Bombe The bombe was an electromechanical device used by British cryptologist s to help decipher German Enigma - machine - encrypted secret messages during World War II . The US Navy and US Army later produced machines to the same functional specification , but engineered differently . The initial design of the bombe was produced in 1939 at the UK Government Code and Cypher School ( GC & CS ) 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 . It was a substantial development from a device that had been designed in 1938 by Polish Cipher Bureau cryptologist Marian Rejewski , and known as the " cryptologic bomb " ( Polish : " " bomba kryptologiczna " " ) . 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 was 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 implemented a polyalphabetic substitution cipher , which turned plaintext into ciphertext and back again . Used properly , this provided a very high degree of security . The Enigma ' s scrambler contained rotors with 26 electrical contacts on each side , whose wiring diverted the current to a different position on the two sides . On depressing a key on the keyboard , an electrical current flowed through an entry drum at the right - hand end of the scrambler , then through the set of rotors to a reflecting drum ( or reflector ) which turned it back through the rotors and entry drum , and out to cause one lamp on the lampboard to be illuminated . At each key depression , at least one of the rotors ( the right - hand or " fast " rotor ) advanced one position , which caused the encipherment to alter . At a certain point , the right - hand rotor caused the middle rotor to advance and in a similar way , the middle rotor caused the left - hand ( or " slow " ) rotor to advance . Each rotor caused the " turnover " of the rotor to its left after a full rotation . The Enigma operator could rotate the wheels by hand to change the letter of the alphabet showing through a window , to set the start position of the rotors for enciphering a message . This three - letter sequence was " message key " . There were 26 × 26 × 26 17 , 576 possible positions of the set of three rotors , and hence different message keys . By opening the lid of the machine and releasing a compression bar , the set of three rotors on their spindle could be removed from the machine and their sequence ( called the " wheel order " at Bletchley Park ) could be altered . Multiplying 17 , 576 by the six possible wheel orders gives 105 , 456 different ways that the scrambler could be set up . In 1930 an additional security feature was introduced for the military Enigmas . This was a plugboard ( " Steckerbrett " in German , shortened to " Stecker " ) that further scrambled the letters . Letters were swapped in pairs : if A was transformed into R then R was transformed into A . This regularity was exploited by Welchman ' s " diagonal board " enhancement to the bombe , which vastly increased its efficiency . With six plug leads in use ( leaving 14 letters " unsteckered " ) this gives 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 meant that a letter was never 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 there was a choice of three from five ( i . e . 60 wheel orders ) for the army and airforce Enigmas , and three out of eight ( 336 wheel orders ) for the navy machines . In addition , ten leads were used on the plugboard leaving only six letters unsteckered . This meant that the airforce and army Enigmas could be set up 15x10 ^ 18 ways . In 1941 the German navy introduced a version of Enigma with rotatable reflector ( the M4 or Four - rotor Enigma ) for communicating with its U - boat s . This could be set up in 18x10 ^ 19 different ways . Four - rotor Enigma . By late 1941 the change in German Navy fortunes in the Battle of the Atlantic , combined with intelligence reports , convinced Admiral Karl Dönitz that the Allies could read German Navy coded communications , and a thin fourth rotor with unknown wiring was added to German Navy Enigmas used for U - boat communications , to produce the " Triton " system , known at Bletchley Park as " Shark " . The Triton had a lock - out that allowed it to remain compatible with three - rotor machines when necessary . As before , the unknown wiring would prevent unauthorized reading of messages . Fortunately for the Allies , in December 1941 , before the machine went into official service , a submarine accidentally sent a message using four rotors , then the same message again using only three , thus disclosing the wiring of the extra rotor . In February 1942 the change in number of rotors used became official , and British ability to read German submarines ' messages largely ceased until new equipment became available that could use the information about the fourth - rotor wiring . The first half of 1942 was the " second happy time " for the German U - boats , with renewed success in attacking Allied shipping . This was due to the security of the new Enigma , and their ability to read convoy messages sent in Allied Naval Cipher No . 3 . 