diff --git a/core/src/glwe_ciphertext.rs b/core/src/glwe_ciphertext.rs
index ed8a39e..56ca1a9 100644
--- a/core/src/glwe_ciphertext.rs
+++ b/core/src/glwe_ciphertext.rs
@@ -435,17 +435,30 @@ where
         VecZnx<DataPt>: VecZnxToMut,
         ScalarZnxDft<DataSk, FFT64>: ScalarZnxDftToRef<FFT64>,
     {
+        #[cfg(debug_assertions)]
+        {
+            assert_eq!(self.rank(), sk_dft.rank());
+            assert_eq!(self.n(), module.n());
+            assert_eq!(pt.n(), module.n());
+            assert_eq!(sk_dft.n(), module.n());
+        }
+
+        let cols: usize = self.rank() + 1;
+
         let (mut c0_big, scratch_1) = scratch.tmp_vec_znx_big(module, 1, self.size()); // TODO optimize size when pt << ct
+        c0_big.zero();
 
         {
-            let (mut c0_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, self.size()); // TODO optimize size when pt << ct
-            module.vec_znx_dft(&mut c0_dft, 0, self, 1);
+            (1..cols).for_each(|i| {
+                // ci_dft = DFT(a[i]) * DFT(s[i])
+                let (mut ci_dft, _) = scratch_1.tmp_vec_znx_dft(module, 1, self.size()); // TODO optimize size when pt << ct
+                module.vec_znx_dft(&mut ci_dft, 0, self, i);
+                module.svp_apply_inplace(&mut ci_dft, 0, sk_dft, i - 1);
+                let ci_big = module.vec_znx_idft_consume(ci_dft);
 
-            // c0_dft = DFT(a) * DFT(s)
-            module.svp_apply_inplace(&mut c0_dft, 0, sk_dft, 0);
-
-            // c0_big = IDFT(c0_dft)
-            module.vec_znx_idft_tmp_a(&mut c0_big, 0, &mut c0_dft, 0);
+                // c0_big += a[i] * s[i]
+                module.vec_znx_big_add_inplace(&mut c0_big, 0, &ci_big, 0);
+            });
         }
 
         // c0_big = (a * s) + (-a * s + m + e) = BIG(m + e)
diff --git a/core/src/test_fft64/glwe.rs b/core/src/test_fft64/glwe.rs
index 48b6cb6..5ffe2dd 100644
--- a/core/src/test_fft64/glwe.rs
+++ b/core/src/test_fft64/glwe.rs
@@ -1,6 +1,6 @@
 use base2k::{
     Decoding, Encoding, FFT64, FillUniform, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned, Stats, VecZnxOps, VecZnxToMut,
-    ZnxViewMut, ZnxZero,
+    ZnxView, ZnxViewMut, ZnxZero,
 };
 use itertools::izip;
 use sampling::source::Source;
@@ -17,18 +17,26 @@ use crate::{
 };
 
 #[test]
-fn encrypt_sk() {
-    let module: Module<FFT64> = Module::<FFT64>::new(32);
-    let log_base2k: usize = 8;
-    let log_k_ct: usize = 54;
-    let log_k_pt: usize = 30;
-    let rank: usize = 1;
+fn encrypt_sk_rank_1() {
+    encrypt_sk(11, 8, 54, 30, 3.2, 1);
+}
 
-    let sigma: f64 = 3.2;
+#[test]
+fn encrypt_sk_rank_2() {
+    encrypt_sk(5, 8, 54, 30, 3.2, 2);
+}
+
+#[test]
+fn encrypt_sk_rank_3() {
+    encrypt_sk(11, 8, 54, 30, 3.2, 3);
+}
+
+fn encrypt_sk(log_n: usize, basek: usize, k_ct: usize, k_pt: usize, sigma: f64, rank: usize) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
     let bound: f64 = sigma * 6.0;
 
-    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_ct, rank);
-    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_pt);
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_ct, rank);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_pt);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -51,8 +59,7 @@ fn encrypt_sk() {
         .iter_mut()
         .for_each(|x| *x = source_xa.next_i64() & 0xFF);
 
