@@ -1,4 +1,8 @@
-use poulpy_hal::{backend_test_suite, cross_backend_test_suite};
+use poulpy_hal::{
+    api::ModuleNew, backend_test_suite, cross_backend_test_suite, layouts::Module, test_suite::convolution::test_convolution,
+};
+
+use crate::FFT64Avx;
 
 cross_backend_test_suite! {
     mod vec_znx,
@@ -115,3 +119,9 @@ test_vec_znx_add_normal => poulpy_hal::test_suite::vec_znx::test_vec_znx_add_normal,
         test_vec_znx_big_sub_small_b_inplace => poulpy_hal::reference::fft64::vec_znx_big::test_vec_znx_big_add_normal,
     }
 }
+
+#[test]
+fn test_convolution_fft64_avx() {
+    let module: Module<FFT64Avx> = Module::<FFT64Avx>::new(64);
+    test_convolution(&module);
+}

@@ -4,14 +4,15 @@ Backend, Data, Module, Scratch, VecZnxBig, VecZnxBigToMut, VecZnxDft, VecZnxDftOwned, VecZnxDftToMut, VecZnxDftToRef,
         VecZnxToRef,
     },
     oep::{
-        VecZnxDftAddImpl, VecZnxDftAddInplaceImpl, VecZnxDftAllocBytesImpl, VecZnxDftAllocImpl, VecZnxDftApplyImpl,
-        VecZnxDftCopyImpl, VecZnxDftFromBytesImpl, VecZnxDftSubImpl, VecZnxDftSubInplaceImpl, VecZnxDftSubNegateInplaceImpl,
-        VecZnxDftZeroImpl, VecZnxIdftApplyConsumeImpl, VecZnxIdftApplyImpl, VecZnxIdftApplyTmpAImpl, VecZnxIdftApplyTmpBytesImpl,
+        VecZnxDftAddImpl, VecZnxDftAddInplaceImpl, VecZnxDftAddScaledInplaceImpl, VecZnxDftAllocBytesImpl, VecZnxDftAllocImpl,
+        VecZnxDftApplyImpl, VecZnxDftCopyImpl, VecZnxDftFromBytesImpl, VecZnxDftSubImpl, VecZnxDftSubInplaceImpl,
+        VecZnxDftSubNegateInplaceImpl, VecZnxDftZeroImpl, VecZnxIdftApplyConsumeImpl, VecZnxIdftApplyImpl,
+        VecZnxIdftApplyTmpAImpl, VecZnxIdftApplyTmpBytesImpl,
     },
     reference::fft64::vec_znx_dft::{
-        vec_znx_dft_add, vec_znx_dft_add_inplace, vec_znx_dft_apply, vec_znx_dft_copy, vec_znx_dft_sub, vec_znx_dft_sub_inplace,
-        vec_znx_dft_sub_negate_inplace, vec_znx_dft_zero, vec_znx_idft_apply, vec_znx_idft_apply_consume,
-        vec_znx_idft_apply_tmpa,
+        vec_znx_dft_add, vec_znx_dft_add_inplace, vec_znx_dft_add_scaled_inplace, vec_znx_dft_apply, vec_znx_dft_copy,
+        vec_znx_dft_sub, vec_znx_dft_sub_inplace, vec_znx_dft_sub_negate_inplace, vec_znx_dft_zero, vec_znx_idft_apply,
+        vec_znx_idft_apply_consume, vec_znx_idft_apply_tmpa,
     },
 };
 
@@ -118,6 +119,22 @@ R: VecZnxDftToMut<Self>,
         A: VecZnxDftToRef<Self>,
     {
         vec_znx_dft_add_inplace(res, res_col, a, a_col);
+    }
+}
+
+unsafe impl VecZnxDftAddScaledInplaceImpl<Self> for FFT64Avx {
+    fn vec_znx_dft_add_scaled_inplace_impl<R, A>(
+        _module: &Module<Self>,
+        res: &mut R,
+        res_col: usize,
+        a: &A,
+        a_col: usize,
+        a_scale: i64,
+    ) where
+        R: VecZnxDftToMut<Self>,
+        A: VecZnxDftToRef<Self>,
+    {
+        vec_znx_dft_add_scaled_inplace(res, res_col, a, a_col, a_scale);
     }
 }
 

