Bombe
The bombe was an electro-mechanical device used by British cryptologists to help decipher German Enigma-machine-encrypted secret messages during World War II. The US Navy and US Army later produced their own machines to the same functional specification, albeit engineered differently both from each other and from Polish and British bombes.
The British bombe was developed from a device known as the "bomba", which had been designed in Poland at the Biuro Szyfrów by cryptologist Marian Rejewski, who had been breaking German Enigma messages for the previous seven years, using it and earlier machines. The initial design of the British bombe was produced in 1939 at the UK Government Code and Cypher School at Bletchley Park by Alan Turing, with an important refinement devised in 1940 by Gordon Welchman. The engineering design and construction was the work of Harold Keen of the British Tabulating Machine Company. The first bombe, code-named Victory, was installed in March 1940 while the second version, Agnus Dei or Agnes, incorporating Welchman's new design, was working by August 1940.
The bombe was designed to discover some of the daily settings of the Enigma machines on the various German military networks: specifically, the set of rotors in use and their positions in the machine; the rotor core start positions for the message—the message key—and one of the wirings of the plugboard.
The Enigma machine
The Enigma is an electro-mechanical rotor machine used for the encryption and decryption of secret messages. It was developed in Germany in the 1920s. The repeated changes of the electrical pathway from the keyboard to the lampboard implement a polyalphabetic substitution cipher, which turns plaintext into ciphertext and back again. The Enigma's scrambler contains rotors with 26 electrical contacts on each side, whose wiring diverts the current to a different position on the two sides. When a key is pressed on the keyboard, an electric current flows through an entry drum at the right-hand end of the scrambler, then through the set of rotors to a reflecting drum which turns it back through the rotors and entry drum, and out to illuminate one of the lamps on the lampboard.At each key depression, the right-hand or "fast" rotor advances one position, which causes the encipherment to change. In addition, once per rotation, the right-hand rotor causes the middle rotor to advance; the middle rotor similarly causes the left-hand rotor to advance. Each rotor's position is indicated by a letter of the alphabet showing through a window. The Enigma operator rotates the wheels by hand to set the start position for enciphering or deciphering a message. The three-letter sequence indicating the start position of the rotors is the "message key". There are 263 17,576 different message keys and different positions of the set of three rotors. By opening the lid of the machine and releasing a compression bar, the set of three rotors on their spindle can be removed from the machine and their sequence altered. Multiplying 17,576 by the six possible wheel orders gives 105,456 different ways that the scrambler can be set up.
Although 105,456 is a large number, it does not guarantee security. A brute-force attack is possible: one could imagine using 100 code clerks who each tried to decode a message using 1000 distinct rotor settings. The Poles developed card catalogs so they could easily find rotor positions; Britain built "
EINS" catalogs. Less intensive methods were also possible. If all message traffic for a day used the same rotor starting position, then frequency analysis for each position could recover the polyalphabetic substitutions. If different rotor starting positions were used, then overlapping portions of a message could be found using the index of coincidence. Many major powers could break Enigma traffic if they knew the rotor wiring. The German military knew the Enigma was weak.In 1930, the German army introduced an additional security feature, a plugboard that further scrambled the letters, both before and after they passed through the rotor-reflector system. The Enigma encryption is a self-inverse function, meaning that it substitutes letters reciprocally: if
A is transformed into R, then R is transformed into A. The plugboard transformation maintained the self-inverse quality, but the plugboard wiring, unlike the rotor positions, does not change during the encryption. This regularity was exploited by Welchman's "diagonal board" enhancement to the bombe, which vastly increased its efficiency. With six plug leads in use, there were 100,391,791,500 possible ways of setting up the plugboard.An important feature of the machine from a cryptanalyst's point of view, and indeed Enigma's Achilles' heel, was that the reflector in the scrambler prevented a letter from being enciphered as itself. Any putative solution that gave, for any location, the same letter in the proposed plaintext and the ciphertext could therefore be eliminated.
In the lead-up to World War II, the Germans made successive improvements to their military Enigma machines. By January 1939, additional rotors had been introduced so that three rotors were chosen from a set of five for the army and air force Enigmas, and three out of eight for the navy machines. In addition, ten leads were used on the plugboard, leaving only six letters unsteckered. This meant that the air force and army Enigmas could be set up in 1.5×1019 ways. In 1941 the German navy introduced a version of Enigma with a rotatable reflector for communicating with its U-boats. This could be set up in 1.8×1020 different ways.
