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The Enigma-M4 (also called ''Schlüssel'' M, more precisely ''Schlüssel'' M Form M4) is a rotor key machine that was used for encrypted communication by the German
Kriegsmarine The (, ) was the navy of Nazi Germany from 1935 to 1945. It superseded the Imperial German Navy of the German Empire (1871–1918) and the inter-war (1919–1935) of the Weimar Republic. The was one of three official military branch, branche ...
during
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
from October 1941. In contrast to the previously used Enigma-M3 and the
Enigma I 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 was employed extensively by Nazi Germany during World War II, in all branches of the G ...
and the Enigma-G used by the German Secret services, the Enigma-M4 is characterized by ''four'' rollers (except for the entry roller and the reverse roller). This makes its encryption
cryptographic Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More gen ...
significantly stronger than that of the other Enigma variants with only ''three'' rotors and therefore could not be broken by the Allies for a long time.


Previous history

All parts of the German
Wehrmacht The ''Wehrmacht'' (, ) were the unified armed forces of Nazi Germany from 1935 to 1945. It consisted of the German Army (1935–1945), ''Heer'' (army), the ''Kriegsmarine'' (navy) and the ''Luftwaffe'' (air force). The designation "''Wehrmac ...
used the rotor cipher machine to
encrypt In cryptography, encryption (more specifically, encoding) is the process of transforming information in a way that, ideally, only authorized parties can decode. This process converts the original representation of the information, known as plai ...
their secret messages. Enigma. However, different models were used. While the army and air force used the Enigma I almost exclusively, there were different model variants of the Enigma-M for the navy, which usually referred to it as the "Schlüssel M". The main difference was the use of more rollers than in the Enigma I, where three rollers could be selected from a range of five. This resulted in 5-4-3 = 60 possible roller positions of the Enigma I. The Enigma-M1, on the other hand, had an assortment of six different rollers (marked with the Roman numerals I to VI), three of which were inserted into the machine. This increased the combinatorial complexity to 6-5-4 = 120 possible roller positions. In the Enigma-M2, the range of rollers had been increased by a further one, so that 7-6-5 = 210 roller layers were now possible. And with the Enigma-M3, which was used by the navy at the beginning of the war, there were eight rollers, three of which were used. This meant that the M3 had 8-7-6 = 336 possible roller positions. While the M1 to M3 models only ever used ''three'' rollers in the machine, the M4 had ''four'' rollers next to each other in the machine. This significantly increased the cryptographic security of the M4 compared to its predecessor models. The operation was described in the naval service regulation ''M.Dv.Nr. 32/1'' with the title "Der Schlüssel M - Verfahren M Allgemein". The key procedure used in the Enigma-M4 was precisely defined in this document. A particularly important part of the key procedure, in addition to correct operation, was the agreement of a common cryptological key. As with all symmetric cryptosystems, the sender and receiver of an encrypted secret message not only had to have the same machine, but also had to set it identically to each other. For this purpose, secret key tables were distributed in advance to all authorized participants. To ensure security within such a large organization as the Kriegsmarine, there were many different key networks, as in the army and air force, for example Aegir for surface warships and auxiliary cruisers overseas, Hydra for warships near the coast, Medusa for U-boats in the Mediterranean, for
battleship A battleship is a large, heavily naval armour, armored warship with a main battery consisting of large naval gun, guns, designed to serve as a capital ship. From their advent in the late 1880s, battleships were among the largest and most form ...
s and
heavy cruiser A heavy cruiser was a type of cruiser, a naval warship designed for long range and high speed, armed generally with naval guns of roughly 203 mm (8 inches) in calibre, whose design parameters were dictated by the Washington Naval Treat ...
s and Triton for the Atlantic submarines. There were other key nets. The Kriegsmarine initially used the Enigma-M3 exclusively for all of them. However, the need was soon recognized to form a separate, specially secured key network for the Einheiten operating on the Hoheher See. In October 1941, a letter from the Oberkommando der Kriegsmarine (OKM) to the Commander of the Battleships introduced the "Neptun key board" as a new key and ordered the use of the Enigma-M4 for this purpose. This took place four months before the M4 was put into service for the U-boats. Unlike Triton, the Neptun key network was not broken at the time.


