Re-organized code for glwe testing

core/src/glwe/mod.rs

@@ -29,3 +29,6 @@ pub use public_key::*;
 pub use secret::*;
 #[allow(unused_imports)]
 pub use trace::*;
+
+#[cfg(test)]
+mod test_fft64;

core/src/glwe/test_fft64/automorphism.rs

@@ -0,0 +1 @@
+

core/src/glwe/test_fft64/encryption.rs

@@ -0,0 +1,180 @@
+use backend::{Decoding, Encoding, FFT64, Module, ScratchOwned, Stats, VecZnxOps, ZnxZero};
+use itertools::izip;
+use sampling::source::Source;
+
+use crate::{FourierGLWECiphertext, GLWECiphertext, GLWEPlaintext, GLWEPublicKey, GLWESecret, Infos};
+
+#[test]
+fn encrypt_sk() {
+    let log_n: usize = 8;
+    (1..4).for_each(|rank| {
+        println!("test encrypt_sk rank: {}", rank);
+        test_encrypt_sk(log_n, 8, 54, 30, 3.2, rank);
+    });
+}
+
+#[test]
+fn encrypt_zero_sk() {
+    let log_n: usize = 8;
+    (1..4).for_each(|rank| {
+        println!("test encrypt_zero_sk rank: {}", rank);
+        test_encrypt_zero_sk(log_n, 8, 64, 3.2, rank);
+    });
+}
+
+#[test]
+fn encrypt_pk() {
+    let log_n: usize = 8;
+    (1..4).for_each(|rank| {
+        println!("test encrypt_pk rank: {}", rank);
+        test_encrypt_pk(log_n, 8, 64, 64, 3.2, rank)
+    });
+}
+
+fn test_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 mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut pt: 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 = ScratchOwned::new(
+        GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k()),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    let mut data_want: Vec<i64> = vec![0i64; module.n()];
+
+    data_want
+        .iter_mut()
+        .for_each(|x| *x = source_xa.next_i64() & 0xFF);
+
+    pt.data.encode_vec_i64(0, basek, k_pt, &data_want, 10);
+
+    ct.encrypt_sk(
+        &module,
+        &pt,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    pt.data.zero();
+
+    ct.decrypt(&module, &mut pt, &sk, scratch.borrow());
+
+    let mut data_have: Vec<i64> = vec![0i64; module.n()];
+
+    pt.data
+        .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() * basek - k_pt)) as f64;
+    izip!(data_want.iter(), data_have.iter()).for_each(|(a, b)| {
+        let b_scaled = (*b as f64) / scale;
+        assert!(
+            (*a as f64 - b_scaled).abs() < 0.1,
+            "{} {}",
+            *a as f64,
+            b_scaled
+        )
+    });
+}
+
+fn test_encrypt_zero_sk(log_n: usize, basek: usize, k_ct: usize, sigma: f64, rank: usize) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    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>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    let mut ct_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ct)
+            | FourierGLWECiphertext::encrypt_sk_scratch_space(&module, basek, k_ct, rank),
+    );
+
+    ct_dft.encrypt_zero_sk(
+        &module,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+    ct_dft.decrypt(&module, &mut pt, &sk, scratch.borrow());
+
+    assert!((sigma - pt.data.std(0, basek) * (k_ct as f64).exp2()) <= 0.2);
+}
+
+fn test_encrypt_pk(log_n: usize, basek: usize, k_ct: usize, k_pk: usize, sigma: f64, rank: usize) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    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]);
+    let mut source_xu: Source = Source::new([0u8; 32]);
+
+    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    let mut pk: GLWEPublicKey<Vec<u8>, FFT64> = GLWEPublicKey::alloc(&module, basek, k_pk, rank);
+    pk.generate_from_sk(&module, &sk, &mut source_xa, &mut source_xe, sigma);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        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()),
+    );
+
+    let mut data_want: Vec<i64> = vec![0i64; module.n()];
+
+    data_want
+        .iter_mut()
+        .for_each(|x| *x = source_xa.next_i64() & 0);
+
+    pt_want.data.encode_vec_i64(0, basek, k_ct, &data_want, 10);
+
+    ct.encrypt_pk(
+        &module,
+        &pt_want,
+        &pk,
+        &mut source_xu,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    ct.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+
+    module.vec_znx_sub_ab_inplace(&mut pt_want.data, 0, &pt_have.data, 0);
+
+    let noise_have: f64 = pt_want.data.std(0, basek).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).abs() < 0.2,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}

