Struct Montgomery64 

pub struct Montgomery64 { /* private fields */ }

Montgomery $R=2^{64}$

use modulo_n_tools::montgomery::{MontgomeryOperation, Montgomery64};
let m = Montgomery64::new(57);
let a = m.powmod(5, 42);
assert_eq!(a, 7);

Trait Implementations

impl MontgomeryOperation<u64, u128> for Montgomery64

fn calc_n_prime(n: &u64, s: u32) -> u64

$NN' \equiv -1 \pmod R$

fn new(n: u64) -> Self

Constructor for ${}\bmod N$

fn reduction(&self, x: u128) -> u64

Montgomery Reduction

fn convert(&self, x: u64) -> u64

$x \mapsto xR \bmod N$

fn powmod<V>(&self, a: T, p: V) -> T

where T: From<u8>, U: Clone + for<'x> Mul<&'x U, Output = U> + From<T>, V: Clone + Ord + ShrAssign<u32> + From<u8> + for<'x> BitAnd<&'x V, Output = V>,

calcutate $a^p \bmod N$