Editing Cryptanalysis of the Enigma (section)

==World War II==
===Polish disclosures===
As the likelihood of war increased in 1939, Britain and France pledged support for Poland in the event of action that threatened its independence.<ref>{{citation |last=Chamberlain |first=Neville |author-link=Neville Chamberlain |date=31 March 1939 |title=European Situation (2.52 p.m.) |periodical=Hansard |publisher=UK Parliament |volume=345 |url=https://api.parliament.uk/historic-hansard/commons/1939/mar/31/european-situation-1 |access-date=3 January 2009}}</ref> In April, Germany withdrew from the [[German–Polish Non-Aggression Pact]] of January 1934. The Polish General Staff, realising what was likely to happen, decided to share their work on Enigma decryption with their western allies. Marian Rejewski later wrote:

{{blockquote|[I]t was not [as Harry Hinsley suggested, cryptological] difficulties of ours that prompted us to work with the British and French, but only the deteriorating political situation. If we had had no difficulties at all we would still, or even the more so, have shared our achievements with our allies as our contribution to the struggle against Germany.<ref name=RejewskiHinsleyP80/><ref>{{Harvnb|Kozaczuk|1984|p=64}}</ref>}}

At a conference near Warsaw on 26 and 27 July 1939, the Poles revealed to the French and British that they had broken Enigma and pledged to give each a [[Polish Enigma double|Polish-reconstructed Enigma]], along with details of their Enigma-solving techniques and equipment, including Zygalski's perforated sheets and Rejewski's [[bomba (cryptography)|cryptologic bomb]].<ref>{{Harvnb|Erskine|2006|p=59}}</ref> In return, the British pledged to prepare two full sets of [[Zygalski sheets]] for all 60 possible wheel orders.<ref>{{Harvnb|Herivel|2008|p=55}}</ref> Dilly Knox was a member of the British delegation. He commented on the fragility of the Polish system's reliance on the repetition in the indicator, because it might "at any moment be cancelled".<ref>{{Harvnb|Copeland|2004|p=246}}</ref> In August, two Polish Enigma doubles were sent to Paris, whence [[Gustave Bertrand]] took one to London, handing it to [[Stewart Menzies]] of Britain's [[Secret Intelligence Service]] at [[London Victoria station|Victoria Station]].<ref>{{Harvnb|Bertrand|1973|pp=60–61}}</ref>

Gordon Welchman, who became head of [[Hut 6]] at Bletchley Park, wrote:

{{blockquote|Hut 6 Ultra would never have gotten off the ground if we had not learned from the Poles, in the nick of time, the details both of the German military version of the commercial Enigma machine, and of the operating procedures that were in use.<ref>{{Harvnb|Welchman|1984|p=289}}</ref>}}

[[Peter Calvocoressi]], who became head of the Luftwaffe section in Hut 3, wrote of the Polish contribution:

{{blockquote|The one moot point is—how valuable? According to the best qualified judges it accelerated the breaking of Enigma by perhaps a year. The British did not adopt Polish techniques but they were enlightened by them.<ref>{{citation |last=Calvocoressi |first=Peter |author-link=Peter Calvocoressi |title=Credit to the Poles |newspaper=The Times |location=London |page=13 |date=23 March 1984}}</ref>}}

===''PC Bruno''===
{{Main|PC Bruno}}
On 5 September 1939 the Cipher Bureau began preparations to evacuate key personnel and equipment from Warsaw. Soon a special evacuation train, the Echelon F, transported them eastward, then south. By the time the Cipher Bureau was ordered to cross the border into allied Romania on 17 September, they had destroyed all sensitive documents and equipment and were down to a single very crowded truck. The vehicle was confiscated at the border by a Romanian officer, who separated the military from the civilian personnel. Taking advantage of the confusion, the three mathematicians ignored the Romanian's instructions. They anticipated that in an internment camp they might be identified by the Romanian security police, in which the German [[Abwehr]] and [[Sicherheitsdienst|SD]] had informers.<ref name="Kozaczuk 1984 70–73, 79">{{harvnb|Kozaczuk|1984|pp=70–73, 79}}</ref>

The mathematicians went to the nearest railroad station, exchanged money, bought tickets, and boarded the first train headed south. After a dozen or so hours, they reached Bucharest, at the other end of Romania. There they went to the British embassy. Told by the British to "come back in a few days", they next tried the French embassy, introducing themselves as "friends of Bolek" (Bertrand's Polish code name) and asking to speak with a French military officer. A French Army colonel telephoned Paris and then issued instructions for the three Poles to be assisted in evacuating to Paris.<ref name="Kozaczuk 1984 70–73, 79"/>

On 20 October 1939, at ''[[PC Bruno]]'' outside Paris, the Polish cryptologists resumed work on German Enigma ciphers, in collaboration with Bletchley Park.<ref>{{Harvnb|Kozaczuk|1984|pp=69–94, 104–11}}</ref>

''PC Bruno'' and Bletchley Park worked together closely, communicating via a [[telegraph]] line secured by the use of Enigma doubles. In January 1940 Alan Turing spent several days at ''PC Bruno'' conferring with his Polish colleagues. He had brought the Poles a full set of Zygalski sheets that had been punched at Bletchley Park by [[John R. F. Jeffreys|John Jeffreys]] using Polish-supplied information, and on 17 January 1940, the Poles made the first break into wartime Enigma traffic—that from 28 October 1939.<ref>{{Harvnb|Kozaczuk|1984|pp=84, 94}} note 8</ref> From that time, until the [[Battle of France|Fall of France]] in June 1940, 17 per cent of the Enigma keys that were found by the allies were solved at ''PC Bruno''.<ref>{{Harvnb|Rejewski|1982|pp=81–82}}</ref>

Just before opening their 10 May 1940 offensive against the Low Countries and France, the Germans made the feared change in the indicator procedure, discontinuing the duplication of the enciphered message key. This meant that the Zygalski sheet method no longer worked.<ref name="Rejewski84P243">{{Harvnb|Rejewski|1984c|p=243}}</ref><ref>{{Harvnb|Rejewski|1984d|pp=269–70}}</ref> Instead, the cryptanalysts had to rely on exploiting the [[#Operating shortcomings|operator weaknesses]] described below, particularly the cillies and the [[Herivel tip]].

After the June Franco-German armistice, the Polish cryptological team resumed work in France's southern ''Free Zone'',<ref>{{cite journal |title=Forgotten heroes of the Enigma story |last=Baker |first=Joanne |date=September 2018 |journal=Nature |volume=561 |issue=7723 |pages=307–308 |bibcode=2018Natur.561..307B |doi=10.1038/d41586-018-06149-y |pmid=30214032 |s2cid=52272490 |url=https://www.nature.com/articles/d41586-018-06149-y}}</ref> although probably not on Enigma.<ref>It is not clear whether, after the June 1940 fall of France, the Cipher Bureau broke Enigma. Rejewski, the principal Polish source, wrote in a posthumously published 1980 paper that at [[Cadix]] "We worked on other ciphers, no longer on Enigma". ({{Harvnb|Kozaczuk|1984|p=270}}). Colonel [[Stefan Mayer]] of Polish Intelligence, however, mentioned the Poles breaking "interesting [machine-enciphered messages] from [Germany's 1941] Balkan campaign coming [in over] the 'Luftwaffe' network..." ({{Harvnb|Kozaczuk|1984|p=116}}). And French intelligence Gen. Gustave Bertrand wrote of Enigma having been read at Cadix. ({{Harvnb|Kozaczuk|1984|p=117}}). Tadeusz Lisicki, Rejewski's and Zygalski's immediate chief later in wartime England but sometimes a dubious source, wrote in 1982 that "Rejewski in [a letter] conceded that Bertrand was doubtless right that at Cadix they had read Enigma, and that the number given by Bertrand, of 673 [Wehrmacht] telegrams, was correct.... The British did not send keys to Cadix; these were found using various tricks such as the sillies [and] Herivel tip described by Welchman, Knox's method, as well as others that Rejewski no longer remembered". ({{Harvnb|Kozaczuk|1984|p=117}}).</ref> Marian Rejewski and Henryk Zygalski, after many travails, perilous journeys, and Spanish imprisonment, finally made it to Britain,<ref>The third mathematician, Jerzy Różycki, had perished together with three Polish and one French colleague in the 1942 sinking of the passenger ship ''Lamoricière'' as they were returning to France from a tour of duty in [[Algeria]].</ref> where they were inducted into the Polish Army and put to work breaking German ''[[SS]]'' and ''[[Sicherheitsdienst|SD]]'' hand ciphers at a Polish signals facility in [[Boxmoor]]. Due to their having been in occupied France, it was thought too risky to invite them to work at Bletchley Park.<ref>{{Harvnb|Kozaczuk|1984|pp=148–55, 205–9}}</ref>

