Dev serialization (#64)

* Added compressed serialization for GLWECiphertext + Ciphertext decompression

* Added compressed serialization for GGLWECiphertext & GLWESwitchingkey

* generalized automorphism test

* Removed ops on scalar_znx, replaced by as_vec_znx/as_vec_znx_mut and then call op on vec_znx

* Added tests for automorphism key encryption

* Added tensorkey compressed

* added ggsw compressed

core/src/glwe/tests/cpu_spqlios/fft64.rs

@@ -0,0 +1,191 @@
+use backend::{
+    hal::{api::ModuleNew, layouts::Module},
+    implementation::cpu_spqlios::FFT64,
+};
+
+use crate::glwe::tests::{
+    generic_automorphism::{test_automorphism, test_automorphism_inplace},
+    generic_encryption::{test_encrypt_pk, test_encrypt_sk, test_encrypt_sk_compressed, test_encrypt_zero_sk},
+    generic_external_product::{test_external_product, test_external_product_inplace},
+    generic_keyswitch::{test_keyswitch, test_keyswitch_inplace},
+    generic_serialization::{test_serialization, test_serialization_compressed},
+    packing::test_packing,
+    trace::test_trace_inplace,
+};
+
+#[test]
+fn encrypt_sk() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    (1..4).for_each(|rank| {
+        println!("test encrypt_sk rank: {}", rank);
+        test_encrypt_sk(&module, 8, 54, 30, 3.2, rank);
+    });
+}
+
+#[test]
+fn encrypt_sk_compressed() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    (1..4).for_each(|rank| {
+        println!("test encrypt_sk rank: {}", rank);
+        test_encrypt_sk_compressed(&module, 8, 54, 30, 3.2, rank);
+    });
+}
+
+#[test]
+fn encrypt_zero_sk() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    (1..4).for_each(|rank| {
+        println!("test encrypt_zero_sk rank: {}", rank);
+        test_encrypt_zero_sk(&module, 8, 64, 3.2, rank);
+    });
+}
+
+#[test]
+fn encrypt_pk() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    (1..4).for_each(|rank| {
+        println!("test encrypt_pk rank: {}", rank);
+        test_encrypt_pk(&module, 8, 64, 64, 3.2, rank)
+    });
+}
+
+#[test]
+fn apply() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_in: usize = 45;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank_in| {
+        (1..4).for_each(|rank_out| {
+            (1..digits + 1).for_each(|di| {
+                let k_ksk: usize = k_in + basek * di;
+                let k_out: usize = k_ksk; // better capture noise
+                println!(
+                    "test keyswitch digits: {} rank_in: {} rank_out: {}",
+                    di, rank_in, rank_out
+                );
+                test_keyswitch(
+                    &module, basek, k_out, k_in, k_ksk, di, rank_in, rank_out, 3.2,
+                );
+            })
+        });
+    });
+}
+
+#[test]
+fn apply_inplace() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_ct: usize = 45;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_ct + basek * di;
+            println!("test keyswitch_inplace digits: {} rank: {}", di, rank);
+            test_keyswitch_inplace(&module, basek, k_ct, k_ksk, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn automorphism_inplace() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_ct: usize = 60;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_ct + basek * di;
+            println!("test automorphism_inplace digits: {} rank: {}", di, rank);
+            test_automorphism_inplace(&module, basek, -5, k_ct, k_ksk, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn automorphism() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_in: usize = 60;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ksk: usize = k_in + basek * di;
+            let k_out: usize = k_ksk; // Better capture noise.
+            println!("test automorphism digits: {} rank: {}", di, rank);
+            test_automorphism(&module, basek, -5, k_out, k_in, k_ksk, di, rank, 3.2);
+        })
+    });
+}
+
+#[test]
+fn external_product() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_in: usize = 45;
+    let digits: usize = k_in.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ggsw: usize = k_in + basek * di;
+            let k_out: usize = k_ggsw; // Better capture noise
+            println!("test external_product digits: {} rank: {}", di, rank);
+            test_external_product(&module, basek, k_out, k_in, k_ggsw, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn external_product_inplace() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let basek: usize = 12;
+    let k_ct: usize = 60;
+    let digits: usize = k_ct.div_ceil(basek);
+    (1..4).for_each(|rank| {
+        (1..digits + 1).for_each(|di| {
+            let k_ggsw: usize = k_ct + basek * di;
+            println!("test external_product digits: {} rank: {}", di, rank);
+            test_external_product_inplace(&module, basek, k_ct, k_ggsw, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn trace_inplace() {
+    let log_n: usize = 8;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    (1..4).for_each(|rank| {
+        println!("test trace_inplace rank: {}", rank);
+        test_trace_inplace(&module, 8, 54, 3.2, rank);
+    });
+}
+
+#[test]
+fn packing() {
+    let log_n: usize = 5;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    test_packing(&module);
+}
+
+#[test]
+fn serialization() {
+    let log_n: usize = 5;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    test_serialization(&module);
+}
+
+#[test]
+fn serialization_compressed() {
+    let log_n: usize = 5;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    test_serialization_compressed(&module);
+}

core/src/glwe/tests/cpu_spqlios/mod.rs

@@ -0,0 +1 @@
+mod fft64;

