crypto_bigint/uint/modular/
reduction.rs

1use crate::{Limb, Uint, WideWord, Word};
2
3/// Returns `(hi, lo)` such that `hi * R + lo = x * y + z + w`.
4#[inline(always)]
5const fn muladdcarry(x: Word, y: Word, z: Word, w: Word) -> (Word, Word) {
6    let res = (x as WideWord)
7        .wrapping_mul(y as WideWord)
8        .wrapping_add(z as WideWord)
9        .wrapping_add(w as WideWord);
10    ((res >> Word::BITS) as Word, res as Word)
11}
12
13/// Algorithm 14.32 in Handbook of Applied Cryptography <https://cacr.uwaterloo.ca/hac/about/chap14.pdf>
14pub const fn montgomery_reduction<const LIMBS: usize>(
15    lower_upper: &(Uint<LIMBS>, Uint<LIMBS>),
16    modulus: &Uint<LIMBS>,
17    mod_neg_inv: Limb,
18) -> Uint<LIMBS> {
19    let (mut lower, mut upper) = *lower_upper;
20
21    let mut meta_carry = Limb(0);
22    let mut new_sum;
23
24    let mut i = 0;
25    while i < LIMBS {
26        let u = lower.limbs[i].0.wrapping_mul(mod_neg_inv.0);
27
28        let (mut carry, _) = muladdcarry(u, modulus.limbs[0].0, lower.limbs[i].0, 0);
29        let mut new_limb;
30
31        let mut j = 1;
32        while j < (LIMBS - i) {
33            (carry, new_limb) = muladdcarry(u, modulus.limbs[j].0, lower.limbs[i + j].0, carry);
34            lower.limbs[i + j] = Limb(new_limb);
35            j += 1;
36        }
37        while j < LIMBS {
38            (carry, new_limb) =
39                muladdcarry(u, modulus.limbs[j].0, upper.limbs[i + j - LIMBS].0, carry);
40            upper.limbs[i + j - LIMBS] = Limb(new_limb);
41            j += 1;
42        }
43
44        (new_sum, meta_carry) = upper.limbs[i].adc(Limb(carry), meta_carry);
45        upper.limbs[i] = new_sum;
46
47        i += 1;
48    }
49
50    // Division is simply taking the upper half of the limbs
51    // Final reduction (at this point, the value is at most 2 * modulus,
52    // so `meta_carry` is either 0 or 1)
53
54    upper.sub_mod_with_carry(meta_carry, modulus, modulus)
55}
crypto_bigint/uint/modular/reduction.rs

crypto_bigint/uint/modular/
reduction.rs
