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112-740: While the Enigma machine was generally used by field units, the T52 was an online machine used by Luftwaffe and German Navy units, which could support the heavy machine, teletypewriter and attendant fixed circuits . It fulfilled a similar role to the Lorenz cipher machines in the German Army . The British cryptanalysts of Bletchley Park codenamed the German teleprinter ciphers Fish , with individual cipher-systems being given further codenames: just as

224-694: A plugboard , were the most complex. Japanese and Italian models were also in use. With its adoption (in slightly modified form) by the German Navy in 1926 and the German Army and Air Force soon after, the name Enigma became widely known in military circles. Pre-war German military planning emphasized fast, mobile forces and tactics, later known as blitzkrieg , which depend on radio communication for command and coordination. Since adversaries would likely intercept radio signals, messages had to be protected with secure encipherment. Compact and easily portable,

336-448: A pseudo-random substitution determined by the electrical pathways inside the machine. The letter indicated by the lamp would be recorded, typically by a second operator, as the cyphertext letter. The action of pressing a key also moved one or more rotors so that the next key press used a different electrical pathway, and thus a different substitution would occur even if the same plaintext letter were entered again. For each key press there

448-504: A 9th-century Arab polymath , in Risalah fi Istikhraj al-Mu'amma ( A Manuscript on Deciphering Cryptographic Messages ). This treatise contains the first description of the method of frequency analysis . Al-Kindi is thus regarded as the first codebreaker in history. His breakthrough work was influenced by Al-Khalil (717–786), who wrote the Book of Cryptographic Messages , which contains

560-674: A breakthrough in factoring would impact the security of RSA. In 1980, one could factor a difficult 50-digit number at an expense of 10 elementary computer operations. By 1984 the state of the art in factoring algorithms had advanced to a point where a 75-digit number could be factored in 10 operations. Advances in computing technology also meant that the operations could be performed much faster. Moore's law predicts that computer speeds will continue to increase. Factoring techniques may continue to do so as well, but will most likely depend on mathematical insight and creativity, neither of which has ever been successfully predictable. 150-digit numbers of

672-414: A cable (8) to plug "D", and another bi-directional switch (9) to light the appropriate lamp. The repeated changes of electrical path through an Enigma scrambler implement a polyalphabetic substitution cipher that provides Enigma's security. The diagram on the right shows how the electrical pathway changes with each key depression, which causes rotation of at least the right-hand rotor. Current passes into

784-454: A cipher failing to hide these statistics . For example, in a simple substitution cipher (where each letter is simply replaced with another), the most frequent letter in the ciphertext would be a likely candidate for "E". Frequency analysis of such a cipher is therefore relatively easy, provided that the ciphertext is long enough to give a reasonably representative count of the letters of the alphabet that it contains. Al-Kindi's invention of

896-471: A cipher machine in 1918 and began marketing the finished product under the brand name Enigma in 1923, initially targeted at commercial markets. Early models were used commercially from the early 1920s, and adopted by military and government services of several countries, most notably Nazi Germany before and during World War II . Several Enigma models were produced, but the German military models, having

1008-522: A cipher simply means finding a weakness in the cipher that can be exploited with a complexity less than brute force. Never mind that brute-force might require 2 encryptions; an attack requiring 2 encryptions would be considered a break...simply put, a break can just be a certificational weakness: evidence that the cipher does not perform as advertised." The results of cryptanalysis can also vary in usefulness. Cryptographer Lars Knudsen (1998) classified various types of attack on block ciphers according to

1120-542: A few hundred letters, and so there was no chance of repeating any combined rotor position during a single session, denying cryptanalysts valuable clues. To make room for the Naval fourth rotors, the reflector was made much thinner. The fourth rotor fitted into the space made available. No other changes were made, which eased the changeover. Since there were only three pawls, the fourth rotor never stepped, but could be manually set into one of 26 possible positions. A device that

1232-450: A full rotation, before the electrical connections were made. This changed the substitution alphabet used for encryption, ensuring that the cryptographic substitution was different at each new rotor position, producing a more formidable polyalphabetic substitution cipher. The stepping mechanism varied slightly from model to model. The right-hand rotor stepped once with each keystroke, and other rotors stepped less frequently. The advancement of

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1344-500: A large problem.) When a recovered plaintext is then combined with its ciphertext, the key is revealed: Knowledge of a key then allows the analyst to read other messages encrypted with the same key, and knowledge of a set of related keys may allow cryptanalysts to diagnose the system used for constructing them. Governments have long recognized the potential benefits of cryptanalysis for intelligence , both military and diplomatic, and established dedicated organizations devoted to breaking

1456-421: A major source of intelligence. Many commentators say the flow of Ultra communications intelligence from the decrypting of Enigma, Lorenz , and other ciphers shortened the war substantially and may even have altered its outcome. The Enigma machine was invented by German engineer Arthur Scherbius at the end of World War I . The German firm Scherbius & Ritter, co-founded by Scherbius, patented ideas for

1568-413: A mature field." However, any postmortems for cryptanalysis may be premature. While the effectiveness of cryptanalytic methods employed by intelligence agencies remains unknown, many serious attacks against both academic and practical cryptographic primitives have been published in the modern era of computer cryptography: Thus, while the best modern ciphers may be far more resistant to cryptanalysis than

