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Encyclopedia > Cryptanalysis of the Enigma
The Enigma cipher machine

Enigma is the name of a family of ciphering machines made famous by their use in World War II and the successful analysis of the cipher by Allied codebreakers. This article discusses the techniques for solving Enigma and the circumstances in which they were developed and applied. See Enigma machine for a description of the machine itself, and Ultra for a discussion of the intelligence gained from reading Enigma. A three-rotor German military Enigma machine showing, from bottom to top, the plugboard, the keyboard, the lamps and the finger-wheels of the rotors emerging from the inner lid (version with labels). ... This article contains technical details about the rotors of the Enigma machine. ... Diagram of cyclometer, from Marian Rejewski’s papers The cyclometer was a cryptologic device designed by the Polish Cipher Bureau (BS-4) to help decrypt the German Enigma machine during the 1930s. ... The method of perforated sheets was a codebreaking technique used against the Enigma machine (see Cryptanalysis of the Enigma). ... The bomba (plural bomby) was a special-purpose codebreaking machine designed by Polish cryptanalysts and used to crack the German Enigma machine prior to World War II. A bomba was designed to exploit an obscure but fatal weakness in the Enigma cipher. ... The Bombe replicated the action of several Enigma machines wired together. ... Ultra (sometimes capitalised ULTRA) was the name used by the British for intelligence resulting from decryption of German communications in World War II. The term eventually became the standard designation in both Britain and the United States for all intelligence from high-level cryptanalytic sources. ... This article is about algorithms for encryption and decryption. ... Combatants Allies: • Soviet Union, • UK & Commonwealth, • USA, • France/Free France, • China, • Poland, • ...and others Axis: • Germany, • Japan, • Italy, • ...and others Commanders Strength Casualties Full list Full list World War II, also known as the Second World War, was a large scale military conflict that took place between 1939 and 1945. ... Cryptanalysis (from the Greek kryptós, hidden, and analýein, to loosen or to untie) is the study of methods for obtaining the meaning of encrypted information without access to the secret information which is normally required to do so. ... A three-rotor German military Enigma machine showing, from bottom to top, the plugboard, the keyboard, the lamps and the finger-wheels of the rotors emerging from the inner lid (version with labels). ... Ultra (sometimes capitalised ULTRA) was the name used by the British for intelligence resulting from decryption of German communications in World War II. The term eventually became the standard designation in both Britain and the United States for all intelligence from high-level cryptanalytic sources. ...

Contents


Strengths of Enigma

The Enigma machine was used commercially from the early 1920s on, and was also adopted by the military and governmental services of a number of nations — most famously, by Nazi Germany before and during World War II (WWII).
The Enigma machine was used commercially from the early 1920s on, and was also adopted by the military and governmental services of a number of nations — most famously, by Nazi Germany before and during World War II (WWII).

Enigma was designed to defeat basic cryptanalysis techniques by continually changing the substitution alphabet. Like other rotor machines, it implemented a polyalphabetic substitution cipher with a long period. With single-notched rotors, the period of the machine was 16,900 (26 × 25 × 26). This long period helped protect against overlapping alphabets. Image File history File links Download high resolution version (1414x1886, 480 KB) Enigma Machine at the Imperial War Museum, London. ... Image File history File links Download high resolution version (1414x1886, 480 KB) Enigma Machine at the Imperial War Museum, London. ... A three-rotor German military Enigma machine showing, from bottom to top, the plugboard, the keyboard, the lamps and the finger-wheels of the rotors emerging from the inner lid (version with labels). ... The 1920s were a decade sometimes referred to as the Jazz Age or the Roaring Twenties, usually applied to America. ... Nazi Germany, or the Third Reich, commonly refers to Germany in the years 1933–1945, when it was under the firm control of the totalitarian and fascist ideology of the Nazi Party, with the Führer Adolf Hitler as dictator. ... Combatants Allies: • Soviet Union, • UK & Commonwealth, • USA, • France/Free France, • China, • Poland, • ...and others Axis: • Germany, • Japan, • Italy, • ...and others Commanders Strength Casualties Full list Full list World War II, also known as the Second World War, was a large scale military conflict that took place between 1939 and 1945. ... In cryptography, a substitution cipher is a method of encryption by which units of plaintext are substituted with ciphertext according to a regular system; the units may be single letters (the most common), pairs of letters, triplets of letters, mixtures of the above, and so forth. ... In cryptography, a rotor machine is a electro-mechanical device used for encrypting and decrypting secret messages. ... A polyalphabetic cipher is any cipher based on substitution, using multiple substitution alphabets. ...


