The Bombeshell at Bletchley: What if Alan Turing had not Broken Enigma

Turing and the Bombes at Bletchley

In 1932, three young Polish mathematicians named Marian Rejewski, Henryk Zygalski, and Jerzy Rózyki were the first to have success in breaking the military version of Enigma (Crypto Museum, 2012). They were provided with information from a German spy codenamed 'Asche' that led them to complete a mathematical analysis that would be crucial in their work, along with a commercial Enigma which they transformed into the military version (Crypto Museum, 2012). Unfortunately for the Poles, the Germans completely replaced their procedure for encrypting their messages on September 25, 1938, thus rendering the Polish Enigma useless (Crypto Museum, 2012). In an attempt to adapt to the new system, Rejewski, Zygalski, and Rózyki developed the Zygalski sheets and the Bomba Kryptologiczna, or 'Bomba' as it would come to be known (Crypto Museum, 2012). Although based off of the information provided from Polish 'Bomba', Turing's approach to cracking Enigma was quite different from that of its predecessor.

Designed in 1939 by Alan Turing, the British 'Bombe' operated on the assumption that somewhere in the Enigma messages was a previously known phrase or 'crib'. Knowledge of these 'cribs' then would lead to several different hypothesis which would be input into the Bombe machines. The way this operated was that there were twenty-six cables, each with twenty-six wires. Each cable and each wire inside a cable corresponded to one letter of the alphabet, essentially creating a system of cables labeled A-Z with wires inside each labeled A-Z (ie. Cable A contained wires a, b, c, d, et cetra). "When the bombe was set in motion the drums in the upper row of each of the three batteries rotated in precise synchrony at 120 rpm. When they had completed one revolution the middle row of drums in each battery rotated to the next position. That is, they rotated 1/26 of one revolution, and when they had rotated through one revolution the lower row of drums rotated to the next position. This continued until either the bombe detected a 'stop' or until the drums had returned to their original positions....A test register was connected to one of the cables, typically the cable representing the letter that appeared most frequently in the menu, so that each of the 26 wires in the cable led into and out of the test register. Each wire was in one of two states which we shall call live and dead, and the register was capable of distinguishing how many of its wires were live....So there are two stop conditions which the bombe looks for, either exactly one live wire or exactly 25 live wires in the test register."(Ellsbury,para. 1, 3, 17) In order to reach a stop state, several different variables had to be tested. If Turing wanted to test the hypothesis that 'A' and 'E' were encrypted together, such that 'A' was 'E' and vice versa, an electric current would be applied to wire a in cable E. This would then cause all of the wires connected to wire a in cable E to become live, and as such, every wire connected to wire e in cable A to become live as well. Now, suppose that a second wire in cable E, wire h, becomes live. This would present a new situation where 'E' and 'H' were encrypted together, such that 'E' was 'H' and 'H' was 'E'. However, since there can only be one pair of encrypted letters, it would be a safe presumption that 'A' and 'E' were not encrypted together, but instead 'E' and 'H'. This process continued until a stop state was reached, either with the one live wire and twenty-five dead wires  indicating that the hypothesis was correct (fig. 1), or conversely, twenty-five live wires and one dead wire indicating that the hypothesis was wrong (fig. 2).

Fig.1

Fig. 2

It was this system of trial and error, combined with the principle of contradiction, that helped defeat the Germans in World War II. Since the Enigma keys were typically altered every two days, messages received on the second day could be decrypted in twenty minutes. However, in the case of the detection of German U-boats and their operations in the Atlantic, various ciphers were used with the key to each cipher being altered daily. The primary cipher, the Heimisch, was used for U-boats in what were considered 'Home Waters'. Alternative ciphers included the Kurzsignalheft, which was used to communicate the sighting of convoys, and the Wetterkurzschlüssel, which was used for weather reports. It were these exact weather reports that Turing and his team used to break the U-boat Enigma.

Everyday, German U-boats would send out weather reports, which were encoded with the Wetterkurzschlüssel and then enciphered. These weather reports were obtained by members of Hut 10 at Bletchley Park who then proceeded to break the ciphers, giving Turing and his team a second set of cribs. Unfortunately for Turing, the Germans introduced a new Enigma machine, code named 'Shark', that used a second version of the Wetterkurzschlüssel as a cipher. This proved to be a major setback for the team in Hut 8; they were essentially blind to Enigma messages for ten months. Turing and his team were able to break Shark with the assistance of weather reports broken by the members of Hut 10.

It was the breaking of Shark that proved fundamental to the Battle of the Atlantic. "On 13 December 1942, Bletchley teleprinted the OIC the positions of over 12 Atlantic U-boats, on dates from 5 to 7 December, as established from Shark weather signals. Hut 8 had penetrated M4 Shark with the help of the weather broadcasts broken by Hut 10. Intelligence from Shark, although sometimes badly delayed, played a critical part in the Battle of the Atlantic, perhaps saving from 500,000 to 750,000 tons of shipping in December 1942 and January 1943 alone." (Helgason, para. 12) With the information gathered from the deciphered messages, convoys were rerouted, allowing Britain to receive their supplies and food, and several supply U-boats were sunk.

Outside of World War II, Turing's work on the bombes propelled technological advancement. Often considered the 'Father of Theoretical Computer Science and Artificial Intelligence', Turing's work on the bombe allowed him to go on to invent the Turing Machine, which is the mathematical equivalent to what is known as the digital computer, the Universal Turing Machine, which, unlike the Turing Machine, can emulate any other machine and can perform multiple calculations, and develop the Imitation Game. The Imitation Game, simply put, is a test designed to test artificial intelligence. Often referred to as the Turing test, Turing described the Imitation Game as a scenario in which a human judge would hold a conversation with two entities, one of which was human and the other a computer. If the judge were less than fifty percent accurate, meaning that they had an equal chance of designating either entity as human or computer, the computer could, Turing proposed, be considered a simulation of a human being and be considered intelligent.

It goes without saying that without Turing's work in World War II, the world would be technologically behind by today's standards. As for the conditions of the war, if Enigma had not been broken, the Allies would still have claimed victory, but World War II would have dragged on for another two to four years and another 14 to 21 million lives would have been lost. D-Day would have occurred a year later than it did, and there could have possibly been a bomb drop in Berlin instead of in Hiroshima or Nagasaki.