Bombe

• 1. Introduction

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  Group Captain Winterbotham called the Bombe a "Bronze Goddess," a name that came from its colour. The operators who fed it menus and listened for its stops used a more grounded description: "great big metal bookcases." The Bombe was the electro-mechanical device that helped British cryptologists crack the German Enigma cipher during the Second World War. The cipher it targeted could be arranged in more ways than any team of clerks could test in a lifetime. How British mathematicians overcame those odds, and why their solution very nearly came too late, are the questions that follow.

• 2. The Enigma's Fatal Flaw

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  At each keypress on the Enigma machine, an electric current traveled from the keyboard through a set of rotors and back through a reflecting drum. It then lit one of the lamps on the lampboard, displaying the encoded letter. The right-hand or "fast" rotor advanced one position with each press, altering the cipher. The right-hand rotor would eventually turn the middle rotor, and the middle rotor would turn the left-hand one.

  Three rotors were chosen from a set of available options, each settable in any of 26 positions. Those choices alone produced 17,576 possible starting configurations for the scrambler. Multiplying by the six possible wheel orders gave 105,456 different ways to configure the basic scrambler.

  In 1930, the German army added a plugboard called the Steckerbrett. It swapped pairs of letters before and after the current passed through the rotors. With six plug leads in use, the plugboard alone could be arranged in over 100 billion ways. Each lead's wiring remained fixed for the duration of a message, unlike the rotors. Combined with the rotor settings, the total configurations placed the cipher far beyond any brute-force attack.

  One property of the Enigma remained constant regardless of its settings: the reflector prevented any letter from being encoded as itself. Any test decryption that produced the same letter in both the plaintext and the ciphertext was automatically wrong. That single mechanical constraint was the Enigma's most exploitable weakness. By January 1939, the army and air force machines chose three rotors from a set of five, while the navy chose three from eight, producing 336 possible wheel orders for naval traffic alone.

  Marian Rejewski, working at the Polish Cipher Bureau, had already found one way to exploit the machine's structure. His machines were running before the British had written their first bombe design.

• 3. The Polish Bomba

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  Six bomby were delivered in November 1938, completing a set of one machine for each of the six possible wheel orders. The bomba kryptologiczna worked under three specific conditions. German operators had to repeat the message key in the transmitted indicator. The number of available Enigma rotors had to remain limited to three. And the plugboard connections had to remain sparse enough that most letters passed through unchanged.

  The Germans dismantled all three conditions in rapid succession. In late 1938, two additional rotors were introduced for loading into the Enigma scrambler, increasing the number of possible wheel orders by a factor of ten. Building 54 more bomby was beyond the Poles' resources. On the 1st of January 1939, the number of plugboard leads was raised to ten, leaving only six letters unsteckered. That change brought the army and air force Enigma's total configurations to approximately 1.5 times ten to the nineteenth power, far beyond the bomba's reach. The Poles had to return to manual methods, the Zygalski sheets.

  Turing's bombe was built on a more general principle than the bomba had used. It required only that cryptanalysts could identify a stretch of likely plaintext, called a crib, at a defined point in the intercepted ciphertext.

• 4. Victory and Agnes

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  Harold "Doc" Keen of the British Tabulating Machine Company at Letchworth was placed in charge of engineering the bombe. A budget of £100,000 funded the project. Each finished machine was about 7 feet wide, 6 feet 6 inches tall, and 2 feet deep, weighing roughly a ton. The front of each bombe held 108 positions for drums, arranged in triplets of three. Each triplet simulated the three rotors of a single Enigma scrambler, and the bombe contained 36 such equivalents in total.

  The top drums of each bombe rotated at 50.4 rpm in the first models and 120 rpm in later ones. The middle drums advanced one position for each full rotation of the top drums, and the bottom drums advanced likewise. Together they cycled through all 17,576 possible positions of a three-rotor Enigma. The drums were colour-coded by rotor type: red for Rotor I, maroon for II, green for III, yellow for IV, and brown for V. The three additional naval rotors were cobalt, jet black, and silver.

  The first bombe, named Victory, was installed in Hut 1 at Bletchley Park on the 18th of March 1940. It was based on Turing's original design and lacked what would become the machine's most powerful feature. Gordon Welchman devised an attachment called the diagonal board. It exploited the symmetry of the Enigma's plugboard to vastly increase the number of rotor settings the bombe could eliminate with each run. The second bombe, Agnus Dei, later shortened to Agnes or Aggie, incorporated this enhancement and was working by the 8th of August 1940. Victory was subsequently returned to Letchworth to have a diagonal board fitted.

  The German shorthand "ANX" was one of the more reliable sources of cribs. Enigma operators used it so consistently that its presence in traffic became predictable, giving cryptanalysts a stretch of likely plaintext at a defined location in each message. A crib was matched against the ciphertext letter by letter. The resulting pattern of relationships was turned into a menu for wiring the bombe. The more loops that menu contained, the fewer false stops the bombe would produce. When the machine stopped, it had found a candidate rotor setting that did not lead to a logical contradiction. There were usually many false stops before the correct one emerged.