After the German occupation of [[Vichy France]], several of those who had worked at ''PC Bruno'' were captured by the Germans. Despite the dire circumstances in which some of them were held, none betrayed the secret of Enigma's decryption.<ref>{{Harvnb|Kozaczuk|1984|p=220}}</ref>

===Operating shortcomings===
Apart from some less-than-ideal inherent characteristics of the Enigma, in practice the system's greatest weakness was the large numbers of messages and some ways that Enigma was used. The basic principle of this sort of enciphering machine is that it should deliver a stream of transformations that are difficult for a cryptanalyst to predict. Some of the instructions to operators, and operator sloppiness, had the opposite effect. Without these operating shortcomings, Enigma would almost certainly not have been broken.<ref>{{Harvnb|Churchhouse|2002|p=122}}</ref>

The shortcomings that Allied cryptanalysts exploited included:

* The production of an early Enigma training manual containing an example of plaintext and its genuine ciphertext, together with the relevant message key. When Rejewski was given this in December 1932, it "made [his reconstruction of the Enigma machine] somewhat easier".<ref name="Rejewski84P243"/>
* Repetition of the message key as described in [[#Rejewski's characteristics method|Rejewski's characteristics method]], above. (This helped in Rejewski's [[Marian Rejewski#Solving the wiring|solving Enigma's wiring]] in 1932, and was continued until May 1940.)
* Repeatedly using the same stereotypical expressions in messages, an early example of what Bletchley Park would later term [[crib (cryptanalysis)|cribs]]. Rejewski wrote that "... we relied on the fact that the greater number of messages began with the letters ''ANX''—German for "to", followed by ''X'' as a spacer".<ref>{{Harvnb|Rejewski|1984c|pp=243–44}}</ref>
* The use of easily guessed keys such as ''AAA'' or ''BBB'', or sequences that reflected the layout of the Enigma keyboard, such as "three [typing] keys that stand next to each other [o]r diagonally [from each other]..."<ref>{{Harvnb|Rejewski|Woytak|1984b|p=235}}</ref> At Bletchley Park such occurrences were called ''cillies''.<ref name="David Kahn 1991 p. 113">{{Harvnb|Kahn|1991|p=113}}</ref><ref>{{Harvnb|Sebag-Montefiore|2004|p=92}}</ref> Cillies in the operation of the four-rotor ''Abwehr'' Enigma included four-letter names and German obscenities. Sometimes, with multi-part messages, the operator would not enter a key for a subsequent part of a message, merely leaving the rotors as they were at the end of the previous part, to become the message key for the next part.<ref>{{Harvnb|Copeland|2004|p=235}}</ref>
* Having only three different rotors for the three positions in the scrambler. (This continued until December 1938, when it was increased to five and then eight for naval traffic in 1940.)
* Using only six plugboard leads, leaving 14 letters ''unsteckered''. (This continued until January 1939 when the number of leads was increased, leaving only a small number of letters unsteckered.)

Other useful shortcomings that were discovered by the British and later the American cryptanalysts included the following, many of which depended on frequent solving of a particular network:

* The practice of re-transmitting a message in an identical, or near-identical, form on different cipher networks. If a message was transmitted using both a low-level cipher that Bletchley Park broke by hand, and Enigma, the decrypt provided an excellent crib for Enigma decipherment.<ref>{{Harvnb|Alexander|c. 1945}} "Background" Para. 38</ref>
* For machines where there was a choice of more rotors than there were slots for them, a rule on some networks stipulated that no rotor should be in the same slot in the scrambler as it had been for the immediately preceding configuration. This reduced the number of wheel orders that had to be tried.<ref>{{Harvnb|Bauer|2007|p=441}}</ref>
* Not allowing a wheel order to be repeated on a monthly setting sheet. This meant that when the keys were being found on a regular basis, economies in excluding possible wheel orders could be made.<ref name="Taunt 1993 108">{{Harvnb|Taunt|1993|p=108}}</ref>
* The stipulation, for Air Force operators, that no letter should be connected on the plugboard to its neighbour in the alphabet. This reduced the problem of identifying the plugboard connections and was automated in some Bombes with a Consecutive Stecker Knock-Out (CSKO) device.<ref>{{Harvnb|Budiansky|2000|p=240}}</ref>
* The sloppy practice that [[John Herivel]] anticipated soon after his arrival at Bletchley Park in January 1940. He thought about the practical actions that an Enigma operator would have to make, and the short-cuts he might employ. He thought that, after setting the alphabet rings to the prescribed setting, and closing the lid, the operator might not turn the rotors by more than a few places in selecting the first part of the indicator. Initially this did not seem to be the case, but after the changes of May 1940, what became known as the [[Herivel tip]] proved to be most useful.<ref name="David Kahn 1991 p. 113"/><ref>{{Harvnb|Welchman|1997|pp=98–100}}</ref><ref>John Herivel, cited by {{Harvnb|Smith|2007|pp=50–51}}</ref>
* The practice of re-using some of the columns of wheel orders, ring settings, or plugboard connections from previous months. The resulting analytical short-cut was christened at Bletchley Park ''Parkerismus'' after Reg Parker, who had, through his meticulous record-keeping, spotted this phenomenon.<ref>{{Harvnb|Welchman|1997|pp=130, 131, 167}}</ref>
* The re-use of a permutation in the German Air Force METEO code as the Enigma ''stecker'' permutation for the day.<ref>{{Harvnb|Bauer|2007|p=442}}</ref>

[[Mavis Lever]], a member of [[Dilly Knox]]'s team, recalled an occasion when there was an unusual message, from the Italian Navy, whose exploitation led to the British victory at the [[Battle of Cape Matapan]]. {{blockquote|The one snag with Enigma of course is the fact that if you press ''A'', you can get every other letter but ''A''. I picked up this message and—one was so used to looking at things and making instant decisions&mdash;I thought: 'Something's gone. What has this chap done? There is not a single ''L'' in this message.'

