v • d • eThe Enigma cipher machine
The Bombe replicated the action of several Enigma machines wired together. The Enigma machine is any one of a family of related electro-mechanical Rotor machines used to generate Ciphers for the Encryption and decryption of This article contains technical details about the rotors of the Enigma machine. The Enigma machines were a family of portable Cipher machines The Biuro Szyfrów ( Polish for " Cipher Bureau " was the Polish Interwar agency charged with both Cryptography (the The method of perforated sheets was a cryptologic technique used by the Polish Cipher Bureau before World War II, and during the war by The Bomba, or Bomba kryptologiczna ( Polish for " Bomb " or " Cryptologic bomb " was a special-purpose Enigma "doubles" were machines produced by the Polish Cipher Bureau, based on Marian Rejewski 's reconstruction of The cyclometer was a cryptologic device designed in the end of 1936 by Marian Rejewski, of the Polish Cipher Bureau 's German section (BS-4 to facilitate Bletchley Park, also known as Station X, is an estate located in the town of Bletchley, in Buckinghamshire, and (since 1967 part of Milton Keynes Banburismus was a process invented by Alan Turing at Bletchley Park in England during the Second World War. John W Herivel (born 1918 is a British Science historian and former World War II Codebreaker at Bletchley Park. Hut 6 was a wartime section of Bletchley Park tasked with the solution of German Army and Air Force Enigma machine ciphers Hut 8 was a section at Bletchley Park (the British World War II Codebreaking station tasked with solving German naval Enigma messages PC Bruno was a Polish - French intelligence station that operated outside Paris during World War II. ULTra ("Urban Light Transport" is a Personal rapid transit system from Advanced Transport Systems Ltd a company based in Cardiff, Wales. Each of the rapidly rotating drums, pictured above in a Bletchley Park museum mockup, simulated the action of an Enigma rotor. Bletchley Park, also known as Station X, is an estate located in the town of Bletchley, in Buckinghamshire, and (since 1967 part of Milton Keynes

In the history of cryptography, the Bombe was an electromechanical device used by British cryptologists to help break German Enigma machine signals during World War II. The history of Cryptography begins thousands of years ago Until recent decades it has been the story of what might be called classic cryptography — that is of The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located See also CategoryCryptographers for an exhaustive list Pre twentieth century Charles Babbage, UK, 19th century Mathematician Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. The Enigma machine is any one of a family of related electro-mechanical Rotor machines used to generate Ciphers for the Encryption and decryption of World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including The bombe was designed by Alan Turing, with an important refinement suggested by Gordon Welchman. Alan Mathison Turing, OBE, FRS (ˈt(jʊ(ərɪŋ (23 June 1912 &ndash 7 June 1954 was an English Mathematician (William Gordon Welchman ( June 15, 1906 – October 8, 1985) was a British mathematician and World War II Codebreaker

The Bombe was named after, and inspired by, a cryptologic device designed in 1938 by Polish Cipher Bureau cryptologist Marian Rejewski, and known as the "cryptologic bomb" (Polish: "bomba kryptologiczna"). The Biuro Szyfrów ( Polish for " Cipher Bureau " was the Polish Interwar agency charged with both Cryptography (the Marian Adam Rejewski ( 16 August 1905 &ndash 13 February 1980 was a Polish Mathematician and cryptologist who in 1932 solved the Enigma machine The Bomba, or Bomba kryptologiczna ( Polish for " Bomb " or " Cryptologic bomb " was a special-purpose Polish ( język polski, polszczyzna) is the Official language of Poland. They were also referred to by Group Captain Winterbotham as "Bronze Goddesses" because their cases were made of bronze,[1] but they were more prosaically described by operators as being "like great big metal bookcases". [2]

A standard services Enigma employed, at any one time, a set of three rotors, each of which could be set in any of 26 positions. In Cryptography, a rotor machine is an electro-mechanical device used for encrypting and decrypting secret messages The bombe tried each possible rotor position and applied a certain test. The test eliminated thousands of positions of the three rotors; the few potential solutions were then examined by hand. In order to use a bombe, however, a cryptanalyst first had to produce a "crib" – a section of ciphertext for which he could guess the corresponding plaintext. In Cryptanalysis, a crib is a sample of Known plaintext, or suspected plaintext; the term originated at Bletchley Park, the British In Cryptography, plaintext is the information which the sender wishes to transmit to the receiver(s

## The Enigma machine

Main article: Enigma machine
The German Enigma plugboard (Steckerbrett), shown here with no cables connected, greatly improved the security of the machine. The Enigma machine is any one of a family of related electro-mechanical Rotor machines used to generate Ciphers for the Encryption and decryption of When in use, there can be up to 13 connections.
The Bombe.