@@ -9,4 +9,7 @@ mod vmp;
 mod zn;
 mod znx;
 
+#[cfg(test)]
+mod tests;
+
 pub struct FFT64Ref {}

@@ -0,0 +1,9 @@
+use poulpy_hal::{api::ModuleNew, layouts::Module, test_suite::convolution::test_convolution};
+
+use crate::FFT64Ref;
+
+#[test]
+fn test_convolution_fft64_ref() {
+    let module: Module<FFT64Ref> = Module::<FFT64Ref>::new(64);
+    test_convolution(&module);
+}

@@ -4,14 +4,15 @@ Backend, Data, Module, Scratch, VecZnxBig, VecZnxBigToMut, VecZnxDft, VecZnxDftOwned, VecZnxDftToMut, VecZnxDftToRef,
         VecZnxToRef,
     },
     oep::{
-        VecZnxDftAddImpl, VecZnxDftAddInplaceImpl, VecZnxDftAllocBytesImpl, VecZnxDftAllocImpl, VecZnxDftApplyImpl,
-        VecZnxDftCopyImpl, VecZnxDftFromBytesImpl, VecZnxDftSubImpl, VecZnxDftSubInplaceImpl, VecZnxDftSubNegateInplaceImpl,
-        VecZnxDftZeroImpl, VecZnxIdftApplyConsumeImpl, VecZnxIdftApplyImpl, VecZnxIdftApplyTmpAImpl, VecZnxIdftApplyTmpBytesImpl,
+        VecZnxDftAddImpl, VecZnxDftAddInplaceImpl, VecZnxDftAddScaledInplaceImpl, VecZnxDftAllocBytesImpl, VecZnxDftAllocImpl,
+        VecZnxDftApplyImpl, VecZnxDftCopyImpl, VecZnxDftFromBytesImpl, VecZnxDftSubImpl, VecZnxDftSubInplaceImpl,
+        VecZnxDftSubNegateInplaceImpl, VecZnxDftZeroImpl, VecZnxIdftApplyConsumeImpl, VecZnxIdftApplyImpl,
+        VecZnxIdftApplyTmpAImpl, VecZnxIdftApplyTmpBytesImpl,
     },
     reference::fft64::vec_znx_dft::{
-        vec_znx_dft_add, vec_znx_dft_add_inplace, vec_znx_dft_apply, vec_znx_dft_copy, vec_znx_dft_sub, vec_znx_dft_sub_inplace,
-        vec_znx_dft_sub_negate_inplace, vec_znx_dft_zero, vec_znx_idft_apply, vec_znx_idft_apply_consume,
-        vec_znx_idft_apply_tmpa,
+        vec_znx_dft_add, vec_znx_dft_add_inplace, vec_znx_dft_add_scaled_inplace, vec_znx_dft_apply, vec_znx_dft_copy,
+        vec_znx_dft_sub, vec_znx_dft_sub_inplace, vec_znx_dft_sub_negate_inplace, vec_znx_dft_zero, vec_znx_idft_apply,
+        vec_znx_idft_apply_consume, vec_znx_idft_apply_tmpa,
     },
 };
 
@@ -108,6 +109,22 @@ A: VecZnxDftToRef<Self>,
         B: VecZnxDftToRef<Self>,
     {
         vec_znx_dft_add(res, res_col, a, a_col, b, b_col);
+    }
+}
+
+unsafe impl VecZnxDftAddScaledInplaceImpl<Self> for FFT64Ref {
+    fn vec_znx_dft_add_scaled_inplace_impl<R, A>(
+        _module: &Module<Self>,
+        res: &mut R,
+        res_col: usize,
+        a: &A,
+        a_col: usize,
+        a_scale: i64,
+    ) where
+        R: VecZnxDftToMut<Self>,
+        A: VecZnxDftToRef<Self>,
+    {
+        vec_znx_dft_add_scaled_inplace(res, res_col, a, a_col, a_scale);
     }
 }
 

