Files
poulpy/core/src/test_fft64/gglwe.rs
2025-05-30 09:05:07 +02:00

638 lines
22 KiB
Rust

use backend::{FFT64, Module, ScalarZnx, ScalarZnxAlloc, ScalarZnxToMut, ScratchOwned, Stats, VecZnxOps, ZnxViewMut};
use sampling::source::Source;
use crate::{
elem::{GetRow, Infos},
ggsw_ciphertext::GGSWCiphertext,
glwe_ciphertext_fourier::GLWECiphertextFourier,
glwe_plaintext::GLWEPlaintext,
keys::{SecretKey, SecretKeyFourier},
keyswitch_key::GLWESwitchingKey,
test_fft64::ggsw::noise_ggsw_product,
};
#[test]
fn encrypt_sk() {
(1..4).for_each(|rank_in| {
(1..4).for_each(|rank_out| {
println!("test encrypt_sk rank_in rank_out: {} {}", rank_in, rank_out);
test_encrypt_sk(12, 8, 54, 3.2, rank_in, rank_out);
});
});
}
#[test]
fn key_switch() {
(1..4).for_each(|rank_in_s0s1| {
(1..4).for_each(|rank_out_s0s1| {
(1..4).for_each(|rank_out_s1s2| {
println!(
"test key_switch : ({},{},{})",
rank_in_s0s1, rank_out_s0s1, rank_out_s1s2
);
test_key_switch(12, 15, 60, 3.2, rank_in_s0s1, rank_out_s0s1, rank_out_s1s2);
})
});
});
}
#[test]
fn key_switch_inplace() {
(1..4).for_each(|rank_in_s0s1| {
(1..4).for_each(|rank_out_s0s1| {
println!(
"test key_switch_inplace : ({},{})",
rank_in_s0s1, rank_out_s0s1
);
test_key_switch_inplace(12, 15, 60, 3.2, rank_in_s0s1, rank_out_s0s1);
});
});
}
#[test]
fn external_product() {
(1..4).for_each(|rank_in| {
(1..4).for_each(|rank_out| {
println!("test external_product rank: {} {}", rank_in, rank_out);
test_external_product(12, 12, 60, 3.2, rank_in, rank_out);
});
});
}
#[test]
fn external_product_inplace() {
(1..4).for_each(|rank_in| {
(1..4).for_each(|rank_out| {
println!(
"test external_product_inplace rank: {} {}",
rank_in, rank_out
);
test_external_product_inplace(12, 12, 60, 3.2, rank_in, rank_out);
});
});
}
fn test_encrypt_sk(log_n: usize, basek: usize, k_ksk: usize, sigma: f64, rank_in: usize, rank_out: usize) {
let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
let rows = (k_ksk + basek - 1) / basek;
let mut ksk: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, rank_in, rank_out);
let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ksk);
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(
GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_ksk, rank_out)
| GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_ksk),
);
let mut sk_in: SecretKey<Vec<u8>> = SecretKey::alloc(&module, rank_in);
sk_in.fill_ternary_prob(0.5, &mut source_xs);
let mut sk_in_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::alloc(&module, rank_in);
sk_in_dft.dft(&module, &sk_in);
let mut sk_out: SecretKey<Vec<u8>> = SecretKey::alloc(&module, rank_out);
sk_out.fill_ternary_prob(0.5, &mut source_xs);
let mut sk_out_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::alloc(&module, rank_out);
sk_out_dft.dft(&module, &sk_out);
ksk.generate_from_sk(
&module,
&sk_in,
&sk_out_dft,
&mut source_xa,
&mut source_xe,
sigma,
scratch.borrow(),
);
let mut ct_glwe_fourier: GLWECiphertextFourier<Vec<u8>, FFT64> =
GLWECiphertextFourier::alloc(&module, basek, k_ksk, rank_out);
(0..ksk.rank_in()).for_each(|col_i| {
(0..ksk.rows()).for_each(|row_i| {
ksk.get_row(&module, row_i, col_i, &mut ct_glwe_fourier);
ct_glwe_fourier.decrypt(&module, &mut pt, &sk_out_dft, scratch.borrow());
