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How to solve a Playfair encryption
Using a computer, there are two ways to attack a Playfair cipher:
- Dictionary attack: It is possible to break a Playfair cipher by guessing the keyword. The word SURPRISE is contained in virtually every English dictionary, so a computer that tests one keyword candidate after the other will sooner or later find it.
- Hill climbing: Hill climbing is the current super-algorithm of historical codebreaking. As George Lasry pointed out, hill climbing (enhanced with simmulated annealing) can break a Playfair cipher of more than 80 letters.
There are several books that explain how a Playfair can be solved without computer support – for instance Helen Fouché Gaines’ Cryptanalysis and André Langie’s Cryptography. The concept is to guess a few words in the cleartext and to derive the 5×5 matrix based on the peculiarities of the Playfair cipher (for instance, if AB->XY then BA->YX). However, breaking a Playfair cryptogram manually is pretty difficult, especially if the ciphertext is short (the examples described in these books refer to messages of several hundred letters). In addition, these books assume that a few words of the cleartext are known. Nevertheless, none of these books describes the complete Playfair codebreaking procedure – instead, most of the trial-and-error reckoning necessary is simply omitted.
A Playfair challenge
Here is a Playfair-encrypted text I created:
Can a reader break this challenge? Here are the details:
- The cleartext has exactly 50 letters (spaces not included). It is written in English.
- I used the software CrypTool 2 for encryption. As far as I know, CrypTool implements the Playfair cipher exactly the way it is explained above.
- The keyword is a random transposition of the alphabet. So, a dictionary attack won’t work.
As mentioned, this challenge might be a pretty hard one, as the ciphertext is so short. Can a reader solve it anyway?
Further reading: A mird in the hand is worth two in the mush: Solving ciphers with Hill Climbing