Statistical Techniques for Language Recognition: an Introduction and Guide for Cryptanalysts

We explain how to apply statistical techniques to solve several language-recognition problems that arise in cryptanalysis and other domains. Language recognition is important in cryptanal-ysis because, among other applications, an exhaustive key search of any cryptosystem from ciphertext alone requires a test that recognizes valid plaintext. Written for cryptanalysts, this guide should also be helpful to others as an introduction to statistical inference on Markov chains. Modeling language as a nite stationary Markov process, we adapt a statistical model of pattern recognition to language recognition. Within this framework we consider four well-deened language-recognition problems: 1) recognizing a known language, 2) distinguishing a known language from uniform noise, 3) distinguishing unknown 0th-order noise from unknown 1st-order language, and 4) detecting non-uniform unknown language. For the second problem we give a most powerful test based on the Neyman-Pearson Lemma. For the other problems, which typically have no uniformly most powerful tests, we give likelihood ratio tests. We also discuss the chi-squared test statistic X 2 and the Index of Coincidence IC. In addition, we point out useful works in the statistics and pattern-matching literature for further reading about these fundamental problems and test statistics.