Three rotors (four after 1941 in the German navy). The first attempts to use genetic algorithms for this task required unrealistic long pieces of ciphertext, but it is shown that the technique can also succeed for much shorter messages. In Section 3, the different settings of the Enigma are analyzed, and the vulnerability in the plugboard is outlined. The section finishes with a brief review of related research. The box plot variant, notch plot, is also described and defined. The measure, Index of Coincidence, is defined and explained. Then, the Genetic Algorithm is described. Section 2 provides background information on the construction and operation principles of Enigma. The remaining paper is organized as follows. We also build upon the existing measure Index of Coincidence, creating a more human-readable representation of the measure which we call Progress Index of Coincidence. The proposed GA attack is faster than earlier ciphertext-only attacks. This paper aims to provide one such building block in the form of a ciphertext-only attack based on genetic algorithms (GA). If not by themselves, they may provide useful building blocks for future crypto-attacks. For this reason, decryption techniques that prove effective on Enigma encryption may also prove effective on other encryption techniques as well. It is to be anticipated that new analysis for breaking the Enigma could apply to other ciphers that build their security on the same principles. ![]() One recent example is the paper by Ostwald and Weierud (Ostwald and Weierud Citation2017), who, in 2017, released “Modern breaking of Enigma ciphertexts” in Cryptologia. The purpose of such research is twofold, to develop modern cryptanalysis or to attack unread authentic traffic from WWII. However, even if the Enigma represents an outdated crypto technology, it still inspires researchers to fill gaps in the Enigma history and to improve on Enigma cryptanalysis. Significant members of this activity included the classical scholar Dennis Knox, mathematicians from Oxford and Cambridge like Peter Twinn, Alan Turing, and Gordon Welchman, as well as the international chess masters Hugh Alexander and Stuart Milner-Barry. ![]() ![]() Footnote 1 Building on the pre-WWII analysis of Polish mathematicians, a huge effort by English and American scientists developed cryptanalytical tools and methods that could break German Enigma traffic daily (Singh Citation2000). The Enigma represents a special form of a polyalphabetic substitution cipher and cannot, by any means, be considered to provide secure encryption by modern standards. The machine has even had books and movies centered around it and its cryptanalysis, with perhaps the most recent release of “The Imitation Game” on the 25th of December 2014 (IMDb Citation2014). Its fame is also reflected in modern textbooks, for example, in Paar- and Pelzl’s “Understanding Cryptography,” where the Enigma is used to illustrate a classical encryption machine (Paar and Pelzl Citation2009). Its importance in the war and cryptanalysis made the Enigma perhaps the most famous cryptographic machine in history. Enigma’s strength, mobility, and user-friendliness allowed its widespread use by the German military during the Second World War. The machine combines the rotor system, invented by two Dutch navy officers in 1915 (de Leeuw Citation2003), with a plugboard resulting in a cipher so advanced that it was thought to be unbreakable (Copeland Citation2004). The Enigma Machine represents a milestone in the history of cryptography.
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