core/src/glwe/tests/generic_automorphism.rs

@@ -0,0 +1,210 @@
+use backend::hal::{
+    api::{
+        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
+        VecZnxAlloc, VecZnxAllocBytes, VecZnxAutomorphism, VecZnxAutomorphismInplace, VecZnxFillUniform, VecZnxStd,
+        VecZnxSwithcDegree,
+    },
+    layouts::{Backend, Module, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
+    },
+};
+use sampling::source::Source;
+
+use crate::{
+    AutomorphismKey, AutomorphismKeyEncryptSkFamily, AutomorphismKeyExec, GGLWEExecLayoutFamily, GLWECiphertext,
+    GLWEDecryptFamily, GLWEKeyswitchFamily, GLWEPlaintext, GLWESecret, GLWESecretExec, Infos,
+    noise::log2_std_noise_gglwe_product,
+};
+
+pub(crate) trait AutomorphismTestModuleFamily<B: Backend> = AutomorphismKeyEncryptSkFamily<B>
+    + GLWEDecryptFamily<B>
+    + GGLWEExecLayoutFamily<B>
+    + GLWEKeyswitchFamily<B>
+    + MatZnxAlloc
+    + VecZnxAlloc
+    + ScalarZnxAllocBytes
+    + VecZnxAllocBytes
+    + VecZnxAutomorphism
+    + VecZnxSwithcDegree
+    + ScalarZnxAlloc
+    + VecZnxAddScalarInplace
+    + VecZnxAutomorphismInplace
+    + VecZnxStd;
+pub(crate) trait AutomorphismTestScratchFamily<B: Backend> = TakeVecZnxDftImpl<B>
+    + TakeVecZnxBigImpl<B>
+    + TakeSvpPPolImpl<B>
+    + ScratchOwnedAllocImpl<B>
+    + ScratchOwnedBorrowImpl<B>
+    + ScratchAvailableImpl<B>
+    + TakeScalarZnxImpl<B>
+    + TakeVecZnxImpl<B>;
+
+pub(crate) fn test_automorphism<B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    p: i64,
+    k_out: usize,
+    k_in: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) where
+    Module<B>: AutomorphismTestModuleFamily<B>,
+    B: AutomorphismTestScratchFamily<B>,
+{
+    let rows: usize = k_in.div_ceil(basek * digits);
+
+    let mut autokey: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(module, basek, k_ksk, rows, digits, rank);
+    let mut ct_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_in, rank);
+    let mut ct_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_out, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_in);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    module.vec_znx_fill_uniform(basek, &mut pt_want.data, 0, k_in, &mut source_xa);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        AutomorphismKey::encrypt_sk_scratch_space(module, basek, autokey.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(module, basek, ct_out.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(module, basek, ct_in.k())
+            | GLWECiphertext::automorphism_scratch_space(
+                module,
+                basek,
+                ct_out.k(),
+                ct_in.k(),
+                autokey.k(),
+                digits,
+                rank,
+            ),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk);
+
+    autokey.encrypt_sk(
+        module,
+        p,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_in.encrypt_sk(
+        module,
+        &pt_want,
+        &sk_exec,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut autokey_exec: AutomorphismKeyExec<Vec<u8>, B> = AutomorphismKeyExec::alloc(module, basek, k_ksk, rows, digits, rank);
+    autokey_exec.prepare(module, &autokey, scratch.borrow());
+
+    ct_out.automorphism(module, &ct_in, &autokey_exec, scratch.borrow());
+
+    let max_noise: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank as f64,
+        k_in,
+        k_ksk,
+    );
+
+    module.vec_znx_automorphism_inplace(p, &mut pt_want.data, 0);
+
+    ct_out.assert_noise(module, &sk_exec, &pt_want, max_noise + 1.0);
+}
+
+pub(crate) fn test_automorphism_inplace<B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    p: i64,
+    k_ct: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) where
+    Module<B>: AutomorphismTestModuleFamily<B>,
+    B: AutomorphismTestScratchFamily<B>,
+{
+    let rows: usize = k_ct.div_ceil(basek * digits);
+
+    let mut autokey: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(module, basek, k_ksk, rows, digits, rank);
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_ct, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    module.vec_znx_fill_uniform(basek, &mut pt_want.data, 0, k_ct, &mut source_xa);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        AutomorphismKey::encrypt_sk_scratch_space(module, basek, autokey.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(module, basek, ct.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(module, basek, ct.k())
+            | GLWECiphertext::automorphism_inplace_scratch_space(module, basek, ct.k(), autokey.k(), digits, rank),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk);
+
+    autokey.encrypt_sk(
+        module,
+        p,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct.encrypt_sk(
+        module,
+        &pt_want,
+        &sk_exec,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut autokey_exec: AutomorphismKeyExec<Vec<u8>, B> = AutomorphismKeyExec::alloc(module, basek, k_ksk, rows, digits, rank);
+    autokey_exec.prepare(module, &autokey, scratch.borrow());
+
+    ct.automorphism_inplace(module, &autokey_exec, scratch.borrow());
+
+    let max_noise: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank as f64,
+        k_ct,
+        k_ksk,
+    );
+
+    module.vec_znx_automorphism_inplace(p, &mut pt_want.data, 0);
+
+    ct.assert_noise(module, &sk_exec, &pt_want, max_noise + 1.0);
+}