module.vec_znx_sub_scalar_inplace(&mut pt.data, 0, row_i, &sk_in.data, col_i);
let std_pt: f64 = pt.data.std(0, basek) * (k_ksk as f64).exp2();
assert!((sigma - std_pt).abs() <= 0.2, "{} {}", sigma, std_pt);
});
});
}
fn test_key_switch(
log_n: usize,
basek: usize,
k_ksk: usize,
sigma: f64,
rank_in_s0s1: usize,
rank_out_s0s1: usize,
rank_out_s1s2: usize,
) {
let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
let rows = (k_ksk + basek - 1) / basek;
let mut ct_gglwe_s0s1: GLWESwitchingKey<Vec<u8>, FFT64> =
GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, rank_in_s0s1, rank_out_s0s1);
let mut ct_gglwe_s1s2: GLWESwitchingKey<Vec<u8>, FFT64> =
GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, rank_out_s0s1, rank_out_s1s2);
let mut ct_gglwe_s0s2: GLWESwitchingKey<Vec<u8>, FFT64> =
GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, rank_in_s0s1, rank_out_s1s2);
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(
GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_ksk, rank_in_s0s1 | rank_out_s0s1)
| GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_ksk)
| GLWESwitchingKey::keyswitch_scratch_space(
&module,
basek,
ct_gglwe_s0s2.k(),
ct_gglwe_s0s2.rank(),
ct_gglwe_s0s1.k(),
ct_gglwe_s0s1.rank(),
ct_gglwe_s1s2.k(),
),
);
let mut sk0: SecretKey<Vec<u8>> = SecretKey::alloc(&module, rank_in_s0s1);
sk0.fill_ternary_prob(0.5, &mut source_xs);
let mut sk0_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::alloc(&module, rank_in_s0s1);
sk0_dft.dft(&module, &sk0);
let mut sk1: SecretKey<Vec<u8>> = SecretKey::alloc(&module, rank_out_s0s1);
sk1.fill_ternary_prob(0.5, &mut source_xs);
let mut sk1_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::alloc(&module, rank_out_s0s1);
sk1_dft.dft(&module, &sk1);
let mut sk2: SecretKey<Vec<u8>> = SecretKey::alloc(&module, rank_out_s1s2);
sk2.fill_ternary_prob(0.5, &mut source_xs);
let mut sk2_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::alloc(&module, rank_out_s1s2);
sk2_dft.dft(&module, &sk2);
// gglwe_{s1}(s0) = s0 -> s1
ct_gglwe_s0s1.generate_from_sk(
&module,
&sk0,
&sk1_dft,
&mut source_xa,
&mut source_xe,
sigma,
scratch.borrow(),
);
// gglwe_{s2}(s1) -> s1 -> s2
ct_gglwe_s1s2.generate_from_sk(
&module,
&sk1,
&sk2_dft,
&mut source_xa,
&mut source_xe,
sigma,
scratch.borrow(),
);
// gglwe_{s1}(s0) (x) gglwe_{s2}(s1) = gglwe_{s2}(s0)
ct_gglwe_s0s2.keyswitch(&module, &ct_gglwe_s0s1, &ct_gglwe_s1s2, scratch.borrow());
let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> =
GLWECiphertextFourier::alloc(&module, basek, k_ksk, rank_out_s1s2);
let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ksk);
(0..ct_gglwe_s0s2.rank_in()).for_each(|col_i| {
(0..ct_gglwe_s0s2.rows()).for_each(|row_i| {
ct_gglwe_s0s2.get_row(&module, row_i, col_i, &mut ct_glwe_dft);
ct_glwe_dft.decrypt(&module, &mut pt, &sk2_dft, scratch.borrow());
module.vec_znx_sub_scalar_inplace(&mut pt.data, 0, row_i, &sk0.data, col_i);
let noise_have: f64 = pt.data.std(0, basek).log2();
let noise_want: f64 = log2_std_noise_gglwe_product(
module.n() as f64,
basek,
0.5,
0.5,
0f64,
sigma * sigma,
0f64,
rank_out_s0s1 as f64,
k_ksk,
k_ksk,
);
assert!(
(noise_have - noise_want).abs() <= 0.1,
"{} {}",
noise_have,
noise_want
);
});
});
}