1680-459: A message could be encrypted on one and decrypted on the other, without the need for a bulky mechanism to switch between encryption and decryption modes. The reflector allowed a more compact design, but it also gave Enigma the property that no letter ever encrypted to itself. This was a severe cryptological flaw that was subsequently exploited by codebreakers. In Model 'C', the reflector could be inserted in one of two different positions. In Model 'D',

1792-437: A network was given the same settings list for its Enigma, valid for a period of time. The procedures for German Naval Enigma were more elaborate and more secure than those in other services and employed auxiliary codebooks . Navy codebooks were printed in red, water-soluble ink on pink paper so that they could easily be destroyed if they were endangered or if the vessel was sunk. Cryptanalysis#Depth Cryptanalysis (from

1904-566: A number of conceptual flaws, including very subtle ones, had been eliminated. One such flaw was the ability to reset the keystream to a fixed point, which led to key reuse by undisciplined machine operators. Following the occupation of Denmark and Norway , the Germans started to use a teleprinter circuit which ran through Sweden . The Swedes immediately tapped the line, in May 1940, and the mathematician and cryptographer Arne Beurling cracked

2016-705: A plate on the left acted as a fourth rotor. From October 1944, the German Abwehr used the Schlüsselgerät 41 . The Abwehr code had been broken on 8 December 1941 by Dilly Knox . Agents sent messages to the Abwehr in a simple code which was then sent on using an Enigma machine. The simple codes were broken and helped break the daily Enigma cipher. This breaking of the code enabled the Double-Cross System to operate. Like other rotor machines,

2128-451: A program. With reciprocal machine ciphers such as the Lorenz cipher and the Enigma machine used by Nazi Germany during World War II , each message had its own key. Usually, the transmitting operator informed the receiving operator of this message key by transmitting some plaintext and/or ciphertext before the enciphered message. This is termed the indicator , as it indicates to the receiving operator how to set his machine to decipher

2240-475: A reduced-round block cipher, as a step towards breaking the full system. Cryptanalysis has coevolved together with cryptography, and the contest can be traced through the history of cryptography —new ciphers being designed to replace old broken designs, and new cryptanalytic techniques invented to crack the improved schemes. In practice, they are viewed as two sides of the same coin: secure cryptography requires design against possible cryptanalysis. Although

2352-416: A rotor can be turned to the correct position by hand, using the grooved finger-wheel which protrudes from the internal Enigma cover when closed. In order for the operator to know the rotor's position, each has an alphabet tyre (or letter ring) attached to the outside of the rotor disc, with 26 characters (typically letters); one of these is visible through the window for that slot in the cover, thus indicating

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2464-512: A rotor other than the left-hand one was called a turnover by the British. This was achieved by a ratchet and pawl mechanism. Each rotor had a ratchet with 26 teeth and every time a key was pressed, the set of spring-loaded pawls moved forward in unison, trying to engage with a ratchet. The alphabet ring of the rotor to the right normally prevented this. As this ring rotated with its rotor, a notch machined into it would eventually align itself with

2576-496: A set of messages. For example, the Vernam cipher enciphers by bit-for-bit combining plaintext with a long key using the " exclusive or " operator, which is also known as " modulo-2 addition " (symbolized by ⊕ ): Deciphering combines the same key bits with the ciphertext to reconstruct the plaintext: (In modulo-2 arithmetic, addition is the same as subtraction.) When two such ciphertexts are aligned in depth, combining them eliminates

2688-421: A similar assessment about Ultra, saying that it shortened the war "by not less than two years and probably by four years"; moreover, he said that in the absence of Ultra, it is uncertain how the war would have ended. In practice, frequency analysis relies as much on linguistic knowledge as it does on statistics, but as ciphers became more complex, mathematics became more important in cryptanalysis. This change

2800-458: A simple substitution cipher . For example, the pin corresponding to the letter E might be wired to the contact for letter T on the opposite face, and so on. Enigma's security comes from using several rotors in series (usually three or four) and the regular stepping movement of the rotors, thus implementing a polyalphabetic substitution cipher. Each rotor can be set to one of 26 starting positions when placed in an Enigma machine. After insertion,

2912-425: A three-rotor German Army/Air Force Enigma, let P denote the plugboard transformation, U denote that of the reflector ( U = U − 1 {\displaystyle U=U^{-1}} ), and L , M , R denote those of the left, middle and right rotors respectively. Then the encryption E can be expressed as After each key press, the rotors turn, changing the transformation. For example, if

3024-469: Is for a third party, a cryptanalyst , to gain as much information as possible about the original ( " plaintext " ), attempting to "break" the encryption to read the ciphertext and learning the secret key so future messages can be decrypted and read. A mathematical technique to do this is called a cryptographic attack . Cryptographic attacks can be characterized in a number of ways: Cryptanalytical attacks can be classified based on what type of information

3136-441: Is that, unlike attacks on symmetric cryptosystems, any cryptanalysis has the opportunity to make use of knowledge gained from the public key . Quantum computers , which are still in the early phases of research, have potential use in cryptanalysis. For example, Shor's Algorithm could factor large numbers in polynomial time , in effect breaking some commonly used forms of public-key encryption. By using Grover's algorithm on