core/src/glwe/tests/generic_encryption.rs

@@ -0,0 +1,225 @@
+use backend::hal::{
+    api::{
+        ScalarZnxAlloc, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAlloc, VecZnxCopy, VecZnxDftAlloc, VecZnxFillUniform,
+        VecZnxStd, VecZnxSubABInplace,
+    },
+    layouts::{Backend, Module, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
+    },
+};
+use sampling::source::Source;
+
+use crate::{
+    GLWECiphertext, GLWECiphertextCompressed, GLWEDecryptFamily, GLWEEncryptPkFamily, GLWEEncryptSkFamily, GLWEOps,
+    GLWEPlaintext, GLWEPublicKey, GLWEPublicKeyExec, GLWESecret, GLWESecretExec, GLWESecretFamily, Infos,
+};
+
+pub(crate) trait EncryptionTestModuleFamily<B: Backend> =
+    GLWEDecryptFamily<B> + GLWESecretFamily<B> + VecZnxAlloc + ScalarZnxAlloc + VecZnxStd;
+
+pub(crate) trait EncryptionTestScratchFamily<B: Backend> = TakeVecZnxDftImpl<B>
+    + TakeVecZnxBigImpl<B>
+    + TakeSvpPPolImpl<B>
+    + ScratchOwnedAllocImpl<B>
+    + ScratchOwnedBorrowImpl<B>
+    + ScratchAvailableImpl<B>
+    + TakeScalarZnxImpl<B>
+    + TakeVecZnxImpl<B>;
+
+pub(crate) fn test_encrypt_sk<B: Backend>(module: &Module<B>, basek: usize, k_ct: usize, k_pt: usize, sigma: f64, rank: usize)
+where
+    Module<B>: EncryptionTestModuleFamily<B> + GLWEEncryptSkFamily<B>,
+    B: EncryptionTestScratchFamily<B>,
+{
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_ct, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_pt);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_pt);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        GLWECiphertext::encrypt_sk_scratch_space(module, basek, ct.k())
+            | GLWECiphertext::decrypt_scratch_space(module, basek, ct.k()),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk);
+
+    module.vec_znx_fill_uniform(basek, &mut pt_want.data, 0, k_pt, &mut source_xa);
+
+    ct.encrypt_sk(
+        module,
+        &pt_want,
+        &sk_exec,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct.decrypt(module, &mut pt_have, &sk_exec, scratch.borrow());
+
+    pt_want.sub_inplace_ab(module, &pt_have);
+
+    let noise_have: f64 = module.vec_znx_std(basek, &pt_want.data, 0) * (ct.k() as f64).exp2();
+    let noise_want: f64 = sigma;
+
+    assert!(noise_have <= noise_want + 0.2);
+}
+
+pub(crate) fn test_encrypt_sk_compressed<B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    k_ct: usize,
+    k_pt: usize,
+    sigma: f64,
+    rank: usize,
+) where
+    Module<B>: EncryptionTestModuleFamily<B> + GLWEEncryptSkFamily<B> + VecZnxCopy,
+    B: EncryptionTestScratchFamily<B>,
+{
+    let mut ct_compressed: GLWECiphertextCompressed<Vec<u8>> = GLWECiphertextCompressed::alloc(module, basek, k_ct, rank);
+
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_pt);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_pt);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        GLWECiphertextCompressed::encrypt_sk_scratch_space(module, basek, k_ct)
+            | GLWECiphertext::decrypt_scratch_space(module, basek, k_ct),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk);
+
+    module.vec_znx_fill_uniform(basek, &mut pt_want.data, 0, k_pt, &mut source_xa);
+
+    let seed_xa: [u8; 32] = [1u8; 32];
+
+    ct_compressed.encrypt_sk(
+        module,
+        &pt_want,
+        &sk_exec,
+        seed_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_ct, rank);
+    ct.decompress(module, &ct_compressed);
+
+    ct.decrypt(module, &mut pt_have, &sk_exec, scratch.borrow());
+
+    pt_want.sub_inplace_ab(module, &pt_have);
+
+    let noise_have: f64 = module.vec_znx_std(basek, &pt_want.data, 0) * (ct.k() as f64).exp2();
+    let noise_want: f64 = sigma;
+
+    assert!(noise_have <= noise_want + 0.2);
+}
+
+pub(crate) fn test_encrypt_zero_sk<B: Backend>(module: &Module<B>, basek: usize, k_ct: usize, sigma: f64, rank: usize)
+where
+    Module<B>: EncryptionTestModuleFamily<B> + GLWEEncryptSkFamily<B>,
+    B: EncryptionTestScratchFamily<B>,
+{
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([1u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk);
+
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_ct, rank);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        GLWECiphertext::decrypt_scratch_space(module, basek, k_ct)
+            | GLWECiphertext::encrypt_sk_scratch_space(module, basek, k_ct),
+    );
+
+    ct.encrypt_zero_sk(
+        module,
+        &sk_exec,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+    ct.decrypt(module, &mut pt, &sk_exec, scratch.borrow());
+
+    assert!((sigma - module.vec_znx_std(basek, &pt.data, 0) * (k_ct as f64).exp2()) <= 0.2);
+}
+
+pub(crate) fn test_encrypt_pk<B: Backend>(module: &Module<B>, basek: usize, k_ct: usize, k_pk: usize, sigma: f64, rank: usize)
+where
+    Module<B>: EncryptionTestModuleFamily<B>
+        + GLWEEncryptPkFamily<B>
+        + GLWEEncryptSkFamily<B>
+        + VecZnxDftAlloc<B>
+        + VecZnxFillUniform
+        + VecZnxSubABInplace,
+    B: EncryptionTestScratchFamily<B>,
+{
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_ct, rank);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_ct);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+    let mut source_xu: Source = Source::new([0u8; 32]);
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk);
+
+    let mut pk: GLWEPublicKey<Vec<u8>> = GLWEPublicKey::alloc(module, basek, k_pk, rank);
+    pk.generate_from_sk(module, &sk_exec, &mut source_xa, &mut source_xe, sigma);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        GLWECiphertext::encrypt_sk_scratch_space(module, basek, ct.k())
+            | GLWECiphertext::decrypt_scratch_space(module, basek, ct.k())
+            | GLWECiphertext::encrypt_pk_scratch_space(module, basek, pk.k()),
+    );
+
+    module.vec_znx_fill_uniform(basek, &mut pt_want.data, 0, k_ct, &mut source_xa);
+
+    let pk_exec: GLWEPublicKeyExec<Vec<u8>, B> = GLWEPublicKeyExec::from(module, &pk, scratch.borrow());
+
+    ct.encrypt_pk(
+        module,
+        &pt_want,
+        &pk_exec,
+        &mut source_xu,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct.decrypt(module, &mut pt_have, &sk_exec, scratch.borrow());
+
+    pt_want.sub_inplace_ab(module, &pt_have);
+
+    let noise_have: f64 = module.vec_znx_std(basek, &pt_want.data, 0).log2();
+    let noise_want: f64 = ((((rank as f64) + 1.0) * module.n() as f64 * 0.5 * sigma * sigma).sqrt()).log2() - (k_ct as f64);
+
+    assert!(
+        noise_have <= noise_want + 0.2,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}