  During 1940, the two bombes broke 178 messages, nearly all successfully. That tally was genuine but fragile. By the end of 1941, the German Navy was preparing a change that would silence the bombes on the most critical traffic entirely.

• 5. The Second Happy Time

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  Admiral Karl Donitz grew suspicious by late 1941 that the Allies were reading German Navy communications. Intelligence reports and a shift in Battle of the Atlantic fortunes confirmed his fears. A fourth rotor was added to the Enigma machines used for U-boat traffic. The Germans called the resulting system Triton; at Bletchley Park it was known as Shark. A thinner reflector was designed to make room for the extra rotor while keeping the machine the same external size.

  The change became official in February 1942, and the Allies immediately lost the ability to read U-boat traffic. The first half of 1942 became the "Second Happy Time" for German submarines. Between January and March 1942, German submarines sank 216 ships off the United States east coast. The US had entered the war without the aircraft, ships, personnel, and doctrine needed for anti-submarine warfare. German submarines were also benefiting from their ability to read Allied convoy messages sent in Naval Cipher No. 3.

  In December 1941, before Triton went into official service, a submarine accidentally sent a message with the fourth rotor in the wrong position. It then retransmitted the same message with the fourth rotor correctly placed. Material captured from a U-boat later confirmed that the fourth rotor did not move during a message and that, under specific settings, it could emulate a three-rotor machine. Those discoveries allowed the codebreakers to work out the wiring of both extra rotors, designated beta and gamma. Bletchley Park launched a program to build faster bombes capable of tackling four-rotor traffic. The British effort alone could not supply enough machines.

• 6. America's Industrial Answer

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  Colonel John Tiltman visited OP-20-G, the US Navy's cryptanalysis office, in April 1942 and recognized the vital American interest in cracking U-boat traffic. A request for $2 million to fund a full Navy bombe program was submitted on the 3rd of September 1942 and approved the following day. The contract went to the National Cash Register Corporation in Dayton, Ohio, establishing the United States Naval Computing Machine Laboratory. Engineering was led by NCR's Joseph Desch.

  In December 1942, Turing was seconded to the British Joint Staff Mission in Washington. He visited the NCR facility in Dayton on the 21st of December. He showed that 336 separate bombes, one per naval rotor order, were not necessary. By applying techniques including Banburismus, the initial order was reduced from 336 machines to 96.

  Each US Navy bombe was 10 feet wide, 7 feet high, 2 feet deep, and weighed 2.5 tons. The fast drum rotated at 1,725 revolutions per minute, 34 times the speed of the earliest British models. A four-rotor run took about 20 minutes; a three-rotor run took roughly 50 seconds. The first machine was completed and tested on the 3rd of May 1943. By the 22nd of June, the first two machines, named Adam and Eve, had broken a particularly difficult German naval cipher. They recovered the Offizier settings for the 9th and the 10th of June. By late autumn 1943, new American machines were entering service at about two per week, with the total eventually reaching around 125. Production stopped in September 1944 after 121 had been built.

  The US Army pursued a separate design through Bell Labs, with a contract signed on the 30th of September 1942. Known as "003" or "Madame X," it used telephone-type relays rather than rotating drums and completed a three-rotor run in about 10 minutes. By May 1945, the combined total of British and American four-rotor bombes had reached 180, and the burden of keeping all those machines running fell to a small group of engineers who understood them more intimately than anyone else alive.

• 7. Maintenance and Legacy

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  Sergeant Jones, later Squadron Leader, was assigned overall responsibility for bombe maintenance by Edward Travis. Gordon Welchman observed later that when others tried to maintain the machines, they realized how fortunate they had been to have him. Each bombe held 720 drums, each drum had 104 wire brushes, and across a fleet of roughly 200 machines the total came to approximately 15 million brushes. Every one had to make reliable electrical contact with its terminal at all times.

  To reduce the risk of losing the fleet to a German bombing raid on Bletchley Park, outstations were established at Adstock, Gayhurst, and Wavendon, all in Buckinghamshire. The original plan had called for about 70 bombes run by approximately 700 members of the Women's Royal Naval Service, the Wrens. The four-rotor naval Enigma made clear that far more than seventy would be needed. New outstations at Stanmore and Eastcote absorbed most of the additional load, and machines from Wavendon and Adstock were transferred there.

  After the war ended, about 50 bombes were retained at RAF Eastcote and the rest were destroyed. The surviving machines were put to work, possibly on Eastern Bloc ciphers. An official history recorded that "some of these machines were to be stored away but others were required to run new jobs" and that sixteen machines "were kept comparatively busy on menus."

  In 1994, a group led by John Harper of the BCS Computer Conservation Society began building a working replica. The project required thirteen years of research and construction. It won an Engineering Heritage Award in March 2009. In May 2018, the replica was moved to the National Museum of Computing on the Bletchley Park site, and the new gallery opened officially on the 23rd of June 2018. The last-manufactured US Navy bombe is on display at the US National Cryptologic Museum. Whether a second US Navy bombe remains in storage in pieces, or no longer exists at all, is still unknown.