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 principle of the bombe . To decipher German military Enigma messages required that the following settings of the machine were discovered . Once these were known , all the messages for that network for that day ( or pair of days in the case of the German navy ) could be decrypted . Internal settings ( that required the lid of the Enigma machine to be opened ) External settings ( that could be changed without opening the machine ) The bombe identified possible initial positions of the rotor cores , and the " stecker partner " of a specified letter for a set of wheel orders . Manual techniques were then used to complete the decryption process . In the words of Gordon Welchman " . . . the task of the bombe was simply to reduce the assumptions of wheel order and scrambler positions that required ' further analysis ' to a manageable number . " Structure . The bombe was an electro - mechanical device that replicated the action of several Enigma machine s 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 thirty six 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 wheel orders . If the menu contained 12 or fewer letters , three different wheel orders could be run on one bombe ; if more than 12 letters , only two . Unlike Enigma rotors , the bombe drums had two sets of input and output contacts , so that they could be connected together in series . 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 ( input and output ) 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 = 17 , 576 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 ( Blue ) ; VII Jet ( Black ) ; VIII Silver . At each position of the rotors , an electrical 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 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 if that decryption produced German language . Bombe menu . A bombe run involved a cryptanalyst first obtaining a " crib " — a section of plaintext that was thought to correspond to the ciphertext . Finding cribs was not at all straightforward ; it required considerable familiarity with German military jargon and the communication habits of the operators . However , the codebreakers were aided by the fact that the Enigma would never encrypt a letter to itself . This helped in testing a possible crib against the ciphertext , as it could rule out a number of cribs and positions , where the same letter occurred in the same position in both the plaintext and the ciphertext . This was termed a " crash " at Bletchley Park . Once a suitable crib had been decided upon , the cryptanalyst would produce a " menu " for wiring up the bombe to test the crib against the ciphertext . The following is a simplified explanation of the process of constructing a menu . Suppose that the crib is ATTACKATDAWN to be tested against a certain stretch of ciphertext , say , WSNPNLKLSTCS . The letters of the crib and the ciphertext were compared to establish pairings between the ciphertext and the crib plaintext . These were then graphed to as in the diagram . It should be borne in mind that the relationships are reciprocal so that A in the plaintext associated with W in the ciphertext is the same as W in the plaintext associated with A in the ciphertext . At position 1 of the plaintext - ciphertext comparison , the letter A is associated with W , but A is also associated with P at position 4 , K at position 7 and T at position 10 . Building up these relationships into such a diagram provided the menu from which the bombe connections and drum start positions would be set up . In the illustration , there are three sequences of letters which form loops ( or " cycles " or " closures " ) , ATLK , TNS and TAWCN . The more loops in the menu , the more candidate rotor settings the bombe could reject , and hence the fewer false stops . Alan Turing conducted a very substantial analysis ( without any electronic aids ) to estimate how many bombe stops would be expected according to the number of letters in the menu and the number of loops . Some of his results are given in the following table . Recent bombe simulations have shown similar results . Stecker values . The German military Enigma included a plugboard ( " Steckerbrett " in German ) which swapped letters ( indicated here by ) before and after the main scrambler ' s change ( indicated by ) . The plugboard connections were known to the cryptanalysts as Stecker values . If there had been no plugboard , it would have been relatively straightforward to test a rotor setting ; a Typex machine modified to replicate Enigma could be set up and the crib letter A encrypted on it , and compared with the ciphertext , W . If they matched , the next letter would be tried , checking that T encrypted to S and so on for the entire length of the crib . If at any point the letters failed to match , the initial rotor setting would be rejected ; most incorrect settings would be ruled out after testing just two letters . This test could be readily mechanised and applied to all 17 , 576 settings of the rotors . However , with the plugboard , it was much harder to perform trial encryptions because it was unknown what the crib and ciphertext letters were transformed to by the plugboard . For example , in the first position , A and W were unknown because the plugboard settings were unknown . Turing ' s solution to working