Structure

The
Construction Construction are processes involved in delivering buildings, infrastructure, industrial facilities, and associated activities through to the end of their life. It typically starts with planning, financing, and design that continues until the a ...
of the Enigma-M4 has some special features compared to the
Enigma I 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 was employed extensively by Nazi Germany during World War II, in all branches of the G ...
. The most important difference is the use of four rollers (rotors) compared to only three in the other models. The four rollers were selected from a range of eight plus two rollers. A distinction had to be made between rollers I to V, which were also used on the Enigma-I, and rollers VI to VIII, which were familiar from the Enigma-M3, and the two rollers specially designed for the Enigma-M4, which were thinner than the others and were therefore referred to as "thin" rollers. The technical reason for the production of thin rollers was the Navy's desire to be able to continue using the same housing as Enigma I and Enigma-M3. For this purpose, the space previously occupied by a (thick) reversing roller now had to be used by a thin reversing roller and one of the newly added thin fourth rollers. Instead of
Roman numerals Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...
, the thin rollers were marked with
Greek letters The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. It was derived from the earlier Phoenician alphabet, and is the earliest known alphabetic script to systematically write vowels as we ...
, namely "β" (
Beta Beta (, ; uppercase , lowercase , or cursive ; or ) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Ancient Greek, beta represented the voiced bilabial plosive . In Modern Greek, it represe ...
) and "γ" (
Gamma Gamma (; uppercase , lowercase ; ) is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop . In Modern Greek, this letter normally repr ...
). Although they could each be manually rotated to one of 26 positions, unlike rollers I to VIII, they did not rotate any further during the encryption process. The wiring diagram of the entry roller and the eight rotating rollers (I to VIII) of the Enigma-M4 was identical to the Enigma I and M3. In particular, the two non-rotating thin rollers "Beta" and "Gamma" and the two equally thin reversing rollers (UKW) "Bruno" and "Caesar". The wiring of the two thin rollers and the reversing rollers was designed in such a way that the combination of the reversing roller (UKW) with the "matching" roller (i.e. Bruno with Beta or Caesar with Gamma) results in exactly the same involutory character permutation as the reverse rollers B and C (thick) of the Enigma I and the Enigma-M3 alone. This served the purpose of
backward compatibility In telecommunications and computing, backward compatibility (or backwards compatibility) is a property of an operating system, software, real-world product, or technology that allows for interoperability with an older legacy system, or with Input ...
with the earlier systems. The only requirement for this was that the spell key of the U-boats was chosen so that it began with "A". Then the left cylinder was in exactly the position in which it worked together with the matching VHF in the same way as the corresponding VHF of the other Enigma models. As with the Model-D, the keys and lamps were arranged in a layout similar to QWERTZU. Only the letters P and L were shifted to the edges of the bottom row, in contrast to QWERTZU. Q W E R T Z U I O A S D F G H J K P Y X C V B N M L In contrast to other models such as the Model-D, Model-K or the Model-T, there was no support for digits on the keyboard. Special characters (as in the Model-G) were also not provided. For data compression, the Navy used signal groups (four letters) and phrases from code books such as the Short signal bookletand the Weather short key which consisted purely of letters.


Operation

To fully set the key, the navy distinguished between "outer" and "inner" key parts. The inner key included the selection of the rollers, the roller position and the ring position. The inner key settings could only be made by an officer, who opened the housing and selected, set up and arranged the rollers accordingly. He then closed the Enigma again and handed it over to the radio operator. The radio operator's task was to make the external key settings, i.e. to insert the ten pairs of plugs into the plug board on the front panel of the M4 according to the day key, close the front flap and then turn the four rollers to the correct starting position. While the inner settings were only changed every two days, the outer settings had to be changed every day. The key change also took place on the high seas at 12:00 D.G.Z. ("German legal time"), for example early in the morning for U-boats operating off the American east coast. The keys ordered were listed on top-secret "key boards" at the time. Here, too, a distinction was made between internal and external settings. The key board intended for the officer with the inner settings looked something like this: Key M " T r i t o n " --------------------------- Month: J u n e 1945 Test number: 123 ------ ---------------- Secret matter of command! ---------------------- Key panel M-General --------------------------- (Schl.T. M Allg.) Inner attitude ------------------ Change 1200 h D.G.Z. -------------------------- ---------------------------------------------- , Months- , , , ayd , Inner attitude , ---------------------------------------------- , 29. , B Beta VII IV V , , , A G N O , ---------------------------------------------- , 27. , B Beta II I VIII , , , A T Y F , ---------------------------------------------- , 25. , B Beta V VI I , , , A M Q T , ---------------------------------------------- Only a few days of the month are shown above as an example, with the days sorted in descending order, as was customary at the time. This made it easy to cut off and destroy the "used" codes from previous days. The other key board, which listed the outer key parts, was similarly structured. Example for June 27, 1945: Internal setting "B Beta II I VIII" means that the officer first had to select roller B (thin) as the reversing roller. Then he had to set the non-rotating Greek roller Beta to ring position A, roller II to ring position T, roller I to ring position Y and finally roller VIII on the far right (as a fast rotor) to ring position F and insert the rollers in the order from left to right. With a little feeling, the ring position could also be set on installed rollers. The officer locked the roller cover and handed the M4 over to the encryptor, who made the external settings using his own documents. Key M " T r i t o n " --------------------------- Month: J u n e 1945 Test number: 123 ------ ---------------- Secret commando matter! ---------------------- Key panel M-General --------------------------- (Schl.T. M Allg.) External setting ------------------ Change 1200 h D.G.Z. -------------------------- ---------------------------------------------------------------------- , Mon- , , Home - , , ths- , P l u g c o n n e c t i o n s , Posi- , , day , , tion , ---------------------------------------------------------------------- , 30. , 18/26 17/4 21/6 3/16 19/14 22/7 8/1 12/25 5/9 10/15 , H F K D , , 29. , 20/13 2/3 10/4 21/24 12/1 6/5 16/18 15/8 7/11 23/26 , O M S R , , 28. , 9/14 4/5 18/24 3/16 20/26 23/21 12/19 13/2 22/6 1/8 , E Y D X , , 27. , 16/2 25/21 6/20 9/17 22/1 15/4 18/26 8/23 3/14 5/19 , T C X K , , 26. , 20/13 26/11 3/4 7/24 14/9 16/10 8/17 12/5 2/6 15/23 , Y S R B , The radio master had to connect the double-pole sockets on the front panel with corresponding double-pole cables. As a rule, exactly ten cables were plugged in. Six letters remained "unplugged". The plug connections in the navy (in contrast to the other parts of the Wehrmacht) were listed numerically and not alphabetically. In the corresponding secret Naval service regulations ''M.Dv.Nr. 32/1'' with the title "Der Schlüssel M - Verfahren M Allgemein" a conversion table was given as an aid for the operator. Now, the key operator had to turn the four rollers to a defined starting position and the Enigma-M4 was ready to encrypt or decrypt radio messages.


