Serendipity

In 1945 Nazi Germany was finally defeated. One of the things that had helped bring about its defeat was the successful breaking of what the German’s thought was an unbreakable code.

At the end of the First World War a German engineer named Arthur Sherbius invented a cipher machine called Enigma. As children, many of us played with substitution ciphers using a kind of code machine consisting of concentric circles on which were printed the alphabet. I remember getting a plastic cipher machine out of a box of cereal. It was made of gold colored plastic and was about the size and thickness of a small jelly jar lid. There were two concentric circles, and the one on the outside moved. After twirling, when I compared the two rings, the A on the outside one might be aligned to the D on the inside, the B to the E, and so on. So I could write a “code” that could only be read if someone knew that when I wrote down the letter F it actually stood for the letter C and so on. Such a simple cipher could be broken in minutes, since there are but a small number of possible combinations and certain letters, such as E and the other vowels, are statistically more common.

The Enigma machine was a much more sophisticated and complicated cipher machine, consisting of at first three, and later, five circles or rings. The relationships between the letters on the rings varied with each keystroke. To know how to put a message back together, the recipient of the message would need to have the keycode that told the machine when and how to make the shifts in the rings. The complexity and shifting nature of the substitutions within a single text made the Enigma machine’s ciphers very hard to decipher. The Germans actually believed they were unbreakable.

Before World War II the Enigma machine was used commercially. It was later adopted by the military and government services of several nations. So in December, 1932 the Polish Cipher Bureau managed to break Germany’s military Enigma ciphers on some of the earlier Enigma machines. Five weeks before the outbreak of the Second World War, Poland gave what they had learned to the French and the British.
The British government then created a military intelligence agency called Ultra. Ultra obtained and broke high-level encrypted enemy radio and teleprinter communications at the Government Code and Cypher School in Bletchley Park. The British called their program “ultra” because it was even more secret than top secret. Many of the participants in the war, ranging from Winston Churchill to Dwight D. Eisenhower believed that the decryptions obtained at Bletchley Park were decisive in the allied victory in World War II. One historian, Sir Harry Hinsley, believes that Ultra shortened the war by two to four years.

And how was it that the British were able to break the Enigma ciphers? It was mostly due to the work of two men: Polish mathematician, Marian Rejewski and British mathematician Alan Turing. In 1932 the Polish intelligence bureau received two German documents and two pages of daily key codes from the French. That allowed Rejewski to make a significant breakthrough in using the theory of permutations and groups to work out the Enigma scrambler wiring. He first worked it out using paper, but ultimately came up with an electro-mechanical device that was called the cryptologic bomb. It could sort through and determine which of the more than seventeen thousand possible keycodes was being used in a text in about two hours. This worked well on the Enigma machines using three rings, but not so well after 1938 when the Germans increased the complexity of their Enigma machines by adding two more rings.

Alan Turing, in 1939, designed an electromechanical “bombe,” building on the earlier work of Marian Rejewski. Turing’s machine was designed for the much more general approach to solving the ciphers. From this early system, the Colossus machine was later constructed in 1943. It was the world’s first electronic, digital, programmable computer. Its purpose was narrow, however, since it was tasked with only one job: decrypting the German codes. And unlike modern computers, Colossus had no internally stored programs. For each task it performed, its operators had to set up plugs and switches in order to physically rewire it.

It wasn’t until after the war, in 1946, that Turing presented a paper to the National Physical Laboratory Executive committee, giving them the first complete design of a stored-program computer. Although it still used vacuum tubes, Turing’s design was a computer of the modern sort: it was flexible and programmable.

The modern computer that is today ubiquitous, and used for everything from word processing to playing Angry Birds, is largely the serendipitous result of the need to find a quicker way to decode German cyphers that had been created by their Enigma machines.