Studieren Sie das Aufgaben-Papier zum RSA-Kryptosystem und lösen Sie die dort enthaltenen Aufgaben.
> module RSA where
> import Data.Char
> import Data.List
> import Data.Maybe
> import Math.NumberTheory.Primes
> import System.Random
> decryptExample msg = 0
> type Key = (Integer,Integer)
> type KeyPair = (Key,Key)
> publicPrivateFor :: Integer -> Integer -> Integer -> Maybe KeyPair
> publicPrivateFor e p q = do
> s <- multiplicativInverse e ((p-1)*(q-1))
> return (let n = p*q in ((e,n),(s ,n)))
> publicPrivate = publicPrivateFor e
> e = (2^17+1)
> gcdExt :: Integer -> Integer -> (Integer,Integer,Integer)
> gcdExt a b = (1, 1, 1)
> multiplicativInverse a b = mkPos$gcdExt a b
> where
> mkPos (1,x,_)
> | x < 0 = Just (x + b)
> | otherwise = Just x
> mkPos (_,_,_) = Nothing
> p = 0x19fbd41d69aa3d86009a967db3379c63cd501f24f7
> q = 0x1b6f141f98eeb619bc0360220160a5f75ea07cdf1d
> pow x y z = x^y `mod` z
> encrypt (public ,n) msg = pow msg public n
> decrypt = encrypt
> primes = sieb [2..]
> where
> sieb (x:xs) = x:sieb [y|y<-xs,y `mod` x /= 0]
> genPrime :: Int -> IO Integer
> genPrime bits = do
> x <- randomRIO (2^(bits - 1), 2^bits - 1)
> if isPrime x then return x else genPrime bits
> genPrimes :: Int -> IO (Integer, Integer)
> genPrimes bits = do
> p1 <- genPrime bits
> genPrim2 p1
> where
> genPrim2 p1 = do
> p2 <- genPrime bits
> if p1 /= p2 then return (p1, p2) else genPrim2 p1
> genKey = do
> (p1,p2) <- genPrimes 1024
> let ks = publicPrivate p1 p2
> if isNothing ks then genKey else return (fromJust ks)
> testRSA1 = do
> (pub,priv) <- genKey
> let enc = encrypt pub
> 123456789009876543211111222233334444555566667777888899990000
> print (decrypt priv enc)
> unicodesize = 2^16
> stringToInteger :: String -> Integer
> stringToInteger xs = 1
> integerToString :: Integer -> String
> integerToString n = ""
> verschlüssel key = (encrypt key).stringToInteger
> entschlüssel key = integerToString.(decrypt key)
> test = do
> (pub,priv) <- genKey
> let enc = verschlüssel pub "hallo welt jetzt mal ein richtig langer text das wird doch wohl gut gehen"
> print (entschlüssel priv enc)
> splitString n str = []
> encryptFile key inFile outFile = do
> content <- readFile inFile
> writeFile outFile $ show $map (verschlüssel key) $ splitString 100 content
> decryptFile key inFile outFile = do
> content <- readFile inFile
> writeFile outFile $ concat $map (entschlüssel key) (read content)
Subato