My chap had been told to send out a dummy message and he had just had a fag [cigarette] and pressed the last key on the keyboard, the ''L''. So that was the only letter that didn't come out. We had got the biggest crib we ever had, the encypherment was ''LLLL'', right through the message and that gave us the new wiring for the wheel [rotor]. That's the sort of thing we were trained to do. Instinctively look for something that had gone wrong or someone who had done something silly and torn up the rule book.<ref>{{Harvnb|Smith|2007|pp=59, 60}}</ref>}}

Postwar debriefings of [[German code breaking in World War II|German cryptographic specialists]], conducted as part of project [[TICOM]], tend to support the view that the Germans were well aware that the un-steckered Enigma was theoretically solvable, but thought that the steckered Enigma had not been solved.{{sfn|Huttenhain|Fricke|1945|pp=4,5}}

===Crib-based decryption===
The term ''[[known-plaintext attack|crib]]'' was used at Bletchley Park to denote any ''[[known plaintext]]'' or ''suspected plaintext'' at some point in an enciphered message.

Britain's Government Code and Cipher School (GC&CS), before its move to Bletchley Park, had realised the value of recruiting mathematicians and logicians to work in codebreaking teams. Alan Turing, a Cambridge University mathematician with an interest in cryptology and in machines for implementing logical operations—and who was regarded by many as a genius—had started work for GC&CS on a part-time basis from about the time of the [[Munich Agreement|Munich Crisis]] in 1938.<ref>{{Harvnb|Hodges|1995}}</ref> Gordon Welchman, another Cambridge mathematician, had also received initial training in 1938,<ref>{{Harvnb|Welchman|1997|p=12}}</ref> and they both reported to Bletchley Park on 4 September 1939, the day after Britain declared war on Germany.

Most of the Polish success had relied on the repetition within the indicator. But as soon as Turing moved to Bletchley Park—where he initially joined Dilly Knox in the research section—he set about seeking methods that did not rely on this weakness, as they correctly anticipated that the German Army and Air Force might follow the German Navy in improving their indicator system.

The Poles had used an early form of crib-based decryption in the days when only six leads were used on the plugboard.<ref name=MahonP13/> The technique became known as the ''Forty Weepy Weepy'' method for the following reason. When a message was a continuation of a previous one, the plaintext would start with ''FORT'' (from ''Fortsetzung'', meaning "continuation") followed by the time of the first message given twice bracketed by the letter ''Y''. At this time numerals were represented by the letters on the top row of the Enigma keyboard. So, "continuation of message sent at 2330" was represented as ''FORTYWEEPYYWEEPY''.

{| class="wikitable" | border=1 style="margin: 1em auto 1em auto; width:30%"
|+ Top row of the Enigma keyboard and the numerals they represented
|-
|align="center" |Q||align="center" |W||align="center" |E||align="center" |R||align="center" |T||align="center" |Z||align="center" |U||align="center" |I||align="center" |O||align="center"|P
|-
|align="center" |1||align="center" |2||align="center" |3||align="center" |4||align="center" |5||align="center" |6||align="center" |7||align="center" |8||align="center" |9||align="center"|0
|-
|}

''Cribs'' were fundamental to the British approach to solving Enigma keys, but guessing the plaintext for a message was a highly skilled business. So in 1940 [[Stuart Milner-Barry]] set up a special ''Crib Room'' in Hut 8.<ref>{{Harvnb|Mahon|1945|p=24}}</ref><ref name="Welchman97p120">{{Harvnb|Welchman|1997|p=120}}</ref>

Foremost among the knowledge needed for identifying cribs was the text of previous decrypts. Bletchley Park maintained detailed indexes<ref>{{citation |title=Bletchley Park Archives: Government Code & Cypher School Card Indexes |url=http://www.bletchleypark.org.uk/edu/archives/gccscoll.rhtm |access-date=8 July 2010 |url-status=dead |archive-url=https://web.archive.org/web/20110429032943/http://www.bletchleypark.org.uk/edu/archives/gccscoll.rhtm |archive-date=29 April 2011}}</ref> of message preambles, of every person, of every ship, of every unit, of every weapon, of every technical term, and of repeated phrases such as forms of address and other German military jargon.<ref>{{Harvnb|Budiansky|2000|p=301}}</ref> For each message the [[traffic analysis]] recorded the radio frequency, the date and time of intercept, and the preamble—which contained the network-identifying discriminant, the time of origin of the message, the callsign of the originating and receiving stations, and the indicator setting. This allowed cross referencing of a new message with a previous one.<ref>{{Harvnb|Welchman|1984|p=56}}</ref> Thus, as [[Derek Taunt]], another Cambridge mathematician-cryptanalyst wrote, the truism that "nothing succeeds like success" is particularly apposite here.<ref name="Taunt 1993 108"/>

Stereotypical messages included ''Keine besonderen Ereignisse'' (literally, "no special occurrences"—perhaps better translated as "nothing to report"),<ref>{{Harvnb|Milner-Barry|1993|p=93}}</ref> ''An die Gruppe'' ("to the group")<ref>{{Harvnb|Smith|2007|p=38}}</ref> and a number that came from weather stations such as ''weub null seqs null null'' ("weather survey 0600"). This was actually rendered as ''WEUBYYNULLSEQSNULLNULL''. The word ''WEUB'' being short for ''Wetterübersicht'', ''YY'' was used as a separator, and ''SEQS'' was common abbreviation of ''sechs'' (German for "six").<ref>{{Harvnb|Taunt|1993|pp=104, 105}}</ref> As another example, Field Marshal [[Erwin Rommel]]'s Quartermaster started all of his messages to his commander with the same formal introduction.<ref>{{Harvnb|Lewin|2001|p=118}}</ref>

With a combination of probable plaintext fragment and the fact that no letter could be enciphered as itself, a corresponding ciphertext fragment could often be tested by trying every possible alignment of the crib against the ciphertext, a procedure known as ''crib-dragging''. This, however, was only one aspect of the processes of solving a key. Derek Taunt has written that the three cardinal personal qualities that were in demand for cryptanalysis were (1) a creative imagination, (2) a well-developed critical faculty, and (3) a habit of meticulousness.<ref>{{Harvnb|Taunt|1993|p=111}}</ref> Skill at solving crossword puzzles was famously tested in recruiting some cryptanalysts. This was useful in working out plugboard settings when a possible solution was being examined. For example, if the crib was the word ''WETTER'' (German for "weather") and a possible decrypt before the plugboard settings had been discovered, was ''TEWWER'', it is easy to see that ''T'' with ''W'' are ''stecker partners''.<ref>{{Harvnb|Singh|1999|p=174}}</ref> These examples, although illustrative of the principles, greatly over-simplify the cryptanalysts' tasks.

A fruitful source of cribs was re-encipherments of messages that had previously been decrypted either from a lower-level manual cipher or from another Enigma network.<ref>{{Harvnb|Mahon|1945|p=44}}</ref> This was called a ''[[kiss (cryptanalysis)|kiss]]'' and happened particularly with German naval messages being sent in the ''dockyard cipher'' and repeated ''verbatim'' in an Enigma cipher. One German agent in Britain, [[Nathalie Sergueiew]], code-named ''Treasure'', who had been [[Double Cross System|'turned']] to work for the Allies, was very verbose in her messages back to Germany, which were then re-transmitted on the ''Abwehr'' Enigma network. She was kept going by [[MI5]] because this provided long cribs, not because of her usefulness as an agent to feed incorrect information to the ''Abwehr''.<ref name="Michael Smith 2007 p. 129">{{Harvnb|Smith|2007|p=129}}</ref>

Occasionally, when there was a particularly urgent need to solve German naval Enigma keys, such as when an [[Arctic convoys of World War II|Arctic convoy]] was about to depart, mines would be laid by the [[Royal Air Force|RAF]] in a defined position, whose grid reference in the German naval system did not contain any of the words (such as ''sechs'' or ''sieben'') for which abbreviations or alternatives were sometimes used.<ref>{{Harvnb|Mahon|1945|p=41}}</ref> The warning message about the mines and then the "all clear" message, would be transmitted both using the ''dockyard cipher'' and the [[U-boat]] Enigma network. This process of ''planting'' a crib was called ''[[gardening (cryptanalysis)|gardening]]''.<ref>{{Harvnb|Morris|1993|p=235}}</ref>

