diff --git a/base2k/examples/rlwe_encrypt.rs b/base2k/examples/rlwe_encrypt.rs
index f66a4d1..1da44e9 100644
--- a/base2k/examples/rlwe_encrypt.rs
+++ b/base2k/examples/rlwe_encrypt.rs
@@ -1,5 +1,5 @@
 use base2k::{
-    BACKEND, Encoding, Infos, Module, Sampling, Scalar, SvpPPol, SvpPPolOps, VecZnx, VecZnxBig, VecZnxBigOps, VecZnxDft,
+    Encoding, FFT64, Infos, Module, Sampling, Scalar, SvpPPol, SvpPPolOps, VecZnx, VecZnxBig, VecZnxBigOps, VecZnxDft,
     VecZnxDftOps, VecZnxOps, alloc_aligned,
 };
 use itertools::izip;
@@ -8,44 +8,48 @@ use sampling::source::Source;
 fn main() {
     let n: usize = 16;
     let log_base2k: usize = 18;
-    let cols: usize = 3;
+    let limbs: usize = 3;
     let msg_cols: usize = 2;
     let log_scale: usize = msg_cols * log_base2k - 5;
-    let module: Module = Module::new(n, BACKEND::FFT64);
+    let module: Module<FFT64> = Module::<FFT64>::new(n);
 
     let mut carry: Vec<u8> = alloc_aligned(module.vec_znx_big_normalize_tmp_bytes());
 
     let seed: [u8; 32] = [0; 32];
     let mut source: Source = Source::new(seed);
 
-    let mut res: VecZnx = module.new_vec_znx(1, cols);
+    let mut res: VecZnx = module.new_vec_znx(1, limbs);
 
     // s <- Z_{-1, 0, 1}[X]/(X^{N}+1)
     let mut s: Scalar = Scalar::new(n);
     s.fill_ternary_prob(0.5, &mut source);
 
     // Buffer to store s in the DFT domain
-    let mut s_ppol: SvpPPol = module.new_svp_ppol();
+    let mut s_ppol: SvpPPol<FFT64> = module.new_svp_ppol();
 
     // s_ppol <- DFT(s)
     module.svp_prepare(&mut s_ppol, &s);
 
     // a <- Z_{2^prec}[X]/(X^{N}+1)
-    let mut a: VecZnx = module.new_vec_znx(1, cols);
-    module.fill_uniform(log_base2k, &mut a, cols, &mut source);
+    let mut a: VecZnx = module.new_vec_znx(1, limbs);
+    module.fill_uniform(log_base2k, &mut a, 0, limbs, &mut source);
+
+    
 
     // Scratch space for DFT values
-    let mut buf_dft: VecZnxDft = module.new_vec_znx_dft(1, a.cols());
+    let mut buf_dft: VecZnxDft<FFT64> = module.new_vec_znx_dft(1, a.limbs());
 
     // Applies buf_dft <- s * a
     module.svp_apply_dft(&mut buf_dft, &s_ppol, &a);
 
     // Alias scratch space
-    let mut buf_big: VecZnxBig = buf_dft.as_vec_znx_big();
+    let mut buf_big: VecZnxBig<FFT64> = buf_dft.as_vec_znx_big();
 
     // buf_big <- IDFT(buf_dft) (not normalized)
     module.vec_znx_idft_tmp_a(&mut buf_big, &mut buf_dft);
 
+    println!("{:?}", buf_big.raw());
+
     let mut m: VecZnx = module.new_vec_znx(1, msg_cols);
 
     let mut want: Vec<i64> = vec![0; n];
@@ -59,13 +63,17 @@ fn main() {
     // buf_big <- m - buf_big
     module.vec_znx_big_sub_small_a_inplace(&mut buf_big, &m);
 
+    println!("{:?}", buf_big.raw());
+
     // b <- normalize(buf_big) + e
-    let mut b: VecZnx = module.new_vec_znx(1, cols);
+    let mut b: VecZnx = module.new_vec_znx(1, limbs);
     module.vec_znx_big_normalize(log_base2k, &mut b, &buf_big, &mut carry);
+    b.print(n);
     module.add_normal(
         log_base2k,
         &mut b,
-        log_base2k * cols,
+        0,
+        log_base2k * limbs,
         &mut source,
         3.2,
         19.0,
@@ -80,14 +88,18 @@ fn main() {
     // buf_big <- a * s + b
     module.vec_znx_big_add_small_inplace(&mut buf_big, &b);
 
+    println!("raw: {:?}", &buf_big.raw());
+
     // res <- normalize(buf_big)
     module.vec_znx_big_normalize(log_base2k, &mut res, &buf_big, &mut carry);
 
+    
+
     // have = m * 2^{log_scale} + e
     let mut have: Vec<i64> = vec![i64::default(); n];
-    res.decode_vec_i64(0, log_base2k, res.cols() * log_base2k, &mut have);
+    res.decode_vec_i64(0, log_base2k, res.limbs() * log_base2k, &mut have);
 
-    let scale: f64 = (1 << (res.cols() * log_base2k - log_scale)) as f64;
+    let scale: f64 = (1 << (res.limbs() * log_base2k - log_scale)) as f64;
     izip!(want.iter(), have.iter())
         .enumerate()
         .for_each(|(i, (a, b))| {
diff --git a/base2k/examples/vector_matrix_product.rs b/base2k/examples/vector_matrix_product.rs
index a69c857..4e8b97e 100644
--- a/base2k/examples/vector_matrix_product.rs
+++ b/base2k/examples/vector_matrix_product.rs
@@ -1,5 +1,5 @@
 use base2k::{
-    BACKEND, Encoding, Infos, Module, VecZnx, VecZnxBig, VecZnxBigOps, VecZnxDft, VecZnxDftOps, VecZnxOps, VmpPMat, VmpPMatOps,
+    Encoding, FFT64, Infos, Module, VecZnx, VecZnxBig, VecZnxBigOps, VecZnxDft, VecZnxDftOps, VecZnxOps, VmpPMat, VmpPMatOps,
     alloc_aligned,
 };
 
@@ -7,50 +7,51 @@ fn main() {
     let log_n: i32 = 5;
     let n: usize = 1 << log_n;
 
-    let module: Module = Module::new(n, BACKEND::FFT64);
+    let module: Module<FFT64> = Module::<FFT64>::new(n);
     let log_base2k: usize = 15;
-    let cols: usize = 5;
-    let log_k: usize = log_base2k * cols - 5;
+    let limbs_vec: usize = 5;
+    let log_k: usize = log_base2k * limbs_vec - 5;
 
-    let rows: usize = cols;
-    let cols: usize = cols + 1;
+    let rows_mat: usize = limbs_vec;
+    let limbs_mat: usize = limbs_vec + 1;
 
     // Maximum size of the byte scratch needed
-    let tmp_bytes: usize = module.vmp_prepare_tmp_bytes(rows, cols) | module.vmp_apply_dft_tmp_bytes(cols, cols, rows, cols);
+    let tmp_bytes: usize = module.vmp_prepare_tmp_bytes(rows_mat, 1, limbs_mat)
+        | module.vmp_apply_dft_tmp_bytes(limbs_vec, limbs_vec, rows_mat, limbs_mat);
 
     let mut buf: Vec<u8> = alloc_aligned(tmp_bytes);
 
     let mut a_values: Vec<i64> = vec![i64::default(); n];
     a_values[1] = (1 << log_base2k) + 1;
 
-    let mut a: VecZnx = module.new_vec_znx(1, rows);
+    let mut a: VecZnx = module.new_vec_znx(1, limbs_vec);
     a.encode_vec_i64(0, log_base2k, log_k, &a_values, 32);
     a.normalize(log_base2k, &mut buf);
 
-    a.print(0, a.cols(), n);
+    a.print(n);
     println!();
 
-    let mut vmp_pmat: VmpPMat = module.new_vmp_pmat(1, rows, cols);
+    let mut vmp_pmat: VmpPMat<FFT64> = module.new_vmp_pmat(rows_mat, 1, limbs_mat);
 
-    (0..a.cols()).for_each(|row_i| {
-        let mut tmp: VecZnx = module.new_vec_znx(1, cols);
-        tmp.at_mut(row_i)[1] = 1 as i64;
+    (0..a.limbs()).for_each(|row_i| {
+        let mut tmp: VecZnx = module.new_vec_znx(1, limbs_mat);
+        tmp.at_limb_mut(row_i)[1] = 1 as i64;
         module.vmp_prepare_row(&mut vmp_pmat, tmp.raw(), row_i, &mut buf);
     });
 
-    let mut c_dft: VecZnxDft = module.new_vec_znx_dft(1, cols);
+    let mut c_dft: VecZnxDft<FFT64> = module.new_vec_znx_dft(1, limbs_mat);
     module.vmp_apply_dft(&mut c_dft, &a, &vmp_pmat, &mut buf);
 
-    let mut c_big: VecZnxBig = c_dft.as_vec_znx_big();
+    let mut c_big: VecZnxBig<FFT64> = c_dft.as_vec_znx_big();
     module.vec_znx_idft_tmp_a(&mut c_big, &mut c_dft);
 
-    let mut res: VecZnx = module.new_vec_znx(1, rows);
+    let mut res: VecZnx = module.new_vec_znx(1, limbs_vec);
     module.vec_znx_big_normalize(log_base2k, &mut res, &c_big, &mut buf);
 
     let mut values_res: Vec<i64> = vec![i64::default(); n];
     res.decode_vec_i64(0, log_base2k, log_k, &mut values_res);
 
-    res.print(0, res.cols(), n);
+    res.print(n);
 
     module.free();
 
diff --git a/base2k/src/encoding.rs b/base2k/src/encoding.rs
index c8c08e9..d4085cb 100644
--- a/base2k/src/encoding.rs
+++ b/base2k/src/encoding.rs
@@ -9,129 +9,130 @@ pub trait Encoding {
     ///
     /// # Arguments
     ///
-    /// * `poly_idx`: the index of the poly where to encode the data.
+    /// * `col_i`: the index of the poly where to encode the data.
     /// * `log_base2k`: base two negative logarithm decomposition of the receiver.
     /// * `log_k`: base two negative logarithm of the scaling of the data.
     /// * `data`: data to encode on the receiver.
     /// * `log_max`: base two logarithm of the infinity norm of the input data.
-    fn encode_vec_i64(&mut self, poly_idx: usize, log_base2k: usize, log_k: usize, data: &[i64], log_max: usize);
+    fn encode_vec_i64(&mut self, col_i: usize, log_base2k: usize, log_k: usize, data: &[i64], log_max: usize);
 
     /// decode a vector of i64 from the receiver.
     ///
     /// # Arguments
     ///
-    /// * `poly_idx`: the index of the poly where to encode the data.
+    /// * `col_i`: the index of the poly where to encode the data.
     /// * `log_base2k`: base two negative logarithm decomposition of the receiver.
     /// * `log_k`: base two logarithm of the scaling of the data.
     /// * `data`: data to decode from the receiver.
-    fn decode_vec_i64(&self, poly_idx: usize, log_base2k: usize, log_k: usize, data: &mut [i64]);
+    fn decode_vec_i64(&self, col_i: usize, log_base2k: usize, log_k: usize, data: &mut [i64]);
 
     /// decode a vector of Float from the receiver.
     ///
     /// # Arguments
-    /// * `poly_idx`: the index of the poly where to encode the data.
+    /// * `col_i`: the index of the poly where to encode the data.
     /// * `log_base2k`: base two negative logarithm decomposition of the receiver.
     /// * `data`: data to decode from the receiver.
-    fn decode_vec_float(&self, poly_idx: usize, log_base2k: usize, data: &mut [Float]);
+    fn decode_vec_float(&self, col_i: usize, log_base2k: usize, data: &mut [Float]);
 
     /// encodes a single i64 on the receiver at the given index.
     ///
     /// # Arguments
     ///
-    /// * `poly_idx`: the index of the poly where to encode the data.
+    /// * `col_i`: the index of the poly where to encode the data.
     /// * `log_base2k`: base two negative logarithm decomposition of the receiver.
     /// * `log_k`: base two negative logarithm of the scaling of the data.
     /// * `i`: index of the coefficient on which to encode the data.
     /// * `data`: data to encode on the receiver.
     /// * `log_max`: base two logarithm of the infinity norm of the input data.
-    fn encode_coeff_i64(&mut self, poly_idx: usize, log_base2k: usize, log_k: usize, i: usize, data: i64, log_max: usize);
+    fn encode_coeff_i64(&mut self, col_i: usize, log_base2k: usize, log_k: usize, i: usize, data: i64, log_max: usize);
 
     /// decode a single of i64 from the receiver at the given index.
     ///
     /// # Arguments
     ///
-    /// * `poly_idx`: the index of the poly where to encode the data.
+    /// * `col_i`: the index of the poly where to encode the data.
     /// * `log_base2k`: base two negative logarithm decomposition of the receiver.
     /// * `log_k`: base two negative logarithm of the scaling of the data.
     /// * `i`: index of the coefficient to decode.
     /// * `data`: data to decode from the receiver.
-    fn decode_coeff_i64(&self, poly_idx: usize, log_base2k: usize, log_k: usize, i: usize) -> i64;
+    fn decode_coeff_i64(&self, col_i: usize, log_base2k: usize, log_k: usize, i: usize) -> i64;
 }
 
 impl Encoding for VecZnx {
-    fn encode_vec_i64(&mut self, poly_idx: usize, log_base2k: usize, log_k: usize, data: &[i64], log_max: usize) {
-        encode_vec_i64(self, poly_idx, log_base2k, log_k, data, log_max)
+    fn encode_vec_i64(&mut self, col_i: usize, log_base2k: usize, log_k: usize, data: &[i64], log_max: usize) {
+        encode_vec_i64(self, col_i, log_base2k, log_k, data, log_max)
     }
 
-    fn decode_vec_i64(&self, poly_idx: usize, log_base2k: usize, log_k: usize, data: &mut [i64]) {
-        decode_vec_i64(self, poly_idx, log_base2k, log_k, data)
+    fn decode_vec_i64(&self, col_i: usize, log_base2k: usize, log_k: usize, data: &mut [i64]) {
+        decode_vec_i64(self, col_i, log_base2k, log_k, data)
     }
 
-    fn decode_vec_float(&self, poly_idx: usize, log_base2k: usize, data: &mut [Float]) {
-        decode_vec_float(self, poly_idx, log_base2k, data)
+    fn decode_vec_float(&self, col_i: usize, log_base2k: usize, data: &mut [Float]) {
+        decode_vec_float(self, col_i, log_base2k, data)
     }
 
-    fn encode_coeff_i64(&mut self, poly_idx: usize, log_base2k: usize, log_k: usize, i: usize, value: i64, log_max: usize) {
-        encode_coeff_i64(self, poly_idx, log_base2k, log_k, i, value, log_max)
+    fn encode_coeff_i64(&mut self, col_i: usize, log_base2k: usize, log_k: usize, i: usize, value: i64, log_max: usize) {
+        encode_coeff_i64(self, col_i, log_base2k, log_k, i, value, log_max)
     }
 
-    fn decode_coeff_i64(&self, poly_idx: usize, log_base2k: usize, log_k: usize, i: usize) -> i64 {
-        decode_coeff_i64(self, poly_idx, log_base2k, log_k, i)
+    fn decode_coeff_i64(&self, col_i: usize, log_base2k: usize, log_k: usize, i: usize) -> i64 {
+        decode_coeff_i64(self, col_i, log_base2k, log_k, i)
     }
 }
 
-fn encode_vec_i64(a: &mut VecZnx, poly_idx: usize, log_base2k: usize, log_k: usize, data: &[i64], log_max: usize) {
-    let cols: usize = (log_k + log_base2k - 1) / log_base2k;
+fn encode_vec_i64(a: &mut VecZnx, col_i: usize, log_base2k: usize, log_k: usize, data: &[i64], log_max: usize) {
+    let limbs: usize = (log_k + log_base2k - 1) / log_base2k;
 
     #[cfg(debug_assertions)]
     {
         assert!(
-            cols <= a.cols(),
-            "invalid argument log_k: (log_k + a.log_base2k - 1)/a.log_base2k={} > a.cols()={}",
-            cols,
-            a.cols()
+            limbs <= a.limbs(),
+            "invalid argument log_k: (log_k + a.log_base2k - 1)/a.log_base2k={} > a.limbs()={}",
+            limbs,
+            a.limbs()
         );
-        assert!(poly_idx < a.size);
+        assert!(col_i < a.cols());
         assert!(data.len() <= a.n())
     }
 
     let data_len: usize = data.len();
     let log_k_rem: usize = log_base2k - (log_k % log_base2k);
 
-    (0..a.cols()).for_each(|i| unsafe {
-        znx_zero_i64_ref(a.n() as u64, a.at_poly_mut_ptr(poly_idx, i));
+    // Zeroes coefficients of the i-th column
+    (0..a.limbs()).for_each(|i| unsafe {
+        znx_zero_i64_ref(a.n() as u64, a.at_mut_ptr(col_i, i));
     });
 
     // If 2^{log_base2k} * 2^{k_rem} < 2^{63}-1, then we can simply copy
     // values on the last limb.
     // Else we decompose values base2k.
     if log_max + log_k_rem < 63 || log_k_rem == log_base2k {
-        a.at_poly_mut(poly_idx, cols - 1)[..data_len].copy_from_slice(&data[..data_len]);
+        a.at_poly_mut(col_i, limbs - 1)[..data_len].copy_from_slice(&data[..data_len]);
     } else {
         let mask: i64 = (1 << log_base2k) - 1;
-        let steps: usize = min(cols, (log_max + log_base2k - 1) / log_base2k);
-        (cols - steps..cols)
+        let steps: usize = min(limbs, (log_max + log_base2k - 1) / log_base2k);
+        (limbs - steps..limbs)
             .rev()
             .enumerate()
             .for_each(|(i, i_rev)| {
                 let shift: usize = i * log_base2k;
-                izip!(a.at_poly_mut(poly_idx, i_rev).iter_mut(), data.iter()).for_each(|(y, x)| *y = (x >> shift) & mask);
+                izip!(a.at_poly_mut(col_i, i_rev).iter_mut(), data.iter()).for_each(|(y, x)| *y = (x >> shift) & mask);
             })
     }
 
     // Case where self.prec % self.k != 0.
     if log_k_rem != log_base2k {
-        let steps: usize = min(cols, (log_max + log_base2k - 1) / log_base2k);
-        (cols - steps..cols).rev().for_each(|i| {
-            a.at_poly_mut(poly_idx, i)[..data_len]
+        let steps: usize = min(limbs, (log_max + log_base2k - 1) / log_base2k);
+        (limbs - steps..limbs).rev().for_each(|i| {
+            a.at_poly_mut(col_i, i)[..data_len]
                 .iter_mut()
                 .for_each(|x| *x <<= log_k_rem);
         })
     }
 }
 
-fn decode_vec_i64(a: &VecZnx, poly_idx: usize, log_base2k: usize, log_k: usize, data: &mut [i64]) {
-    let cols: usize = (log_k + log_base2k - 1) / log_base2k;
+fn decode_vec_i64(a: &VecZnx, col_i: usize, log_base2k: usize, log_k: usize, data: &mut [i64]) {
+    let limbs: usize = (log_k + log_base2k - 1) / log_base2k;
     #[cfg(debug_assertions)]
     {
         assert!(
@@ -140,26 +141,26 @@ fn decode_vec_i64(a: &VecZnx, poly_idx: usize, log_base2k: usize, log_k: usize,
             data.len(),
             a.n()
         );
-        assert!(poly_idx < a.size());
+        assert!(col_i < a.cols());
     }
-    data.copy_from_slice(a.at_poly(poly_idx, 0));
+    data.copy_from_slice(a.at_poly(col_i, 0));
     let rem: usize = log_base2k - (log_k % log_base2k);
-    (1..cols).for_each(|i| {
-        if i == cols - 1 && rem != log_base2k {
+    (1..limbs).for_each(|i| {
+        if i == limbs - 1 && rem != log_base2k {
             let k_rem: usize = log_base2k - rem;
-            izip!(a.at_poly(poly_idx, i).iter(), data.iter_mut()).for_each(|(x, y)| {
+            izip!(a.at_poly(col_i, i).iter(), data.iter_mut()).for_each(|(x, y)| {
                 *y = (*y << k_rem) + (x >> rem);
             });
         } else {
-            izip!(a.at_poly(poly_idx, i).iter(), data.iter_mut()).for_each(|(x, y)| {
+            izip!(a.at_poly(col_i, i).iter(), data.iter_mut()).for_each(|(x, y)| {
                 *y = (*y << log_base2k) + x;
             });
         }
     })
 }
 
-fn decode_vec_float(a: &VecZnx, poly_idx: usize, log_base2k: usize, data: &mut [Float]) {
-    let cols: usize = a.cols();
+fn decode_vec_float(a: &VecZnx, col_i: usize, log_base2k: usize, data: &mut [Float]) {
+    let limbs: usize = a.limbs();
     #[cfg(debug_assertions)]
     {
         assert!(
@@ -168,23 +169,23 @@ fn decode_vec_float(a: &VecZnx, poly_idx: usize, log_base2k: usize, data: &mut [
             data.len(),
             a.n()
         );
-        assert!(poly_idx < a.size());
+        assert!(col_i < a.cols());
     }
 
-    let prec: u32 = (log_base2k * cols) as u32;
+    let prec: u32 = (log_base2k * limbs) as u32;
 