@@ -0,0 +1,109 @@
+use crate::{
+    api::{
+        ModuleN, ScratchTakeBasic, SvpApplyDftToDft, SvpPPolAlloc, SvpPPolBytesOf, SvpPrepare, VecZnxDftAddScaledInplace,
+        VecZnxDftBytesOf,
+    },
+    layouts::{Backend, Module, Scratch, VecZnxDftToMut, VecZnxDftToRef, VecZnxToRef, ZnxInfos, ZnxZero},
+};
+
+impl<BE: Backend> Convolution<BE> for Module<BE>
+where
+    Self: Sized
+        + ModuleN
+        + SvpPPolAlloc<BE>
+        + SvpApplyDftToDft<BE>
+        + SvpPrepare<BE>
+        + SvpPPolBytesOf
+        + VecZnxDftBytesOf
+        + VecZnxDftAddScaledInplace<BE>,
+    Scratch<BE>: ScratchTakeBasic,
+{
+}
+
+pub trait Convolution<BE: Backend>
+where
+    Self: Sized
+        + ModuleN
+        + SvpPPolAlloc<BE>
+        + SvpApplyDftToDft<BE>
+        + SvpPrepare<BE>
+        + SvpPPolBytesOf
+        + VecZnxDftBytesOf
+        + VecZnxDftAddScaledInplace<BE>,
+    Scratch<BE>: ScratchTakeBasic,
+{
+    fn convolution_tmp_bytes(&self, res_size: usize) -> usize {
+        self.bytes_of_svp_ppol(1) + self.bytes_of_vec_znx_dft(1, res_size)
+    }
+
+    /// Evaluates a bivariate convolution over Z[X, Y] / (X^N + 1) where Y = 2^-K
+    /// and scales the result by 2^{res_scale * K}
+    ///
+    /// # Example
+    /// a = [a00, a10, a20, a30] = (a00 * 2^-K + a01 * 2^-2K) + (a10 * 2^-K + a11 * 2^-2K) * X ...
+    ///     [a01, a11, a21, a31]
+    ///
+    /// b = [b00, b10, b20, b30] = (b00 * 2^-K + b01 * 2^-2K) + (b10 * 2^-K + b11 * 2^-2K) * X ...
+    ///     [b01, b11, b21, b31]
+    ///
+    /// If res_scale = 0:
+    /// res = [  0,   0,   0,   0] = (r01 * 2^-2K + r02 * 2^-3K + r03 * 2^-4K + r04 * 2^-5K) + ...
+    ///       [r01, r11, r21, r31]
+    ///       [r02, r12, r22, r32]
+    ///       [r03, r13, r23, r33]
+    ///       [r04, r14, r24, r34]
+    ///
+    /// If res_scale = 1:
+    /// res = [r01, r11, r21, r31] = (r01 * 2^-K + r02 * 2^-2K + r03 * 2^-3K + r04 * 2^-4K + r05 * 2^-5K) + ...
+    ///       [r02, r12, r22, r32]
+    ///       [r03, r13, r23, r33]
+    ///       [r04, r14, r24, r34]
+    ///       [r05, r15, r25, r35]
+    ///
+    /// If res_scale = -1:
+    /// res = [  0,   0,   0,   0] = (r01 * 2^-3K + r02 * 2^-4K + r03 * 2^-5K) + ...
+    ///       [  0,   0,   0,   0]
+    ///       [r01, r11, r21, r31]
+    ///       [r02, r12, r22, r32]
+    ///       [r03, r13, r23, r33]
+    ///
+    /// If res.size() < a.size() + b.size() + 1 + res_scale, result is truncated accordingly in the Y dimension.
+    fn convolution<R, A, B>(&self, res: &mut R, res_scale: i64, a: &A, b: &B, scratch: &mut Scratch<BE>)
+    where
+        R: VecZnxDftToMut<BE>,
+        A: VecZnxToRef,
+        B: VecZnxDftToRef<BE>,
+    {
+        let res: &mut crate::layouts::VecZnxDft<&mut [u8], BE> = &mut res.to_mut();
+        let a: &crate::layouts::VecZnx<&[u8]> = &a.to_ref();
+        let b: &crate::layouts::VecZnxDft<&[u8], BE> = &b.to_ref();
+
+        assert!(res.cols() >= a.cols() + b.cols() - 1);
+
+        res.zero();
+
+        let (mut ppol, scratch_1) = scratch.take_svp_ppol(self, 1);
+        let (mut res_tmp, _) = scratch_1.take_vec_znx_dft(self, 1, res.size());
+
+        for a_col in 0..a.cols() {
+            for a_limb in 0..a.size() {
+                // Prepares the j-th limb of the i-th col of A
+                self.svp_prepare(&mut ppol, 0, &a.as_scalar_znx_ref(a_col, a_limb), 0);
+
+                for b_col in 0..b.cols() {
+                    // Multiplies with the i-th col of B
+                    self.svp_apply_dft_to_dft(&mut res_tmp, 0, &ppol, 0, b, b_col);
+
+                    // Adds on the [a_col + b_col] of res, scaled by 2^{-(a_limb + 1) * Base2K}
+                    self.vec_znx_dft_add_scaled_inplace(
+                        res,
+                        a_col + b_col,
+                        &res_tmp,
+                        0,
+                        -(1 + a_limb as i64) + res_scale,
+                    );
+                }
+            }
+        }
+    }
+}

