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);
+            module.glwe_rotate_inplace(-t, a, scratch_1);
 
             // tmp_b = a * X^-t - b
-            tmp_b.sub(module, a, b);
-            tmp_b.rsh(module, 1, scratch_1);
+            module.glwe_sub(&mut tmp_b, a, b);
+            module.glwe_rsh(1, &mut tmp_b, scratch_1);
 
             // a = a * X^-t + b
-            a.add_inplace(module, b);
-            a.rsh(module, 1, scratch_1);
+            module.glwe_add_inplace(a, b);
+            module.glwe_rsh(1, a, scratch_1);
 
-            tmp_b.normalize_inplace(module, scratch_1);
+            module.glwe_normalize_inplace(&mut tmp_b, scratch_1);
 
             // tmp_b = phi(a * X^-t - b)
-            tmp_b.automorphism_inplace(module, auto_key, scratch_1);
+            module.glwe_automorphism_inplace(&mut tmp_b, auto_key, scratch_1);
 
             // a = a * X^-t + b - phi(a * X^-t - b)
-            a.sub_inplace_ab(module, &tmp_b);
-            a.normalize_inplace(module, scratch_1);
+            module.glwe_sub_inplace(a, &tmp_b);
+            module.glwe_normalize_inplace(a, scratch_1);
 
             // a = a + b * X^t - phi(a * X^-t - b) * X^t
             //   = a + b * X^t - phi(a * X^-t - b) * - phi(X^t)
             //   = a + b * X^t + phi(a - b * X^t)
-            a.rotate_inplace(module, t, scratch_1);
+            module.glwe_rotate_inplace(t, a, scratch_1);
         } else {
-            a.rsh(module, 1, scratch);
+            module.glwe_rsh(1, a, scratch);
             // a = a + phi(a)
-            a.automorphism_add_inplace(module, auto_key, scratch);
+            module.glwe_automorphism_add_inplace(a, auto_key, scratch);
         }
     } else if let Some(b) = b.as_deref_mut() {
         let t: i64 = 1 << (b.n().log2() - i - 1);
 
-        let (mut tmp_b, scratch_1) = scratch.take_glwe_ct(b);
-        tmp_b.rotate(module, t, b);
-        tmp_b.rsh(module, 1, scratch_1);
+        let (mut tmp_b, scratch_1) = scratch.take_glwe_ct(module, b);
+        module.glwe_rotate(t, &mut tmp_b, b);
+        module.glwe_rsh(1, &mut tmp_b, scratch_1);
 
         // a = (b* X^t - phi(b* X^t))
-        b.automorphism_sub_negate(module, &tmp_b, auto_key, scratch_1);
+        module.glwe_automorphism_sub_negate(b, &tmp_b, auto_key, scratch_1);
     }
 }

@@ -1,173 +1,188 @@
 use std::collections::HashMap;
 
 use poulpy_hal::{
-    api::{
-        ScratchAvailable, VecZnxBigAddSmallInplace, VecZnxBigAutomorphismInplace, VecZnxBigNormalize, VecZnxBigNormalizeTmpBytes,
-        VecZnxCopy, VecZnxDftApply, VecZnxDftBytesOf, VecZnxIdftApplyConsume, VecZnxNormalize, VecZnxNormalizeTmpBytes,
-        VecZnxRshInplace, VmpApplyDftToDft, VmpApplyDftToDftAdd, VmpApplyDftToDftTmpBytes,
-    },
-    layouts::{Backend, DataMut, DataRef, Module, Scratch, VecZnx},
+    api::ModuleLogN,
+    layouts::{Backend, DataMut, GaloisElement, Module, Scratch, VecZnx},
 };
 
 use crate::{
-    layouts::{Base2K, GGLWEInfos, GLWE, GLWEInfos, GLWELayout, LWEInfos, prepared::AutomorphismKeyPrepared},
-    operations::GLWEOperations,
+    GLWEAutomorphism, GLWECopy, GLWEShift, ScratchTakeCore,
+    layouts::{
+        Base2K, GGLWEInfos, GLWE, GLWEInfos, GLWELayout, GLWEToMut, GLWEToRef, LWEInfos,
+        prepared::{AutomorphismKeyPreparedToRef, GetAutomorphismGaloisElement},
+    },
 };
 
 impl GLWE<Vec<u8>> {
-    pub fn trace_galois_elements<B: Backend>(module: &Module<B>) -> Vec<i64> {
-        let mut gal_els: Vec<i64> = Vec::new();
-        (0..module.log_n()).for_each(|i| {
-            if i == 0 {
-                gal_els.push(-1);
-            } else {
-                gal_els.push(module.galois_element(1 << (i - 1)));
-            }
-        });
-        gal_els
-    }
-
-    pub fn trace_tmp_bytes<B: Backend, OUT, IN, KEY>(module: &Module<B>, out_infos: &OUT, in_infos: &IN, key_infos: &KEY) -> usize
+    pub fn trace_galois_elements<M, BE: Backend>(module: &M) -> Vec<i64>
     where
-        OUT: GLWEInfos,
-        IN: GLWEInfos,
-        KEY: GGLWEInfos,
-        Module<B>: VecZnxDftBytesOf + VmpApplyDftToDftTmpBytes + VecZnxBigNormalizeTmpBytes + VecZnxNormalizeTmpBytes,
+        M: GLWETrace<BE>,
     {
-        let trace: usize = Self::automorphism_inplace_tmp_bytes(module, out_infos, key_infos);
-        if in_infos.base2k() != key_infos.base2k() {
-            let glwe_conv: usize = VecZnx::bytes_of(
-                module.n(),
-                (key_infos.rank_out() + 1).into(),
-                out_infos.k().min(in_infos.k()).div_ceil(key_infos.base2k()) as usize,
-            ) + module.vec_znx_normalize_tmp_bytes();
-            return glwe_conv + trace;
-        }
-
-        trace
+        module.glwe_trace_galois_elements()
     }
 
