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use rand_chacha::{
rand_core::{RngCore, SeedableRng},
ChaCha20Rng,
};
use num_bigint::BigUint;
use num_traits::cast::ToPrimitive;
use crate::Seed;
mod small_primes;
use small_primes::*;
// NIST recomends 5 rounds for miller rabin. This implementation does 8. Apple uses 16. Three iterations has a probability of 2^80 of failing
const MILLER_RABIN_ROUNDS: usize = 16;
const ZERO: u64 = 0;
const ONE: u64 = 1;
const TWO: u64 = 2;
pub struct Generator {
seed: Seed,
rng: ChaCha20Rng,
}
impl Generator {
/// Creates a new [Generator] from the provided [Seed].
///
/// The [Seed] is used to generate cryptographically secure random numbers, and should come
/// from a source of high-grade entropy.
///
/// See the [Entropy (computing) - Wikipedia](https://en.wikipedia.org/wiki/Entropy_(computing)#Embedded_systems) article for general pitfalls to avoid.
///
/// As a last resort, users may want to generate seeds on systems with good sources of entropy,
/// and transfer the seed to the embedded system. If that technique is used, unique seeds
/// should be generated per-device.
pub fn from_seed(seed: Seed) -> Self {
Self {
seed,
rng: ChaCha20Rng::from_seed(seed),
}
}
/// Creates a new [Generator] using system entropy.
///
/// Generates the seed from system entropy, see [getrandom](https://docs.rs/getrandom/latest).
#[cfg(feature = "std")]
pub fn from_entropy() -> Self {
let mut seed = [0u8; 32];
rand::thread_rng().fill_bytes(&mut seed);
Self {
seed,
rng: ChaCha20Rng::from_seed(seed),
}
}
/// Generates a new prime.
pub fn new_prime(&mut self) -> u64 {
loop {
// all primes generated by the SDK examples are 32-bit
// exponentially decreasing any security...
let candidate = self.rng.next_u64();
if Self::is_prime(candidate, &mut self.rng) {
return candidate;
}
}
}
/// Sets the CSPRNG seed to a new value.
pub fn set_seed(&mut self, seed: Seed) {
self.seed = seed;
self.rng = ChaCha20Rng::from_seed(self.seed);
}
fn is_prime(candidate: u64, rng: &mut ChaCha20Rng) -> bool {
candidate != ZERO
&& (Self::is_odd(candidate) || candidate == TWO)
&& Self::div_small_primes(candidate)
&& Self::fermat(candidate, rng)
&& Self::miller_rabin(candidate, rng)
}
fn is_even(n: u64) -> bool {
n % TWO == 0
}
fn is_odd(n: u64) -> bool {
!Self::is_even(n)
}
fn gen_range(low: u64, high: u64, rng: &mut ChaCha20Rng) -> u64 {
use rand::distributions::uniform::{UniformInt, UniformSampler};
let uniform = UniformInt::<u64>::new_inclusive(low, high);
uniform.sample(rng)
}
fn div_small_primes(candidate: u64) -> bool {
for p in SMALL_PRIMES.iter().map(|&p| p as u64) {
if candidate == p {
return true;
}
if candidate % p == 0 {
return false;
}
}
true
}
fn fermat(candidate: u64, rng: &mut ChaCha20Rng) -> bool {
for _ in 0..MILLER_RABIN_ROUNDS {
let a = Self::gen_range(TWO, candidate - TWO, rng);
let ab = BigUint::from(a);
let exp = BigUint::from(candidate - ONE);
let mb = BigUint::from(candidate);
if ab.modpow(&exp, &mb).to_u64().unwrap() != ONE {
return false;
}
}
true
}
fn miller_rabin(candidate: u64, rng: &mut ChaCha20Rng) -> bool {
if candidate == TWO {
return true;
}
let (d, s) = Self::rewrite(candidate);
let step = s.saturating_sub(ONE);
let two = BigUint::from(TWO);
let db = BigUint::from(d);
let nb = BigUint::from(candidate);
for _ in 0..MILLER_RABIN_ROUNDS {
let a = Self::gen_range(TWO, candidate - ONE, rng);
// (a ^ d mod n)
let ab = BigUint::from(a);
let mut x = ab.modpow(&db, &nb).to_u64().unwrap_or(ONE);
if x == ONE || x == (candidate - ONE) {
continue;
} else {
let mut break_early = false;
for _ in ZERO..step {
let xb = BigUint::from(x);
x = xb.modpow(&two, &nb).to_u64().unwrap_or(ONE);
if x == ONE {
return false;
} else if x == (candidate - ONE) {
break_early = true;
break;
}
}
if !break_early {
return false;
}
}
}
true
}
fn rewrite(n: u64) -> (u64, u64) {
let mut s = ZERO;
let mut d = n - ONE;
while Self::is_even(d) {
d /= TWO;
s += ONE;
}
(d, s)
}
}