@@ -1,3 +1,4 @@
+mod convolution;
 mod module;
 mod scratch;
 mod svp_ppol;
@@ -7,6 +8,7 @@ mod vec_znx_dft;
 mod vmp_pmat;
 mod zn;
 
+pub use convolution::*;
 pub use module::*;
 pub use scratch::*;
 pub use svp_ppol::*;

@@ -164,10 +164,10 @@ #[allow(clippy::too_many_arguments)]
 pub trait VecZnxBigNormalize<B: Backend> {
     fn vec_znx_big_normalize<R, A>(
         &self,
-        res_basek: usize,
+        res_base2k: usize,
         res: &mut R,
         res_col: usize,
-        a_basek: usize,
+        a_base2k: usize,
         a: &A,
         a_col: usize,
         scratch: &mut Scratch<B>,

@@ -60,6 +60,13 @@ R: VecZnxDftToMut<B>,
         A: VecZnxDftToRef<B>;
 }
 
+pub trait VecZnxDftAddScaledInplace<B: Backend> {
+    fn vec_znx_dft_add_scaled_inplace<R, A>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize, a_scale: i64)
+    where
+        R: VecZnxDftToMut<B>,
+        A: VecZnxDftToRef<B>;
+}
+
 pub trait VecZnxDftSub<B: Backend> {
     fn vec_znx_dft_sub<R, A, D>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize, b: &D, b_col: usize)
     where