fn test_key_switch_inplace(log_n: usize, basek: usize, k_ksk: usize, sigma: f64, rank_in_s0s1: usize, rank_out_s0s1: usize) {
let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
let rows: usize = (k_ksk + basek - 1) / basek;
let mut ct_gglwe_s0s1: GLWESwitchingKey<Vec<u8>, FFT64> =
GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, rank_in_s0s1, rank_out_s0s1);
let mut ct_gglwe_s1s2: GLWESwitchingKey<Vec<u8>, FFT64> =
GLWESwitchingKey::alloc(&module, basek, k_ksk, rows, rank_out_s0s1, rank_out_s0s1);
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(
GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k_ksk, rank_out_s0s1)
| GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k_ksk)
| GLWESwitchingKey::keyswitch_inplace_scratch_space(
&module,
basek,
ct_gglwe_s0s1.k(),
ct_gglwe_s0s1.rank(),
ct_gglwe_s1s2.k(),
),
);
let mut sk0: SecretKey<Vec<u8>> = SecretKey::alloc(&module, rank_in_s0s1);
sk0.fill_ternary_prob(0.5, &mut source_xs);
let mut sk0_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::alloc(&module, rank_in_s0s1);
sk0_dft.dft(&module, &sk0);
let mut sk1: SecretKey<Vec<u8>> = SecretKey::alloc(&module, rank_out_s0s1);
sk1.fill_ternary_prob(0.5, &mut source_xs);
let mut sk1_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::alloc(&module, rank_out_s0s1);
sk1_dft.dft(&module, &sk1);
let mut sk2: SecretKey<Vec<u8>> = SecretKey::alloc(&module, rank_out_s0s1);
sk2.fill_ternary_prob(0.5, &mut source_xs);
let mut sk2_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::alloc(&module, rank_out_s0s1);
sk2_dft.dft(&module, &sk2);
// gglwe_{s1}(s0) = s0 -> s1
ct_gglwe_s0s1.generate_from_sk(
&module,
&sk0,
&sk1_dft,
&mut source_xa,
&mut source_xe,
sigma,
scratch.borrow(),
);
// gglwe_{s2}(s1) -> s1 -> s2
ct_gglwe_s1s2.generate_from_sk(
&module,
&sk1,
&sk2_dft,
&mut source_xa,
&mut source_xe,
sigma,
scratch.borrow(),
);
// gglwe_{s1}(s0) (x) gglwe_{s2}(s1) = gglwe_{s2}(s0)
ct_gglwe_s0s1.keyswitch_inplace(&module, &ct_gglwe_s1s2, scratch.borrow());
let ct_gglwe_s0s2: GLWESwitchingKey<Vec<u8>, FFT64> = ct_gglwe_s0s1;
let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> =
GLWECiphertextFourier::alloc(&module, basek, k_ksk, rank_out_s0s1);
let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k_ksk);
(0..ct_gglwe_s0s2.rank_in()).for_each(|col_i| {
(0..ct_gglwe_s0s2.rows()).for_each(|row_i| {
ct_gglwe_s0s2.get_row(&module, row_i, col_i, &mut ct_glwe_dft);
ct_glwe_dft.decrypt(&module, &mut pt, &sk2_dft, scratch.borrow());
module.vec_znx_sub_scalar_inplace(&mut pt.data, 0, row_i, &sk0.data, col_i);
let noise_have: f64 = pt.data.std(0, basek).log2();
let noise_want: f64 = log2_std_noise_gglwe_product(
module.n() as f64,
basek,
0.5,
0.5,
0f64,
sigma * sigma,
0f64,
rank_out_s0s1 as f64,
k_ksk,
k_ksk,
);
assert!(
(noise_have - noise_want).abs() <= 0.1,
"{} {}",
noise_have,
noise_want
);
});
});
}
fn test_external_product(log_n: usize, basek: usize, k: usize, sigma: f64, rank_in: usize, rank_out: usize) {
let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
let rows: usize = (k + basek - 1) / basek;
let mut ct_gglwe_in: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::alloc(&module, basek, k, rows, rank_in, rank_out);
let mut ct_gglwe_out: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::alloc(&module, basek, k, rows, rank_in, rank_out);
