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use crate::{CtChoice, Limb, Uint, WideWord, Word};
/// Algorithm 14.32 in Handbook of Applied Cryptography <https://cacr.uwaterloo.ca/hac/about/chap14.pdf>
pub const fn montgomery_reduction<const LIMBS: usize>(
lower_upper: &(Uint<LIMBS>, Uint<LIMBS>),
modulus: &Uint<LIMBS>,
mod_neg_inv: Limb,
) -> Uint<LIMBS> {
let (mut lower, mut upper) = *lower_upper;
let mut meta_carry: WideWord = 0;
let mut i = 0;
while i < LIMBS {
let u = (lower.limbs[i].0.wrapping_mul(mod_neg_inv.0)) as WideWord;
let new_limb =
(u * modulus.limbs[0].0 as WideWord).wrapping_add(lower.limbs[i].0 as WideWord);
let mut carry = new_limb >> Word::BITS;
let mut j = 1;
while j < (LIMBS - i) {
let new_limb = (u * modulus.limbs[j].0 as WideWord)
.wrapping_add(lower.limbs[i + j].0 as WideWord)
.wrapping_add(carry);
carry = new_limb >> Word::BITS;
lower.limbs[i + j] = Limb(new_limb as Word);
j += 1;
}
while j < LIMBS {
let new_limb = (u * modulus.limbs[j].0 as WideWord)
.wrapping_add(upper.limbs[i + j - LIMBS].0 as WideWord)
.wrapping_add(carry);
carry = new_limb >> Word::BITS;
upper.limbs[i + j - LIMBS] = Limb(new_limb as Word);
j += 1;
}
let new_sum = (upper.limbs[i].0 as WideWord)
.wrapping_add(carry)
.wrapping_add(meta_carry);
meta_carry = new_sum >> Word::BITS;
upper.limbs[i] = Limb(new_sum as Word);
i += 1;
}
// Division is simply taking the upper half of the limbs
// Final reduction (at this point, the value is at most 2 * modulus)
let must_reduce = CtChoice::from_lsb(meta_carry as Word).or(Uint::ct_gt(modulus, &upper).not());
upper = upper.wrapping_sub(&Uint::ct_select(&Uint::ZERO, modulus, must_reduce));
upper
}
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