out the stecker values ( plugboard connections ) was to note that , even though the values for , say , A or W , were unknown , the crib still provided known relationships amongst these values ; that is , the values after the plugboard transformation . Using these relationships , a cryptanalyst could reason from one to another and , potentially , derive a logical contradiction , in which case the rotor setting under consideration could be ruled out . A worked example of such reasoning might go as follows : a cryptanalyst might suppose that AY . Looking at position 10 of the crib : ciphertext comparison , we observe that A encrypts to T , or , expressed as a formula : Due to the function being its own inverse , we can apply it to both sides of the equation and obtain the following : This gives us a relationship between A and T . If A = Y , and for the rotor setting under consideration Y = Q ( say ) , we can deduce that While the crib does not allow us to determine what the values after the plugboard are , it does provide a constraint between them . In this case , it shows how T is completely determined if A is known . Likewise , we can also observe that T encrypts to L at position 8 . Using , we can deduce the steckered value for L as well using a similar argument , to get , say , Similarly , in position 6 , K encrypts to L . As the Enigma machine is self - reciprocal , this means that at the same position L would also encrypt to K . Knowing this , we can apply the argument once more to deduce a value for " P ( " K , which might be : And again , the same sort of reasoning applies at position 7 to get : However , in this case , we have derived a contradiction , since , by hypothesis , we assumed that A = Y at the outset . This means that the initial assumption must have been incorrect , and so that ( for this rotor setting ) A ≠ Y ( this type of argument is termed " reductio ad absurdum " or " proof by contradiction " ) . The cryptanalyst hypothesised one plugboard interconnection for the bombe to test . The other stecker values and the ring settings were worked out by hand methods . Automated deduction . To automate these logical deductions , the bombe took the form of an electrical circuit . Current flowed around the circuit near - instantaneously , and represented all the possible logical deductions which could be made at that position . To form this circuit , the bombe used several sets of Enigma rotor stacks wired up together according to the instructions given on a menu , derived from a crib . Because each Enigma machine had 26 inputs and outputs , the replica Enigma stacks are connected to each other using 26 - way cables . In addition , each Enigma stack rotor setting is offset a number of places as determined by its position in the crib ; for example , an Enigma stack corresponding to the fifth letter in the crib would be four places further on than that corresponding to the first letter . In practice . Practical bombes used several stacks of rotors spinning together to test multiple hypotheses about possible setups of the Enigma machine , such as the order of the rotors in the stack . While Turing ' s bombe worked in theory , it required impractically long cribs to rule out sufficiently large numbers of settings . Gordon Welchman came up with a way of using the symmetry of the Enigma stecker to increase the power of the bombe . His suggestion was an attachment called the " diagonal board " that further improved the bombe ' s effectiveness . The British bombe . The Polish cryptologic " bomba " ( Polish : " bomba kryptologiczna " ; plural " bomby " ) had been useful only as long as three conditions were met . First , the form of the indicator had to include the repetition of the message key ; second , the number of rotors available had to be limited to three , giving six different " wheel orders " ( the three rotors and their order within the machine ) ; and third , the number of plug - board leads had to remain relatively small so that the majority of letters were " unsteckered " . Six machines were built , one for each possible rotor order . The " bomby " were delivered in November 1938 , but barely a month later the Germans introduced two additional rotors for loading into the Enigma scrambler , increasing the number of wheel orders by a factor of ten . Building another 54 " bomby " was beyond the Poles ' resources . Also , on 1 January 1939 , the number of plug - board leads was increased to ten . The Poles therefore had to return to manual methods , the Zygalski sheets . Alan Turing designed the British bombe on a more general principle , the assumption of the presence of text , called a " crib " , that cryptanalysts could predict was likely to be present at a defined point in the message . This technique is termed a " known plaintext attack " and had been used to a limited extent by the Poles , e . g . , the Germans ' use of " ANX " — German for " To , " followed by " X " as a spacer . The bombes were built by the British Tabulating Machine Company at Letchworth under the direction of Harold ' Doc ' Keen . Each machine was about wide , tall , deep and weighed about a ton . On the front of each bombe were 108 places where drums could be mounted . The drums were in three groups of 12 triplets . Each triplet , arranged vertically , corresponded to the three rotors of an Enigma scrambler . The bombe drums ' input and output contacts went to cable connectors , allowing the bombe to be wired up according to the menu . The ' fast ' drum rotated at a speed of 50 . 