License	BSD-style
Maintainer	Danny Navarro <j@dannynavarro.net>
Stability	experimental
Portability	Good
Safe Haskell	None
Language	Haskell2010

Crypto.Number.F2m

Description

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.

Synopsis

Documentation

type BinaryPolynomial = Integer Source

Binary Polynomial represented by an integer

addF2m :: Integer -> Integer -> Integer Source

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

mulF2m Source

Arguments

:: BinaryPolynomial	Irreducible binary polynomial
-> Integer
-> Integer
-> Integer

Multiplication over F₂m.

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

squareF2m Source

Arguments

:: BinaryPolynomial	Irreducible binary polynomial
-> Integer
-> Integer

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

modF2m Source

Arguments

:: BinaryPolynomial	Irreducible binary polynomial
-> Integer
-> Integer

Binary polynomial reduction modulo using long division algorithm.

invF2m Source

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 Source

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