An Exact A * Method for Solving Letter Substitution

An Exact A* Method for Solving Letter Substitution Ciphers Eric Corlett Master of Science Graduate Department of Computer Science University of Toronto 2011 Letter-substitution ciphers encode a document from a known or hypothesized language into an unknown writing system or an unknown encoding of a known writing system. The process of solving these ciphers is a problem that can occur in a number of practical applications, such as in the problem of determining the encodings of electronic documents in which the language is known, but the encoding standard is not. It has also been used in OCR applications. In this paper, we introduce a novel method for deciphering letter-substitution ciphers. We do this by formulating a variant of the Viterbi algorithm for use as an A* heuristic over partial solutions of a given cipher. This heuristic can then be used as a guide in an A* search for the correct solution. We give an overview of the classical Viterbi and A* search algorithms, go on to describe of our proposed algorithm, and prove its correctness. We then test our algorithm on a selection of ciphers formed from Wikipedia articles, and show that our algorithm has the potential to be a viable, practical method for efficiently solving decipherment problems. We also find, however, that it does have a number of shortcomings, most notably a high variation in running time between similar ciphers. In response to this, we describe potential sources of information to offset this variability and use this information to improve our original algorithm. We test this improved algorithm on both the original ciphers and a selection of newly collected ciphers and find an average improvement in time and an across-the-board im-