encrypt :: Integer -> Integer -> String -> String
encrypt 0 0 msg =
  let primes      = take 90 $ filter isPrime [1..]
      p1          = last primes
      p2          = last $ init primes
      tot         = totient p1 p2
      e           =  myE tot
      n           = p1  * p2
      rsa_encoded =  rsa_encode n e $ encode msg
      encrypted   = show rsa_encoded
      d           =  myD e n tot
      decrypted   = decode $ rsa_decode d n rsa_encoded
  in "enc: "       ++ encrypted
      ++ "; dec: " ++ decrypted
      ++ "; p1: "  ++ show p1
      ++ "; p2: "  ++ show p2
      ++ "; tot: " ++ show tot
      ++ "; e: "   ++ show e
      ++ "; n: "   ++ show n
      ++ "; d: "   ++ show d
encrypt e n msg =
  let rsa_encoded = rsa_encode n e $ encode msg
      encrypted   = concatMap show rsa_encoded
  in "enc:" ++ encrypted

decrypt :: Integer -> Integer -> String -> String
decrypt d n msg =
  let decrypted = decode $ rsa_decode d n (read msg)
  in "dec: " ++ decrypted


encode :: String -> [Integer]
encode s = map (toInteger . fromEnum) s

rsa_encode :: Integer -> Integer -> [Integer] -> [Integer]
rsa_encode n e numbers = map (\num -> (num ^ e) `mod` n) numbers

rsa_decode :: Integer -> Integer -> [Integer] -> [Integer]
rsa_decode d n ciphers = map (\c -> (c ^ d) `mod` n) ciphers

decode :: [Integer] -> String
decode encoded = map (chr . fromInteger) encoded

divisors :: Integer -> [Integer]
divisors n = [m | m <- [1..n] , n `mod` m == 0 ]

isPrime :: Integer -> Bool
isPrime n = divisors n == [1,n]

totient :: Integer -> Integer -> Integer
totient prime1 prime2 = (prime1 - 1) * (prime2 - 1)

myE :: Integer -> Integer
myE tot = head [ n | n <- [2..tot - 1] , gcd n tot == 1 ]

myD :: Integer -> Integer -> Integer  -> Integer
myD e n phi = head [ d | d <- [1..n] , (d * e) `mod` phi == 1 ]