Editing Cryptanalysis of the Enigma (section)

===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>