Enigma

A German inventor named Arthur Scherbius created the Enigma machine. Germany used this machine as a system of encryption before and during World War II. The three main components of the Enigma machine were a plug board, three scramblers, and a reflector. The plug board swapped six pairs of letters before they entered the rest of the machine. This part of the Enigma machine added another level of complexity to the decrypting operation, since you would have to know which letters were set to switch as they went through the machine if you wanted to see the correct message. The scramblers are the most important part of the Enigma machine. Each of the three scramblers consisted of a mono alphabetic cipher, which encrypted one plain-text letter to cipher-text letter. Each letter that was entered into the machine went through each of the three scramblers thus encrypting it three times. The most important feature of the scramblers was that after each letter was encrypted, they would change their orientation to create a new cipher in the following manner. The first scrambler would rotate 1/26 of a revolution, and after one whole revolution, it would turn the second scrambler 1/26 of a revolution. After one whole revolution of the second scrambler, it would eventually turn the third scrambler one notch. This is a similar to a car odometer; the rotor representing a single mile has to rotate once completely before the rotor representing 10's of miles rotates by one unit. Because of this rotation of three scramblers, the cipher text obtained after typing in the same letter consecutively would only repeat itself after the 17,576th letter. The last part of the Enigma machine was the reflector. If a letter 'f' goes into the reflector, it could come out as a letter 'p', and then get sent back through the three scramblers in reverse order, through the plug board, and finally show up as the encrypted letter. The reflector allows users to use the Enigma machine in the same way for both encrypting and decrypting messages. Alan Turing and a group of scientists broke the Enigma cipher during the war. The breaking of this code led to the Allies' ability to intercept and decode the Germans' messages. Some people say that the war could have had a completely different outcome if the enigma cipher was not broken.

Some interesting facts about the Enigma machine:

On the actual Enigma machine, the three scramblers could be switched, meaning that there were 6 different orders that they could be positioned in. (123, 132, 213, 231, 312, 321) Also, each scrambler could be rotated to any one of 26 initial orientations, yielding 26*26*26 = 17,576 different settings. Also the number of ways of swapping six pairs of letters out of 26 is 100,391,791,500! So the total number of keys available is 6*17,576*100,391,791,500 = 10,586,916,764,424,000!! Now that is a pretty impressive number.

Works Cited

Sale, Tony. Enigma. 13 Sept. 2004. http://www.codesandciphers.org.uk/enigma

Hodges, Andrew. Cryptography. 12 Sept. 2004 http://www.trincoll.edu/depts/cpsc/cryptography/enigma.html

Teitelbaum, Jeremy T. 13 Sept. 2004 http://raphael.math.uic.edu/~jeremy/crypt/enigma.html

Maziakowski, Lech. Enigma, The History of Solving. 13 Sept. 2004. http://www.enigmahistory.org

Muise, Sylvain. The Enigma Machine. 12 Sept. 2004. http://www.mapleapps.com/categories/mathematics/Cryptography/html/enigma.html