Key room

The size of the key space of the Enigma-M4 can be calculated from the four individual partial keys and the number of different key settings possible in each case. The total key space of the Enigma-M4 results from the following four factors: ; a) die Walzenlage : Three out of eight reels are selected for the right three places. In addition, one of two Greek rollers for the left-hand position and one of two reversing rollers on the far left. This results in 2-2-(8-7-6) = 1344 possible roller positions (corresponds to a "
key length In cryptography, key size or key length refers to the number of bits in a key used by a cryptographic algorithm (such as a cipher). Key length defines the upper-bound on an algorithm's security (i.e. a logarithmic measure of the fastest known at ...
" of about 10 
bit The bit is the most basic unit of information in computing and digital communication. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as ...
). ; b) the ring position : There are 26 different ring positions for each of the two right-hand rollers. The rings of the two left-hand rollers do not contribute to the enlargement of the key space, as the Greek roller is not indexed. A total of 262 = 676 ring positions (corresponds to about 9 bits) are relevant. ; c) the roller position : There are 26 different roller positions for each of the four rollers. (The reverse roller cannot be adjusted.) A total of 264 = 456,976 roller positions are therefore available (corresponds to just under 19 bit). If the ring position is assumed to be known, 263-262 = 16,900 initial positions to be eliminated as cryptographically redundant. This leaves 440,076 roller positions as relevant (also corresponds to about 19 bit). ; d) the plug connections : A maximum of 13 plug connections can be made between the 26 letters. Based on the case of the empty connector board (considered as number zero in the table below), there are 26 options for the first connection for one connector end and then another 25 for the other end of the cable. This means that there are 26-25 different options for plugging in the first cable. However, as it does not matter in which order the two cable ends are plugged in, half of the options are omitted. This leaves 26-25/2 = 325 possibilities for the first connection. For the second, you get 24-23/2 = 276 possibilities. In general, there are (26-2''n''+2)-(26-2''n''+1)/2 possibilities for the ''n''-th plug connection (see also: Gaussian summation formula). The total number of possible plug combinations when using several plugs results from the product of the possibilities for the individual plug connections. However, since the order of execution is not important here either (it is cryptographically equivalent if, for example, A is plugged in first with X and then B with Y or vice versa, first B with Y and then A with X), the corresponding cases must not be considered as key combinations. In the case of two plug connections, these are exactly half of the cases. The previously determined product must therefore be divided by 2. With three plug connections, there are 6 possible sequences for performing the plug connections, all six of which are cryptographically equivalent. The product must therefore be divided by 6. In the general case, with ''n'' plug connections, the product of the previously determined possibilities is divided by ''n''! (Faculty). The number of possibilities for exactly ''n'' plug connections is given by : \frac \prod_^n \frac \;=\; \frac For the M4, exactly ten plug connections had to be made. According to the table above, this results in 150,738,274,937,250 (more than 150 trillion) plug-in possibilities (corresponds to about 47 bits). The total key space of an Enigma-M4 with three rollers selected from a stock of eight, one of two Greek rollers and one of two reverse rollers and using ten connectors can be calculated from the product of the 1344 roller positions, 676 ring positions, 439,400 roller positions and 150,738,274,937,250 connector possibilities determined in sections a) to d) above. It amounts to: : 1344 · 676 · 440.076 · 150.738.274.937.250 = 60.269.444.695.419.208.913.664.000 That is more than 6-1025 possibilities and corresponds to a key length of almost 86 
bit The bit is the most basic unit of information in computing and digital communication. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as ...
. The key room is huge. However, as explained in more detail in the Main article about the Enigma, the size of the keyspace is only a necessary, but not a sufficient condition for the security of a cryptographic method. Even a method as simple as a simple monoalphabetic substitution (using 26 letters like the M4) has a key space of 26! (factorial), which is roughly 4-1026 and corresponds to about 88 bits and is thus even slightly larger than the Enigma-M4. Nevertheless, a monoalphabetic substitution is very uncertain and can easily be broken ( deciphered).