core/src/glwe/test_fft64/external_product.rs

@@ -0,0 +1,856 @@
+use backend::{
+    Decoding, Encoding, FFT64, FillUniform, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned, Stats, VecZnxOps, ZnxViewMut,
+    ZnxZero,
+};
+use itertools::izip;
+use sampling::source::Source;
+
+use crate::{
+    FourierGLWECiphertext, GGSWCiphertext, GLWECiphertext, GLWEPlaintext, GLWEPublicKey, GLWESecret, Infos,
+    automorphism::AutomorphismKey,
+    keyswitch_key::GLWESwitchingKey,
+    test_fft64::{log2_std_noise_gglwe_product, noise_ggsw_product},
+};
+
+#[test]
+fn encrypt_sk() {
+    let log_n: usize = 8;
+    (1..4).for_each(|rank| {
+        println!("test encrypt_sk rank: {}", rank);
+        test_encrypt_sk(log_n, 8, 54, 30, 3.2, rank);
+    });
+}
+
+#[test]
+fn encrypt_zero_sk() {
+    let log_n: usize = 8;
+    (1..4).for_each(|rank| {
+        println!("test encrypt_zero_sk rank: {}", rank);
+        test_encrypt_zero_sk(log_n, 8, 64, 3.2, rank);
+    });
+}
+
+#[test]
+fn encrypt_pk() {
+    let log_n: usize = 8;
+    (1..4).for_each(|rank| {
+        println!("test encrypt_pk rank: {}", rank);
+        test_encrypt_pk(log_n, 8, 64, 64, 3.2, rank)
+    });
+}
+
+#[test]
+fn keyswitch() {
+    let log_n: usize = 8;
+    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(log_n, basek, k_out, k_in, k_ksk, di, rank_in, rank_out, 3.2);
+            })
+        });
+    });
+}
+
+#[test]
+fn keyswitch_inplace() {
+    let log_n: usize = 8;
+    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(log_n, basek, k_ct, k_ksk, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn external_product() {
+    let log_n: usize = 8;
+    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(log_n, basek, k_out, k_in, k_ggsw, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn external_product_inplace() {
+    let log_n: usize = 8;
+    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(log_n, basek, k_ct, k_ggsw, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn automorphism_inplace() {
+    let log_n: usize = 8;
+    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(log_n, basek, -5, k_ct, k_ksk, di, rank, 3.2);
+        });
+    });
+}
+
+#[test]
+fn automorphism() {
+    let log_n: usize = 8;
+    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(log_n, basek, -5, k_out, k_in, k_ksk, di, rank, 3.2);
+        })
+    });
+}
+
+fn test_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 mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::alloc(&module, basek, k_ct, rank);
+    let mut pt: 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 = ScratchOwned::new(
+        GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k()),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    let mut data_want: Vec<i64> = vec![0i64; module.n()];
+
+    data_want
+        .iter_mut()
+        .for_each(|x| *x = source_xa.next_i64() & 0xFF);
+
+    pt.data.encode_vec_i64(0, basek, k_pt, &data_want, 10);
+
+    ct.encrypt_sk(
+        &module,
+        &pt,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    pt.data.zero();
+
+    ct.decrypt(&module, &mut pt, &sk, scratch.borrow());
+
+    let mut data_have: Vec<i64> = vec![0i64; module.n()];
+
+    pt.data
+        .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() * basek - k_pt)) as f64;
+    izip!(data_want.iter(), data_have.iter()).for_each(|(a, b)| {
+        let b_scaled = (*b as f64) / scale;
+        assert!(
+            (*a as f64 - b_scaled).abs() < 0.1,
+            "{} {}",
+            *a as f64,
+            b_scaled
+        )
+    });
+}
+
+fn test_encrypt_zero_sk(log_n: usize, basek: usize, k_ct: usize, sigma: f64, rank: usize) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    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>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    let mut ct_dft: FourierGLWECiphertext<Vec<u8>, FFT64> = FourierGLWECiphertext::alloc(&module, basek, k_ct, rank);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        FourierGLWECiphertext::decrypt_scratch_space(&module, basek, k_ct)
+            | FourierGLWECiphertext::encrypt_sk_scratch_space(&module, basek, k_ct, rank),
+    );
+
+    ct_dft.encrypt_zero_sk(
+        &module,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+    ct_dft.decrypt(&module, &mut pt, &sk, scratch.borrow());
+
+    assert!((sigma - pt.data.std(0, basek) * (k_ct as f64).exp2()) <= 0.2);
+}
+
+fn test_encrypt_pk(log_n: usize, basek: usize, k_ct: usize, k_pk: usize, sigma: f64, rank: usize) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    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]);
+    let mut source_xu: Source = Source::new([0u8; 32]);
+
+    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    let mut pk: GLWEPublicKey<Vec<u8>, FFT64> = GLWEPublicKey::alloc(&module, basek, k_pk, rank);
+    pk.generate_from_sk(&module, &sk, &mut source_xa, &mut source_xe, sigma);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        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()),