core/src/glwe/tests/generic_external_product.rs

@@ -0,0 +1,233 @@
+use backend::hal::{
+    api::{
+        MatZnxAlloc, ScalarZnxAlloc, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace, VecZnxAlloc,
+        VecZnxAllocBytes, VecZnxFillUniform, VecZnxRotateInplace, VecZnxStd, ZnxViewMut,
+    },
+    layouts::{Backend, Module, ScalarZnx, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
+    },
+};
+use sampling::source::Source;
+
+use crate::{
+    GGSWCiphertext, GGSWCiphertextExec, GGSWLayoutFamily, GLWECiphertext, GLWEDecryptFamily, GLWEEncryptSkFamily,
+    GLWEExternalProductFamily, GLWEPlaintext, GLWESecret, GLWESecretExec, GLWESecretFamily, Infos, noise::noise_ggsw_product,
+};
+
+pub(crate) trait ExternalProductTestModuleFamily<B: Backend> = GLWEEncryptSkFamily<B>
+    + GLWEDecryptFamily<B>
+    + GLWESecretFamily<B>
+    + GLWEExternalProductFamily<B>
+    + GGSWLayoutFamily<B>
+    + MatZnxAlloc
+    + VecZnxAlloc
+    + ScalarZnxAlloc
+    + VecZnxAllocBytes
+    + VecZnxAddScalarInplace
+    + VecZnxRotateInplace
+    + VecZnxStd;
+
+pub(crate) trait ExternalProductTestScratchFamily<B: Backend> = TakeVecZnxDftImpl<B>
+    + TakeVecZnxBigImpl<B>
+    + TakeSvpPPolImpl<B>
+    + ScratchOwnedAllocImpl<B>
+    + ScratchOwnedBorrowImpl<B>
+    + ScratchAvailableImpl<B>
+    + TakeScalarZnxImpl<B>
+    + TakeVecZnxImpl<B>;
+
+pub(crate) fn test_external_product<B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    k_out: usize,
+    k_in: usize,
+    k_ggsw: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) where
+    Module<B>: ExternalProductTestModuleFamily<B>,
+    B: ExternalProductTestScratchFamily<B>,
+{
+    let rows: usize = k_in.div_ceil(basek * digits);
+
+    let mut ct_ggsw: GGSWCiphertext<Vec<u8>> = GGSWCiphertext::alloc(module, basek, k_ggsw, rows, digits, rank);
+    let mut ct_glwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_in, rank);
+    let mut ct_glwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_out, rank);
+    let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.scalar_znx_alloc(1);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_in);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    // Random input plaintext
+    module.vec_znx_fill_uniform(basek, &mut pt_want.data, 0, k_in, &mut source_xa);
+
+    pt_want.data.at_mut(0, 0)[1] = 1;
+
+    let k: usize = 1;
+
+    pt_rgsw.raw_mut()[k] = 1; // X^{k}
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        GGSWCiphertext::encrypt_sk_scratch_space(module, basek, ct_ggsw.k(), rank)
+            | GLWECiphertext::encrypt_sk_scratch_space(module, basek, ct_glwe_in.k())
+            | GLWECiphertext::external_product_scratch_space(
+                module,
+                basek,
+                ct_glwe_out.k(),
+                ct_glwe_in.k(),
+                ct_ggsw.k(),
+                digits,
+                rank,
+            ),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk);
+
+    ct_ggsw.encrypt_sk(
+        module,
+        &pt_rgsw,
+        &sk_exec,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe_in.encrypt_sk(
+        module,
+        &pt_want,
+        &sk_exec,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let ct_ggsw_exec: GGSWCiphertextExec<Vec<u8>, B> = GGSWCiphertextExec::from(module, &ct_ggsw, scratch.borrow());
+
+    ct_glwe_out.external_product(module, &ct_glwe_in, &ct_ggsw_exec, scratch.borrow());
+
+    module.vec_znx_rotate_inplace(k as i64, &mut pt_want.data, 0);
+
+    let var_gct_err_lhs: f64 = sigma * sigma;
+    let var_gct_err_rhs: f64 = 0f64;
+
+    let var_msg: f64 = 1f64 / module.n() as f64; // X^{k}
+    let var_a0_err: f64 = sigma * sigma;
+    let var_a1_err: f64 = 1f64 / 12f64;
+
+    let max_noise: f64 = noise_ggsw_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        var_msg,
+        var_a0_err,
+        var_a1_err,
+        var_gct_err_lhs,
+        var_gct_err_rhs,
+        rank as f64,
+        k_in,
+        k_ggsw,
+    );
+
+    ct_glwe_out.assert_noise(module, &sk_exec, &pt_want, max_noise + 0.5);
+}
+
+pub(crate) fn test_external_product_inplace<B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    k_ct: usize,
+    k_ggsw: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) where
+    Module<B>: ExternalProductTestModuleFamily<B>,
+    B: ExternalProductTestScratchFamily<B>,
+{
+    let rows: usize = k_ct.div_ceil(basek * digits);
+
+    let mut ct_ggsw: GGSWCiphertext<Vec<u8>> = GGSWCiphertext::alloc(module, basek, k_ggsw, rows, digits, rank);
+    let mut ct_glwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_ct, rank);
+    let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.scalar_znx_alloc(1);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    // Random input plaintext
+    module.vec_znx_fill_uniform(basek, &mut pt_want.data, 0, k_ct, &mut source_xa);
+
+    pt_want.data.at_mut(0, 0)[1] = 1;
+
+    let k: usize = 1;
+
+    pt_rgsw.raw_mut()[k] = 1; // X^{k}
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        GGSWCiphertext::encrypt_sk_scratch_space(module, basek, ct_ggsw.k(), rank)
+            | GLWECiphertext::encrypt_sk_scratch_space(module, basek, ct_glwe.k())
+            | GLWECiphertext::external_product_inplace_scratch_space(module, basek, ct_glwe.k(), ct_ggsw.k(), digits, rank),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk);
+
+    ct_ggsw.encrypt_sk(
+        module,
+        &pt_rgsw,
+        &sk_exec,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.encrypt_sk(
+        module,
+        &pt_want,
+        &sk_exec,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let ct_ggsw_exec: GGSWCiphertextExec<Vec<u8>, B> = GGSWCiphertextExec::from(module, &ct_ggsw, scratch.borrow());
+
+    ct_glwe.external_product_inplace(module, &ct_ggsw_exec, scratch.borrow());
+
+    module.vec_znx_rotate_inplace(k as i64, &mut pt_want.data, 0);
+
+    let var_gct_err_lhs: f64 = sigma * sigma;
+    let var_gct_err_rhs: f64 = 0f64;
+
+    let var_msg: f64 = 1f64 / module.n() as f64; // X^{k}
+    let var_a0_err: f64 = sigma * sigma;
+    let var_a1_err: f64 = 1f64 / 12f64;
+
+    let max_noise: f64 = noise_ggsw_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        var_msg,
+        var_a0_err,
+        var_a1_err,
+        var_gct_err_lhs,
+        var_gct_err_rhs,
+        rank as f64,
+        k_ct,
+        k_ggsw,
+    );
+
+    ct_glwe.assert_noise(module, &sk_exec, &pt_want, max_noise + 0.5);
+}

