Those fun folks at Numberphile have produced a great video showing how the Allies, led by Alan Turing, broke Germany's Enigma code in World War II. Cambridge mathematician James Grime explains that cryptologists exploited the code's fatal flaw- that a letter could not be coded as itself- to devise a method for deciphering German messages in under 20 minutes.
One of the real pleasures of the video is seeing how an actual Enigma machine worked. Today's codes are written on algorithms buried in computers. By contrast, the Enigma machine's wires, rotors, and light bulbs are satisfyingly mechanical, like a really, really good decoder ring.
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