The Enigma machines added other possibilities. The sequence of alphabets used was different if the rotors were started in position ABC, as opposed to ACB; each rotor had a rotatable ring which could be set in different positions, and the starting position of each rotor was also variable. Most of the military Enigmas also featured a plugboard (German: Steckerbrett) which exchanged letters. Even so, this complex combination key could be easily communicated to another user, comprising as it did only a few simple items: rotors to be used, rotor order, ring positions, starting positions, and plugboard connections. Potentially this made the Enigma an excellent system. A key is a piece of information that controls the operation of a cryptography algorithm. ...


Involution

The fact that encipherment was the same operation as decipherment was, at the time, considered to be an advantage of the Enigma. The most common versions were symmetrical in the sense that decipherment works in the same way as encipherment — when one types in the ciphertext, the sequence of lit lamps corresponds to the plaintext. However, this works only if the deciphering machine has the same starting configuration (that is, rotor choice, sequence, alphabet ring settings, and initial positions) as had the enciphering machine. These changed regularly (at first monthly, then weekly, then daily and even, toward war's end in some networks, more often) and were specified in key schedules distributed to Enigma users. In mathematics, an involution is a function that is its own inverse, so that f(f(x)) = x for all x in the domain of f. ... Decipherment is the analysis of documents written in ancient languages, where the language is unknown, or knowledge of the language has been lost. ... In cryptography, encryption is the process of obscuring information to make it unreadable without special knowledge. ...


Security properties

The various Enigma models provided different levels of security. The presence of a plugboard (Stecker) substantially increased the complexity of the machine. In general, unsteckered Enigma could be attacked using hand methods, while breaking versions with a plugboard was more involved, and often required the use of machines.


The Enigma machine had a number of properties that proved helpful to cryptanalysts. First, a letter could never be encrypted to itself (with the exception of the early models A and B, which lacked a reflector). This was of great help in finding cribs — short sections of plaintext that are known (or suspected) to be somewhere in a ciphertext. This property can be used to help deduce where the crib occurs. For a possible location, if any letter in the crib matches a letter in the ciphertext at the same position, the location can be ruled out; at Bletchley Park, this was termed a "crash." A three-rotor German military Enigma machine showing, from bottom to top, the plugboard, the keyboard, the lamps and the finger-wheels of the rotors emerging from the inner lid (version with labels). ... In cryptanalysis, a crib is a sample of known plaintext; the term originated at Bletchley Park, the British codebreaking operation during World War II (WWII). ... The plain text term has a different meaning. ... During World War II, British and American cryptographers at Bletchley Park broke a large number of Axis codes and ciphers, including the German Enigma machine. ...


Another property of the Enigma was that it was self-reciprocal: encryption is performed identically to decryption. This imposed constraints on the type of scrambling that Enigma could provide at each position, and this property was used in a number of codebreaking methods. In mathematics, an involution is a function that is its own inverse, so that f(f(x)) = x for all x in the domain of f. ...


A weakness of many Enigma models was that the rightmost rotor turned a constant number of places before the next rotor turned.


Apart from the less-than-ideal inherent characteristics of the machine, the way Enigma was used proved its greatest weakness in practice. Mistakes by operators were common, and a number of the officially-specified procedures for using Enigma provided avenues for attack. It has been suggested by some of those working on its cryptanalysis at Bletchley Park that the Enigma would have been unbreakable in practice had its operators not been so error-prone, and had its operating procedures been better thought out[citation needed].


Unsteckered Enigma

The unsteckered Enigma — Enigma without a plugboard — was solved relatively easily. The British read messages sent during the Spanish Civil War, and also read some Italian traffic enciphered early in World War II (see Ultra). The Spanish Civil War (July 1936–April 1939) was a conflict in which the incumbent Second Spanish Republic and political left-wing groups fought against a right-wing nationalist insurrection led by General Francisco Franco, who eventually succeeded in ousting the Republican government and establishing a dictatorship. ... Ultra (sometimes capitalised ULTRA) was the name used by the British for intelligence resulting from decryption of German communications in World War II. The term eventually became the standard designation in both Britain and the United States for all intelligence from high-level cryptanalytic sources. ...


Solution before World War II

The Saxon Palace, in Warsaw, where German Enigma ciphers were first broken (1932).

In early 1930s the German Army began using a Enigma with a plugboard, greatly increasing its security. While British and French cryptanalysts had no success with this version of Enigma, their Polish counterparts, starting with the work of Marian Rejewski, were able to solve the rotor wiring and read German Enigma traffic. Image File history File links Palac_Saski_(2). ... Image File history File links Palac_Saski_(2). ... Rendering of the Saxon Palace, as it is to be rebuilt. ... // Events and trends A public speech by Benito Mussolini, founder of the Fascist movement The 1930s were described as an abrupt shift to more radical lifestyles, as countries were struggling to find a solution to the global depression. ... Marian Rejewski (probably 1932, the year he broke Enigma). ...


