An Investigation into the Security of Machine Ciphers

Abstract

The history of classical ciphers is well documented with a lot of material available on their cryptanalysis. The modern ciphers are also being well researched. Due to the evolution of machine ciphers in a sensitive era involving the First and the Second World War, they are fairly less explored. Although publications are available on their analysis by experts, however, a lot of them are still kept confidential in the NSA archives. This thesis presents an insight of the two types of cipher machines, covering their operation and cryptanalysis under black-box conditions. Rotor is a scrambling device which gives rise to different permutations when rotated. A combination of rotors with varying rate of rotation owes to the security of rotor machines. The permutations produced by a rotor follow a pattern that is unique for a single rotor. This research presents an approach to mathematically link these patterns to recover the wiring of an unknown rotor. Given a stack of rotors with each rotor giving rise to a unique but related permutation, theory of permutations can be applied in a similar way to recover the unknown wiring. A one and a half rotor machine is designed as it presents the simplest model for a reciprocal rotor machine. A detailed account of the application of this technique to a one and a half rotor machine is given using only ciphertext. This approach is extended to a two and a half rotor machine. Finally, the method is applied to cryptanalyze the famous Enigma machine. Unlike the rotor machines, where the input is substituted by another alphabet based on its position in the plaintext, in pinwheel cipher the input is relatively shifted by an amount determined by the displacement count of lug cage at that position. The underlying plaintext exhibits certain properties as far as the frequency distribution of alphabets is concerned. The number of shift values vary depending on the complexity of the pinwheel cipher. The statistical properties of the underlying plaintext are utilized to divide the ciphertext into smaller number of groups in order to recover the pinwheels. As with the case of rotor machines, a small variant of the pinwheel cipher is first investigated. The approach is extended to a variant of M-209 cipher machine which has 6 wheels having lengths that are relatively prime. The techniques employed are compared with already known techniques and further areas of research are also highlighted.