diff --git a/base2k/spqlios-arithmetic b/base2k/spqlios-arithmetic
index 515d616..07f3c8d 160000
--- a/base2k/spqlios-arithmetic
+++ b/base2k/spqlios-arithmetic
@@ -1 +1 @@
-Subproject commit 515d616a8ba858b7e858a63dc0fa768eb70ebb99
+Subproject commit 07f3c8d2b8cf9e3a41e9577d06852d6f52e80e88
diff --git a/base2k/src/ffi/vec_znx_dft.rs b/base2k/src/ffi/vec_znx_dft.rs
index 54fb117..bcdf5e2 100644
--- a/base2k/src/ffi/vec_znx_dft.rs
+++ b/base2k/src/ffi/vec_znx_dft.rs
@@ -75,3 +75,19 @@ unsafe extern "C" {
         a_size: u64,
     );
 }
+
+unsafe extern "C" {
+    pub unsafe fn vec_znx_dft_automorphism(
+        module: *const MODULE,
+        d: i64,
+        res_dft: *mut VEC_ZNX_DFT,
+        res_size: u64,
+        a_dft: *const VEC_ZNX_DFT,
+        a_size: u64,
+        tmp: *mut u8,
+    );
+}
+
+unsafe extern "C" {
+    pub unsafe fn vec_znx_dft_automorphism_tmp_bytes(module: *const MODULE) -> u64;
+}
diff --git a/base2k/src/vec_znx_dft.rs b/base2k/src/vec_znx_dft.rs
index 4ad8525..367270d 100644
--- a/base2k/src/vec_znx_dft.rs
+++ b/base2k/src/vec_znx_dft.rs
@@ -1,7 +1,7 @@
 use crate::ffi::vec_znx_big::vec_znx_big_t;
 use crate::ffi::vec_znx_dft;
 use crate::ffi::vec_znx_dft::{bytes_of_vec_znx_dft, vec_znx_dft_t};
-use crate::{alloc_aligned, VecZnx};
+use crate::{alloc_aligned, VecZnx, DEFAULTALIGN};
 use crate::{assert_alignement, Infos, Module, VecZnxBig, BACKEND};
 
 pub struct VecZnxDft {
@@ -135,15 +135,28 @@ pub trait VecZnxDftOps {
     /// b <- IDFT(a), uses a as scratch space.
     fn vec_znx_idft_tmp_a(&self, b: &mut VecZnxBig, a: &mut VecZnxDft, a_cols: usize);
 
-    fn vec_znx_idft(
+    fn vec_znx_idft(&self, b: &mut VecZnxBig, a: &VecZnxDft, a_cols: usize, tmp_bytes: &mut [u8]);
+
+    fn vec_znx_dft(&self, b: &mut VecZnxDft, a: &VecZnx, a_cols: usize);
+
+    fn vec_znx_dft_automorphism(
         &self,
-        b: &mut VecZnxBig,
+        k: i64,
+        b: &mut VecZnxDft,
+        b_cols: usize,
         a: &VecZnxDft,
         a_cols: usize,
+    );
+
+    fn vec_znx_dft_automorphism_inplace(
+        &self,
+        k: i64,
+        a: &mut VecZnxDft,
+        a_cols: usize,
         tmp_bytes: &mut [u8],
     );
 
-    fn vec_znx_dft(&self, b: &mut VecZnxDft, a: &VecZnx, a_cols: usize);
+    fn vec_znx_dft_automorphism_tmp_bytes(&self) -> usize;
 }
 
 impl VecZnxDftOps for Module {
@@ -161,10 +174,10 @@ impl VecZnxDftOps for Module {
 
     fn new_vec_znx_dft_from_bytes(&self, cols: usize, tmp_bytes: &mut [u8]) -> VecZnxDft {
         debug_assert!(
-            tmp_bytes.len() >= <Module as VecZnxDftOps>::bytes_of_vec_znx_dft(self, cols),
+            tmp_bytes.len() >= Self::bytes_of_vec_znx_dft(self, cols),
             "invalid bytes: bytes.len()={} < bytes_of_vec_znx_dft={}",
             tmp_bytes.len(),
-            <Module as VecZnxDftOps>::bytes_of_vec_znx_dft(self, cols)
+            Self::bytes_of_vec_znx_dft(self, cols)
         );
         #[cfg(debug_assertions)]
         {
@@ -223,33 +236,27 @@ impl VecZnxDftOps for Module {
     }
 