Deciphering

British cryptanalysts had been working on the deciphering the Enigma at
Bletchley Park Bletchley Park is an English country house and Bletchley Park estate, estate in Bletchley, Milton Keynes (Buckinghamshire), that became the principal centre of Allies of World War II, Allied World War II cryptography, code-breaking during the S ...
, about northwest of
London London is the Capital city, capital and List of urban areas in the United Kingdom, largest city of both England and the United Kingdom, with a population of in . London metropolitan area, Its wider metropolitan area is the largest in Wester ...
, since the outbreak of the war. The most important tool was a special electromechanical machine called the Turing bomb, which was invented by the English mathematician
Alan Turing Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. He was highly influential in the development of theoretical computer ...
and which could be used to determine the valid day keys. This required "probable words", i.e. text passages that appear in the plaintext to be deciphered. The cryptanalysts benefited from the German thoroughness in writing routine messages, such as weather reports, with recurring patterns that could be used for deciphering. With the help of the Turing bomb, it was possible from January 1940 to decipher first the radio messages encrypted by the Luftwaffe and later also those of the army. The encryption method used by the Kriegsmarine, i.e. the ''Schlüssel M'', proved to be much more resistant to decryption attempts. Even the Enigma-M3, with its only three (and not yet four) cylinders, was more difficult to break than the Enigma I used by the Luftwaffe and the army. In addition to the use of a larger range of cylinders (eight instead of just five to choose from), this was also largely due to a particularly sophisticated '' Verfahren zur Spruchschlüsselvereinbarung'', which the navy used. The British codebreakers only succeeded in breaking into the ''Schlüssel M'' in May 1941 after capture of the German U-boat together with an intact M3 engine and all secret documents (
codebook A codebook is a type of document used for gathering and storing cryptography codes. Originally, codebooks were often literally , but today "codebook" is a byword for the complete record of a series of codes, regardless of physical format. Cr ...
s) including the important double-letter exchange boards by the British
destroyer In naval terminology, a destroyer is a fast, maneuverable, long-endurance warship intended to escort larger vessels in a fleet, convoy, or carrier battle group and defend them against a wide range of general threats. They were conceived i ...
on May 9, 1941. There was a particularly painful interruption ("black-out") for the British when the M3 was replaced by the M4 (with four rollers) in the U-boats on February 1, 1942. This procedure, called ''Schlüsselnetz Triton'' by the Germans and "Shark" (German: "Hai") by the British, could not be broken for ten months, a period called by the U-boat sailors the "
Second Happy Time The Second Happy Time (; officially (), and also known among German submarine commanders as the "American Shooting Season") was a phase in the Battle of the Atlantic during which Axis submarines attacked merchant shipping and Allied naval ve ...
", during which the German U-boats again scored major successes. The break-in in "Shark" was not achieved until December 1942, after the British destroyer took down the German U-boat in the Mediterranean Sea on October 30, 1942. ''U-559'' was boarded and important secret key documents were captured such as short signal booklet and weather shortcut key, with the help of which Bletchley Park also managed to overcome the Enigma-M4 and Triton. However, it initially took several days to decipher the messages, which reduced the information value. From 1943, the Americans came to the rescue, under the leadership of Joseph Desch at the
United States Naval Computing Machine Laboratory The United States Naval Computing Machine Laboratory (NCML) was a highly secret design and manufacturing site for code-breaking machinery located in Building 26 of the National Cash Register (NCR) company in Dayton, Ohio and operated by the Uni ...
(NCML), based at the
National Cash Register Company NCR Voyix Corporation, previously known as NCR Corporation and National Cash Register, is a global software, consulting and technology company providing several professional services and electronic products. It manufactured self-service kios ...
(NCR) in
Dayton Dayton () is a city in Montgomery County, Ohio, United States, and its county seat. It is the List of cities in Ohio, sixth-most populous city in Ohio, with a population of 137,644 at the 2020 United States census, 2020 census. The Dayton metro ...
(
Ohio Ohio ( ) is a U.S. state, state in the Midwestern United States, Midwestern region of the United States. It borders Lake Erie to the north, Pennsylvania to the east, West Virginia to the southeast, Kentucky to the southwest, Indiana to the ...
), more than 120 units as of April 1943 produced high-speed variants of the British ''bomb'' that were specifically targeted against the M4. American agencies, such as the Signal Security Agency (SSA), the Communications Supplementary Activity (CSAW), and the United States Coast Guard Unit 387 (USCG Unit 387) relieved the British of much of the time-consuming day-to-day key finding and were able to break Triton quickly and routinely. The British now left the M4's key detection to their American allies and their fast ''Desch Bombes''. From September 1943, deciphering M4 radio messages usually took less than 24 hours. Even if a radio message could be completely deciphered, not all parts were always understandable, because position information was "overcoded" using a special procedure and thus specially protected. The Kriegsmarine had introduced the so-called address book procedure for this purpose in November 1941. On June 4, 1944, the capture of again brought up-to-date key material: short signal booklet, identification group booklet and, above all, the so-called address book procedure. This was the urgently sought secret procedure for overcoding the U-boat locations. The yield of secret material from ''U-505'' equaled that of ''U–110'' and ''U–559''. Throughout the war, more than a million naval radio messages were deciphered in Hut Eight (Barrack 8) at Bletchley Park more than one million naval radio messages were deciphered. This covers the period from the fall of 1941 until the unconditional surrender of the Wehrmacht in May 1945, whereby, with the exception of the "blackout" between February and December 1942, it was possible to maintain the uninterrupted nature of deciphering for most of the time.


