The Enigma machines are a series of electro-mechanical rotor cipher machines developed and used in the early- to mid-20th century to protect commercial and military communication. Enigma was invented by the German engineer Arthur Scherbius at the end of World War I. Early models were used commercially from the early 1920s, adopted by military and government services of several countries, most notably Nazi Germany before and during World War II. Several different Enigma models were produced, but the German military models, having a plugboard, were the most complex. Japanese and Italian models were in use. Around December 1932, Marian Rejewski, a Polish mathematician and cryptanalyst, while working at the Polish Cipher Bureau, used the theory of permutations and flaws in the German military message encipherment procedures to break the message keys of the plugboard Enigma machine. Rejewski achieved this result without knowledge of the wiring of the machine, so the result did not allow the Poles to decrypt actual messages.
The French spy Hans-Thilo Schmidt obtained 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 the Poles, Rejewski used some of that material and the message traffic in September and October to solve for the unknown rotor wiring. The Polish mathematicians were able to build their own Enigma machines, which were called Enigma doubles. Rejewski was aided by cryptanalysts Jerzy Różycki and Henryk Zygalski, both of whom had been recruited with Rejewski from Poznań University; the Polish Cipher Bureau developed techniques to defeat the plugboard and find all components of the daily key, which enabled the Cipher Bureau to read the German Enigma messages starting from January 1933. Over time, the German cryptographic procedures improved, the Cipher Bureau developed techniques and designed mechanical devices to continue reading the Enigma traffic; as part of that effort, the Poles exploited quirks of the rotors, compiled catalogues, built a cyclometer to help make a catalogue with 100,000 entries, made Zygalski sheets and built the electro-mechanical cryptologic bomb to search for rotor settings.
In 1938, the Germans added complexity to the Enigma machines that became too expensive for the Poles to counter. The Poles had six bomby, but when the Germans added two more rotors, ten times as many bomby were needed, the Poles did not have the resources. On 26 and 27 July 1939, in Pyry near Warsaw, the Poles initiated French and British military intelligence representatives into their Enigma-decryption techniques and equipment, including Zygalski sheets and the cryptologic bomb, promised each delegation a Polish-reconstructed Enigma; the demonstration represented a vital basis for the British continuation and effort. 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 was German procedural flaws, operator mistakes, failure to systematically introduce changes in encipherment procedures, Allied capture of key tables and hardware that, during the war, enabled Allied cryptologists to succeed and "turned the tide" in the Allies' favour.
The German firm Scherbius & Ritter, co-founded by Arthur Scherbius, patented ideas for a cipher machine in 1918 and began marketing the finished product under the brand name Enigma in 1923 targeted at commercial markets. With its adoption by the German Navy in 1926 and the German Army and Air Force soon after, the name Enigma became known in military circles; the word enigma is a Latin word, derived from the Ancient Greek word enigma used in English, but not native German. Like other rotor machines, the Enigma machine is a combination of mechanical and electrical subsystems; the mechanical subsystem consists of a keyboard. The mechanical parts act in such a way; 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 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 from a battery, flows through the pressed key, into the newly configured set of circuits and back out again lighting one display lamp, which shows the output letter. For example, when encrypting a message starting ANX... the operator would first press the A key, the Z lamp might light, so Z would be the first letter of the ciphertext. The operator would next press N, X in the same fashion, so on. Current flowed from the battery through a depressed bi-directional keyboard switch to the plugboard. Next, it passed through the plug "A" via the entry wheel, through the wiring of the three or four installed rotors, entered the reflector; the reflector returned the current, via an different path, back through the rotors and entry wheel, proceeding through plug "S" connected with a cable to plug "D", another bi-directional switch to light the appropriate lamp. The repeated changes of electrical
Poland the Republic of Poland, is a country located in Central Europe. It is divided into 16 administrative subdivisions, covering an area of 312,696 square kilometres, has a temperate seasonal climate. With a population of 38.5 million people, Poland is the sixth most populous member state of the European Union. Poland's capital and largest metropolis is Warsaw. Other major cities include Kraków, Łódź, Wrocław, Poznań, Gdańsk, Szczecin. Poland is bordered by the Baltic Sea, Russia's Kaliningrad Oblast and Lithuania to the north and Ukraine to the east and Czech Republic, to the south, Germany to the west; the establishment of the Polish state can be traced back to AD 966, when Mieszko I, ruler of the realm coextensive with the territory of present-day Poland, converted to Christianity. The Kingdom of Poland was founded in 1025, in 1569 it cemented its longstanding political association with the Grand Duchy of Lithuania by signing the Union of Lublin; this union formed the Polish–Lithuanian Commonwealth, one of the largest and most populous countries of 16th and 17th century Europe, with a uniquely liberal political system which adopted Europe's first written national constitution, the Constitution of 3 May 1791.