-    pub fn trace_inplace_tmp_bytes<B: Backend, OUT, KEY>(module: &Module<B>, out_infos: &OUT, key_infos: &KEY) -> usize
+    pub fn trace_tmp_bytes<R, A, K, M, BE: Backend>(module: &M, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
     where
-        OUT: GLWEInfos,
-        KEY: GGLWEInfos,
-        Module<B>: VecZnxDftBytesOf + VmpApplyDftToDftTmpBytes + VecZnxBigNormalizeTmpBytes + VecZnxNormalizeTmpBytes,
+        R: GLWEInfos,
+        A: GLWEInfos,
+        K: GGLWEInfos,
+        M: GLWETrace<BE>,
     {
-        Self::trace_tmp_bytes(module, out_infos, out_infos, key_infos)
+        module.glwe_automorphism_tmp_bytes(res_infos, a_infos, key_infos)
     }
 }
 
-impl<DataSelf: DataMut> GLWE<DataSelf> {
-    pub fn trace<DataLhs: DataRef, DataAK: DataRef, B: Backend>(
+impl<D: DataMut> GLWE<D> {
+    pub fn trace<A, K, M, BE: Backend>(
         &mut self,
-        module: &Module<B>,
+        module: &M,
         start: usize,
         end: usize,
-        lhs: &GLWE<DataLhs>,
-        auto_keys: &HashMap<i64, AutomorphismKeyPrepared<DataAK, B>>,
-        scratch: &mut Scratch<B>,
+        a: &A,
+        keys: &HashMap<i64, K>,
+        scratch: &mut Scratch<BE>,
     ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxBigAutomorphismInplace<B>
-            + VecZnxRshInplace<B>
-            + VecZnxCopy
-            + VecZnxNormalizeTmpBytes
-            + VecZnxNormalize<B>,
-        Scratch<B>: ScratchAvailable,
+        A: GLWEToRef,
+        K: AutomorphismKeyPreparedToRef<BE> + GGLWEInfos + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+        M: GLWETrace<BE>,
     {
-        self.copy(module, lhs);
-        self.trace_inplace(module, start, end, auto_keys, scratch);
+        module.glwe_trace(self, start, end, a, keys, scratch);
     }
 
-    pub fn trace_inplace<DataAK: DataRef, B: Backend>(
+    pub fn trace_inplace<K, M, BE: Backend>(
         &mut self,
-        module: &Module<B>,
+        module: &M,
         start: usize,
         end: usize,
-        auto_keys: &HashMap<i64, AutomorphismKeyPrepared<DataAK, B>>,
-        scratch: &mut Scratch<B>,
+        keys: &HashMap<i64, K>,
+        scratch: &mut Scratch<BE>,
     ) where
-        Module<B>: VecZnxDftBytesOf
-            + VmpApplyDftToDftTmpBytes
-            + VecZnxBigNormalizeTmpBytes
-            + VmpApplyDftToDft<B>
-            + VmpApplyDftToDftAdd<B>
-            + VecZnxDftApply<B>
-            + VecZnxIdftApplyConsume<B>
-            + VecZnxBigAddSmallInplace<B>
-            + VecZnxBigNormalize<B>
-            + VecZnxBigAutomorphismInplace<B>
-            + VecZnxRshInplace<B>
-            + VecZnxNormalizeTmpBytes
-            + VecZnxNormalize<B>,
-        Scratch<B>: ScratchAvailable,
+        K: AutomorphismKeyPreparedToRef<BE> + GGLWEInfos + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+        M: GLWETrace<BE>,
+    {
+        module.glwe_trace_inplace(self, start, end, keys, scratch);
+    }
+}
+
+impl<BE: Backend> GLWETrace<BE> for Module<BE> where
+    Self: ModuleLogN + GaloisElement + GLWEAutomorphism<BE> + GLWEShift<BE> + GLWECopy
+{
+}
+
+pub trait GLWETrace<BE: Backend>
+where
+    Self: ModuleLogN + GaloisElement + GLWEAutomorphism<BE> + GLWEShift<BE> + GLWECopy,
+{
+    fn glwe_trace_galois_elements(&self) -> Vec<i64> {
+        (0..self.log_n())
+            .map(|i| {
+                if i == 0 {
+                    -1
+                } else {
+                    self.galois_element(1 << (i - 1))
+                }
+            })
+            .collect()
+    }
+
+    fn glwe_trace_tmp_bytes<R, A, K>(&self, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
+    where
+        R: GLWEInfos,
+        A: GLWEInfos,
+        K: GGLWEInfos,
     {
-        let basek_ksk: Base2K = auto_keys
-            .get(auto_keys.keys().next().unwrap())
-            .unwrap()
-            .base2k();
+        let trace: usize = self.glwe_automorphism_tmp_bytes(res_infos, a_infos, key_infos);
+        if a_infos.base2k() != key_infos.base2k() {
+            let glwe_conv: usize = VecZnx::bytes_of(
+                self.n(),
+                (key_infos.rank_out() + 1).into(),
+                res_infos.k().min(a_infos.k()).div_ceil(key_infos.base2k()) as usize,
+            ) + self.vec_znx_normalize_tmp_bytes();
+            return glwe_conv + trace;
+        }
+
+        trace
+    }
+
+    fn glwe_trace<R, A, K>(&self, res: &mut R, start: usize, end: usize, a: &A, keys: &HashMap<i64, K>, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        A: GLWEToRef,
+        K: AutomorphismKeyPreparedToRef<BE> + GGLWEInfos + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        self.glwe_copy(res, a);
+        self.glwe_trace_inplace(res, start, end, keys, scratch);
+    }
+
+    fn glwe_trace_inplace<R, K>(&self, res: &mut R, start: usize, end: usize, keys: &HashMap<i64, K>, scratch: &mut Scratch<BE>)
+    where
+        R: GLWEToMut,
+        K: AutomorphismKeyPreparedToRef<BE> + GGLWEInfos + GetAutomorphismGaloisElement,
+        Scratch<BE>: ScratchTakeCore<BE>,
+    {
+        let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
+
+        let basek_ksk: Base2K = keys.get(keys.keys().next().unwrap()).unwrap().base2k();
 