Although ''cillies'' were not actually cribs, the ''chit-chat'' in clear that Enigma operators indulged in among themselves often gave a clue as to the cillies that they might generate.<ref>{{Harvnb|Smith|2007|p=102}}</ref>

When captured German Enigma operators revealed that they had been instructed to encipher numbers by spelling them out rather than using the top row of the keyboard, Alan Turing reviewed decrypted messages and determined that the word ''eins'' ("one") appeared in 90% of messages.{{citation needed|date=February 2015}} Turing automated the crib process, creating the ''Eins Catalogue'', which assumed that ''eins'' was encoded at all positions in the plaintext. The catalogue included every possible rotor position for ''EINS'' with that day's ''wheel order'' and plugboard connections.<ref>{{cite web |title=The 1944 Bletchley Park Cryptographic Dictionary |publisher=codesandciphers.org.uk |url=https://www.codesandciphers.org.uk/documents/cryptdict/page34.htm |access-date=8 August 2020}}</ref>

===British ''bombe''===
{{Main|Bombe}}
The British bombe was an electromechanical device designed by Alan Turing soon after he arrived at Bletchley Park in September 1939. [[Harold Keen|Harold "Doc" Keen]] of the [[British Tabulating Machine Company]] (BTM) in [[Letchworth]] ({{convert|35|km|mi}} from Bletchley) was the engineer who turned Turing's ideas into a working machine—under the codename CANTAB.<ref>{{citation|contribution=BTM – British Tabulatuing Machine Company Ltd |contribution-url=http://www.jharper.demon.co.uk/btm1.htm |editor-last=Harper |editor-first=John |title=The British Bombe CANTAB |url=http://www.jharper.demon.co.uk/bombe1.htm |url-status=dead |archive-url=https://web.archive.org/web/20131204202741/http://www.jharper.demon.co.uk/bombe1.htm |archive-date=2013-12-04}}</ref> Turing's specification developed the ideas of the Poles' [[Bomba (cryptography)|''bomba kryptologiczna'']] but was designed for the much more general crib-based decryption.

The bombe helped to identify the ''wheel order'', the initial positions of the rotor cores, and the ''stecker partner'' of a specified letter. This was achieved by examining all 17,576 possible scrambler positions for a set of ''wheel orders'' on a comparison between a crib and the ciphertext, so as to eliminate possibilities that [[contradiction|contradicted]] the Enigma's known characteristics. 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".<ref name="Welchman97p120"/>

[[File:RebuiltBombeFrontView.jpg|thumb|300px|right|The working rebuilt bombe now at [[The National Museum of Computing]] on Bletchley Park. Each of the rotating drums simulates the action of an Enigma rotor. There are 36 Enigma-equivalents and, on the right end of the middle row, three ''indicator'' drums.]]

The demountable drums on the front of the bombe were wired identically to the connections made by Enigma's different rotors. Unlike them, however, the input and output contacts for the left-hand and the right-hand sides were separate, making 104 contacts between each drum and the rest of the machine.<ref>{{citation |last=Sale |first=Tony |author-link=Anthony Sale |contribution=Alan Turing, the Enigma and the Bombe |contribution-url=https://www.codesandciphers.org.uk/virtualbp/tbombe/tbombe.htm |editor-last=Sale |editor-first=Tony |editor-link=Anthony Sale |title=The Enigma cipher machine |url=https://www.codesandciphers.org.uk/enigma/}}</ref> This allowed a set of scramblers to be connected [[series and parallel circuits#Series circuits|in series]] by means of 26-way cables. Electrical connections between the rotating drums' wiring and the rear plugboard were by means of metal brushes. When the bombe detected a scrambler position with no contradictions, it stopped and the operator would note the position before restarting it.

Although Welchman had been given the task of studying Enigma traffic [[call sign]]s and discriminants, he knew from Turing about the bombe design and early in 1940, before the first pre-production bombe was delivered, he showed him an idea to increase its effectiveness.<ref>{{Harvnb|Hodges|1983|p=183}}</ref> It exploited the reciprocity in plugboard connections, to reduce considerably the number of scrambler settings that needed to be considered further. This became known as the ''diagonal board'' and was subsequently incorporated to great effect in all the bombes.<ref name="Welchman97p245"/><ref>{{Harvnb|Ellsbury|1998b}}</ref>

A cryptanalyst would prepare a crib for comparison with the ciphertext. This was a complicated and sophisticated task, which later took the Americans some time to master. As well as the crib, a decision as to which of the many possible ''wheel orders'' could be omitted had to be made. Turing's [[Banburismus]] was used in making this major economy. The cryptanalyst would then compile a [[Bombe#Bombe menu|''menu'']] which specified the connections of the cables of the patch panels on the back of the machine, and a particular letter whose ''stecker partner'' was sought. The menu reflected the relationships between the letters of the crib and those of the ciphertext. Some of these formed loops (or ''closures'' as Turing called them) in a similar way to the ''cycles'' that the Poles had exploited.

The reciprocal nature of the plugboard meant that no letter could be connected to more than one other letter. When there was a contradiction of two different letters apparently being ''stecker partners'' with the letter in the menu, the bombe would detect this, and move on. If, however, this happened with a letter that was not part of the menu, a false stop could occur. In refining down the set of stops for further examination, the cryptanalyst would eliminate stops that contained such a contradiction. The other plugboard connections and the settings of the alphabet rings would then be worked out before the scrambler positions at the possible true stops were tried out on [[Typex]] machines that had been adapted to mimic Enigmas. All the remaining stops would correctly decrypt the crib, but only the true stop would produce the correct plaintext of the whole message.<ref name=CarterStopsKeys/>

To avoid wasting scarce bombe time on menus that were likely to yield an excessive number of false stops, Turing performed a lengthy probability analysis (without any electronic aids) of the estimated number of stops per rotor order. It was adopted as standard practice only to use menus that were estimated to produce no more than four stops per ''wheel order''. This allowed an 8-letter crib for a 3-closure menu, an 11-letter crib for a 2-closure menu, and a 14-letter crib for a menu with only one closure. If there was no closure, at least 16 letters were required in the crib.<ref name=CarterStopsKeys>{{citation |last=Carter |first=Frank |title=From Bombe 'stops' to Enigma keys |year=2004 |url=http://www.bletchleypark.org.uk/content/bombestops.pdf |access-date=1 March 2009 |url-status=dead |archive-url=https://web.archive.org/web/20100108030414/http://www.bletchleypark.org.uk/content/bombestops.pdf |archive-date=8 January 2010}}</ref> The longer the crib, however, the more likely it was that ''turn-over'' of the middle rotor would have occurred.

The production model 3-rotor bombes contained 36 scramblers arranged in three banks of twelve. Each bank was used for a different ''wheel order'' by fitting it with the drums that corresponded to the Enigma rotors being tested. The first bombe was named ''Victory'' and was delivered to Bletchley Park on 18 March 1940. The next one, which included the diagonal board, was delivered on 8 August 1940. It was referred to as a ''spider bombe'' and was named ''Agnus Dei'' which soon became ''Agnes'' and then ''Aggie''. The production of British bombes was relatively slow at first, with only five bombes being in use in June 1941, 15 by the year end,<ref>{{Harvnb|Copeland|2004|pp=253–256}}</ref> 30 by September 1942, 49 by January 1943<ref>{{Harvnb|Budiansky|2000|p=230}}</ref> but eventually 210 at the end of the war.