More than a century after the Partitions of Poland at the end of the 18th century, Poland regained its independence in 1918 with the Treaty of Versailles. In September 1939, World War II started with the invasion of Poland by Germany, followed by the Soviet Union invading Poland in accordance with the Molotov–Ribbentrop Pact. More than six million Polish citizens, including 90% of the country's Jews, perished in the war. In 1947, the Polish People's Republic was established as a satellite state under Soviet influence. In the aftermath of the Revolutions of 1989, most notably through the emergence of the Solidarity movement, Poland reestablished itself as a presidential democratic republic. Poland is regional power, it has the fifth largest economy by GDP in the European Union and one of the most dynamic economies in the world achieving a high rank on the Human Development Index. Additionally, the Polish Stock Exchange in Warsaw is the largest and most important in Central Europe. Poland is a developed country, which maintains a high-income economy along with high standards of living, life quality, safety and economic freedom.
Having a developed school educational system, the country provides free university education, state-funded social security, a universal health care system for all citizens. Poland has 15 UNESCO World Heritage Sites. Poland is a member state of the European Union, the Schengen Area, the United Nations, NATO, the OECD, the Three Seas Initiative, the Visegrád Group; the origin of the name "Poland" derives from the West Slavic tribe of Polans that inhabited the Warta river basin of the historic Greater Poland region starting in the 6th century. The origin of the name "Polanie" itself derives from the early Slavic word "pole". In some languages, such as Hungarian, Lithuanian and Turkish, the exonym for Poland is Lechites, which derives from the name of a semi-legendary ruler of Polans, Lech I. Early Bronze Age in Poland begun around 2400 BC, while the Iron Age commenced in 750 BC. During this time, the Lusatian culture, spanning both the Bronze and Iron Ages, became prominent; the most famous archaeological find from the prehistory and protohistory of Poland is the Biskupin fortified settlement, dating from the Lusatian culture of the early Iron Age, around 700 BC.
Throughout the Antiquity period, many distinct ancient ethnic groups populated the regions of what is now Poland in an era that dates from about 400 BC to 500 AD. These groups are identified as Celtic, Slavic and Germanic tribes. Recent archeological findings in the Kujawy region, confirmed the presence of the Roman Legions on the territory of Poland; these were most expeditionary missions sent out to protect the amber trade. The exact time and routes of the original migration and settlement of Slavic peoples lacks written records and can only be defined as fragmented; the Slavic tribes who would form Poland migrated to these areas in the second half of the 5th century AD. Up until the creation of Mieszko's state and his subsequent conversion to Christianity in 966 AD, the main religion of Slavic tribes that inhabited the geographical area of present-day Poland was Slavic paganism. With the Baptism of Poland the Polish rulers accepted Christianity and the religious authority of the Roman Church.