3248-421: The " plaintext " ) is sent securely to a recipient by the sender first converting it into an unreadable form ( " ciphertext " ) using an encryption algorithm . The ciphertext is sent through an insecure channel to the recipient. The recipient decrypts the ciphertext by applying an inverse decryption algorithm , recovering the plaintext. To decrypt the ciphertext, the recipient requires a secret knowledge from

3360-416: The Enigma , cryptanalysis and the broader field of information security remain quite active. Asymmetric cryptography (or public-key cryptography ) is cryptography that relies on using two (mathematically related) keys; one private, and one public. Such ciphers invariably rely on "hard" mathematical problems as the basis of their security, so an obvious point of attack is to develop methods for solving

3472-483: The Greek kryptós , "hidden", and analýein , "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown. In addition to mathematical analysis of cryptographic algorithms, cryptanalysis includes

Siemens and Halske T52 - Misplaced Pages Continue

3584-520: The Schreibmax , a small printer that could print the 26 letters on a narrow paper ribbon. This eliminated the need for a second operator to read the lamps and transcribe the letters. The Schreibmax was placed on top of the Enigma machine and was connected to the lamp panel. To install the printer, the lamp cover and light bulbs had to be removed. It improved both convenience and operational security;

3696-543: The Vigenère cipher , which uses a repeating key to select different encryption alphabets in rotation, was considered to be completely secure ( le chiffre indéchiffrable —"the indecipherable cipher"). Nevertheless, Charles Babbage (1791–1871) and later, independently, Friedrich Kasiski (1805–81) succeeded in breaking this cipher. During World War I , inventors in several countries developed rotor cipher machines such as Arthur Scherbius ' Enigma , in an attempt to minimise

3808-642: The plugboard to the rotor assembly. If the plugboard is not present, the entry wheel instead connects the keyboard and lampboard to the rotor assembly. While the exact wiring used is of comparatively little importance to security, it proved an obstacle to Rejewski's progress during his study of the rotor wirings. The commercial Enigma connects the keys in the order of their sequence on a QWERTZ keyboard: Q → A , W → B , E → C and so on. The military Enigma connects them in straight alphabetical order: A → A , B → B , C → C , and so on. It took inspired guesswork for Rejewski to penetrate

3920-402: The (unused in this instance, so shown closed) plug "A" (3) via the entry wheel (4), through the wiring of the three (Wehrmacht Enigma) or four ( Kriegsmarine M4 and Abwehr variants) installed rotors (5), and enters the reflector (6). The reflector returns the current, via an entirely different path, back through the rotors (5) and entry wheel (4), proceeding through plug "S" (7) connected with

4032-556: The 26 lights above the keyboard illuminated at each key press. If plaintext is entered, the illuminated letters are the ciphertext . Entering ciphertext transforms it back into readable plaintext. The rotor mechanism changes the electrical connections between the keys and the lights with each keypress. The security of the system depends on machine settings that were generally changed daily, based on secret key lists distributed in advance, and on other settings that were changed for each message. The receiving station would have to know and use

4144-591: The Cipher Bureau to read German Enigma messages starting from January 1933. Over time, the German cryptographic procedures improved, and the Cipher Bureau developed techniques and designed mechanical devices to continue reading Enigma traffic. As part of that effort, the Poles exploited quirks of the rotors, compiled catalogues, built a cyclometer (invented by Rejewski) to help make a catalogue with 100,000 entries, invented and produced Zygalski sheets , and built

4256-598: The Enigma machine filled that need. Hans-Thilo Schmidt was a German who spied for the French , obtaining access to German cipher materials that included the daily keys used in September and October 1932. Those keys included the plugboard settings. The French passed the material to Poland . Around December 1932, Marian Rejewski , a Polish mathematician and cryptologist at the Polish Cipher Bureau , used

4368-424: The Enigma machine is a combination of mechanical and electrical subsystems. The mechanical subsystem consists of a keyboard ; a set of rotating disks called rotors arranged adjacently along a spindle ; one of various stepping components to turn at least one rotor with each key press, and a series of lamps, one for each letter. These design features are the reason that the Enigma machine was originally referred to as

4480-736: The German Lorenz cipher and the Japanese Purple code , and a variety of classical schemes): Attacks can also be characterised by the resources they require. Those resources include: It is sometimes difficult to predict these quantities precisely, especially when the attack is not practical to actually implement for testing. But academic cryptanalysts tend to provide at least the estimated order of magnitude of their attacks' difficulty, saying, for example, "SHA-1 collisions now 2 ." Bruce Schneier notes that even computationally impractical attacks can be considered breaks: "Breaking

4592-605: The German forces in Finland, and of course the German embassy in Stockholm . In total, the Swedes intercepted 500,000 German messages and decrypted 350,000. However, poor security meant the Germans eventually became aware of this. An improvement in T52 security in 1942 was defeated by the Swedes. However, a second upgrade in mid-1943 was not, and the flow of decrypted messages came to an end. The British first detected T52 traffic in

