diff --git a/base2k/src/scalar_znx.rs b/base2k/src/scalar_znx.rs
index 8da145f..fa812a8 100644
--- a/base2k/src/scalar_znx.rs
+++ b/base2k/src/scalar_znx.rs
@@ -130,7 +130,7 @@ pub trait ScalarZnxOps {
         A: ScalarZnxToRef;
 
     /// Applies the automorphism X^i -> X^ik on the selected column of `a`.
-    fn vec_znx_automorphism_inplace<A>(&self, k: i64, a: &mut A, a_col: usize)
+    fn scalar_znx_automorphism_inplace<A>(&self, k: i64, a: &mut A, a_col: usize)
     where
         A: ScalarZnxToMut;
 }
@@ -162,7 +162,7 @@ impl<B: Backend> ScalarZnxOps for Module<B> {
         }
     }
 
-    fn vec_znx_automorphism_inplace<A>(&self, k: i64, a: &mut A, a_col: usize)
+    fn scalar_znx_automorphism_inplace<A>(&self, k: i64, a: &mut A, a_col: usize)
     where
         A: ScalarZnxToMut,
     {
diff --git a/base2k/src/vec_znx_big.rs b/base2k/src/vec_znx_big.rs
index 8b3223b..eba90e9 100644
--- a/base2k/src/vec_znx_big.rs
+++ b/base2k/src/vec_znx_big.rs
@@ -1,6 +1,6 @@
 use crate::ffi::vec_znx_big;
 use crate::znx_base::{ZnxInfos, ZnxView};
-use crate::{Backend, DataView, DataViewMut, FFT64, Module, ZnxSliceSize, ZnxViewMut, ZnxZero, alloc_aligned};
+use crate::{alloc_aligned, Backend, DataView, DataViewMut, Module, VecZnx, ZnxSliceSize, ZnxViewMut, ZnxZero, FFT64};
 use std::fmt;
 use std::marker::PhantomData;
 
@@ -97,7 +97,18 @@ impl<D, B: Backend> VecZnxBig<D, B> {
 impl<D> VecZnxBig<D, FFT64>
 where
     VecZnxBig<D, FFT64>: VecZnxBigToMut<FFT64> + ZnxInfos,
-{
+{   
+    // Consumes the VecZnxBig to return a VecZnx. 
+    // Useful when no normalization is needed.
+    pub fn to_vec_znx_small(self) -> VecZnx<D>{
+        VecZnx{
+            data: self.data,
+            n: self.n,
+            cols: self.cols,
+            size: self.size,
+        }
+    }
+
     /// Extracts the a_col-th column of 'a' and stores it on the self_col-th column [Self].
     pub fn extract_column<C>(&mut self, self_col: usize, a: &VecZnxBig<C, FFT64>, a_col: usize)
     where
diff --git a/base2k/src/vec_znx_big_ops.rs b/base2k/src/vec_znx_big_ops.rs
index 8208c97..f6dad7a 100644
--- a/base2k/src/vec_znx_big_ops.rs
+++ b/base2k/src/vec_znx_big_ops.rs
@@ -147,6 +147,7 @@ pub trait VecZnxBigOps<BACKEND: Backend> {
     fn vec_znx_big_automorphism_inplace<A>(&self, k: i64, a: &mut A, a_col: usize)
     where
         A: VecZnxBigToMut<BACKEND>;
+
 }
 
 pub trait VecZnxBigScratch {
@@ -169,6 +170,7 @@ impl<B: Backend> VecZnxBigAlloc<B> for Module<B> {
 }
 