-    pt.data
-        .encode_vec_i64(0, log_base2k, log_k_pt, &data_want, 10);
+    pt.data.encode_vec_i64(0, basek, k_pt, &data_want, 10);
 
     ct.encrypt_sk(
         &module,
@@ -72,10 +79,10 @@ fn encrypt_sk() {
     let mut data_have: Vec<i64> = vec![0i64; module.n()];
 
     pt.data
-        .decode_vec_i64(0, log_base2k, pt.size() * log_base2k, &mut data_have);
+        .decode_vec_i64(0, basek, pt.size() * basek, &mut data_have);
 
     // TODO: properly assert the decryption noise through std(dec(ct) - pt)
-    let scale: f64 = (1 << (pt.size() * log_base2k - log_k_pt)) as f64;
+    let scale: f64 = (1 << (pt.size() * basek - k_pt)) as f64;
     izip!(data_want.iter(), data_have.iter()).for_each(|(a, b)| {
         let b_scaled = (*b as f64) / scale;
         assert!(
@@ -90,14 +97,14 @@ fn encrypt_sk() {
 #[test]
 fn encrypt_zero_sk() {
     let module: Module<FFT64> = Module::<FFT64>::new(1024);
-    let log_base2k: usize = 8;
-    let log_k_ct: usize = 55;
+    let basek: usize = 8;
+    let k_ct: usize = 55;
     let rank: usize = 1;
 
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_ct);
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([1u8; 32]);
@@ -108,7 +115,7 @@ fn encrypt_zero_sk() {
     let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module, rank);
     sk_dft.dft(&module, &sk);
 
-    let mut ct_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::new(&module, log_base2k, log_k_ct, rank);
+    let mut ct_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::new(&module, basek, k_ct, rank);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWECiphertextFourier::decrypt_scratch_space(&module, ct_dft.size())
@@ -126,22 +133,22 @@ fn encrypt_zero_sk() {
     );
     ct_dft.decrypt(&module, &mut pt, &sk_dft, scratch.borrow());
 
-    assert!((sigma - pt.data.std(0, log_base2k) * (log_k_ct as f64).exp2()) <= 0.2);
+    assert!((sigma - pt.data.std(0, basek) * (k_ct as f64).exp2()) <= 0.2);
 }
 
 #[test]
 fn encrypt_pk() {
     let module: Module<FFT64> = Module::<FFT64>::new(32);
-    let log_base2k: usize = 8;
-    let log_k_ct: usize = 54;
+    let basek: usize = 8;
+    let k_ct: usize = 54;
     let log_k_pk: usize = 64;
     let rank: usize = 1;
 
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_ct, rank);
-    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_ct);
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_ct, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -153,7 +160,7 @@ fn encrypt_pk() {
     let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module, rank);
     sk_dft.dft(&module, &sk);
 
-    let mut pk: GLWEPublicKey<Vec<u8>, FFT64> = GLWEPublicKey::new(&module, log_base2k, log_k_pk, rank);
+    let mut pk: GLWEPublicKey<Vec<u8>, FFT64> = GLWEPublicKey::new(&module, basek, log_k_pk, rank);
     pk.generate(
         &module,
         &sk_dft,
@@ -175,9 +182,7 @@ fn encrypt_pk() {
         .iter_mut()
         .for_each(|x| *x = source_xa.next_i64() & 0);
 
-    pt_want
-        .data
-        .encode_vec_i64(0, log_base2k, log_k_ct, &data_want, 10);
+    pt_want.data.encode_vec_i64(0, basek, k_ct, &data_want, 10);
 
     ct.encrypt_pk(
         &module,
@@ -190,34 +195,33 @@ fn encrypt_pk() {
         scratch.borrow(),
     );
 
-    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_ct);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct);
 
     ct.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
 
     module.vec_znx_sub_ab_inplace(&mut pt_want, 0, &pt_have, 0);
 
