# Enigma (machine)

Enigma brand sign
The Enigma key machine (on the left at the edge of the picture: two separate rollers )
The nameplate of the above machine shows below the letter A , which marked the Army and Air Force Enigma, the serial number 604 , the coded production code jla for the manufacturer Heimsoeth & Rinke and the year of manufacture 40 (for 1940).

The Enigma ( Greek αἴνιγμα aínigma , German ' Rätsel ' , spelling also: ENIGMA ) is a rotor key machine that was used in the Second World War to encrypt the Wehrmacht's communications. The police , secret services , diplomatic services , SD , SS , Reichspost and Reichsbahn also use them for secret communication. Despite various improvements in encryption quality introduced before and during the war, the Allies succeeded in deciphering German radio messages almost continuously with a high level of personnel and machine effort .

## history

Arthur Scherbius received his first patent for the Enigma on February 23, 1918 (photo 1913).
Drawing from his patent US1657411 : Ciphering Machine. Registered on February 6, 1923 .
The Writing Enigma (1923) was the first in a long line of models

After the First World War , the German military looked for a replacement for the now outdated, cumbersome and insecure manual encryption methods , such as ÜBCHI , ABC-Ciffre and ADFGX , which had been used until then. For this purpose, machine procedures came into consideration because they promised easier handling and improved cryptographic security. With the introduction of the electric typewriter and the teleprinter at the beginning of the 20th century, several inventors, some independently of one another and almost simultaneously, came up with the idea of ​​the rotor principle for encrypting texts. The first were the two Dutch naval officers Theo A. van Hengel and RPC Spengler in Batavia (then capital of the Dutch East Indies , now Jakarta , capital of Indonesia ) in 1915 . However, they were not allowed to apply for a patent for their invention. The next was in 1917 the American Edward Hugh Hebern ( patent application 1921 ). In 1918, the German was followed by Arthur Scherbius  (picture) and finally in 1919 the Dutchman Hugo Koch and the Swede Arvid Gerhard Damm , all their ideas rotor cipher machines for patent anmeldeten.

The inventor of the Enigma was Arthur Scherbius (1878–1929), an electrical engineer with a doctorate , whose first patent on this was dated February 23, 1918 (see also: Enigma patents ). In the same year on April 15, he offered his new invention to the Imperial Navy , which, however, did not consider the use of machine encryption necessary and rejected him. After the war he decided to market the machine for civil use. The Chiffriermaschinen-Aktiengesellschaft (ChiMaAG) was founded on July 9, 1923 in Berlin ( W 35 , Steglitzer Str. 2, today Pohlstrasse in Berlin-Tiergarten ) for production purposes. The first model of the Enigma, called "Die Schreibende Enigma(picture) , was commercially available for purchase at trade fairs , such as in 1923 in Leipzig and Bern and in 1924 at the International Postal Congress of the Universal Postal Union in Stockholm .

This aroused the interest of the German military, who had learned of the Allied successes in decoding through publications such as Winston Churchill's “The World Crisis” and Julian Corbett's “Naval Operations” . This included the British deciphering of German naval radio messages, which was achieved with the help of the German signal book ( code book ) recovered from the stranded cruiser Magdeburg by allied Russian divers , the French deciphering of ÜBCHI , an early manual key method of the Imperial Army , and its successors, the ABC and ABCD -Chiffre , also the British decipherment of the Zimmermann telegram , after which the USA entered the war , and the French decipherment of the ADFGX and ADFGVX cipher , which culminated in the Radiogramme de la Victoire ( German "Funkspruch des Sieges" ).

Since the German military absolutely wanted to avoid a repetition of this cryptographic catastrophe of the First World War , they recognized the new type of machine encryption as the most secure solution. In 1926, the Enigma was initially used by the Reichsmarine under the name " Radio Key C ", two years later by the army on a trial basis and then disappeared from the civilian market. Shortly after the start of series production , Scherbius had a fatal accident in 1929 . In 1934 Rudolf Heimsoeth and Elsbeth Rinke took over ChiMaAG. Under the new company " Heimsoeth & Rinke " (H&R) they continued the development and production of the machine in Berlin. The time of National Socialism had already begun. In the course of arming the Wehrmacht , a reliable encryption system was required, and nothing stood in the way of the Enigma's success.