Significance for the history of war

The decoding of the M4 radio traffic was of enormous importance for the Allied Progress in der U-Boot-Abwehr. The reports from the boats with precise position and course information provided the Allies with a complete strategic situation picture. The U-boats also betrayed themselves simply by sending radio telegrams, which could be detected and localized by
radio direction finding Direction finding (DF), radio direction finding (RDF), or radiogoniometry is the use of radio waves to determine the direction to a radio source. The source may be a cooperating radio transmitter or may be an inadvertent source, a natural ...
such as
Huff-Duff High-frequency direction finding, usually known by its abbreviation HF/DF or nickname huff-duff, is a type of radio direction finder (RDF) introduced in World War II. High frequency (HF) refers to a radio band that can effectively communicate ove ...
by Allied warships. Radar as a means of radiolocation at sea and ASDIC, an early form of
sonar Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigate, measure distances ( ranging), communicate with or detect objects o ...
, for sound detection under water was another important
tactical Tactic(s) or Tactical may refer to: * Tactic (method), a conceptual action implemented as one or more specific tasks ** Military tactics, the disposition and maneuver of units on a particular sea or battlefield ** Chess tactics ** Political tact ...
tool for submarine hunting. But none of this provided as complete a picture of the situation as the radio transmissions. The immediate consequence of the American decryptions was the sinking of eleven of the eighteen German Versorgungs-U-Boote ("''Milchkühe''") within a few months in 1943. This led to a weakening of all Atlantic U-boats, which could no longer be supplied at sea, but had to make the long and dangerous journey home through the
Bay of Biscay The Bay of Biscay ( ) is a gulf of the northeast Atlantic Ocean located south of the Celtic Sea. It lies along the western coast of France from Point Penmarc'h to the Spanish border, and along the northern coast of Spain, extending westward ...
to the U-boat bases on the French west coast. Especially for the execution of ''
Operation Overlord Operation Overlord was the codename for the Battle of Normandy, the Allies of World War II, Allied operation that launched the successful liberation of German-occupied Western Front (World War II), Western Europe during World War II. The ope ...
'', the planned invasion of Normandy, it was crucial for the Allied leadership to have the most comprehensive, up-to-date and, of course, correct picture of the situation. After the capture of ''U 505'' immediately before the planned ''
D-Day The Normandy landings were the landing operations and associated airborne operations on 6 June 1944 of the Allied invasion of Normandy in Operation Overlord during the Second World War. Codenamed Operation Neptune and often referred to as ...
'', which then took place two days later on June 6, they feared that the German key procedures could suddenly be changed as a result of the capture of U 505 becoming known. This might have prevented the breaking of the Enigma keys on the day of the invasion, with potentially fatal consequences for the invasion forces. In fact, however, everything remained unchanged and so the day key could be broken in less than two hours after midnight using the ''Cribs'' "WETTERVORHERSAGEBISKAYA", which the British cryptanalysts could easily guess and assumed correctly and the invasion succeeded. Many German U-boat drivers, above all the former chief of the
B-Dienst The ''B-Dienst'' (, observation service), also called x''B-Dienst'', X-''B-Dienst'' and χ''B-Dienst'', was a Department of the German Naval Intelligence Service (, MND III) of the Oberkommando der Marine, OKM that dealt with the interception and ...
(observation service) of the Kriegsmarine, were still very sure long after the war that "their" four-roller key machine was "unbreakable". When British information became known in 1974 which clearly proved that the opposite was the case, this caused a real shock among the survivors of the U-boat war, because of the approximately 40,000 German submariners, around 30,000 had not returned home from deployment - the highest loss rate of all German branches of the armed forces. The special historical significance of the Enigma-M4 and its decryption is underlined by a statement made by former British Prime Minister
Winston Churchill Sir Winston Leonard Spencer Churchill (30 November 1874 – 24 January 1965) was a British statesman, military officer, and writer who was Prime Minister of the United Kingdom from 1940 to 1945 (Winston Churchill in the Second World War, ...
: "The only thing that really frightened me during the war was the U-boat peril." (German: "''Das einzige, wovor ich im Krieg wirklich Angst hatte, war die U-Boot-Gefahr."'')


