Using a keyword

A more complex approach would be to choose a word, and somehow combine each letter of this word with successive letters of the message. A trivial example of this that is used in the computing world is to convert the message and the word (or key) into a binary representation and then use XOR (exclusive OR) to combine the two streams of bits. To allow for the fact that the key is (presumably) shorter than the message we repeat it over and over again to provide enough bits to enocde the message.

However, there are still at least two ways we can attempt to crack this sort of message.

• If them message is many times longer than the key then we can use the same method as for the simple letter substitution code - since if we know that the key has length $n$ then then letters in the message at positions $n$, $2n$, $3n\cdots$ will all get encrypted with the same letter from the codeword. Since the each letter in the coded message is the result of a 1-1 function between the corresponding letter in the plaintext (unencrypted) form of the message and the corresponding letter from the codeword it is easy to see that this is no better than a letter subsitution code.

• We can use a knowledge of what the message is likely to contain to obtain the key. We can then use the key to decrypt the rest of the message. For example, if we were decoding something we suspected to be a letter it would be reasonable to assume that it contained `Dear, ' somewhere near the beginning. Since the encoding function for each letter was 1-1 it has an inverse - and we can use this to calculate the key given part of the origional message. Of course by making the function more obscure (less easy to guess) we make the inverse harder to find, but this is obfuscation not encryption. If the algorithm is used by many people this wouldn't work anyway .. since they would all have a knowledge of the function. Even if the function was hidden in software we could reverse engineer the software to reveal the function.