Siemens and Halske T52 - Misplaced Pages Continue

4704-550: The Lorenz machine, and also means that the T52 is not just a pseudorandom number generator -and-XOR cipher. For example, if a cipher clerk erred and sent two different messages using exactly the same settings—a depth of two in Bletchley jargon—this could be detected statistically but was not immediately and trivially solvable as it would be with the Lorenz. Siemens produced several and mostly incompatible versions of

4816-551: The Polish Enigma-decryption techniques and equipment, including Zygalski sheets and the cryptologic bomb, and promised each delegation a Polish-reconstructed Enigma (the devices were soon delivered). In September 1939, British Military Mission 4, which included Colin Gubbins and Vera Atkins , went to Poland, intending to evacuate cipher-breakers Marian Rejewski , Jerzy Różycki , and Henryk Zygalski from

4928-467: The Polish equipment and techniques. Gordon Welchman , who became head of Hut 6 at Bletchley Park, wrote: "Hut 6 Ultra would never have got 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." The Polish transfer of theory and technology at Pyry formed

5040-484: The T52 was called Sturgeon , the Lorenz machine was codenamed Tunny . The teleprinters of the day emitted each character as five parallel bits on five lines, typically encoded in the Baudot code or something similar. The T52 had ten pinwheels , which were stepped in a complex nonlinear way, based in later models on their positions from various relays in the past, but in such a way that they could never stall. Each of

5152-605: The T52: the T52a and T52b, which differed only in their electrical noise suppression, and the T52c, T52d and T52e. While the T52a/b and T52c were cryptologically weak, the last two were more advanced devices; the movement of the wheels was intermittent, the decision on whether or not to advance them being controlled by logic circuits which took input data from the wheels themselves. In addition,

5264-545: The actual word " cryptanalysis " is relatively recent (it was coined by William Friedman in 1920), methods for breaking codes and ciphers are much older. David Kahn notes in The Codebreakers that Arab scholars were the first people to systematically document cryptanalytic methods. The first known recorded explanation of cryptanalysis was given by Al-Kindi (c. 801–873, also known as "Alkindus" in Europe),

5376-419: The additional naval rotors VI, VII and VIII each had two notches. The position of the notch on each rotor was determined by the letter ring which could be adjusted in relation to the core containing the interconnections. The points on the rings at which they caused the next wheel to move were as follows. The design also included a feature known as double-stepping . This occurred when each pawl aligned with both

5488-476: The amount and quality of secret information that was discovered: Academic attacks are often against weakened versions of a cryptosystem, such as a block cipher or hash function with some rounds removed. Many, but not all, attacks become exponentially more difficult to execute as rounds are added to a cryptosystem, so it's possible for the full cryptosystem to be strong even though reduced-round variants are weak. Nonetheless, partial breaks that come close to breaking

5600-553: The attacker has available. As a basic starting point it is normally assumed that, for the purposes of analysis, the general algorithm is known; this is Shannon's Maxim "the enemy knows the system" – in its turn, equivalent to Kerckhoffs's principle . This is a reasonable assumption in practice – throughout history, there are countless examples of secret algorithms falling into wider knowledge, variously through espionage , betrayal and reverse engineering . (And on occasion, ciphers have been broken through pure deduction; for example,

5712-411: The attacker may need to choose particular plaintexts to be encrypted or even to ask for plaintexts to be encrypted using several keys related to the secret key . Furthermore, it might only reveal a small amount of information, enough to prove the cryptosystem imperfect but too little to be useful to real-world attackers. Finally, an attack might only apply to a weakened version of cryptographic tools, like

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5824-454: The body of the rotor, 26 wires connect each pin on one side to a contact on the other in a complex pattern. Most of the rotors are identified by Roman numerals, and each issued copy of rotor I, for instance, is wired identically to all others. The same is true for the special thin beta and gamma rotors used in the M4 naval variant. By itself, a rotor performs only a very simple type of encryption ,

5936-445: The cipher machine. Sending two or more messages with the same key is an insecure process. To a cryptanalyst the messages are then said to be "in depth." This may be detected by the messages having the same indicator by which the sending operator informs the receiving operator about the key generator initial settings for the message. Generally, the cryptanalyst may benefit from lining up identical enciphering operations among

6048-500: The codes and ciphers of other nations, for example, GCHQ and the NSA , organizations which are still very active today. Even though computation was used to great effect in the cryptanalysis of the Lorenz cipher and other systems during World War II, it also made possible new methods of cryptography orders of magnitude more complex than ever before. Taken as a whole, modern cryptography has become much more impervious to cryptanalysis than

6160-449: The common key, leaving just a combination of the two plaintexts: The individual plaintexts can then be worked out linguistically by trying probable words (or phrases), also known as "cribs," at various locations; a correct guess, when combined with the merged plaintext stream, produces intelligible text from the other plaintext component: The recovered fragment of the second plaintext can often be extended in one or both directions, and

6272-575: The country. The cryptologists, however, had been evacuated by their own superiors into Romania, at the time a Polish-allied country. On the way, for security reasons, the Polish Cipher Bureau personnel had deliberately destroyed their records and equipment. From Romania they traveled on to France, where they resumed their cryptological work, collaborating by teletype with the British , who began work on decrypting German Enigma messages, using

