At Bletchley Park in 1940, Alan Turing and his colleagues faced a cipher with roughly 15 quintillion possible settings. This episode explains how the Enigma machine worked, from its rotors and reflector to the plugboard that added 150 trillion combinations, and why the German military believed the sheer math made it unbreakable. It then traces how a single structural flaw, the fact that Enigma could never encipher a letter as itself, opened the door to the Bombe.

Building on Marian Rejewski's Polish Bomba, Turing designed a machine that mechanized proof by contradiction, testing hypotheses with electrical current and rejecting impossible settings until it hit a stop. Gordon Welchman's diagonal board made it far more efficient, the fourth-rotor Shark network blinded the Allies in 1942, and Joseph Desch's team at NCR in Dayton built American  ...