A refinement that was developed for use on messages from those networks that disallowed the plugboard (''Stecker'') connection of adjacent letters, was the ''Consecutive Stecker Knock Out''. This was fitted to 40 bombes and produced a useful reduction in false stops.<ref>{{Harvnb|Bauer|2002|p=482}}</ref>

Initially the bombes were operated by ex-BTM servicemen, but in March 1941 the first detachment of members of the [[Women's Royal Naval Service]] (known as ''Wrens'') arrived at Bletchley Park to become bombe operators. By 1945 there were some 2,000 Wrens operating the bombes.<ref>{{Harvnb|Smith|2007|p=75}}</ref> Because of the risk of bombing, relatively few of the bombes were located at Bletchley Park. The largest two outstations were at [[Eastcote]] (some 110 bombes and 800 Wrens) and Stanmore (some 50 bombes and 500 Wrens). There were also bombe outstations at Wavendon, Adstock, and Gayhurst. Communication with Bletchley Park was by [[teleprinter]] links.

When the German Navy started using 4-rotor Enigmas, about sixty 4-rotor bombes were produced at Letchworth, some with the assistance of the [[General Post Office]].<ref>{{citation|contribution=Bombe Types |contribution-url=http://www.jharper.demon.co.uk/types1.htm |editor-last=Harper |editor-first=John |title=The British Bombe CANTAB |url=http://www.jharper.demon.co.uk/bombe1.htm |url-status=dead |archive-url=https://web.archive.org/web/20131204202741/http://www.jharper.demon.co.uk/bombe1.htm |archive-date=2013-12-04}}</ref> The [[NCR Corporation|NCR]]-manufactured [[Bombe#US Navy Bombe|US Navy 4-rotor bombes]] were, however, very fast and the most successful. They were extensively used by Bletchley Park over teleprinter links (using the [[Combined Cipher Machine]]) to [[OP-20-G]]<ref>{{Harvnb|Mahon|1945|p=89}}
</ref> for both 3-rotor and 4-rotor jobs.<ref>{{Harvnb|Wenger|Engstrom|Meader|1998}}</ref>

===''Luftwaffe'' Enigma===
Although the German army, SS, police, and railway all used Enigma with similar procedures, it was the ''Luftwaffe'' (Air Force) that was the first and most fruitful source of Ultra intelligence during the war. The messages were decrypted in [[Hut 6]] at Bletchley Park and turned into intelligence reports in [[Hut 3]].<ref>{{Harvnb|Calvocoressi|2001|p=74}}</ref> The network code-named 'Red' at Bletchley Park was broken regularly and quickly from 22 May 1940 until the end of hostilities. Indeed, the Air Force section of Hut 3 expected the new day's Enigma settings to have been established in Hut 6 by breakfast time. The relative ease of solving this network's settings was a product of plentiful cribs and frequent German operating mistakes.<ref>{{Harvnb|Calvocoressi|2001|p=87}}</ref> Luftwaffe chief [[Hermann Göring]] was known to use it for trivial communications, including informing squadron commanders to make sure the pilots he was going to decorate had been properly deloused. Such messages became known as "Göring funnies" to the staff at Bletchley Park.{{citation needed|date=June 2013}}

===''Abwehr'' Enigma===
[[File:Enigma-G.jpg|thumb|Enigma Model G, used by the ''[[Abwehr]]''. It had three ordinary rotors and a rotating reflector, multiple notches on the rotor rings, but no plugboard.]]

[[Dilly Knox]]'s last great cryptanalytical success, before his untimely death in February 1943, was the solving of the ''[[Abwehr]]'' Enigma in 1941. Intercepts of traffic which had an 8-letter indicator sequence before the usual 5-letter groups led to the suspicion that a 4-rotor machine was being used.<ref>{{Harvnb|Twinn|1993|p=127}}</ref> The assumption was correctly made that the indicator consisted of a 4-letter message key enciphered twice. The machine itself was similar to a [[Enigma machine#Military Enigma|Model G Enigma]], with three conventional rotors, though it did not have a plug board. The principal difference to the model G was that it was equipped with a reflector that was advanced by the stepping mechanism once it had been set by hand to its starting position (in all other variants, the reflector was fixed). Collecting a set of enciphered message keys for a particular day allowed ''cycles'' (or ''boxes'' as Knox called them) to be assembled in a similar way to the method used by the Poles in the 1930s.<ref name=FCarterAbwehr/>

Knox was able to derive, using his ''buttoning up'' procedure,<ref name=CarterButtoningUp/> some of the wiring of the rotor that had been loaded in the fast position on that day. Progressively he was able to derive the wiring of all three rotors. Once that had been done, he was able to work out the wiring of the reflector.<ref name=FCarterAbwehr>{{citation |last=Carter |first=Frank |title=The Abwehr Enigma Machine |url=http://www.bletchleypark.org.uk/resources/file.rhtm/261894/web+abwehr2.pdf |access-date=24 April 2009 |url-status=dead |archive-url=https://web.archive.org/web/20071002221359/http://www.bletchleypark.org.uk/resources/file.rhtm/261894/web+abwehr2.pdf |archive-date=2 October 2007}}</ref> Deriving the indicator setting for that day was achieved using Knox's time-consuming ''rodding'' procedure.<ref name=CarterRodding/> This involved a great deal of trial and error, imagination, and crossword puzzle-solving skills, but was helped by ''cillies''.

The ''Abwehr'' was the [[military intelligence|intelligence]] and [[espionage|counter-espionage]] service of the German High Command. The spies that it placed in enemy countries used a lower level cipher (which was broken by [[Oliver Strachey]]'s section at Bletchley Park) for their transmissions. However, the messages were often then re-transmitted word-for-word on the ''Abwehr's'' internal Enigma networks, which gave the best possible crib for deciphering that day's indicator setting. Interception and analysis of ''Abwehr'' transmissions led to the remarkable state of affairs that allowed MI5 to give a categorical assurance that all the German spies in Britain were controlled as [[double agents]] working for the Allies under the [[Double Cross System]].<ref name="Michael Smith 2007 p. 129"/>

===German Army Enigma===
In the summer of 1940 following the [[Armistice of 22 June 1940|Franco-German armistice]], most Army Enigma traffic was travelling by land lines rather than radio and so was not available to Bletchley Park. The air [[Battle of Britain]] was crucial, so it was not surprising that the concentration of scarce resources was on ''Luftwaffe'' and ''Abwehr'' traffic. It was not until early in 1941 that the first breaks were made into German Army Enigma traffic, and it was the spring of 1942 before it was broken reliably, albeit often with some delay.<ref>{{Harvnb|Calvocoressi|2001|p=99}}</ref> It is unclear whether the German Army Enigma operators made deciphering more difficult by making fewer operating mistakes.<ref>{{Harvnb|Sullivan|Weierud|2005|p=215}}</ref>

===German Naval Enigma===
The German Navy used Enigma in the same way as the German Army and Air Force until 1 May 1937, when they changed to a substantially different system. This used the same sort of setting sheet but, importantly, it included the ground key for a period of two, sometimes three days. The message setting was concealed in the indicator by selecting a trigram from a book (the ''[[Discriminant Book|Kenngruppenbuch]]'', or K-Book) and performing a bigram substitution on it.<ref>{{citation |last=Supreme Command of the Navy |title=The Enigma General Procedure (Der Schluessel M Verfahren M Allgemein) |work=The Bletchley Park translated Enigma Instruction Manual, transcribed, and formatted by [[Tony Sale]] |place=Berlin |publisher=Supreme Command of the German Navy |year=1940 |url=https://www.codesandciphers.org.uk/documents/egenproc/egenproc.pdf |access-date=26 November 2009}}</ref> This defeated the Poles, although they suspected some sort of bigram substitution.