-    assert!(((1.0f64 / 12.0).sqrt() - pt_want.data.std(0, log_base2k) * (log_k_ct as f64).exp2()).abs() < 0.2);
+    assert!(((1.0f64 / 12.0).sqrt() - pt_want.data.std(0, basek) * (k_ct as f64).exp2()).abs() < 0.2);
 }
 
 #[test]
 fn keyswitch() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
-    let log_base2k: usize = 12;
+    let basek: usize = 12;
     let log_k_grlwe: usize = 60;
     let log_k_rlwe_in: usize = 45;
     let log_k_rlwe_out: usize = 60;
-    let rows: usize = (log_k_rlwe_in + log_base2k - 1) / log_base2k;
+    let rows: usize = (log_k_rlwe_in + basek - 1) / basek;
     let rank: usize = 1;
 
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_grlwe: GLWESwitchingKey<Vec<u8>, FFT64> =
-        GLWESwitchingKey::new(&module, log_base2k, log_k_grlwe, rows, rank, rank);
-    let mut ct_rlwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_in, rank);
-    let mut ct_rlwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_out, rank);
-    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_in);
-    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_out);
+    let mut ct_grlwe: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::new(&module, basek, log_k_grlwe, rows, rank, rank);
+    let mut ct_rlwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, log_k_rlwe_in, rank);
+    let mut ct_rlwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, log_k_rlwe_out, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, log_k_rlwe_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, log_k_rlwe_out);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -226,7 +230,7 @@ fn keyswitch() {
     // Random input plaintext
     pt_want
         .data
-        .fill_uniform(log_base2k, 0, pt_want.size(), &mut source_xa);
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWESwitchingKey::encrypt_sk_scratch_space(&module, rank, ct_grlwe.size())
@@ -280,10 +284,10 @@ fn keyswitch() {
 
     module.vec_znx_sub_ab_inplace(&mut pt_have, 0, &pt_want, 0);
 
-    let noise_have: f64 = pt_have.data.std(0, log_base2k).log2();
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
     let noise_want: f64 = noise_grlwe_rlwe_product(
         module.n() as f64,
-        log_base2k,
+        basek,
         0.5,
         0.5,
         0f64,
@@ -304,20 +308,19 @@ fn keyswitch() {
 #[test]
 fn keyswich_inplace() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
-    let log_base2k: usize = 12;
+    let basek: usize = 12;
     let log_k_grlwe: usize = 60;
     let log_k_rlwe: usize = 45;
-    let rows: usize = (log_k_rlwe + log_base2k - 1) / log_base2k;
+    let rows: usize = (log_k_rlwe + basek - 1) / basek;
     let rank: usize = 1;
 
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_grlwe: GLWESwitchingKey<Vec<u8>, FFT64> =
-        GLWESwitchingKey::new(&module, log_base2k, log_k_grlwe, rows, rank, rank);
-    let mut ct_rlwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe, rank);
-    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe);
-    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe);
+    let mut ct_grlwe: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::new(&module, basek, log_k_grlwe, rows, rank, rank);
+    let mut ct_rlwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, log_k_rlwe, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, log_k_rlwe);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, log_k_rlwe);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -326,7 +329,7 @@ fn keyswich_inplace() {
     // Random input plaintext
     pt_want
         .data
-        .fill_uniform(log_base2k, 0, pt_want.size(), &mut source_xa);
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
 
     let mut scratch: ScratchOwned = ScratchOwned::new(
         GLWESwitchingKey::encrypt_sk_scratch_space(&module, rank, ct_grlwe.size())
@@ -375,10 +378,10 @@ fn keyswich_inplace() {
 
     module.vec_znx_sub_ab_inplace(&mut pt_have, 0, &pt_want, 0);
 
