Files
poulpy/src/modulus/impl_u64/montgomery.rs
2024-12-20 13:22:40 +01:00

267 lines
8.7 KiB
Rust

use crate::modulus::ReduceOnce;
use crate::modulus::montgomery::{MontgomeryPrecomp, Montgomery};
use crate::modulus::barrett::{BarrettPrecomp};
extern crate test;
/// MontgomeryPrecomp is a set of methods implemented for MontgomeryPrecomp<u64>
/// enabling Montgomery arithmetic over u64 values.
impl MontgomeryPrecomp<u64>{
/// Returns an new instance of MontgomeryPrecomp<u64>.
/// This method will fail if gcd(q, 2^64) != 1.
#[inline(always)]
pub fn new(q: u64) -> MontgomeryPrecomp<u64>{
assert!(q & 1 != 0, "Invalid argument: gcd(q={}, radix=2^64) != 1", q);
let mut q_inv: u64 = 1;
let mut q_pow = q;
for _i in 0..63{
q_inv = q_inv.wrapping_mul(q_pow);
q_pow = q_pow.wrapping_mul(q_pow);
}
let mut precomp = Self{
q: q,
barrett: BarrettPrecomp::new(q),
q_inv: q_inv,
one: Montgomery(0),
minus_one: Montgomery(0),
};
precomp.one = precomp.prepare(1);
precomp.minus_one = Montgomery(q-precomp.one.value());
precomp
}
/// Returns 2^64 mod q as a Montgomery<u64>.
#[inline(always)]
pub fn one(&self) -> Montgomery<u64>{
self.one
}
/// Returns (q-1) * 2^64 mod q as a Montgomery<u64>.
#[inline(always)]
pub fn minus_one(&self) -> Montgomery<u64>{
self.minus_one
}
/// Returns lhs * 2^64 mod q as a Montgomery<u64>.
#[inline(always)]
pub fn prepare(&self, lhs: u64) -> Montgomery<u64>{
let mut rhs = Montgomery(0);
self.prepare_assign(lhs, &mut rhs);
rhs
}
/// Assigns lhs * 2^64 mod q to rhs.
#[inline(always)]
pub fn prepare_assign(&self, lhs: u64, rhs: &mut Montgomery<u64>){
self.prepare_lazy_assign(lhs, rhs);
rhs.value_mut().reduce_once_assign(self.q);
}
/// Returns lhs * 2^64 mod q in range [0, 2q-1] as a Montgomery<u64>.
#[inline(always)]
pub fn prepare_lazy(&self, lhs: u64) -> Montgomery<u64>{
let mut rhs = Montgomery(0);
self.prepare_lazy_assign(lhs, &mut rhs);
rhs
}
/// Assigns lhs * 2^64 mod q in range [0, 2q-1] to rhs.
#[inline(always)]
pub fn prepare_lazy_assign(&self, lhs: u64, rhs: &mut Montgomery<u64>){
let (_, mhi) = lhs.widening_mul(*self.barrett.value_lo());
*rhs = Montgomery((lhs.wrapping_mul(*self.barrett.value_hi()).wrapping_add(mhi)).wrapping_mul(self.q).wrapping_neg());
}
/// Returns lhs * (2^64)^-1 mod q as a u64.
#[inline(always)]
pub fn unprepare(&self, lhs: Montgomery<u64>) -> u64{
let mut rhs = 0u64;
self.unprepare_assign(lhs, &mut rhs);
rhs
}
/// Assigns lhs * (2^64)^-1 mod q to rhs.
#[inline(always)]
pub fn unprepare_assign(&self, lhs: Montgomery<u64>, rhs: &mut u64){
self.unprepare_lazy_assign(lhs, rhs);
rhs.reduce_once_assign(self.q);
}
/// Returns lhs * (2^64)^-1 mod q in range [0, 2q-1].
#[inline(always)]
pub fn unprepare_lazy(&self, lhs: Montgomery<u64>) -> u64{
let mut rhs = 0u64;
self.unprepare_lazy_assign(lhs, &mut rhs);
rhs
}
/// Assigns lhs * (2^64)^-1 mod q in range [0, 2q-1] to rhs.
#[inline(always)]
pub fn unprepare_lazy_assign(&self, lhs: Montgomery<u64>, rhs: &mut u64){
let (_, r) = self.q.widening_mul(lhs.value().wrapping_mul(self.q_inv));
*rhs = self.q - r
}
/// Returns lhs * rhs * (2^{64})^-1 mod q.
#[inline(always)]
pub fn mul_external(&self, lhs: Montgomery<u64>, rhs: u64) -> u64{
let mut r = self.mul_external_lazy(lhs, rhs);
r.reduce_once_assign(self.q);
r
}
/// Assigns lhs * rhs * (2^{64})^-1 mod q to rhs.
#[inline(always)]
pub fn mul_external_assign(&self, lhs: Montgomery<u64>, rhs: &mut u64){
self.mul_external_lazy_assign(lhs, rhs);
rhs.reduce_once_assign(self.q);
}
/// Returns lhs * rhs * (2^{64})^-1 mod q in range [0, 2q-1].
#[inline(always)]
pub fn mul_external_lazy(&self, lhs: Montgomery<u64>, rhs: u64) -> u64{
let mut result: u64 = rhs;
self.mul_external_lazy_assign(lhs, &mut result);
result
}
/// Assigns lhs * rhs * (2^{64})^-1 mod q in range [0, 2q-1] to rhs.