Security check

Due to various suspicious events, the German side conducted several investigations into the security of its own machine. A significant example of the German considerations, procedures, conclusions and measures derived from them can be found in an English-language, highly secret interrogation protocol classified at the time as ''TOP SECRET "ULTRA"'', which was published immediately after the war, on June 21, 1945, by the Allied (British-American) TICOM ( Target Intelligence Committee) at the Marine Intelligence School in Flensburg-Mürwik. It records the statements of the German naval officer, Lt.z.S Hans-Joachim Frowein, who from July to December 1944 had been assigned to the OKM/4 Skl II (Abteilung II der
Seekriegsleitung The ''Seekriegsleitung'' or SKL (Maritime Warfare Command) was a higher command staff section of the Kaiserliche Marine and the Kriegsmarine The (, ) was the navy of Nazi Germany from 1935 to 1945. It superseded the Imperial German Navy of ...
) to investigate the safety of the M4. The leading German cryptanalyst Wilhelm Tranow, who was also interrogated in this context, explained that the reason for this investigation was the extremely high rate of losses suffered by the German U-boats, particularly in 1943 and the first half of 1944. The German naval command could not explain this, especially why U-boats were sunk in very specific positions, and again asked themselves the question: "Is the machine safe?" To clarify this question, Frowein was seconded from Skl III to Skl II for six months from July 1944 with the order to carry out a thorough investigation into the safety of the four-roller Enigma. Two other officers and ten men were assigned to him for this purpose. They began their investigations with the assumption that the enemy knew the machine, including all the rollers, and that they had a suspected clear text (''Crib'') of 25 letters in length. The reason for choosing this relatively short ''crib'' length was their knowledge that U-Boat radio messages were often very short. The result of their investigation was that this was sufficient to open up the roller position and plug. Frowein was able to explain in detail to the British interrogators his thoughts and procedures at the time when it came to unraveling his own machine. Although neither he nor any of his colleagues had any previous experience in the cryptanalysis of key machines, such as the commercial Enigma, they had succeeded in breaking the M4 within six months, at least in theory. The methods developed were strikingly similar to those actually used by the British in ''B.P.'', but of course Frowein did not know this. As he went on to explain, he had also realized that his break-in method would be severely disrupted if the left or middle roller within the ''crib'' were to advance. This would have required case distinctions in the cryptanalysis, which would have increased the workload by a factor of 26, which was considered to be practically unacceptably high for a potential attacker. After presenting the results, the naval command came to the conclusion that although the M3 and even the M4 were theoretically vulnerable to attack, this would no longer be the case if it was ensured that the roller advance (of the middle roller) occurred sufficiently frequently. In December 1944, it was therefore ordered that, with immediate effect, only rollers with two Transfer notches, i.e. one of rollers VI, VII or VIII, could be used as the right-hand roller. This measure halved the number of possible roller positions (from 8-7-6 = 336 to 8-7-3 = 168), which meant a weakening of the combinatorial complexity, but at the same time strengthened the machine against the recognized weakness. The Kriegsmarine also passed on the results of the investigation to the other parts of the Wehrmacht, which continued to use only the Enigma I, which was cryptographically weaker than the M4, with only three cylinders and the resulting 60 cylinder layers. According to Frowein's statement in the TICOM report, the '' Heeresführung'' was "astonished at the Navy's view based on this investigation" (''...the Army were astonished at the Navy's view based on this investigation).