 impl VecZnxBigOps<FFT64> for Module<FFT64> {
+
     fn vec_znx_big_add<R, A, B>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize, b: &B, b_col: usize)
     where
         R: VecZnxBigToMut<FFT64>,
diff --git a/core/src/automorphism.rs b/core/src/automorphism.rs
index ed6a954..8741bf9 100644
--- a/core/src/automorphism.rs
+++ b/core/src/automorphism.rs
@@ -1,6 +1,6 @@
 use base2k::{
     Backend, FFT64, MatZnxDft, MatZnxDftOps, MatZnxDftToMut, MatZnxDftToRef, Module, ScalarZnx, ScalarZnxDftOps, ScalarZnxOps,
-    ScalarZnxToRef, Scratch, VecZnxDft, VecZnxDftToMut, VecZnxDftToRef,
+    ScalarZnxToRef, Scratch, VecZnx, VecZnxDft, VecZnxDftOps, VecZnxDftToMut, VecZnxDftToRef, VecZnxOps, ZnxZero,
 };
 use sampling::source::Source;
 
@@ -8,6 +8,7 @@ use crate::{
     elem::{GetRow, Infos, SetRow},
     gglwe_ciphertext::GGLWECiphertext,
     ggsw_ciphertext::GGSWCiphertext,
+    glwe_ciphertext::GLWECiphertext,
     glwe_ciphertext_fourier::GLWECiphertextFourier,
     keys::{SecretKey, SecretKeyFourier},
     keyswitch_key::GLWESwitchingKey,
@@ -203,6 +204,103 @@ impl<DataSelf> AutomorphismKey<DataSelf, FFT64>
 where
     MatZnxDft<DataSelf, FFT64>: MatZnxDftToMut<FFT64> + MatZnxDftToRef<FFT64>,
 {
+    pub fn automorphism<DataLhs, DataRhs>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &AutomorphismKey<DataLhs, FFT64>,
+        rhs: &AutomorphismKey<DataRhs, FFT64>,
+        scratch: &mut base2k::Scratch,
+    ) where
+        MatZnxDft<DataLhs, FFT64>: MatZnxDftToRef<FFT64>,
+        MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+    {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(
+                self.rank_in(),
+                lhs.rank_in(),
+                "ksk_out input rank: {} != ksk_in input rank: {}",
+                self.rank_in(),
+                lhs.rank_in()
+            );
+            assert_eq!(
+                lhs.rank_out(),
+                rhs.rank_in(),
+                "ksk_in output rank: {} != ksk_apply input rank: {}",
+                self.rank_out(),
+                rhs.rank_in()
+            );
+            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;
+
+        let (tmp_dft_data, scratch1) = scratch.tmp_vec_znx_dft(module, cols_out, lhs.size());
+
+        let mut tmp_dft: GLWECiphertextFourier<&mut [u8], FFT64> = GLWECiphertextFourier::<&mut [u8], FFT64> {
+            data: tmp_dft_data,
+            basek: lhs.basek(),
+            k: lhs.k(),
+        };
+
+        (0..self.rank_in()).for_each(|col_i| {
+            (0..self.rows()).for_each(|row_j| {
+                // Extracts relevant row
+                lhs.get_row(module, row_j, col_i, &mut tmp_dft);
+
+                // Get a VecZnxBig from scratch space
+                let (mut tmp_idft_data, scratch2) = scratch1.tmp_vec_znx_big(module, cols_out, self.size());
+
+                // Switches input outside of DFT
+                (0..cols_out).for_each(|i| {
+                    module.vec_znx_idft(&mut tmp_idft_data, i, &tmp_dft.data, i, scratch2);
+                });
+
+                // Consumes to small vec znx
+                let mut tmp_idft_small_data: VecZnx<&mut [u8]> = tmp_idft_data.to_vec_znx_small();
+
+                // Reverts the automorphis key from (-pi^{-1}_{k}(s)a + s, a) to (-sa + pi_{k}(s), a)
+                (0..cols_out).for_each(|i| {
+                    module.vec_znx_automorphism_inplace(self.p(), &mut tmp_idft_small_data, i);
+                });
+
+                // Wraps into ciphertext
+                let mut tmp_idft: GLWECiphertext<&mut [u8]> = GLWECiphertext::<&mut [u8]> {
+                    data: tmp_idft_small_data,
+                    basek: self.basek(),
+                    k: self.k(),
+                };
+
+                // Key-switch (-sa + pi_{k}(s), a) to (-pi^{-1}_{k'}(s)a + pi_{k}(s), a)
+                tmp_idft.keyswitch_inplace(module, &rhs.key, scratch2);
+
+                // Applies back the automorphism X^{k}: (-pi^{-1}_{k'}(s)a + pi_{k}(s), a) -> (-pi^{-1}_{k'+k}(s)a + s, a)
+                // and switches back to DFT domain
+                (0..self.rank_out() + 1).for_each(|i| {
+                    module.vec_znx_automorphism_inplace(rhs.p(), &mut tmp_idft, i);
+                    module.vec_znx_dft(&mut tmp_dft, i, &tmp_idft, i);
+                });
+
+                // Sets back the relevant row
+                self.set_row(module, row_j, col_i, &tmp_dft);
+            });
+        });
+
+        tmp_dft.data.zero();
+
+        (self.rows().min(lhs.rows())..self.rows()).for_each(|row_i| {
+            (0..self.rank_in()).for_each(|col_j| {
+                self.set_row(module, row_i, col_j, &tmp_dft);
+            });
+        });
+    }
+
     pub fn keyswitch<DataLhs, DataRhs>(
         &mut self,
         module: &Module<FFT64>,
diff --git a/core/src/glwe_ciphertext.rs b/core/src/glwe_ciphertext.rs
index 422f2cc..245ee26 100644
--- a/core/src/glwe_ciphertext.rs
+++ b/core/src/glwe_ciphertext.rs
@@ -299,6 +299,70 @@ where
         })
     }
 