6384-473: The crucial basis for the subsequent World War II British Enigma-decryption effort at Bletchley Park , where Welchman worked. During the war, British cryptologists decrypted a vast number of messages enciphered on Enigma. The intelligence gleaned from this source, codenamed " Ultra " by the British, was a substantial aid to the Allied war effort. Though Enigma had some cryptographic weaknesses, in practice it

6496-592: The cyphertext and — as long as all the settings of the deciphering machine were identical to those of the enciphering machine — for every key press the reverse substitution would occur and the plaintext message would emerge. In use, the Enigma required a list of daily key settings and auxiliary documents. In German military practice, communications were divided into separate networks, each using different settings. These communication nets were termed keys at Bletchley Park , and were assigned code names , such as Red , Chaffinch , and Shark . Each unit operating in

6608-472: The electromechanical cryptologic bomba (invented by Rejewski) to search for rotor settings. In 1938 the Poles had six bomby (plural of bomba ), but when that year the Germans added two more rotors, ten times as many bomby would have been needed to read the traffic. On 26 and 27 July 1939, in Pyry , just south of Warsaw , the Poles initiated French and British military intelligence representatives into

6720-703: The end of the European war by up to two years, to determining the eventual result. The war in the Pacific was similarly helped by 'Magic' intelligence. Cryptanalysis of enemy messages played a significant part in the Allied victory in World War II. F. W. Winterbotham , quoted the western Supreme Allied Commander, Dwight D. Eisenhower , at the war's end as describing Ultra intelligence as having been "decisive" to Allied victory. Sir Harry Hinsley , official historian of British Intelligence in World War II, made

6832-483: The exact settings employed by the transmitting station to decrypt a message. Although Nazi Germany introduced a series of improvements to the Enigma over the years that hampered decryption efforts, they did not prevent Poland from cracking the machine as early as December 1932 and reading messages prior to and into the war. Poland's sharing of their achievements enabled the Allies to exploit Enigma-enciphered messages as

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6944-401: The extra characters can be combined with the merged plaintext stream to extend the first plaintext. Working back and forth between the two plaintexts, using the intelligibility criterion to check guesses, the analyst may recover much or all of the original plaintexts. (With only two plaintexts in depth, the analyst may not know which one corresponds to which ciphertext, but in practice this is not

7056-590: The first use of permutations and combinations to list all possible Arabic words with and without vowels. Frequency analysis is the basic tool for breaking most classical ciphers . In natural languages, certain letters of the alphabet appear more often than others; in English , " E " is likely to be the most common letter in any sample of plaintext . Similarly, the digraph "TH" is the most likely pair of letters in English, and so on. Frequency analysis relies on

7168-467: The five plaintext bits was then XORed with the XOR sum of 3 taps from the pinwheels, and then cyclically adjacent pairs of plaintext bits were swapped or not, according to XOR sums of three (different) output bits . The numbers of pins on all the wheels were coprime , and the triplets of bits that controlled each XOR or swap were selectable through a plugboard. This produced a much more complex cipher than

7280-677: The frequency analysis technique for breaking monoalphabetic substitution ciphers was the most significant cryptanalytic advance until World War II. Al-Kindi's Risalah fi Istikhraj al-Mu'amma described the first cryptanalytic techniques, including some for polyalphabetic ciphers , cipher classification, Arabic phonetics and syntax, and most importantly, gave the first descriptions on frequency analysis. He also covered methods of encipherments, cryptanalysis of certain encipherments, and statistical analysis of letters and letter combinations in Arabic. An important contribution of Ibn Adlan (1187–1268)

7392-539: The key that unlock[s] other messages. In a sense, then, cryptanalysis is dead. But that is not the end of the story. Cryptanalysis may be dead, but there is – to mix my metaphors – more than one way to skin a cat. Kahn goes on to mention increased opportunities for interception, bugging , side channel attacks , and quantum computers as replacements for the traditional means of cryptanalysis. In 2010, former NSA technical director Brian Snow said that both academic and government cryptographers are "moving very slowly forward in

7504-499: The keyboard through the plugboard, and proceeded to the entry-rotor or Eintrittswalze . Each letter on the plugboard had two jacks. Inserting a plug disconnected the upper jack (from the keyboard) and the lower jack (to the entry-rotor) of that letter. The plug at the other end of the crosswired cable was inserted into another letter's jacks, thus switching the connections of the two letters. Other features made various Enigma machines more secure or more convenient. Some M4 Enigmas used

7616-594: The kind once used in RSA have been factored. The effort was greater than above, but was not unreasonable on fast modern computers. By the start of the 21st century, 150-digit numbers were no longer considered a large enough key size for RSA. Numbers with several hundred digits were still considered too hard to factor in 2005, though methods will probably continue to improve over time, requiring key size to keep pace or other methods such as elliptic curve cryptography to be used. Another distinguishing feature of asymmetric schemes

7728-511: The lamp panel and light bulbs be removed. The remote panel made it possible for a person to read the decrypted plaintext without the operator seeing it. In 1944, the Luftwaffe introduced a plugboard switch, called the Uhr (clock), a small box containing a switch with 40 positions. It replaced the standard plugs. After connecting the plugs, as determined in the daily key sheet, the operator turned