In December 1932, a 27-year-old Polish mathematician, Marian Rejewski, who had joined the Polish Cipher Bureau in September that year, made one of the most important breakthroughs in cryptologic history by using algebraic mathematical techniques to solve the Enigma wiring. This article is in need of attention from an expert on the subject. ... Marian Rejewski (probably 1932, the year he broke Enigma). ... The Biuro Szyfrów ( (?), Polish for Cipher Bureau) was the Polish agency concerned with cryptology between World Wars I and II. The Bureau enjoyed notable successes against Soviet cryptography during the Polish-Soviet War, helping to preserve Polands independence. ... Cryptography (from Greek kryptós, hidden, and gráphein, to write) is, traditionally, the study of means of converting information from its normal, comprehensible form into an incomprehensible format, rendering it unreadable without secret knowledge — the art of encryption. ...


At the time, the indicator procedure was to encrypt an operator-selected message setting twice, with the machine at its "ground setting," and to place the twice-encrypted message setting at the opening of the message. For instance, if an operator picked QRS as their 'message setting', the operator would set the machine to the day's ground settings, and then type QRSQRS. This might be encrypted as JXDRFT. The feature of Enigma that Rejewski exploited was that the disk moved three positions between the two sets of QRS — knowing that J and R were originally the same letter, as were XF and DT, was vital information. Although the original letters were unknown, it was known that, while there were a huge number of rotor settings, there were only a small number of rotor wirings that would change a letter from J to R, X to F and D to T, and so on. Rejewski called these patterns chains. This article is about algorithms for encryption and decryption. ...


The Poles became very experienced in exploiting even very subtle cryptological mistakes the Germans made. A blatant one, however, was the printing of a complete set of plaintext-key-ciphertext as a training example in an early Enigma manual, a copy of which Rejewski managed to get his hands on.


Finding the proper chains from the 105,456 possibilities was a tremendous task. The Poles, particularly Rejewski's classmates Jerzy Różycki and Henryk Zygalski, developed a number of methods. The British had also developed such a technique when they succeeded in breaking the common commercial Enigma, though they failed to break the military versions of the Enigma. Jerzy Różycki, about 1928. ... Henryk Zygalski, about 1930. ...

Replica of a bombe machine
Enlarge
Replica of a bombe machine

Analysis of thousands of possibilities represents a vast human effort, if done by hand. To help in this, Marian Rejewski about October 1938 invented an electro-mechanical device which was dubbed the "cryptologic bomb": the name originated from the characteristic muffled noise it produced when operating; alternative names puckishly given the device by Polish Cipher Bureau personnel were "washing machine" and "mangle." The French and British later modified the spelling to "bombe." In mid-November 1938 the Polish bombs were ready, and reconstruction of daily keys went on apace. Rejewski has written about the device: "The bomb method, invented in the fall of 1938, consisted largely in the automation and acceleration of the process of reconstructing daily keys. Each cryptologic bomb (six were built in Warsaw for the Cipher Bureau before September 1939) essentially constituted an electrically powered aggregate of six Enigmas. It took the place of about one hundred workers and shortened the time for obtaining a key to about two hours." (Rejewski, in Kozaczuk, Enigma 1984, p. 290.) Cardboard replica of a British Bombe made for the movie Enigma and now on display at Bletchley Park. ... Cardboard replica of a British Bombe made for the movie Enigma and now on display at Bletchley Park. ... The Bombe replicated the action of several Enigma machines wired together. ... Marian Rejewski (probably 1932, the year he broke Enigma). ... Look up October in Wiktionary, the free dictionary. ... 1938 (MCMXXXVIII) was a common year starting on Saturday (link will take you to calendar). ... The bomba (plural bomby) was a special-purpose codebreaking machine designed by Polish cryptanalysts and used to crack the German Enigma machine prior to World War II. A bomba was designed to exploit an obscure but fatal weakness in the Enigma cipher. ... The Biuro Szyfrów ( (?), Polish for Cipher Bureau) was the Polish agency concerned with cryptology between World Wars I and II. The Bureau enjoyed notable successes against Soviet cryptography during the Polish-Soviet War, helping to preserve Polands independence. ... Look up November in Wiktionary, the free dictionary. ... 1938 (MCMXXXVIII) was a common year starting on Saturday (link will take you to calendar). ... 1938 (MCMXXXVIII) was a common year starting on Saturday (link will take you to calendar). ... Warsaw (Polish Warszawa, (?), in full The Capital City of Warsaw, Polish: Miasto Stołeczne Warszawa) is the capital of Poland and its largest city. ... In the history of cryptography, the Biuro Szyfr w was the Cypher Bureau of Polish Military Intelligence. ... 1984 (MCMLXXXIV) was a leap year starting on Sunday of the Gregorian calendar. ...