     // b <- IDFT(a), scratch space size obtained with [vec_znx_idft_tmp_bytes].
-    fn vec_znx_idft(
-        &self,
-        b: &mut VecZnxBig,
-        a: &VecZnxDft,
-        a_cols: usize,
-        tmp_bytes: &mut [u8],
-    ) {
-        debug_assert!(
-            b.cols() >= a_cols,
-            "invalid c_vector: b.cols()={} < a_cols={}",
-            b.cols(),
-            a_cols
-        );
-        debug_assert!(
-            a.cols() >= a_cols,
-            "invalid c_vector: a.cols()={} < a_cols={}",
-            a.cols(),
-            a_cols
-        );
-        debug_assert!(
-            tmp_bytes.len() >= <Module as VecZnxDftOps>::vec_znx_idft_tmp_bytes(self),
-            "invalid tmp_bytes: tmp_bytes.len()={} < self.vec_znx_idft_tmp_bytes()={}",
-            tmp_bytes.len(),
-            <Module as VecZnxDftOps>::vec_znx_idft_tmp_bytes(self)
-        );
+    fn vec_znx_idft(&self, b: &mut VecZnxBig, a: &VecZnxDft, a_cols: usize, tmp_bytes: &mut [u8]) {
         #[cfg(debug_assertions)]
         {
+            assert!(
+                b.cols() >= a_cols,
+                "invalid c_vector: b.cols()={} < a_cols={}",
+                b.cols(),
+                a_cols
+            );
+            assert!(
+                a.cols() >= a_cols,
+                "invalid c_vector: a.cols()={} < a_cols={}",
+                a.cols(),
+                a_cols
+            );
+            assert!(
+                tmp_bytes.len() >= Self::vec_znx_idft_tmp_bytes(self),
+                "invalid tmp_bytes: tmp_bytes.len()={} < self.vec_znx_idft_tmp_bytes()={}",
+                tmp_bytes.len(),
+                Self::vec_znx_idft_tmp_bytes(self)
+            );
             assert_alignement(tmp_bytes.as_ptr())
         }
         unsafe {
@@ -263,4 +270,132 @@ impl VecZnxDftOps for Module {
             )
         }
     }
+
+    fn vec_znx_dft_automorphism(
+        &self,
+        k: i64,
+        b: &mut VecZnxDft,
+        b_cols: usize,
+        a: &VecZnxDft,
+        a_cols: usize,
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert!(
+                b.cols() >= a_cols,
+                "invalid c_vector: b.cols()={} < a_cols={}",
+                b.cols(),
+                a_cols
+            );
+            assert!(
+                a.cols() >= a_cols,
+                "invalid c_vector: a.cols()={} < a_cols={}",
+                a.cols(),
+                a_cols
+            );
+        }
+        unsafe {
+            vec_znx_dft::vec_znx_dft_automorphism(
+                self.ptr,
+                k,
+                b.ptr as *mut vec_znx_dft_t,
+                b_cols as u64,
+                a.ptr as *const vec_znx_dft_t,
+                a_cols as u64,
+                [0u8; 0].as_mut_ptr(),
+            );
+        }
+    }
+
+    fn vec_znx_dft_automorphism_inplace(
+        &self,
+        k: i64,
+        a: &mut VecZnxDft,
+        a_cols: usize,
+        tmp_bytes: &mut [u8],
+    ) {
+        #[cfg(debug_assertions)]
+        {
+            assert!(
+                a.cols() >= a_cols,
+                "invalid c_vector: a.cols()={} < a_cols={}",
+                a.cols(),
+                a_cols
+            );
+            assert!(
+                tmp_bytes.len() >= Self::vec_znx_dft_automorphism_tmp_bytes(self),
+                "invalid tmp_bytes: tmp_bytes.len()={} < self.vec_znx_dft_automorphism_tmp_bytes()={}",
+                tmp_bytes.len(),
+                Self::vec_znx_dft_automorphism_tmp_bytes(self)
+            );
+            assert_alignement(tmp_bytes.as_ptr())
+        }
+        unsafe {
+            vec_znx_dft::vec_znx_dft_automorphism(
+                self.ptr,
+                k,
+                a.ptr as *mut vec_znx_dft_t,
+                a_cols as u64,
+                a.ptr as *const vec_znx_dft_t,
+                a_cols as u64,
+                tmp_bytes.as_mut_ptr(),
+            );
+        }
+    }
+
+    fn vec_znx_dft_automorphism_tmp_bytes(&self) -> usize {
+        unsafe {
+            std::cmp::max(
+                vec_znx_dft::vec_znx_dft_automorphism_tmp_bytes(self.ptr) as usize,
+                DEFAULTALIGN,
+            )
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use crate::{
+        alloc_aligned, Module, Sampling, VecZnx, VecZnxDft, VecZnxDftOps, VecZnxOps, BACKEND,
+    };
+    use itertools::izip;
+    use sampling::source::{new_seed, Source};
+
+    #[test]
+    fn test_automorphism_dft() {
+        let module: Module = Module::new(128, BACKEND::FFT64);
+
+        let cols: usize = 2;
+        let log_base2k: usize = 17;
+        let mut a: VecZnx = module.new_vec_znx(cols);
+        let mut a_dft: VecZnxDft = module.new_vec_znx_dft(cols);
+        let mut b_dft: VecZnxDft = module.new_vec_znx_dft(cols);
+
+        let mut source: Source = Source::new(new_seed());
+        module.fill_uniform(log_base2k, &mut a, cols, &mut source);
+
+        let mut tmp_bytes: Vec<u8> = alloc_aligned(module.vec_znx_dft_automorphism_tmp_bytes());
+
+        let p: i64 = -5;
+
+        // a_dft <- DFT(a)
+        module.vec_znx_dft(&mut a_dft, &a, cols);
+
+        // a_dft <- AUTO(a_dft)
+        module.vec_znx_dft_automorphism_inplace(p, &mut a_dft, cols, &mut tmp_bytes);
+
+        // a <- AUTO(a)
+        module.vec_znx_automorphism_inplace(p, &mut a, cols);
+
+        // b_dft <- DFT(AUTO(a))
+        module.vec_znx_dft(&mut b_dft, &a, cols);
+
+        let a_f64: &[f64] = a_dft.raw(&module);
+        let b_f64: &[f64] = b_dft.raw(&module);
+        izip!(a_f64.iter(), b_f64.iter()).for_each(|(ai, bi)| {
+            assert!((ai - bi).abs() <= 1e-9, "{:+e} > 1e-9", (ai - bi).abs());
+        });
+
+        module.free()
+    }
 }