It is estimated that just over 40,000 machines were made. In the course of time up to the end of the war in 1945 and beyond, for example in Korea in 1965 , many different models and variants of the Enigma were used. The most widely used one was the Enigma I (read: "Enigma one"), which was used by the Reichswehr from 1930 and later by the Wehrmacht and which embodied the machine key method most frequently used on the German side during World War II. (On the American side, it was the M-209 developed by the Swede Boris Hagelin with around 140,000 units .)

After the war, the British sold captured Enigma copies to various countries in Africa and the Middle East, including Israel .

## principle

The most important functional groups of the Enigma I
The roller set contains three exchangeable and rotating rollers, each of which can take up 26 rotary positions (01 to 26), as well as a fixed reversing roller on the left (here VHF B)

The Enigma I essentially consists of the keyboard for entering letters, a set of three interchangeable rollers and a light bulb field for display. The set of rollers is the heart of the encryption. The three rollers are arranged side by side so that they can rotate independently. Each of them has 26 electrical contacts on both sides . Each contact is assigned one of the 26 capital letters of the Latin alphabet . In each case a contact on one side of a roller is connected to a contact on the other side of the roller by an insulated wire inside the roller. All in all, different for each roller, all 26 contacts on one side of a roller are electrically connected in pairs and irregularly with the 26 contacts on the other side (see also: wiring table in the following chapter ).

If you press a letter key , electric current flows from a 4.5 volt battery in the Enigma via the pressed key through the set of rollers and lights up an indicator lamp. The lit letter corresponds to the encryption of the pressed letter. Since the reels continue to turn with each press of a button, similar to a mechanical odometer , the secret key alphabet changes after each letter.

If you enter “OTTO”, the “PQWS” lamps, for example, light up one after the other. It is important and cryptographically strong that each letter is encrypted in a different way due to the rotation of the rollers, in the example the front O from OTTO to P, but the rear to S. There are many different (secret) " alphabets ", which are used for encryption and calls this polyalphabetic substitution . In contrast, a monoalphabetic substitution only uses a single secret alphabet , and a plaintext letter is always converted into the same ciphertext letter ("OTTO" for example into "GLLG"). If the reels of the Enigma did not turn, you would only get a simple monoalphabetic encryption.

## construction

Sketch: Circuit diagram of the Enigma consisting of
battery (1),
keyboard (2),
connector board (3, 7) with
plug-in cable (8),
roller set (5) with
inlet roller (4) and reversing roller (6) and
the lamp field (9)
Internal mechanics of the machine: In the back left the set of rollers (reflector B with the three rotors) and on the right the battery housing. In front of it the lamp field (without light bulbs) and the keyboard levers.

The Enigma including the wooden housing weighs around 12 kg and the external dimensions (L × W × H) are around 340 mm × 280 mm × 150 mm (data without the housing: 10.35 kg and 310 mm × 255 mm × 130 mm). Its inventor says: "The machine is built very similar to a typewriter and is operated exactly like it."

In contrast to a typewriter, however, the Enigma cipher machine has a set of rollers made up of three rotatable rotors (with a diameter of around 100 mm). To the right of the three rotatable rollers (5) (see numbers highlighted in yellow in the schematic diagram) there is the entry roller (4) ( stator ), which does not rotate and its contacts via 26 wires (only four of them are shown here) with the letter keys ( 2) are connected. To the left of the roller set is the reversing roller (6) (VHF), which is also fixed on the Enigma I. The reversing roller (also called: reflector ) is an invention (patented on March 21, 1926) by Willi Korn , an employee of Scherbius. It only has 26 contacts on its right-hand side (again only four of them are shown in the sketch), which are connected to one another in pairs. The reversing roller has the effect that the current, which initially passes through the roller set from right to left, is deflected and flows through it again, now from left to right. The current leaves the roller set as it came, again via the entry roller.