The Poles were able to decrypt a large portion of German Enigma traffic from December 1932. Rejewski had been aided in his reconstruction of Enigma's wiring by documents obtained by French military intelligence from an agent in Berlin (Hans Thilo-Schmidt, codenamed Asché by the French) who had access to Enigma key-schedules and manuals. Look up December in Wiktionary, the free dictionary. ... 1932 (MCMXXXII) was a leap year starting on Friday (the link will take you to a full 1932 calendar). ... Military intelligence (abbreviated MI, int. ... Hans-Thilo Schmidt (13 May 1888 – 1943) code named Asché, was a spy who, during the 1930s, sold secrets about the Germans Enigma machine to the French. ...


However, in 1939 the German Army increased the complexity of its Enigma operating procedures. Initially only three rotors had been in use, and their sequence in the slots was changed periodically. Now two additional rotors were introduced; three of the five would be in use at any given time. The Germans also stopped transmitting a twice-enciphered individual three-letter message setting at the beginning of a message, thus putting an end to one of the Poles' original methods of cryptological attack. 1939 (MCMXXXIX) was a common year starting on Sunday (link will take you to calendar). ...


Polish intelligence had been reading Enigma-generated cryptograms since December 1932. Subsequent modifications in the machine and its operating procedures caused periodic "blackouts" requiring the Poles (and, after July 1939, also the British) to find new ways of breaking into the ciphers. In April and May 1939 Poland contracted military alliances with Britain and France. The Poles, realizing the pace and direction of changes in the European political situation, decided in mid-1939 to share their work. At a conference in Warsaw on July 25, 1939, they pledged to give the French and British each a Polish-reconstructed Enigma, along with details of Enigma-solving techniques that they had developed, such as Zygalski's "perforated sheets" and the "cryptologic bomb" (Polish: Bomba kryptologiczna). The two "Enigma doubles" were shipped to Paris, whence Gustave Bertrand brought one to London for the British, turning it over at Victoria Station, as he was to recall in his Enigma, to Stewart Menzies of Britain's Secret Intelligence Service. Until then, German military Enigma traffic had utterly defeated the British and French, and they had faced the disturbing prospect that German communications would remain "black" to them for the duration of the coming war. A cryptogram is a type of word puzzle popularly printed in some newspapers and magazines. ... Look up July in Wiktionary, the free dictionary July is the seventh month of the year in the Gregorian Calendar and one of seven Gregorian months with the length of 31 days. ... 1939 (MCMXXXIX) was a common year starting on Sunday (link will take you to calendar). ... July 25 is the 206th day (207th in leap years) of the year in the Gregorian calendar, with 159 days remaining. ... 1939 (MCMXXXIX) was a common year starting on Sunday (link will take you to calendar). ... The method of perforated sheets was a codebreaking technique used against the Enigma machine (see Cryptanalysis of the Enigma). ... The bomba (plural bomby) was a special-purpose codebreaking machine designed by Polish cryptanalysts and used to crack the German Enigma machine prior to World War II. A bomba was designed to exploit an obscure but fatal weakness in the Enigma cipher. ... Gustave Bertrand (died 1976) was a French military intelligence officer who made a vital contribution to the decryption, by Polands Cipher Bureau, of German Enigma ciphers beginning in December 1932. ... Victoria station may refer to: London Victoria station Manchester Victoria station Victoria tube station Victoria Station, a restaurant chain which uses real train boxcars as dining rooms. ... Sir Stewart Graham Menzies (January 30, 1890 - May 29, 1968) was the Chief of MI6, British Secret Intelligence Service, during and after the World War II. Stewart Graham Menzies was born in London into a wealthy family. ... The Secret Intelligence Service (SIS), more commonly known as MI6 (originally Military Intelligence Section 6), or the Secret Service or simply Six, is the United Kingdoms external security agency. ...


During the German invasion of Poland in September 1939, key Cipher Bureau personnel were evacuated southeastward and — after the Soviets invaded eastern Poland on September 17 — into Romania, on the way destroying their cryptologic equipment and documentation. Eventually, crossing Yugoslavia and still-neutral Italy, they reached France. There, at PC Bruno outside Paris, they resumed their work on breaking German Enigma ciphers, continuing it into the subsequent Battle of France. Look up September in Wiktionary, the free dictionary. ... 1939 (MCMXXXIX) was a common year starting on Sunday (link will take you to calendar). ... In the history of cryptography, the Biuro Szyfr w was the Cypher Bureau of Polish Military Intelligence. ... September 17 is the 260th day of the year (261st in leap years). ... PC Bruno was the code name for the intelligence station operated at a farmhouse in the west of France to which French cryptanalysts retired after Paris was captured by the Germans in 1940. ... The Eiffel Tower has become a symbol of Paris throughout the world. ... Combatants Allies (France, Britain, Canada, Poland, Belgium, Netherlands, Luxembourg) Germany, Italy Commanders Maurice Gamelin, Maxime Weygand (French) Lord Gort (British Expeditionary Force) Gerd von Rundstedt (Army Group A) Fedor von Bock (Army Group B) Wilhelm von Leeb (Army Group C) H.R.H. Umberto di Savoia (Army Group West) Strength...