+    );
+
+    let mut data_want: Vec<i64> = vec![0i64; module.n()];
+
+    data_want
+        .iter_mut()
+        .for_each(|x| *x = source_xa.next_i64() & 0);
+
+    pt_want.data.encode_vec_i64(0, basek, k_ct, &data_want, 10);
+
+    ct.encrypt_pk(
+        &module,
+        &pt_want,
+        &pk,
+        &mut source_xu,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    ct.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+
+    module.vec_znx_sub_ab_inplace(&mut pt_want.data, 0, &pt_have.data, 0);
+
+    let noise_have: f64 = pt_want.data.std(0, basek).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).abs() < 0.2,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_keyswitch(
+    log_n: usize,
+    basek: usize,
+    k_out: usize,
+    k_in: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank_in: usize,
+    rank_out: usize,
+    sigma: f64,
+) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_in.div_ceil(basek * digits);
+
+    let mut ksk: GLWESwitchingKey<Vec<u8>, FFT64> =
+        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 pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
+
+    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]);
+
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ksk.k(), rank_out)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_out.k())
+            | 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>, FFT64> = GLWESecret::alloc(&module, rank_in);
+    sk_in.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    let mut sk_out: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank_out);
+    sk_out.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    ksk.generate_from_sk(
+        &module,
+        &sk_in,
+        &sk_out,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_in.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk_in,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_out.keyswitch(&module, &ct_in, &ksk, scratch.borrow());
+    ct_out.decrypt(&module, &mut pt_have, &sk_out, scratch.borrow());
+
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+    let noise_want: 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,
+    );
+
+    println!("{} vs. {}", noise_have, noise_want);
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_keyswitch_inplace(log_n: usize, basek: usize, k_ct: usize, k_ksk: usize, digits: usize, rank: usize, sigma: f64) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_ct.div_ceil(basek * digits);
+
+    let mut ct_grlwe: GLWESwitchingKey<Vec<u8>, FFT64> = 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 pt_have: 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]);
+
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, ct_grlwe.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_glwe.k())
+            | GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct_glwe.k())
+            | GLWECiphertext::keyswitch_inplace_scratch_space(&module, basek, ct_glwe.k(), ct_grlwe.k(), digits, rank),
+    );
+
+    let mut sk0: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk0.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    let mut sk1: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk1.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    ct_grlwe.generate_from_sk(
+        &module,
+        &sk0,
+        &sk1,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk0,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.keyswitch_inplace(&module, &ct_grlwe, scratch.borrow());
+
+    ct_glwe.decrypt(&module, &mut pt_have, &sk1, scratch.borrow());
+
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+    let noise_want: 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,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_automorphism(
+    log_n: usize,
+    basek: usize,
+    p: i64,
+    k_out: usize,
+    k_in: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_in.div_ceil(basek * digits);
+
+    let mut autokey: AutomorphismKey<Vec<u8>, FFT64> = 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 pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
+
+    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]);
+
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        AutomorphismKey::generate_from_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>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    autokey.generate_from_sk(
+        &module,
+        p,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_in.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_out.automorphism(&module, &ct_in, &autokey, scratch.borrow());
+    ct_out.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+    module.vec_znx_automorphism_inplace(p, &mut pt_want.data, 0);
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+    module.vec_znx_normalize_inplace(basek, &mut pt_have.data, 0, scratch.borrow());