let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k, rows, rank_out);
let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
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(
GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k, rank_out)
| GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k)
| GLWESwitchingKey::external_product_scratch_space(
&module,
basek,
ct_gglwe_out.k(),
ct_gglwe_in.k(),
ct_rgsw.k(),
rank_out,
)
| GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k, rank_out),
);
let r: usize = 1;
pt_rgsw.to_mut().raw_mut()[r] = 1; // X^{r}
let mut sk_in: SecretKey<Vec<u8>> = SecretKey::alloc(&module, rank_in);
sk_in.fill_ternary_prob(0.5, &mut source_xs);
let mut sk_in_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::alloc(&module, rank_in);
sk_in_dft.dft(&module, &sk_in);
let mut sk_out: SecretKey<Vec<u8>> = SecretKey::alloc(&module, rank_out);
sk_out.fill_ternary_prob(0.5, &mut source_xs);
let mut sk_out_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::alloc(&module, rank_out);
sk_out_dft.dft(&module, &sk_out);
// gglwe_{s1}(s0) = s0 -> s1
ct_gglwe_in.generate_from_sk(
&module,
&sk_in,
&sk_out_dft,
&mut source_xa,
&mut source_xe,
sigma,
scratch.borrow(),
);
ct_rgsw.encrypt_sk(
&module,
&pt_rgsw,
&sk_out_dft,
&mut source_xa,
&mut source_xe,
sigma,
scratch.borrow(),
);
// gglwe_(m) (x) RGSW_(X^k) = gglwe_(m * X^k)
ct_gglwe_out.external_product(&module, &ct_gglwe_in, &ct_rgsw, scratch.borrow());
scratch = ScratchOwned::new(
GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k, rank_out)
| GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k)
| GLWESwitchingKey::external_product_scratch_space(
&module,
basek,
ct_gglwe_out.k(),
ct_gglwe_in.k(),
ct_rgsw.k(),
rank_out,
)
| GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k, rank_out),
);
let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k, rank_out);
let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k);
(0..rank_in).for_each(|i| {
module.vec_znx_rotate_inplace(r as i64, &mut sk_in.data, i); // * X^{r}
});
(0..rank_in).for_each(|col_i| {
(0..ct_gglwe_out.rows()).for_each(|row_i| {
ct_gglwe_out.get_row(&module, row_i, col_i, &mut ct_glwe_dft);
ct_glwe_dft.decrypt(&module, &mut pt, &sk_out_dft, scratch.borrow());
module.vec_znx_sub_scalar_inplace(&mut pt.data, 0, row_i, &sk_in.data, col_i);
let noise_have: f64 = pt.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,
0.5,
var_msg,
var_a0_err,
var_a1_err,
var_gct_err_lhs,
var_gct_err_rhs,
rank_out as f64,
k,
k,
);
assert!(
(noise_have - noise_want).abs() <= 0.1,
"{} {}",
noise_have,
noise_want
);
});
});
}
fn test_external_product_inplace(log_n: usize, basek: usize, k: usize, sigma: f64, rank_in: usize, rank_out: usize) {
let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
let rows: usize = (k + basek - 1) / basek;
let mut ct_gglwe: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::alloc(&module, basek, k, rows, rank_in, rank_out);
let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::alloc(&module, basek, k, rows, rank_out);
let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
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(
GLWESwitchingKey::encrypt_sk_scratch_space(&module, basek, k, rank_out)