4 rpm in the first models and 120 rpm in later ones , when the time to set up and run through all 17 , 576 possible positions for one rotor order was about 20 minutes . The first bombe , which was based on Turing ' s original design and so lacked a diagonal board , was installed in " Hut 1 " at Bletchley Park on 18 March 1940 and was named " Victory " . The second bombe , named " " Agnus dei " " , later shortened to " Agnes " , or " Aggie " , was equipped with Welchman ' s diagonal board , and was installed on 8 August 1940 ; " Victory " was later returned to Letchworth to have a diagonal board fitted . . The bombes were later moved from " Hut 1 " to " Hut 11 " . The bombe was referred to by Group Captain Winterbotham as a " Bronze Goddess " because of its colour . The devices were more prosaically described by operators as being " like great big metal bookcases " . During 1940 , 178 messages were broken on the two machines , nearly all successfully . Because of the danger of bombes at Bletchley Park being lost if there were to be a bombing raid , bombe outstations were established , at Adstock , Gayhurst and Wavendon . In June – August 1941 there were 4 to 6 bombes at B . P . , and when Wavendon was completed , Bletchley , Adstock and Wavenden had a total of 24 to 30 bombes . When Gayhurst became operational there were a total of 40 to 46 bombes , and it was expected that the total would increase to about 70 bombes run by some 700 Wrens . But in 1942 with the introduction of the naval four - rotor Enigma , " far more than seventy bombes " would be needed . New outstations were established at Stanmore and Eastcote , and the Wavendon and Adstock bombes were moved to them , though the Gayhurst site was retained . The few bombes left at B . P . were used for demonstration and training purposes only . Production of bombes by BTM at Letchworth in wartime conditions , was nowhere near as rapid as the Americans later achieved at NCR in Dayton , Ohio . Sergeant Jones was given the overall responsibility for Bombe maintenance by Edward Travis . Later Squadron Leader and not to be confused with Eric Jones , he was one of the original bombe maintenance engineers , and experienced in BTM techniques . Welchman said that later in the war when other people tried to maintain them , we realised how lucky we were to have him . About 15 million delicate wire brushes on the drums had to make reliable contact with the terminals on the template . There were 104 brushes per drum , 720 drums per bombe , and ultimately around 200 bombes . After World War II , some fifty bombes were retained at Eastcote , while the rest were destroyed . The surviving bombes were put to work , possibly on Eastern bloc ciphers . The official history of the bombe states that " some of these machines were to be stored away but others were required to run new jobs and sixteen machines were kept comparatively busy on menus . It is interesting to note that most of the jobs came up and the operating , checking and other times maintained were faster than the best times during the war periods . " A team led by John Harper conducted a 13 - year project to reconstruct a working bombe . This was successful , and the reconstructed bombe can be seen at Bletchley Park Museum . In March 2009 it won an Engineering Heritage Award . Response to the Four - rotor Enigma . A program was initiated by Bletchley Park to design much faster bombes that could decrypt the four - rotor system in a reasonable time . There were two streams of development . One , with an electronic sensing unit , was produced by Charles Wynn - Williams of the Telecommunications Research Establishment ( TRE ) at Malvern . The other was designed by Harold Keen at BTM , Letchworth . Initial delivery was scheduled for August or September 1942 . Unlike the situation at Bletchley Park , the United States armed services did not share a combined cryptanalytical service . Indeed there was considerable rivalry between the US Army ' s facility , the Signals Intelligence Service ( SIS ) , and that of the US Navy known as OP - 20 - G . Before the US joined the war , there was collaboration with Britain , albeit with a considerable amount of caution on Britain ' s side because of the extreme importance of Germany and her allies not learning that its codes were being broken . Despite some worthwhile collaboration amongst the cryptanalysts , their superiors took some time to achieve a trusting relationship in which both British and American bombes were used to mutual benefit . In February 1941 , Captain Abe Sinkov and Lieutenant Leo Rosen of the US Army , and US Naval Lieutenants Robert Weeks and Prescott Currier , arrived at Bletchley Park bringing , amongst other things , a replica of the ' Purple ' cipher machine for the Bletchley Park ' s Japanese section in Hut 7 . The four returned to America after ten weeks , with a naval