However, the transition from paganism was not a smooth and instantaneous process for the rest of the population as evident from the pagan reaction of the 1030s. Poland began to form into a recognizable unitary and territorial entity around the middle of the 10th century under the Piast dynasty. Poland's first documented ruler, Mieszko I, accepted Christianity with the Baptism of Poland in 966, as the new official religion of his subjects; the bulk of the population converted in the course of the next few centuries. In 1000, Boleslaw the Brave, continuing the policy of his father Mieszko, held a Congress of Gniezno and created the metropolis of Gniezno and the dioceses of Kraków, Kołobrzeg, Wrocław. However, the pagan unrest led to the transfer of the capital to Kraków in 1038 by Casimir I the Restorer. In 1109, Prince Bolesław III Wrymouth defeated the King of Germany Henry V at the Battle of Hundsfeld, stopping the Ge
Lt. Col. Karol Gwido Langer was, from at least mid-1931, chief of the Polish General Staff's Cipher Bureau, which from December 1932 decrypted Germany's military Enigma-machine ciphers. Poland's prewar achievements paved the way for Britain's World War II Ultra secret. Langer was born in Zsolna, Upper Hungary but spent his childhood in Cieszyn in Silesia, where his family came from. By according to Polish military historian Władysław Kozaczuk, the Bureau had been formed by merger of the Radio Intelligence Office and the Polish-Cryptography Office. Langer remained at the head of the Cipher Bureau and its successor field agency until the latter was disbanded in November 1942 upon the German occupation of southern France's Vichy "Free Zone." Major Langer had on 15 January 1929, after a tour of duty as chief of staff of the First Infantry Division, become chief of the General Staff's Radio Intelligence Office, subsequently of the Cipher Bureau. As the Cipher Bureau's chief, Langer was responsible for Polish cryptography.
Langer's Cipher Bureau has become famous for having in December 1932 broken the German Enigma cipher and read it through the German invasion of France in May–June 1940, after that. In March 1943, as Lt. Col. Langer, his deputy, Major Maksymilian Ciężki, head of the prewar B. S.-4, Lt. Antoni Palluth and civilians Edward Fokczyński and Kazimierz Gaca were attempting to cross from German-occupied France into Spain, they were betrayed by their French guide and captured by the Germans. Interrogated about work on Enigma, Langer "decided mix truth with lies, present my lies in such a way that they had the veneer of truth." He told the Germans that before the war the Bureau had sporadically solved Enigma ciphers, but that during the war they had no longer been able to. Langer advised the panel of his interrogators that, since Major Ciężki knew more about the subject than he, they should summon Ciężki. "They agreed, Ciężki managed to convince them that the changes made before the war made decryption during the war impossible."
The two Polish officers thus succeeded in protecting the secret of Allied Enigma decryption, thereby enabling Ultra to continue doing its vital work for Allied victory. After Langer and Ciężki had been liberated by the Allies and had reached Britain, Langer was crushed to find himself blamed for his men's capture in France by the Germans, he died at the Polish Army signals camp at Kinross, Scotland, on 30 March 1948 and was buried in Wellshill Cemetery in Perth, Scotland to be next to the 381 Polish pilots buried in that cemetery. His grave was marked by a standard Commonwealth War Graves Commission headstone. On 1 December 2010 his remains were exhumed, following a request by his daughter Hanna Kublicka-Piottuch. On 10 December Langer's remains received a funeral with full military honors and were interred at the communal cemetery in Cieszyn, Poland, his new gravestone is of black granite and describes his role in the breaking of the German Enigma ciphers. Grand Cross of the Order of Polonia Restituta Cross of Valour – twice Gold Cross of Merit Cross of Independence Medal Międzysojuszniczy = Medaille Interalliée List of Poles Władysław Kozaczuk, Enigma: How the German Machine Cipher Was Broken, How It Was Read by the Allies in World War Two and translated by Christopher Kasparek, Frederick, MD, University Publications of America, 1984, ISBN 0-89093-547-5.
Hugh Sebag-Montefiore, Enigma: the Battle for the Code, Weidenfeld & Nicolson, 2000, ISBN 0-297-84251-X
Cryptography or cryptology is the practice and study of techniques for secure communication in the presence of third parties called adversaries. More cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, electrical engineering, communication science, physics. Applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, military communications. Cryptography prior to the modern age was synonymous with encryption, the conversion of information from a readable state to apparent nonsense; the originator of an encrypted message shares the decoding technique only with intended recipients to preclude access from adversaries. The cryptography literature uses the names Alice for the sender, Bob for the intended recipient, Eve for the adversary. Since the development of rotor cipher machines in World War I and the advent of computers in World War II, the methods used to carry out cryptology have become complex and its application more widespread.