7840-476: The message. Poorly designed and implemented indicator systems allowed first Polish cryptographers and then the British cryptographers at Bletchley Park to break the Enigma cipher system. Similar poor indicator systems allowed the British to identify depths that led to the diagnosis of the Lorenz SZ40/42 cipher system, and the comprehensive breaking of its messages without the cryptanalysts seeing

7952-424: The military variants, the notches are located on the alphabet ring. The Army and Air Force Enigmas were used with several rotors, initially three. On 15 December 1938, this changed to five, from which three were chosen for a given session. Rotors were marked with Roman numerals to distinguish them: I, II, III, IV and V, all with single turnover notches located at different points on the alphabet ring. This variation

8064-469: The modification. With the exception of models A and B , the last rotor came before a 'reflector' (German: Umkehrwalze , meaning 'reversal rotor'), a patented feature unique to Enigma among the period's various rotor machines. The reflector connected outputs of the last rotor in pairs, redirecting current back through the rotors by a different route. The reflector ensured that Enigma would be self-reciprocal ; thus, with two identically configured machines,

8176-482: The operator. It was introduced on German Army versions in 1928, and was soon adopted by the Reichsmarine (German Navy). The plugboard contributed more cryptographic strength than an extra rotor, as it had 150 trillion possible settings (see below). Enigma without a plugboard (known as unsteckered Enigma ) could be solved relatively straightforwardly using hand methods; these techniques were generally defeated by

8288-452: The original cryptosystem may mean that a full break will follow; the successful attacks on DES , MD5 , and SHA-1 were all preceded by attacks on weakened versions. In academic cryptography, a weakness or a break in a scheme is usually defined quite conservatively: it might require impractical amounts of time, memory, or known plaintexts. It also might require the attacker be able to do things many real-world attackers can't: for example,

8400-409: The other face housing 26 corresponding electrical contacts in the form of circular plates. The pins and contacts represent the alphabet  — typically the 26 letters A–Z, as will be assumed for the rest of this description. When the rotors are mounted side by side on the spindle, the pins of one rotor rest against the plate contacts of the neighbouring rotor, forming an electrical connection. Inside

8512-401: The other rotors or fixed wiring on either end of the spindle. When the rotors are properly aligned, each key on the keyboard is connected to a unique electrical pathway through the series of contacts and internal wiring. Current, typically from a battery, flows through the pressed key, into the newly configured set of circuits and back out again, ultimately lighting one display lamp , which shows

8624-422: The output letter. For example, when encrypting a message starting ANX... , the operator would first press the A key, and the Z lamp might light, so Z would be the first letter of the ciphertext . The operator would next press N , and then X in the same fashion, and so on. Current flows from the battery (1) through a depressed bi-directional keyboard switch (2) to the plugboard (3). Next, it passes through

8736-528: The past, through machines like the British Bombes and Colossus computers at Bletchley Park in World War II , to the mathematically advanced computerized schemes of the present. Methods for breaking modern cryptosystems often involve solving carefully constructed problems in pure mathematics , the best-known being integer factorization . In encryption , confidential information (called

8848-518: The pawl, allowing it to engage with the ratchet, and advance the rotor on its left. The right-hand pawl, having no rotor and ring to its right, stepped its rotor with every key depression. For a single-notch rotor in the right-hand position, the middle rotor stepped once for every 26 steps of the right-hand rotor. Similarly for rotors two and three. For a two-notch rotor, the rotor to its left would turn over twice for each rotation. The first five rotors to be introduced (I–V) contained one notch each, while

8960-417: The pen-and-paper systems of the past, and now seems to have the upper hand against pure cryptanalysis. The historian David Kahn notes: Many are the cryptosystems offered by the hundreds of commercial vendors today that cannot be broken by any known methods of cryptanalysis. Indeed, in such systems even a chosen plaintext attack , in which a selected plaintext is matched against its ciphertext, cannot yield

9072-404: The plugboard with ten pairs of letters connected, the military Enigma has 158,962,555,217,826,360,000 different settings (nearly 159 quintillion or about 67 bits ). A German Enigma operator would be given a plaintext message to encrypt. After setting up his machine, he would type the message on the Enigma keyboard. For each letter pressed, one lamp lit indicating a different letter according to

9184-499: The plugboard, driving Allied cryptanalysts to develop special machines to solve it. A cable placed onto the plugboard connected letters in pairs; for example, E and Q might be a steckered pair. The effect was to swap those letters before and after the main rotor scrambling unit. For example, when an operator pressed E , the signal was diverted to Q before entering the rotors. Up to 13 steckered pairs might be used at one time, although only 10 were normally used. Current flowed from

9296-420: The printer could be installed remotely such that the signal officer operating the machine no longer had to see the decrypted plaintext . Another accessory was the remote lamp panel Fernlesegerät . For machines equipped with the extra panel, the wooden case of the Enigma was wider and could store the extra panel. A lamp panel version could be connected afterwards, but that required, as with the Schreibmax , that

9408-399: The problem. The security of two-key cryptography depends on mathematical questions in a way that single-key cryptography generally does not, and conversely links cryptanalysis to wider mathematical research in a new way. Asymmetric schemes are designed around the (conjectured) difficulty of solving various mathematical problems. If an improved algorithm can be found to solve the problem, then