     // 2^{log_base2k}
     let base = Float::with_val(prec, (1 << log_base2k) as f64);
 
     // y[i] = sum x[j][i] * 2^{-log_base2k*j}
-    (0..cols).for_each(|i| {
+    (0..limbs).for_each(|i| {
         if i == 0 {
-            izip!(a.at_poly(poly_idx, cols - i - 1).iter(), data.iter_mut()).for_each(|(x, y)| {
+            izip!(a.at_poly(col_i, limbs - i - 1).iter(), data.iter_mut()).for_each(|(x, y)| {
                 y.assign(*x);
                 *y /= &base;
             });
         } else {
-            izip!(a.at_poly(poly_idx, cols - i - 1).iter(), data.iter_mut()).for_each(|(x, y)| {
+            izip!(a.at_poly(col_i, limbs - i - 1).iter(), data.iter_mut()).for_each(|(x, y)| {
                 *y += Float::with_val(prec, *x);
                 *y /= &base;
             });
@@ -192,61 +193,61 @@ fn decode_vec_float(a: &VecZnx, poly_idx: usize, log_base2k: usize, data: &mut [
     });
 }
 
-fn encode_coeff_i64(a: &mut VecZnx, poly_idx: usize, log_base2k: usize, log_k: usize, i: usize, value: i64, log_max: usize) {
-    let cols: usize = (log_k + log_base2k - 1) / log_base2k;
+fn encode_coeff_i64(a: &mut VecZnx, col_i: usize, log_base2k: usize, log_k: usize, i: usize, value: i64, log_max: usize) {
+    let limbs: usize = (log_k + log_base2k - 1) / log_base2k;
 
     #[cfg(debug_assertions)]
     {
         assert!(i < a.n());
         assert!(
-            cols <= a.cols(),
-            "invalid argument log_k: (log_k + a.log_base2k - 1)/a.log_base2k={} > a.cols()={}",
-            cols,
-            a.cols()
+            limbs <= a.limbs(),
+            "invalid argument log_k: (log_k + a.log_base2k - 1)/a.log_base2k={} > a.limbs()={}",
+            limbs,
+            a.limbs()
         );
-        assert!(poly_idx < a.size());
+        assert!(col_i < a.cols());
     }
 
     let log_k_rem: usize = log_base2k - (log_k % log_base2k);
-    (0..a.cols()).for_each(|j| a.at_poly_mut(poly_idx, j)[i] = 0);
+    (0..a.limbs()).for_each(|j| a.at_poly_mut(col_i, j)[i] = 0);
 
     // If 2^{log_base2k} * 2^{log_k_rem} < 2^{63}-1, then we can simply copy
     // values on the last limb.
     // Else we decompose values base2k.
     if log_max + log_k_rem < 63 || log_k_rem == log_base2k {
-        a.at_poly_mut(poly_idx, cols - 1)[i] = value;
+        a.at_poly_mut(col_i, limbs - 1)[i] = value;
     } else {
         let mask: i64 = (1 << log_base2k) - 1;
-        let steps: usize = min(cols, (log_max + log_base2k - 1) / log_base2k);
-        (cols - steps..cols)
+        let steps: usize = min(limbs, (log_max + log_base2k - 1) / log_base2k);
+        (limbs - steps..limbs)
             .rev()
             .enumerate()
             .for_each(|(j, j_rev)| {
-                a.at_poly_mut(poly_idx, j_rev)[i] = (value >> (j * log_base2k)) & mask;
+                a.at_poly_mut(col_i, j_rev)[i] = (value >> (j * log_base2k)) & mask;
             })
     }
 
     // Case where prec % k != 0.
     if log_k_rem != log_base2k {
-        let steps: usize = min(cols, (log_max + log_base2k - 1) / log_base2k);
-        (cols - steps..cols).rev().for_each(|j| {
-            a.at_poly_mut(poly_idx, j)[i] <<= log_k_rem;
+        let steps: usize = min(limbs, (log_max + log_base2k - 1) / log_base2k);
+        (limbs - steps..limbs).rev().for_each(|j| {
+            a.at_poly_mut(col_i, j)[i] <<= log_k_rem;
         })
     }
 }
 
-fn decode_coeff_i64(a: &VecZnx, poly_idx: usize, log_base2k: usize, log_k: usize, i: usize) -> i64 {
+fn decode_coeff_i64(a: &VecZnx, col_i: usize, log_base2k: usize, log_k: usize, i: usize) -> i64 {
     #[cfg(debug_assertions)]
     {
         assert!(i < a.n());
-        assert!(poly_idx < a.size())
+        assert!(col_i < a.cols())
     }
 
     let cols: usize = (log_k + log_base2k - 1) / log_base2k;
     let data: &[i64] = a.raw();
     let mut res: i64 = data[i];
     let rem: usize = log_base2k - (log_k % log_base2k);
-    let slice_size: usize = a.n() * a.size();
+    let slice_size: usize = a.n() * a.limbs();
     (1..cols).for_each(|i| {
         let x = data[i * slice_size];
         if i == cols - 1 && rem != log_base2k {
@@ -275,13 +276,13 @@ mod tests {
         let mut source: Source = Source::new([0u8; 32]);
         let raw: &mut [i64] = a.raw_mut();
         raw.iter_mut().enumerate().for_each(|(i, x)| *x = i as i64);
-        (0..a.size()).for_each(|poly_idx| {
+        (0..a.cols()).for_each(|col_i| {
             let mut have: Vec<i64> = vec![i64::default(); n];
             have.iter_mut()
                 .for_each(|x| *x = (source.next_i64() << 56) >> 56);
-            a.encode_vec_i64(poly_idx, log_base2k, log_k, &have, 10);
+            a.encode_vec_i64(col_i, log_base2k, log_k, &have, 10);
             let mut want: Vec<i64> = vec![i64::default(); n];
-            a.decode_vec_i64(poly_idx, log_base2k, log_k, &mut want);
+            a.decode_vec_i64(col_i, log_base2k, log_k, &mut want);
             izip!(want, have).for_each(|(a, b)| assert_eq!(a, b, "{} != {}", a, b));
         });
     }
@@ -296,12 +297,12 @@ mod tests {
         let mut source = Source::new([0u8; 32]);
         let raw: &mut [i64] = a.raw_mut();
         raw.iter_mut().enumerate().for_each(|(i, x)| *x = i as i64);
-        (0..a.size()).for_each(|poly_idx| {
+        (0..a.cols()).for_each(|col_i| {
             let mut have: Vec<i64> = vec![i64::default(); n];
             have.iter_mut().for_each(|x| *x = source.next_i64());
-            a.encode_vec_i64(poly_idx, log_base2k, log_k, &have, 64);
+            a.encode_vec_i64(col_i, log_base2k, log_k, &have, 64);
             let mut want = vec![i64::default(); n];
-            a.decode_vec_i64(poly_idx, log_base2k, log_k, &mut want);
+            a.decode_vec_i64(col_i, log_base2k, log_k, &mut want);
             izip!(want, have).for_each(|(a, b)| assert_eq!(a, b, "{} != {}", a, b));
         })
     }
diff --git a/base2k/src/ffi/vec_znx_big.rs b/base2k/src/ffi/vec_znx_big.rs
index e1222c3..8c06e90 100644
--- a/base2k/src/ffi/vec_znx_big.rs
+++ b/base2k/src/ffi/vec_znx_big.rs
@@ -8,17 +8,17 @@ pub struct vec_znx_big_t {
 pub type VEC_ZNX_BIG = vec_znx_big_t;
 
 unsafe extern "C" {
-    pub fn bytes_of_vec_znx_big(module: *const MODULE, size: u64) -> u64;
+    pub unsafe fn bytes_of_vec_znx_big(module: *const MODULE, size: u64) -> u64;
 }
 unsafe extern "C" {
-    pub fn new_vec_znx_big(module: *const MODULE, size: u64) -> *mut VEC_ZNX_BIG;
+    pub unsafe fn new_vec_znx_big(module: *const MODULE, size: u64) -> *mut VEC_ZNX_BIG;
 }
 unsafe extern "C" {
-    pub fn delete_vec_znx_big(res: *mut VEC_ZNX_BIG);
+    pub unsafe fn delete_vec_znx_big(res: *mut VEC_ZNX_BIG);
 }
 
 unsafe extern "C" {
-    pub fn vec_znx_big_add(
+    pub unsafe fn vec_znx_big_add(
         module: *const MODULE,
         res: *mut VEC_ZNX_BIG,
         res_size: u64,
@@ -29,7 +29,7 @@ unsafe extern "C" {
     );
 }
 unsafe extern "C" {
-    pub fn vec_znx_big_add_small(
+    pub unsafe fn vec_znx_big_add_small(
         module: *const MODULE,
         res: *mut VEC_ZNX_BIG,
         res_size: u64,
@@ -41,7 +41,7 @@ unsafe extern "C" {
     );
 }
 unsafe extern "C" {
-    pub fn vec_znx_big_add_small2(
+    pub unsafe fn vec_znx_big_add_small2(
         module: *const MODULE,
         res: *mut VEC_ZNX_BIG,
         res_size: u64,
@@ -54,7 +54,7 @@ unsafe extern "C" {
     );
 }
 unsafe extern "C" {
-    pub fn vec_znx_big_sub(
+    pub unsafe fn vec_znx_big_sub(
         module: *const MODULE,
         res: *mut VEC_ZNX_BIG,
         res_size: u64,
@@ -65,7 +65,7 @@ unsafe extern "C" {
     );
 }
 unsafe extern "C" {
-    pub fn vec_znx_big_sub_small_b(
+    pub unsafe fn vec_znx_big_sub_small_b(
         module: *const MODULE,
         res: *mut VEC_ZNX_BIG,
         res_size: u64,
@@ -77,7 +77,7 @@ unsafe extern "C" {
     );
 }
 unsafe extern "C" {
-    pub fn vec_znx_big_sub_small_a(
+    pub unsafe fn vec_znx_big_sub_small_a(
         module: *const MODULE,
         res: *mut VEC_ZNX_BIG,
         res_size: u64,
@@ -89,7 +89,7 @@ unsafe extern "C" {
     );
 }
 unsafe extern "C" {
-    pub fn vec_znx_big_sub_small2(
+    pub unsafe fn vec_znx_big_sub_small2(
         module: *const MODULE,
         res: *mut VEC_ZNX_BIG,
         res_size: u64,
@@ -101,8 +101,13 @@ unsafe extern "C" {
         b_sl: u64,
     );
 }
+
 unsafe extern "C" {
-    pub fn vec_znx_big_normalize_base2k(
+    pub unsafe fn vec_znx_big_normalize_base2k_tmp_bytes(module: *const MODULE) -> u64;
+}
+
+unsafe extern "C" {
+    pub unsafe fn vec_znx_big_normalize_base2k(
         module: *const MODULE,
         log2_base2k: u64,
         res: *mut i64,
@@ -113,34 +118,9 @@ unsafe extern "C" {
         tmp_space: *mut u8,
     );
 }
-unsafe extern "C" {
-    pub fn vec_znx_big_normalize_base2k_tmp_bytes(module: *const MODULE) -> u64;
-}
 
 unsafe extern "C" {
-    pub fn vec_znx_big_automorphism(
-        module: *const MODULE,
-        p: i64,
-        res: *mut VEC_ZNX_BIG,
-        res_size: u64,
-        a: *const VEC_ZNX_BIG,
-        a_size: u64,
-    );
-}
-
-unsafe extern "C" {
-    pub fn vec_znx_big_rotate(
-        module: *const MODULE,
-        p: i64,
-        res: *mut VEC_ZNX_BIG,
-        res_size: u64,
-        a: *const VEC_ZNX_BIG,
-        a_size: u64,
-    );
-}
-
-unsafe extern "C" {
-    pub fn vec_znx_big_range_normalize_base2k(
+    pub unsafe fn vec_znx_big_range_normalize_base2k(
         module: *const MODULE,
         log2_base2k: u64,
         res: *mut i64,
@@ -153,6 +133,29 @@ unsafe extern "C" {
         tmp_space: *mut u8,
     );
 }
+
 unsafe extern "C" {
-    pub fn vec_znx_big_range_normalize_base2k_tmp_bytes(module: *const MODULE) -> u64;
+    pub unsafe fn vec_znx_big_range_normalize_base2k_tmp_bytes(module: *const MODULE) -> u64;
+}
+
+unsafe extern "C" {
+    pub unsafe fn vec_znx_big_automorphism(
+        module: *const MODULE,
+        p: i64,
+        res: *mut VEC_ZNX_BIG,
+        res_size: u64,
+        a: *const VEC_ZNX_BIG,
+        a_size: u64,
+    );
+}
+
+unsafe extern "C" {
+    pub unsafe fn vec_znx_big_rotate(
+        module: *const MODULE,
+        p: i64,
+        res: *mut VEC_ZNX_BIG,
+        res_size: u64,
+        a: *const VEC_ZNX_BIG,
+        a_size: u64,
+    );
 }
diff --git a/base2k/src/infos.rs b/base2k/src/infos.rs
index ba799d7..764a7fe 100644
--- a/base2k/src/infos.rs
+++ b/base2k/src/infos.rs
@@ -1,28 +1,4 @@
-#[derive(Copy, Clone)]
-#[repr(C)]
-pub struct LAYOUT{
-    /// Ring degree.
-    n: usize,
-    /// Number of logical rows in the layout.
-    rows: usize,
-    /// Number of polynomials per row.
-    cols: usize,
-    /// Number of limbs per polynomial.
-    size: usize,
-    /// Whether limbs are interleaved inside a row.
-    ///
-    /// For example, for (rows, cols, size) = (2, 2, 3):
-    /// 
-    /// - `true`: layout is ((a0, b0, a1, b1, a2, b2), (c0, d0, c1, d1, c2, d2))
-    /// - `false`: layout is ((a0, a1, a2, b0, b1, b2), (c0, c1, c2, d0, d1, d2))
-    interleaved : bool,
-}
-
 pub trait Infos {
-
-    /// Returns the full layout.
-    fn layout(&self) -> LAYOUT;
-
     /// Returns the ring degree of the polynomials.
     fn n(&self) -> usize;
 
@@ -36,8 +12,8 @@ pub trait Infos {
     fn cols(&self) -> usize;
 
     /// Returns the number of limbs per polynomial.
-    fn size(&self) -> usize;
+    fn limbs(&self) -> usize;
 
-    /// Whether limbs are interleaved across rows.
-    fn interleaved(&self) -> bool;
+    /// Returns the total number of small polynomials.
+    fn poly_count(&self) -> usize;
 }
diff --git a/base2k/src/lib.rs b/base2k/src/lib.rs
index ec0d2b7..5144afd 100644
--- a/base2k/src/lib.rs
+++ b/base2k/src/lib.rs
@@ -27,7 +27,7 @@ pub use vmp::*;
 pub const GALOISGENERATOR: u64 = 5;
 pub const DEFAULTALIGN: usize = 64;
 
-pub fn is_aligned_custom<T>(ptr: *const T, align: usize) -> bool {
+fn is_aligned_custom<T>(ptr: *const T, align: usize) -> bool {
     (ptr as usize) % align == 0
 }
 
@@ -54,13 +54,10 @@ pub fn cast_mut<T, V>(data: &[T]) -> &mut [V] {
     unsafe { std::slice::from_raw_parts_mut(ptr, len) }
 }
 
-use std::alloc::{Layout, alloc};
-use std::ptr;
-
 /// Allocates a block of bytes with a custom alignement.
 /// Alignement must be a power of two and size a multiple of the alignement.
 /// Allocated memory is initialized to zero.
-pub fn alloc_aligned_custom_u8(size: usize, align: usize) -> Vec<u8> {
+fn alloc_aligned_custom_u8(size: usize, align: usize) -> Vec<u8> {
     assert!(
         align.is_power_of_two(),
         "Alignment must be a power of two but is {}",
@@ -74,8 +71,8 @@ pub fn alloc_aligned_custom_u8(size: usize, align: usize) -> Vec<u8> {
         align
     );
     unsafe {
-        let layout: Layout = Layout::from_size_align(size, align).expect("Invalid alignment");
-        let ptr: *mut u8 = alloc(layout);
+        let layout: std::alloc::Layout = std::alloc::Layout::from_size_align(size, align).expect("Invalid alignment");
+        let ptr: *mut u8 = std::alloc::alloc(layout);
         if ptr.is_null() {
             panic!("Memory allocation failed");
         }
@@ -86,18 +83,11 @@ pub fn alloc_aligned_custom_u8(size: usize, align: usize) -> Vec<u8> {
             align
         );
         // Init allocated memory to zero
-        ptr::write_bytes(ptr, 0, size);
+        std::ptr::write_bytes(ptr, 0, size);
         Vec::from_raw_parts(ptr, size, size)
     }
 }
 
-/// Allocates a block of bytes aligned with [DEFAULTALIGN].
-/// Size must be amultiple of [DEFAULTALIGN].
-/// /// Allocated memory is initialized to zero.
-pub fn alloc_aligned_u8(size: usize) -> Vec<u8> {
-    alloc_aligned_custom_u8(size, DEFAULTALIGN)
-}
-
 /// Allocates a block of T aligned with [DEFAULTALIGN].
 /// Size of T * size msut be a multiple of [DEFAULTALIGN].
 pub fn alloc_aligned_custom<T>(size: usize, align: usize) -> Vec<T> {
diff --git a/base2k/src/module.rs b/base2k/src/module.rs
index 8cbdbca..205cf62 100644
--- a/base2k/src/module.rs
+++ b/base2k/src/module.rs
@@ -1,5 +1,6 @@
 use crate::GALOISGENERATOR;
 use crate::ffi::module::{MODULE, delete_module_info, module_info_t, new_module_info};
+use std::marker::PhantomData;
 
 #[derive(Copy, Clone)]
 #[repr(u8)]
@@ -8,37 +9,50 @@ pub enum BACKEND {
     NTT120,
 }
 
-pub struct Module {
-    pub ptr: *mut MODULE,
-    pub n: usize,
-    pub backend: BACKEND,
+pub trait Backend {
+    const KIND: BACKEND;
+    fn module_type() -> u32;
 }
 
-impl Module {
+pub struct FFT64;
+pub struct NTT120;
+
+impl Backend for FFT64 {
+    const KIND: BACKEND = BACKEND::FFT64;
+    fn module_type() -> u32 {
+        0
+    }
+}
+
+impl Backend for NTT120 {
+    const KIND: BACKEND = BACKEND::NTT120;
+    fn module_type() -> u32 {
+        1
+    }
+}
+
+pub struct Module<B: Backend> {
+    pub ptr: *mut MODULE,
+    pub n: usize,
+    _marker: PhantomData<B>,
+}
+
+impl<B: Backend> Module<B> {
     // Instantiates a new module.
-    pub fn new(n: usize, module_type: BACKEND) -> Self {
+    pub fn new(n: usize) -> Self {
         unsafe {
-            let module_type_u32: u32;
-            match module_type {
-                BACKEND::FFT64 => module_type_u32 = 0,
-                BACKEND::NTT120 => module_type_u32 = 1,
-            }
-            let m: *mut module_info_t = new_module_info(n as u64, module_type_u32);
+            let m: *mut module_info_t = new_module_info(n as u64, B::module_type());
             if m.is_null() {
                 panic!("Failed to create module.");
             }
             Self {
                 ptr: m,
                 n: n,
-                backend: module_type,
+                _marker: PhantomData,
             }
         }
     }
 
-    pub fn backend(&self) -> BACKEND {
-        self.backend
-    }
-
     pub fn n(&self) -> usize {
         self.n
     }
diff --git a/base2k/src/sampling.rs b/base2k/src/sampling.rs
index 064c1e2..db9a79b 100644
--- a/base2k/src/sampling.rs
+++ b/base2k/src/sampling.rs
@@ -1,16 +1,17 @@
-use crate::{Infos, Module, VecZnx};
+use crate::{Backend, Infos, Module, VecZnx};
 use rand_distr::{Distribution, Normal};
 use sampling::source::Source;
 
 pub trait Sampling {
-    /// Fills the first `cols` cols with uniform values in \[-2^{log_base2k-1}, 2^{log_base2k-1}\]
-    fn fill_uniform(&self, log_base2k: usize, a: &mut VecZnx, cols: usize, source: &mut Source);
+    /// Fills the first `limbs` limbs with uniform values in \[-2^{log_base2k-1}, 2^{log_base2k-1}\]
+    fn fill_uniform(&self, log_base2k: usize, a: &mut VecZnx, col_i: usize, limbs: usize, source: &mut Source);
 
     /// Adds vector sampled according to the provided distribution, scaled by 2^{-log_k} and bounded to \[-bound, bound\].
     fn add_dist_f64<D: Distribution<f64>>(
         &self,
         log_base2k: usize,
         a: &mut VecZnx,
+        col_i: usize,
         log_k: usize,
         source: &mut Source,
         dist: D,
@@ -18,24 +19,35 @@ pub trait Sampling {
     );
 
     /// Adds a discrete normal vector scaled by 2^{-log_k} with the provided standard deviation and bounded to \[-bound, bound\].
-    fn add_normal(&self, log_base2k: usize, a: &mut VecZnx, log_k: usize, source: &mut Source, sigma: f64, bound: f64);
+    fn add_normal(
+        &self,
+        log_base2k: usize,
+        a: &mut VecZnx,
+        col_i: usize,
+        log_k: usize,
+        source: &mut Source,
+        sigma: f64,
+        bound: f64,
+    );
 }
 