Timeline

The following is a list of some important dates in the history of the Enigma-M4. Legend: o No deciphering # Deciphering succeeds The three gaps (o) in the deciphering ability of the Allies are striking. The reasons for this are: * In October 1941, "Triton" was formed as a separate key network just for the U-boats (initially still with the M3). * In February 1942, the M4 was introduced for the U-boats, which could only be overcome ten months later in December ("second happy time"). * In March 1943, there was a new edition of the weather shortcut. From September 1943, the M4 radio messages were usually broken within 24 hours. The M4 was manufactured from 1941, initially at the main Konski & Krüger production plant in
Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
. (K&K) in
Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
. From 1942, production was also outsourced to other locations (see also: List of Enigma production codes). A large proportion (around 45%) of the production of the M4 from 1942 was carried out by Olympia Büromaschinenwerke AG in
Erfurt Erfurt () is the capital (political), capital and largest city of the Central Germany (cultural area), Central German state of Thuringia, with a population of around 216,000. It lies in the wide valley of the Gera (river), River Gera, in the so ...
. The following figures are available:


Authentic radio message

An example is a communication from Lieutenant Captain Hartwig Looks, commander of the German U-boat ''U 264'', which was encrypted with an Enigma-M4 on November 19, 1942, shortly before the end of the black-out. Before the encryption, the radio operator transmitted the text in Enigma notation, which he then encrypted letter by letter with the M4 and finally sent the ciphertext in Morse code. As the Enigma can only encode uppercase letters, numbers were written out digit by digit, punctuation marks were replaced by "Y" for comma and "X" for period, proper names were enclosed in "J" and important terms or letters were doubled or tripled to protect against misunderstandings caused by transmission errors. It was also customary for the navy to arrange the text in groups of four, while the army and air force used groups of five. Short radio messages and the almost unavoidable spelling and transmission errors in practice make deciphering based on statistical analyses difficult. A more detailed plaintext: : By U 264 Hartwig Looks - Radio Telegram 1132/19 - Contents: : During an attack by depth charge (ordnance)/water bombs we were pushed under water. The last enemy location we detected was at 8:30 o'clock in naval square AJ 9863 (), heading 220 degrees, speed 8 
knot A knot is an intentional complication in Rope, cordage which may be practical or decorative, or both. Practical knots are classified by function, including List of hitch knots, hitches, List of bend knots, bends, List of loop knots, loop knots, ...
. We are joining. Weather data:
barometric pressure Atmospheric pressure, also known as air pressure or barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1,013.2 ...
1014  millibar falling.
wind Wind is the natural movement of atmosphere of Earth, air or other gases relative to a planetary surface, planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heatin ...
from north-northeast,
strength Strength may refer to: Personal trait *Physical strength, as in people or animals *Character strengths like those listed in the Values in Action Inventory *The exercise of willpower Physics * Mechanical strength, the ability to withstand ...
 4.
Visibility In meteorology, visibility is the measure of the distance at which an object or light can be clearly discerned. It depends on the Transparency and translucency, transparency of the surrounding air and as such, it is unchanging no matter the amb ...
10 
nautical mile A nautical mile is a unit of length used in air, marine, and space navigation, and for the definition of territorial waters. Historically, it was defined as the meridian arc length corresponding to one minute ( of a degree) of latitude at t ...
s. Shortened plain text: From Looks - FT 1132/19 - Contents: Pressed under water during attack, Wabos. Last enemy position 0830 hrs Mar.-Qu. AJ 9863, 220 degrees, 8 nm. Push to. 14 mb, falling. NNO 4. visibility 10. Transcribed plain text in groups of four: vonv onjl ooks jfff ttte inse insd reiz woyy eins neun inha ltxx beia ngri ffun terw asse rged ruec ktyw abos xlet zter gegn erst andn ulac htdr einu luhr marq uant onjo tane unac htse chsd reiy zwoz wonu lgra dyac htsm ysto ssen achx eins vier mbfa ellt ynnn nnno oovi erys icht eins null Ciphertext (with spelling and transcription errors): NCZW VUSX PNYM INHZ XMQX SFWX WLKJ AHSH NMCO CCAK UQPM KCSM HKSE INJU SBLK IOSX CKUB HMLL XCSJ USRR DVKO HULX WCCB GVLI YXEO AHXR HKKF VDRE WEZL XOBA FGYU JQUK GRTV UKAM EURB VEKS UHHV OYHA BCJW MAKL FKLM YFVN RIZR VVRT KOFD ANJM OLBG FFLE OPRG TFLV RHOW OPBE KVWM UQFM PWPA RMFH AGKX IIBG The ciphertext could be deciphered on February 2, 2006, with the following key settings: Basic position and key: Roller position: UKW Bruno-Beta-II-IV-I Ring position: AAAV Plug: AT BL DF GJ HM NW OP QY RZ VX Saying key: VJNA Deciphered text (with spelling and transcription errors, breaks and spaces for readability): von von j looks j hff ttt eins eins drei zwo yy qnns neun inhalt xx bei angriff unter wasser gedrueckt y wabos x letzter gegnerstand nul acht drei nul uhr mar qu anton jota neun acht seyhs drei y zwo zwo nul grad y acht sm y stosse nach x ekns vier mb faellt y nnn nnn ooo vier y sicht eins null At 232 characters (group number 58), the text is unusually long and uses neither a short signal booklet nor the weather abbreviation key. The weather information "Air pressure 1014 mb falling, wind north-north-east with 4 Bft, visibility 10 nm" would have been shortened by a weather abbreviation (WKS) to 8 charactersOberkommando der Kriegsmarine (Ed.): ''Wetterkurzschlüssel'' (= ''Geheimer Wetter und Seeschlüssel der Kriegsmariene''). 3rd edition. Berlin 1942 (cryptomuseum.com DF. hrbw apeh instead of the 44 characters used eins vier mbfa ellt ynnn nnno oovi erys icht eins null