         #[cfg(debug_assertions)]
         {
-            assert_eq!(self.n(), module.n() as u32);
+            assert_eq!(res.n(), self.n() as u32);
             assert!(start < end);
-            assert!(end <= module.log_n());
-            for key in auto_keys.values() {
-                assert_eq!(key.n(), module.n() as u32);
+            assert!(end <= self.log_n());
+            for key in keys.values() {
+                assert_eq!(key.n(), self.n() as u32);
                 assert_eq!(key.base2k(), basek_ksk);
-                assert_eq!(key.rank_in(), self.rank());
-                assert_eq!(key.rank_out(), self.rank());
+                assert_eq!(key.rank_in(), res.rank());
+                assert_eq!(key.rank_out(), res.rank());
             }
         }
 
-        if self.base2k() != basek_ksk {
-            let (mut self_conv, scratch_1) = scratch.take_glwe_ct(&GLWELayout {
-                n: module.n().into(),
-                base2k: basek_ksk,
-                k: self.k(),
-                rank: self.rank(),
-            });
+        if res.base2k() != basek_ksk {
+            let (mut self_conv, scratch_1) = scratch.take_glwe_ct(
+                self,
+                &GLWELayout {
+                    n: self.n().into(),
+                    base2k: basek_ksk,
+                    k: res.k(),
+                    rank: res.rank(),
+                },
+            );
 
-            for j in 0..(self.rank() + 1).into() {
-                module.vec_znx_normalize(
+            for j in 0..(res.rank() + 1).into() {
+                self.vec_znx_normalize(
                     basek_ksk.into(),
                     &mut self_conv.data,
                     j,
                     basek_ksk.into(),
-                    &self.data,
+                    res.data(),
                     j,
                     scratch_1,
                 );
             }
 
             for i in start..end {
-                self_conv.rsh(module, 1, scratch_1);
+                self.glwe_rsh(1, &mut self_conv, scratch_1);
 
                 let p: i64 = if i == 0 {
                     -1
                 } else {
-                    module.galois_element(1 << (i - 1))
+                    self.galois_element(1 << (i - 1))
                 };
 
-                if let Some(key) = auto_keys.get(&p) {
-                    self_conv.automorphism_add_inplace(module, key, scratch_1);
+                if let Some(key) = keys.get(&p) {
+                    self.glwe_automorphism_add_inplace(&mut self_conv, key, scratch_1);
                 } else {
-                    panic!("auto_keys[{p}] is empty")
+                    panic!("keys[{p}] is empty")
                 }
             }
 
-            for j in 0..(self.rank() + 1).into() {
-                module.vec_znx_normalize(
-                    self.base2k().into(),
-                    &mut self.data,
+            for j in 0..(res.rank() + 1).into() {
+                self.vec_znx_normalize(
+                    res.base2k().into(),
+                    res.data_mut(),
                     j,
                     basek_ksk.into(),
                     &self_conv.data,
@@ -177,18 +192,18 @@ );
             }
         } else {
             for i in start..end {
-                self.rsh(module, 1, scratch);
+                self.glwe_rsh(1, res, scratch);
 
                 let p: i64 = if i == 0 {
                     -1
                 } else {
-                    module.galois_element(1 << (i - 1))
+                    self.galois_element(1 << (i - 1))
                 };
 
-                if let Some(key) = auto_keys.get(&p) {
-                    self.automorphism_add_inplace(module, key, scratch);
+                if let Some(key) = keys.get(&p) {
+                    self.glwe_automorphism_add_inplace(res, key, scratch);
                 } else {
-                    panic!("auto_keys[{p}] is empty")
+                    panic!("keys[{p}] is empty")
                 }
             }
         }