-impl Sampling for Module {
-    fn fill_uniform(&self, log_base2k: usize, a: &mut VecZnx, cols: usize, source: &mut Source) {
+impl<B: Backend> Sampling for Module<B> {
+    fn fill_uniform(&self, log_base2k: usize, a: &mut VecZnx, col_i: usize, limbs: usize, source: &mut Source) {
         let base2k: u64 = 1 << log_base2k;
         let mask: u64 = base2k - 1;
         let base2k_half: i64 = (base2k >> 1) as i64;
-        let size: usize = a.n() * cols;
-        a.raw_mut()[..size]
-            .iter_mut()
-            .for_each(|x| *x = (source.next_u64n(base2k, mask) as i64) - base2k_half);
+        (0..limbs).for_each(|j| {
+            a.at_poly_mut(col_i, j)
+                .iter_mut()
+                .for_each(|x| *x = (source.next_u64n(base2k, mask) as i64) - base2k_half);
+        })
     }
 
     fn add_dist_f64<D: Distribution<f64>>(
         &self,
         log_base2k: usize,
         a: &mut VecZnx,
+        col_i: usize,
         log_k: usize,
         source: &mut Source,
         dist: D,
@@ -50,28 +62,42 @@ impl Sampling for Module {
         let log_base2k_rem: usize = log_k % log_base2k;
 
         if log_base2k_rem != 0 {
-            a.at_mut(a.cols() - 1).iter_mut().for_each(|a| {
-                let mut dist_f64: f64 = dist.sample(source);
-                while dist_f64.abs() > bound {
-                    dist_f64 = dist.sample(source)
-                }
-                *a += (dist_f64.round() as i64) << log_base2k_rem;
-            });
+            a.at_poly_mut(col_i, a.limbs() - 1)
+                .iter_mut()
+                .for_each(|a| {
+                    let mut dist_f64: f64 = dist.sample(source);
+                    while dist_f64.abs() > bound {
+                        dist_f64 = dist.sample(source)
+                    }
+                    *a += (dist_f64.round() as i64) << log_base2k_rem;
+                });
         } else {
-            a.at_mut(a.cols() - 1).iter_mut().for_each(|a| {
-                let mut dist_f64: f64 = dist.sample(source);
-                while dist_f64.abs() > bound {
-                    dist_f64 = dist.sample(source)
-                }
-                *a += dist_f64.round() as i64
-            });
+            a.at_poly_mut(col_i, a.limbs() - 1)
+                .iter_mut()
+                .for_each(|a| {
+                    let mut dist_f64: f64 = dist.sample(source);
+                    while dist_f64.abs() > bound {
+                        dist_f64 = dist.sample(source)
+                    }
+                    *a += dist_f64.round() as i64
+                });
         }
     }
 
-    fn add_normal(&self, log_base2k: usize, a: &mut VecZnx, log_k: usize, source: &mut Source, sigma: f64, bound: f64) {
+    fn add_normal(
+        &self,
+        log_base2k: usize,
+        a: &mut VecZnx,
+        col_i: usize,
+        log_k: usize,
+        source: &mut Source,
+        sigma: f64,
+        bound: f64,
+    ) {
         self.add_dist_f64(
             log_base2k,
             a,
+            col_i,
             log_k,
             source,
             Normal::new(0.0, sigma).unwrap(),
diff --git a/base2k/src/svp.rs b/base2k/src/svp.rs
index bc37f86..e293668 100644
--- a/base2k/src/svp.rs
+++ b/base2k/src/svp.rs
@@ -1,6 +1,8 @@
+use std::marker::PhantomData;
+
 use crate::ffi::svp::{self, svp_ppol_t};
 use crate::ffi::vec_znx_dft::vec_znx_dft_t;
-use crate::{BACKEND, LAYOUT, Module, VecZnx, VecZnxDft, assert_alignement};
+use crate::{Backend, FFT64, Module, VecZnx, VecZnxDft, assert_alignement};
 
 use crate::{Infos, alloc_aligned, cast_mut};
 use rand::seq::SliceRandom;
@@ -14,7 +16,7 @@ pub struct Scalar {
     pub ptr: *mut i64,
 }
 
-impl Module {
+impl<B: Backend> Module<B> {
     pub fn new_scalar(&self) -> Scalar {
         Scalar::new(self.n())
     }
@@ -117,9 +119,8 @@ impl Scalar {
     pub fn as_vec_znx(&self) -> VecZnx {
         VecZnx {
             n: self.n,
-            size: 1, // TODO REVIEW IF NEED TO ADD size TO SCALAR
             cols: 1,
-            layout: LAYOUT::COL(1, 1),
+            limbs: 1,
             data: Vec::new(),
             ptr: self.ptr,
         }
@@ -132,7 +133,7 @@ pub trait ScalarOps {
     fn new_scalar_from_bytes(&self, bytes: &mut [u8]) -> Scalar;
     fn new_scalar_from_bytes_borrow(&self, tmp_bytes: &mut [u8]) -> Scalar;
 }
-impl ScalarOps for Module {
+impl<B: Backend> ScalarOps for Module<B> {
     fn bytes_of_scalar(&self) -> usize {
         Scalar::bytes_of(self.n())
     }
@@ -147,17 +148,17 @@ impl ScalarOps for Module {
     }
 }
 
-pub struct SvpPPol {
+pub struct SvpPPol<B: Backend> {
     pub n: usize,
     pub data: Vec<u8>,
     pub ptr: *mut u8,
-    pub backend: BACKEND,
+    _marker: PhantomData<B>,
 }
 
 /// A prepared [crate::Scalar] for [SvpPPolOps::svp_apply_dft].
 /// An [SvpPPol] an be seen as a [VecZnxDft] of one limb.
-impl SvpPPol {
-    pub fn new(module: &Module) -> Self {
+impl SvpPPol<FFT64> {
+    pub fn new(module: &Module<FFT64>) -> Self {
         module.new_svp_ppol()
     }
 
@@ -166,11 +167,11 @@ impl SvpPPol {
         self.n
     }
 
-    pub fn bytes_of(module: &Module) -> usize {
+    pub fn bytes_of(module: &Module<FFT64>) -> usize {
         module.bytes_of_svp_ppol()
     }
 
-    pub fn from_bytes(module: &Module, bytes: &mut [u8]) -> SvpPPol {
+    pub fn from_bytes(module: &Module<FFT64>, bytes: &mut [u8]) -> Self {
         #[cfg(debug_assertions)]
         {
             assert_alignement(bytes.as_ptr());
@@ -181,12 +182,12 @@ impl SvpPPol {
                 n: module.n(),
                 data: Vec::from_raw_parts(bytes.as_mut_ptr(), bytes.len(), bytes.len()),
                 ptr: bytes.as_mut_ptr(),
-                backend: module.backend(),
+                _marker: PhantomData,
             }
         }
     }
 
-    pub fn from_bytes_borrow(module: &Module, tmp_bytes: &mut [u8]) -> SvpPPol {
+    pub fn from_bytes_borrow(module: &Module<FFT64>, tmp_bytes: &mut [u8]) -> Self {
         #[cfg(debug_assertions)]
         {
             assert_alignement(tmp_bytes.as_ptr());
@@ -196,7 +197,7 @@ impl SvpPPol {
             n: module.n(),
             data: Vec::new(),
             ptr: tmp_bytes.as_mut_ptr(),
-            backend: module.backend(),
+            _marker: PhantomData,
         }
     }
 
@@ -206,9 +207,9 @@ impl SvpPPol {
     }
 }
 
-pub trait SvpPPolOps {
+pub trait SvpPPolOps<B: Backend> {
     /// Allocates a new [SvpPPol].
-    fn new_svp_ppol(&self) -> SvpPPol;
+    fn new_svp_ppol(&self) -> SvpPPol<B>;
 
     /// Returns the minimum number of bytes necessary to allocate
     /// a new [SvpPPol] through [SvpPPol::from_bytes] ro.
@@ -217,30 +218,30 @@ pub trait SvpPPolOps {
     /// Allocates a new [SvpPPol] from an array of bytes.
     /// The array of bytes is owned by the [SvpPPol].
     /// The method will panic if bytes.len() < [SvpPPolOps::bytes_of_svp_ppol]
-    fn new_svp_ppol_from_bytes(&self, bytes: &mut [u8]) -> SvpPPol;
+    fn new_svp_ppol_from_bytes(&self, bytes: &mut [u8]) -> SvpPPol<B>;
 
     /// Allocates a new [SvpPPol] from an array of bytes.
     /// The array of bytes is borrowed by the [SvpPPol].
     /// The method will panic if bytes.len() < [SvpPPolOps::bytes_of_svp_ppol]
-    fn new_svp_ppol_from_bytes_borrow(&self, tmp_bytes: &mut [u8]) -> SvpPPol;
+    fn new_svp_ppol_from_bytes_borrow(&self, tmp_bytes: &mut [u8]) -> SvpPPol<B>;
 
     /// Prepares a [crate::Scalar] for a [SvpPPolOps::svp_apply_dft].
-    fn svp_prepare(&self, svp_ppol: &mut SvpPPol, a: &Scalar);
+    fn svp_prepare(&self, svp_ppol: &mut SvpPPol<B>, a: &Scalar);
 
     /// Applies the [SvpPPol] x [VecZnxDft] product, where each limb of
     /// the [VecZnxDft] is multiplied with [SvpPPol].
-    fn svp_apply_dft(&self, c: &mut VecZnxDft, a: &SvpPPol, b: &VecZnx);
+    fn svp_apply_dft(&self, c: &mut VecZnxDft<B>, a: &SvpPPol<B>, b: &VecZnx);
 }
 
-impl SvpPPolOps for Module {
-    fn new_svp_ppol(&self) -> SvpPPol {
+impl SvpPPolOps<FFT64> for Module<FFT64> {
+    fn new_svp_ppol(&self) -> SvpPPol<FFT64> {
         let mut data: Vec<u8> = alloc_aligned::<u8>(self.bytes_of_svp_ppol());
         let ptr: *mut u8 = data.as_mut_ptr();
-        SvpPPol {
+        SvpPPol::<FFT64> {
             data: data,
             ptr: ptr,
             n: self.n(),
-            backend: self.backend(),
+            _marker: PhantomData,
         }
     }
 
@@ -248,19 +249,19 @@ impl SvpPPolOps for Module {
         unsafe { svp::bytes_of_svp_ppol(self.ptr) as usize }
     }
 
-    fn new_svp_ppol_from_bytes(&self, bytes: &mut [u8]) -> SvpPPol {
+    fn new_svp_ppol_from_bytes(&self, bytes: &mut [u8]) -> SvpPPol<FFT64> {
         SvpPPol::from_bytes(self, bytes)
     }
 
-    fn new_svp_ppol_from_bytes_borrow(&self, tmp_bytes: &mut [u8]) -> SvpPPol {
+    fn new_svp_ppol_from_bytes_borrow(&self, tmp_bytes: &mut [u8]) -> SvpPPol<FFT64> {
         SvpPPol::from_bytes_borrow(self, tmp_bytes)
     }
 
-    fn svp_prepare(&self, svp_ppol: &mut SvpPPol, a: &Scalar) {
+    fn svp_prepare(&self, svp_ppol: &mut SvpPPol<FFT64>, a: &Scalar) {
         unsafe { svp::svp_prepare(self.ptr, svp_ppol.ptr as *mut svp_ppol_t, a.as_ptr()) }
     }
 
-    fn svp_apply_dft(&self, c: &mut VecZnxDft, a: &SvpPPol, b: &VecZnx) {
+    fn svp_apply_dft(&self, c: &mut VecZnxDft<FFT64>, a: &SvpPPol<FFT64>, b: &VecZnx) {
         unsafe {
             svp::svp_apply_dft(
                 self.ptr,
diff --git a/base2k/src/vec_znx.rs b/base2k/src/vec_znx.rs
index 71a315e..aff1ce9 100644
--- a/base2k/src/vec_znx.rs
+++ b/base2k/src/vec_znx.rs
@@ -1,4 +1,4 @@
-use crate::LAYOUT;
+use crate::Backend;
 use crate::cast_mut;
 use crate::ffi::vec_znx;
 use crate::ffi::znx;
@@ -22,11 +22,11 @@ pub struct VecZnx {
     /// Polynomial degree.
     pub n: usize,
 
-    /// Number of limbs
-    pub size: usize,
+    /// The number of polynomials
+    pub cols: usize,
 
-    /// Layout
-    pub layout: LAYOUT,
+    /// The number of limbs per polynomial (a.k.a small polynomials).
+    pub limbs: usize,
 
     /// Polynomial coefficients, as a contiguous array. Each col is equally spaced by n.
     pub data: Vec<i64>,
@@ -35,58 +35,60 @@ pub struct VecZnx {
     pub ptr: *mut i64,
 }
 
-pub fn bytes_of_vec_znx(n: usize, layout: LAYOUT, size: usize) -> usize {
-    n * layout.size() * size * 8
+pub fn bytes_of_vec_znx(n: usize, cols: usize, limbs: usize) -> usize {
+    n * cols * limbs * size_of::<i64>()
 }
 
 impl VecZnx {
     /// Returns a new struct implementing [VecZnx] with the provided data as backing array.
     ///
-    /// The struct will take ownership of buf[..[VecZnx::bytes_of]]
+    /// The struct will take ownership of buf[..[Self::bytes_of]]
     ///
     /// User must ensure that data is properly alligned and that
-    /// the size of data is equal to [VecZnx::bytes_of].
-    pub fn from_bytes(n: usize, layout: LAYOUT, size: usize, bytes: &mut [u8]) -> Self {
+    /// the limbs of data is equal to [Self::bytes_of].
+    pub fn from_bytes(n: usize, cols: usize, limbs: usize, bytes: &mut [u8]) -> Self {
         #[cfg(debug_assertions)]
         {
-            assert!(size > 0);
-            assert_eq!(bytes.len(), Self::bytes_of(n, layout, size));
+            assert!(cols > 0);
+            assert!(limbs > 0);
+            assert_eq!(bytes.len(), Self::bytes_of(n, cols, limbs));
             assert_alignement(bytes.as_ptr());
         }
         unsafe {
             let bytes_i64: &mut [i64] = cast_mut::<u8, i64>(bytes);
             let ptr: *mut i64 = bytes_i64.as_mut_ptr();
-            VecZnx {
+            Self {
                 n: n,
-                size: size,
-                layout: layout,
+                cols: cols,
+                limbs: limbs,
                 data: Vec::from_raw_parts(ptr, bytes.len(), bytes.len()),
                 ptr: ptr,
             }
         }
     }
 
-    pub fn from_bytes_borrow(n: usize, layout: LAYOUT, size: usize, bytes: &mut [u8]) -> Self {
+    pub fn from_bytes_borrow(n: usize, cols: usize, limbs: usize, bytes: &mut [u8]) -> Self {
         #[cfg(debug_assertions)]
         {
-            assert!(size > 0);
-            assert!(bytes.len() >= Self::bytes_of(n, layout, size));
+            assert!(cols > 0);
+            assert!(limbs > 0);
+            assert!(bytes.len() >= Self::bytes_of(n, cols, limbs));
             assert_alignement(bytes.as_ptr());
         }
-        VecZnx {
+        Self {
             n: n,
-            size: size,
-            layout: layout,
+            cols: cols,
+            limbs: limbs,
             data: Vec::new(),
             ptr: bytes.as_mut_ptr() as *mut i64,
         }
     }
 
-    pub fn bytes_of(n: usize, layout: LAYOUT, size: usize) -> usize {
-        bytes_of_vec_znx(n, layout, size)
+    pub fn bytes_of(n: usize, cols: usize, limbs: usize) -> usize {
+        bytes_of_vec_znx(n, cols, limbs)
     }
 
-    pub fn copy_from(&mut self, a: &VecZnx) {
+    pub fn copy_from(&mut self, a: &Self) {
         copy_vec_znx_from(self, a);
     }
 
@@ -94,15 +96,15 @@ impl VecZnx {
         self.data.len() == 0
     }
 
-    /// Total size is [VecZnx::n()] * [VecZnx::size()] * [VecZnx::size()].
+    /// Total limbs is [Self::n()] * [Self::poly_count()].
     pub fn raw(&self) -> &[i64] {
-        unsafe { std::slice::from_raw_parts(self.ptr, self.n * self.size * self.size) }
+        unsafe { std::slice::from_raw_parts(self.ptr, self.n * self.poly_count()) }
     }
 
     /// Returns a reference to backend slice of the receiver.
-    /// Total size is [VecZnx::n()] * [VecZnx::size()] * [VecZnx::size()].
+    /// Total size is [Self::n()] * [Self::poly_count()].
     pub fn raw_mut(&mut self) -> &mut [i64] {
-        unsafe { std::slice::from_raw_parts_mut(self.ptr, self.n * self.size * self.size) }
+        unsafe { std::slice::from_raw_parts_mut(self.ptr, self.n * self.poly_count()) }
     }
 
     /// Returns a non-mutable pointer to the backedn slice of the receiver.
@@ -115,76 +117,55 @@ impl VecZnx {
         self.ptr
     }
 
-    /// Returns a non-mutable pointer starting a the j-th column.
-    pub fn at_ptr(&self, i: usize) -> *const i64 {
+    /// Returns a non-mutable pointer starting a the (i, j)-th small poly.
+    pub fn at_ptr(&self, i: usize, j: usize) -> *const i64 {
         #[cfg(debug_assertions)]
         {
-            assert!(i < self.size);
+            assert!(i < self.cols());
+            assert!(j < self.limbs());
         }
-        let offset: usize = self.n * self.size * i;
+        let offset: usize = self.n * (j * self.cols() + i);
         self.ptr.wrapping_add(offset)
     }
 
-    /// Returns non-mutable reference to the ith-column.
-    /// The slice contains [VecZnx::size()] small polynomials, each of [VecZnx::n()] coefficients.
-    pub fn at(&self, i: usize) -> &[i64] {
-        unsafe { std::slice::from_raw_parts(self.at_ptr(i), self.n * self.size) }
+    /// Returns a non-mutable reference to the i-th limb.
+    /// The returned array is of size [Self::n()] * [Self::cols()].
+    pub fn at_limb(&self, i: usize) -> &[i64] {
+        unsafe { std::slice::from_raw_parts(self.at_ptr(0, i), self.n * self.cols()) }
     }
 
-    /// Returns a non-mutable pointer starting a the j-th column of the i-th polynomial.
-    pub fn at_poly_ptr(&self, i: usize, j: usize) -> *const i64 {
-        #[cfg(debug_assertions)]
-        {
-            assert!(i < self.size);
-            assert!(j < self.size);
-        }
-        let offset: usize = self.n * (self.size * j + i);
-        self.ptr.wrapping_add(offset)
-    }
-
-    /// Returns non-mutable reference to the j-th column of the i-th polynomial.
-    /// The slice contains one small polynomial of [VecZnx::n()] coefficients.
+    /// Returns a non-mutable reference to the (i, j)-th poly.
+    /// The returned array is of size [Self::n()].
     pub fn at_poly(&self, i: usize, j: usize) -> &[i64] {
-        unsafe { std::slice::from_raw_parts(self.at_poly_ptr(i, j), self.n) }
+        unsafe { std::slice::from_raw_parts(self.at_ptr(i, j), self.n) }
     }
 
-    /// Returns a mutable pointer starting a the j-th column.
-    pub fn at_mut_ptr(&self, i: usize) -> *mut i64 {
+    /// Returns a mutable pointer starting a the (i, j)-th small poly.
+    pub fn at_mut_ptr(&mut self, i: usize, j: usize) -> *mut i64 {
         #[cfg(debug_assertions)]
         {
-            assert!(i < self.size);
+            assert!(i < self.cols());
+            assert!(j < self.limbs());
         }
-        let offset: usize = self.n * self.size * i;
+
+        let offset: usize = self.n * (j * self.cols() + i);
         self.ptr.wrapping_add(offset)
     }
 
-    /// Returns mutable reference to the ith-column.
-    /// The slice contains [VecZnx::size()] small polynomials, each of [VecZnx::n()] coefficients.
-    pub fn at_mut(&mut self, i: usize) -> &mut [i64] {
-        unsafe { std::slice::from_raw_parts_mut(self.at_mut_ptr(i), self.n * self.size) }
+    /// Returns a mutable reference to the i-th limb.
+    /// The returned array is of size [Self::n()] * [Self::cols()].
+    pub fn at_limb_mut(&mut self, i: usize) -> &mut [i64] {
+        unsafe { std::slice::from_raw_parts_mut(self.at_mut_ptr(0, i), self.n * self.cols()) }
     }
 
-    /// Returns a mutable pointer starting a the j-th column of the i-th polynomial.
-    pub fn at_poly_mut_ptr(&mut self, i: usize, j: usize) -> *mut i64 {
-        #[cfg(debug_assertions)]
-        {
-            assert!(i < self.size);
-            assert!(j < self.size);
-        }
-
-        let offset: usize = self.n * (self.size * j + i);
-        self.ptr.wrapping_add(offset)
-    }
-
-    /// Returns mutable reference to the j-th column of the i-th polynomial.
-    /// The slice contains one small polynomial of [VecZnx::n()] coefficients.
+    /// Returns a mutable reference to the (i, j)-th poly.
+    /// The returned array is of size [Self::n()].
     pub fn at_poly_mut(&mut self, i: usize, j: usize) -> &mut [i64] {
-        let ptr: *mut i64 = self.at_poly_mut_ptr(i, j);
-        unsafe { std::slice::from_raw_parts_mut(ptr, self.n) }
+        unsafe { std::slice::from_raw_parts_mut(self.at_mut_ptr(i, j), self.n) }
     }
 
     pub fn zero(&mut self) {
-        unsafe { znx::znx_zero_i64_ref((self.n * self.size * self.size) as u64, self.ptr) }
+        unsafe { znx::znx_zero_i64_ref((self.n * self.poly_count()) as u64, self.ptr) }
     }
 
     pub fn normalize(&mut self, log_base2k: usize, carry: &mut [u8]) {
@@ -195,48 +176,47 @@ impl VecZnx {
         rsh(log_base2k, self, k, carry)
     }
 