9520-399: The ratchet of its rotor and the rotating notched ring of the neighbouring rotor. If a pawl engaged with a ratchet through alignment with a notch, as it moved forward it pushed against both the ratchet and the notch, advancing both rotors. In a three-rotor machine, double-stepping affected rotor two only. If, in moving forward, the ratchet of rotor three was engaged, rotor two would move again on

9632-503: The reflector could be set in 26 possible positions, although it did not move during encryption. In the Abwehr Enigma, the reflector stepped during encryption in a manner similar to the other wheels. In the German Army and Air Force Enigma, the reflector was fixed and did not rotate; there were four versions. The original version was marked 'A', and was replaced by Umkehrwalze B on 1 November 1937. A third version, Umkehrwalze C

9744-690: The repetition that had been exploited to break the Vigenère system. In World War I , the breaking of the Zimmermann Telegram was instrumental in bringing the United States into the war. In World War II , the Allies benefitted enormously from their joint success cryptanalysis of the German ciphers – including the Enigma machine and the Lorenz cipher – and Japanese ciphers, particularly 'Purple' and JN-25 . 'Ultra' intelligence has been credited with everything between shortening

9856-410: The right-hand rotor R is rotated n positions, the transformation becomes where ρ is the cyclic permutation mapping A to B, B to C, and so forth. Similarly, the middle and left-hand rotors can be represented as j and k rotations of M and L . The encryption transformation can then be described as Combining three rotors from a set of five, each of the 3 rotor settings with 26 positions, and

9968-551: The rotational position of the rotor. In early models, the alphabet ring was fixed to the rotor disc. A later improvement was the ability to adjust the alphabet ring relative to the rotor disc. The position of the ring was known as the Ringstellung ("ring setting"), and that setting was a part of the initial setup needed prior to an operating session. In modern terms it was a part of the initialization vector . Each rotor contains one or more notches that control rotor stepping. In

10080-458: The rotor-based cipher machine during its intellectual inception in 1915. An electrical pathway is a route for current to travel. By manipulating this phenomenon the Enigma machine was able to scramble messages. The mechanical parts act by forming a varying electrical circuit . When a key is pressed, one or more rotors rotate on the spindle. On the sides of the rotors are a series of electrical contacts that, after rotation, line up with contacts on

10192-506: The same space as the three-rotor version. This was accomplished by replacing the original reflector with a thinner one and by adding a thin fourth rotor. That fourth rotor was one of two types, Beta or Gamma , and never stepped, but could be manually set to any of 26 positions. One of the 26 made the machine perform identically to the three-rotor machine. To avoid merely implementing a simple (solvable) substitution cipher, every key press caused one or more rotors to step by one twenty-sixth of

10304-498: The sender, usually a string of letters, numbers, or bits , called a cryptographic key . The concept is that even if an unauthorized person gets access to the ciphertext during transmission, without the secret key they cannot convert it back to plaintext. Encryption has been used throughout history to send important military, diplomatic and commercial messages, and today is very widely used in computer networking to protect email and internet communication. The goal of cryptanalysis

10416-406: The set of rotors, into and back out of the reflector, and out through the rotors again. The greyed-out lines are other possible paths within each rotor; these are hard-wired from one side of each rotor to the other. The letter A encrypts differently with consecutive key presses, first to G , and then to C . This is because the right-hand rotor steps (rotates one position) on each key press, sending

10528-452: The signal on a completely different route. Eventually other rotors step with a key press. The rotors (alternatively wheels or drums , Walzen in German) form the heart of an Enigma machine. Each rotor is a disc approximately 10 cm (3.9 in) in diameter made from Ebonite or Bakelite with 26 brass , spring-loaded, electrical contact pins arranged in a circle on one face, with

10640-404: The study of side-channel attacks that do not target weaknesses in the cryptographic algorithms themselves, but instead exploit weaknesses in their implementation. Even though the goal has been the same, the methods and techniques of cryptanalysis have changed drastically through the history of cryptography, adapting to increasing cryptographic complexity, ranging from the pen-and-paper methods of

10752-509: The subsequent keystroke, resulting in two consecutive steps. Rotor two also pushes rotor one forward after 26 steps, but since rotor one moves forward with every keystroke anyway, there is no double-stepping. This double-stepping caused the rotors to deviate from odometer -style regular motion. With three wheels and only single notches in the first and second wheels, the machine had a period of 26×25×26 = 16,900 (not 26×26×26, because of double-stepping). Historically, messages were limited to

10864-540: The summer and autumn of 1942 on a link between Sicily and Libya , codenamed "Sturgeon", and another from the Aegean to Sicily , codenamed "Mackerel". Operators of both links were in the habit of enciphering several messages with the same machine settings, producing large numbers of depths . These depths were analysed by Michael Crum. The British at Bletchley Park later also broke into Sturgeon, although they did not break it as regularly as they broke Enigma or Tunny. This

10976-401: The switch into one of the 40 positions, each producing a different combination of plug wiring. Most of these plug connections were, unlike the default plugs, not pair-wise. In one switch position, the Uhr did not swap letters, but simply emulated the 13 stecker wires with plugs. The Enigma transformation for each letter can be specified mathematically as a product of permutations . Assuming