@@ -1,17 +1,18 @@
 use crate::{
     api::{
-        VecZnxDftAdd, VecZnxDftAddInplace, VecZnxDftAlloc, VecZnxDftApply, VecZnxDftBytesOf, VecZnxDftCopy, VecZnxDftFromBytes,
-        VecZnxDftSub, VecZnxDftSubInplace, VecZnxDftSubNegateInplace, VecZnxDftZero, VecZnxIdftApply, VecZnxIdftApplyConsume,
-        VecZnxIdftApplyTmpA, VecZnxIdftApplyTmpBytes,
+        VecZnxDftAdd, VecZnxDftAddInplace, VecZnxDftAddScaledInplace, VecZnxDftAlloc, VecZnxDftApply, VecZnxDftBytesOf,
+        VecZnxDftCopy, VecZnxDftFromBytes, VecZnxDftSub, VecZnxDftSubInplace, VecZnxDftSubNegateInplace, VecZnxDftZero,
+        VecZnxIdftApply, VecZnxIdftApplyConsume, VecZnxIdftApplyTmpA, VecZnxIdftApplyTmpBytes,
     },
     layouts::{
         Backend, Data, Module, Scratch, VecZnxBig, VecZnxBigToMut, VecZnxDft, VecZnxDftOwned, VecZnxDftToMut, VecZnxDftToRef,
         VecZnxToRef,
     },
     oep::{
-        VecZnxDftAddImpl, VecZnxDftAddInplaceImpl, VecZnxDftAllocBytesImpl, VecZnxDftAllocImpl, VecZnxDftApplyImpl,
-        VecZnxDftCopyImpl, VecZnxDftFromBytesImpl, VecZnxDftSubImpl, VecZnxDftSubInplaceImpl, VecZnxDftSubNegateInplaceImpl,
-        VecZnxDftZeroImpl, VecZnxIdftApplyConsumeImpl, VecZnxIdftApplyImpl, VecZnxIdftApplyTmpAImpl, VecZnxIdftApplyTmpBytesImpl,
+        VecZnxDftAddImpl, VecZnxDftAddInplaceImpl, VecZnxDftAddScaledInplaceImpl, VecZnxDftAllocBytesImpl, VecZnxDftAllocImpl,
+        VecZnxDftApplyImpl, VecZnxDftCopyImpl, VecZnxDftFromBytesImpl, VecZnxDftSubImpl, VecZnxDftSubInplaceImpl,
+        VecZnxDftSubNegateInplaceImpl, VecZnxDftZeroImpl, VecZnxIdftApplyConsumeImpl, VecZnxIdftApplyImpl,
+        VecZnxIdftApplyTmpAImpl, VecZnxIdftApplyTmpBytesImpl,
     },
 };
 
@@ -126,6 +127,19 @@ R: VecZnxDftToMut<B>,
         A: VecZnxDftToRef<B>,
     {
         B::vec_znx_dft_add_inplace_impl(self, res, res_col, a, a_col);
+    }
+}
+
+impl<B> VecZnxDftAddScaledInplace<B> for Module<B>
+where
+    B: Backend + VecZnxDftAddScaledInplaceImpl<B>,
+{
+    fn vec_znx_dft_add_scaled_inplace<R, A>(&self, res: &mut R, res_col: usize, a: &A, a_col: usize, a_scale: i64)
+    where
+        R: VecZnxDftToMut<B>,
+        A: VecZnxDftToRef<B>,
+    {
+        B::vec_znx_dft_add_scaled_inplace_impl(self, res, res_col, a, a_col, a_scale);
     }
 }
 

@@ -4,6 +4,7 @@ marker::PhantomData,
     ptr::NonNull,
 };
 
+use bytemuck::Pod;
 use rand_distr::num_traits::Zero;
 
 use crate::{
@@ -13,8 +14,8 @@ };
 
 #[allow(clippy::missing_safety_doc)]
 pub trait Backend: Sized {
-    type ScalarBig: Copy + Zero + Display + Debug;
-    type ScalarPrep: Copy + Zero + Display + Debug;
+    type ScalarBig: Copy + Zero + Display + Debug + Pod;
+    type ScalarPrep: Copy + Zero + Display + Debug + Pod;
     type Handle: 'static;
     fn layout_prep_word_count() -> usize;
     fn layout_big_word_count() -> usize;