@@ -2,7 +2,7 @@ use poulpy_hal::layouts::{Backend, DataMut, Module, Scratch};
 
 use crate::{
     ScratchTakeCore,
-    keyswitching::glwe_ct::GLWEKeySwitch,
+    keyswitching::glwe_ct::GLWEKeyswitch,
     layouts::{
         AutomorphismKey, AutomorphismKeyToRef, GGLWE, GGLWEInfos, GGLWEToMut, GGLWEToRef, GLWESwitchingKey,
         GLWESwitchingKeyToRef,
@@ -16,7 +16,7 @@ where
         R: GGLWEInfos,
         A: GGLWEInfos,
         K: GGLWEInfos,
-        M: GGLWEKeySwitch<BE>,
+        M: GGLWEKeyswitch<BE>,
     {
         module.glwe_keyswitch_tmp_bytes(res_infos, a_infos, key_infos)
     }
@@ -28,7 +28,7 @@ where
         A: AutomorphismKeyToRef,
         B: GLWESwitchingKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
-        M: GGLWEKeySwitch<BE>,
+        M: GGLWEKeyswitch<BE>,
     {
         module.gglwe_keyswitch(&mut self.key.key, &a.to_ref().key.key, b, scratch);
     }
@@ -37,7 +37,7 @@ pub fn keyswitch_inplace<A, M, BE: Backend>(&mut self, module: &M, a: &A, scratch: &mut Scratch<BE>)
     where
         A: GLWESwitchingKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
-        M: GGLWEKeySwitch<BE>,
+        M: GGLWEKeyswitch<BE>,
     {
         module.gglwe_keyswitch_inplace(&mut self.key.key, a, scratch);
     }
@@ -49,7 +49,7 @@ where
         R: GGLWEInfos,
         A: GGLWEInfos,
         K: GGLWEInfos,
-        M: GGLWEKeySwitch<BE>,
+        M: GGLWEKeyswitch<BE>,
     {
         module.glwe_keyswitch_tmp_bytes(res_infos, a_infos, key_infos)
     }
@@ -61,7 +61,7 @@ where
         A: GLWESwitchingKeyToRef,
         B: GLWESwitchingKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
-        M: GGLWEKeySwitch<BE>,
+        M: GGLWEKeyswitch<BE>,
     {
         module.gglwe_keyswitch(&mut self.key, &a.to_ref().key, b, scratch);
     }
@@ -70,7 +70,7 @@ pub fn keyswitch_inplace<A, M, BE: Backend>(&mut self, module: &M, a: &A, scratch: &mut Scratch<BE>)
     where
         A: GLWESwitchingKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
-        M: GGLWEKeySwitch<BE>,
+        M: GGLWEKeyswitch<BE>,
     {
         module.gglwe_keyswitch_inplace(&mut self.key, a, scratch);
     }
@@ -82,7 +82,7 @@ where
         R: GGLWEInfos,
         A: GGLWEInfos,
         K: GGLWEInfos,
-        M: GGLWEKeySwitch<BE>,
+        M: GGLWEKeyswitch<BE>,
     {
         module.glwe_keyswitch_tmp_bytes(res_infos, a_infos, key_infos)
     }
@@ -94,7 +94,7 @@ where
         A: GGLWEToRef,
         B: GLWESwitchingKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
-        M: GGLWEKeySwitch<BE>,
+        M: GGLWEKeyswitch<BE>,
     {
         module.gglwe_keyswitch(self, a, b, scratch);
     }
@@ -103,17 +103,17 @@ pub fn keyswitch_inplace<A, M, BE: Backend>(&mut self, module: &M, a: &A, scratch: &mut Scratch<BE>)
     where
         A: GLWESwitchingKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
-        M: GGLWEKeySwitch<BE>,
+        M: GGLWEKeyswitch<BE>,
     {
         module.gglwe_keyswitch_inplace(self, a, scratch);
     }
 }
 
-impl<BE: Backend> GGLWEKeySwitch<BE> for Module<BE> where Self: GLWEKeySwitch<BE> {}
+impl<BE: Backend> GGLWEKeyswitch<BE> for Module<BE> where Self: GLWEKeyswitch<BE> {}
 
-pub trait GGLWEKeySwitch<BE: Backend>
+pub trait GGLWEKeyswitch<BE: Backend>
 where
-    Self: GLWEKeySwitch<BE>,
+    Self: GLWEKeyswitch<BE>,
 {
     fn gglwe_keyswitch_tmp_bytes<R, A, K>(&self, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
     where

@@ -2,7 +2,7 @@ use poulpy_hal::layouts::{Backend, DataMut, Scratch, VecZnx};
 
 use crate::{
     GGSWExpandRows, ScratchTakeCore,
-    keyswitching::glwe_ct::GLWEKeySwitch,
+    keyswitching::glwe_ct::GLWEKeyswitch,
     layouts::{
         GGLWEInfos, GGSW, GGSWInfos, GGSWToMut, GGSWToRef,
         prepared::{GLWESwitchingKeyPreparedToRef, TensorKeyPreparedToRef},
@@ -22,7 +22,7 @@ R: GGSWInfos,
         A: GGSWInfos,
         K: GGLWEInfos,
         T: GGLWEInfos,
-        M: GGSWKeySwitch<BE>,
+        M: GGSWKeyswitch<BE>,
     {
         module.ggsw_keyswitch_tmp_bytes(res_infos, a_infos, key_infos, tsk_infos)
     }
@@ -35,7 +35,7 @@ A: GGSWToRef,
         K: GLWESwitchingKeyPreparedToRef<BE>,
         T: TensorKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
-        M: GGSWKeySwitch<BE>,
+        M: GGSWKeyswitch<BE>,
     {
         module.ggsw_keyswitch(self, a, key, tsk, scratch);
     }
@@ -45,15 +45,15 @@ where
         K: GLWESwitchingKeyPreparedToRef<BE>,
         T: TensorKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
-        M: GGSWKeySwitch<BE>,
+        M: GGSWKeyswitch<BE>,
     {
         module.ggsw_keyswitch_inplace(self, key, tsk, scratch);
     }
 }
 
