Trait modulo_n_tools::montgomery::MontgomeryOperation

pub trait MontgomeryOperation<T, U> {
    fn calc_n_prime(n: &T, s: u32) -> T;
    fn new(n: T) -> Self;
    fn reduction(&self, x: U) -> T;
    fn convert(&self, x: T) -> T;

    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>,
    { ... }
}

Montgomery modular multiplication

use modulo_n_tools::montgomery::{MontgomeryOperation, Montgomery64};
let m = Montgomery64::new(97);
let a = m.powmod(2, 77);
assert_eq!(a, 65);

Required methods

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

$NN' \equiv -1 \pmod R$

fn new(n: T) -> Self

Constructor for ${}\bmod N$

fn reduction(&self, x: U) -> T

Montgomery Reduction

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

$x \mapsto xR \bmod N$

Provided methods

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 $a^p \bmod N$

Implementors

impl MontgomeryOperation<u32, u64> for Montgomery32

impl MontgomeryOperation<u64, u128> for Montgomery64

impl<T> MontgomeryOperation<T, T> for Montgomery<T> where
    T: Clone + Ord + for<'x> BitAndAssign<&'x T> + for<'x> AddAssign<&'x T> + for<'x> SubAssign<&'x T> + for<'x> MulAssign<&'x T> + for<'x> BitAnd<&'x T, Output = T> + for<'x> Sub<&'x T, Output = T> + for<'x> Rem<&'x T, Output = T> + Neg<Output = T> + Shl<u32, Output = T> + ShrAssign<u32> + ShlAssign<u32> + From<u8>,