The German Army and Air Force Enigma machines used a stack of three rotors with 26 electrical contacts on each end. The wiring between the input and output contacts within each rotor was scrambled. The three rotors were connected to a non-rotating reflecting drum, or reflector, which redirected electrical current back in reverse order through the rotors. The Enigma machine is any one of a family of related electro-mechanical Rotor machines used to generate Ciphers for the Encryption and decryption of The set of rotors and the reflector is termed the scrambler, denoted by S in this article. Each rotor could be set into one of 26 positions, resulting in 26 × 25 × 26 = 16,900 (not 26 X 26 X 26 because of the double stepping of the second rotor, see [1]). possible ways the rotor stack could rearrange the letters of the alphabet. The initial positions of the rotors formed part of the secret key of the Enigma, and the purpose of the bombe was to recover these positions of the rotors. At each step of the encryption, at least one of the rotors (the "fast rotor") advanced a position. At certain points the other rotors were also advanced, but when using the bombe, it was, for a small stretch of letters, assumed that only the fast rotor moved, and that the others remained stationary. We denote this by writing S1 for some given position of the scrambler, and S2 for the same position but with the fast rotor advanced one position, and similarly S3, S4 and so forth.

An additional complication in the German military Enigma machines was a plugboard (Steckerbrett in German, shortened to "Stecker") that further scrambled the letters. The large number of possible stecker wirings made cryptanalysis much more difficult. 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. Here, we denote the plugboard by P. Because the plugboard simply swapped pairs, applying P twice restored the original, so that P(P(x)) = x.

The encryption can be viewed as first applying P, then S, then P again. Mathematically, the Enigma encryption E can be written: E(x) = P(S(P(x))). The Enigma also has a "self-reciprocal" property: decryption is the same as encryption, so that E(E(x)) = x.

## The principle of the bombe

A deduction step used by the bombe; while the actual intermediate values after the plugboard P – the "steckered" values – are unknown, if one is guessed then it is possible to use the crib to deduce other steckered values. Here, a guess that P(A)=Y can be used to deduce that P(T)=Q because A and T are linked at the 10th position in the crib.

In the bombe, a set of rotors with the same internal wiring as the German Enigma rotors was used – but designed to be spun by a motor, stepping through all possible rotor settings. The bombe rotors had a double set of contacts and wiring to emulate the Enigma reflection. A bombe would consist of a number of these sets of rotors wired up according to a menu prepared by codebreakers. At each position of the rotors, an electrical test would be applied. For a large number of the settings, the test would lead to a logical contradiction, ruling out that setting. If the test did not lead to a logical contradiction, the machine would stop and ring a bell, and the candidate solution would be examined further, typically on a replica of the German Enigma machine, to see if that decryption produced German. The German language (de ''Deutsch'') is a West Germanic language and one of the world's major languages. There might be incorrect guesses and many false matches before the correct match was found.

### Cribs

The test worked by making deductions from a short piece of known (or guessed) plaintext, known as a crib. For example, a codebreaker might suspect that the phrase ATTACKATDAWN was the message corresponding to a certain stretch of ciphertext, say, WSNPNLKLSTCS:

 Position 1 2 3 4 5 6 7 8 9 10 11 12 Crib A T T A C K A T D A W N Ciphertext W S N P N L K L S T C S

Finding cribs was not always straightforward; it required considerable familiarity with German military jargon and the communication habits of the operators (see crib). In Cryptanalysis, a crib is a sample of Known plaintext, or suspected plaintext; the term originated at Bletchley Park, the British However, the codebreakers were aided by the fact that the Enigma would never encrypt a letter to itself. This helped in locating the position of a crib in a plaintext, as it could rule out a number of positions where a letter from the crib "clashed" with the same letter in the ciphertext.

### The plugboard

The German military Enigma included a plugboard (P) which provided a secret wiring which swapped letters before and after the main scrambler (S). If there had been no plugboard, it would have been relatively straightforward to test a rotor setting; a replica 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 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. For example, in the first position, P(A) and P(W) were unknown because the plugboard settings were unknown.