Several months before the German invasion of France, in January 1940, British mathematician Alan Turing came to Bruno for several days to confer with his Polish mathematician colleagues. 1940 (MCMXL) was a leap year starting on Monday (the link is to a full 1940 calendar). ... Alan Turing is often considered the father of modern computer science. ...


After the French-German armistice, the Polish Cipher Bureau continued its work in France's southern "Free Zone" (Vichy France) and in French Algeria, at constant risk of discovery and imprisonment or worse. When Germany took over Vichy France in November 1942, the Poles once again had to flee. The Cipher Bureau's chiefs, Colonel Gwido Langer and Major Maksymilian Ciężki, and some of the technical staff were captured by the Germans but, despite extensive interrogation, managed to preserve the secret of Enigma decryption. The mathematicians Marian Rejewski and Henryk Zygalski, after a perilous Odyssey that took them across France, into a Spanish prison, to Portugal and at last by ship to Gibraltar, finally made it to Britain. (The third mathematician, Jerzy Różycki, had perished in the sinking of a passenger ship while returning in 1942 to southern France from a tour of duty in Algeria.) Look up November in Wiktionary, the free dictionary. ... This article is about the year. ... Gwido Langer (died March 30, 1948) was chief of the Polish General Staffs Cipher Bureau from at least mid-1931. ... In the early 1930s, as an Army captain, he was chief of the Polish Army General Staff Biuro Szyfrów (Cipher Bureau) German Section (BS4). ... Marian Rejewski (probably 1932, the year he broke Enigma). ... Henryk Zygalski, about 1930. ... Jerzy Różycki, about 1928. ... This article is about the year. ...


In Britain, Rejewski and Zygalski were inducted as privates into the Polish Army. Eventually they were promoted to second lieutenant, then lieutenant, and put to work breaking German SS and SD ciphers at a Polish signals facility in Boxmoor; they were not invited to work on Enigma at Bletchley Park. SS or ss or Ss may be: The Schutzstaffel, a Nazi paramilitary force Steamship (SS) (ship prefix) The United States Secret Service A submarine not powered by nuclear energy (SS) (United States Navy designator), see SSN A Soviet/Russian surface-to-surface missile, as listed by NATO reporting name Shortstop... SD or sd is an acronym that may mean: Sales and Distribution, business San Diego, a U.S. city SanDisk, a company that created the widley used SD Card Secure Digital, memory card format Sicherheitsdienst (German), Security Police, the intelligence service of the Nazi SS Snare drum Social Democrats (Slovenia... Boxmoor is a small suburb of Hemel Hempstead in Hertfordshire, England. ...


Until 1945, numerous enhancements were made to the system, although the Germans considered it unbreakable for all practical purposes.

See also: Cyclometer , Perforated sheets , Cryptologic bomb.

Diagram of cyclometer, from Marian Rejewski’s papers The cyclometer was a cryptologic device designed by the Polish Cipher Bureau (BS-4) to help decrypt the German Enigma machine during the 1930s. ... The method of perforated sheets was a codebreaking technique used against the Enigma machine (see Cryptanalysis of the Enigma). ... The bomba (plural bomby) was a special-purpose codebreaking machine designed by Polish cryptanalysts and used to crack the German Enigma machine prior to World War II. A bomba was designed to exploit an obscure but fatal weakness in the Enigma cipher. ...

World War II

Early work

British codebreakers had adopted the Polish Enigma-breaking techniques, but had to remain alert to German cryptographic advances. The German Army had changed its practices (more rotors, a more secure indicator system, etc.). The German Navy — some of whose Enigma ciphers the Poles had broken — had always used more secure procedures.


The Herivel tip (also known as Herivelismus), suggested by John Herivel, was an effect which relied on operators failing to choose a random rotor positions for their indicators after changing the rotor ring settings, effectively sending the ring settings almost in the clear. John W. Herivel (born 1918/1919) is a British science historian and former World War II codebreaker at Bletchley Park. ...


German Army and Air Force Enigma-machine operators also gave the decrypters immense help on a number of occasions. In one instance an operator was asked to send a test message, and simply hit the T key repeatedly and sent the resulting letters. A British analyst received from the intercept stations a long message without a single T in it, and immediately realised what had happened. In other cases, Enigma operators would constantly use the same settings as message keys, often their own initials or those of girlfriends (called "cillies," after an operator with the apparent initials "C.I.L."). Analysts were set to finding these messages in the sea of intercepts every day, allowing Bletchley to use the original Polish techniques to find the initial settings for the day. Other German operators used "form letters" for daily reports, notably weather reports, in which case the same crib might be used every day. In telecommunication, the term intercept has the following meanings: 1. ...


