For these classical cryptosystems, we need to establish a few conventions before we get down the the real work.

Numerical Representation

We will establish the following mapping from characters to integers:

$$ \begin{array}{c c c c} a & b & c & d & \cdots & z \\ \downarrow & \downarrow & \downarrow & \downarrow & \cdots & \downarrow \\ 0 & 1 & 2 & 3 & \cdots & 25 \\ \end{array} $$

To follow this convention I will use the following functions:

-- file : CryptoTools.hs

import Data.Char (toUpper)

charToIdx:: Char -> Int
charToIdx = subtract 65 . fromEnum . toUpper

idxToChar :: Int -> Char
idxToChar = toEnum . (+ 65)

The functions toEnum and fromEnum will convert between characters and ascii values. I chose to convert to uppercase quite arbitrarily, and we could have just as well used toLower along with 97 (ascii ‘a’) rather than 65 (ascii ‘A’) to zero our indexing.

Plaintext vs. Ciphertext

We will make the convention that plaintext (in our case, strings in plain english), will be represented as all lowercase characters. It follows then that we make ciphertext (text that has been encrypted) all capitol letters.

ghci> encrypt "plaintext"
"CIPHERTEXT"

Cleaning Input

It is common practice for plaintext to be stripped of spaces, punctuation, numbers, etc. This is done partly for historical reasons, and partly for simplicity. When attempting to hand-crack a cipher, it is much more difficult to crack ciphertext with no spaces, as you cannot use word and sentence structure to your advantage.

So we will use a function for cleaning plaintext before encryption:

-- file : CryptoTools.hs

import Data.Char (isAlpha)

clean :: String -> String
clean = filter isAlpha