-    pub fn switch_degree(&self, a: &mut VecZnx) {
+    pub fn switch_degree(&self, a: &mut Self) {
         switch_degree(a, self)
     }
 
-    pub fn print(&self, poly: usize, size: usize, n: usize) {
-        (0..size).for_each(|i| println!("{}: {:?}", i, &self.at_poly(poly, i)[..n]))
+    // Prints the first `n` coefficients of each limb
+    pub fn print(&self, n: usize) {
+        (0..self.limbs()).for_each(|i| println!("{}: {:?}", i, &self.at_limb(i)[..n]))
     }
 }
 
 impl Infos for VecZnx {
-    /// Returns the base 2 logarithm of the [VecZnx] degree.
-    fn log_n(&self) -> usize {
-        (usize::BITS - (self.n - 1).leading_zeros()) as _
-    }
-
-    /// Returns the [VecZnx] degree.
     fn n(&self) -> usize {
         self.n
     }
 
-    fn size(&self) -> usize {
-        self.size
+    fn log_n(&self) -> usize {
+        (usize::BITS - (self.n() - 1).leading_zeros()) as _
     }
 
-    fn layout(&self) -> LAYOUT {
-        self.layout
-    }
-
-    /// Returns the number of size of the [VecZnx].
-    fn size(&self) -> usize {
-        self.size
-    }
-
-    /// Returns the number of rows of the [VecZnx].
     fn rows(&self) -> usize {
         1
     }
+
+    fn cols(&self) -> usize {
+        self.cols
+    }
+
+    fn limbs(&self) -> usize {
+        self.limbs
+    }
+
+    fn poly_count(&self) -> usize {
+        self.cols * self.limbs
+    }
 }
 
 /// Copies the coefficients of `a` on the receiver.
 /// Copy is done with the minimum size matching both backing arrays.
+/// Panics if the cols do not match.
 pub fn copy_vec_znx_from(b: &mut VecZnx, a: &VecZnx) {
+    assert_eq!(b.cols(), a.cols());
     let data_a: &[i64] = a.raw();
     let data_b: &mut [i64] = b.raw_mut();
     let size = min(data_b.len(), data_a.len());
@@ -245,21 +225,20 @@ pub fn copy_vec_znx_from(b: &mut VecZnx, a: &VecZnx) {
 
 impl VecZnx {
     /// Allocates a new [VecZnx] composed of #size polynomials of Z\[X\].
-    pub fn new(n: usize, size: usize, size: usize) -> Self {
+    pub fn new(n: usize, cols: usize, limbs: usize) -> Self {
         #[cfg(debug_assertions)]
         {
             assert!(n > 0);
             assert!(n & (n - 1) == 0);
-            assert!(size > 0);
-            assert!(size <= u8::MAX as usize);
-            assert!(size > 0);
+            assert!(cols > 0);
+            assert!(limbs > 0);
         }
-        let mut data: Vec<i64> = alloc_aligned::<i64>(n * size * size);
+        let mut data: Vec<i64> = alloc_aligned::<i64>(n * cols * limbs);
         let ptr: *mut i64 = data.as_mut_ptr();
         Self {
             n: n,
-            layout: LAYOUT::COL(1, size as u8),
-            size: size,
+            cols: cols,
+            limbs: limbs,
             data: data,
             ptr: ptr,
         }
@@ -278,16 +257,16 @@ impl VecZnx {
 
         if !self.borrowing() {
             self.data
-                .truncate((self.size() - k / log_base2k) * self.n() * self.size());
+                .truncate(self.n() * self.cols() * (self.limbs() - k / log_base2k));
         }
 
-        self.size -= k / log_base2k;
+        self.limbs -= k / log_base2k;
 
         let k_rem: usize = k % log_base2k;
 
         if k_rem != 0 {
             let mask: i64 = ((1 << (log_base2k - k_rem - 1)) - 1) << k_rem;
-            self.at_mut(self.size() - 1)
+            self.at_limb_mut(self.limbs() - 1)
                 .iter_mut()
                 .for_each(|x: &mut i64| *x &= mask)
         }
@@ -305,31 +284,31 @@ pub fn switch_degree(b: &mut VecZnx, a: &VecZnx) {
         b.zero();
     }
 
-    let size = min(a.size(), b.size());
+    let limbs: usize = min(a.limbs(), b.limbs());
 
-    (0..size).for_each(|i| {
+    (0..limbs).for_each(|i| {
         izip!(
-            a.at(i).iter().step_by(gap_in),
-            b.at_mut(i).iter_mut().step_by(gap_out)
+            a.at_limb(i).iter().step_by(gap_in),
+            b.at_limb_mut(i).iter_mut().step_by(gap_out)
         )
         .for_each(|(x_in, x_out)| *x_out = *x_in);
     });
 }
 
-fn normalize_tmp_bytes(n: usize, size: usize) -> usize {
-    n * size * std::mem::size_of::<i64>()
+fn normalize_tmp_bytes(n: usize, limbs: usize) -> usize {
+    n * limbs * std::mem::size_of::<i64>()
 }
 
 fn normalize(log_base2k: usize, a: &mut VecZnx, tmp_bytes: &mut [u8]) {
     let n: usize = a.n();
-    let size: usize = a.size();
+    let cols: usize = a.cols();
 
     debug_assert!(
-        tmp_bytes.len() >= normalize_tmp_bytes(n, size),
+        tmp_bytes.len() >= normalize_tmp_bytes(n, cols),
         "invalid tmp_bytes: tmp_bytes.len()={} < normalize_tmp_bytes({}, {})",
         tmp_bytes.len(),
         n,
-        size,
+        cols,
     );
     #[cfg(debug_assertions)]
     {
@@ -340,45 +319,45 @@ fn normalize(log_base2k: usize, a: &mut VecZnx, tmp_bytes: &mut [u8]) {
 
     unsafe {
         znx::znx_zero_i64_ref(n as u64, carry_i64.as_mut_ptr());
-        (0..a.size()).rev().for_each(|i| {
+        (0..a.limbs()).rev().for_each(|i| {
             znx::znx_normalize(
-                (n * size) as u64,
+                (n * cols) as u64,
                 log_base2k as u64,
-                a.at_mut_ptr(i),
+                a.at_mut_ptr(0, i),
                 carry_i64.as_mut_ptr(),
-                a.at_mut_ptr(i),
+                a.at_mut_ptr(0, i),
                 carry_i64.as_mut_ptr(),
             )
         });
     }
 }
 
-pub fn rsh_tmp_bytes(n: usize, size: usize) -> usize {
-    n * size * std::mem::size_of::<i64>()
+pub fn rsh_tmp_bytes(n: usize, limbs: usize) -> usize {
+    n * limbs * std::mem::size_of::<i64>()
 }
 
 pub fn rsh(log_base2k: usize, a: &mut VecZnx, k: usize, tmp_bytes: &mut [u8]) {
     let n: usize = a.n();
-    let size: usize = a.size();
+    let limbs: usize = a.limbs();
 
     #[cfg(debug_assertions)]
     {
         assert!(
-            tmp_bytes.len() >= rsh_tmp_bytes(n, size),
+            tmp_bytes.len() >= rsh_tmp_bytes(n, limbs),
             "invalid carry: carry.len()/8={} < rsh_tmp_bytes({}, {})",
             tmp_bytes.len() >> 3,
             n,
-            size,
+            limbs,
         );
         assert_alignement(tmp_bytes.as_ptr());
     }
 
-    let size: usize = a.size();
+    let limbs: usize = a.limbs();
     let size_steps: usize = k / log_base2k;
 
-    a.raw_mut().rotate_right(n * size * size_steps);
+    a.raw_mut().rotate_right(n * limbs * size_steps);
     unsafe {
-        znx::znx_zero_i64_ref((n * size * size_steps) as u64, a.as_mut_ptr());
+        znx::znx_zero_i64_ref((n * limbs * size_steps) as u64, a.as_mut_ptr());
     }
 
     let k_rem = k % log_base2k;
@@ -387,13 +366,13 @@ pub fn rsh(log_base2k: usize, a: &mut VecZnx, k: usize, tmp_bytes: &mut [u8]) {
         let carry_i64: &mut [i64] = cast_mut(tmp_bytes);
 
         unsafe {
-            znx::znx_zero_i64_ref((n * size) as u64, carry_i64.as_mut_ptr());
+            znx::znx_zero_i64_ref((n * limbs) as u64, carry_i64.as_mut_ptr());
         }
 
         let log_base2k: usize = log_base2k;
 
-        (size_steps..size).for_each(|i| {
-            izip!(carry_i64.iter_mut(), a.at_mut(i).iter_mut()).for_each(|(ci, xi)| {
+        (size_steps..limbs).for_each(|i| {
+            izip!(carry_i64.iter_mut(), a.at_limb_mut(i).iter_mut()).for_each(|(ci, xi)| {
                 *xi += *ci << log_base2k;
                 *ci = get_base_k_carry(*xi, k_rem);
                 *xi = (*xi - *ci) >> k_rem;
@@ -412,14 +391,15 @@ pub trait VecZnxOps {
     ///
     /// # Arguments
     ///
-    /// * `size`: the number of size.
-    fn new_vec_znx(&self, size: usize, size: usize) -> VecZnx;
+    /// * `cols`: the number of polynomials.
+    /// * `limbs`: the number of limbs per polynomial (a.k.a small polynomials).
+    fn new_vec_znx(&self, cols: usize, limbs: usize) -> VecZnx;
 
     /// Returns the minimum number of bytes necessary to allocate
     /// a new [VecZnx] through [VecZnx::from_bytes].
-    fn bytes_of_vec_znx(&self, size: usize, size: usize) -> usize;
+    fn bytes_of_vec_znx(&self, cols: usize, size: usize) -> usize;
 
-    fn vec_znx_normalize_tmp_bytes(&self, size: usize) -> usize;
+    fn vec_znx_normalize_tmp_bytes(&self, cols: usize) -> usize;
 
     /// c <- a + b.
     fn vec_znx_add(&self, c: &mut VecZnx, a: &VecZnx, b: &VecZnx);
@@ -471,17 +451,17 @@ pub trait VecZnxOps {
     fn vec_znx_merge(&self, b: &mut VecZnx, a: &Vec<VecZnx>);
 }
 
-impl VecZnxOps for Module {
-    fn new_vec_znx(&self, size: usize, size: usize) -> VecZnx {
-        VecZnx::new(self.n(), size, size)
+impl<B: Backend> VecZnxOps for Module<B> {
+    fn new_vec_znx(&self, cols: usize, limbs: usize) -> VecZnx {
+        VecZnx::new(self.n(), cols, limbs)
     }
 
-    fn bytes_of_vec_znx(&self, size: usize, size: usize) -> usize {
-        bytes_of_vec_znx(self.n(), size, size)
+    fn bytes_of_vec_znx(&self, cols: usize, limbs: usize) -> usize {
+        bytes_of_vec_znx(self.n(), cols, limbs)
     }
 
-    fn vec_znx_normalize_tmp_bytes(&self, size: usize) -> usize {
-        unsafe { vec_znx::vec_znx_normalize_base2k_tmp_bytes(self.ptr) as usize * size }
+    fn vec_znx_normalize_tmp_bytes(&self, cols: usize) -> usize {
+        unsafe { vec_znx::vec_znx_normalize_base2k_tmp_bytes(self.ptr) as usize * cols }
     }
 
     // c <- a + b
@@ -497,14 +477,14 @@ impl VecZnxOps for Module {
             vec_znx::vec_znx_add(
                 self.ptr,
                 c.as_mut_ptr(),
-                c.size() as u64,
-                (n * c.size()) as u64,
+                c.limbs() as u64,
+                (n * c.limbs()) as u64,
                 a.as_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
                 b.as_ptr(),
-                b.size() as u64,
-                (n * b.size()) as u64,
+                b.limbs() as u64,
+                (n * b.limbs()) as u64,
             )
         }
     }
@@ -521,14 +501,14 @@ impl VecZnxOps for Module {
             vec_znx::vec_znx_add(
                 self.ptr,
                 b.as_mut_ptr(),
-                b.size() as u64,
-                (n * b.size()) as u64,
+                b.limbs() as u64,
+                (n * b.limbs()) as u64,
                 a.as_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
                 b.as_ptr(),
-                b.size() as u64,
-                (n * b.size()) as u64,
+                b.limbs() as u64,
+                (n * b.limbs()) as u64,
             )
         }
     }
@@ -546,14 +526,14 @@ impl VecZnxOps for Module {
             vec_znx::vec_znx_sub(
                 self.ptr,
                 c.as_mut_ptr(),
-                c.size() as u64,
-                (n * c.size()) as u64,
+                c.limbs() as u64,
+                (n * c.limbs()) as u64,
                 a.as_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
                 b.as_ptr(),
-                b.size() as u64,
-                (n * b.size()) as u64,
+                b.limbs() as u64,
+                (n * b.limbs()) as u64,
             )
         }
     }
@@ -570,14 +550,14 @@ impl VecZnxOps for Module {
             vec_znx::vec_znx_sub(
                 self.ptr,
                 b.as_mut_ptr(),
-                b.size() as u64,
-                (n * b.size()) as u64,
+                b.limbs() as u64,
+                (n * b.limbs()) as u64,
                 a.as_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
                 b.as_ptr(),
-                b.size() as u64,
-                (n * b.size()) as u64,
+                b.limbs() as u64,
+                (n * b.limbs()) as u64,
             )
         }
     }
@@ -594,14 +574,14 @@ impl VecZnxOps for Module {
             vec_znx::vec_znx_sub(
                 self.ptr,
                 b.as_mut_ptr(),
-                b.size() as u64,
-                (n * b.size()) as u64,
+                b.limbs() as u64,
+                (n * b.limbs()) as u64,
                 b.as_ptr(),
-                b.size() as u64,
-                (n * b.size()) as u64,
+                b.limbs() as u64,
+                (n * b.limbs()) as u64,
                 a.as_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
             )
         }
     }
@@ -617,11 +597,11 @@ impl VecZnxOps for Module {
             vec_znx::vec_znx_negate(
                 self.ptr,
                 b.as_mut_ptr(),
-                b.size() as u64,
-                (n * b.size()) as u64,
+                b.limbs() as u64,
+                (n * b.limbs()) as u64,
                 a.as_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
             )
         }
     }
@@ -636,11 +616,11 @@ impl VecZnxOps for Module {
             vec_znx::vec_znx_negate(
                 self.ptr,
                 a.as_mut_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
                 a.as_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
             )
         }
     }
@@ -657,11 +637,11 @@ impl VecZnxOps for Module {
                 self.ptr,
                 k,
                 b.as_mut_ptr(),
-                b.size() as u64,
-                (n * b.size()) as u64,
+                b.limbs() as u64,
+                (n * b.limbs()) as u64,
                 a.as_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
             )
         }
     }
@@ -677,11 +657,11 @@ impl VecZnxOps for Module {
                 self.ptr,
                 k,
                 a.as_mut_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
                 a.as_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
             )
         }
     }
@@ -697,7 +677,7 @@ impl VecZnxOps for Module {
     ///
     /// # Panics
     ///
-    /// The method will panic if the argument `a` is greater than `a.size()`.
+    /// The method will panic if the argument `a` is greater than `a.limbs()`.
     fn vec_znx_automorphism(&self, k: i64, b: &mut VecZnx, a: &VecZnx) {
         let n: usize = self.n();
         #[cfg(debug_assertions)]
@@ -710,11 +690,11 @@ impl VecZnxOps for Module {
                 self.ptr,
                 k,
                 b.as_mut_ptr(),
-                b.size() as u64,
-                (n * b.size()) as u64,
+                b.limbs() as u64,
+                (n * b.limbs()) as u64,
                 a.as_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
             );
         }
     }
@@ -729,7 +709,7 @@ impl VecZnxOps for Module {
     ///
     /// # Panics
     ///
-    /// The method will panic if the argument `size` is greater than `self.size()`.
+    /// The method will panic if the argument `size` is greater than `self.limbs()`.
     fn vec_znx_automorphism_inplace(&self, k: i64, a: &mut VecZnx) {
         let n: usize = self.n();
         #[cfg(debug_assertions)]
@@ -741,11 +721,11 @@ impl VecZnxOps for Module {
                 self.ptr,
                 k,
                 a.as_mut_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
                 a.as_ptr(),
-                a.size() as u64,
-                (n * a.size()) as u64,
+                a.limbs() as u64,
+                (n * a.limbs()) as u64,
             );
         }
     }
diff --git a/base2k/src/vec_znx_big.rs b/base2k/src/vec_znx_big.rs
index 705a5ec..b19f126 100644
--- a/base2k/src/vec_znx_big.rs
+++ b/base2k/src/vec_znx_big.rs
@@ -1,24 +1,26 @@
 use crate::ffi::vec_znx_big::{self, vec_znx_big_t};
-use crate::{BACKEND, Infos, LAYOUT, Module, VecZnx, VecZnxDft, alloc_aligned, assert_alignement};
+use crate::{Backend, FFT64, Infos, Module, VecZnx, VecZnxDft, alloc_aligned, assert_alignement};
+use std::marker::PhantomData;
 
-pub struct VecZnxBig {
+pub struct VecZnxBig<B: Backend> {
     pub data: Vec<u8>,
     pub ptr: *mut u8,
     pub n: usize,
-    pub size: usize,
     pub cols: usize,
-    pub layout: LAYOUT,
-    pub backend: BACKEND,
+    pub limbs: usize,
+    pub _marker: PhantomData<B>,
 }
 
-impl VecZnxBig {
+impl VecZnxBig<FFT64> {
     /// Returns a new [VecZnxBig] with the provided data as backing array.
     /// User must ensure that data is properly alligned and that
     /// the size of data is at least equal to [Module::bytes_of_vec_znx_big].
-    pub fn from_bytes(module: &Module, size: usize, cols: usize, bytes: &mut [u8]) -> Self {
+    pub fn from_bytes(module: &Module<FFT64>, cols: usize, limbs: usize, bytes: &mut [u8]) -> Self {
         #[cfg(debug_assertions)]
         {
-            assert_eq!(bytes.len(), module.bytes_of_vec_znx_big(size, cols));
+            assert!(cols > 0);
+            assert!(limbs > 0);
+            assert_eq!(bytes.len(), module.bytes_of_vec_znx_big(cols, limbs));
             assert_alignement(bytes.as_ptr())
         };
         unsafe {
@@ -26,91 +28,84 @@ impl VecZnxBig {
                 data: Vec::from_raw_parts(bytes.as_mut_ptr(), bytes.len(), bytes.len()),
                 ptr: bytes.as_mut_ptr(),
                 n: module.n(),
-                size: size,
-                layout: LAYOUT::COL,
                 cols: cols,
-                backend: module.backend,
+                limbs: limbs,
+                _marker: PhantomData,
             }
         }
     }
 
-    pub fn from_bytes_borrow(module: &Module, size: usize, cols: usize, bytes: &mut [u8]) -> Self {
+    pub fn from_bytes_borrow(module: &Module<FFT64>, cols: usize, limbs: usize, bytes: &mut [u8]) -> Self {
         #[cfg(debug_assertions)]
         {
-            assert_eq!(bytes.len(), module.bytes_of_vec_znx_big(size, cols));
+            assert!(cols > 0);
+            assert!(limbs > 0);
+            assert_eq!(bytes.len(), module.bytes_of_vec_znx_big(cols, limbs));
             assert_alignement(bytes.as_ptr());
         }
         Self {
             data: Vec::new(),
             ptr: bytes.as_mut_ptr(),
             n: module.n(),
-            size: size,
-            layout: LAYOUT::COL,
             cols: cols,
-            backend: module.backend,
+            limbs: limbs,
+            _marker: PhantomData,
         }
     }
 
-    pub fn as_vec_znx_dft(&mut self) -> VecZnxDft {
-        VecZnxDft {
+    pub fn as_vec_znx_dft(&mut self) -> VecZnxDft<FFT64> {
+        VecZnxDft::<FFT64> {
             data: Vec::new(),
             ptr: self.ptr,
             n: self.n,
-            size: self.size,
-            layout: LAYOUT::COL,
             cols: self.cols,
-            backend: self.backend,
+            limbs: self.limbs,
+            _marker: self._marker,
         }
     }
 
-    pub fn backend(&self) -> BACKEND {
-        self.backend
+    /// Returns a non-mutable reference to the entire contiguous array of the [VecZnxDft].
+    pub fn raw(&self) -> &[i64] {
+        let ptr: *const i64 = self.ptr as *const i64;
+        unsafe { &std::slice::from_raw_parts(ptr, self.n() * self.poly_count()) }
     }
 