The bombe

Alan Turing, chief of Hut Eight (Naval Enigma) at Bletchley Park, made important contributions to efficient Enigma-breaking, as did Gordon Welchman, head of Hut Six. Alan Turing is often considered the father of modern computer science. ... Hut 8 was a section at Bletchley Park (the British World War II codebreaking station) tasked with solving German naval Enigma messages. ... During World War II, British and American cryptographers at Bletchley Park broke a large number of Axis codes and ciphers, including the German Enigma machine. ... William Gordon Welchman (15 June 1906–8 October 1985) was a British mathematician and World War II codebreaker at Bletchley Park. ... Hut 6 at Bletchley Park in 2004 Hut 6 was a wartime section of Bletchley Park tasked with the solution of German Army and Air Force Enigma machine ciphers. ...


One important approach to breaking the ciphers relied on the fact that the reflector (a patented feature of the Enigma machines) guaranteed that no letter could be enciphered as itself. This was combined with knowledge of common German phrases such as "Heil Hitler" or "please respond," which might occur frequently in certain plaintexts; such a successful guess at a plaintext was known at Bletchley as a crib. With a probable plaintext fragment and the knowledge that no letter could be enciphered as itself, a corresponding ciphertext fragment could often be guessed by trying every possible alignment of the crib against the ciphertext, a procedure known as crib dragging. Out of the possible guesses, some would turn out to be true plaintext-ciphertext pairs. This provided a clue to message settings. In cryptanalysis, a crib is a sample of known plaintext; the term originated at Bletchley Park, the British codebreaking operation during World War II (WWII). ... This article is about algorithms for encryption and decryption. ...


The British bombe, designed by Alan Turing and Gordon Welchman, relied on cribs. Assume that a triple loop is found, e.g. abc. That means that, with a crib, plaintext letter a is mapped to cipher b, plain b to c, and plain c to cipher a again within a short distance (ideally plain: abc, cipher: bca). Now the rotor mechanisms of three Enigmas are assembled serially in-line and set to the original rotor positions, with their offset (here 1 step each) accordingly. Then a corresponding physical wire closed loop is obtained. This can be detected with lamps connected to the rotor contacts. The lamp in the wire loop will stay dark. Now the rotor systems are turned synchronously. If only one lamp stays dark because of the one wire loop, the Steckerfeld may be quickly calculated, and the positions with all lamps lit rejected. This typically happens several times in the 17,576 possible rotor settings.


Naval Enigma

Kriegsmarine procedures were much more secure, and the Navy Enigma variant featured a set of eight rotors from which the three operating ones were selected. This meant that there were 336 possible rotor combinations alone. Bletchley Park made no useful headway into Kriegsmarine Enigma until mid-1940 with the capture of the armed trawler, Polares. The latter yielded enough intact cryptographic material that by June or July 1940, Hut 8 at least knew what content to expect in Kriegsmarine messages, and knew the details of the encipherment and decipherment procedures. However, the 336 possible rotor selections, together with a lack of usable cribs, made the usual cryptanalysis methods almost useless. 1940 (MCMXL) was a leap year starting on Monday (the link is to a full 1940 calendar). ...


Hut 8 therefore developed "Banburismus," a method using Bayesian statistics to derive a bombe menu from the "message settings" rather than the messages themselves. In doing so, they would identify at least the rightmost rotor being used in the cipher that day. If Hut 8 were lucky, they managed to identify the rightmost and middle rotors, leaving only six wheel orders to be run on the bombes. Banburismus was a process invented by Alan Turing at Bletchley Park during the Second World War. ... Bayesian inference is statistical inference in which probabilities are interpreted not as frequencies or proportions or the like, but rather as degrees of belief. ...


Later in the war, British codebreakers learnt to fully exploit a crucial security flaw associated with German weather reports: they were broadcast from weatherships to Germany in lower-level ciphers, easy to decrypt, then retransmitted to U-boats at sea in Enigma, thus giving Bletchley Park regular cribs. This was crucial in attacking the special four-rotor U-boat Enigma machine introduced in 1942. U-boat is also a nickname for some diesel locomotives built by GE; see List of GE locomotives October 1939. ... This article is about the year. ...


On May 7, 1941, the Royal Navy captured a German weather ship, together with cipher equipment and codes. They did it again shortly afterwards. And two days later U-boat U-110 was captured, complete with Enigma machine, codebook, operating manual and other information. As a result, Naval Enigma was readable directly through the end of June, and from then on Banburismus allowed it to be read fairly continuously until newer, faster Bombes rendered the procedure unneccessary in mid-1943. May 7 is the 127th day of the year in the Gregorian Calendar (128th in leap years). ... For the movie, see 1941 (film) 1941 (MCMXLI) was a common year starting on Wednesday. ... Unterseeboot 110 (U-110) has been the designation of two submarines of the German Navy. ... Banburismus was a process invented by Alan Turing at Bletchley Park during the Second World War. ... 1943 (MCMXLIII) is a common year starting on Friday. ...