Modern cryptography is based on mathematical theory and computer science practice. It is theoretically possible to break such a system, but it is infeasible to do so by any known practical means; these schemes are therefore termed computationally secure. There exist information-theoretically secure schemes that provably cannot be broken with unlimited computing power—an example is the one-time pad—but these schemes are more difficult to use in practice than the best theoretically breakable but computationally secure mechanisms; the growth of cryptographic technology has raised a number of legal issues in the information age. Cryptography's potential for use as a tool for espionage and sedition has led many governments to classify it as a weapon and to limit or prohibit its use and export. In some jurisdictions where the use of cryptography is legal, laws permit investigators to compel the disclosure of encryption keys for documents relevant to an investigation. Cryptography plays a major role in digital rights management and copyright infringement of digital media.
The first use of the term cryptograph dates back to the 19th century—originating from The Gold-Bug, a novel by Edgar Allan Poe. Until modern times, cryptography referred exclusively to encryption, the process of converting ordinary information into unintelligible form. Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. A cipher is a pair of algorithms that create the reversing decryption; the detailed operation of a cipher is controlled both by the algorithm and in each instance by a "key". The key is a secret a short string of characters, needed to decrypt the ciphertext. Formally, a "cryptosystem" is the ordered list of elements of finite possible plaintexts, finite possible cyphertexts, finite possible keys, the encryption and decryption algorithms which correspond to each key. Keys are important both formally and in actual practice, as ciphers without variable keys can be trivially broken with only the knowledge of the cipher used and are therefore useless for most purposes.
Ciphers were used directly for encryption or decryption without additional procedures such as authentication or integrity checks. There are two kinds of cryptosystems: asymmetric. In symmetric systems the same key is used to decrypt a message. Data manipulation in symmetric systems is faster than asymmetric systems as they use shorter key lengths. Asymmetric systems use a public key to encrypt a private key to decrypt it. Use of asymmetric systems enhances the security of communication. Examples of asymmetric systems include RSA, ECC. Symmetric models include the used AES which replaced the older DES. In colloquial use, the term "code" is used to mean any method of encryption or concealment of meaning. However, in cryptography, code has a more specific meaning, it means the replacement of a unit of plaintext with a code word. Cryptanalysis is the term used for the study of methods for obtaining the meaning of encrypted information without access to the key required to do so; some use the terms cryptography and cryptology interchangeably in English, while others use cryptography to refer to the use and practice of cryptographic techniques and cryptology to refer to the combined study of cryptography and cryptanalysis.
English is more flexible than several other languages in which crypto
Enigma rotor details
This article contains technical details about the rotors of the Enigma machine. Understanding the way the machine encrypts requires taking into account the current position of each rotor, the ring setting and its internal wiring. Since the same wires are used for forwards and backwards legs, a major cryptographic weakness is that no letter can map to itself; the effect of rotation on the rotors can be demonstrated with some examples. As an example, let us take rotor type I of Enigma I without any ring setting offset, it can be seen that an A is encoded as an E, a B encoded as a K, a K is encoded as an N. Notice that every letter is encoded into another. In the case of the reflectors, in this example Wide B is taken where an A is returned as a Y and the Y is returned as an A. Notice that the wirings are connected as a loop between two letters; when a rotor has stepped, the offset must be taken into account to know what the output is, where it enters the next rotor. If for example rotor I is in the B-position, an A enters at the letter B, wired to the K.