-    /// Returns a non-mutable reference of `T` of the entire contiguous array of the [VecZnxDft].
-    /// When using [`crate::FFT64`] as backend, `T` should be [f64].
-    /// When using [`crate::NTT120`] as backend, `T` should be [i64].
-    /// The length of the returned array is cols * n.
-    pub fn raw<T>(&self, module: &Module) -> &[T] {
-        let ptr: *const T = self.ptr as *const T;
-        let len: usize = (self.cols() * module.n() * 8) / std::mem::size_of::<T>();
-        unsafe { &std::slice::from_raw_parts(ptr, len) }
+    // Prints the first `n` coefficients of each limb
+    pub fn print(&self, n: usize) {
+        let raw: &[i64] = self.raw();
+        (0..self.limbs()).for_each(|i| println!("{}: {:?}", i, &raw[i * self.n() * self.cols()..i * self.n() * self.cols()+n]))
     }
 }
 
-impl Infos for VecZnxBig {
-    /// Returns the base 2 logarithm of the [VecZnx] degree.
+impl<B: Backend> Infos for VecZnxBig<B> {
     fn log_n(&self) -> usize {
         (usize::BITS - (self.n - 1).leading_zeros()) as _
     }
 
-    /// Returns the [VecZnx] degree.
     fn n(&self) -> usize {
         self.n
     }
 
-    fn size(&self) -> usize {
-        self.size
-    }
-
-    fn layout(&self) -> LAYOUT {
-        self.layout
-    }
-
-    /// Returns the number of cols of the [VecZnx].
     fn cols(&self) -> usize {
         self.cols
     }
 
-    /// Returns the number of rows of the [VecZnx].
     fn rows(&self) -> usize {
         1
     }
+
+    fn limbs(&self) -> usize {
+        self.limbs
+    }
+
+    fn poly_count(&self) -> usize {
+        self.cols * self.limbs
+    }
 }
 
-pub trait VecZnxBigOps {
+pub trait VecZnxBigOps<B: Backend> {
     /// Allocates a vector Z[X]/(X^N+1) that stores not normalized values.
-    fn new_vec_znx_big(&self, size: usize, cols: usize) -> VecZnxBig;
+    fn new_vec_znx_big(&self, cols: usize, limbs: usize) -> VecZnxBig<B>;
 
     /// Returns a new [VecZnxBig] with the provided bytes array as backing array.
     ///
@@ -118,12 +113,13 @@ pub trait VecZnxBigOps {
     ///
     /// # Arguments
     ///
-    /// * `cols`: the number of cols of the [VecZnxBig].
+    /// * `cols`: the number of polynomials..
+    /// * `limbs`: the number of limbs (a.k.a small polynomials) per polynomial.
     /// * `bytes`: a byte array of size at least [Module::bytes_of_vec_znx_big].
     ///
     /// # Panics
     /// If `bytes.len()` < [Module::bytes_of_vec_znx_big].
-    fn new_vec_znx_big_from_bytes(&self, size: usize, cols: usize, bytes: &mut [u8]) -> VecZnxBig;
+    fn new_vec_znx_big_from_bytes(&self, cols: usize, limbs: usize, bytes: &mut [u8]) -> VecZnxBig<B>;
 
     /// Returns a new [VecZnxBig] with the provided bytes array as backing array.
     ///
@@ -131,33 +127,44 @@ pub trait VecZnxBigOps {
     ///
     /// # Arguments
     ///
-    /// * `cols`: the number of cols of the [VecZnxBig].
+    /// * `cols`: the number of polynomials..
+    /// * `limbs`: the number of limbs (a.k.a small polynomials) per polynomial.
     /// * `bytes`: a byte array of size at least [Module::bytes_of_vec_znx_big].
     ///
     /// # Panics
     /// If `bytes.len()` < [Module::bytes_of_vec_znx_big].
-    fn new_vec_znx_big_from_bytes_borrow(&self, size: usize, cols: usize, tmp_bytes: &mut [u8]) -> VecZnxBig;
+    fn new_vec_znx_big_from_bytes_borrow(&self, cols: usize, limbs: usize, tmp_bytes: &mut [u8]) -> VecZnxBig<B>;
 
     /// Returns the minimum number of bytes necessary to allocate
     /// a new [VecZnxBig] through [VecZnxBig::from_bytes].
-    fn bytes_of_vec_znx_big(&self, size: usize, cols: usize) -> usize;
+    fn bytes_of_vec_znx_big(&self, cols: usize, limbs: usize) -> usize;
 
-    /// b <- b - a
-    fn vec_znx_big_sub_small_a_inplace(&self, b: &mut VecZnxBig, a: &VecZnx);
+    /// b[VecZnxBig] <- b[VecZnxBig] - a[VecZnx]
+    ///
+    /// # Behavior
+    ///
+    /// [VecZnxBig] (3 cols and 4 limbs)
+    /// [a0, b0, c0] [a1, b1, c1] [a2, b2, c2] [a3, b3, c3]
+    /// -
+    /// [VecZnx] (2 cols and 3 limbs)
+    /// [d0, e0] [d1, e1] [d2, e2]
+    /// =
+    /// [a0-d0, b0-e0, c0] [a1-d1, b1-e1, c1] [a2-d2, b2-e2, c2] [a3, b3, c3]
+    fn vec_znx_big_sub_small_a_inplace(&self, b: &mut VecZnxBig<B>, a: &VecZnx);
 
     /// c <- b - a
-    fn vec_znx_big_sub_small_a(&self, c: &mut VecZnxBig, a: &VecZnx, b: &VecZnxBig);
+    fn vec_znx_big_sub_small_a(&self, c: &mut VecZnxBig<B>, a: &VecZnx, b: &VecZnxBig<B>);
 
     /// c <- b + a
-    fn vec_znx_big_add_small(&self, c: &mut VecZnxBig, a: &VecZnx, b: &VecZnxBig);
+    fn vec_znx_big_add_small(&self, c: &mut VecZnxBig<B>, a: &VecZnx, b: &VecZnxBig<B>);
 
     /// b <- b + a
-    fn vec_znx_big_add_small_inplace(&self, b: &mut VecZnxBig, a: &VecZnx);
+    fn vec_znx_big_add_small_inplace(&self, b: &mut VecZnxBig<B>, a: &VecZnx);
 
     fn vec_znx_big_normalize_tmp_bytes(&self) -> usize;
 
     /// b <- normalize(a)
-    fn vec_znx_big_normalize(&self, log_base2k: usize, b: &mut VecZnx, a: &VecZnxBig, tmp_bytes: &mut [u8]);
+    fn vec_znx_big_normalize(&self, log_base2k: usize, b: &mut VecZnx, a: &VecZnxBig<B>, tmp_bytes: &mut [u8]);
 
     fn vec_znx_big_range_normalize_base2k_tmp_bytes(&self) -> usize;
 
@@ -165,100 +172,111 @@ pub trait VecZnxBigOps {
         &self,
         log_base2k: usize,
         res: &mut VecZnx,
-        a: &VecZnxBig,
+        a: &VecZnxBig<B>,
         a_range_begin: usize,
         a_range_xend: usize,
         a_range_step: usize,
         tmp_bytes: &mut [u8],
     );
 
-    fn vec_znx_big_automorphism(&self, gal_el: i64, b: &mut VecZnxBig, a: &VecZnxBig);
+    fn vec_znx_big_automorphism(&self, gal_el: i64, b: &mut VecZnxBig<B>, a: &VecZnxBig<B>);
 
-    fn vec_znx_big_automorphism_inplace(&self, gal_el: i64, a: &mut VecZnxBig);
+    fn vec_znx_big_automorphism_inplace(&self, gal_el: i64, a: &mut VecZnxBig<B>);
 }
 
-impl VecZnxBigOps for Module {
-    fn new_vec_znx_big(&self, size: usize, cols: usize) -> VecZnxBig {
-        let mut data: Vec<u8> = alloc_aligned::<u8>(self.bytes_of_vec_znx_big(size, cols));
+impl VecZnxBigOps<FFT64> for Module<FFT64> {
+    fn new_vec_znx_big(&self, cols: usize, limbs: usize) -> VecZnxBig<FFT64> {
+        #[cfg(debug_assertions)]
+        {
+            assert!(cols > 0);
+            assert!(limbs > 0);
+        }
+        let mut data: Vec<u8> = alloc_aligned::<u8>(self.bytes_of_vec_znx_big(cols, limbs));
         let ptr: *mut u8 = data.as_mut_ptr();
-        VecZnxBig {
+        VecZnxBig::<FFT64> {
             data: data,
             ptr: ptr,
             n: self.n(),
-            size: size,
-            layout: LAYOUT::COL,
             cols: cols,
-            backend: self.backend(),
+            limbs: limbs,
+            _marker: PhantomData,
         }
     }
 
-    fn new_vec_znx_big_from_bytes(&self, size: usize, cols: usize, bytes: &mut [u8]) -> VecZnxBig {
-        VecZnxBig::from_bytes(self, size, cols, bytes)
+    fn new_vec_znx_big_from_bytes(&self, cols: usize, limbs: usize, bytes: &mut [u8]) -> VecZnxBig<FFT64> {
+        VecZnxBig::from_bytes(self, cols, limbs, bytes)
     }
 
-    fn new_vec_znx_big_from_bytes_borrow(&self, size: usize, cols: usize, tmp_bytes: &mut [u8]) -> VecZnxBig {
-        VecZnxBig::from_bytes_borrow(self, size, cols, tmp_bytes)
+    fn new_vec_znx_big_from_bytes_borrow(&self, cols: usize, limbs: usize, tmp_bytes: &mut [u8]) -> VecZnxBig<FFT64> {
+        VecZnxBig::from_bytes_borrow(self, cols, limbs, tmp_bytes)
     }
 
-    fn bytes_of_vec_znx_big(&self, size: usize, cols: usize) -> usize {
-        unsafe { vec_znx_big::bytes_of_vec_znx_big(self.ptr, cols as u64) as usize * size }
+    fn bytes_of_vec_znx_big(&self, cols: usize, limbs: usize) -> usize {
+        unsafe { vec_znx_big::bytes_of_vec_znx_big(self.ptr, limbs as u64) as usize * cols }
     }
 
-    fn vec_znx_big_sub_small_a_inplace(&self, b: &mut VecZnxBig, a: &VecZnx) {
+    /// [VecZnxBig] (3 cols and 4 limbs)
+    /// [a0, b0, c0] [a1, b1, c1] [a2, b2, c2] [a3, b3, c3]
+    /// -
+    /// [VecZnx] (2 cols and 3 limbs)
+    /// [d0, e0] [d1, e1] [d2, e2]
+    /// =
+    /// [a0-d0, b0-e0, c0] [a1-d1, b1-e1, c1] [a2-d2, b2-e2, c2] [a3, b3, c3]
+    fn vec_znx_big_sub_small_a_inplace(&self, b: &mut VecZnxBig<FFT64>, a: &VecZnx) {
         unsafe {
             vec_znx_big::vec_znx_big_sub_small_a(
                 self.ptr,
                 b.ptr as *mut vec_znx_big_t,
-                b.cols() as u64,
+                b.poly_count() as u64,
                 a.as_ptr(),
-                a.cols() as u64,
+                a.poly_count() as u64,
                 a.n() as u64,
                 b.ptr as *mut vec_znx_big_t,
-                b.cols() as u64,
+                b.poly_count() as u64,
             )
         }
     }
 
-    fn vec_znx_big_sub_small_a(&self, c: &mut VecZnxBig, a: &VecZnx, b: &VecZnxBig) {
+    fn vec_znx_big_sub_small_a(&self, c: &mut VecZnxBig<FFT64>, a: &VecZnx, b: &VecZnxBig<FFT64>) {
         unsafe {
             vec_znx_big::vec_znx_big_sub_small_a(
                 self.ptr,
                 c.ptr as *mut vec_znx_big_t,
-                c.cols() as u64,
+                c.poly_count() as u64,
                 a.as_ptr(),
-                a.cols() as u64,
+                a.poly_count() as u64,
                 a.n() as u64,
                 b.ptr as *mut vec_znx_big_t,
-                b.cols() as u64,
+                b.poly_count() as u64,
             )
         }
     }
 
-    fn vec_znx_big_add_small(&self, c: &mut VecZnxBig, a: &VecZnx, b: &VecZnxBig) {
+    fn vec_znx_big_add_small(&self, c: &mut VecZnxBig<FFT64>, a: &VecZnx, b: &VecZnxBig<FFT64>) {
         unsafe {
             vec_znx_big::vec_znx_big_add_small(
                 self.ptr,
                 c.ptr as *mut vec_znx_big_t,
-                c.cols() as u64,
+                c.poly_count() as u64,
                 b.ptr as *mut vec_znx_big_t,
-                b.cols() as u64,
+                b.poly_count() as u64,
                 a.as_ptr(),
-                a.cols() as u64,
+                a.poly_count() as u64,
                 a.n() as u64,
             )
         }
     }
 
-    fn vec_znx_big_add_small_inplace(&self, b: &mut VecZnxBig, a: &VecZnx) {
+    fn vec_znx_big_add_small_inplace(&self, b: &mut VecZnxBig<FFT64>, a: &VecZnx) {
         unsafe {
             vec_znx_big::vec_znx_big_add_small(
                 self.ptr,
                 b.ptr as *mut vec_znx_big_t,
-                b.cols() as u64,
+                b.poly_count() as u64,
                 b.ptr as *mut vec_znx_big_t,
-                b.cols() as u64,
+                b.poly_count() as u64,
                 a.as_ptr(),
-                a.cols() as u64,
+                a.poly_count() as u64,
                 a.n() as u64,
             )
         }
@@ -268,12 +286,12 @@ impl VecZnxBigOps for Module {
         unsafe { vec_znx_big::vec_znx_big_normalize_base2k_tmp_bytes(self.ptr) as usize }
     }
 
-    fn vec_znx_big_normalize(&self, log_base2k: usize, b: &mut VecZnx, a: &VecZnxBig, tmp_bytes: &mut [u8]) {
+    fn vec_znx_big_normalize(&self, log_base2k: usize, b: &mut VecZnx, a: &VecZnxBig<FFT64>, tmp_bytes: &mut [u8]) {
         debug_assert!(
-            tmp_bytes.len() >= <Module as VecZnxBigOps>::vec_znx_big_normalize_tmp_bytes(self),
+            tmp_bytes.len() >= Self::vec_znx_big_normalize_tmp_bytes(self),
             "invalid tmp_bytes: tmp_bytes.len()={} <= self.vec_znx_big_normalize_tmp_bytes()={}",
             tmp_bytes.len(),
-            <Module as VecZnxBigOps>::vec_znx_big_normalize_tmp_bytes(self)
+            Self::vec_znx_big_normalize_tmp_bytes(self)
         );
         #[cfg(debug_assertions)]
         {
@@ -284,10 +302,10 @@ impl VecZnxBigOps for Module {
                 self.ptr,
                 log_base2k as u64,
                 b.as_mut_ptr(),
-                b.cols() as u64,
+                b.limbs() as u64,
                 b.n() as u64,
                 a.ptr as *mut vec_znx_big_t,
-                a.cols() as u64,
+                a.limbs() as u64,
                 tmp_bytes.as_mut_ptr(),
             )
         }
@@ -301,17 +319,17 @@ impl VecZnxBigOps for Module {
         &self,
         log_base2k: usize,
         res: &mut VecZnx,
-        a: &VecZnxBig,
+        a: &VecZnxBig<FFT64>,
         a_range_begin: usize,
         a_range_xend: usize,
         a_range_step: usize,
         tmp_bytes: &mut [u8],
     ) {
         debug_assert!(
-            tmp_bytes.len() >= <Module as VecZnxBigOps>::vec_znx_big_range_normalize_base2k_tmp_bytes(self),
+            tmp_bytes.len() >= Self::vec_znx_big_range_normalize_base2k_tmp_bytes(self),
             "invalid tmp_bytes: tmp_bytes.len()={} <= self.vec_znx_big_range_normalize_base2k_tmp_bytes()={}",
             tmp_bytes.len(),
-            <Module as VecZnxBigOps>::vec_znx_big_range_normalize_base2k_tmp_bytes(self)
+            Self::vec_znx_big_range_normalize_base2k_tmp_bytes(self)
         );
         #[cfg(debug_assertions)]
         {
@@ -322,7 +340,7 @@ impl VecZnxBigOps for Module {
                 self.ptr,
                 log_base2k as u64,
                 res.as_mut_ptr(),
-                res.cols() as u64,
+                res.limbs() as u64,
                 res.n() as u64,
                 a.ptr as *mut vec_znx_big_t,
                 a_range_begin as u64,
@@ -333,28 +351,28 @@ impl VecZnxBigOps for Module {
         }
     }
 
-    fn vec_znx_big_automorphism(&self, gal_el: i64, b: &mut VecZnxBig, a: &VecZnxBig) {
+    fn vec_znx_big_automorphism(&self, gal_el: i64, b: &mut VecZnxBig<FFT64>, a: &VecZnxBig<FFT64>) {
         unsafe {
             vec_znx_big::vec_znx_big_automorphism(
                 self.ptr,
                 gal_el,
                 b.ptr as *mut vec_znx_big_t,
-                b.cols() as u64,
+                b.poly_count() as u64,
                 a.ptr as *mut vec_znx_big_t,
-                a.cols() as u64,
+                a.poly_count() as u64,
             );
         }
     }
 
-    fn vec_znx_big_automorphism_inplace(&self, gal_el: i64, a: &mut VecZnxBig) {
+    fn vec_znx_big_automorphism_inplace(&self, gal_el: i64, a: &mut VecZnxBig<FFT64>) {
         unsafe {
             vec_znx_big::vec_znx_big_automorphism(
                 self.ptr,
                 gal_el,
                 a.ptr as *mut vec_znx_big_t,
-                a.cols() as u64,
+                a.poly_count() as u64,
                 a.ptr as *mut vec_znx_big_t,
-                a.cols() as u64,
+                a.poly_count() as u64,
             );
         }
     }
diff --git a/base2k/src/vec_znx_dft.rs b/base2k/src/vec_znx_dft.rs
index b512fd8..ec4067f 100644
--- a/base2k/src/vec_znx_dft.rs
+++ b/base2k/src/vec_znx_dft.rs
@@ -1,136 +1,139 @@
 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::{BACKEND, Infos, LAYOUT, Module, VecZnxBig, assert_alignement};
+use crate::{Backend, FFT64, Infos, Module, VecZnxBig, assert_alignement};
 use crate::{DEFAULTALIGN, VecZnx, alloc_aligned};
+use std::marker::PhantomData;
 
-pub struct VecZnxDft {
+pub struct VecZnxDft<B: Backend> {
     pub data: Vec<u8>,
     pub ptr: *mut u8,
     pub n: usize,
-    pub size: usize,
-    pub layout: LAYOUT,
     pub cols: usize,
-    pub backend: BACKEND,
+    pub limbs: usize,
+    pub _marker: PhantomData<B>,
 }
 
-impl VecZnxDft {
+impl VecZnxDft<FFT64> {
+    pub fn new(module: &Module<FFT64>, cols: usize, limbs: usize) -> Self {
+        let mut data: Vec<u8> = alloc_aligned::<u8>(module.bytes_of_vec_znx_dft(cols, limbs));
+        let ptr: *mut u8 = data.as_mut_ptr();
+        Self {
+            data: data,
+            ptr: ptr,
+            n: module.n(),
+            limbs: limbs,
+            cols: cols,
+            _marker: PhantomData,
+        }
+    }
     /// Returns a new [VecZnxDft] with the provided data as backing array.
     /// User must ensure that data is properly alligned and that
     /// the size of data is at least equal to [Module::bytes_of_vec_znx_dft].
-    pub fn from_bytes(module: &Module, size: usize, cols: usize, bytes: &mut [u8]) -> VecZnxDft {
+    pub fn from_bytes(module: &Module<FFT64>, cols: usize, limbs: usize, bytes: &mut [u8]) -> Self {
         #[cfg(debug_assertions)]
         {
-            assert_eq!(bytes.len(), module.bytes_of_vec_znx_dft(size, cols));
+            assert!(cols > 0);
+            assert!(limbs > 0);
+            assert_eq!(bytes.len(), module.bytes_of_vec_znx_dft(cols, limbs));
             assert_alignement(bytes.as_ptr())
         }
         unsafe {
-            VecZnxDft {
+            Self {
                 data: Vec::from_raw_parts(bytes.as_mut_ptr(), bytes.len(), bytes.len()),
                 ptr: bytes.as_mut_ptr(),
                 n: module.n(),
-                size: size,
-                layout: LAYOUT::COL,
                 cols: cols,
-                backend: module.backend,
+                limbs: limbs,
+                _marker: PhantomData,
             }
         }
     }
 
-    pub fn from_bytes_borrow(module: &Module, size: usize, cols: usize, bytes: &mut [u8]) -> VecZnxDft {
+    pub fn from_bytes_borrow(module: &Module<FFT64>, cols: usize, limbs: usize, bytes: &mut [u8]) -> Self {
         #[cfg(debug_assertions)]
         {
-            assert_eq!(bytes.len(), module.bytes_of_vec_znx_dft(size, cols));
+            assert!(cols > 0);
+            assert!(limbs > 0);
+            assert_eq!(bytes.len(), module.bytes_of_vec_znx_dft(cols, limbs));
             assert_alignement(bytes.as_ptr());
         }
-        VecZnxDft {
+        Self {
             data: Vec::new(),
             ptr: bytes.as_mut_ptr(),
             n: module.n(),
-            size: size,
-            layout: LAYOUT::COL,
             cols: cols,
-            backend: module.backend,
+            limbs: limbs,
+            _marker: PhantomData,
         }
     }
 