The procedure for the naval sending operator was as follows. First they selected a trigram from the K-Book, say YLA. They then looked in the appropriate columns of the K-Book and selected another trigram, say YVT, and wrote it in the boxes at the top of the message form:
{| class="wikitable" | border="1" style="margin: 1em auto 1em auto"
|-
| align="center" | . ||align="center" | Y ||align="center" | V || align="center" | T
|-
| align="center" | Y || align="center" | L || align="center" | A || align="center" | .
|}
They then filled in the "dots" with any letters, giving say:
{| class="wikitable" | border="1" style="margin: 1em auto 1em auto"
|-
| align="center" | Q ||align="center" | Y ||align="center" | V || align="center" | T
|-
| align="center" | Y || align="center" | L || align="center" | A || align="center" | G
|}
Finally they looked up the vertical pairs of letters in the Bigram Tables
{{center|QY→UB YL→LK VA→RS TG→PW}}
and wrote down the resultant pairs, UB, LK, RS, and PW which were transmitted as two four letter groups at the start and end of the enciphered message. The receiving operator performed the converse procedure to obtain the message key for setting his Enigma rotors.

As well as these ''Kriegsmarine'' procedures being much more secure than those of the German Army and Air Force, the German Navy Enigma introduced three more rotors (VI, VII, and VIII), early in 1940.<ref>{{Harvnb|Copeland|2004|p=225}}</ref> The choice of three rotors from eight meant that there were a total of 336 possible permutations of rotors and their positions.

Alan Turing decided to take responsibility for German naval Enigma because "no one else was doing anything about it and I could have it to myself".<ref>{{Harvnb|Alexander|c. 1945}} Ch. II Para. 11</ref> He established [[Hut 8]] with [[Peter Twinn]] and two "girls".<ref>{{Harvnb|Copeland|2004|p=258}}</ref> Turing used the indicators and message settings for traffic from 1–8 May 1937 that the Poles had worked out, and some very elegant deductions to diagnose the complete indicator system. After the messages were deciphered they were translated for transmission to the Admiralty in Hut 4.

====German Navy 3-rotor Enigma====
The first break of wartime traffic was in December 1939, into signals that had been intercepted in November 1938, when only three rotors and six plugboard leads had been in use.<ref name=MahonP22>{{Harvnb|Mahon|1945|p=22}}</ref> It used "Forty Weepy Weepy" cribs.

A captured German ''Funkmaat'' ("radio operator") named Meyer had revealed that numerals were now spelt out as words. EINS, the German for "one", was present in about 90% of genuine German Navy messages. An EINS catalogue was compiled consisting of the encipherment of EINS at all 105,456 rotor settings.<ref>{{Harvnb|Alexander|c. 1945}} Ch. II Para. 21</ref> These were compared with the ciphertext, and when matches were found, about a quarter of them yielded the correct plaintext. Later this process was automated in Mr Freeborn's section using [[Unit record equipment|Hollerith equipment]]. When the ground key was known, this EINS-ing procedure could yield three bigrams for the tables that were then gradually assembled.<ref name=MahonP22/>

Further progress required more information from German Enigma users. This was achieved through a succession of ''pinches'', the capture of Enigma parts and codebooks. The first of these was on 12 February 1940, when rotors VI and VII, whose wiring was at that time unknown, were captured from the {{GS|U-33|1936|6}}, by minesweeper {{HMS|Gleaner|J83|6}}.

On 26 April 1940, the Narvik-bound German patrol boat ''VP2623'', disguised as a Dutch trawler named ''Polares'', was captured by {{HMS|Griffin|H31|6}}. This yielded an instruction manual, codebook sheets, and a record of some transmissions, which provided complete cribs. This confirmed that Turing's deductions about the trigram/bigram process were correct and allowed a total of six days' messages to be broken, the last of these using the first of the bombes.<ref name=MahonP22/> However, the numerous possible rotor sequences, together with a paucity of usable cribs, made the methods used against the Army and Air Force Enigma messages of very limited value with respect to the Navy messages.

At the end of 1939, Turing extended the [[Clock (cryptography)|clock method]] invented by the Polish cryptanalyst [[Jerzy Różycki]]. Turing's method became known as "[[Banburismus]]". Turing said that at that stage "I was not sure that it would work in practice, and was not in fact sure until some days had actually broken".<ref>{{Harvnb|Mahon|1945|p=14}}</ref> Banburismus used large cards printed in Banbury (hence the Banburismus name) to discover correlations and a statistical scoring system to determine likely rotor orders (''Walzenlage'') to be tried on the bombes. The practice conserved scarce bombe time and allowed more messages to be attacked. In practice, the 336 possible rotor orders could be reduced to perhaps 18 to be run on the bombes.<ref>{{Harvnb|Alexander|c. 1945}} "Background" Para. 42</ref> Knowledge of the bigrams was essential for Banburismus, and building up the tables took a long time. This lack of visible progress led to [[Francis Birch (cryptographer)|Frank Birch]], head of the Naval Section, to write on 21 August 1940 to [[Edward Travis]], Deputy Director of Bletchley Park: {{blockquote|"I'm worried about Naval Enigma. I've been worried for a long time, but haven't liked to say as much... Turing and Twinn are like people waiting for a miracle, without believing in miracles..."<ref>{{Harvnb|Mahon|1945|p=2}}</ref>}}

Schemes for capturing Enigma material were conceived including, in September 1940, [[Operation Ruthless]] by Lieutenant Commander [[Ian Fleming]] (author of the [[James Bond]] novels). When this was cancelled, Birch told Fleming that "Turing and Twinn came to me like undertakers cheated of a nice corpse..."<ref>{{Harvnb|Batey|2008|pp=4–6}}</ref>

A major advance came through [[Operation Claymore]], a [[British Commandos|commando]] raid on the [[Lofoten Islands]] on 4 March 1941. The German [[naval trawler|armed trawler]] ''Krebs'' was captured, including the complete Enigma keys for February, but no bigram tables or K-book. However, the material was sufficient to reconstruct the bigram tables by "EINS-ing", and by late March they were almost complete.<ref>{{Harvnb|Mahon|1945|p=26}}</ref>

Banburismus then started to become extremely useful. Hut 8 was expanded and moved to 24-hour working, and a crib room was established. The story of Banburismus for the next two years was one of improving methods, of struggling to get sufficient staff, and of a steady growth in the relative and absolute importance of cribbing as the increasing numbers of bombes made the running of cribs ever faster.<ref>{{Harvnb|Alexander|c. 1945}} Ch. III Para. 5</ref> Of value in this period were further "pinches" such as those from the [[German weather ship Lauenburg#The weather ships and Enigma|German weather ships]] ''München'' and ''Lauenburg'' and the submarines {{GS|U-110|1940|2}} and {{GS|U-559||2}}.

Despite the introduction of the 4-rotor Enigma for Atlantic U-boats, the analysis of traffic enciphered with the 3-rotor Enigma proved of immense value to the Allied navies. Banburismus was used until July 1943, when it became more efficient to use the many more bombes that had become available.