The letters of a crib can be graphed to provide a menu which specifies how to set up a bombe run. Some sequences of letters form loops, or closures. This menu includes the loops ATLK, TNS and TAWCN. The more loops in the menu, the more candidate rotor settings the bombe can reject, and hence fewer false stops.

Turing's solution was to note that, even though the values for, say, P(A) or P(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 guess that P(A)=Y. Looking at position 10, we notice that A encrypts to T, or, expressed as a formula:

$\texttt{T} = P(S_{10}(P(\texttt{A})))$

Because P is its own inverse, we can apply the function to both sides to obtain the following equation:

$P(\texttt{T}) = S_{10}(P(\texttt{A}))$

This gives us a relationship between P(A) and P(T); if P(A)=Y, and for the rotor setting under consideration, S10(Y)=Q (say), we can deduce that

$P(\texttt{T}) = S_{10}(P(\texttt{A})) = S_{10}(\texttt{Y})=\texttt{Q}.$

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 P(T) is completely determined if P(A) is known.

Likewise, we can also observe that T encrypts to L at position 8. Using S8, we can deduce the steckered value for L as well using a similar argument, to get, say,

$P(\texttt{L}) = S_{8}(P(\texttt{T})) = S_{8}(\texttt{Q})=\texttt{G}.$

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:

$P(\texttt{K}) = S_{6}(P(\texttt{L})) = S_{6}(\texttt{G})=\texttt{F}.$

And again, the same sort of reasoning applies at position 7 to get:

$P(\texttt{A}) = S_{7}(P(\texttt{K})) = S_{7}(\texttt{F})=\texttt{N}.$

However, in this case, we have derived a contradiction, since, by hypothesis, we assumed that P(A)=Y at the outset. In Classical logic, a contradiction consists of a logical incompatibility between two or more Propositions It occurs when the propositions taken together yield This means that the initial assumption must have been incorrect, and so that (for this rotor setting) P(A)Y (this type of argument is termed "reductio ad absurdum" or "proof by contradiction"). Reductio ad absurdum ( Latin for "reduction to the absurd" also known as an apagogical argument, reductio ad impossibile

For a single setting of the rotors, a cryptanalyst could try each possibility for P(A); if all of the possibilities lead to a contradiction, then the rotor setting can be eliminated from consideration. The bombe mechanises this process, performing the logical deductions near-instantaneously using electrical connections, and repeating the test for all 17,576 possible settings of the rotors.

### Automating deduction using an electrical circuit

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. (William Gordon Welchman ( June 15, 1906 – October 8, 1985) was a British mathematician and World War II Codebreaker His suggestion was an attachment called the diagonal board that further improved the bombe's effectiveness. [3]

## The British bombe

The bombes were built by the British Tabulating Machine Company at Letchworth. The British Tabulating Machine Company (BTM was a firm which manufactured and sold Hollerith punched-card machines and other data-processing equipment For the US businessman see William Pryor Letchworth. For the New York State Park see Letchworth State Park. The machine was built under the direction of Harold 'Doc' Keen and was codenamed CANTAB. Harold Hall "Doc" Keen (1894–1973 was a British Engineer who oversaw the construction of the British Bombe, a Codebreaking machine Each British bombe was about 7 feet wide, 6 feet 6 inches tall and 2 feet deep and weighed about a ton. On the front of each bombe were 108 places where rotors could be mounted. The rotors were in three groups of 12 triplets. Each triplet, arranged vertically, corresponded to the three Enigma rotors. The bombe rotors had a double set of contacts and wiring to emulate the Enigma reflection. The input and output of each triplet of rotors went to cable connectors, allowing the bombe to be rewired according to the Turing and Welchman methodologies as applied to individual ciphertexts.

## History and use

At the rear of the machine, the Bombe required a large amount of complex plugging to connect the drums according to the settings in the menu. This is only a partially-complete Bombe rebuild at the Bletchley Park museum. Bletchley Park, also known as Station X, is an estate located in the town of Bletchley, in Buckinghamshire, and (since 1967 part of Milton Keynes

Using Polish cryptological techniques, British cryptanalysts at Bletchley Park were, at the beginning of World War II, able to read Enigma messages by exploiting weaknesses in German operating procedures. Bletchley Park, also known as Station X, is an estate located in the town of Bletchley, in Buckinghamshire, and (since 1967 part of Milton Keynes The British cryptologists were concerned that the Germans might at any moment change their procedures, rendering those cryptological methods obsolete.