     /// Cast a [VecZnxDft] into a [VecZnxBig].
     /// The returned [VecZnxBig] shares the backing array
     /// with the original [VecZnxDft].
-    pub fn as_vec_znx_big(&mut self) -> VecZnxBig {
-        VecZnxBig {
+    pub fn as_vec_znx_big(&mut self) -> VecZnxBig<FFT64> {
+        VecZnxBig::<FFT64> {
             data: Vec::new(),
             ptr: self.ptr,
             n: self.n,
-            layout: LAYOUT::COL,
-            size: self.size,
             cols: self.cols,
-            backend: self.backend,
+            limbs: self.limbs,
+            _marker: PhantomData,
         }
     }
 
-    pub fn backend(&self) -> BACKEND {
-        self.backend
+    pub fn raw(&self) -> &[f64] {
+        let ptr: *mut f64 = self.ptr as *mut f64;
+        let size: usize = self.n() * self.poly_count();
+        unsafe { &std::slice::from_raw_parts(ptr, size) }
     }
 
-    /// Returns a non-mutable reference of `T` of the entire contiguous array of the [VecZnxDft].
-    /// When using [`crate::FFT64`] as backend, `T` should be [f64].
-    /// When using [`crate::NTT120`] as backend, `T` should be [i64].
-    /// The length of the returned array is cols * n.
-    pub fn raw<T>(&self, module: &Module) -> &[T] {
-        let ptr: *const T = self.ptr as *const T;
-        let len: usize = (self.cols() * module.n() * 8) / std::mem::size_of::<T>();
-        unsafe { &std::slice::from_raw_parts(ptr, len) }
+    pub fn at(&self, col_i: usize) -> &[f64] {
+        &self.raw()[col_i * self.n() * self.limbs()..(col_i + 1) * self.n() * self.limbs()]
     }
 
-    pub fn at<T>(&self, module: &Module, col_i: usize) -> &[T] {
-        &self.raw::<T>(module)[col_i * module.n()..(col_i + 1) * module.n()]
+    pub fn raw_mut(&mut self) -> &mut [f64] {
+        let ptr: *mut f64 = self.ptr as *mut f64;
+        let size: usize = self.n() * self.poly_count();
+        unsafe { std::slice::from_raw_parts_mut(ptr, size) }
     }
 
-    /// Returns a mutable reference of `T` of the entire contiguous array of the [VecZnxDft].
-    /// When using [`crate::FFT64`] as backend, `T` should be [f64].
-    /// When using [`crate::NTT120`] as backend, `T` should be [i64].
-    /// The length of the returned array is cols * n.
-    pub fn raw_mut<T>(&self, module: &Module) -> &mut [T] {
-        let ptr: *mut T = self.ptr as *mut T;
-        let len: usize = (self.cols() * module.n() * 8) / std::mem::size_of::<T>();
-        unsafe { std::slice::from_raw_parts_mut(ptr, len) }
-    }
-
-    pub fn at_mut<T>(&self, module: &Module, col_i: usize) -> &mut [T] {
-        &mut self.raw_mut::<T>(module)[col_i * module.n()..(col_i + 1) * module.n()]
+    pub fn at_mut(&mut self, col_i: usize) -> &mut [f64] {
+        let n: usize = self.n();
+        let limbs:usize = self.limbs();
+        &mut self.raw_mut()[col_i * n * limbs..(col_i + 1) * n * limbs]
     }
 }
 
-impl Infos for VecZnxDft {
-    /// Returns the base 2 logarithm of the [VecZnx] degree.
-    fn log_n(&self) -> usize {
-        (usize::BITS - (self.n - 1).leading_zeros()) as _
-    }
-
-    /// Returns the [VecZnx] degree.
+impl<B: Backend> Infos for VecZnxDft<B> {
     fn n(&self) -> usize {
         self.n
     }
 
-    fn layout(&self) -> LAYOUT {
-        self.layout
+    fn log_n(&self) -> usize {
+        (usize::BITS - (self.n() - 1).leading_zeros()) as _
+    }
+
+    fn rows(&self) -> usize {
+        1
     }
 
-    /// Returns the number of cols of the [VecZnx].
     fn cols(&self) -> usize {
         self.cols
     }
 
-    /// Returns the number of rows of the [VecZnx].
-    fn rows(&self) -> usize {
-        1
+    fn limbs(&self) -> usize {
+        self.limbs
+    }
+
+    fn poly_count(&self) -> usize {
+        self.cols * self.limbs
     }
 }
 
-pub trait VecZnxDftOps {
+pub trait VecZnxDftOps<B: Backend> {
     /// Allocates a vector Z[X]/(X^N+1) that stores normalized in the DFT space.
-    fn new_vec_znx_dft(&self, size: usize, cols: usize) -> VecZnxDft;
+    fn new_vec_znx_dft(&self, cols: usize, limbs: usize) -> VecZnxDft<B>;
 
     /// Returns a new [VecZnxDft] with the provided bytes array as backing array.
     ///
@@ -143,7 +146,7 @@ pub trait VecZnxDftOps {
     ///
     /// # Panics
     /// If `bytes.len()` < [Module::bytes_of_vec_znx_dft].
-    fn new_vec_znx_dft_from_bytes(&self, size: usize, cols: usize, bytes: &mut [u8]) -> VecZnxDft;
+    fn new_vec_znx_dft_from_bytes(&self, cols: usize, limbs: usize, bytes: &mut [u8]) -> VecZnxDft<B>;
 
     /// Returns a new [VecZnxDft] with the provided bytes array as backing array.
     ///
@@ -156,7 +159,7 @@ pub trait VecZnxDftOps {
     ///
     /// # Panics
     /// If `bytes.len()` < [Module::bytes_of_vec_znx_dft].
-    fn new_vec_znx_dft_from_bytes_borrow(&self, size: usize, cols: usize, bytes: &mut [u8]) -> VecZnxDft;
+    fn new_vec_znx_dft_from_bytes_borrow(&self, cols: usize, limbs: usize, bytes: &mut [u8]) -> VecZnxDft<B>;
 
     /// Returns a new [VecZnxDft] with the provided bytes array as backing array.
     ///
@@ -167,61 +170,51 @@ pub trait VecZnxDftOps {
     ///
     /// # Panics
     /// If `bytes.len()` < [Module::bytes_of_vec_znx_dft].
-    fn bytes_of_vec_znx_dft(&self, size: usize, cols: usize) -> usize;
+    fn bytes_of_vec_znx_dft(&self, cols: usize, limbs: usize) -> usize;
 
     /// Returns the minimum number of bytes necessary to allocate
     /// a new [VecZnxDft] through [VecZnxDft::from_bytes].
     fn vec_znx_idft_tmp_bytes(&self) -> usize;
 
     /// b <- IDFT(a), uses a as scratch space.
-    fn vec_znx_idft_tmp_a(&self, b: &mut VecZnxBig, a: &mut VecZnxDft);
+    fn vec_znx_idft_tmp_a(&self, b: &mut VecZnxBig<B>, a: &mut VecZnxDft<B>);
 
-    fn vec_znx_idft(&self, b: &mut VecZnxBig, a: &VecZnxDft, tmp_bytes: &mut [u8]);
+    fn vec_znx_idft(&self, b: &mut VecZnxBig<B>, a: &VecZnxDft<B>, tmp_bytes: &mut [u8]);
 
-    fn vec_znx_dft(&self, b: &mut VecZnxDft, a: &VecZnx);
+    fn vec_znx_dft(&self, b: &mut VecZnxDft<B>, a: &VecZnx);
 
-    fn vec_znx_dft_automorphism(&self, k: i64, b: &mut VecZnxDft, a: &VecZnxDft);
+    fn vec_znx_dft_automorphism(&self, k: i64, b: &mut VecZnxDft<B>, a: &VecZnxDft<B>);
 
-    fn vec_znx_dft_automorphism_inplace(&self, k: i64, a: &mut VecZnxDft, tmp_bytes: &mut [u8]);
+    fn vec_znx_dft_automorphism_inplace(&self, k: i64, a: &mut VecZnxDft<B>, tmp_bytes: &mut [u8]);
 
     fn vec_znx_dft_automorphism_tmp_bytes(&self) -> usize;
 }
 
-impl VecZnxDftOps for Module {
-    fn new_vec_znx_dft(&self, size: usize, cols: usize) -> VecZnxDft {
-        let mut data: Vec<u8> = alloc_aligned::<u8>(self.bytes_of_vec_znx_dft(size, cols));
-        let ptr: *mut u8 = data.as_mut_ptr();
-        VecZnxDft {
-            data: data,
-            ptr: ptr,
-            n: self.n(),
-            size: size,
-            layout: LAYOUT::COL,
-            cols: cols,
-            backend: self.backend(),
-        }
+impl VecZnxDftOps<FFT64> for Module<FFT64> {
+    fn new_vec_znx_dft(&self, cols: usize, limbs: usize) -> VecZnxDft<FFT64> {
+        VecZnxDft::<FFT64>::new(&self, cols, limbs)
     }
 
-    fn new_vec_znx_dft_from_bytes(&self, size: usize, cols: usize, tmp_bytes: &mut [u8]) -> VecZnxDft {
-        VecZnxDft::from_bytes(self, size, cols, tmp_bytes)
+    fn new_vec_znx_dft_from_bytes(&self, cols: usize, limbs: usize, tmp_bytes: &mut [u8]) -> VecZnxDft<FFT64> {
+        VecZnxDft::from_bytes(self, cols, limbs, tmp_bytes)
     }
 
-    fn new_vec_znx_dft_from_bytes_borrow(&self, size: usize, cols: usize, tmp_bytes: &mut [u8]) -> VecZnxDft {
-        VecZnxDft::from_bytes_borrow(self, size, cols, tmp_bytes)
+    fn new_vec_znx_dft_from_bytes_borrow(&self, cols: usize, limbs: usize, tmp_bytes: &mut [u8]) -> VecZnxDft<FFT64> {
+        VecZnxDft::from_bytes_borrow(self, cols, limbs, tmp_bytes)
     }
 
-    fn bytes_of_vec_znx_dft(&self, size: usize, cols: usize) -> usize {
-        unsafe { bytes_of_vec_znx_dft(self.ptr, cols as u64) as usize * size }
+    fn bytes_of_vec_znx_dft(&self, cols: usize, limbs: usize) -> usize {
+        unsafe { bytes_of_vec_znx_dft(self.ptr, limbs as u64) as usize * cols }
     }
 
-    fn vec_znx_idft_tmp_a(&self, b: &mut VecZnxBig, a: &mut VecZnxDft) {
+    fn vec_znx_idft_tmp_a(&self, b: &mut VecZnxBig<FFT64>, a: &mut VecZnxDft<FFT64>) {
         unsafe {
             vec_znx_dft::vec_znx_idft_tmp_a(
                 self.ptr,
                 b.ptr as *mut vec_znx_big_t,
-                b.cols() as u64,
+                b.poly_count() as u64,
                 a.ptr as *mut vec_znx_dft_t,
-                a.cols() as u64,
+                a.poly_count() as u64,
             )
         }
     }
@@ -234,21 +227,21 @@ impl VecZnxDftOps for Module {
     ///
     /// # Panics
     /// If b.cols < a_cols
-    fn vec_znx_dft(&self, b: &mut VecZnxDft, a: &VecZnx) {
+    fn vec_znx_dft(&self, b: &mut VecZnxDft<FFT64>, a: &VecZnx) {
         unsafe {
             vec_znx_dft::vec_znx_dft(
                 self.ptr,
                 b.ptr as *mut vec_znx_dft_t,
-                b.cols() as u64,
+                b.limbs() as u64,
                 a.as_ptr(),
-                a.cols() as u64,
-                a.n() as u64,
+                a.limbs() as u64,
+                (a.n() * a.cols()) as u64,
             )
         }
     }
 
     // b <- IDFT(a), scratch space size obtained with [vec_znx_idft_tmp_bytes].
-    fn vec_znx_idft(&self, b: &mut VecZnxBig, a: &VecZnxDft, tmp_bytes: &mut [u8]) {
+    fn vec_znx_idft(&self, b: &mut VecZnxBig<FFT64>, a: &VecZnxDft<FFT64>, tmp_bytes: &mut [u8]) {
         #[cfg(debug_assertions)]
         {
             assert!(
@@ -263,29 +256,29 @@ impl VecZnxDftOps for Module {
             vec_znx_dft::vec_znx_idft(
                 self.ptr,
                 b.ptr as *mut vec_znx_big_t,
-                b.cols() as u64,
+                b.poly_count() as u64,
                 a.ptr as *const vec_znx_dft_t,
-                a.cols() as u64,
+                a.poly_count() as u64,
                 tmp_bytes.as_mut_ptr(),
             )
         }
     }
 
-    fn vec_znx_dft_automorphism(&self, k: i64, b: &mut VecZnxDft, a: &VecZnxDft) {
+    fn vec_znx_dft_automorphism(&self, k: i64, b: &mut VecZnxDft<FFT64>, a: &VecZnxDft<FFT64>) {
         unsafe {
             vec_znx_dft::vec_znx_dft_automorphism(
                 self.ptr,
                 k,
                 b.ptr as *mut vec_znx_dft_t,
-                b.cols() as u64,
+                b.poly_count() as u64,
                 a.ptr as *const vec_znx_dft_t,
-                a.cols() as u64,
+                a.poly_count() as u64,
                 [0u8; 0].as_mut_ptr(),
             );
         }
     }
 
-    fn vec_znx_dft_automorphism_inplace(&self, k: i64, a: &mut VecZnxDft, tmp_bytes: &mut [u8]) {
+    fn vec_znx_dft_automorphism_inplace(&self, k: i64, a: &mut VecZnxDft<FFT64>, tmp_bytes: &mut [u8]) {
         #[cfg(debug_assertions)]
         {
             assert!(
@@ -301,9 +294,9 @@ impl VecZnxDftOps for Module {
                 self.ptr,
                 k,
                 a.ptr as *mut vec_znx_dft_t,
-                a.cols() as u64,
+                a.poly_count() as u64,
                 a.ptr as *const vec_znx_dft_t,
-                a.cols() as u64,
+                a.poly_count() as u64,
                 tmp_bytes.as_mut_ptr(),
             );
         }
@@ -321,41 +314,47 @@ impl VecZnxDftOps for Module {
 
 #[cfg(test)]
 mod tests {
-    use crate::{BACKEND, Module, Sampling, VecZnx, VecZnxDft, VecZnxDftOps, VecZnxOps, alloc_aligned};
+    use crate::{FFT64, Module, Sampling, VecZnx, VecZnxDft, VecZnxDftOps, VecZnxOps, alloc_aligned};
     use itertools::izip;
     use sampling::source::{Source, new_seed};
 
     #[test]
     fn test_automorphism_dft() {
-        let module: Module = Module::new(128, BACKEND::FFT64);
+        let module: Module<FFT64> = Module::<FFT64>::new(128);
 
-        let cols: usize = 2;
+        let limbs: usize = 2;
         let log_base2k: usize = 17;
-        let mut a: VecZnx = module.new_vec_znx(1, cols);
-        let mut a_dft: VecZnxDft = module.new_vec_znx_dft(1, cols);
-        let mut b_dft: VecZnxDft = module.new_vec_znx_dft(1, cols);
+        let mut a: VecZnx = module.new_vec_znx(1, limbs);
+        let mut a_dft: VecZnxDft<FFT64> = module.new_vec_znx_dft(1, limbs);
+        let mut b_dft: VecZnxDft<FFT64> = module.new_vec_znx_dft(1, limbs);
 
         let mut source: Source = Source::new(new_seed());
-        module.fill_uniform(log_base2k, &mut a, cols, &mut source);
+        module.fill_uniform(log_base2k, &mut a, 0, limbs, &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);
 
+        
+
         // a_dft <- AUTO(a_dft)
         module.vec_znx_dft_automorphism_inplace(p, &mut a_dft, &mut tmp_bytes);
 
+        println!("123");
+
         // a <- AUTO(a)
         module.vec_znx_automorphism_inplace(p, &mut a);
 
         // b_dft <- DFT(AUTO(a))
         module.vec_znx_dft(&mut b_dft, &a);
 
-        let a_f64: &[f64] = a_dft.raw(&module);
-        let b_f64: &[f64] = b_dft.raw(&module);
+        let a_f64: &[f64] = a_dft.raw();
+        let b_f64: &[f64] = b_dft.raw();
         izip!(a_f64.iter(), b_f64.iter()).for_each(|(ai, bi)| {
             assert!((ai - bi).abs() <= 1e-9, "{:+e} > 1e-9", (ai - bi).abs());
         });
diff --git a/base2k/src/vmp.rs b/base2k/src/vmp.rs
index b04232d..05dd027 100644
--- a/base2k/src/vmp.rs
+++ b/base2k/src/vmp.rs
@@ -1,7 +1,8 @@
 use crate::ffi::vec_znx_big::vec_znx_big_t;
 use crate::ffi::vec_znx_dft::vec_znx_dft_t;
 use crate::ffi::vmp::{self, vmp_pmat_t};
-use crate::{BACKEND, Infos, LAYOUT, Module, VecZnx, VecZnxBig, VecZnxDft, alloc_aligned, assert_alignement};
+use crate::{Backend, FFT64, Infos, Module, VecZnx, VecZnxBig, VecZnxDft, alloc_aligned, assert_alignement};
+use std::marker::PhantomData;
 
 /// Vector Matrix Product Prepared Matrix: a vector of [VecZnx],
 /// stored as a 3D matrix in the DFT domain in a single contiguous array.
@@ -9,28 +10,23 @@ use crate::{BACKEND, Infos, LAYOUT, Module, VecZnx, VecZnxBig, VecZnxDft, alloc_
 ///
 /// [VmpPMat] is used to permform a vector matrix product between a [VecZnx]/[VecZnxDft] and a [VmpPMat].
 /// See the trait [VmpPMatOps] for additional information.
-pub struct VmpPMat {
+pub struct VmpPMat<B: Backend> {
     /// Raw data, is empty if borrowing scratch space.
     data: Vec<u8>,
     /// Pointer to data. Can point to scratch space.
     ptr: *mut u8,
-    /// The size of the decomposition basis (i.e. nb. [VecZnxDft]).
-    rows: usize,
-    /// The size of each [VecZnxDft].
-    cols: usize,
-    /// The ring degree of each [VecZnxDft].      
+    /// The ring degree of each polynomial.
     n: usize,
-    /// 1nd dim: the number of stacked [VecZnxDft] per decomposition basis (row-dimension).
-    /// A value greater than one enables to compute a sum of [VecZnx] x [VmpPMat].
-    /// 2st dim: the number of stacked [VecZnxDft]  (col-dimension).
-    /// A value greater than one enables to compute multiple [VecZnx] x [VmpPMat] in parallel.
-    layout: LAYOUT,
-    /// The backend fft or ntt.
-    backend: BACKEND,
+    /// Number of rows
+    rows: usize,
+    /// Number of cols
+    cols: usize,
+    /// The number of small polynomials
+    limbs: usize,
+    _marker: PhantomData<B>,
 }
 
-impl Infos for VmpPMat {
-    /// Returns the ring dimension of the [VmpPMat].
+impl<B: Backend> Infos for VmpPMat<B> {
     fn n(&self) -> usize {
         self.n
     }
@@ -39,29 +35,39 @@ impl Infos for VmpPMat {
         (usize::BITS - (self.n() - 1).leading_zeros()) as _
     }
 
-    fn size(&self) -> usize {
-        self.size
-    }
-
-    fn layout(&self) -> LAYOUT {
-        self.layout
-    }
-
-    /// Returns the number of rows (i.e. of [VecZnxDft]) of the [VmpPMat]
     fn rows(&self) -> usize {
         self.rows
     }
 
-    /// Returns the number of cols of the [VmpPMat].
-    /// The number of cols refers to the number of cols  
-    /// of each [VecZnxDft].
-    /// This method is equivalent to [Self::cols].
     fn cols(&self) -> usize {
         self.cols
     }
+
+    fn limbs(&self) -> usize {
+        self.limbs
+    }
+
+    fn poly_count(&self) -> usize {
+        self.rows * self.cols * self.limbs
+    }
 }
 
-impl VmpPMat {
+impl VmpPMat<FFT64> {
+
+    fn new(module: &Module<FFT64>, rows: usize, cols: usize, limbs: usize) -> VmpPMat<FFT64> {
+        let mut data: Vec<u8> = alloc_aligned::<u8>(module.bytes_of_vmp_pmat(rows, cols, limbs));
+        let ptr: *mut u8 = data.as_mut_ptr();
+        VmpPMat::<FFT64> {
+            data: data,
+            ptr: ptr,
+            n: module.n(),
+            rows: rows,
+            cols: cols,
+            limbs: limbs,
+            _marker: PhantomData,
+        }
+    }
+
     pub fn as_ptr(&self) -> *const u8 {
         self.ptr
     }
@@ -74,41 +80,31 @@ impl VmpPMat {
         self.data.len() == 0
     }
 
