1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
|
//! Random number generator support
use super::Uint;
use crate::{Limb, NonZero, Random, RandomMod};
use rand_core::CryptoRngCore;
use subtle::ConstantTimeLess;
impl<const LIMBS: usize> Random for Uint<LIMBS> {
/// Generate a cryptographically secure random [`Uint`].
fn random(mut rng: &mut impl CryptoRngCore) -> Self {
let mut limbs = [Limb::ZERO; LIMBS];
for limb in &mut limbs {
*limb = Limb::random(&mut rng)
}
limbs.into()
}
}
impl<const LIMBS: usize> RandomMod for Uint<LIMBS> {
/// Generate a cryptographically secure random [`Uint`] which is less than
/// a given `modulus`.
///
/// This function uses rejection sampling, a method which produces an
/// unbiased distribution of in-range values provided the underlying
/// CSRNG is unbiased, but runs in variable-time.
///
/// The variable-time nature of the algorithm should not pose a security
/// issue so long as the underlying random number generator is truly a
/// CSRNG, where previous outputs are unrelated to subsequent
/// outputs and do not reveal information about the RNG's internal state.
fn random_mod(mut rng: &mut impl CryptoRngCore, modulus: &NonZero<Self>) -> Self {
let mut n = Self::ZERO;
let n_bits = modulus.as_ref().bits_vartime();
let n_limbs = (n_bits + Limb::BITS - 1) / Limb::BITS;
let mask = Limb::MAX >> (Limb::BITS * n_limbs - n_bits);
loop {
for i in 0..n_limbs {
n.limbs[i] = Limb::random(&mut rng);
}
n.limbs[n_limbs - 1] = n.limbs[n_limbs - 1] & mask;
if n.ct_lt(modulus).into() {
return n;
}
}
}
}
#[cfg(test)]
mod tests {
use crate::{NonZero, RandomMod, U256};
use rand_core::SeedableRng;
#[test]
fn random_mod() {
let mut rng = rand_chacha::ChaCha8Rng::seed_from_u64(1);
// Ensure `random_mod` runs in a reasonable amount of time
let modulus = NonZero::new(U256::from(42u8)).unwrap();
let res = U256::random_mod(&mut rng, &modulus);
// Sanity check that the return value isn't zero
assert_ne!(res, U256::ZERO);
// Ensure `random_mod` runs in a reasonable amount of time
// when the modulus is larger than 1 limb
let modulus = NonZero::new(U256::from(0x10000000000000001u128)).unwrap();
let res = U256::random_mod(&mut rng, &modulus);
// Sanity check that the return value isn't zero
assert_ne!(res, U256::ZERO);
}
}
|
