Enigma

The Enigma was a portable cipher machine, roughly the size of a typewriter, that could encrypt and decrypt secret messages. It used electro-mechanical rotors to convert a message to a secret code, and then another machine could decode that same message and print out the original message. This machine was commercially available beginning in the early 1920s. The Nazi German military version generated codes widely thought to be unbreakable.

Nazi Germany used the Enigma during World War II to send messages about its military maneuvers. A 27-year-old Polish mathematician (cryptologist) named Marian Rejewski used advanced mathematics (permutation theory with some group theory) to break ("crack") the Enigma codes. He then helped design working "doubles" of the Enigmas that could find the keys necessary for decryption. By 1938 the Poles were decrypting most of the German messages, and the Poles shared their marvelous discovery with Great Britain and France.

The breakthrough enabled the Allies to anticipate German military maneuvers, although sometimes the Allies would allow an attack to occur successfully in order to avoid signalling to the Germans that their code had been broken. The Allied code-breaking effort was known as "Ultra", as in "ultra-secret".

At the end of the war, Allied General Dwight Eisenhower said that Ultra was "decisive" to the Allied victory over Germany. British Prime Minister Winston Churchill also declared, "It was thanks to Ultra that we won the war." The breaking of the German codes prevented it from completely blockading Britain with U-boats and enabled the Allied forces to make key strategic decisions throughout the war.