-    /// Returns a non-mutable reference of `T` of the entire contiguous array of the [VmpPMat].
-    /// When using [`crate::FFT64`] as backend, `T` should be [f64].
-    /// When using [`crate::NTT120`] as backend, `T` should be [i64].
-    /// The length of the returned array is rows * cols * n.
-    pub fn raw<T>(&self) -> &[T] {
-        let ptr: *const T = self.ptr as *const T;
-        let len: usize = (self.rows() * self.cols() * self.n() * 8) / std::mem::size_of::<T>();
-        unsafe { &std::slice::from_raw_parts(ptr, len) }
+    /// Returns a non-mutable reference to the entire contiguous array of the [VmpPMat].
+    pub fn raw(&self) -> &[f64] {
+        let ptr: *const f64 = self.ptr as *const f64;
+        let size: usize = self.n() * self.poly_count();
+        unsafe { &std::slice::from_raw_parts(ptr, size) }
     }
 
-    /// Returns a non-mutable reference of `T` of the entire contiguous array of the [VmpPMat].
-    /// When using [`crate::FFT64`] as backend, `T` should be [f64].
-    /// When using [`crate::NTT120`] as backend, `T` should be [i64].
-    /// The length of the returned array is rows * cols * n.
-    pub fn raw_mut<T>(&self) -> &mut [T] {
-        let ptr: *mut T = self.ptr as *mut T;
-        let len: usize = (self.rows() * self.cols() * self.n() * 8) / std::mem::size_of::<T>();
-        unsafe { std::slice::from_raw_parts_mut(ptr, len) }
+    /// Returns a mutable reference of to the entire contiguous array of the [VmpPMat].
+    pub fn raw_mut(&self) -> &mut [f64] {
+        let ptr: *mut f64 = self.ptr as *mut f64;
+        let size: usize = self.n() * self.poly_count();
+        unsafe { std::slice::from_raw_parts_mut(ptr, size) }
     }
 
     /// Returns a copy of the backend array at index (i, j) of the [VmpPMat].
-    /// When using [`crate::FFT64`] as backend, `T` should be [f64].
-    /// When using [`crate::NTT120`] as backend, `T` should be [i64].
     ///
     /// # Arguments
     ///
     /// * `row`: row index (i).
     /// * `col`: col index (j).
-    pub fn at<T: Default + Copy>(&self, row: usize, col: usize) -> Vec<T> {
-        let mut res: Vec<T> = alloc_aligned(self.n);
+    pub fn at(&self, row: usize, col: usize) -> Vec<f64> {
+        let mut res: Vec<f64> = alloc_aligned(self.n);
 
         if self.n < 8 {
-            res.copy_from_slice(
-                &self.raw::<T>()[(row + col * self.rows()) * self.n()..(row + col * self.rows()) * (self.n() + 1)],
-            );
+            res.copy_from_slice(&self.raw()[(row + col * self.rows()) * self.n()..(row + col * self.rows()) * (self.n() + 1)]);
         } else {
             (0..self.n >> 3).for_each(|blk| {
                 res[blk * 8..(blk + 1) * 8].copy_from_slice(&self.at_block(row, col, blk)[..8]);
@@ -118,43 +114,37 @@ impl VmpPMat {
         res
     }
 
-    /// When using [`crate::FFT64`] as backend, `T` should be [f64].
-    /// When using [`crate::NTT120`] as backend, `T` should be [i64].
-    fn at_block<T>(&self, row: usize, col: usize, blk: usize) -> &[T] {
+    fn at_block(&self, row: usize, col: usize, blk: usize) -> &[f64] {
         let nrows: usize = self.rows();
-        let ncols: usize = self.cols();
-        if col == (ncols - 1) && (ncols & 1 == 1) {
-            &self.raw::<T>()[blk * nrows * ncols * 8 + col * nrows * 8 + row * 8..]
+        let nsize: usize = self.limbs();
+        if col == (nsize - 1) && (nsize & 1 == 1) {
+            &self.raw()[blk * nrows * nsize * 8 + col * nrows * 8 + row * 8..]
         } else {
-            &self.raw::<T>()[blk * nrows * ncols * 8 + (col / 2) * (2 * nrows) * 8 + row * 2 * 8 + (col % 2) * 8..]
+            &self.raw()[blk * nrows * nsize * 8 + (col / 2) * (2 * nrows) * 8 + row * 2 * 8 + (col % 2) * 8..]
         }
     }
-
-    fn backend(&self) -> BACKEND {
-        self.backend
-    }
 }
 
 /// This trait implements methods for vector matrix product,
 /// that is, multiplying a [VecZnx] with a [VmpPMat].
-pub trait VmpPMatOps {
-    fn bytes_of_vmp_pmat(&self, size: usize, rows: usize, cols: usize) -> usize;
+pub trait VmpPMatOps<B: Backend> {
+    fn bytes_of_vmp_pmat(&self, rows: usize, cols: usize, limbs: usize) -> usize;
 
     /// Allocates a new [VmpPMat] with the given number of rows and columns.
     ///
     /// # Arguments
     ///
     /// * `rows`: number of rows (number of [VecZnxDft]).
-    /// * `cols`: number of cols (number of cols of each [VecZnxDft]).
-    fn new_vmp_pmat(&self, size: usize, rows: usize, cols: usize) -> VmpPMat;
+    /// * `size`: number of size (number of size of each [VecZnxDft]).
+    fn new_vmp_pmat(&self, rows: usize, cols: usize, limbs: usize) -> VmpPMat<B>;
 
     /// Returns the number of bytes needed as scratch space for [VmpPMatOps::vmp_prepare_contiguous].
     ///
     /// # Arguments
     ///
     /// * `rows`: number of rows of the [VmpPMat] used in [VmpPMatOps::vmp_prepare_contiguous].
-    /// * `cols`: number of cols of the [VmpPMat] used in [VmpPMatOps::vmp_prepare_contiguous].
-    fn vmp_prepare_tmp_bytes(&self, rows: usize, cols: usize) -> usize;
+    /// * `size`: number of size of the [VmpPMat] used in [VmpPMatOps::vmp_prepare_contiguous].
+    fn vmp_prepare_tmp_bytes(&self, rows: usize, cols: usize, size: usize) -> usize;
 
     /// Prepares a [VmpPMat] from a contiguous array of [i64].
     /// The helper struct [Matrix3D] can be used to contruct and populate
@@ -165,18 +155,7 @@ pub trait VmpPMatOps {
     /// * `b`: [VmpPMat] on which the values are encoded.
     /// * `a`: the contiguous array of [i64] of the 3D matrix to encode on the [VmpPMat].
     /// * `buf`: scratch space, the size of buf can be obtained with [VmpPMatOps::vmp_prepare_tmp_bytes].
-    fn vmp_prepare_contiguous(&self, b: &mut VmpPMat, a: &[i64], buf: &mut [u8]);
-
-    /// Prepares a [VmpPMat] from a vector of [VecZnx].
-    ///
-    /// # Arguments
-    ///
-    /// * `b`: [VmpPMat] on which the values are encoded.
-    /// * `a`: the vector of [VecZnx] to encode on the [VmpPMat].
-    /// * `buf`: scratch space, the size of buf can be obtained with [VmpPMatOps::vmp_prepare_tmp_bytes].
-    ///
-    /// The size of buf can be obtained with [VmpPMatOps::vmp_prepare_tmp_bytes].
-    fn vmp_prepare_dblptr(&self, b: &mut VmpPMat, a: &[&[i64]], buf: &mut [u8]);
+    fn vmp_prepare_contiguous(&self, b: &mut VmpPMat<B>, a: &[i64], buf: &mut [u8]);
 
     /// Prepares the ith-row of [VmpPMat] from a [VecZnx].
     ///
@@ -188,7 +167,7 @@ pub trait VmpPMatOps {
     /// * `buf`: scratch space, the size of buf can be obtained with [VmpPMatOps::vmp_prepare_tmp_bytes].
     ///
     /// The size of buf can be obtained with [VmpPMatOps::vmp_prepare_tmp_bytes].
-    fn vmp_prepare_row(&self, b: &mut VmpPMat, a: &[i64], row_i: usize, tmp_bytes: &mut [u8]);
+    fn vmp_prepare_row(&self, b: &mut VmpPMat<B>, a: &[i64], row_i: usize, tmp_bytes: &mut [u8]);
 
     /// Extracts the ith-row of [VmpPMat] into a [VecZnxBig].
     ///
@@ -197,7 +176,7 @@ pub trait VmpPMatOps {
     /// * `b`: the [VecZnxBig] to on which to extract the row of the [VmpPMat].
     /// * `a`: [VmpPMat] on which the values are encoded.
     /// * `row_i`: the index of the row to extract.
-    fn vmp_extract_row(&self, b: &mut VecZnxBig, a: &VmpPMat, row_i: usize);
+    fn vmp_extract_row(&self, b: &mut VecZnxBig<B>, a: &VmpPMat<B>, row_i: usize);
 
     /// Prepares the ith-row of [VmpPMat] from a [VecZnxDft].
     ///
@@ -208,7 +187,7 @@ pub trait VmpPMatOps {
     /// * `row_i`: the index of the row to prepare.
     ///
     /// The size of buf can be obtained with [VmpPMatOps::vmp_prepare_tmp_bytes].
-    fn vmp_prepare_row_dft(&self, b: &mut VmpPMat, a: &VecZnxDft, row_i: usize);
+    fn vmp_prepare_row_dft(&self, b: &mut VmpPMat<B>, a: &VecZnxDft<B>, row_i: usize);
 
     /// Extracts the ith-row of [VmpPMat] into a [VecZnxDft].
     ///
@@ -217,17 +196,17 @@ pub trait VmpPMatOps {
     /// * `b`: the [VecZnxDft] to on which to extract the row of the [VmpPMat].
     /// * `a`: [VmpPMat] on which the values are encoded.
     /// * `row_i`: the index of the row to extract.
-    fn vmp_extract_row_dft(&self, b: &mut VecZnxDft, a: &VmpPMat, row_i: usize);
+    fn vmp_extract_row_dft(&self, b: &mut VecZnxDft<B>, a: &VmpPMat<B>, row_i: usize);
 
     /// Returns the size of the stratch space necessary for [VmpPMatOps::vmp_apply_dft].
     ///
     /// # Arguments
     ///
-    /// * `c_cols`: number of cols of the output [VecZnxDft].
-    /// * `a_cols`: number of cols of the input [VecZnx].
+    /// * `c_size`: number of size of the output [VecZnxDft].
+    /// * `a_size`: number of size of the input [VecZnx].
     /// * `rows`: number of rows of the input [VmpPMat].
-    /// * `cols`: number of cols of the input [VmpPMat].
-    fn vmp_apply_dft_tmp_bytes(&self, c_cols: usize, a_cols: usize, rows: usize, cols: usize) -> usize;
+    /// * `size`: number of size of the input [VmpPMat].
+    fn vmp_apply_dft_tmp_bytes(&self, c_size: usize, a_size: usize, rows: usize, size: usize) -> usize;
 
     /// Applies the vector matrix product [VecZnxDft] x [VmpPMat].
     ///
@@ -235,8 +214,8 @@ pub trait VmpPMatOps {
     /// where each [crate::Scalar] is a limb of the input [VecZnxDft] (equivalent to an [crate::SvpPPol])
     /// and each vector a [VecZnxDft] (row) of the [VmpPMat].
     ///
-    /// As such, given an input [VecZnx] of `i` cols and a [VmpPMat] of `i` rows and
-    /// `j` cols, the output is a [VecZnx] of `j` cols.
+    /// As such, given an input [VecZnx] of `i` size and a [VmpPMat] of `i` rows and
+    /// `j` size, the output is a [VecZnx] of `j` size.
     ///
     /// If there is a mismatch between the dimensions the largest valid ones are used.
     ///
@@ -253,7 +232,7 @@ pub trait VmpPMatOps {
     /// * `a`: the left operand [VecZnx] of the vector matrix product.
     /// * `b`: the right operand [VmpPMat] of the vector matrix product.
     /// * `buf`: scratch space, the size can be obtained with [VmpPMatOps::vmp_apply_dft_tmp_bytes].
-    fn vmp_apply_dft(&self, c: &mut VecZnxDft, a: &VecZnx, b: &VmpPMat, buf: &mut [u8]);
+    fn vmp_apply_dft(&self, c: &mut VecZnxDft<B>, a: &VecZnx, b: &VmpPMat<B>, buf: &mut [u8]);
 
     /// Applies the vector matrix product [VecZnxDft] x [VmpPMat] and adds on the receiver.
     ///
@@ -261,8 +240,8 @@ pub trait VmpPMatOps {
     /// where each [crate::Scalar] is a limb of the input [VecZnxDft] (equivalent to an [crate::SvpPPol])
     /// and each vector a [VecZnxDft] (row) of the [VmpPMat].
     ///
-    /// As such, given an input [VecZnx] of `i` cols and a [VmpPMat] of `i` rows and
-    /// `j` cols, the output is a [VecZnx] of `j` cols.
+    /// As such, given an input [VecZnx] of `i` size and a [VmpPMat] of `i` rows and
+    /// `j` size, the output is a [VecZnx] of `j` size.
     ///
     /// If there is a mismatch between the dimensions the largest valid ones are used.
     ///
@@ -279,17 +258,17 @@ pub trait VmpPMatOps {
     /// * `a`: the left operand [VecZnx] of the vector matrix product.
     /// * `b`: the right operand [VmpPMat] of the vector matrix product.
     /// * `buf`: scratch space, the size can be obtained with [VmpPMatOps::vmp_apply_dft_tmp_bytes].
-    fn vmp_apply_dft_add(&self, c: &mut VecZnxDft, a: &VecZnx, b: &VmpPMat, buf: &mut [u8]);
+    fn vmp_apply_dft_add(&self, c: &mut VecZnxDft<B>, a: &VecZnx, b: &VmpPMat<B>, buf: &mut [u8]);
 
     /// Returns the size of the stratch space necessary for [VmpPMatOps::vmp_apply_dft_to_dft].
     ///
     /// # Arguments
     ///
-    /// * `c_cols`: number of cols of the output [VecZnxDft].
-    /// * `a_cols`: number of cols of the input [VecZnxDft].
+    /// * `c_size`: number of size of the output [VecZnxDft].
+    /// * `a_size`: number of size of the input [VecZnxDft].
     /// * `rows`: number of rows of the input [VmpPMat].
-    /// * `cols`: number of cols of the input [VmpPMat].
-    fn vmp_apply_dft_to_dft_tmp_bytes(&self, c_cols: usize, a_cols: usize, rows: usize, cols: usize) -> usize;
+    /// * `size`: number of size of the input [VmpPMat].
+    fn vmp_apply_dft_to_dft_tmp_bytes(&self, c_size: usize, a_size: usize, rows: usize, size: usize) -> usize;
 
     /// Applies the vector matrix product [VecZnxDft] x [VmpPMat].
     /// The size of `buf` is given by [VmpPMatOps::vmp_apply_dft_to_dft_tmp_bytes].
@@ -298,8 +277,8 @@ pub trait VmpPMatOps {
     /// where each [crate::Scalar] is a limb of the input [VecZnxDft] (equivalent to an [crate::SvpPPol])
     /// and each vector a [VecZnxDft] (row) of the [VmpPMat].
     ///
-    /// As such, given an input [VecZnx] of `i` cols and a [VmpPMat] of `i` rows and
-    /// `j` cols, the output is a [VecZnx] of `j` cols.
+    /// As such, given an input [VecZnx] of `i` size and a [VmpPMat] of `i` rows and
+    /// `j` size, the output is a [VecZnx] of `j` size.
     ///
     /// If there is a mismatch between the dimensions the largest valid ones are used.
     ///
@@ -316,7 +295,7 @@ pub trait VmpPMatOps {
     /// * `a`: the left operand [VecZnxDft] of the vector matrix product.
     /// * `b`: the right operand [VmpPMat] of the vector matrix product.
     /// * `buf`: scratch space, the size can be obtained with [VmpPMatOps::vmp_apply_dft_to_dft_tmp_bytes].
-    fn vmp_apply_dft_to_dft(&self, c: &mut VecZnxDft, a: &VecZnxDft, b: &VmpPMat, buf: &mut [u8]);
+    fn vmp_apply_dft_to_dft(&self, c: &mut VecZnxDft<B>, a: &VecZnxDft<B>, b: &VmpPMat<B>, buf: &mut [u8]);
 
     /// Applies the vector matrix product [VecZnxDft] x [VmpPMat] and adds on top of the receiver instead of overwritting it.
     /// The size of `buf` is given by [VmpPMatOps::vmp_apply_dft_to_dft_tmp_bytes].
@@ -325,8 +304,8 @@ pub trait VmpPMatOps {
     /// where each [crate::Scalar] is a limb of the input [VecZnxDft] (equivalent to an [crate::SvpPPol])
     /// and each vector a [VecZnxDft] (row) of the [VmpPMat].
     ///
-    /// As such, given an input [VecZnx] of `i` cols and a [VmpPMat] of `i` rows and
-    /// `j` cols, the output is a [VecZnx] of `j` cols.
+    /// As such, given an input [VecZnx] of `i` size and a [VmpPMat] of `i` rows and
+    /// `j` size, the output is a [VecZnx] of `j` size.
     ///
     /// If there is a mismatch between the dimensions the largest valid ones are used.
     ///
@@ -343,7 +322,7 @@ pub trait VmpPMatOps {
     /// * `a`: the left operand [VecZnxDft] of the vector matrix product.
     /// * `b`: the right operand [VmpPMat] of the vector matrix product.
     /// * `buf`: scratch space, the size can be obtained with [VmpPMatOps::vmp_apply_dft_to_dft_tmp_bytes].
-    fn vmp_apply_dft_to_dft_add(&self, c: &mut VecZnxDft, a: &VecZnxDft, b: &VmpPMat, buf: &mut [u8]);
+    fn vmp_apply_dft_to_dft_add(&self, c: &mut VecZnxDft<B>, a: &VecZnxDft<B>, b: &VmpPMat<B>, buf: &mut [u8]);
 
     /// Applies the vector matrix product [VecZnxDft] x [VmpPMat] in place.
     /// The size of `buf` is given by [VmpPMatOps::vmp_apply_dft_to_dft_tmp_bytes].
@@ -352,8 +331,8 @@ pub trait VmpPMatOps {
     /// where each [crate::Scalar] is a limb of the input [VecZnxDft] (equivalent to an [crate::SvpPPol])
     /// and each vector a [VecZnxDft] (row) of the [VmpPMat].
     ///
-    /// As such, given an input [VecZnx] of `i` cols and a [VmpPMat] of `i` rows and
-    /// `j` cols, the output is a [VecZnx] of `j` cols.
+    /// As such, given an input [VecZnx] of `i` size and a [VmpPMat] of `i` rows and
+    /// `j` size, the output is a [VecZnx] of `j` size.
     ///
     /// If there is a mismatch between the dimensions the largest valid ones are used.
     ///
@@ -369,38 +348,29 @@ pub trait VmpPMatOps {
     /// * `b`: the input and output of the vector matrix product, as a [VecZnxDft].
     /// * `a`: the right operand [VmpPMat] of the vector matrix product.
     /// * `buf`: scratch space, the size can be obtained with [VmpPMatOps::vmp_apply_dft_to_dft_tmp_bytes].
-    fn vmp_apply_dft_to_dft_inplace(&self, b: &mut VecZnxDft, a: &VmpPMat, buf: &mut [u8]);
+    fn vmp_apply_dft_to_dft_inplace(&self, b: &mut VecZnxDft<B>, a: &VmpPMat<B>, buf: &mut [u8]);
 }
 
-impl VmpPMatOps for Module {
-    fn bytes_of_vmp_pmat(&self, size: usize, rows: usize, cols: usize) -> usize {
-        unsafe { vmp::bytes_of_vmp_pmat(self.ptr, rows as u64, cols as u64) as usize * size }
+impl VmpPMatOps<FFT64> for Module<FFT64> {
+
+    fn new_vmp_pmat(&self, rows: usize, cols: usize, limbs: usize) -> VmpPMat<FFT64> {
+        VmpPMat::<FFT64>::new(self, rows, cols, limbs)
     }
 
-    fn new_vmp_pmat(&self, size: usize, rows: usize, cols: usize) -> VmpPMat {
-        let mut data: Vec<u8> = alloc_aligned::<u8>(self.bytes_of_vmp_pmat(size, rows, cols));
-        let ptr: *mut u8 = data.as_mut_ptr();
-        VmpPMat {
-            data: data,
-            ptr: ptr,
-            n: self.n(),
-            size: size,
-            layout: LAYOUT::COL,
-            cols: cols,
-            rows: rows,
-            backend: self.backend(),
-        }
+    fn bytes_of_vmp_pmat(&self, rows: usize, cols: usize, limbs: usize) -> usize {
+        unsafe { vmp::bytes_of_vmp_pmat(self.ptr, rows as u64, (limbs* cols) as u64) as usize  }
     }
 
-    fn vmp_prepare_tmp_bytes(&self, rows: usize, cols: usize) -> usize {
-        unsafe { vmp::vmp_prepare_tmp_bytes(self.ptr, rows as u64, cols as u64) as usize }
+    fn vmp_prepare_tmp_bytes(&self, rows: usize, cols: usize, size: usize) -> usize {
+        unsafe { vmp::vmp_prepare_tmp_bytes(self.ptr, rows as u64, (size * cols) as u64) as usize  }
     }
 
