Crypto.Number.F2m

This module provides basic arithmetic operations over F₂m. Performance is not optimal and it doesn't provide protection against timing attacks. The m parameter is implicitly derived from the irreducible polynomial where applicable.

Documentation

addF2m :: Integer -> Integer -> Integer

Addition over F₂m. This is just a synonym of xor.

mulF2m

Arguments

:: BinaryPolynomial

Irreducible binary polynomial

-> Integer

-> Integer

-> Integer

Multiplication over F₂m.

n1 * n2 (in F(2^m))

squareF2m

Arguments

:: BinaryPolynomial

Irreducible binary polynomial

-> Integer

-> Integer

Squaring over F₂m. TODO: This is still slower than mulF2m.

modF2m

Arguments

:: Integer

Irreducible binary polynomial

-> Integer

-> Integer

Binary polynomial reduction modulo using long division algorithm.

invF2m

Arguments

:: BinaryPolynomial

Irreducible binary polynomial

-> Integer

-> Maybe Integer

Inversion of @n over F₂m using extended Euclidean algorithm.

If @n doesn't have an inverse, Nothing is returned.

divF2m

Arguments

:: BinaryPolynomial

Irreducible binary polynomial

-> Integer

Dividend

-> Integer

Quotient

-> Maybe Integer

Division over F₂m. If the dividend doesn't have an inverse it returns Nothing.

Compute n1 / n2