#[inline(always)]
pub fn mul_external_lazy_assign(&self, lhs: Montgomery<u64>, rhs: &mut u64){
let (mlo, mhi) = lhs.value().widening_mul(*rhs);
let (_, hhi) = self.q.widening_mul(mlo.wrapping_mul(self.q_inv));
*rhs = mhi.wrapping_add(self.q - hhi)
}
/// Returns lhs * rhs * (2^{64})^-1 mod q in range [0, 2q-1].
#[inline(always)]
pub fn mul_internal(&self, lhs: Montgomery<u64>, rhs: Montgomery<u64>) -> Montgomery<u64>{
Montgomery(self.mul_external(lhs, *rhs.value()))
}
/// Assigns lhs * rhs * (2^{64})^-1 mod q to rhs.
#[inline(always)]
pub fn mul_internal_assign(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
self.mul_external_assign(lhs, rhs.value_mut());
}
/// Returns lhs * rhs * (2^{64})^-1 mod q in range [0, 2q-1].
#[inline(always)]
pub fn mul_internal_lazy(&self, lhs: Montgomery<u64>, rhs: Montgomery<u64>) -> Montgomery<u64>{
Montgomery(self.mul_external_lazy(lhs, *rhs.value()))
}
/// Assigns lhs * rhs * (2^{64})^-1 mod q in range [0, 2q-1] to rhs.
#[inline(always)]
pub fn mul_internal_lazy_assign(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
self.mul_external_lazy_assign(lhs, rhs.value_mut());
}
#[inline(always)]
pub fn add_internal(&self, lhs: Montgomery<u64>, rhs: Montgomery<u64>) -> Montgomery<u64>{
Montgomery(self.barrett.reduce(rhs.value() + lhs.value()))
}
/// Assigns lhs + rhs to rhs.
#[inline(always)]
pub fn add_internal_lazy_assign(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
*rhs.value_mut() += lhs.value()
}
/// Assigns lhs + rhs - q if (lhs + rhs) >= q to rhs.
#[inline(always)]
pub fn add_internal_reduce_once_assign(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
self.add_internal_lazy_assign(lhs, rhs);
rhs.value_mut().reduce_once_assign(self.q);
}
#[inline(always)]
pub fn reduce(&self, lhs: u64) -> u64{
self.barrett.reduce(lhs)
}
/// Returns lhs mod q in range [0, 2q-1].
#[inline(always)]
pub fn reduce_lazy(&self, lhs: u64) -> u64{
self.barrett.reduce_lazy(lhs)
}
#[inline(always)]
pub fn reduce_assign(&self, lhs: &mut u64){
self.barrett.reduce_assign(lhs)
}
/// Returns lhs mod q in range [0, 2q-1].
#[inline(always)]
pub fn reduce_lazy_assign(&self, lhs: &mut u64){
self.barrett.reduce_lazy_assign(lhs)
}
/// Returns (x^exponent) * 2^64 mod q.
#[inline(always)]
pub fn pow(&self, x: Montgomery<u64>, exponent:u64) -> Montgomery<u64>{
let mut y: Montgomery<u64> = self.one();
let mut x_mut: Montgomery<u64> = x;
let mut i: u64 = exponent;
while i > 0{
if i & 1 == 1{
self.mul_internal_assign(x_mut, &mut y);
}
self.mul_internal_assign(x_mut, &mut x_mut);
i >>= 1;
}
y.value_mut().reduce_once_assign(self.q);
y
}
}
/// Returns x^exponent mod q.
/// This function internally instantiate a new MontgomeryPrecomp<u64>
/// To be used when called only a few times and if there
/// is no Prime instantiated with q.
fn pow(x:u64, exponent:u64, q:u64) -> u64{
let montgomery: MontgomeryPrecomp<u64> = MontgomeryPrecomp::<u64>::new(q);
let mut y_mont: Montgomery<u64> = montgomery.one();
let mut x_mont: Montgomery<u64> = montgomery.prepare(x);
while exponent > 0{
if exponent & 1 == 1{
montgomery.mul_internal_assign(x_mont, &mut y_mont);
}
montgomery.mul_internal_assign(x_mont, &mut x_mont);
}
montgomery.unprepare(y_mont)
}
#[cfg(test)]
mod tests {
use crate::modulus::montgomery;
use super::*;
use test::Bencher;
#[test]
fn test_mul_external() {
let q: u64 = 0x1fffffffffe00001;
let m_precomp = montgomery::MontgomeryPrecomp::new(q);
let x: u64 = 0x5f876e514845cc8b;
let y: u64 = 0xad726f98f24a761a;
let y_mont = m_precomp.prepare(y);
assert!(m_precomp.mul_external(y_mont, x) == (x as u128 * y as u128 % q as u128) as u64);
}
#[bench]
fn bench_mul_external(b: &mut Bencher){
let q: u64 = 0x1fffffffffe00001;
let m_precomp = montgomery::MontgomeryPrecomp::new(q);
let mut x: u64 = 0x5f876e514845cc8b;
let y: u64 = 0xad726f98f24a761a;
let y_mont = m_precomp.prepare(y);
b.iter(|| m_precomp.mul_external_assign(y_mont, &mut x));
}
}