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use crate::oracle::LpnOracle;
use m4ri_rust::friendly::BinMatrix;
use m4ri_rust::friendly::BinVector;
use rayon::prelude::*;
use crate::codes::BinaryCode;
use rand::prelude::*;
pub fn sparse_secret_reduce(oracle: &mut LpnOracle) {
println!("Reducing to a sparse secret");
let k = oracle.k as usize;
let mut rng = thread_rng();
let (m, c_prime, e, samples) = loop {
let (a, b, e, samples) = {
let samples: Vec<_> = oracle
.samples
.choose_multiple(&mut rng, k)
.cloned()
.collect();
let mut b = BinVector::with_capacity(k);
let mut e = BinVector::with_capacity(k);
(
BinMatrix::new(
samples
.iter()
.map(|q| {
b.push(q.c);
e.push(q.e);
q.a.clone()
})
.collect(),
),
b,
e,
samples,
)
};
if a.clone().echelonize() == k {
break (a, b, e, samples);
}
};
let original_secret = oracle.secret.clone();
println!(
"the secret prior to reduction to a sparse secret was: {:?}",
original_secret
);
debug_assert_eq!((&original_secret * &m.transposed()) + e, c_prime);
oracle.secret = &(&m * &original_secret) + &c_prime;
debug_assert_eq!(
(&oracle.secret + &c_prime) * m.transposed().inverted(),
original_secret
);
let m_t_inv = m.inverted();
for q in samples.into_iter() {
oracle.samples.remove_item(&q);
}
let secret = &oracle.secret;
oracle.samples.par_iter_mut().for_each(|query| {
let new_v = &query.a * &m_t_inv;
query.c ^= &new_v * &c_prime;
debug_assert_eq!((secret * &new_v) ^ query.e, query.c);
query.a = new_v;
});
oracle.sparse_transform_matrix = Some(m);
oracle.sparse_transform_vector = Some(c_prime);
oracle.delta_s = oracle.delta;
}
pub fn unsparse_secret(oracle: &LpnOracle, secret: &BinVector) -> BinVector {
let m = &oracle
.sparse_transform_matrix
.clone()
.expect("Not a sparse oracle");
let c_prime = &oracle.sparse_transform_vector.clone().unwrap();
(secret + c_prime) * m.transposed().inverted()
}
pub fn code_reduce<T: BinaryCode + Sync>(oracle: &mut LpnOracle, code: &T) {
assert!(
oracle.delta_s > 0.0,
"This reduction only works for sparse secrets!"
);
assert_eq!(
oracle.k as usize,
code.length(),
"The length of the code does not match the problem size!"
);
println!("Decoding samples");
oracle.samples.par_iter_mut().for_each(|query| {
(*query).a = code.decode_to_message(&query.a).expect("Couldn't decode??");
debug_assert_eq!(query.a.len(), code.dimension());
});
println!("Note that we transformed the secret $s$ into $s'=s*G^T$!");
let gen_t = code.generator_matrix().transposed();
oracle.secret = &oracle.secret * &gen_t;
debug_assert_eq!(oracle.secret.len(), code.dimension());
oracle.k = code.dimension() as u32;
println!("Computing new delta");
oracle.delta *= code.bias(oracle.delta_s);
println!("New delta = {}", oracle.delta);
}
#[cfg(test)]
mod test {
use super::*;
use crate::codes::HammingCode15_11;
use crate::lf1::fwht_solve;
#[test]
fn test_unsparse() {
let mut oracle: LpnOracle = LpnOracle::new(15, 1.0 / 4.0);
oracle.secret = BinVector::from_function(15, |x| x % 2 == 0);
let secret = oracle.secret.clone();
oracle.get_samples(1000);
sparse_secret_reduce(&mut oracle);
let unsps = unsparse_secret(&oracle, &oracle.secret);
assert_eq!(secret, unsps, "sparse/unsparse unequal");
}
#[test]
fn test_reduction() {
let mut oracle: LpnOracle = LpnOracle::new(15, 1.0 / 8.0);
oracle.secret = BinVector::from_function(15, |x| x % 2 == 0);
oracle.get_samples(1_000_000);
sparse_secret_reduce(&mut oracle);
let code = HammingCode15_11;
code_reduce(&mut oracle, &code);
let secret = oracle.secret.clone();
let fwht_solution = fwht_solve(oracle.clone());
assert_eq!(secret, fwht_solution, "Found wrong solution");
}
}