Archive for May 1st, 2010

On the Beale Cipher, Part III

May 1st, 2010 No comments

In this post I'm including a compressed archive of some results I have obtained by following through on my previous post:  I used the Declaration of Independence transition probability matrix I calculated based on a text I found online, and also used the standard frequencies of letters or of first words of the English language in this "augmented frequency analysis," as prior beliefs.  One of the crucial things to notice is that, regardless of prior beliefs, our posterior belief significantly changes once we take into account the proportions of transitions in the actual purported key (the Declaration of Independence), which may be why some cryptographers, by following a simple statistical argument, may think the cipher is written in a language other than English.

The whole idea is that, with the information as provided in this .xls file, one can begin making educated guesses as to particular cipher numbers (as an example, "I think 5 is an 'e'" [not that I do, by the way]), which implies modifying the probability distribution, and propagating such beliefs through the whole cipher, furthermore uncovering particular patterns, and going again.  You need not be absolutely certain of your educated guess: you can surmise two or three letters fit a particular cipher number, and propagate such belief to see where it takes you.  As I have said, processing time is currently 20 minutes per run (propagating throughout the whole cipher) until I (or someone else) enhances on my coding and develops a more efficient method.

Let me know your discoveries (as will I)!  It think working a little bit on this may be fun and interesting and may uncover interesting mathematical relationships.