@@ -6,8 +6,8 @@
 use crate::{
     alloc_aligned,
     layouts::{
-        Data, DataMut, DataRef, DataView, DataViewMut, DigestU64, FillUniform, ReaderFrom, ToOwnedDeep, WriterTo, ZnxInfos,
-        ZnxSliceSize, ZnxView, ZnxViewMut, ZnxZero,
+        Data, DataMut, DataRef, DataView, DataViewMut, DigestU64, FillUniform, ReaderFrom, ScalarZnx, ToOwnedDeep, WriterTo,
+        ZnxInfos, ZnxSliceSize, ZnxView, ZnxViewMut, ZnxZero,
     },
     source::Source,
 };
@@ -23,6 +23,26 @@ pub n: usize,
     pub cols: usize,
     pub size: usize,
     pub max_size: usize,
+}
+
+impl<D: DataRef> VecZnx<D> {
+    pub fn as_scalar_znx_ref(&self, col: usize, limb: usize) -> ScalarZnx<&[u8]> {
+        ScalarZnx {
+            data: bytemuck::cast_slice(self.at(col, limb)),
+            n: self.n,
+            cols: 1,
+        }
+    }
+}
+
+impl<D: DataMut> VecZnx<D> {
+    pub fn as_scalar_znx_mut(&mut self, col: usize, limb: usize) -> ScalarZnx<&mut [u8]> {
+        ScalarZnx {
+            n: self.n,
+            cols: 1,
+            data: bytemuck::cast_slice_mut(self.at_mut(col, limb)),
+        }
+    }
 }
 
 impl<D: Data + Default> Default for VecZnx<D> {

@@ -4,6 +4,7 @@ use crate::{
     layouts::{Backend, Data, DataMut, DataRef},
     source::Source,
 };
+use bytemuck::Pod;
 use rand_distr::num_traits::Zero;
 
 pub trait ZnxInfos {
@@ -50,7 +51,7 @@ fn data_mut(&mut self) -> &mut Self::D;
 }
 
 pub trait ZnxView: ZnxInfos + DataView<D: DataRef> {
-    type Scalar: Copy + Zero + Display + Debug;
+    type Scalar: Copy + Zero + Display + Debug + Pod;
 
     /// Returns a non-mutable pointer to the underlying coefficients array.
     fn as_ptr(&self) -> *const Self::Scalar {

@@ -104,6 +104,23 @@ D: VecZnxDftToRef<B>;
 }
 
 /// # THIS TRAIT IS AN OPEN EXTENSION POINT (unsafe)
+/// * See TODO reference implementation.
+/// * See [crate::api::VecZnxDftAddScaledInplace] for corresponding public API.
+/// # Safety [crate::doc::backend_safety] for safety contract.
+pub unsafe trait VecZnxDftAddScaledInplaceImpl<B: Backend> {
+    fn vec_znx_dft_add_scaled_inplace_impl<R, A>(
+        module: &Module<B>,
+        res: &mut R,
+        res_col: usize,
+        a: &A,
+        a_col: usize,
+        a_scale: i64,
+    ) where
+        R: VecZnxDftToMut<B>,
+        A: VecZnxDftToRef<B>;
+}
+
+/// # THIS TRAIT IS AN OPEN EXTENSION POINT (unsafe)
 /// * See the [poulpy-backend/src/cpu_fft64_ref/vec_znx_dft.rs](https://github.com/phantomzone-org/poulpy/blob/main/poulpy-backend/src/cpu_fft64_ref/vec_znx_dft.rs) reference implementation.
 /// * See [crate::api::VecZnxDftAddInplace] for corresponding public API.
 /// # Safety [crate::doc::backend_safety] for safety contract.

@@ -92,6 +92,44 @@ BE::reim_add_inplace(res.at_mut(res_col, j), a.at(a_col, j));
     }
 }
 