-    let noise_have: f64 = pt_have.data.std(0, log_base2k).log2();
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
     let noise_want: f64 = noise_grlwe_rlwe_product(
         module.n() as f64,
-        log_base2k,
+        basek,
         0.5,
         0.5,
         0f64,
@@ -399,22 +402,22 @@ fn keyswich_inplace() {
 #[test]
 fn external_product() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
-    let log_base2k: usize = 12;
+    let basek: usize = 12;
     let log_k_grlwe: usize = 60;
     let log_k_rlwe_in: usize = 45;
     let log_k_rlwe_out: usize = 60;
-    let rows: usize = (log_k_rlwe_in + log_base2k - 1) / log_base2k;
+    let rows: usize = (log_k_rlwe_in + basek - 1) / basek;
     let rank: usize = 1;
 
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_grlwe, rows, rank);
-    let mut ct_rlwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_in, rank);
-    let mut ct_rlwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_out, rank);
+    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, basek, log_k_grlwe, rows, rank);
+    let mut ct_rlwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, log_k_rlwe_in, rank);
+    let mut ct_rlwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, log_k_rlwe_out, rank);
     let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
-    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_in);
-    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, log_k_rlwe_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, log_k_rlwe_out);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -423,7 +426,7 @@ fn external_product() {
     // Random input plaintext
     pt_want
         .data
-        .fill_uniform(log_base2k, 0, pt_want.size(), &mut source_xa);
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
 
     pt_want.to_mut().at_mut(0, 0)[1] = 1;
 
@@ -479,7 +482,7 @@ fn external_product() {
 
     module.vec_znx_sub_ab_inplace(&mut pt_have, 0, &pt_want, 0);
 
-    let noise_have: f64 = pt_have.data.std(0, log_base2k).log2();
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
 
     let var_gct_err_lhs: f64 = sigma * sigma;
     let var_gct_err_rhs: f64 = 0f64;
@@ -490,7 +493,7 @@ fn external_product() {
 
     let noise_want: f64 = noise_rgsw_product(
         module.n() as f64,
-        log_base2k,
+        basek,
         0.5,
         var_msg,
         var_a0_err,
@@ -512,21 +515,21 @@ fn external_product() {
 #[test]
 fn external_product_inplace() {
     let module: Module<FFT64> = Module::<FFT64>::new(2048);
-    let log_base2k: usize = 12;
+    let basek: usize = 12;
     let log_k_grlwe: usize = 60;
     let log_k_rlwe_in: usize = 45;
     let log_k_rlwe_out: usize = 60;
-    let rows: usize = (log_k_rlwe_in + log_base2k - 1) / log_base2k;
+    let rows: usize = (log_k_rlwe_in + basek - 1) / basek;
     let rank: usize = 1;
 
     let sigma: f64 = 3.2;
     let bound: f64 = sigma * 6.0;
 
-    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, log_base2k, log_k_grlwe, rows, rank);
-    let mut ct_rlwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, log_base2k, log_k_rlwe_in, rank);
+    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, basek, log_k_grlwe, rows, rank);
+    let mut ct_rlwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, log_k_rlwe_in, rank);
     let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
-    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_in);
-    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, log_base2k, log_k_rlwe_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, log_k_rlwe_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, log_k_rlwe_out);
 
     let mut source_xs: Source = Source::new([0u8; 32]);
     let mut source_xe: Source = Source::new([0u8; 32]);
@@ -535,7 +538,7 @@ fn external_product_inplace() {
     // Random input plaintext
     pt_want
         .data
-        .fill_uniform(log_base2k, 0, pt_want.size(), &mut source_xa);
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
 
     pt_want.to_mut().at_mut(0, 0)[1] = 1;
 
@@ -586,7 +589,7 @@ fn external_product_inplace() {
 
     module.vec_znx_sub_ab_inplace(&mut pt_have, 0, &pt_want, 0);
 
-    let noise_have: f64 = pt_have.data.std(0, log_base2k).log2();
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
 
     let var_gct_err_lhs: f64 = sigma * sigma;
     let var_gct_err_rhs: f64 = 0f64;
@@ -597,7 +600,7 @@ fn external_product_inplace() {
 
     let noise_want: f64 = noise_rgsw_product(
         module.n() as f64,
-        log_base2k,
+        basek,
         0.5,
         var_msg,
         var_a0_err,