Wednesday, January 22, 2014

Caesar Cipher

A Caesar cipher is a very simple encryption technique where each letter is shifted a fixed number of characters in the alphabet. It is named after Julius Caesar, who apparently used this technique in some of his letters.

For example, if we were to encode "FACTOR" by shifting each character to the right by three letters, we would get "IDFWRU". The "F" shifts to "I", the "A" shifts to "D", the "C" shifts to "F", etc.

Let's implement this in Factor!

First, we implement a word to shift a character (uppercase by convention) a specified number of letters. Using "A" as our "zero" point by subtracting, shifting modulo 26 character ascii alphabet, then re-adding the ascii value for "A" (65):

: caesar-shift ( ch n -- ch' )
    [ CHAR: A - ] dip + 26 rem CHAR: A + ;

Next, a word for shifting every letter in a string (preserving numbers and punctuation):

: caesar-map ( str n -- str' )
    '[ dup CHAR: A CHAR: Z between? [ _ caesar-shift ] when ] map ;

This lets us implement the encrypt and decrypt words. Encrypting is simple and decrypting is mapping with a negative shift number:

: caesar-encrypt ( plain n -- encrypted ) caesar-map ;

: caesar-decrypt ( encrypted n -- plain ) neg caesar-map ;

Trying it out:

IN: scratchpad "HELLO, WORLD!" 3 caesar-encrypt .

IN: scratchpad "KHOOR, ZRUOG!" 3 caesar-decrypt .