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The Enigma machine cipher was famously broken at Bletchley Park, but for many years GCHQ did not want anyone to know how it was actually done. Beginning with the Enigma machine itself, and its illusory security features, this presentation travels across the different attacks on Enigma from the earliest pre-war attempts to the later sophisticated machine decryption methods. These attacks drew on group theory and the post-Hilbert ideas of incomplete logical systems as well as more traditional cryptanalytical approaches based on language structure. Once the theory was established, creating a fast, workable system for finding Enigma keys required an engineering solution, using binary logic to eliminate wrong settings ?€¡° a radically new approach leading to the ascendancy of digital computing. Dermot Turing is the acclaimed author of??Prof, a biography of his famous uncle,??The Story of Computing, and most recently X, Y and Z ?€¡° the real story of how Enigma was broken.