56 lines
1.8 KiB
Rust
56 lines
1.8 KiB
Rust
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use crate::{Limb, Uint, WideWord, Word};
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/// Returns `(hi, lo)` such that `hi * R + lo = x * y + z + w`.
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#[inline(always)]
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const fn muladdcarry(x: Word, y: Word, z: Word, w: Word) -> (Word, Word) {
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let res = (x as WideWord)
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.wrapping_mul(y as WideWord)
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.wrapping_add(z as WideWord)
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.wrapping_add(w as WideWord);
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((res >> Word::BITS) as Word, res as Word)
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}
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/// Algorithm 14.32 in Handbook of Applied Cryptography <https://cacr.uwaterloo.ca/hac/about/chap14.pdf>
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pub const fn montgomery_reduction<const LIMBS: usize>(
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lower_upper: &(Uint<LIMBS>, Uint<LIMBS>),
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modulus: &Uint<LIMBS>,
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mod_neg_inv: Limb,
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) -> Uint<LIMBS> {
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let (mut lower, mut upper) = *lower_upper;
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let mut meta_carry = Limb(0);
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let mut new_sum;
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let mut i = 0;
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while i < LIMBS {
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let u = lower.limbs[i].0.wrapping_mul(mod_neg_inv.0);
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let (mut carry, _) = muladdcarry(u, modulus.limbs[0].0, lower.limbs[i].0, 0);
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let mut new_limb;
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let mut j = 1;
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while j < (LIMBS - i) {
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(carry, new_limb) = muladdcarry(u, modulus.limbs[j].0, lower.limbs[i + j].0, carry);
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lower.limbs[i + j] = Limb(new_limb);
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j += 1;
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}
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while j < LIMBS {
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(carry, new_limb) =
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muladdcarry(u, modulus.limbs[j].0, upper.limbs[i + j - LIMBS].0, carry);
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upper.limbs[i + j - LIMBS] = Limb(new_limb);
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j += 1;
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}
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(new_sum, meta_carry) = upper.limbs[i].adc(Limb(carry), meta_carry);
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upper.limbs[i] = new_sum;
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i += 1;
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}
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// Division is simply taking the upper half of the limbs
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// Final reduction (at this point, the value is at most 2 * modulus,
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// so `meta_carry` is either 0 or 1)
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upper.sub_mod_with_carry(meta_carry, modulus, modulus)
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}
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