radio direction finding unit and many documents including a ' paper Enigma ' . Currier later wrote : The main response to the Four - rotor Enigma was the US Navy bombe , which was manufactured in much less constrained facilities than were available in wartime Britain . US Navy Bombe . Colonel John Tiltman , who later became Deputy Director at Bletchley Park , visited the US Navy cryptanalysis office ( OP - 20 - G ) in April 1942 and recognised America ' s vital interest in deciphering U - boat traffic . The urgent need , doubts about the British engineering workload and slow progress , prompted the US to start investigating designs for a Navy bombe , based on the full blueprint s and wiring diagrams received by US Naval Lieutenants Robert Ely and Joseph Eachus at Bletchley Park in July 1942 . Funding for a full , $ 2 million , navy development effort was requested on 3 September 1942 and approved the following day . Commander Edward Travis , Deputy Director and Frank Birch , Head of the German Naval Section travelled from Bletchley Park to Washington in September 1942 . With Carl Frederick Holden , US Director of Naval Communications they established , on 2 October 1942 , a UK : US accord which may have " a stronger claim than BRUSA to being the forerunner of the UKUSA Agreement , " being the first agreement " to establish the special Sigint relationship between the two countries , " and " it set the pattern for UKUSA , in that the United States was very much the senior partner in the alliance . " It established a relationship of " full collaboration " between Bletchley Park and OP - 20 - G . An all electronic solution to the problem of a fast bombe was considered , but rejected for pragmatic reasons , and a contract was let with the National Cash Register Corporation ( NCR ) in Dayton , Ohio . This established the United States Naval Computing Machine Laboratory . Engineering development was led by NCR ' s Joseph Desch . Alan Turing , who had written a memorandum to OP - 20 - G ( probably in 1941 ) , was seconded to the British Joint Staff Mission in Washington in December 1942 , because of his exceptionally wide knowledge about the bombes and the methods of their use . He was asked to look at the bombes that were being built by NCR and at the security of certain speech cipher equipment under development at Bell Labs . He visited OP - 20 - G , and went to NCR in Dayton on the 21 December . He was able to show that it was not necessary to build 336 Bombes , one for each possible rotor order , by utilising techniques such as Banburismus . The initial order was scaled down to 96 machines . The US Navy bombes used drums for the Enigma rotors in much the same way as the British bombes . They had eight Enigma - equivalents on the front and eight on the back . The fast drum rotated at 1 , 725 rpm , 34 times the speed of the early British bombes . ' Stops ' were detected electronically using thermionic valves ( vacuum tubes ) — mostly thyratron s — for the high speed circuits . When a ' stop ' was found the machine over - ran as it slowed , reversed to the position found and printed it out before restarting . The running time for a 4 - rotor run was about 20 minutes , and for a 3 - rotor run , about 50 seconds . Each machine was wide , high , deep and weighed 2 . 5 tons . The first machine was completed and tested on 3 May 1943 . By 22 June , the first two machines , called ' Adam ' and ' Eve ' broke a particularly difficult German naval cipher , the " Offizier " settings for 9 and 10 June . A P Mahon , who had joined the Naval Section in Hut 8 in 1941 , reported in his official 1945 " History of Hut Eight 1939 - 1945 " : These bombes were faster , and soon more available , than the British bombes at Bletchley Park and its outstations . Consequently they were put to use for Hut 6 as well as Hut 8 work . In Alexander ' s " Cryptographic History of Work on German Naval Enigma " , he wrote as follows . Production was stopped in September 1944 after 121 bombes had been made . The last - manufactured US Navy bombe is on display at the US National Cryptologic Museum . Jack Ingram , former Curator of the museum , describes being told of the existence of a second bombe and searching for it but not finding it whole . Whether it remains in storage in pieces , waiting to be discovered , or no longer exists , is unknown . US Army Bombe . The US Army Bombe was physically very different from the British and US Navy bombes . A contract was signed with Bell Labs on 30 September 1942 . The machine was designed to analyse 3 - rotor , not 4 - rotor traffic . It did not use drums to represent the Enigma rotors , using instead telephone - type relays . It could , however , handle one problem that the bombes with drums could not . The set of ten bombes consisted of a total of 144 Enigma - equivalents , each mounted on a rack approximately long high and wide . There were 12 control stations which could allocate any of the Enigma - equivalents into the desired configuration by means of plugboards . Rotor order changes did not require the mechanical process of changing drums , but was achieved in about half a minute by means of push buttons . A 3 - rotor run took about 10 minutes .