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use crate::oracle::LpnOracle;
use m4ri_rust::friendly::solve_left;
use m4ri_rust::friendly::BinMatrix;
use m4ri_rust::friendly::BinVector;
use rand::prelude::*;
#[allow(clippy::many_single_char_names, clippy::needless_pass_by_value)]
pub fn pooled_gauss_solve(oracle: LpnOracle) -> BinVector {
let k = oracle.k;
let alpha = 0.5f64.powi(k as i32);
let tau = (1.0 - oracle.delta) / 2.0;
let beta = ((1f64 - tau) / 2f64).powi(k as i32);
let m: f64 = (((1.5 * (1.0 / alpha).ln()).sqrt() + (1.0 / beta).ln().sqrt()) / (0.5 - tau))
.powi(2)
.floor();
let c = (tau * m + (3.0 * (0.5 - tau) * (1.0 / alpha).ln() * m).sqrt().floor()) as u32;
let m = m as usize;
let mut rng = thread_rng();
println!(
"Attempting Pooled Gauss solving method, k={}, tau={}",
k, tau
);
println!("Target secret weight <= {}", c);
println!("Building (Am, b) with length {}", m);
let (am, bm) = sample_matrix(m, &oracle, &mut rng);
debug_assert_eq!(am.ncols(), k as usize);
debug_assert_eq!(am.nrows(), m);
debug_assert_eq!(bm.nrows(), m);
debug_assert_eq!(bm.ncols(), 1);
let test = |s_prime: &BinMatrix, tries: &mut usize| {
debug_assert_eq!(s_prime.nrows(), oracle.k as usize);
debug_assert_eq!(s_prime.ncols(), 1);
*tries += 1;
if *tries % 1000 == 0 {
println!("Attempt {}...", tries);
}
let mut testproduct = &am * s_prime;
testproduct += &bm;
let result = testproduct.as_vector().count_ones() <= c;
debug_assert_eq!(
result,
s_prime.as_vector() == oracle.secret,
"Test will reject or accept an (in)correct secret with weight {} <= {}",
testproduct.as_vector().count_ones(),
c
);
result
};
println!("Starting random sampling of invertible (A, b)");
let mut tries = 0;
let s_prime = loop {
let (a, mut b) = loop {
let (a_try, b_try) = sample_matrix(k as usize, &oracle, &mut rng);
if a_try.clone().echelonize() == k as usize {
break (a_try, b_try);
}
};
if !solve_left(a, &mut b) {
println!("Somehow, solving failed....");
continue;
}
let result = { test(&b, &mut tries) };
if result {
println!("Found after {} tries", tries);
break b;
}
};
s_prime.as_vector()
}
fn sample_matrix(k: usize, oracle: &LpnOracle, rng: &mut ThreadRng) -> (BinMatrix, BinMatrix) {
let samples = oracle.samples.choose_multiple(rng, k);
let mut b_bits = BinVector::with_capacity(k as usize);
(
BinMatrix::new(
samples
.into_iter()
.map(|q| {
b_bits.push(q.c);
q.a.clone()
})
.collect(),
),
b_bits.as_column_matrix(),
)
}
#[cfg(test)]
mod test {
use super::*;
#[test]
fn run_gauss() {
let mut oracle: LpnOracle = LpnOracle::new(32, 1.0 / 32.0);
oracle.get_samples(40555);
let secret = oracle.secret.clone();
let solution = pooled_gauss_solve(oracle);
assert_eq!(solution, secret);
}
}