-pub trait GGSWKeySwitch<BE: Backend>
+pub trait GGSWKeyswitch<BE: Backend>
 where
-    Self: GLWEKeySwitch<BE> + GGSWExpandRows<BE>,
+    Self: GLWEKeyswitch<BE> + GGSWExpandRows<BE>,
 {
     fn ggsw_keyswitch_tmp_bytes<R, A, K, T>(&self, res_infos: &R, a_infos: &A, key_infos: &K, tsk_infos: &T) -> usize
     where
@@ -127,5 +127,3 @@
         self.ggsw_expand_row(res, tsk, scratch);
     }
 }
-
-impl<DataSelf: DataMut> GGSW<DataSelf> {}

@@ -16,14 +16,14 @@ },
 };
 
 impl GLWE<Vec<u8>> {
-    pub fn keyswitch_tmp_bytes<M, R, A, B, BE: Backend>(module: &M, res_infos: &R, a_infos: &A, b_infos: &B) -> usize
+    pub fn keyswitch_tmp_bytes<M, R, A, B, BE: Backend>(module: &M, res_infos: &R, a_infos: &A, key_infos: &B) -> usize
     where
         R: GLWEInfos,
         A: GLWEInfos,
         B: GGLWEInfos,
-        M: GLWEKeySwitch<BE>,
+        M: GLWEKeyswitch<BE>,
     {
-        module.glwe_keyswitch_tmp_bytes(res_infos, a_infos, b_infos)
+        module.glwe_keyswitch_tmp_bytes(res_infos, a_infos, key_infos)
     }
 }
 
@@ -32,7 +32,7 @@ pub fn keyswitch<A, B, M, BE: Backend>(&mut self, module: &M, a: &A, b: &B, scratch: &mut Scratch<BE>)
     where
         A: GLWEToRef,
         B: GLWESwitchingKeyPreparedToRef<BE>,
-        M: GLWEKeySwitch<BE>,
+        M: GLWEKeyswitch<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         module.glwe_keyswitch(self, a, b, scratch);
@@ -41,14 +41,14 @@
     pub fn keyswitch_inplace<A, M, BE: Backend>(&mut self, module: &M, a: &A, scratch: &mut Scratch<BE>)
     where
         A: GLWESwitchingKeyPreparedToRef<BE>,
-        M: GLWEKeySwitch<BE>,
+        M: GLWEKeyswitch<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         module.glwe_keyswitch_inplace(self, a, scratch);
     }
 }
 
-impl<BE: Backend> GLWEKeySwitch<BE> for Module<BE> where
+impl<BE: Backend> GLWEKeyswitch<BE> for Module<BE> where
     Self: Sized
         + ModuleN
         + VecZnxDftBytesOf
@@ -69,7 +69,7 @@ + VecZnxNormalizeTmpBytes
 {
 }
 
-pub trait GLWEKeySwitch<BE: Backend>
+pub trait GLWEKeyswitch<BE: Backend>
 where
     Self: Sized
         + ModuleN
@@ -89,7 +89,7 @@ + VecZnxBigNormalize<BE>
         + VecZnxNormalize<BE>
         + VecZnxNormalizeTmpBytes,
 {
-    fn glwe_keyswitch_tmp_bytes<R, A, B>(&self, res_infos: &R, a_infos: &A, b_infos: &B) -> usize
+    fn glwe_keyswitch_tmp_bytes<R, A, B>(&self, res_infos: &R, a_infos: &A, key_infos: &B) -> usize
     where
         R: GLWEInfos,
         A: GLWEInfos,
@@ -97,44 +97,44 @@ B: GGLWEInfos,
     {
         let in_size: usize = a_infos
             .k()
-            .div_ceil(b_infos.base2k())
-            .div_ceil(b_infos.dsize().into()) as usize;
+            .div_ceil(key_infos.base2k())
+            .div_ceil(key_infos.dsize().into()) as usize;
         let out_size: usize = res_infos.size();
-        let ksk_size: usize = b_infos.size();
-        let res_dft: usize = self.bytes_of_vec_znx_dft((b_infos.rank_out() + 1).into(), ksk_size); // TODO OPTIMIZE
-        let ai_dft: usize = self.bytes_of_vec_znx_dft((b_infos.rank_in()).into(), in_size);
+        let ksk_size: usize = key_infos.size();
+        let res_dft: usize = self.bytes_of_vec_znx_dft((key_infos.rank_out() + 1).into(), ksk_size); // TODO OPTIMIZE
+        let ai_dft: usize = self.bytes_of_vec_znx_dft((key_infos.rank_in()).into(), in_size);
         let vmp: usize = self.vmp_apply_dft_to_dft_tmp_bytes(
             out_size,
             in_size,
             in_size,
-            (b_infos.rank_in()).into(),
-            (b_infos.rank_out() + 1).into(),
+            (key_infos.rank_in()).into(),
+            (key_infos.rank_out() + 1).into(),
             ksk_size,
-        ) + self.bytes_of_vec_znx_dft((b_infos.rank_in()).into(), in_size);
+        ) + self.bytes_of_vec_znx_dft((key_infos.rank_in()).into(), in_size);
         let normalize_big: usize = self.vec_znx_big_normalize_tmp_bytes();
-        if a_infos.base2k() == b_infos.base2k() {
+        if a_infos.base2k() == key_infos.base2k() {
             res_dft + ((ai_dft + vmp) | normalize_big)
-        } else if b_infos.dsize() == 1 {
+        } else if key_infos.dsize() == 1 {
             // In this case, we only need one column, temporary, that we can drop once a_dft is computed.
             let normalize_conv: usize = VecZnx::bytes_of(self.n(), 1, in_size) + self.vec_znx_normalize_tmp_bytes();
             res_dft + (((ai_dft + normalize_conv) | vmp) | normalize_big)
         } else {
             // Since we stride over a to get a_dft when dsize > 1, we need to store the full columns of a with in the base conversion.
-            let normalize_conv: usize = VecZnx::bytes_of(self.n(), (b_infos.rank_in()).into(), in_size);
+            let normalize_conv: usize = VecZnx::bytes_of(self.n(), (key_infos.rank_in()).into(), in_size);
             res_dft + ((ai_dft + normalize_conv + (self.vec_znx_normalize_tmp_bytes() | vmp)) | normalize_big)
         }
     }
 