+/// res = res + a * 2^{a_scale * base2k}.
+pub fn vec_znx_dft_add_scaled_inplace<R, A, BE>(res: &mut R, res_col: usize, a: &A, a_col: usize, a_scale: i64)
+where
+    BE: Backend<ScalarPrep = f64> + ReimAddInplace,
+    R: VecZnxDftToMut<BE>,
+    A: VecZnxDftToRef<BE>,
+{
+    let a: VecZnxDft<&[u8], BE> = a.to_ref();
+    let mut res: VecZnxDft<&mut [u8], BE> = res.to_mut();
+
+    #[cfg(debug_assertions)]
+    {
+        assert_eq!(a.n(), res.n());
+    }
+
+    let res_size: usize = res.size();
+    let a_size: usize = a.size();
+
+    if a_scale > 0 {
+        let shift: usize = (a_scale as usize).min(a_size);
+        let sum_size: usize = a_size.min(res_size).saturating_sub(shift);
+        for j in 0..sum_size {
+            BE::reim_add_inplace(res.at_mut(res_col, j), a.at(a_col, j + shift));
+        }
+    } else if a_scale < 0 {
+        let shift: usize = (a_scale.unsigned_abs() as usize).min(res_size);
+        let sum_size: usize = a_size.min(res_size).saturating_sub(shift);
+        for j in 0..sum_size {
+            BE::reim_add_inplace(res.at_mut(res_col, j + shift), a.at(a_col, j));
+        }
+    } else {
+        let sum_size: usize = a_size.min(res_size);
+        for j in 0..sum_size {
+            BE::reim_add_inplace(res.at_mut(res_col, j), a.at(a_col, j));
+        }
+    }
+}
+
 pub fn vec_znx_dft_copy<R, A, BE>(step: usize, offset: usize, res: &mut R, res_col: usize, a: &A, a_col: usize)
 where
     BE: Backend<ScalarPrep = f64> + ReimCopy + ReimZero,