| GLWECiphertextFourier::decrypt_scratch_space(&module, basek, k)
| GLWESwitchingKey::external_product_inplace_scratch_space(&module, basek, k, k, rank_out)
| GGSWCiphertext::encrypt_sk_scratch_space(&module, basek, k, rank_out),
);
let r: usize = 1;
pt_rgsw.to_mut().raw_mut()[r] = 1; // X^{r}
let mut sk_in: SecretKey<Vec<u8>> = SecretKey::alloc(&module, rank_in);
sk_in.fill_ternary_prob(0.5, &mut source_xs);
let mut sk_in_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::alloc(&module, rank_in);
sk_in_dft.dft(&module, &sk_in);
let mut sk_out: SecretKey<Vec<u8>> = SecretKey::alloc(&module, rank_out);
sk_out.fill_ternary_prob(0.5, &mut source_xs);
let mut sk_out_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::alloc(&module, rank_out);
sk_out_dft.dft(&module, &sk_out);
// gglwe_{s1}(s0) = s0 -> s1
ct_gglwe.generate_from_sk(
&module,
&sk_in,
&sk_out_dft,
&mut source_xa,
&mut source_xe,
sigma,
scratch.borrow(),
);
ct_rgsw.encrypt_sk(
&module,
&pt_rgsw,
&sk_out_dft,
&mut source_xa,
&mut source_xe,
sigma,
scratch.borrow(),
);
// gglwe_(m) (x) RGSW_(X^k) = gglwe_(m * X^k)
ct_gglwe.external_product_inplace(&module, &ct_rgsw, scratch.borrow());
let mut ct_glwe_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::alloc(&module, basek, k, rank_out);
let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::alloc(&module, basek, k);
(0..rank_in).for_each(|i| {
module.vec_znx_rotate_inplace(r as i64, &mut sk_in.data, i); // * X^{r}
});
(0..rank_in).for_each(|col_i| {
(0..ct_gglwe.rows()).for_each(|row_i| {
ct_gglwe.get_row(&module, row_i, col_i, &mut ct_glwe_dft);
ct_glwe_dft.decrypt(&module, &mut pt, &sk_out_dft, scratch.borrow());
module.vec_znx_sub_scalar_inplace(&mut pt.data, 0, row_i, &sk_in.data, col_i);
let noise_have: f64 = pt.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,
0.5,
var_msg,
var_a0_err,
var_a1_err,
var_gct_err_lhs,
var_gct_err_rhs,
rank_out as f64,
k,
k,
);
assert!(
(noise_have - noise_want).abs() <= 0.1,
"{} {}",
noise_have,
noise_want
);
});
});
}
pub(crate) fn var_noise_gglwe_product(
n: f64,
basek: usize,
var_xs: f64,
var_msg: f64,
var_a_err: f64,
var_gct_err_lhs: f64,
var_gct_err_rhs: f64,
rank_in: f64,
a_logq: usize,
b_logq: usize,
) -> f64 {
let a_logq: usize = a_logq.min(b_logq);
let a_cols: usize = (a_logq + basek - 1) / basek;
let b_scale = 2.0f64.powi(b_logq as i32);
let a_scale: f64 = 2.0f64.powi((b_logq - a_logq) as i32);
let base: f64 = (1 << (basek)) as f64;
let var_base: f64 = base * base / 12f64;
// lhs = a_cols * n * (var_base * var_gct_err_lhs + var_e_a * var_msg * p^2)
// rhs = a_cols * n * var_base * var_gct_err_rhs * var_xs
let mut noise: f64 = (a_cols as f64) * n * var_base * (var_gct_err_lhs + var_xs * var_gct_err_rhs);
noise += var_msg * var_a_err * a_scale * a_scale * n;
noise *= rank_in;
noise /= b_scale * b_scale;
noise
}
pub(crate) fn log2_std_noise_gglwe_product(
n: f64,
basek: usize,
var_xs: f64,
var_msg: f64,
var_a_err: f64,
var_gct_err_lhs: f64,
var_gct_err_rhs: f64,
rank_in: f64,
a_logq: usize,
b_logq: usize,
) -> f64 {
let mut noise: f64 = var_noise_gglwe_product(
n,
basek,
var_xs,
var_msg,
var_a_err,
var_gct_err_lhs,
var_gct_err_rhs,
rank_in,
a_logq,
b_logq,
);
noise = noise.sqrt();
noise.log2().min(-1.0) // max noise is [-2^{-1}, 2^{-1}]
}