11088-485: The system is weakened. For example, the security of the Diffie–Hellman key exchange scheme depends on the difficulty of calculating the discrete logarithm . In 1983, Don Coppersmith found a faster way to find discrete logarithms (in certain groups), and thereby requiring cryptographers to use larger groups (or different types of groups). RSA 's security depends (in part) upon the difficulty of integer factorization –

11200-472: The theory of permutations, and flaws in the German military-message encipherment procedures, to break message keys of the plugboard Enigma machine. Rejewski used the French supplied material and the message traffic that took place in September and October to solve for the unknown rotor wiring. Consequently, the Polish mathematicians were able to build their own Enigma machines, dubbed " Enigma doubles ". Rejewski

11312-545: The two earliest models in two weeks, using just pen and paper (a feat later replicated by Bill Tutte at Bletchley Park with the Lorenz teleprinter device used by the German High Command). The telephone company Ericsson manufactured a number of T52 analogue machines that could decode the messages once the key settings had been found by hand. The Swedes then read traffic in the system for three years, not only between Berlin and Oslo, but also between Germany and

11424-488: Was German procedural flaws, operator mistakes, failure to systematically introduce changes in encipherment procedures, and Allied capture of key tables and hardware that, during the war, enabled Allied cryptologists to succeed. The Abwehr used different versions of Enigma machines. In November 1942, during Operation Torch , a machine was captured which had no plugboard and the three rotors had been changed to rotate 11, 15, and 19 times rather than once every 26 letters, plus

11536-420: Was aided by fellow mathematician-cryptologists Jerzy Różycki and Henryk Zygalski , both of whom had been recruited with Rejewski from Poznań University , which had been selected for its students' knowledge of the German language, since that area was held by Germany prior to World War I. The Polish Cipher Bureau developed techniques to defeat the plugboard and find all components of the daily key, which enabled

11648-646: Was designed, but not implemented before the war's end, was the Lückenfüllerwalze (gap-fill wheel) that implemented irregular stepping. It allowed field configuration of notches in all 26 positions. If the number of notches was a relative prime of 26 and the number of notches were different for each wheel, the stepping would be more unpredictable. Like the Umkehrwalze-D it also allowed the internal wiring to be reconfigured. The current entry wheel ( Eintrittswalze in German), or entry stator , connects

11760-418: Was employed extensively by Nazi Germany during World War II , in all branches of the German military . The Enigma machine was considered so secure that it was used to encipher the most top-secret messages. The Enigma has an electromechanical rotor mechanism that scrambles the 26 letters of the alphabet. In typical use, one person enters text on the Enigma's keyboard and another person writes down which of

11872-478: Was on sample size for use of frequency analysis. In Europe, Italian scholar Giambattista della Porta (1535–1615) was the author of a seminal work on cryptanalysis, De Furtivis Literarum Notis . Successful cryptanalysis has undoubtedly influenced history; the ability to read the presumed-secret thoughts and plans of others can be a decisive advantage. For example, in England in 1587, Mary, Queen of Scots

11984-578: Was particularly evident before and during World War II , where efforts to crack Axis ciphers required new levels of mathematical sophistication. Moreover, automation was first applied to cryptanalysis in that era with the Polish Bomba device, the British Bombe , the use of punched card equipment, and in the Colossus computers – the first electronic digital computers to be controlled by

12096-493: Was partly because the T52 was by far the most complex cipher of the three, but also because the Luftwaffe very often retransmitted Sturgeon messages using easier-to-attack (or already broken) ciphers, making it unnecessary to attack Sturgeon. Enigma machine The Enigma machine is a cipher device developed and used in the early- to mid-20th century to protect commercial , diplomatic, and military communication. It

12208-631: Was probably intended as a security measure, but ultimately allowed the Polish Clock Method and British Banburismus attacks. The Naval version of the Wehrmacht Enigma had always been issued with more rotors than the other services: At first six, then seven, and finally eight. The additional rotors were marked VI, VII and VIII, all with different wiring, and had two notches, resulting in more frequent turnover. The four-rotor Naval Enigma (M4) machine accommodated an extra rotor in

12320-453: Was rotation of at least the right hand rotor and less often the other two, resulting in a different substitution alphabet being used for every letter in the message. This process continued until the message was completed. The cyphertext recorded by the second operator would then be transmitted, usually by radio in Morse code , to an operator of another Enigma machine. This operator would type in

12432-450: Was tried and executed for treason as a result of her involvement in three plots to assassinate Elizabeth I of England . The plans came to light after her coded correspondence with fellow conspirators was deciphered by Thomas Phelippes . In Europe during the 15th and 16th centuries, the idea of a polyalphabetic substitution cipher was developed, among others by the French diplomat Blaise de Vigenère (1523–96). For some three centuries,

12544-399: Was used briefly in 1940, possibly by mistake, and was solved by Hut 6 . The fourth version, first observed on 2 January 1944, had a rewireable reflector, called Umkehrwalze D , nick-named Uncle Dick by the British, allowing the Enigma operator to alter the connections as part of the key settings. The plugboard ( Steckerbrett in German) permitted variable wiring that could be reconfigured by

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