Programming Praxis – Steganography

In today’s Programming Praxis exercise, our goal is to implement a cipher that hides messages in spam emails. Let’s gets started, shall we?

Some imports:

import Control.Applicative
import Data.Bits
import Data.Char
import Data.List
import Data.List.Split (chunk)
import System.Random (randomRIO)

First we define the allowed characters (without numbers since they are treated a differently from the rest).

chars :: String
chars = ['A'..'Z'] ++ ['a'..'z'] ++ ". "

Neither the key nor the message can contain any other characters, so we make a function to remove all other characters.

sanitize :: String -> String
sanitize = flip intersect $ chars ++ ['0'..'9']

Making a key consists of removing duplicate characters, appending the rest and inserting the remaining numbers in their correct places.

makeKey :: String -> String
makeKey phrase = addDigits $ union (nub $ sanitize phrase) chars where
    addDigits = (=<<) (\c -> maybe [c] ((c:) . return) . lookup c $
                             filter (flip notElem phrase . snd) $
                             zip ('j':['a'..'i']) ['0'..'9'])

Next, we need a function to encode/decode the pairs of letters.

cipher :: (Int -> Int -> Int) -> String -> [String] -> String
cipher op key = (f =<<) where
    f ~[a,b] | c1 == c2  = [get (op r1 1) c1, get (op r2 1) c2]
             | r1 == r2  = [get r1 (op c1 1), get r2 (op c2 1)]
             | otherwise = [get r1 c2       , get r2 c1      ]
        where (r1,c1) = maybe (0,0) (`divMod` 8) $ elemIndex a key
              (r2,c2) = maybe (0,0) (`divMod` 8) $ elemIndex b key
              get r c = key !! (8 * mod r 8 + mod c 8)

The words are loaded from the given dictionary and divided into two lists based on whether their length is even or odd. For every bit of information a random word is selected from the appropriate list.

getWords :: FilePath -> [Bool] -> IO String
getWords dict bs = do
    (evens, odds) <- partition (even . length) . filter (\w -> all isAlpha w &&
                         length w < 9) . lines <$> readFile dict
    let pick xs = fmap (xs !!) $ randomRIO (0, length xs - 1)
    fmap unwords $ mapM (\b -> pick $ if b then odds else evens) bs

Hiding a message is a matter of doing all the required steps in the right order. Unlike the provided solution I used a 7-bit encoding since it saves me from having to make another lookup table.

hide :: FilePath -> String -> String -> IO String
hide dict key = getWords dict . (>>= \c -> map (testBit $ fromEnum c) [0..6]) .
                cipher (+) key . split . sanitize where
                    split [] = []
                    split (a:b:cs) | a /= b = [a,b  ] : split cs
                    split (a:cs) = [a,'X'] : split cs

To retrieve the original message we simply undo all the steps.

unhide :: String -> String -> String
unhide key = cipher (-) key . chunk 2 . map (toEnum .
                 foldr (flip setBit . fst) 0 . filter snd . zip [0..]) .
             chunk 7 . map (odd . length) . words

Some tests to see if everything is working properly:

main :: IO ()
main = do let key = makeKey "President Obama’s visit to a Chrysler plant in Tol\
                    \edo, Ohio, on Friday was the culmination of a campaign to \
                    \portray the auto bailouts as a brilliant success with no u\
                    \npleasant side effects."
          hidden <- hide "74550com.mon" key "Bonsai Code"
          putStrLn hidden
          print $ unhide key hidden == "Bonsai CodeX"

          let key2 = makeKey "a4b3c2"
          let msg2 = "abcd1234"
          print . (== msg2) . unhide key2 =<< hide "74550com.mon" key2 msg2

Yup. Make sure the recipient knows when you’re sending the message though, since it will undoubtedly get caught by the spam filter.

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