The table shows the then top secret wiring diagram of the five rotating rollers I to V available on the Enigma I and the reversing rollers A (used until 1937), B (in use from 1937) and C (1940 and 1941 sporadically), which was classified as a " secret matter of command " used):

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
I       E K M F L G D Q V Z N T O W Y H X U S P A I B R C J
II      A J D K S I R U X B L H W T M C Q G Z N P Y F V O E
III     B D F H J L C P R T X V Z N Y E I W G A K M U S Q O
IV      E S O V P Z J A Y Q U I R H X L N F T G K D C M W B
V       V Z B R G I T Y U P S D N H L X A W M J Q O F E C K
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
UKW A   E J M Z A L Y X V B W F C R Q U O N T S P I K H G D
UKW B   Y R U H Q S L D P X N G O K M I E B F Z C W V J A T
UKW C   F V P J I A O Y E D R Z X W G C T K U Q S B N M H L

At the front of the device there is a plug board with double-pole sockets for each of the 26 letters. The current from the letter key (2) is routed via this plug board (3) before it reaches the entry roller (4). After running through the set of rollers, it flows a second time over the connector board (7, 8) and finally brings one of the 26 letter lamps (9) to light up. The letter lamps as well as the keyboard and the sockets are arranged similarly to a German typewriter keyboard:

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

## function

Plug board
(in the picture A is connected to J and S to O)

When the letter key is pressed, for example A, the battery current is switched through to the socket of the same name on the plug board via the A key. If socket A is connected to another socket by an externally attached cable (“plugged in”), A is swapped with another letter, for example J. If no cable is plugged in ("not plugged in"), the current goes directly to contact A of the entry roller.

For the further description of the function, reference is made to the figure "Current flow" (initially only upper half). It is used for illustration purposes only and is a simplified representation of the rotating roller set (with left, middle and right rotor) and the static reversing roller (English: Reflector ). For reasons of clarity, the number of letters in the sketch has been reduced from 26 to 8 (only A to H).

Assuming the letter A is not plugged in, the current is passed via the entry roller (it is not shown in the sketch) to input contact A on the right-hand roller. Their wiring causes a substitution (replacement) of the letter by another. The current that enters from the right at input contact A leaves the roller on its left side at output contact B. Thus, A is replaced by B by the right roller.

Current flow
Upper half: A is encrypted in G
Lower half: A is encrypted in C.

The current now reaches the middle roller via contact B. Since when wiring a roller it is quite possible that (as in the picture) an input contact is connected to the output contact of the same name, B remains unchanged here. The current leaves the middle roller via contact B and enters the left roller. Their wiring ensures that the current is routed from input contact B to output contact D. The current has now passed through all three (rotatable) rollers once and has reached the reversing roller. It only has contacts on the right side and connects the letters in pairs, for example D with E.

The current now flows through the set of rollers a second time, but now from left to right. Through the reversing roller, it reaches the left roller via contact E. Here, for example, E is wired to C. As a result, the current continues to flow via contact C into the middle roller, leaves it again via contact F and flows into the right roller. The current finally leaves the right roller at contact G.

The further flow of current is not evident from the sketch, but is easily explained. After exiting the roller set, the current is fed back to the plug board via the entry roller. If the letter G is plugged into another letter, then a final permutation takes place. If G is not plugged in, lamp G lights up. It only lights up as long as button A is held down, since the changeover contact is only switched to the battery when the button is pressed. If you let go of it, the lamp goes out. In the example shown, the letter A, whose key was pressed at the beginning and is still pressed, is encrypted as the letter G.

If the text to be encrypted is "AACHENISTGERETTET", an A must be entered again. So button A is released and pressed a second time. It is important that with the mechanical pressure on the button with the help of an indexing mechanism, the right roller is rotated by one position at the same time. The middle roller only rotates after 26 steps of the right roller. In the lower half of the picture “Current flow” the situation is sketched after the right roller has rotated one position (downwards).

As can be seen from the sketch, the path for the current entering again at contact A of the right roller has changed radically. It now takes a completely different path than before with the middle and left rollers as well as the reversing roller, although these rollers have not turned. The result is a different encryption of the letter A, which is now converted to C.

## service

 Left side of a roller. The transfer notch can be seen on the left edge. Right side of a roller. The Roman number “V” and the serial number “A16775” identify this roller.
This key board contains, in contrast to the commonly used ones, an additional column “Plug connections on the reversing cylinder”, as it was used from 1944 on some units of the Luftwaffe (see also: Reversing cylinder D ).
All ten cables are already plugged in here. The label “Please note!” Is clearly visible in the lid, above it a filter disk that was clamped onto the lamp field in bright outside light to improve the contrast and make reading easier, and at the very top a strip with replacement light bulbs.
Enlarged section of the sticker with information on maintaining the machine

The Enigma I initially had three, and from 1939 five different rollers, which were numbered with Roman numerals (I, II, III, IV and V). The user selected three of the five rollers according to a secret key table, which provided for changing settings for each day, and used them according to the arrangement prescribed in the daily key under the heading “Roller position”.