-    fn glwe_keyswitch<R, A, B>(&self, res: &mut R, a: &A, b: &B, scratch: &mut Scratch<BE>)
+    fn glwe_keyswitch<R, A, K>(&self, res: &mut R, a: &A, key: &K, scratch: &mut Scratch<BE>)
     where
         R: GLWEToMut,
         A: GLWEToRef,
-        B: GLWESwitchingKeyPreparedToRef<BE>,
+        K: GLWESwitchingKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
         let a: &GLWE<&[u8]> = &a.to_ref();
-        let b: &GLWESwitchingKeyPrepared<&[u8], BE> = &b.to_ref();
+        let b: &GLWESwitchingKeyPrepared<&[u8], BE> = &key.to_ref();
 
         assert_eq!(
             a.rank(),
@@ -181,14 +181,14 @@ );
         })
     }
 
-    fn glwe_keyswitch_inplace<R, A>(&self, res: &mut R, a: &A, scratch: &mut Scratch<BE>)
+    fn glwe_keyswitch_inplace<R, K>(&self, res: &mut R, key: &K, scratch: &mut Scratch<BE>)
     where
         R: GLWEToMut,
-        A: GLWESwitchingKeyPreparedToRef<BE>,
+        K: GLWESwitchingKeyPreparedToRef<BE>,
         Scratch<BE>: ScratchTakeCore<BE>,
     {
         let res: &mut GLWE<&mut [u8]> = &mut res.to_mut();
-        let a: &GLWESwitchingKeyPrepared<&[u8], BE> = &a.to_ref();
+        let a: &GLWESwitchingKeyPrepared<&[u8], BE> = &key.to_ref();
 
         assert_eq!(
             res.rank(),
@@ -239,11 +239,11 @@ impl GLWE<Vec<u8>> {}
 
 impl<DataSelf: DataMut> GLWE<DataSelf> {}
 
-fn keyswitch_internal<BE: Backend, M, DR, DA, DB>(
+pub(crate) fn keyswitch_internal<BE: Backend, M, DR, DA, DB>(
     module: &M,
     mut res: VecZnxDft<DR, BE>,
     a: &GLWE<DA>,
-    b: &GLWESwitchingKeyPrepared<DB, BE>,
+    key: &GLWESwitchingKeyPrepared<DB, BE>,
     scratch: &mut Scratch<BE>,
 ) -> VecZnxBig<DR, BE>
 where
@@ -265,12 +265,12 @@ + VecZnxNormalize<BE>,
     Scratch<BE>: ScratchTakeCore<BE>,
 {
     let base2k_in: usize = a.base2k().into();
-    let base2k_out: usize = b.base2k().into();
+    let base2k_out: usize = key.base2k().into();
     let cols: usize = (a.rank() + 1).into();
     let a_size: usize = (a.size() * base2k_in).div_ceil(base2k_out);
-    let pmat: &VmpPMat<DB, BE> = &b.key.data;
+    let pmat: &VmpPMat<DB, BE> = &key.key.data;
 
-    if b.dsize() == 1 {
+    if key.dsize() == 1 {
         let (mut ai_dft, scratch_1) = scratch.take_vec_znx_dft(module, cols - 1, a.size());
 
         if base2k_in == base2k_out {
@@ -295,7 +295,7 @@ }
 
         module.vmp_apply_dft_to_dft(&mut res, &ai_dft, pmat, scratch_1);
     } else {
-        let dsize: usize = b.dsize().into();
+        let dsize: usize = key.dsize().into();
 
         let (mut ai_dft, scratch_1) = scratch.take_vec_znx_dft(module, cols - 1, a_size.div_ceil(dsize));
         ai_dft.data_mut().fill(0);

@@ -5,7 +5,7 @@ };
 
 use crate::{
     ScratchTakeCore,
-    keyswitching::glwe_ct::GLWEKeySwitch,
+    keyswitching::glwe_ct::GLWEKeyswitch,
     layouts::{
         GGLWEInfos, GLWE, GLWEAlloc, GLWELayout, LWE, LWEInfos, LWEToMut, LWEToRef, Rank, TorusPrecision,
         prepared::{LWESwitchingKeyPrepared, LWESwitchingKeyPreparedToRef},
@@ -40,7 +40,7 @@ impl<BE: Backend> LWEKeySwitch<BE> for Module<BE> where Self: LWEKeySwitch<BE> {}
 
 pub trait LWEKeySwitch<BE: Backend>
 where
-    Self: GLWEKeySwitch<BE> + GLWEAlloc,
+    Self: GLWEKeyswitch<BE> + GLWEAlloc,
 {
     fn lwe_keyswitch_tmp_bytes<R, A, K>(&self, res_infos: &R, a_infos: &A, key_infos: &K) -> usize
     where