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+
+    println!("{}", noise_have);
+
+    let noise_want: 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,
+    );
+
+    assert!(
+        noise_have <= noise_want + 1.0,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_automorphism_inplace(
+    log_n: usize,
+    basek: usize,
+    p: i64,
+    k_ct: usize,
+    k_ksk: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_ct.div_ceil(basek * digits);
+
+    let mut autokey: AutomorphismKey<Vec<u8>, FFT64> = 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 pt_have: 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]);
+
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
+
+    let mut scratch: ScratchOwned = ScratchOwned::new(
+        AutomorphismKey::generate_from_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>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    autokey.generate_from_sk(
+        &module,
+        p,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct.automorphism_inplace(&module, &autokey, scratch.borrow());
+    ct.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+    module.vec_znx_automorphism_inplace(p, &mut pt_want.data, 0);
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+    module.vec_znx_normalize_inplace(basek, &mut pt_have.data, 0, scratch.borrow());
+
+    let noise_have: f64 = pt_have.data.std(0, basek).log2();
+    let noise_want: 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,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_external_product(
+    log_n: usize,
+    basek: usize,
+    k_out: usize,
+    k_in: usize,
+    k_ggsw: usize,
+    digits: usize,
+    rank: usize,
+    sigma: f64,
+) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    let rows: usize = k_in.div_ceil(basek * digits);
+
+    let mut ct_ggsw: GGSWCiphertext<Vec<u8>, FFT64> = 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.new_scalar_znx(1);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_in);
+    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_out);
+
+    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
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &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 = ScratchOwned::new(
+        GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, ct_ggsw.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_glwe_out.k())
+            | 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>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    ct_ggsw.encrypt_sk(
+        &module,
+        &pt_rgsw,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe_in.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe_out.external_product(&module, &ct_glwe_in, &ct_ggsw, scratch.borrow());
+
+    ct_glwe_out.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+
+    module.vec_znx_rotate_inplace(k as i64, &mut pt_want.data, 0);
+
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+
+    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;
+
+    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 noise_want: 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,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}
+
+fn test_external_product_inplace(log_n: usize, basek: usize, k_ct: usize, k_ggsw: usize, digits: usize, rank: usize, sigma: f64) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+    let rows: usize = k_ct.div_ceil(basek * digits);
+
+    let mut ct_ggsw: GGSWCiphertext<Vec<u8>, FFT64> = 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.new_scalar_znx(1);
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+    let mut pt_have: 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
+    pt_want
+        .data
+        .fill_uniform(basek, 0, pt_want.size(), &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 = ScratchOwned::new(
+        GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, ct_ggsw.k(), rank)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct_glwe.k())
+            | 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>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    ct_ggsw.encrypt_sk(
+        &module,
+        &pt_rgsw,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.encrypt_sk(
+        &module,
+        &pt_want,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    ct_glwe.external_product_inplace(&module, &ct_ggsw, scratch.borrow());
+
+    ct_glwe.decrypt(&module, &mut pt_have, &sk, scratch.borrow());
+
+    module.vec_znx_rotate_inplace(k as i64, &mut pt_want.data, 0);
+
+    module.vec_znx_sub_ab_inplace(&mut pt_have.data, 0, &pt_want.data, 0);
+
+    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;
+
+    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 noise_want: 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,
+    );
+
+    assert!(
+        (noise_have - noise_want).abs() <= 0.5,
+        "{} {}",
+        noise_have,
+        noise_want
+    );
+}