@@ -0,0 +1,162 @@
+use crate::{
+    api::{
+        Convolution, ModuleN, ScratchOwnedAlloc, ScratchOwnedBorrow, ScratchTakeBasic, TakeSlice, VecZnxBigNormalize,
+        VecZnxDftAlloc, VecZnxDftApply, VecZnxIdftApplyConsume, VecZnxNormalizeInplace,
+    },
+    layouts::{
+        Backend, FillUniform, Scratch, ScratchOwned, VecZnx, VecZnxBig, VecZnxDft, VecZnxToMut, VecZnxToRef, ZnxInfos, ZnxView,
+        ZnxViewMut, ZnxZero,
+    },
+    source::Source,
+};
+
+pub fn test_convolution<M, BE: Backend>(module: &M)
+where
+    M: ModuleN
+        + Convolution<BE>
+        + VecZnxDftAlloc<BE>
+        + VecZnxDftApply<BE>
+        + VecZnxIdftApplyConsume<BE>
+        + VecZnxBigNormalize<BE>
+        + VecZnxNormalizeInplace<BE>,
+    Scratch<BE>: ScratchTakeBasic,
+    ScratchOwned<BE>: ScratchOwnedAlloc<BE> + ScratchOwnedBorrow<BE>,
+{
+    let mut source: Source = Source::new([0u8; 32]);
+
+    let base2k: usize = 12;
+
+    for a_cols in 1..3 {
+        for b_cols in 1..3 {
+            for a_size in 1..5 {
+                for b_size in 1..5 {
+                    let mut a: VecZnx<Vec<u8>> = VecZnx::alloc(module.n(), a_cols, a_size);
+                    let mut b: VecZnx<Vec<u8>> = VecZnx::alloc(module.n(), b_cols, b_size);
+
+                    let mut c_want: VecZnx<Vec<u8>> = VecZnx::alloc(module.n(), a_cols + b_cols - 1, b_size + a_size);
+                    let mut c_have: VecZnx<Vec<u8>> = VecZnx::alloc(module.n(), c_want.cols(), c_want.size());
+
+                    let mut scratch: ScratchOwned<BE> = ScratchOwned::alloc(module.convolution_tmp_bytes(c_want.size()));
+
+                    a.fill_uniform(base2k, &mut source);
+                    b.fill_uniform(base2k, &mut source);
+
+                    let mut b_dft: VecZnxDft<Vec<u8>, BE> = module.vec_znx_dft_alloc(b.cols(), b.size());
+
+                    for i in 0..b.cols() {
+                        module.vec_znx_dft_apply(1, 0, &mut b_dft, i, &b, i);
+                    }
+
+                    for mut res_scale in 0..2 * c_want.size() as i64 + 1 {
+                        res_scale -= c_want.size() as i64;
+
+                        let mut c_have_dft: VecZnxDft<Vec<u8>, BE> = module.vec_znx_dft_alloc(c_have.cols(), c_have.size());
+                        module.convolution(&mut c_have_dft, res_scale, &a, &b_dft, scratch.borrow());
+
+                        let c_have_big: VecZnxBig<Vec<u8>, BE> = module.vec_znx_idft_apply_consume(c_have_dft);
+
+                        for i in 0..c_have.cols() {
+                            module.vec_znx_big_normalize(
+                                base2k,
+                                &mut c_have,
+                                i,
+                                base2k,
+                                &c_have_big,
+                                i,
+                                scratch.borrow(),
+                            );
+                        }
+
+                        convolution_naive(
+                            module,
+                            base2k,
+                            &mut c_want,
+                            res_scale,
+                            &a,
+                            &b,
+                            scratch.borrow(),
+                        );
+
+                        assert_eq!(c_want, c_have);
+                    }
+                }
+            }
+        }
+    }
+}
+
+fn convolution_naive<R, A, B, M, BE: Backend>(
+    module: &M,
+    base2k: usize,
+    res: &mut R,
+    res_scale: i64,
+    a: &A,
+    b: &B,
+    scratch: &mut Scratch<BE>,
+) where
+    R: VecZnxToMut,
+    A: VecZnxToRef,
+    B: VecZnxToRef,
+    M: VecZnxNormalizeInplace<BE>,
+    Scratch<BE>: TakeSlice,
+{
+    let res: &mut VecZnx<&mut [u8]> = &mut res.to_mut();
+    let a: &VecZnx<&[u8]> = &a.to_ref();
+    let b: &VecZnx<&[u8]> = &b.to_ref();
+
+    assert!(res.cols() >= a.cols() + b.cols() - 1);
+
+    res.zero();
+
+    for a_col in 0..a.cols() {
+        for a_limb in 0..a.size() {
+            for b_col in 0..b.cols() {
+                for b_limb in 0..b.size() {
+                    let res_scale_abs = res_scale.unsigned_abs() as usize;
+
+                    let mut res_limb: usize = a_limb + b_limb + 1;
+
+                    if res_scale <= 0 {
+                        res_limb += res_scale_abs;
+
+                        if res_limb < res.size() {
+                            negacyclic_convolution_naive_add(
+                                res.at_mut(a_col + b_col, res_limb),
+                                a.at(a_col, a_limb),
+                                b.at(b_col, b_limb),
+                            );
+                        }
+                    } else if res_limb >= res_scale_abs {
+                        res_limb -= res_scale_abs;
+
+                        if res_limb < res.size() {
+                            negacyclic_convolution_naive_add(
+                                res.at_mut(a_col + b_col, res_limb),
+                                a.at(a_col, a_limb),
+                                b.at(b_col, b_limb),
+                            );
+                        }
+                    }
+                }
+            }
+        }
+    }
+
+    for i in 0..res.cols() {
+        module.vec_znx_normalize_inplace(base2k, res, i, scratch);
+    }
+}
+
+fn negacyclic_convolution_naive_add(res: &mut [i64], a: &[i64], b: &[i64]) {
+    let n: usize = res.len();
+    for i in 0..n {
+        let ai: i64 = a[i];
+        let lim: usize = n - i;
+        for j in 0..lim {
+            res[i + j] += ai * b[j];
+        }
+        for j in lim..n {
+            res[i + j - n] -= ai * b[j];
+        }
+    }
+}

@@ -1,3 +1,4 @@
+pub mod convolution;
 pub mod serialization;
 pub mod svp;
 pub mod vec_znx;