@@ -2,3 +2,8 @@ mod gglwe_ct;
 mod ggsw_ct;
 mod glwe_ct;
 mod lwe_ct;
+
+pub use gglwe_ct::*;
+// pub use gglwe_ct::*;
+pub use glwe_ct::*;
+pub use lwe_ct::*;

@@ -6,6 +6,7 @@
 use crate::layouts::{
     Base2K, Dnum, Dsize, GGLWEInfos, GLWE, GLWEInfos, GLWESwitchingKey, GLWESwitchingKeyAlloc, GLWESwitchingKeyToMut,
     GLWESwitchingKeyToRef, LWEInfos, Rank, RingDegree, TorusPrecision,
+    prepared::{GetAutomorphismGaloisElement, SetAutomorphismGaloisElement},
 };
 use byteorder::{LittleEndian, ReadBytesExt, WriteBytesExt};
 
@@ -25,6 +26,18 @@ #[derive(PartialEq, Eq, Clone)]
 pub struct AutomorphismKey<D: Data> {
     pub(crate) key: GLWESwitchingKey<D>,
     pub(crate) p: i64,
+}
+
+impl<D: DataMut> SetAutomorphismGaloisElement for AutomorphismKey<D> {
+    fn set_p(&mut self, p: i64) {
+        self.p = p
+    }
+}
+
+impl<D: DataRef> GetAutomorphismGaloisElement for AutomorphismKey<D> {
+    fn p(&self) -> i64 {
+        self.p
+    }
 }
 
 impl<D: Data> AutomorphismKey<D> {

@@ -14,10 +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 encryption::SIGMA;
 

@@ -1,326 +1,342 @@
 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, Module, 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,
 {
-}
-
-impl<D: DataMut> GLWEOperations for GLWE<D> where GLWE<D>: GLWEToMut + GLWEInfos {}
-
-pub trait GLWEOperations: GLWEToMut + GLWEInfos + SetGLWEInfos + Sized {
-    fn add<A, B, BACKEND: Backend>(&mut self, module: &Module<BACKEND>, a: &A, b: &B)
+    fn glwe_add<R, A, B>(&self, res: &mut R, a: &A, b: &B)
     where
-        A: GLWEToRef + GLWEInfos,
-        B: GLWEToRef + GLWEInfos,
-        Module<BACKEND>: 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: &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 = (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_add(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);
             });
         }
 
-        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, BACKEND: Backend>(&mut self, module: &Module<BACKEND>, a: &A)
+    fn glwe_add_inplace<R, A>(&self, res: &mut R, a: &A)
     where
-        A: GLWEToRef + GLWEInfos,
-        Module<BACKEND>: 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_add_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, BACKEND: Backend>(&mut self, module: &Module<BACKEND>, a: &A, b: &B)
+impl<BE: Backend> GLWEAdd for Module<BE> where Self: ModuleN + VecZnxAdd + VecZnxCopy + VecZnxAddInplace {}
+
+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,
-        Module<BACKEND>: VecZnxSub + VecZnxCopy + VecZnxNegateInplace,
+        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_sub(&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);
-                module.vec_znx_negate_inplace(&mut self_mut.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 sub_inplace_ab<A, BACKEND: Backend>(&mut self, module: &Module<BACKEND>, a: &A)
+    fn glwe_sub_inplace<R, A>(&self, res: &mut R, a: &A)
     where
-        A: GLWEToRef + GLWEInfos,
-        Module<BACKEND>: VecZnxSubInplace,
+        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_sub_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_inplace_ba<A, BACKEND: Backend>(&mut self, module: &Module<BACKEND>, a: &A)
+    fn glwe_sub_negate_inplace<R, A>(&self, res: &mut R, a: &A)
     where
-        A: GLWEToRef + GLWEInfos,
-        Module<BACKEND>: 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!(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_negate_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 rotate<A, B: Backend>(&mut self, module: &Module<B>, k: i64, 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,
-        Module<B>: VecZnxRotate,
+        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();
 
-        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_rotate(k, &mut self_mut.data, i, &a_ref.data, i);
+            self.vec_znx_rotate(k, res.data_mut(), i, a.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<B: Backend>(&mut self, module: &Module<B>, k: i64, scratch: &mut Scratch<B>)
+    fn glwe_rotate_inplace<R>(&self, k: i64, res: &mut R, scratch: &mut Scratch<BE>)
     where
-        Module<B>: VecZnxRotateInplace<B>,
+        R: GLWEToMut,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        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);
+        (0..(res.rank() + 1).into()).for_each(|i| {
+            self.vec_znx_rotate_inplace(k, res.data_mut(), i, scratch);
         });
     }
+}
 
-    fn mul_xp_minus_one<A, B: Backend>(&mut self, module: &Module<B>, k: i64, a: &A)
+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
-        A: GLWEToRef + GLWEInfos,
-        Module<B>: 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();
 
-        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.rank(), a.rank());
 
-        (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);
-        });
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_mul_xp_minus_one(k, res.data_mut(), i, a.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 mul_xp_minus_one_inplace<B: Backend>(&mut self, module: &Module<B>, k: i64, scratch: &mut Scratch<B>)
+    fn glwe_mul_xp_minus_one_inplace<R>(&self, k: i64, res: &mut R, scratch: &mut Scratch<BE>)
     where
-        Module<B>: VecZnxMulXpMinusOneInplace<B>,
+        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_mul_xp_minus_one_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 copy<A, M>(&mut self, module: &M, 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: VecZnxCopy,
+        R: GLWEToMut,
+        A: GLWEToRef,
     {
-        #[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 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.rank(), a.rank());
 