core/src/glwe/test_fft64/keyswitch.rs

@@ -0,0 +1 @@
+

core/src/glwe/test_fft64/mod.rs

@@ -0,0 +1,6 @@
+pub mod automorphism;
+pub mod encryption;
+pub mod external_product;
+pub mod keyswitch;
+pub mod packing;
+pub mod trace;

core/src/glwe/test_fft64/packing.rs

@@ -0,0 +1,139 @@
+use crate::{AutomorphismKey, GLWECiphertext, GLWEOps, GLWEPlaintext, GLWESecret, StreamPacker};
+use std::collections::HashMap;
+
+use backend::{Encoding, FFT64, Module, ScratchOwned, Stats};
+use sampling::source::Source;
+
+#[test]
+fn packing() {
+    let log_n: usize = 5;
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    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 = ScratchOwned::new(
+        GLWECiphertext::encrypt_sk_scratch_space(&module, basek, k_ct)
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, k_ct)
+            | AutomorphismKey::generate_from_sk_scratch_space(&module, basek, k_ksk, rank)
+            | StreamPacker::scratch_space(&module, basek, k_ct, k_ksk, digits, rank),
+    );
+
+    let mut sk: GLWESecret<Vec<u8>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(&module, 0.5, &mut source_xs);
+
+    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;
+    });
+    pt.data.encode_vec_i64(0, basek, pt_k, &data, 32);
+
+    let gal_els: Vec<i64> = StreamPacker::galois_elements(&module);
+
+    let mut auto_keys: HashMap<i64, AutomorphismKey<Vec<u8>, FFT64>> = HashMap::new();
+    gal_els.iter().for_each(|gal_el| {
+        let mut key: AutomorphismKey<Vec<u8>, FFT64> = AutomorphismKey::alloc(&module, basek, k_ksk, rows, digits, rank);
+        key.generate_from_sk(
+            &module,
+            *gal_el,
+            &sk,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            scratch.borrow(),
+        );
+        auto_keys.insert(*gal_el, key);
+    });
+
+    let log_batch: usize = 0;
+
+    let mut packer: StreamPacker = StreamPacker::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,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut res: Vec<GLWECiphertext<Vec<u8>>> = Vec::new();
+
+    (0..module.n() >> log_batch).for_each(|i| {
+        ct.encrypt_sk(
+            &module,
+            &pt,
+            &sk,
+            &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, &mut res, Some(&ct), &auto_keys, scratch.borrow());
+        } else {
+            packer.add(
+                &module,
+                &mut res,
+                None::<&GLWECiphertext<Vec<u8>>>,
+                &auto_keys,
+                scratch.borrow(),
+            )
+        }
+    });
+
+    packer.flush(&module, &mut res, &auto_keys, scratch.borrow());
+    packer.reset();
+
+    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ct);
+
+    res.iter().enumerate().for_each(|(i, res_i)| {
+        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;
+            }
+        });
+        pt_want.data.encode_vec_i64(0, basek, pt_k, &data, 32);
+
+        res_i.decrypt(&module, &mut pt, &sk, scratch.borrow());
+
+        if i & 1 == 0 {
+            pt.sub_inplace_ab(&module, &pt_want);
+        } else {
+            pt.add_inplace(&module, &pt_want);
+        }
+
+        let noise_have = pt.data.std(0, basek).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/test_fft64/trace.rs

@@ -0,0 +1,113 @@
+use std::collections::HashMap;
+
+use backend::{FFT64, FillUniform, Module, ScratchOwned, Stats, VecZnxOps, ZnxView, ZnxViewMut};
+use sampling::source::Source;
+
+use crate::{AutomorphismKey, GLWECiphertext, GLWEPlaintext, GLWESecret, Infos, test_fft64::var_noise_gglwe_product};
+
+#[test]
+fn trace_inplace() {
+    let log_n: usize = 8;
+    (1..4).for_each(|rank| {
+        println!("test trace_inplace rank: {}", rank);
+        test_trace_inplace(log_n, 8, 54, 3.2, rank);
+    });
+}
+
+fn test_trace_inplace(log_n: usize, basek: usize, k: usize, sigma: f64, rank: usize) {
+    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
+
+    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 = ScratchOwned::new(
+        GLWECiphertext::encrypt_sk_scratch_space(&module, basek, ct.k())
+            | GLWECiphertext::decrypt_scratch_space(&module, basek, ct.k())
+            | AutomorphismKey::generate_from_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>, FFT64> = GLWESecret::alloc(&module, rank);
+    sk.fill_ternary_prob(&&module, 0.5, &mut source_xs);
+
+    let mut data_want: Vec<i64> = vec![0i64; module.n()];
+
+    data_want
+        .iter_mut()
+        .for_each(|x| *x = source_xa.next_i64() & 0xFF);
+
+    pt_have
+        .data
+        .fill_uniform(basek, 0, pt_have.size(), &mut source_xa);
+
+    ct.encrypt_sk(
+        &module,
+        &pt_have,
+        &sk,
+        &mut source_xa,
+        &mut source_xe,
+        sigma,
+        scratch.borrow(),
+    );
+
+    let mut auto_keys: HashMap<i64, AutomorphismKey<Vec<u8>, FFT64>> = HashMap::new();
+    let gal_els: Vec<i64> = GLWECiphertext::trace_galois_elements(&module);
+    gal_els.iter().for_each(|gal_el| {
+        let mut key: AutomorphismKey<Vec<u8>, FFT64> = AutomorphismKey::alloc(&module, basek, k_autokey, rows, digits, rank);
+        key.generate_from_sk(
+            &module,
+            *gal_el,
+            &sk,
+            &mut source_xa,
+            &mut source_xe,
+            sigma,
+            scratch.borrow(),
+        );
+        auto_keys.insert(*gal_el, key);
+    });
+
+    ct.trace_inplace(&module, 0, 5, &auto_keys, scratch.borrow());
+    ct.trace_inplace(&module, 5, 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, 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 = pt_want.data.std(0, basek).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
+    );
+}