core/src/glwe/tests/generic_keyswitch.rs

@@ -0,0 +1,209 @@
+use backend::hal::{
+    api::{
+        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
+        VecZnxAlloc, VecZnxAllocBytes, VecZnxFillUniform, VecZnxStd, VecZnxSwithcDegree,
+    },
+    layouts::{Backend, Module, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
+    },
+};
+use sampling::source::Source;
+
+use crate::{
+    GGLWEExecLayoutFamily, GLWECiphertext, GLWEDecryptFamily, GLWEKeyswitchFamily, GLWEPlaintext, GLWESecret, GLWESecretExec,
+    GLWESecretFamily, GLWESwitchingKey, GLWESwitchingKeyEncryptSkFamily, GLWESwitchingKeyExec, Infos,
+    noise::log2_std_noise_gglwe_product,
+};
+
+pub(crate) trait KeySwitchTestModuleFamily<B: Backend> = GLWESecretFamily<B>
+    + GLWESwitchingKeyEncryptSkFamily<B>
+    + GLWEKeyswitchFamily<B>
+    + GLWEDecryptFamily<B>
+    + GGLWEExecLayoutFamily<B>
+    + MatZnxAlloc
+    + VecZnxAlloc
+    + ScalarZnxAlloc
+    + ScalarZnxAllocBytes
+    + VecZnxAllocBytes
+    + VecZnxStd
+    + VecZnxSwithcDegree
+    + VecZnxAddScalarInplace;
+
+pub(crate) trait KeySwitchTestScratchFamily<B: Backend> = TakeVecZnxDftImpl<B>
+    + TakeVecZnxBigImpl<B>
+    + TakeSvpPPolImpl<B>
+    + ScratchOwnedAllocImpl<B>
+    + ScratchOwnedBorrowImpl<B>
+    + ScratchAvailableImpl<B>
+    + TakeScalarZnxImpl<B>
+    + TakeVecZnxImpl<B>;
+
+pub(crate) fn test_keyswitch<B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    k_out: usize,
+    k_in: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank_in: usize,
+    rank_out: usize,
+    sigma: f64,
+) where
+    Module<B>: KeySwitchTestModuleFamily<B>,
+    B: KeySwitchTestScratchFamily<B>,
+{
+    let rows: usize = k_in.div_ceil(basek * digits);
+
+    let mut ksk: GLWESwitchingKey<Vec<u8>> = GLWESwitchingKey::alloc(module, basek, k_ksk, rows, digits, rank_in, rank_out);
+    let mut ct_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_in, rank_in);
+    let mut ct_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_out, rank_out);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_in);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    module.vec_znx_fill_uniform(basek, &mut pt_want.data, 0, k_in, &mut source_xa);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        GLWESwitchingKey::encrypt_sk_scratch_space(module, basek, ksk.k(), rank_in, rank_out)
+            | GLWECiphertext::encrypt_sk_scratch_space(module, basek, ct_in.k())
+            | GLWECiphertext::keyswitch_scratch_space(
+                module,
+                basek,
+                ct_out.k(),
+                ct_in.k(),
+                ksk.k(),
+                digits,
+                rank_in,
+                rank_out,
+            ),
+    );
+
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank_in);
+    sk_in.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_in_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk_in);
+
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank_out);
+    sk_out.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_out_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk_out);
+
+    ksk.encrypt_sk(
+        module,
+        &sk_in,
+        &sk_out,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_in.encrypt_sk(
+        module,
+        &pt_want,
+        &sk_in_exec,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let ksk_exec: GLWESwitchingKeyExec<Vec<u8>, B> = GLWESwitchingKeyExec::from(module, &ksk, scratch.borrow());
+
+    ct_out.keyswitch(module, &ct_in, &ksk_exec, scratch.borrow());
+
+    let max_noise: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank_in as f64,
+        k_in,
+        k_ksk,
+    );
+
+    ct_out.assert_noise(module, &sk_out_exec, &pt_want, max_noise + 0.5);
+}
+
+pub(crate) fn test_keyswitch_inplace<B: Backend>(
+    module: &Module<B>,
+    basek: usize,
+    k_ct: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) where
+    Module<B>: KeySwitchTestModuleFamily<B>,
+    B: KeySwitchTestScratchFamily<B>,
+{
+    let rows: usize = k_ct.div_ceil(basek * digits);
+
+    let mut ksk: GLWESwitchingKey<Vec<u8>> = GLWESwitchingKey::alloc(module, basek, k_ksk, rows, digits, rank, rank);
+    let mut ct_glwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_ct, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_ct);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    module.vec_znx_fill_uniform(basek, &mut pt_want.data, 0, k_ct, &mut source_xa);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        GLWESwitchingKey::encrypt_sk_scratch_space(module, basek, ksk.k(), rank, rank)
+            | GLWECiphertext::encrypt_sk_scratch_space(module, basek, ct_glwe.k())
+            | GLWECiphertext::keyswitch_inplace_scratch_space(module, basek, ct_glwe.k(), ksk.k(), digits, rank),
+    );
+
+    let mut sk_in: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk_in.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_in_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk_in);
+
+    let mut sk_out: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk_out.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_out_exec: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk_out);
+
+    ksk.encrypt_sk(
+        module,
+        &sk_in,
+        &sk_out,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.encrypt_sk(
+        module,
+        &pt_want,
+        &sk_in_exec,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let ksk_exec: GLWESwitchingKeyExec<Vec<u8>, B> = GLWESwitchingKeyExec::from(module, &ksk, scratch.borrow());
+
+    ct_glwe.keyswitch_inplace(module, &ksk_exec, scratch.borrow());
+
+    let max_noise: f64 = log2_std_noise_gglwe_product(
+        module.n() as f64,
+        basek * digits,
+        0.5,
+        0.5,
+        0f64,
+        sigma * sigma,
+        0f64,
+        rank as f64,
+        k_ct,
+        k_ksk,
+    );
+
+    ct_glwe.assert_noise(module, &sk_out_exec, &pt_want, max_noise + 0.5);
+}