In addition to U-110, Naval Enigma machines or settings books were captured from a total of 7 U-boats and 8 German surface ships, including U-boats U-505 (1944) and U-559 (1942), two German weather-reporting trawlers, and a small vessel (the Krebs) captured during a raid on the Lofoten Islands off Norway. Several other imaginative techniques were dreamed up, including Ian Fleming's suggestion to crash captured German bombers into the sea near German ships, hoping the planes' crews would be rescued by the ships' crews, which would then be taken captive, along with the ships' cryptographic materials, by commandos concealed in the planes. U-505 shortly after being captured Unterseeboot 505 was a Type IXC U-boat of the Kriegsmarine, notable for its capture by the United States Navy in 1944, and presently a museum ship in Chicago, Illinois. ... 1944 (MCMXLIV) was a leap year starting on Saturday (link will take you to calendar). ... Unterseeboot 559 (U-559) was a Type VIIC U-boat of the Kriegsmarine. ... This article is about the year. ... Henningsvær, a fishing village in Lofoten during fishing season (April, 2001). ... Ian Fleming Commander Ian Lancaster Fleming, RNVR (May 28, 1908 – August 12, 1964) was an English author and journalist, best remembered for writing the James Bond series of novels as well as the childrens story, Chitty Chitty Bang Bang. ... The French Navy commando Jaubert storm the Alcyon in a mock assault. ...


However, as had been the case with the Poles, the new tricks only reduced the number of potential settings for a message. The number remaining was still huge, and due to the new rotors that the Germans had added from time to time, that number was larger than the Poles had been left with. In order to solve this problem the Allies, especially the US, "went industrial" and produced much larger versions of the Polish cryptologic bomb that could rapidly test thousands of possible keys. The American efforts on the M4 Enigma were lead by Joseph Desch, an engineer working for the National Cash Register Corporation. The bomba (plural bomby) was a special-purpose codebreaking machine designed by Polish cryptanalysts and used to crack the German Enigma machine prior to World War II. A bomba was designed to exploit an obscure but fatal weakness in the Enigma cipher. ... Joseph Desch (1907 - August 3, 1987) was born in Dayton, Ohio in 1907 to a Catholic family of wagon makers. ... World Headquarters - Dayton, Ohio NCR Corporation is a technology company, specialising in solutions for the retail, and financial industries, as well as decision support systems. ...


German suspicions about Enigma security

By 1945, almost all German Enigma traffic (Wehrmacht, Kriegsmarine, Luftwaffe, Abwehr, SD, etc.) could be decrypted within a day or two, yet the Germans remained confident of its security. They considered Enigma traffic sufficiently secure that they openly discussed their plans and movements, handing the Allies huge amounts of information, not all of which was properly used. For example, both Rommel's actions at the Kasserine Pass, and German preparations for the Battle of the Bulge were clearly foreshadowed in decrypted Enigma traffic, but the information was not properly appreciated in either case. Wehrmacht ▶ (help· info) was the name of the armed forces of Germany from 1935 to 1945. ... The Kriegsmarine (or War Navy) was the name of the German Navy between 1935 and 1945, during the Nazi regime, superseding the Reichsmarine. ... The Deutsche Luftwaffe or (help· info) (German: Air Arm, IPA: [luftvafə]) is the commonly used term for the German air force. ... The Abwehr was a German intelligence organization from 1921 to 1944. ... SD Insignia Patch The Sicherheitsdienst (SD, Security Service) was the intelligence service of the SS. The organization was the first Nazi Party intelligence organization to be established and was considered a sister organization with the Gestapo. ... The Battle of the Kasserine Pass took place in World War II during the Battle of Tunisia, fought between the German Afrika Korps under General Erwin Rommel, and the Americans under General Lloyd Fredendall in the Kasserine Pass (a 2 mile wide gap in the Dorsal Chain of the Atlas... Combatants Western Allies Germany Commanders Dwight D. Eisenhower Gerd von Rundstedt Strength 500,000 men, 400 tanks, 400 guns (Dec 16 - start of the Battle) 600,000 men, 600 tanks, 1,900 guns (Dec 16 - start of the Battle) Casualties 80,987 casualties (10,276 dead, 23,218 missing, 47...