Four-rotor Enigma
By late 1941 a change in German Navy fortunes in the Battle of the Atlantic, combined with intelligence reports, convinced Admiral Karl Dönitz that the Allies were able to read the German Navy's coded communications, and a fourth rotor with unknown wiring was added to German Navy Enigmas used for U-boat communications, producing the Triton system, known at Bletchley Park as Shark. This was coupled with a thinner reflector design to make room for the extra rotor. The Triton was designed in such a way that it remained compatible with three-rotor machines when necessary: one of the extra 'fourth' rotors, the 'beta', was designed so that when it was paired with the thin 'B' reflector, and the rotor and ring were set to 'A', the pair acted as a 'B' reflector coupled with three rotors. Fortunately for the Allies, in December 1941, before the machine went into official service, a submarine accidentally sent a message with the fourth rotor in the wrong position, and then retransmitted the message with the rotor in the correct position to emulate the three-rotor machine. In February 1942 the change in the number of rotors used became official, and the Allies' ability to read German submarines' messages ceased until a snatch from a captured U-boat revealed not only the four-rotor machine's ability to emulate a three-rotor machine, but also that the fourth rotor did not move during a message. This along with the aforementioned retransmission eventually allowed the code breakers to figure out the wiring of both the 'beta' and 'gamma' fourth rotors.The first half of 1942 was the "Second Happy Time" for the German U-boats, with renewed success in attacking Allied shipping, as the US had just entered war unprepared for the onslaught, lacking in anti-submarine warfare aircraft, ships, personnel, doctrine and organization. Also, the security of the new Enigma and the Germans' ability to read Allied convoy messages sent in Naval Cipher No. 3 contributed to their success. Between January and March 1942, German submarines sank 216 ships off the US east coast. In May 1942 the US began using the convoy system and requiring a blackout of coastal cities so that ships would not be silhouetted against their lights, but this yielded only slightly improved security for Allied shipping. The Allies' failure to change their cipher for three months, together with the fact that Allied messages never contained any raw Enigma decrypts, helped convince the Germans that their messages were secure. Conversely, the Allies learned that the Germans had broken the naval cipher almost immediately from Enigma decrypts, but lost many ships due to the delay in changing the cipher.
The principle of the bombe
The following settings of the Enigma machine must be discovered to decipher German military Enigma messages. Once these are known, all the messages for that network for that day could be decrypted.Internal settings
- The selection of rotors in use in the Enigma's scrambler, and their positions on the spindle. Possible rotor orders numbered 60 for army and air force networks and 336 for the naval networks.
- The positions of the alphabet rings' turnover notch in relation to the core of each rotor in use. There are 26 possible ring settings for each rotor.
- The plugboard connections. The ten leads could be arranged in different combinations.
- The scrambler rotor positions at the start of enciphering the message key —up to May 1940; or thereafter the initial positions of each rotor at the start of enciphering the message from which the base position could be derived. There are possible three-letter keys.
Structure
The bombe was an electro-mechanical device that replicated the action of several Enigma machines wired together. A standard German Enigma employed, at any one time, a set of three rotors, each of which could be set in any of 26 positions. The standard British bombe contained 36 Enigma equivalents, each with three drums wired to produce the same scrambling effect as the Enigma rotors. A bombe could run two or three jobs simultaneously.Each job would have a 'menu' that had to be run against a number of different rotor orders. If the [|menu] contained 12 or fewer letters, three different rotor orders could be run on one bombe; if more than 12 letters, only two.
In order to simulate Enigma rotors, each rotor drum of the bombe had two complete sets of contacts, one for input towards the reflector and the other for output from the reflector, so that the reflected signal could pass back through a separate set of contacts. Each drum had 104 wire brushes, which made contact with the plate onto which they were loaded. The brushes and the corresponding set of contacts on the plate were arranged in four concentric circles of 26. The outer pair of circles were equivalent to the current in an Enigma passing in one direction through the scrambler, and the inner pair equivalent to the current flowing in the opposite direction.
The interconnections within the drums between the two sets of input and output contacts were both identical to those of the relevant Enigma rotor. There was permanent wiring between the inner two sets of contacts of the three input/output plates. From there, the circuit continued to a plugboard located on the left-hand end panel, which was wired to imitate an Enigma reflector and then back through the outer pair of contacts. At each end of the "double-ended Enigma", there were sockets on the back of the machine, into which 26-way cables could be plugged.
The bombe drums were arranged with the top one of the three simulating the left-hand rotor of the Enigma scrambler, the middle one the middle rotor, and the bottom one the right-hand rotor. The top drums were all driven in synchrony by an electric motor. For each full rotation of the top drums, the middle drums were incremented by one position, and likewise for the middle and bottom drums, giving the total of 26 × 26 × 26 = positions of the 3-rotor Enigma scrambler.
The drums were colour-coded according to which Enigma rotor they emulated: I red; II maroon; III green; IV yellow; V brown; VI cobalt ; VII jet ; VIII silver.
At each position of the rotors, an electric current would or would not flow in each of the 26 wires, and this would be tested in the bombe's comparator unit. For a large number of positions, the test would lead to a logical contradiction, ruling out that setting. If the test did not lead to a contradiction, the machine would stop.
The operator would then find the point at which the test passed, record the candidate solution by reading the positions of the indicator drums and the indicator unit on the Bombe's right-hand end panel. The operator then restarted the run. The candidate solutions, stops as they were called, were processed further to eliminate as many false stops as possible. Typically, there were many false bombe stops before the correct one was found.
The candidate solutions for the set of wheel orders were subject to extensive further cryptanalytical work. This progressively eliminated the false stops, built up the set of plugboard connections and established the positions of the rotor alphabet rings. Eventually, the result would be tested on a Typex machine that had been modified to replicate an Enigma, to see whether that decryption produced German language.