Literature

* Arthur O. Bauer: ''Funkpeilung als alliierte Waffe gegen deutsche U-Boote 1939–1945''. Self-published, Diemen Netherlands 1997, . *
Friedrich L. Bauer Friedrich Ludwig "Fritz" Bauer (10 June 1924 – 26 March 2015) was a German pioneer of computer science and professor at the Technical University of Munich. Life Bauer earned his Abitur in 1942 and served in the Wehrmacht during World War ...
: ''Entzifferte Geheimnisse. Methoden und Maximen der Kryptologie.'' 3rd, revised and expanded edition. Springer, Berlin u. a. 2000, . * Ralph Erskine, Frode Weierud:'' Naval Enigma – M4 and its Rotors.'' In: ''
Cryptologia ''Cryptologia'' is a journal in cryptography published six times per year since January 1977. Its remit is all aspects of cryptography, with a special emphasis on historical aspects of the subject. The founding editors were Brian J. Winkel, Davi ...
.'' Band 11, Nr. 4, 1987, p. 235–244, doi:10.1080/0161-118791862063. * Stephen Harper: ''Kampf um Enigma. Die Jagd auf U-559''. Mittler, Hamburg 2001, . * OKM: ''Der Schlüssel M – Verfahren M Allgemein''. Berlin 1940
cryptomuseum.com
(PDF; 3,3 MB) * Joachim Schröder: ''Folgenschwerer Fund – Der „Fall" U 110 und die sensationelle Erbeutung der „Enigma"''. In: ''Clausewitz – Das Magazin für Militärgeschichte'', Heft 1, 2015, p. 56–61. *
Hugh Sebag-Montefiore Nicholas Hugh Sebag-Montefiore (born 5 March 1955) is a British writer. He trained as a barrister before becoming a journalist and then a non-fiction writer. Biography He has published two books on the history of the Second World War, of whic ...
: ''Enigma – The battle for the code''. Cassell Military Paperbacks, London 2004, .


External links

Details
''Enigma M4''
inCrypto Museum.

Photo gallery and explanations of the M4 and accessories.

by A. P. Mahon.
Die verschiedenen Arten von U-Boot-Funksprüchen
(PDF, 378 kB), Excerpts from the book by Arthur O. Bauer.

Capture of the weather short key and the short signal booklet. Documents
Der Schlüssel M
(PDF; 3,3 MB), Scan of the original 1940 regulation at the Crypto Museum.
Doppelbuchstabentauschtafeln
Password: "Source".
Doppelbuchstabentauschtafeln
Password: "Sea".
Doppelbuchstabentauschtafel B
Password: "River" (authentic spelling). Decipherments
''Breaking German Navy Ciphers''
modern decipherment of the M4.

modern decipherment of the M4. *

' by Ralph Erskine. Exhibits Photos, videos and audios
Foto
of a "Greek roller" Beta (β) in the Crypto Museum.
Video-Interview
with Hartwig Looks (2003) for a convoy attack on YouTube (4 min 15 s). Reproduction projects
Replica of an M4

Replica of an M4
Simulations of the M4

Enigma I, M3 and M4 realistically visualized.
MAC OS



References

{{reflist Maritime communication Communication