Solving the Olum 2 cipher: a new approach to cryptanalysis of transposition ciphers

Abstract

Olum 2 is one of two ciphers created more than 75 years ago by mathematician Paul Olum to challenge his Manhattan Project officemate, physicist Richard Feynman. In this manuscript, I describe the first successful decryption of Olum 2 using a novel approach to cryptanalysis of transposition ciphers. To decrypt Olum 2, I generated the bigrams and trigrams for all possible transposition intervals. I then identified transposition intervals with multiple bigrams and trigrams that occur frequently in English. I calculated the ratios of their English frequencies to the frequencies of bigrams and trigrams generated by a random reordering of the ciphertext. This enabled me to identify letter sequences with the highest probability of being true cipher message components rather than occurring by chance. In Olum 2, Professor Olum divided the message into sections of thirty-five letters and applied a rotating key to change the order of transposition for each successive section. His strategy not only confounded Professor Feynman but also proved impervious to several decryption programs in use today that assume a uniform transposition has been applied throughout the cipher. The decryption methods described in this manuscript can assist in the decryption of other ciphers employing a variety of transposition methods.