% Copyright (C) 2004 Brian Alliet
\documentclass[11pt]{article}
\usepackage{palatino}
\usepackage{fullpage}
\usepackage{parskip}
\usepackage{lhs}
\usepackage{amsmath}

\begin{document}

\title{RSA}
\author{Brian Alliet}
\maketitle

\ignore{
\begin{code}
module RSA (
    rsaEncrypt,
    rsaGenKey
    ) where

import Random (RandomGen)

import Brianweb.Math.NumberTheory

\end{code}
}

\section{RSA Algorithm}

\begin{code}
rsaEncrypt :: Integer -> Integer -> Integer -> Integer
rsaEncrypt pq e m = powMod pq m e
\end{code}

\begin{code}
rsaGenKey :: RandomGen a => Int -> a -> ((Integer,Integer,Integer,Integer),a)
rsaGenKey bits rg0
    | gcd e phi /= 1 = rsaGenKey bits rg2
    | otherwise = ((p,q,e,d),rg2)
    where
        bitsq = bits `div` 2
        bitsp = bits - bitsq
        (p,rg1) = getPrime bitsp rg0
        (q,rg2) = getPrime bitsq rg1
        phi = (p-1)*(q-1)
        e = 65537
        d = multInvMod phi e
\end{code}

\section{Math Functions}
\input{Brianweb/Math/NumberTheory.lhs}

\input{RSAMain.lhs}

\end{document}