Struct ModularArithmetic 

pub struct ModularArithmetic {
    pub modulus: u64,
}

Modular arithmetic helpers with support for common field operations.

WARNING

Educational implementation only.

Fields

modulus: u64

The modulus

Implementations

impl ModularArithmetic

pub fn new(modulus: u64) -> Self

Create a new modular arithmetic context with the given modulus.

pub fn add(&self, a: u64, b: u64) -> u64

Add two values mod p.

pub fn sub(&self, a: u64, b: u64) -> u64

Subtract two values mod p.

pub fn mul(&self, a: u64, b: u64) -> u64

Multiply two values mod p.

pub fn pow(&self, a: u64, e: u64) -> u64

Fast exponentiation a^e mod p using repeated squaring.

pub fn inv(&self, a: u64) -> Option<u64>

Modular inverse a^{-1} mod p (requires gcd(a, p) = 1).

pub fn legendre(&self, a: u64) -> i64

Legendre symbol (a | p): 1 if a is a quadratic residue mod prime p, -1 if not, 0 if p | a. Uses Euler’s criterion: a^{(p-1)/2} mod p.

WARNING

Assumes modulus is an odd prime; undefined otherwise.