-        (0..(self_mut.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_copy(&mut self_mut.data, i, &a_ref.data, i);
-        });
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_copy(res.data_mut(), i, a.data(), i);
+        }
 
-        self.set_k(a.k().min(self.max_k()));
-        self.set_base2k(a.base2k());
+        res.set_k(a.k().min(res.max_k()));
+        res.set_base2k(a.base2k());
     }
+}
 
-    fn rsh<B: Backend>(&mut self, module: &Module<B>, k: usize, scratch: &mut Scratch<B>)
+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
-        Module<B>: VecZnxRshInplace<B>,
+        R: GLWEToMut,
+        Scratch<BE>: ScratchTakeCore<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);
-        })
+        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);
+        }
     }
+}
 
-    fn normalize<A, B: Backend>(&mut self, module: &Module<B>, a: &A, scratch: &mut Scratch<B>)
+impl GLWE<Vec<u8>> {
+    pub fn rsh_tmp_bytes(n: usize) -> usize {
+        VecZnx::rsh_tmp_bytes(n)
+    }
+}
+
+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
-        A: GLWEToRef + GLWEInfos,
-        Module<B>: VecZnxNormalize<B>,
+        R: GLWEToMut,
+        A: GLWEToRef,
+        Scratch<BE>: ScratchTakeCore<BE>,
     {
-        #[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 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.rank(), a.rank());
 
-        (0..(self_mut.rank() + 1).into()).for_each(|i| {
-            module.vec_znx_normalize(
-                a.base2k().into(),
-                &mut self_mut.data,
+        for i in 0..res.rank().as_usize() + 1 {
+            self.vec_znx_normalize(
+                res.base2k().into(),
+                res.data_mut(),
                 i,
                 a.base2k().into(),
-                &a_ref.data,
+                a.data(),
                 i,
                 scratch,
             );
-        });
-        self.set_base2k(a.base2k());
-        self.set_k(a.k().min(self.k()));
+        }
+
+        res.set_k(a.k().min(res.k()));
     }
 
-    fn normalize_inplace<B: Backend>(&mut self, module: &Module<B>, scratch: &mut Scratch<B>)
+    fn glwe_normalize_inplace<R>(&self, res: &mut R, scratch: &mut Scratch<BE>)
     where
-        Module<B>: VecZnxNormalizeInplace<B>,
+        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_normalize_inplace(self_mut.base2k().into(), &mut self_mut.data, i, scratch);
-        });
-    }
-}
-
-impl GLWE<Vec<u8>> {
-    pub fn rsh_tmp_bytes(n: usize) -> usize {
-        VecZnx::rsh_tmp_bytes(n)
+        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);
+        }
     }
 }
 

@@ -8,3 +8,12 @@
 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
+    }
+}

@@ -2,7 +2,10 @@ use std::{fmt::Display, marker::PhantomData, ptr::NonNull};
 
 use rand_distr::num_traits::Zero;
 
-use crate::GALOISGENERATOR;
+use crate::{
+    GALOISGENERATOR,
+    api::{ModuleLogN, ModuleN},
+};
 
 #[allow(clippy::missing_safety_doc)]
 pub trait Backend: Sized {
@@ -75,35 +78,48 @@ #[inline]
     pub fn log_n(&self) -> usize {
         (usize::BITS - (self.n() - 1).leading_zeros()) as _
     }
+}
 
-    #[inline]
-    pub fn cyclotomic_order(&self) -> u64 {
+pub trait CyclotomicOrder
+where
+    Self: ModuleN,
+{
+    fn cyclotomic_order(&self) -> i64 {
         (self.n() << 1) as _
     }
+}
 
+impl<BE: Backend> ModuleLogN for Module<BE> where Self: ModuleN {}
+
+impl<BE: Backend> CyclotomicOrder for Module<BE> where Self: ModuleN {}
+
+pub trait GaloisElement
+where
+    Self: CyclotomicOrder,
+{
     // Returns GALOISGENERATOR^|generator| * sign(generator)
-    #[inline]
-    pub fn galois_element(&self, generator: i64) -> i64 {
+    fn galois_element(&self, generator: i64) -> i64 {
         if generator == 0 {
             return 1;
         }
-        ((mod_exp_u64(GALOISGENERATOR, generator.unsigned_abs() as usize) & (self.cyclotomic_order() - 1)) as i64)
-            * generator.signum()
+
+        let g_exp: u64 = mod_exp_u64(GALOISGENERATOR, generator.unsigned_abs() as usize) & (self.cyclotomic_order() - 1) as u64;
+        g_exp as i64 * generator.signum()
     }
 
     // Returns gen^-1
-    #[inline]
-    pub fn galois_element_inv(&self, gal_el: i64) -> i64 {
+    fn galois_element_inv(&self, gal_el: i64) -> i64 {
         if gal_el == 0 {
             panic!("cannot invert 0")
         }
-        ((mod_exp_u64(
-            gal_el.unsigned_abs(),
-            (self.cyclotomic_order() - 1) as usize,
-        ) & (self.cyclotomic_order() - 1)) as i64)
-            * gal_el.signum()
+
+        let g_exp: u64 =
+            mod_exp_u64(GALOISGENERATOR, (self.cyclotomic_order() - 1) as usize) & (self.cyclotomic_order() - 1) as u64;
+        g_exp as i64 * gal_el.signum()
     }
 }
+
+impl<BE: Backend> GaloisElement for Module<BE> where Self: CyclotomicOrder {}
 
 impl<B: Backend> Drop for Module<B> {
     fn drop(&mut self) {