RSA-criptography-hs

The RSA criptography in haskell, made for learning purposes. How to use:

If you already have the public and private keys:

Just call the functions encrypt m (e, n) and decript c (d, n ). d, n = private key; e,n = public key.

If you do not have the keys:

Call the function rsaE m seed, and provide your number m - that you want to encript - and a random seed. To decript do the same thing with rsaD m seed, providing your number and the same seed.

Steps:

• Choose two different prime numbers: The easiest way to do this was with the method ramdomRIO (a,b), but, as this was made for learning purposes, I chose to use randomR instead. The difference is that randomR needs a random number generator g, which is provided by the seed ‘k’.
• Calculate the totient;

  if x /= y then return ((x - 1) * (y -1))

• Choose an integer e that is coprime to the totient. “e” is the public key exponent;

  publicKey :: Integer -> Integer -> Int -> Integer -> IO Integer publicKey m n k e = do

  y <- calculateTotient m n k if (gcd e y) == 1 then return e else publicKey m n k (e + 1)

• Compute d = 1 + k*totient(n).”d” is kept as the private key exponent;
• Just encript or decript:

  encrypt :: Integer -> (Integer, Integer) -> Integer encrypt m (e, n) = ((m^e) `mod` n)

  decript :: Integer -> (Integer, Integer) -> Integer decript c (d, n ) = (c^d `mod` n)