What is the Enigma?

The Enigma was an encryption machine used by the German military during World War II for encoding and decoding secret messages.

It was invented in 1918 and was first used only commercially. When the German military adopted it for its use, it was intensified with a series of rotors, a plugboard, and other enhancements to make it virtually impossible to decipher the code. Through espionage and with the help of a German traitor, the French were able to obtain an actual Enigma machine. They passed the information to the British and the Poles, and all three nations worked on figuring out how to break the Enigma code.

The French and the British cryptanalysts were not able to make any significant progress. In Poland, however, Marian Rejewski and his team were able to capitalize on a shortcoming of the Enigma machine, which was that it would never encode any letter back into itself again as it encoded a message.

Rejewski and his team discovered several theorems, primarily in the field of Group Theory as it pertains to permutations, which allowed them to dramatically reduce the number of guesses on how the Enigma was set up. They also built a computer and called it the Bomba; it was capable of cracking the German Enigma code!

Unfortunately, if the Germans were to change the settings of the Enigma machine at least once a day, then just one Bomba was not enough. You would need about 60 of them running simultaneously, and then you'd have a reasonable chance of succeeding sometime during the course of the day, before the Germans changed the Enigma settings again.

On July 24 and 25, 1939, when Rejewski felt that the German invasion of Poland was imminent and that he didn't have enough time to improve the Bomba sufficiently enough, he invited the French and British cryptanalysts to Poland so that he could share everything he had with them. Needless to say, they were very impressed with the progress the Poles made, since, realistically speaking, they were still trying to figure out how to even start dealing with the Enigma.

Germany invaded Poland on September 1, 1939. The British decided that this time they would recruit their best mathematicians, chess players, bridge players, and solvers of crossword puzzles to work on cracking the Enigma. Among them was Alan Turing.

Turing's approach was to take the Polish Bomba and continue to improve and modify it using ideas of his own and those of his team. As this computer was being modified, he also renamed it to the Bombe.

In time, Turing and his team were very successful. They were able to reduce the number of searches that needed to be done by the Bombe to such a minimum that it cracked the German Enigma early every day. The story is told that any secret message to Hitler was read by Churchill before Hitler even got it.