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#![warn(missing_docs, unused_imports)]
mod primes;
use crate::primes::FIRST_PRIMES;
use rug::integer::IsPrime;
use rug::Integer;
use scicrypt_traits::randomness::GeneralRng;
use scicrypt_traits::randomness::SecureRng;
const REPS: u32 = 25;
pub fn gen_prime<R: SecureRng>(bit_length: u32, rng: &mut GeneralRng<R>) -> Integer {
'outer: loop {
let mut candidate = Integer::from(Integer::random_bits(bit_length, &mut rng.rug_rng()));
candidate.set_bit(bit_length - 1, true);
candidate.set_bit(0, true);
let prime_count: usize = bit_length as usize / 3;
let mods: Vec<u32> = FIRST_PRIMES[..prime_count]
.iter()
.map(|p| candidate.mod_u(*p))
.collect();
let mut delta = 0;
let max_delta = u32::MAX - FIRST_PRIMES.last().unwrap();
candidate = 'sieve: loop {
for i in 1..prime_count {
if (mods[i] + delta) % FIRST_PRIMES[i] == 0 {
delta += 2;
if delta > max_delta {
continue 'outer;
}
continue 'sieve;
}
}
break candidate + delta;
};
if candidate.is_probably_prime(REPS) != IsPrime::No {
return candidate;
}
}
}
pub fn gen_safe_prime<R: SecureRng>(bit_length: u32, rng: &mut GeneralRng<R>) -> Integer {
'outer: loop {
let mut candidate = Integer::from(Integer::random_bits(bit_length, &mut rng.rug_rng()));
candidate.set_bit(bit_length - 1, true);
candidate.set_bit(0, true);
let prime_count: usize = bit_length as usize / 3;
let mods: Vec<u32> = FIRST_PRIMES[..prime_count]
.iter()
.map(|p| candidate.mod_u(*p))
.collect();
let mut delta = 0;
let max_delta = u32::MAX - FIRST_PRIMES[prime_count - 1];
candidate = 'sieve: loop {
for i in 1..prime_count {
if (mods[i] + delta) % FIRST_PRIMES[i] <= 1 {
delta += 4;
if delta > max_delta {
continue 'outer;
}
continue 'sieve;
}
}
break candidate + delta;
};
if candidate.is_probably_prime(REPS) != IsPrime::No {
let candidate_reduced = Integer::from(&candidate >> 1);
if candidate_reduced.is_probably_prime(REPS) != IsPrime::No {
return candidate;
}
}
}
}
pub fn gen_rsa_modulus<R: SecureRng>(
bit_length: u32,
rng: &mut GeneralRng<R>,
) -> (Integer, Integer) {
let p = gen_safe_prime(bit_length / 2, rng);
let q = gen_safe_prime(bit_length / 2, rng);
let n = Integer::from(&p * &q);
let lambda: Integer = (p - Integer::from(1)).lcm(&(q - Integer::from(1)));
(n, lambda)
}
pub fn gen_coprime<R: SecureRng>(other: &Integer, rng: &mut GeneralRng<R>) -> Integer {
loop {
let candidate = Integer::from(other.random_below_ref(&mut rng.rug_rng()));
if Integer::from(candidate.gcd_ref(other)) == 1 {
return candidate;
}
}
}
#[cfg(test)]
mod tests {
use crate::{gen_prime, gen_safe_prime};
use rand_core::OsRng;
use rug::Integer;
use scicrypt_traits::randomness::GeneralRng;
fn assert_primality_100_000_factors(integer: &Integer) {
let (_, hi) = primal::estimate_nth_prime(100_000);
for prime in primal::Sieve::new(hi as usize).primes_from(0) {
assert!(
!integer.is_divisible_u(prime as u32),
"{} is divisible by {}",
integer,
prime
);
}
}
#[test]
fn test_gen_prime_for_factors() {
let mut rng = GeneralRng::new(OsRng);
let generated_prime = gen_prime(256, &mut rng);
assert_primality_100_000_factors(&generated_prime);
}
#[test]
fn test_gen_safe_prime_for_factors() {
let mut rng = GeneralRng::new(OsRng);
let generated_prime = gen_safe_prime(256, &mut rng);
assert_primality_100_000_factors(&generated_prime);
let sophie_germain_prime = generated_prime >> 1;
assert_primality_100_000_factors(&sophie_germain_prime);
}
}