core/src/glwe/tests/generic_serialization.rs

@@ -0,0 +1,23 @@
+use backend::hal::{
+    api::VecZnxAlloc,
+    layouts::{Backend, Module},
+    tests::serialization::test_reader_writer_interface,
+};
+
+use crate::{GLWECiphertext, GLWECiphertextCompressed};
+
+pub(crate) fn test_serialization<B: Backend>(module: &Module<B>)
+where
+    Module<B>: VecZnxAlloc,
+{
+    let original: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, 12, 54, 3);
+    test_reader_writer_interface(original);
+}
+
+pub(crate) fn test_serialization_compressed<B: Backend>(module: &Module<B>)
+where
+    Module<B>: VecZnxAlloc,
+{
+    let original: GLWECiphertextCompressed<Vec<u8>> = GLWECiphertextCompressed::alloc(module, 12, 54, 3);
+    test_reader_writer_interface(original);
+}

core/src/glwe/tests/mod.rs

@@ -0,0 +1,8 @@
+mod cpu_spqlios;
+mod generic_automorphism;
+mod generic_encryption;
+mod generic_external_product;
+mod generic_keyswitch;
+mod generic_serialization;
+mod packing;
+mod trace;

core/src/glwe/tests/packing.rs

@@ -0,0 +1,177 @@
+use std::collections::HashMap;
+
+use backend::hal::{
+    api::{
+        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
+        VecZnxAlloc, VecZnxAllocBytes, VecZnxAutomorphism, VecZnxBigSubSmallBInplace, VecZnxEncodeVeci64, VecZnxRotateInplace,
+        VecZnxStd, VecZnxSwithcDegree,
+    },
+    layouts::{Backend, Module, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
+    },
+};
+use sampling::source::Source;
+
+use crate::{
+    AutomorphismKey, AutomorphismKeyExec, GGLWEExecLayoutFamily, GLWECiphertext, GLWEDecryptFamily, GLWEKeyswitchFamily, GLWEOps,
+    GLWEPacker, GLWEPackingFamily, GLWEPlaintext, GLWESecret, GLWESecretExec, GLWESecretFamily, GLWESwitchingKeyEncryptSkFamily,
+};
+
+pub(crate) trait PackingTestModuleFamily<B: Backend> = GLWEPackingFamily<B>
+    + GLWESecretFamily<B>
+    + GLWESwitchingKeyEncryptSkFamily<B>
+    + GLWEKeyswitchFamily<B>
+    + GLWEDecryptFamily<B>
+    + GGLWEExecLayoutFamily<B>
+    + MatZnxAlloc
+    + VecZnxAlloc
+    + ScalarZnxAlloc
+    + ScalarZnxAllocBytes
+    + VecZnxAllocBytes
+    + VecZnxStd
+    + VecZnxSwithcDegree
+    + VecZnxAddScalarInplace
+    + VecZnxEncodeVeci64
+    + VecZnxRotateInplace
+    + VecZnxAutomorphism
+    + VecZnxBigSubSmallBInplace<B>;
+
+pub(crate) trait PackingTestScratchFamily<B: Backend> = TakeVecZnxDftImpl<B>
+    + TakeVecZnxBigImpl<B>
+    + TakeSvpPPolImpl<B>
+    + ScratchOwnedAllocImpl<B>
+    + ScratchOwnedBorrowImpl<B>
+    + ScratchAvailableImpl<B>
+    + TakeScalarZnxImpl<B>
+    + TakeVecZnxImpl<B>;
+
+pub(crate) fn test_packing<B: Backend>(module: &Module<B>)
+where
+    Module<B>: PackingTestModuleFamily<B>,
+    B: PackingTestScratchFamily<B>,
+{
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let basek: usize = 18;
+    let k_ct: usize = 36;
+    let pt_k: usize = 18;
+    let rank: usize = 3;
+    let sigma: f64 = 3.2;
+    let digits: usize = 1;
+    let k_ksk: usize = k_ct + basek * digits;
+
+    let rows: usize = k_ct.div_ceil(basek * digits);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        GLWECiphertext::encrypt_sk_scratch_space(module, basek, k_ct)