+    pub(crate) fn keyswitch_from_fourier<DataLhs, DataRhs>(
+        &mut self,
+        module: &Module<FFT64>,
+        lhs: &GLWECiphertextFourier<DataLhs, FFT64>,
+        rhs: &GLWESwitchingKey<DataRhs, FFT64>,
+        scratch: &mut Scratch,
+    ) where
+        VecZnxDft<DataLhs, FFT64>: VecZnxDftToRef<FFT64>,
+        MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
+    {
+        let basek: usize = self.basek();
+
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(lhs.rank(), rhs.rank_in());
+            assert_eq!(self.rank(), rhs.rank_out());
+            assert_eq!(self.basek(), basek);
+            assert_eq!(lhs.basek(), basek);
+            assert_eq!(rhs.n(), module.n());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(lhs.n(), module.n());
+            assert!(
+                scratch.available()
+                    >= GLWECiphertextFourier::keyswitch_scratch_space(
+                        module,
+                        self.size(),
+                        self.rank(),
+                        lhs.size(),
+                        lhs.rank(),
+                        rhs.size(),
+                    )
+            );
+        }
+
+        let cols_in: usize = rhs.rank_in();
+        let cols_out: usize = rhs.rank_out() + 1;
+
+        // Buffer of the result of VMP in DFT
+        let (mut res_dft, scratch1) = scratch.tmp_vec_znx_dft(module, cols_out, rhs.size()); // Todo optimise
+
+        {
+            // Applies VMP
+            let (mut ai_dft, scratch2) = scratch1.tmp_vec_znx_dft(module, cols_in, lhs.size());
+            (0..cols_in).for_each(|col_i| {
+                module.vec_znx_dft_copy(&mut ai_dft, col_i, lhs, col_i + 1);
+            });
+            module.vmp_apply(&mut res_dft, &ai_dft, rhs, scratch2);
+        }
+
+        // Switches result of VMP outside of DFT
+        let mut res_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume::<&mut [u8]>(res_dft);
+
+        {
+            // Switches lhs 0-th outside of DFT domain and adds on
+            let (mut a0_big, scratch2) = scratch1.tmp_vec_znx_big(module, 1, lhs.size());
+            module.vec_znx_idft(&mut a0_big, 0, lhs, 0, scratch2);
+            module.vec_znx_big_add_inplace(&mut res_big, 0, &a0_big, 0);
+        }
+
+        (0..cols_out).for_each(|i| {
+            module.vec_znx_big_normalize(basek, self, i, &res_big, i, scratch1);
+        });
+    }
+
     pub fn keyswitch<DataLhs, DataRhs>(
         &mut self,
         module: &Module<FFT64>,
diff --git a/core/src/glwe_ciphertext_fourier.rs b/core/src/glwe_ciphertext_fourier.rs
index ebbe9cf..4c22507 100644
--- a/core/src/glwe_ciphertext_fourier.rs
+++ b/core/src/glwe_ciphertext_fourier.rs
@@ -174,60 +174,21 @@ where
         VecZnxDft<DataLhs, FFT64>: VecZnxDftToRef<FFT64>,
         MatZnxDft<DataRhs, FFT64>: MatZnxDftToRef<FFT64>,
     {
-        let basek: usize = self.basek();
-
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(lhs.rank(), rhs.rank_in());
-            assert_eq!(self.rank(), rhs.rank_out());
-            assert_eq!(self.basek(), basek);
-            assert_eq!(lhs.basek(), basek);
-            assert_eq!(rhs.n(), module.n());
-            assert_eq!(self.n(), module.n());
-            assert_eq!(lhs.n(), module.n());
-            assert!(
-                scratch.available()
-                    >= GLWECiphertextFourier::keyswitch_scratch_space(
-                        module,
-                        self.size(),
-                        self.rank(),
-                        lhs.size(),
-                        lhs.rank(),
-                        rhs.size(),
-                    )
-            );
-        }
-
-        let cols_in: usize = rhs.rank_in();
         let cols_out: usize = rhs.rank_out() + 1;
 