====M4 (German Navy 4-rotor Enigma)====
[[File:Bletchley Park Naval Enigma IMG 3604.JPG|thumb|The German Navy 4-rotor Enigma machine (M4) which was introduced for U-boat traffic on 1 February 1942]]
On 1 February 1942, the Enigma messages to and from Atlantic U-boats, which Bletchley Park called "Shark", became significantly different from the rest of the traffic, which they called "Dolphin".<ref>{{Harvnb|Alexander|c. 1945}} Ch. III Para. 20</ref>

This was because a new Enigma version had been brought into use. It was a development of the [[3-rotor Enigma]] with the reflector replaced by a thin rotor and a thin reflector. Eventually, there were two fourth-position rotors that were called Beta and Gamma and two thin reflectors, Bruno and Caesar, which could be used in any combination. These rotors were not advanced by the rotor to their right, in the way that rotors I through VIII were.

The introduction of the [[fourth rotor]] did not catch Bletchley Park by surprise, because captured material dated January 1941 had made reference to its development as an adaptation of the 3-rotor machine, with the fourth rotor wheel to be a reflector wheel.<ref>{{Harvnb|Mahon|1945|p=62}}</ref> Indeed, because of operator errors, the wiring of the new fourth rotor had already been worked out.

This major challenge could not be met by using existing methods and resources for a number of reasons.
# The work on the Shark cipher would have to be independent of the continuing work on messages in the Dolphin cipher.
# Solving Shark keys on 3-rotor bombes would have taken 50 to 100 times as long as an average Air Force or Army job.
# U-boat cribs at this time were extremely poor.<ref>{{Harvnb|Alexander|c. 1945}} Ch. III Para. 21</ref>

It seemed, therefore, that effective, fast, 4-rotor bombes were the only way forward. This was an immense problem and it gave a great deal of trouble. Work on a high speed machine had been started by [[C. E. Wynn-Williams|Wynn-Williams]] of the [[Telecommunications Research Establishment|TRE]] late in 1941 and some nine months later [[Harold Keen]] of BTM started work independently. Early in 1942, Bletchley Park were a long way from possessing a high speed machine of any sort.<ref>{{Harvnb|Mahon|1945|p=63}}</ref>

Eventually, after a long period of being unable to decipher U-boat messages, a source of cribs was found. This was the [[Kurzsignale|Kurzsignale (short signals)]], a code which the German navy used to minimise the duration of transmissions, thereby reducing the risk of being located by [[high-frequency direction finding]] techniques. The messages were only 22 characters long and were used to report sightings of possible Allied targets.<ref>{{citation |last=Sale |first=Tony |author-link=Anthony Sale |title=The Breaking of German Naval Enigma: U Boat Contact Signals |series=Codes and Ciphers in the Second World War: The history, science and engineering of cryptanalysis in World War II |url=https://www.codesandciphers.org.uk/virtualbp/navenigma/navenig10.htm |access-date=1 December 2008}}</ref> A copy of the code book had been captured from {{GS|U-110|1940|2}} on 9 May 1941. A similar coding system was used for weather reports from U-boats, the ''Wetterkurzschlüssel'', (Weather Short Code Book). A copy of this had been captured from {{GS|U-559||2}} on 29 or 30 October 1942.<ref>{{Harvnb|Budiansky|2000|pp=341–343}}</ref> These short signals had been used for deciphering 3-rotor Enigma messages and it was discovered that the new rotor had a neutral position at which it, and its matching reflector, behaved just like a 3-rotor Enigma reflector. This allowed messages enciphered at this neutral position to be deciphered by a 3-rotor machine, and hence deciphered by a standard bombe. Deciphered Short Signals provided good material for bombe menus for Shark.<ref>{{Harvnb|Mahon|1945|p=64}}</ref> Regular deciphering of U-boat traffic restarted in December 1942.<ref>{{Harvnb|Mahon|1945|p=77}}</ref>

===Italian naval Enigma===
{{see also|Cryptanalysis of Italian naval codes}}
In 1940 Dilly Knox wanted to establish whether the Italian Navy were still using the same system that he had cracked during the Spanish Civil War; he instructed his assistants to use rodding to see whether the crib ''PERX'' (''per'' being Italian for "for" and ''X'' being used to indicate a space between words) worked for the first part of the message. After three months there was no success, but [[Mavis Batey|Mavis Lever]], a 19-year-old student, found that rodding produced ''PERS'' for the first four letters of one message. She then (against orders) tried beyond this and obtained ''PERSONALE'' (Italian for "personal"). This confirmed that the Italians were indeed using the same machines and procedures.<ref name=CarterRodding/>

The subsequent breaking of Italian naval Enigma ciphers led to substantial Allied successes. The cipher-breaking was disguised by sending a [[aerial reconnaissance|reconnaissance aircraft]] to the known location of a warship before attacking it, so that the Italians assumed that this was how they had been discovered. The Royal Navy's victory at the [[Battle of Cape Matapan]] in March 1941 was considerably helped by Ultra intelligence obtained from Italian naval Enigma signals.<ref name=batey>{{Citation |last=Batey |first=Mavis | author-link = Mavis Batey |title=Breaking Italian Naval Enigma |year=2011 |page=81}} in {{Harvnb|Erskine|Smith|2011|pp=79–92}}</ref>

===American ''bombes''===
{{Further-text|[[Bombe#US Navy Bombe|US Navy Bombe]] and [[Bombe#US Army Bombe|US Army Bombe]]}}
Unlike the situation at Bletchley Park, the United States armed services did not share a combined cryptanalytical service. 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 among 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 [[Abraham Sinkov]] and Lieutenant [[Leo Rosen]] of the US Army, and Lieutenants Robert Weeks and [[Prescott Currier]] of the US Navy, arrived at Bletchley Park, bringing, among other things, a replica of the [[Type B Cipher Machine|"Purple" cipher machine]] for Bletchley Park's Japanese section in [[Hut 7]].<ref>{{Harvnb|Budiansky|2000|p=176}}</ref> The four returned to America after ten weeks, with a naval radio direction-finding unit and many documents,<ref>{{Harvnb|Budiansky|2000|p=179}}</ref> including a "paper Enigma".<ref>{{Harvnb|Jacobsen|2000}}</ref>

The main American response to the 4-rotor Enigma was the US Navy bombe, which was manufactured in much less constrained facilities than were available in wartime Britain. 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 Navy Lieutenants Robert Ely and Joseph Eachus at Bletchley Park in July 1942.<ref>{{Harvnb|Budiansky|2000|p=238}}</ref><ref>{{Harvnb|Wilcox|2001|p=21}}</ref> Funding for a full, $2 million, Navy development effort was requested on 3 September 1942 and approved the following day.

[[File:US-bombe.jpg|thumb|US Navy bombe. It contained 16 four-rotor Enigma-equivalents and was much faster than the British bombe.]]
Commander Edward Travis, Deputy Director and [[Francis Birch (cryptographer)|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 [[1943 BRUSA Agreement|BRUSA]] to being the forerunner of the [[UK–USA Security Agreement|UKUSA Agreement]]", being the first agreement "to establish the special [[signals intelligence|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".<ref>{{Harvnb|Erskine|1999|pp=187–197}}</ref> It established a relationship of "full collaboration" between Bletchley Park and OP-20-G.<ref>{{Harvnb|Budiansky|2000|p=239}}</ref>

An all electronic solution to the problem of a fast bombe was considered,<ref>{{Harvnb|Budiansky|2000|p=241}}</ref> but rejected for pragmatic reasons, and a contract was let with the [[NCR Corporation|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]], a brilliant inventor and engineer. He had already been working on electronic counting devices.<ref>{{citation |last=Desch |first=Joseph R. |author-link=Joseph Desch |title=1942 Research Report |date=21 January 1942 |url=https://www.daytoncodebreakers.org/wp-content/uploads/42rep.pdf |access-date=20 July 2013}}</ref>