+            | AutomorphismKey::encrypt_sk_scratch_space(module, basek, k_ksk, rank)
+            | GLWEPacker::scratch_space(module, basek, k_ct, k_ksk, digits, rank),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk);
+
+    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_ct);
+    let mut data: Vec<i64> = vec![0i64; module.n()];
+    data.iter_mut().enumerate().for_each(|(i, x)| {
+        *x = i as i64;
+    });
+
+    module.encode_vec_i64(basek, &mut pt.data, 0, pt_k, &data, 32);
+
+    let gal_els: Vec<i64> = GLWEPacker::galois_elements(module);
+
+    let mut auto_keys: HashMap<i64, AutomorphismKeyExec<Vec<u8>, B>> = HashMap::new();
+    let mut tmp: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(module, basek, k_ksk, rows, digits, rank);
+    gal_els.iter().for_each(|gal_el| {
+        tmp.encrypt_sk(
+            module,
+            *gal_el,
+            &sk,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            scratch.borrow(),
+        );
+        let atk_exec: AutomorphismKeyExec<Vec<u8>, B> = AutomorphismKeyExec::from(module, &tmp, scratch.borrow());
+        auto_keys.insert(*gal_el, atk_exec);
+    });
+
+    let log_batch: usize = 0;
+
+    let mut packer: GLWEPacker = GLWEPacker::new(module, log_batch, basek, k_ct, rank);
+
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k_ct, rank);
+
+    ct.encrypt_sk(
+        module,
+        &pt,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let log_n: usize = module.log_n();
+
+    (0..module.n() >> log_batch).for_each(|i| {
+        ct.encrypt_sk(
+            module,
+            &pt,
+            &sk_dft,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            scratch.borrow(),
+        );
+
+        pt.rotate_inplace(module, -(1 << log_batch)); // X^-batch * pt
+
+        if reverse_bits_msb(i, log_n as u32) % 5 == 0 {
+            packer.add(module, Some(&ct), &auto_keys, scratch.borrow());
+        } else {
+            packer.add(
+                module,
+                None::<&GLWECiphertext<Vec<u8>>>,
+                &auto_keys,
+                scratch.borrow(),
+            )
+        }
+    });
+
+    let mut res = GLWECiphertext::alloc(module, basek, k_ct, rank);
+    packer.flush(module, &mut res);
+
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k_ct);
+    let mut data: Vec<i64> = vec![0i64; module.n()];
+    data.iter_mut().enumerate().for_each(|(i, x)| {
+        if i % 5 == 0 {
+            *x = reverse_bits_msb(i, log_n as u32) as i64;
+        }
+    });
+
+    module.encode_vec_i64(basek, &mut pt_want.data, 0, pt_k, &data, 32);
+
+    res.decrypt(module, &mut pt, &sk_dft, scratch.borrow());
+
+    pt.sub_inplace_ab(module, &pt_want);
+
+    let noise_have: f64 = module.vec_znx_std(basek, &pt.data, 0).log2();
+    // println!("noise_have: {}", noise_have);
+    assert!(
+        noise_have < -((k_ct - basek) as f64),
+        "noise: {}",
+        noise_have
+    );
+}
+
+#[inline(always)]
+fn reverse_bits_msb(x: usize, n: u32) -> usize {
+    x.reverse_bits() >> (usize::BITS - n)
+}