Because of the offset this K enters the next rotor in the J position. With the rotors I, II and III, wide B-reflector, all ring settings in A-position, start position AAA, typing AAAAA will produce the encoded sequence BDZGO; the ring settings, or Ringstellung, are used to change the position of the internal wiring relative to the rotor. They do the alphabet ring on the exterior; those are fixed to the rotor. Changing the ring setting will therefore change the positions of the wiring, relative to the turnover-point and start position; the ring setting will rotate the wiring. Where rotor I in the A-position encodes an A into an E, with a ring setting offset B-02 it will be encoded into K As mentioned before these encodings only happen after the key is pressed and the rotor has turned. Tracing the signal on the rotors AAA is therefore only possible if a key is pressed while the rotors were in the position AAZ. With the rotors I, II, III, wide B-reflector, all ring settings in B-position, start position AAA, typing AAAAA will produce the encoded sequence EWTYX.
This table shows. Each rotor is a simple substitution cipher; the letters are listed as connected to alphabet order. If the first letter of a rotor is E, this means that the A is wired to the E; this does not mean that E is wired to A. This looped wiring is only the case with the reflectors. TerminologyThe reflector is known as the reversing drum or, from the German, the Umkehrwalze or UKW. Technical comments related to Enigma modifications 1939-1945. In 1941 it became known to the Swiss, it was decided to make some design modifications. One of the modifications consisted in modifying the wheel stepping on the Swiss Army machine; the slow, left-hand wheel was made stationary during operation while the second wheel stepped with every key stroke. The third wheel and the UKW would step in the normal fashion with Enigma stepping for the third wheel; the stationary but rotatable left-hand wheel was meant to make up for the missing stecker connections on the commercial machine. Swiss Army Enigma machines were the only machines modified.
The surviving Swiss Air Force machines do not show any signs of modification. Machines used by the diplomatic service were not altered either; the single turnover notch positioned on the left side of the rotor triggers the stepping motion by engaging the ratchet teeth of the wheel to the left. Rotors had two turnover notches; the table below lists the turnover notch point of each rotor. In the following examples you can observe a double step sequence; the used rotors are I, II, III, with turnovers on Q, E and V. It is the right rotor's behavior. Normal sequence:AAU — normal step of right rotor AAV — right rotor goes in V—notch position ABW — right rotor takes middle rotor one step further ABX — normal step of right rotorDouble step sequence:ADU — normal step of right rotor ADV — right rotor goes in V—notch position AEW — right rotor steps, takes middle rotor one step further, now in its own E—notch position BFX — normal step of right rotor, double step of middle rotor, normal step of left rotor BFY — normal step of right rotor The introduction of the fourth rotor was anticipated because captured material dated January 1941 had made reference to the development of a fourth rotor wheel.
On 1 February 1942, the Enigma messages began to be encoded using a new Enigma version, brought into use. The previous 3-rotor Enigma model had been modified with the old reflector replaced by a thin rotor and a new thin reflector. Breaking Shark on 3-rotor bombes would have taken 50 to 100 times as long as an average Air Force or Army message, it seemed, that effective, fast, 4-rotor bombes were the only way forward. Encoding mistakes by cipher clerks allowed the British to determine the wiring of the new reflector and its rotor. Mahon, A. P; the History of Hut 8 1939–1945, Richmond, Surrey, TW9 4DU: National Archives, Reference HW 25/2 enigvar2.pdf enigmabombe.htm ultraenigmawirings.htm g-312.zip
Cryptanalysis of the Enigma
Cryptanalysis of the Enigma ciphering system enabled the western Allies in World War II to read substantial amounts of Morse-coded radio communications of the Axis powers, enciphered using Enigma machines. This yielded military intelligence which, along with that from other decrypted Axis radio and teleprinter transmissions, was given the codename Ultra; this was considered by western Supreme Allied Commander Dwight D. Eisenhower to have been "decisive" to the Allied victory; the Enigma machines were a family of portable cipher machines with rotor scramblers. Good operating procedures, properly enforced, would have made the plugboard Enigma machine unbreakable. However, most of the German military forces, secret services and civilian agencies that used Enigma employed poor operating procedures, it was these poor procedures that allowed the Enigma machines to be reverse-engineered and the ciphers to be read; the German plugboard-equipped Enigma became Nazi Germany's principal crypto-system. It was broken by the Polish General Staff's Cipher Bureau in December 1932, with the aid of French-supplied intelligence material obtained from a German spy.