After the war, American TICOM project teams found and detained a considerable number of German cryptographic personnel. Among the things the Americans learned was that German cryptographers, at least, understood very well that Enigma messages might be read; they knew Enigma was not unbreakable. They just found it impossible to imagine anyone going to the immense effort required. When Abwehr personnel who had worked on Fish cryptography and Russian traffic were interned at Rosenheim around May 21, 1945, they were not at all surprised that Enigma had been broken, only that someone had mustered all the resources in time to actually do it. Admiral Dönitz had been advised that that was the least likely of all security problems. TICOM (Target Intelligence Committee) was a project formed in World War II by the United States to find and seize German intelligence assets, particularly cryptographic ones. ... The Abwehr was a German intelligence organization from 1921 to 1944. ... Fish (sometimes FISH) was the Allied codename for any of several German teleprinter stream ciphers used during World War II. While a large number of links were monitored, at least three different encryption systems were distinguished: Tunny — the Lorenz SZ 40/42 from Lorenz Electric. ... May 21 is the 141st day of the year in the Gregorian calendar (142nd in leap years). ... 1945 (MCMXLV) was a common year starting on Monday (the link is to a full 1945 calendar). ... Karl Dönitz â–¶(?) (pronounced ) (September 16, 1891 – December 24, 1980) was a naval leader in Germany during World War II. Despite never joining the Nazi Party, Dönitz attained the high rank of Grand Admiral (Großadmiral) and served as Commander in Chief of Submarines (), and later Commander in Chief...


After World War II

Modern computers can be used to solve Enigma using a variety of techniques[1]. There is even a project to decipher some remaining messages [1] using distributed computing. Distributed computing is an aspect of computer science that deals with the coordination of multiple computers in remote physical locations in order to accomplish a common objective or task. ...


References

  1. Geoff Sullivan and Frode Weierud, "Breaking German Army Ciphers" in Cryptologia 24(3), July 2005, pp. 210–212
  • Stephen Budiansky, Battle of Wits: the Complete Story of Codebreaking in World War II, 2002, ISBN 0743217349.
  • Jim DeBrosse and Colin Burke, The Secret in Building 26: The Untold Story of America's Ultra War Against the U-boat Enigma Codes, 2004, ISBN 0375508074.
  • Kris Gaj, Arkadiusz Orłowski: Facts and Myths of Enigma: Breaking Stereotypes. EUROCRYPT 2003: 106–122. Online version (PDF).
  • James Gannon, Stealing Secrets, Telling Lies: How Spies and Codebreakers Helped Shape the Twentieth Century, Washington, D.C., Brassey's, 2001, ISBN 1-57488-367-4.
  • James J. Gillogly, "Ciphertext-only Cryptanalysis of Enigma," Cryptologia, 19 (4), 1995, pp. 405–412. Online version.
  • David Kahn, Seizing the Enigma: the Race to Break the German U-Boat Codes, 1939-1943, Houghton Mifflin, 1991, ISBN 0-395-42739-8.
  • Władysław Kozaczuk, Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two, edited and translated by Christopher Kasparek, Frederick, MD, University Publications of America, 1984.
  • Władysław Kozaczuk, Jerzy Straszak, Enigma: How the Poles Broke the Nazi Code, Hippocrene Books, 2004, ISBN 078180941X.
  • A. Ray Miller, The Cryptographic Mathematics of Enigma, 2001, [2].
  • Marian Rejewski, "An Application of the Theory of Permutations in Breaking the Enigma Cipher," Applicationes mathematicae, 16(4), 1980. Online version (PDF).
  • Alan M. Turing, "Treatise on Enigma" (parts online, PDF): [3]
  • Gordon Welchman The Hut Six Story: Breaking the Enigma codes, M & M Baldwin, 3rd Edition, 1997, ISBN 0947712348

James Gannon is a freelance writer and producer of documentaries for NBC News. ... James J. Gillogly is an American computer scientist and cryptographer. ... Cryptologia is a journal in cryptography published quarterly since 1977. ... David Kahn is a US historian, journalist and writer. ... Władysław Kozaczuk (1923 — 2003, Warsaw, Poland) was a Polish historian who published a dozen books, several of them in multiple editions. ... Christopher Kasparek (born 1945) is a writer and a translator from Polish into English. ... 1984 (MCMLXXXIV) was a leap year starting on Sunday of the Gregorian calendar. ... 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ... Marian Rejewski (probably 1932, the year he broke Enigma). ... Alan Turing is often considered the father of modern computer science. ... William Gordon Welchman (15 June 1906–8 October 1985) was a British mathematician and World War II codebreaker at Bletchley Park. ...

External links


  Results from FactBites:
 
Cryptanalysis of the Enigma (1887 words)
Enigma, and most rotor designs, had a fundamental flaw: the rightmost rotor would rotate a set number of places before the next would rotate (26 in the initial version).
Enigma had an additional fundamental weakness: the machine had the property that a letter would never be encrypted to itself.
However, when the German Navy began using Enigma in the mid-1920s, decryption of their messages was impossible in practice, as it was also when the German Army began to use a slightly different version in the early 1930's.
  More results at FactBites »

 
 

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