Alan Turing, who had written a memorandum to OP-20-G (probably in 1941),<ref>{{Harvnb|Turing|c. 1941|pp=341–352}}</ref> 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.<ref>{{citation |title=Bletchley Park Text: November 1942: Departure of Alan Turing from BP |url=http://cipherweb.open.ac.uk/cgi-bin/cipher-demo/mobile/sms_categories_xml.py? |access-date=16 April 2010}}{{dead link|date=August 2017 |bot=InternetArchiveBot |fix-attempted=yes}}</ref> He visited OP-20-G, and went to NCR in Dayton on 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]].<ref>{{Harvnb|Budiansky|2000|p=242}}</ref> 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, but were very much faster. The first machine was completed and tested on 3 May 1943. Soon these bombes were more available than the British bombes at Bletchley Park and its outstations, and as a consequence they were put to use for Hut 6 as well as Hut 8 work.<ref name="Welchman97p135" >{{Harvnb|Welchman|1997|p=135}}</ref> A total of 121 Navy bombes were produced.<ref name=WengerWilcoxP52/>

The US Army also produced a version of a bombe. It was physically very different from the British and US Navy bombes. A contract was signed with [[Bell Labs]] on 30 September 1942.<ref>{{Harvnb|Sebag-Montefiore|2004|p=254}}</ref> 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.<ref name="Welchman97p135"/><ref name=WengerWilcoxP52/> The set of ten bombes consisted of a total of 144 Enigma-equivalents, each mounted on a rack approximately {{convert|7|ft|m}} long {{convert|8|ft|m}} high and {{convert|6|in|mm}} 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.<ref name=WengerWilcoxP51 >{{Harvnb|Wenger|1945|p=51}}</ref> A 3-rotor run took about 10 minutes.<ref name=WengerWilcoxP52 >{{Harvnb|Wenger|1945|p=52}}</ref>

===German suspicions===
The German navy was concerned that Enigma could be compromised. They printed key schedules in water-soluble inks so that they could not be salvaged.<ref name="Kahn 1991 201">{{harvnb|Kahn|1991|p=201}}</ref> They policed their operators and disciplined them when they made errors that could compromise the cipher.<ref>{{harvnb|Kahn|1991|pp=45–46}}</ref> The navy minimised its exposure. For example, ships that might be captured or run aground did not carry Enigma machines. When ships were lost in circumstances where the enemy might salvage them, the Germans investigated.<ref>{{harvnb|Kahn|1991|p=199}}</ref> After investigating some losses in 1940, Germany changed some message indicators.<ref>{{harvnb|Kahn|1991|p=200}}</ref>

In April 1940, the British [[Battles of Narvik|sank eight German destroyers in Norway]]. The Germans concluded that it was unlikely that the British were reading Enigma.<ref name="Kahn 1991 201"/>

In May 1941, the British deciphered some messages that gave the location of some supply ships for the [[German battleship Bismarck|battleship ''Bismarck'']] and the [[German cruiser Prinz Eugen|cruiser ''Prinz Eugen'']]. As part of the ''[[Operation Rheinübung]]'' commerce raid, the Germans had assigned five tankers, two supply ships, and two scouts to support the warships. After the ''Bismarck'' was sunk, the British directed its forces to sink the supporting ships ''Belchen'', ''Esso Hamburg'', ''Egerland'', and some others. The Admiralty specifically did not target the tanker ''Gedania'' and the scout ''Gonzenheim'', figuring that sinking so many ships within one week would indicate to Germany that Britain was reading Enigma. However, by chance, British forces found those two ships and sank them.<ref>{{harvnb|Kahn|1991|pp=201–202}}</ref> The Germans investigated, but concluded Enigma had not been breached by either seizures or brute-force cryptanalysis. Nevertheless, the Germans took some steps to make Enigma more secure. Grid locations (an encoded latitude and longitude) were further disguised using digraph tables and a numeric offset.<ref>{{harvnb|Kahn|1991|pp=204–205}}</ref> The U-boats were given their own network, ''Triton'', to minimise the chance of a cryptanalytic attack.

In August 1941, the British captured {{GS|U-570||2}}. The Germans concluded the crew would have destroyed the important documents, so the cipher was safe. Even if the British had captured the materials intact and could read Enigma, the British would lose that ability when the keys changed on 1 November.<ref name="Kahn 1991 206">{{harvnb|Kahn|1991|p=206}}</ref>

Although Germany realised that convoys were avoiding its [[wolfpack (naval tactic)|wolfpacks]], it did not attribute that ability to reading Enigma traffic. Instead, [[Karl Dönitz|Dönitz]] thought that Britain was using radar and direction finding.<ref name="Kahn 1991 206"/> The ''Kriegsmarine'' continued to increase the number of networks to avoid superimposition attacks on Enigma. At the beginning of 1943, the ''Kriegsmarine'' had 13 networks.<ref>{{harvnb|Kahn|1991|p=209}}</ref>

The ''Kriegsmarine'' also improved the Enigma. On 1 February 1942, it started using the four-rotor Enigma.<ref>{{harvnb|Kahn|1991|p=210}}</ref> The improved security meant that convoys no longer had as much information about the whereabouts of wolfpacks, and were therefore less able to avoid areas where they would be attacked. The increased success of wolfpack attacks following the strengthening of the encryption might have given the Germans a clue that the previous Enigma codes had been broken. However, that recognition did not happen because other things changed at the same time: the United States had entered the war, and Dönitz had sent U-boats to raid the US East Coast, where there were many easy targets.<ref>{{harvnb|Kahn|1991|pp=210–211}}</ref>

In early 1943, Dönitz was worried that the Allies were reading Enigma. Germany's own cryptanalysis of Allied communications showed surprising accuracy in its estimates of wolfpack sizes. It was concluded, however, that Allied direction finding was the source. The Germans also recovered a [[cavity magnetron]], used to generate radar waves, from a downed British bomber. The conclusion was that the Enigma was secure. The Germans were still suspicious, so each submarine got its own key net in June 1944.<ref>{{harvnb|Kahn|1991|pp=260–262}}</ref>

By 1945, almost all German Enigma traffic (Wehrmacht military; comprising the [[German Army (Wehrmacht)|Heer]], Kriegsmarine, and Luftwaffe; and German intelligence and security services like the Abwehr, SD, etc.) could be decrypted within a day or two, yet the Germans remained confident of its security.<ref>{{Harvnb|Ferris|2005|p=165}}</ref> They openly discussed their plans and movements, handing the Allies huge amounts of information, not all of which was used effectively. For example, Rommel's actions at [[Battle of Kasserine Pass|Kasserine Pass]] were clearly foreshadowed in decrypted Enigma traffic, but the Americans did not properly appreciate the information.{{citation needed|date=August 2012}}

After the war, Allied [[TICOM]] project teams found and detained a considerable number of German cryptographic personnel.{{sfn|Rezabek|2017}} Among the things learned was that German cryptographers, at least, understood very well that Enigma messages might be read; they knew Enigma was not unbreakable.{{sfn|Huttenhain|Fricke|1945|pp=4,5}} They just found it impossible to imagine anyone going to the immense effort required.<ref>{{Harvnb|Bamford|2001|p=17}}</ref> When Abwehr personnel who had worked on [[Fish (cryptography)|Fish cryptography]] and Russian traffic were interned at [[Rosenheim]] around May 1945, they were not at all surprised that Enigma had been broken,{{cn|date=January 2025}}{{dubious|date=January 2025}}<!--The revelation about the existence of Enigma was not made until 1973--> only that someone had mustered all the resources in time to actually do it. Admiral [[Karl Dönitz|Dönitz]] had been advised that a cryptanalytic attack was the least likely of all security problems.{{citation needed|date=January 2020}}