To preempt this, British mathematician Alan Turing designed the bombe on a more general principle – the assumption of the presence of text that analysts could guess somewhere in the message, a cryptanalytical technique known as cribbing, also termed a "known-plaintext attack. Alan Mathison Turing, OBE, FRS (ˈt(jʊ(ərɪŋ (23 June 1912 &ndash 7 June 1954 was an English Mathematician The known-plaintext attack (KPA is an Attack model for Cryptanalysis where the attacker has samples of both the Plaintext and its encrypted " (Actually, the Poles had likewise exploited "cribs," e. g. the Germans' use of "ANX" — German for "To," followed by "X" as a spacer. )

The first bombe, which was based on Turing's original design and so lacked a diagonal board, arrived at Bletchley Park in March 1940 and was named "Victory. Year 1940 ( MCMXL) was a Leap year starting on Monday (link will display the full 1940 calendar of the Gregorian calendar. " The second bombe – "Agnus" – was equipped with Welchman's diagonal board, and was installed on 8 August 1940; bombes of this type were called "Spider" bombes. Events 1220 - Sweden is defeated by Estonian tribes in the Battle of Lihula. Year 1940 ( MCMXL) was a Leap year starting on Monday (link will display the full 1940 calendar of the Gregorian calendar.

By the end of March 1941, a more advanced version of the Bombe had been developed, the "Jumbo" machine.

During 1940, 178 messages were broken on the two machines, nearly all successfully. By the end of 1941, there were 16 bombes in use. By the end of 1942, this had increased to 49; at the end of 1943, that figure had more than doubled to 99 bombes in operation. By May 1945, there were 211 operational machines, requiring nearly 2,000 staff to run.

The Germans generally changed settings each day at midnight; the British goal was to find the new settings before the day was out, preferably by noon. With a motor spinning at 120 RPM, all permutations could be tested in under 6 hours. On average, it took half that time to find the correct match.

There were five bombe outstations off-site at Adstock, Gayhurst, Wavendon, Stanmore, and Eastcote. Adstock is a Village and Civil parish within Aylesbury Vale district in Buckinghamshire, England, about 3 miles north west of Gayhurst is a Village and Civil parish in the Borough of Milton Keynes, ceremonial Buckinghamshire in England. Wavendon is a Village and Civil parish in the south east of the Borough of Milton Keynes and ceremonial Buckinghamshire, England. Stanmore is a place in the London Borough of Harrow, England It is a suburban development situated 11 miles (18 km north west of Charing Cross. Eastcote is a place in the London Borough of Hillingdon. The 2001 UK census gave the population of the Eastcote and South Ruislip Ward as 11480

Once the British had given the Americans the details about the bombe and its use, the US had the National Cash Register Company manufacture a great many additional bombes, which they (the US) then used to assist in the code-breaking. NCR Corporation ( is a technology company specializing in products for the retail and financial sectors These ran much faster than the British version, so fast that unlike the British model, which would freeze immediately (and ring a bell) when a possible solution was detected, the NCR model, upon detecting a possible solution, had to "remember" that setting and then reverse its rotors to back up to it (meanwhile the bell rang).

After World War II, some fifty bombes were retained at Eastcote, while the rest were destroyed. Eastcote is a place in the London Borough of Hillingdon. The 2001 UK census gave the population of the Eastcote and South Ruislip Ward as 11480 The surviving bombes were put to work, possibly on Eastern bloc ciphers (Smith, 1998). During the Cold War, the term Communist Bloc (or Soviet Bloc) was used to refer to the Soviet Union and countries it either controlled or that were 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. "

In September 2006, it was announced that a team led by John Harper were nearing the end of a 10 year-long project to reconstruct a working Bombe[2].

## The challenge of the four rotor Enigma machine

US bombe

By late 1941 the change in German Navy fortunes, combined with intelligence reports, convinced Admiral Karl Dönitz that the Allies could read German Navy communications, and a thin fourth rotor with unknown wiring was added to German Navy Enigmas to produce the Triton system. Karl Dönitz (ˈdøːnɪts) (16 September 1891 &ndash 24 December 1980 was a German naval Commander who served 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.