-    fn vmp_prepare_contiguous(&self, b: &mut VmpPMat, a: &[i64], tmp_bytes: &mut [u8]) {
-        debug_assert_eq!(a.len(), b.n * b.rows * b.cols);
-        debug_assert!(tmp_bytes.len() >= self.vmp_prepare_tmp_bytes(b.rows(), b.cols()));
+    fn vmp_prepare_contiguous(&self, b: &mut VmpPMat<FFT64>, a: &[i64], tmp_bytes: &mut [u8]) {
+        
         #[cfg(debug_assertions)]
         {
+            assert_eq!(a.len(), b.n() * b.poly_count());
+            assert!(tmp_bytes.len() >= self.vmp_prepare_tmp_bytes(b.rows(), b.cols(), b.limbs()));
             assert_alignement(tmp_bytes.as_ptr());
         }
         unsafe {
@@ -409,40 +379,17 @@ impl VmpPMatOps for Module {
                 b.as_mut_ptr() as *mut vmp_pmat_t,
                 a.as_ptr(),
                 b.rows() as u64,
-                b.cols() as u64,
+                (b.limbs()*b.cols()) as u64,
                 tmp_bytes.as_mut_ptr(),
             );
         }
     }
 
-    fn vmp_prepare_dblptr(&self, b: &mut VmpPMat, a: &[&[i64]], tmp_bytes: &mut [u8]) {
-        let ptrs: Vec<*const i64> = a.iter().map(|v| v.as_ptr()).collect();
+    fn vmp_prepare_row(&self, b: &mut VmpPMat<FFT64>, a: &[i64], row_i: usize, tmp_bytes: &mut [u8]) {
         #[cfg(debug_assertions)]
-        {
-            debug_assert_eq!(a.len(), b.rows);
-            a.iter().for_each(|ai| {
-                debug_assert_eq!(ai.len(), b.n * b.cols);
-            });
-            debug_assert!(tmp_bytes.len() >= self.vmp_prepare_tmp_bytes(b.rows(), b.cols()));
-            assert_alignement(tmp_bytes.as_ptr());
-        }
-        unsafe {
-            vmp::vmp_prepare_dblptr(
-                self.ptr,
-                b.as_mut_ptr() as *mut vmp_pmat_t,
-                ptrs.as_ptr(),
-                b.rows() as u64,
-                b.cols() as u64,
-                tmp_bytes.as_mut_ptr(),
-            );
-        }
-    }
-
-    fn vmp_prepare_row(&self, b: &mut VmpPMat, a: &[i64], row_i: usize, tmp_bytes: &mut [u8]) {
-        #[cfg(debug_assertions)]
-        {
-            assert_eq!(a.len(), b.cols() * self.n());
-            assert!(tmp_bytes.len() >= self.vmp_prepare_tmp_bytes(b.rows(), b.cols()));
+        {   
+            assert_eq!(a.len(), b.limbs() * self.n() * b.cols());
+            assert!(tmp_bytes.len() >= self.vmp_prepare_tmp_bytes(b.rows(), b.cols(), b.limbs()));
             assert_alignement(tmp_bytes.as_ptr());
         }
         unsafe {
@@ -452,16 +399,17 @@ impl VmpPMatOps for Module {
                 a.as_ptr(),
                 row_i as u64,
                 b.rows() as u64,
-                b.cols() as u64,
+                (b.limbs()*b.cols()) as u64,
                 tmp_bytes.as_mut_ptr(),
             );
         }
     }
 
-    fn vmp_extract_row(&self, b: &mut VecZnxBig, a: &VmpPMat, row_i: usize) {
+    fn vmp_extract_row(&self, b: &mut VecZnxBig<FFT64>, a: &VmpPMat<FFT64>, row_i: usize) {
         #[cfg(debug_assertions)]
         {
             assert_eq!(a.n(), b.n());
+            assert_eq!(a.limbs(), b.limbs());
             assert_eq!(a.cols(), b.cols());
         }
         unsafe {
@@ -471,16 +419,16 @@ impl VmpPMatOps for Module {
                 a.as_ptr() as *const vmp_pmat_t,
                 row_i as u64,
                 a.rows() as u64,
-                a.cols() as u64,
+                (a.limbs()*a.cols()) as u64,
             );
         }
     }
 
-    fn vmp_prepare_row_dft(&self, b: &mut VmpPMat, a: &VecZnxDft, row_i: usize) {
+    fn vmp_prepare_row_dft(&self, b: &mut VmpPMat<FFT64>, a: &VecZnxDft<FFT64>, row_i: usize) {
         #[cfg(debug_assertions)]
         {
             assert_eq!(a.n(), b.n());
-            assert_eq!(a.cols(), b.cols());
+            assert_eq!(a.limbs(), b.limbs());
         }
         unsafe {
             vmp::vmp_prepare_row_dft(
@@ -489,16 +437,16 @@ impl VmpPMatOps for Module {
                 a.ptr as *const vec_znx_dft_t,
                 row_i as u64,
                 b.rows() as u64,
-                b.cols() as u64,
+                b.limbs() as u64,
             );
         }
     }
 
-    fn vmp_extract_row_dft(&self, b: &mut VecZnxDft, a: &VmpPMat, row_i: usize) {
+    fn vmp_extract_row_dft(&self, b: &mut VecZnxDft<FFT64>, a: &VmpPMat<FFT64>, row_i: usize) {
         #[cfg(debug_assertions)]
         {
             assert_eq!(a.n(), b.n());
-            assert_eq!(a.cols(), b.cols());
+            assert_eq!(a.limbs(), b.limbs());
         }
         unsafe {
             vmp::vmp_extract_row_dft(
@@ -507,48 +455,47 @@ impl VmpPMatOps for Module {
                 a.as_ptr() as *const vmp_pmat_t,
                 row_i as u64,
                 a.rows() as u64,
-                a.cols() as u64,
+                a.limbs() as u64,
             );
         }
     }
 
-    fn vmp_apply_dft_tmp_bytes(&self, res_cols: usize, a_cols: usize, gct_rows: usize, gct_cols: usize) -> usize {
+    fn vmp_apply_dft_tmp_bytes(&self, res_size: usize, a_size: usize, gct_rows: usize, gct_size: usize) -> usize {
         unsafe {
             vmp::vmp_apply_dft_tmp_bytes(
                 self.ptr,
-                res_cols as u64,
-                a_cols as u64,
+                res_size as u64,
+                a_size as u64,
                 gct_rows as u64,
-                gct_cols as u64,
+                gct_size as u64,
             ) as usize
         }
     }
 
-    fn vmp_apply_dft(&self, c: &mut VecZnxDft, a: &VecZnx, b: &VmpPMat, tmp_bytes: &mut [u8]) {
-        debug_assert!(tmp_bytes.len() >= self.vmp_apply_dft_tmp_bytes(c.cols(), a.cols(), b.rows(), b.cols()));
+    fn vmp_apply_dft(&self, c: &mut VecZnxDft<FFT64>, a: &VecZnx, b: &VmpPMat<FFT64>, tmp_bytes: &mut [u8]) {
+        debug_assert!(tmp_bytes.len() >= self.vmp_apply_dft_tmp_bytes(c.limbs(), a.limbs(), b.rows(), b.limbs()));
         #[cfg(debug_assertions)]
         {
             assert_alignement(tmp_bytes.as_ptr());
-            assert_eq!(a.size()*a.size(), b.size());
         }
         unsafe {
             vmp::vmp_apply_dft(
                 self.ptr,
                 c.ptr as *mut vec_znx_dft_t,
-                c.cols() as u64,
+                c.limbs() as u64,
                 a.as_ptr(),
-                a.cols() as u64,
-                (a.n()*a.size()) as u64,
+                a.limbs() as u64,
+                (a.n() * a.cols()) as u64,
                 b.as_ptr() as *const vmp_pmat_t,
                 b.rows() as u64,
-                b.cols() as u64,
+                b.limbs() as u64,
                 tmp_bytes.as_mut_ptr(),
             )
         }
     }
 
-    fn vmp_apply_dft_add(&self, c: &mut VecZnxDft, a: &VecZnx, b: &VmpPMat, tmp_bytes: &mut [u8]) {
-        debug_assert!(tmp_bytes.len() >= self.vmp_apply_dft_tmp_bytes(c.cols(), a.cols(), b.rows(), b.cols()));
+    fn vmp_apply_dft_add(&self, c: &mut VecZnxDft<FFT64>, a: &VecZnx, b: &VmpPMat<FFT64>, tmp_bytes: &mut [u8]) {
+        debug_assert!(tmp_bytes.len() >= self.vmp_apply_dft_tmp_bytes(c.limbs(), a.limbs(), b.rows(), b.limbs()));
         #[cfg(debug_assertions)]
         {
             assert_alignement(tmp_bytes.as_ptr());
@@ -557,32 +504,32 @@ impl VmpPMatOps for Module {
             vmp::vmp_apply_dft_add(
                 self.ptr,
                 c.ptr as *mut vec_znx_dft_t,
-                c.cols() as u64,
+                c.limbs() as u64,
                 a.as_ptr(),
-                a.cols() as u64,
-                (a.n()*a.size()) as u64,
+                a.limbs() as u64,
+                (a.n() * a.limbs()) as u64,
                 b.as_ptr() as *const vmp_pmat_t,
                 b.rows() as u64,
-                b.cols() as u64,
+                b.limbs() as u64,
                 tmp_bytes.as_mut_ptr(),
             )
         }
     }
 
-    fn vmp_apply_dft_to_dft_tmp_bytes(&self, res_cols: usize, a_cols: usize, gct_rows: usize, gct_cols: usize) -> usize {
+    fn vmp_apply_dft_to_dft_tmp_bytes(&self, res_size: usize, a_size: usize, gct_rows: usize, gct_size: usize) -> usize {
         unsafe {
             vmp::vmp_apply_dft_to_dft_tmp_bytes(
                 self.ptr,
-                res_cols as u64,
-                a_cols as u64,
+                res_size as u64,
+                a_size as u64,
                 gct_rows as u64,
-                gct_cols as u64,
+                gct_size as u64,
             ) as usize
         }
     }
 
-    fn vmp_apply_dft_to_dft(&self, c: &mut VecZnxDft, a: &VecZnxDft, b: &VmpPMat, tmp_bytes: &mut [u8]) {
-        debug_assert!(tmp_bytes.len() >= self.vmp_apply_dft_to_dft_tmp_bytes(c.cols(), a.cols(), b.rows(), b.cols()));
+    fn vmp_apply_dft_to_dft(&self, c: &mut VecZnxDft<FFT64>, a: &VecZnxDft<FFT64>, b: &VmpPMat<FFT64>, tmp_bytes: &mut [u8]) {
+        debug_assert!(tmp_bytes.len() >= self.vmp_apply_dft_to_dft_tmp_bytes(c.limbs(), a.limbs(), b.rows(), b.limbs()));
         #[cfg(debug_assertions)]
         {
             assert_alignement(tmp_bytes.as_ptr());
@@ -591,19 +538,19 @@ impl VmpPMatOps for Module {
             vmp::vmp_apply_dft_to_dft(
                 self.ptr,
                 c.ptr as *mut vec_znx_dft_t,
-                c.cols() as u64,
+                c.limbs() as u64,
                 a.ptr as *const vec_znx_dft_t,
-                a.cols() as u64,
+                a.limbs() as u64,
                 b.as_ptr() as *const vmp_pmat_t,
                 b.rows() as u64,
-                b.cols() as u64,
+                b.limbs() as u64,
                 tmp_bytes.as_mut_ptr(),
             )
         }
     }
 
-    fn vmp_apply_dft_to_dft_add(&self, c: &mut VecZnxDft, a: &VecZnxDft, b: &VmpPMat, tmp_bytes: &mut [u8]) {
-        debug_assert!(tmp_bytes.len() >= self.vmp_apply_dft_to_dft_tmp_bytes(c.cols(), a.cols(), b.rows(), b.cols()));
+    fn vmp_apply_dft_to_dft_add(&self, c: &mut VecZnxDft<FFT64>, a: &VecZnxDft<FFT64>, b: &VmpPMat<FFT64>, tmp_bytes: &mut [u8]) {
+        debug_assert!(tmp_bytes.len() >= self.vmp_apply_dft_to_dft_tmp_bytes(c.limbs(), a.limbs(), b.rows(), b.limbs()));
         #[cfg(debug_assertions)]
         {
             assert_alignement(tmp_bytes.as_ptr());
@@ -612,19 +559,19 @@ impl VmpPMatOps for Module {
             vmp::vmp_apply_dft_to_dft_add(
                 self.ptr,
                 c.ptr as *mut vec_znx_dft_t,
-                c.cols() as u64,
+                c.limbs() as u64,
                 a.ptr as *const vec_znx_dft_t,
-                a.cols() as u64,
+                a.limbs() as u64,
                 b.as_ptr() as *const vmp_pmat_t,
                 b.rows() as u64,
-                b.cols() as u64,
+                b.limbs() as u64,
                 tmp_bytes.as_mut_ptr(),
             )
         }
     }
 
-    fn vmp_apply_dft_to_dft_inplace(&self, b: &mut VecZnxDft, a: &VmpPMat, tmp_bytes: &mut [u8]) {
-        debug_assert!(tmp_bytes.len() >= self.vmp_apply_dft_to_dft_tmp_bytes(b.cols(), b.cols(), a.rows(), a.cols()));
+    fn vmp_apply_dft_to_dft_inplace(&self, b: &mut VecZnxDft<FFT64>, a: &VmpPMat<FFT64>, tmp_bytes: &mut [u8]) {
+        debug_assert!(tmp_bytes.len() >= self.vmp_apply_dft_to_dft_tmp_bytes(b.limbs(), b.limbs(), a.rows(), a.limbs()));
         #[cfg(debug_assertions)]
         {
             assert_alignement(tmp_bytes.as_ptr());
@@ -633,12 +580,12 @@ impl VmpPMatOps for Module {
             vmp::vmp_apply_dft_to_dft(
                 self.ptr,
                 b.ptr as *mut vec_znx_dft_t,
-                b.cols() as u64,
+                b.limbs() as u64,
                 b.ptr as *mut vec_znx_dft_t,
-                b.cols() as u64,
+                b.limbs() as u64,
                 a.as_ptr() as *const vmp_pmat_t,
                 a.rows() as u64,
-                a.cols() as u64,
+                a.limbs() as u64,
                 tmp_bytes.as_mut_ptr(),
             )
         }
@@ -648,44 +595,45 @@ impl VmpPMatOps for Module {
 #[cfg(test)]
 mod tests {
     use crate::{
-        Module, Sampling, VecZnx, VecZnxBig, VecZnxBigOps, VecZnxDft, VecZnxDftOps, VecZnxOps, VmpPMat, VmpPMatOps, alloc_aligned,
+        FFT64, Module, Sampling, VecZnx, VecZnxBig, VecZnxBigOps, VecZnxDft, VecZnxDftOps, VecZnxOps, VmpPMat, VmpPMatOps,
+        alloc_aligned,
     };
     use sampling::source::Source;
 
     #[test]
     fn vmp_prepare_row_dft() {
-        let module: Module = Module::new(32, crate::BACKEND::FFT64);
+        let module: Module<FFT64> = Module::<FFT64>::new(32);
         let vpmat_rows: usize = 4;
-        let vpmat_cols: usize = 5;
+        let vpmat_size: usize = 5;
         let log_base2k: usize = 8;
-        let mut a: VecZnx = module.new_vec_znx(1, vpmat_cols);
-        let mut a_dft: VecZnxDft = module.new_vec_znx_dft(1, vpmat_cols);
-        let mut a_big: VecZnxBig = module.new_vec_znx_big(1, vpmat_cols);
-        let mut b_big: VecZnxBig = module.new_vec_znx_big(1, vpmat_cols);
-        let mut b_dft: VecZnxDft = module.new_vec_znx_dft(1, vpmat_cols);
-        let mut vmpmat_0: VmpPMat = module.new_vmp_pmat(1, vpmat_rows, vpmat_cols);
-        let mut vmpmat_1: VmpPMat = module.new_vmp_pmat(1, vpmat_rows, vpmat_cols);
+        let mut a: VecZnx = module.new_vec_znx(1, vpmat_size);
+        let mut a_dft: VecZnxDft<FFT64> = module.new_vec_znx_dft(1, vpmat_size);
+        let mut a_big: VecZnxBig<FFT64> = module.new_vec_znx_big(1, vpmat_size);
+        let mut b_big: VecZnxBig<FFT64> = module.new_vec_znx_big(1, vpmat_size);
+        let mut b_dft: VecZnxDft<FFT64> = module.new_vec_znx_dft(1, vpmat_size);
+        let mut vmpmat_0: VmpPMat<FFT64> = module.new_vmp_pmat(vpmat_rows, 1, vpmat_size);
+        let mut vmpmat_1: VmpPMat<FFT64> = module.new_vmp_pmat(vpmat_rows, 1, vpmat_size);
 
-        let mut tmp_bytes: Vec<u8> = alloc_aligned(module.vmp_prepare_tmp_bytes(vpmat_rows, vpmat_cols));
+        let mut tmp_bytes: Vec<u8> = alloc_aligned(module.vmp_prepare_tmp_bytes(vpmat_rows, 1, vpmat_size));
 
         for row_i in 0..vpmat_rows {
             let mut source: Source = Source::new([0u8; 32]);
-            module.fill_uniform(log_base2k, &mut a, vpmat_cols, &mut source);
+            module.fill_uniform(log_base2k, &mut a, 0, vpmat_size, &mut source);
             module.vec_znx_dft(&mut a_dft, &a);
             module.vmp_prepare_row(&mut vmpmat_0, &a.raw(), row_i, &mut tmp_bytes);
 
             // Checks that prepare(vmp_pmat, a) = prepare_dft(vmp_pmat, a_dft)
             module.vmp_prepare_row_dft(&mut vmpmat_1, &a_dft, row_i);
-            assert_eq!(vmpmat_0.raw::<u8>(), vmpmat_1.raw::<u8>());
+            assert_eq!(vmpmat_0.raw(), vmpmat_1.raw());
 
             // Checks that a_dft = extract_dft(prepare(vmp_pmat, a), b_dft)
             module.vmp_extract_row_dft(&mut b_dft, &vmpmat_0, row_i);
-            assert_eq!(a_dft.raw::<u8>(&module), b_dft.raw::<u8>(&module));
+            assert_eq!(a_dft.raw(), b_dft.raw());
 
             // Checks that a_big = extract(prepare_dft(vmp_pmat, a_dft), b_big)
             module.vmp_extract_row(&mut b_big, &vmpmat_0, row_i);
             module.vec_znx_idft(&mut a_big, &a_dft, &mut tmp_bytes);
-            assert_eq!(a_big.raw::<i64>(&module), b_big.raw::<i64>(&module));
+            assert_eq!(a_big.raw(), b_big.raw());
         }
 
         module.free();
diff --git a/rlwe/src/ciphertext.rs b/rlwe/src/ciphertext.rs
index 9d1fe1a..73addb5 100644
--- a/rlwe/src/ciphertext.rs
+++ b/rlwe/src/ciphertext.rs
@@ -1,6 +1,6 @@
 use crate::elem::{Elem, ElemCommon};
 use crate::parameters::Parameters;
-use base2k::{Infos, LAYOUT, Module, VecZnx, VmpPMat};
+use base2k::{Infos, Layout, Module, VecZnx, VmpPMat};
 
 pub struct Ciphertext<T>(pub Elem<T>);
 
@@ -38,7 +38,7 @@ where
         self.elem().size()
     }
 
-    fn layout(&self) -> LAYOUT {
+    fn layout(&self) -> Layout {
         self.elem().layout()
     }
 
diff --git a/rlwe/src/elem.rs b/rlwe/src/elem.rs
index e7e61c4..656cc3a 100644
--- a/rlwe/src/elem.rs
+++ b/rlwe/src/elem.rs
@@ -1,4 +1,4 @@
-use base2k::{Infos, LAYOUT, Module, VecZnx, VecZnxOps, VmpPMat, VmpPMatOps};
+use base2k::{Infos, Layout, Module, VecZnx, VecZnxOps, VmpPMat, VmpPMatOps};
 
 pub struct Elem<T> {
     pub value: Vec<T>,
@@ -71,7 +71,7 @@ pub trait ElemCommon<T> {
     fn elem(&self) -> &Elem<T>;
     fn elem_mut(&mut self) -> &mut Elem<T>;
     fn size(&self) -> usize;
-    fn layout(&self) -> LAYOUT;
+    fn layout(&self) -> Layout;
     fn rows(&self) -> usize;
     fn cols(&self) -> usize;
     fn log_base2k(&self) -> usize;
@@ -102,7 +102,7 @@ impl<T: Infos> ElemCommon<T> for Elem<T> {
         self.value.len()
     }
 
-    fn layout(&self) -> LAYOUT {
+    fn layout(&self) -> Layout {
         self.value[0].layout()
     }
 
diff --git a/rlwe/src/plaintext.rs b/rlwe/src/plaintext.rs
index 86f7e32..258756b 100644
--- a/rlwe/src/plaintext.rs
+++ b/rlwe/src/plaintext.rs
@@ -1,7 +1,7 @@
 use crate::ciphertext::Ciphertext;
 use crate::elem::{Elem, ElemCommon, ElemVecZnx};
 use crate::parameters::Parameters;
-use base2k::{LAYOUT, Module, VecZnx};
+use base2k::{Layout, Module, VecZnx};
 
 pub struct Plaintext(pub Elem<VecZnx>);
 
@@ -79,7 +79,7 @@ impl ElemCommon<VecZnx> for Plaintext {
         self.elem().size()
     }
 
-    fn layout(&self) -> LAYOUT {
+    fn layout(&self) -> Layout {
         self.elem().layout()
     }