A month before the outbreak of World War II, at a conference held near Warsaw, the Polish Cipher Bureau shared its Enigma-breaking techniques and technology with the French and British. During the German invasion of Poland, core Polish Cipher Bureau personnel were evacuated, via Romania, to France where they established the PC Bruno signals intelligence station with French facilities support. Successful cooperation among the Poles, the French, the British at Bletchley Park continued until June 1940, when France surrendered to the Germans. From this beginning, the British Government Code and Cypher School at Bletchley Park built up an extensive cryptanalytic capability; the decryption was of Luftwaffe and a few Heer messages, as the Kriegsmarine employed much more secure procedures for using Enigma. Alan Turing, a Cambridge University mathematician and logician, provided much of the original thinking that led to the design of the cryptanalytical bombe machines that were instrumental in breaking the naval Enigma.
However, the Kriegsmarine introduced an Enigma version with a fourth rotor for its U-boats, resulting in a prolonged period when these messages could not be decrypted. With the capture of relevant cipher keys and the use of much faster US Navy bombes, rapid reading of U-boat messages resumed; the Enigma machines produced a polyalphabetic substitution cipher. During World War I, inventors in several countries realized that a purely random key sequence, containing no repetitive pattern, would, in principle, make a polyalphabetic substitution cipher unbreakable; this led to the development of rotor cipher machines which alter each character in the plaintext to produce the ciphertext, by means of a scrambler comprising a set of rotors that alter the electrical path from character to character, between the input device and the output device. This constant altering of the electrical pathway produces a long period before the pattern—the key sequence or substitution alphabet—repeats. Decrypting enciphered messages involves three stages, defined somewhat differently in that era than in modern cryptography.
First, there is the identification of the system in use, in this case Enigma. Today, it is assumed that an attacker knows how the encipherment process works and breaking is used for solving a key. Enigma machines, had so many potential internal wiring states that reconstructing the machine, independent of particular settings, was a difficult task; the Enigma rotor cipher machine was an excellent system. It generated a polyalphabetic substitution cipher, with a period before repetition of the substitution alphabet, much longer than any message, or set of messages, sent with the same key. A major weakness of the system, was that no letter could be enciphered to itself; this meant that some possible solutions could be eliminated because of the same letter appearing in the same place in both the ciphertext and the putative piece of plaintext. Comparing the possible plaintext Keine besonderen Ereignisse, with a section of ciphertext, might produce the following: The mechanism of the Enigma consisted of a keyboard connected to a battery and a current entry plate or wheel, at the right hand end of the scrambler.
This contained a set of 26 contacts that made electrical connection with the set of 26 spring-loaded pins on the right hand rotor. The internal wiring of the core of each rotor provided an electrical pathway from the pins on one side to different connection points on the other; the left hand side of each rotor made electrical connection with the rotor to its left. The leftmost rotor made contact with the reflector; the reflector provided a set of thirteen paired connections to return the current back through the scrambler rotors, to the lampboard where a lamp under a letter was illuminated. Whenever a key on the keyboard was pressed, the stepping motion was actuated, advancing the rightmost rotor one position; because it moved with each key pressed it is sometimes called the fast rotor. When a notch on that rotor engaged with a pawl on the middle rotor, that too moved. There are a huge n
Banburismus was a cryptanalytic process developed by Alan Turing at Bletchley Park in Britain during the Second World War. It was used by Bletchley Park's Hut 8 to help break German Kriegsmarine messages enciphered on Enigma machines; the process used sequential conditional probability to infer information about the settings of the Enigma machine. It gave rise to Turing's invention of the ban as a measure of the weight of evidence in favour of a hypothesis; this concept was applied in Turingery and all the other methods used for breaking the Lorenz cipher. The aim of Banburismus was to reduce the time required of the electromechanical Bombe machines by identifying the most right-hand and middle wheels of the Enigma. Hut 8 performed the procedure continuously for two years, stopping only in 1943 when sufficient bombe time became available. Banburismus was a development of the "clock method" invented by the Polish cryptanalyst Jerzy Różycki. Hugh Alexander was regarded as the best of the Banburists.