That spring was the "second happy time" for the submarines, with renewed German success in attacking Allied shipping due to the security of their own communications and their ability to read convoy messages sent in Allied Naval Cipher No. The Second Happy Time was the informal name for a phase in the Second Battle of the Atlantic during which Axis Submarines attacked Merchant shipping 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 blackouts of coastal cities so that ships would not be silhouetted against their lights, but this yielded only slightly improved security for Allied shipping.

A crash program was begun at Bletchley Park to design bombes that could decrypt the four-rotor system, with delivery scheduled for August or September 1942. Bletchley Park, also known as Station X, is an estate located in the town of Bletchley, in Buckinghamshire, and (since 1967 part of Milton Keynes The urgent need, doubts about the British design, and slow progress with it prompted the US to start investigating designs for a parallel effort, based in part on wiring diagrams provided to US Navy officers during a visit to Bletchley Park in July 1942. Funding for a full US development effort was requested on 3 September 1942 and approved the following day. Events 36 BC - In the Battle of Naulochus, Marcus Vipsanius Agrippa, Admiral of Octavian, defeats Sextus Pompeius Development was led by Joseph Desch of the National Cash Register Company at the United States Naval Computing Machine Laboratory in Dayton, Ohio. Joseph Desch (1907&ndash August 3 1987) was an American engineer NCR Corporation ( is a technology company specializing in products for the retail and financial sectors The United States Naval Computing Machine Laboratory was a highly secret design and manufacturing site for Code-breaking machinery located in Building 26 of the National Dayton is a city in southwestern Ohio, United States. It is the County seat and largest city of Montgomery County.

The U. S. bombes became available starting in late May 1943. They were 10 feet wide, 7 feet high, 2 feet deep and weighed 2 1/2 tons. About 120 were made before production was stopped in September 1944 due to rapid progress in the war. Year 1944 ( MCMXLIV) was a Leap year starting on Saturday (link will display full calendar of the Gregorian calendar. The last-manufactured United States bombe is on display at the National Cryptologic Museum. The United States National Cryptologic Museum is a museum of cryptologic history affiliated with the National Security Agency (NSA Jack Ingram, 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.

• Cryptanalysis of the Enigma
• Cryptologic bomb - a special-purpose machine designed about October 1938 by Polish Cipher Bureau cryptologist Marian Rejewski to break German Enigma machine ciphers. The Enigma machines were a family of portable Cipher machines The Bomba, or Bomba kryptologiczna ( Polish for " Bomb " or " Cryptologic bomb " was a special-purpose The Biuro Szyfrów ( Polish for " Cipher Bureau " was the Polish Interwar agency charged with both Cryptography (the Marian Adam Rejewski ( 16 August 1905 &ndash 13 February 1980 was a Polish Mathematician and cryptologist who in 1932 solved the Enigma machine
• Colossus computer
• Heath Robinson

## References

1. ^ Winterbotham, F. The Colossus machines were electronic Computing devices used by British codebreakers to read Encrypted German messages during Heath Robinson was a machine used by British Codebreakers at Bletchley Park during World War II to solve messages in a German Teleprinter cipher W. (2001 [1974]). The ULTRA Secret. Orion Books Ltd, 15. ISBN 0-75283-751-6.
2. ^ Mary Stewart, 'Bombe' Operator, interviewed in "The Men Who Cracked Enigma", UKTV History Channel documentary series "Heroes of World War II", 2003
3. ^ Welchman, G. (1998 [1982]). The Hut Six story. Hut 6 was a wartime section of Bletchley Park tasked with the solution of German Army and Air Force Enigma machine ciphers M&M baldwin, 77. ISBN 0-947712-34-8.
• Donald Davies, "The Bombe – a Remarkable Logic Machine," Cryptologia, 23(2), April 1999, pp. Cryptologia is a journal in Cryptography published quarterly since January 1977. 108–138.
• Donald Davies, "Effectiveness of the Diagonal Board," Cryptologia, 23(3), July 1999, pp. Cryptologia is a journal in Cryptography published quarterly since January 1977. 229–239.
• John Keen, "Harold 'Doc' Keen and the Bletchley Park bombe," 2003.
• Michael Smith, Station X, Channel 4 Books, 1998, ISBN 0-330-41929-3.
• Gordon Welchman, The Hut Six Story: Breaking the Enigma Codes, M&M Baldwin, 1997, 1998, ISBN 0-947712-34-8. (William Gordon Welchman ( June 15, 1906 – October 8, 1985) was a British mathematician and World War II Codebreaker