core/src/glwe/tests/trace.rs

@@ -0,0 +1,152 @@
+use std::collections::HashMap;
+
+use backend::hal::{
+    api::{
+        MatZnxAlloc, ScalarZnxAlloc, ScalarZnxAllocBytes, ScratchOwnedAlloc, ScratchOwnedBorrow, VecZnxAddScalarInplace,
+        VecZnxAlloc, VecZnxAllocBytes, VecZnxAutomorphism, VecZnxBigAutomorphismInplace, VecZnxBigSubSmallBInplace, VecZnxCopy,
+        VecZnxEncodeVeci64, VecZnxFillUniform, VecZnxNormalizeInplace, VecZnxRotateInplace, VecZnxRshInplace, VecZnxStd,
+        VecZnxSubABInplace, VecZnxSwithcDegree, ZnxView, ZnxViewMut,
+    },
+    layouts::{Backend, Module, ScratchOwned},
+    oep::{
+        ScratchAvailableImpl, ScratchOwnedAllocImpl, ScratchOwnedBorrowImpl, TakeScalarZnxImpl, TakeSvpPPolImpl,
+        TakeVecZnxBigImpl, TakeVecZnxDftImpl, TakeVecZnxImpl,
+    },
+};
+use sampling::source::Source;
+
+use crate::{
+    AutomorphismKey, AutomorphismKeyExec, GGLWEExecLayoutFamily, GLWECiphertext, GLWEDecryptFamily, GLWEKeyswitchFamily,
+    GLWEPlaintext, GLWESecret, GLWESecretExec, GLWESecretFamily, GLWESwitchingKeyEncryptSkFamily, Infos,
+    noise::var_noise_gglwe_product,
+};
+
+pub(crate) trait TraceTestModuleFamily<B: Backend> = GLWESecretFamily<B>
+    + GLWESwitchingKeyEncryptSkFamily<B>
+    + GLWEKeyswitchFamily<B>
+    + GLWEDecryptFamily<B>
+    + GGLWEExecLayoutFamily<B>
+    + MatZnxAlloc
+    + VecZnxAlloc
+    + ScalarZnxAlloc
+    + ScalarZnxAllocBytes
+    + VecZnxAllocBytes
+    + VecZnxStd
+    + VecZnxSwithcDegree
+    + VecZnxAddScalarInplace
+    + VecZnxEncodeVeci64
+    + VecZnxRotateInplace
+    + VecZnxBigSubSmallBInplace<B>
+    + VecZnxBigAutomorphismInplace<B>
+    + VecZnxCopy
+    + VecZnxAutomorphism
+    + VecZnxRshInplace;
+
+pub(crate) trait TraceTestScratchFamily<B: Backend> = TakeVecZnxDftImpl<B>
+    + TakeVecZnxBigImpl<B>
+    + TakeSvpPPolImpl<B>
+    + ScratchOwnedAllocImpl<B>
+    + ScratchOwnedBorrowImpl<B>
+    + ScratchAvailableImpl<B>
+    + TakeScalarZnxImpl<B>
+    + TakeVecZnxImpl<B>;
+
+pub(crate) fn test_trace_inplace<B: Backend>(module: &Module<B>, basek: usize, k: usize, sigma: f64, rank: usize)
+where
+    Module<B>: TraceTestModuleFamily<B>,
+    B: TraceTestScratchFamily<B>,
+{
+    let k_autokey: usize = k + basek;
+
+    let digits: usize = 1;
+    let rows: usize = k.div_ceil(basek * digits);
+
+    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(module, basek, k, rank);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(module, basek, k);
+
+    let mut source_xs: Source = Source::new([0u8; 32]);
+    let mut source_xe: Source = Source::new([0u8; 32]);
+    let mut source_xa: Source = Source::new([0u8; 32]);
+
+    let mut scratch: ScratchOwned<B> = ScratchOwned::alloc(
+        GLWECiphertext::encrypt_sk_scratch_space(module, basek, ct.k())
+            | GLWECiphertext::decrypt_scratch_space(module, basek, ct.k())
+            | AutomorphismKey::encrypt_sk_scratch_space(module, basek, k_autokey, rank)
+            | GLWECiphertext::trace_inplace_scratch_space(module, basek, ct.k(), k_autokey, digits, rank),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>> = GLWESecret::alloc(module, rank);
+    sk.fill_ternary_prob(0.5, &mut source_xs);
+    let sk_dft: GLWESecretExec<Vec<u8>, B> = GLWESecretExec::from(module, &sk);
+
+    let mut data_want: Vec<i64> = vec![0i64; module.n()];
+
+    data_want
+        .iter_mut()
+        .for_each(|x| *x = source_xa.next_i64() & 0xFF);
+
+    module.vec_znx_fill_uniform(basek, &mut pt_have.data, 0, k, &mut source_xa);
+
+    ct.encrypt_sk(
+        module,
+        &pt_have,
+        &sk_dft,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut auto_keys: HashMap<i64, AutomorphismKeyExec<Vec<u8>, B>> = HashMap::new();
+    let gal_els: Vec<i64> = GLWECiphertext::trace_galois_elements(module);
+    let mut tmp: AutomorphismKey<Vec<u8>> = AutomorphismKey::alloc(module, basek, k_autokey, rows, digits, rank);
+    gal_els.iter().for_each(|gal_el| {
+        tmp.encrypt_sk(
+            module,
+            *gal_el,
+            &sk,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            scratch.borrow(),
+        );
+        let atk_exec: AutomorphismKeyExec<Vec<u8>, B> = AutomorphismKeyExec::from(module, &tmp, scratch.borrow());
+        auto_keys.insert(*gal_el, atk_exec);
+    });
+
+    ct.trace_inplace(module, 0, 5, &auto_keys, scratch.borrow());
+    ct.trace_inplace(module, 5, module.log_n(), &auto_keys, scratch.borrow());
+
+    (0..pt_want.size()).for_each(|i| pt_want.data.at_mut(0, i)[0] = pt_have.data.at(0, i)[0]);
+
+    ct.decrypt(module, &mut pt_have, &sk_dft, scratch.borrow());
+
+    module.vec_znx_sub_ab_inplace(&mut pt_want.data, 0, &pt_have.data, 0);
+    module.vec_znx_normalize_inplace(basek, &mut pt_want.data, 0, scratch.borrow());
+
+    let noise_have: f64 = module.vec_znx_std(basek, &pt_want.data, 0).log2();
+
+    let mut noise_want: f64 = var_noise_gglwe_product(
+        module.n() as f64,
+        basek,
+        0.5,
+        0.5,
+        1.0 / 12.0,
+        sigma * sigma,
+        0.0,
+        rank as f64,
+        k,
+        k_autokey,
+    );
+    noise_want += sigma * sigma * (-2.0 * (k) as f64).exp2();
+    noise_want += module.n() as f64 * 1.0 / 12.0 * 0.5 * rank as f64 * (-2.0 * (k) as f64).exp2();
+    noise_want = noise_want.sqrt().log2();
+
+    assert!(
+        (noise_have - noise_want).abs() < 1.0,
+        "{} > {}",
+        noise_have,
+        noise_want
+    );
+}