He and I. J. Good considered the process more an intellectual game than a job, it was "not easy enough to be trivial, but not difficult enough to cause a nervous breakdown". In the first few months after arriving at Bletchley Park in September 1939, Alan Turing deduced that the message-settings of Kriegsmarine Enigma signals were enciphered on a common Grundstellung, were super-enciphered with a bigram and a trigram lookup table; these trigram tables were in a book called the Kenngruppenbuch. However, without the bigram tables, Hut 8 were unable to start attacking the traffic. A breakthrough was achieved after the Narvik pinch in which the disguised armed trawler Polares, on its way to Narvik in Norway, was seized by HMS Griffin in the North Sea on 26 April 1940; the Germans did not have time to destroy all their cryptographic documents, the captured material revealed the precise form of the indicating system, supplied the plugboard connections and Grundstellung for 23 and 24 April and the operators' log, which gave a long stretch of paired plaintext and enciphered message for the 25th and 26th.
The bigram tables themselves were not part of the capture, but Hut 8 were able to use the settings-lists to read retrospectively, all the Kriegsmarine traffic, intercepted from 22 to 27 April. This allowed them do a partial reconstruction of the bigram tables and start the first attempt to use Banburismus to attack Kriegsmarine traffic, from 30 April onwards. Eligible days were those where at least 200 messages were received and for which the partial bigram-tables deciphered the indicators; the first day to be broken was 8 May 1940, thereafter celebrated as "Foss's Day" in honour of Hugh Foss, the cryptanalyst who achieved the feat. This task took until November that year, by which time the intelligence was out of date, but it did show that Banburismus could work, it allowed much more of the bigram tables to be reconstructed, which in turn allowed 14 April and 26 June to be broken. However, the Kriegsmarine had changed the bigram tables on 1 July. By the end of 1940, much of the theory of the Banburismus scoring system had been worked out.
The First Lofoten pinch from the trawler Krebs on 3 March 1941 provided the complete keys for February – but no bigram tables or K book. The consequent decrypts allowed the statistical scoring system to be refined so that Banburismus could become the standard procedure against Kriegsmarine Enigma until mid-1943. Banburismus utilised a weakness in the indicator procedure of Kriegsmarine Enigma traffic. Unlike the German Army and Airforce Enigma procedures, the Kriegsmarine used a Grundstellung provided by key lists, so it was the same for all messages on a particular day; this meant that the three-letter indicators were all enciphered with the same rotor settings so that they were all in depth with each other. The indicators for two messages were never the same, but it could happen that, part-way through a message, the rotor positions became the same as the starting position of the rotors for another message, the parts of the two messages that overlapped in this way were in depth; the principle behind Banburismus is simple.
If two sentences in English or German are written down one above the other, a count is made of how a letter in one message is the same as the corresponding letter in the other message. For a random sequence, the repeat rate for single letters is expected to be 1 in 26, for the German Navy messages it was shown to be 1 in 17. If the two messages were in depth the matches occur just as they did in the plaintexts. However, if the messages were not in depth the two ciphertexts will compare as if they were random, giving a repeat rate of about 1 in 26; this allows an attacker to take two messages whose indicators differ only in the third character, slide them against each other looking for the giveaway repeat pattern that shows where they align in depth. The comparison of two messages to look for repeats was made easier by punching the messages onto thin cards about 250 mm high by several metres wide. A hole at the top of a column on the card represented an'A' at that position, a hole at the bottom represented a'Z'.
The two message-cards were laid on top of each other on a light-box and where the light shone through, there was a repeat. This made it much simpler to count the repeats; the cards were printed in Banbury in Oxfordshire. They became known as'banburies' at Bl