-        // Buffer of the result of VMP in DFT
-        let (mut res_dft, scratch1) = scratch.tmp_vec_znx_dft(module, cols_out, rhs.size()); // Todo optimise
-
-        {
-            // Applies VMP
-            let (mut ai_dft, scratch2) = scratch1.tmp_vec_znx_dft(module, cols_in, lhs.size());
-            (0..cols_in).for_each(|col_i| {
-                module.vec_znx_dft_copy(&mut ai_dft, col_i, lhs, col_i + 1);
-            });
-            module.vmp_apply(&mut res_dft, &ai_dft, rhs, scratch2);
-        }
-
-        // Switches result of VMP outside of DFT
-        let mut res_big: VecZnxBig<&mut [u8], FFT64> = module.vec_znx_idft_consume::<&mut [u8]>(res_dft);
-
-        {
-            // Switches lhs 0-th outside of DFT domain and adds on
-            let (mut a0_big, scratch2) = scratch1.tmp_vec_znx_big(module, 1, lhs.size());
-            module.vec_znx_idft(&mut a0_big, 0, lhs, 0, scratch2);
-            module.vec_znx_big_add_inplace(&mut res_big, 0, &a0_big, 0);
-        }
-
         // Space fr normalized VMP result outside of DFT domain
-        let (mut res_small, scratch2) = scratch1.tmp_vec_znx(module, cols_out, lhs.size());
+        let (res_idft_data, scratch1) = scratch.tmp_vec_znx(module, cols_out, lhs.size());
+
+        let mut res_idft: GLWECiphertext<&mut [u8]> = GLWECiphertext::<&mut [u8]> {
+            data: res_idft_data,
+            basek: self.basek,
+            k: self.k,
+        };
+
+        res_idft.keyswitch_from_fourier(module, self, rhs, scratch1);
+
         (0..cols_out).for_each(|i| {
-            module.vec_znx_big_normalize(basek, &mut res_small, i, &res_big, i, scratch2);
-            module.vec_znx_dft(self, i, &res_small, i);
+            module.vec_znx_dft(self, i, &res_idft, i);
         });
     }