The " key table" tabulated the valid daily keys for a full month, which were changed at midnight (exceptions: in the case of the Luftwaffe , the change happened at 3 o'clock in the morning. For the navy see Enigma-M4 ). Only three days of the month are shown below as an example, whereby, as was common at the time, the days are sorted in descending order. This allows the encryptor to cut off and destroy the codes used up in the past few days.

Example for the 29th of the month: Roller position I IV III means that roller I on the left (as a slow rotor), roller IV in the middle and roller III on the right (as a fast rotor). (With a few exceptions, the VHF B was always used as the reversing roller.) The rings that are attached to the outside of the roller body and determine the offset between the internal wiring of the rollers and the letter to which the transfer takes place on the next roller are on the Set the 16th, 26th and 8th letters of the alphabet, i.e. P, Z and H.

Tag  Walzenlage  Ringstellung  ---- Steckerverbindungen ----
31  III  I  IV    01 17 22    AH BL CX DI ER FK GU NP OQ TY
30   II  V   I    18 24 11    BN DZ EP FX GT HW IY OU QV RS
29    I IV III    16 26 08    AD CN ET FL GI JV KZ PU QY WX

The ring position was often (as here) listed numerically and not alphabetically, presumably to prevent confusion with the other partial keys. As an aid for the operator “to convert the numbers into letters or vice versa”, a conversion table is attached to the inside of the Enigma's housing cover as part of the label “Please note!”.

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Finally, the double-pole sockets on the front panel must be wired with corresponding double-pole cables. As a rule, exactly ten cables were plugged in. The upper socket of each socket pair has a slightly larger diameter (4 mm) than the lower one (3 mm), so that the plugs can only be inserted in one orientation. In this way, the desired electrical crossover and thus the exchange of the two letters was achieved. Six letters were left unplugged. (This rule of the six self-steckered letters helped the code breakers .)

In order to reduce the risk of guessing the keys, the German authorities have invented some rules for drawing up the key tables. For example, it was (temporarily) forbidden for a roller position that was already in use on one day of the month to be repeated on another day of the month. (The British recognized this and called it the non-repeating rule .) A roller was also not allowed to be in the same place in the roller set on two consecutive days of the month ( non-clashing rule ). A third rule should prevent the guessing of obvious plug combinations. It was forbidden for two letters in the alphabet to be put together. (The British Codebreakers also used this in their favor and called it Consecutive Connector Knock-Out CSKO .)

All these regulations have the opposite effect, namely a weakening of the encryption. They made work easier for the code breakers, who, due to the rules mentioned, were able to exclude more and more key combinations, especially as a month progressed.

After inserting the three rollers and adjusting the rings and plugging in the ten plug connections according to the key panel, the operator closed the flap above the set of rollers and the front flap. The latter brought about a firm pressure on the connector and secure contact as well as protection against spying on the key. The Enigma was then ready for encryption or decryption, provided the user turned the three (rotating) rollers into the correct starting position.

The key procedures of the Navy differed significantly from those of the other branches of the Wehrmacht and were key guidance The key M described. (The full font is available as a web link in the Documents section .)

In order to ensure that not all radio messages of a key network are encrypted with identical keys, which would make the texts vulnerable, it was prescribed to set an individual starting position of the three reels for each message, called the "saying key ". The procedures for this changed from time to time and were not the same for all parts of the Wehrmacht . In army and air force was from May 1, 1940 (nine days before the start of the campaign in the west ) the following in the "key guide to Enigma machine" described scheme, for example, the following plain text is to be transmitted:

“The Wehrmacht High Command announces: Aachen has been saved. The threat was averted by the bundled deployment of the aid workers and the rescue of the city ensured at around 6:00 p.m. "

Since the Enigma can only encrypt capital letters and no digits or punctuation marks and also does not recognize spaces , the plain text shown above must first be prepared accordingly before encryption. Punctuation marks are replaced by "X", proper names are doubled and enclosed in "X" and numbers are written out digit by digit. It was also common to replace the “ch” and “ck” with “Q” (except for proper names) and then to divide the text into groups of five. You get the following plain text prepared for encryption:

DASOB ERKOM MANDO DERWE HRMAQ TGIBT BEKAN NTXAA CHENX AACHE
NXIST GERET TETXD URQGE BUEND ELTEN EINSA TZDER HILFS KRAEF
TEKON NTEDI EBEDR OHUNG ABGEW ENDET UNDDI ERETT UNGDE RSTAD
TGEGE NXEIN SXAQT XNULL XNULL XUHRS IQERG ESTEL LTWER DENX
Plain text of a radio message from August 29, 1941

The encryptor has set his Enigma I, as described above, to the day key, e.g. for the 29th of the month. (Roller position B I IV III, ring position 16 26 08 and plug connections AD CN ET FL GI JV KZ PU QY WX. Both this and the steps described below can be realistically reproduced using freely available computer simulations , see also: Enigma simulations and simulations under Web links .) The operator now thinks of a random basic position, for example "QWE", and sets the three rollers so that exactly these three letters are visible in the display windows. Now he comes up with a random key with three letters, for example "RTZ". He encrypts this with his Enigma and watches how the "EWG" lamps light up one after the other. He openly communicates the message key encrypted in this way to the recipient together with the randomly selected basic position as an indicator as well as the time and the number of letters in the text as the "message head".

According to the then applicable H.Dv. G. 14 (= Army Service Regulations, secret, No. 14), the message header contains the time as a four-digit number, the number of letters in the message including the five letters of the identification group as well as the selected basic position and the encrypted message key (example: 2220 - 204 - qweewg). In general, all letters were handwritten in lower case because they could be written down more quickly than using upper case letters . An authentic slogan form with the slogan "kr - 2300 - 182 - zzxprq -", where "kr" (abbreviation for "war important" or "war emergency report" with the conspicuous Morse code - · - · - · ) stands as a symbol for "urgent", can be seen under web links as "Spruch Nr. 233". It concerns a request for ammunition for the heavy field howitzer (sFH).

Kenngruppe booklets of the Navy ( captured here from the German submarine U 505 ) were printed with water-soluble ink on pink blotting paper so that they could be destroyed quickly in the event of danger.

Next, the operator selects three code group letters that are valid for this day using a code group table, for example “NOW”. The identification group has no cryptological meaning, it only serves the recipient of the message to recognize that the message is really intended for him and that it can also be decrypted with authorization. To disguise the identification group, the three letters are freely permuted by the sender and supplemented by two " filler letters ", for example "XY", which can be randomly changed for each saying . "NOW" becomes "OWN" and finally "XYOWN". These five letters are placed in front of the ciphertext as the first group of five, unencrypted.

The encryptor now sets the three reels of his Enigma to the phrase key "RTZ" chosen by him and encrypts the above plain text, that is, he enters every single letter of the plain text via the keyboard of the Enigma and reads the light that lights up as ciphertext letters and write it down. Together with the message head and the camouflaged identification group, the following radio message results:

Kopf: 2220 – 204 – QWE EWG -
XYOWN LJPQH SVDWC LYXZQ FXHIU VWDJO BJNZX RCWEO TVNJC IONTF
QNSXW ISXKH JDAGD JVAKU KVMJA JHSZQ QJHZO IAVZO WMSCK ASRDN
XKKSR FHCXC MPJGX YIJCC KISYY SHETX VVOVD QLZYT NJXNU WKZRX
UJFXM BDIBR VMJKR HTCUJ QPTEE IYNYN JBEAQ JCLMU ODFWM ARQCF
OBWN
Sound sample of a secret Morse transmission.
General Guderian (standing in the Sd.Kfz. 251/3 radio armored vehicle ) waits for a radio message to be deciphered (1940).

The header and ciphertext are broadcast as Morse code and recorded by the recipient. This first checks whether the number of letters (here: 204) is correct and the saying was received without mutilation . Then he looks at the identification group, i.e. the first group of five, ignores the first two letters and sees "OWN". He sorts the three letters in alphabetical order, receives “NOW”, looks in his identification group table, discovers these identification group letters there and can now be sure that the saying is intended for him and that he can decipher it. His Enigma is already set identical to that of the sender in terms of roller position, ring position and plug connections in accordance with the day code he is familiar with. He still lacks the spell key, i.e. the correct starting position of the reels to decipher the spell. He receives this information from the indicator "QWE EWG" in the message head, which he interprets as follows: Set the rollers to the basic position "QWE" and then press "EWG". Now he can watch the "RTZ" lamps light up on his Enigma one after the other. This is the key to be set.

He now turns the reels to the starting position “RTZ” and begins to enter the ciphertext, beginning with the second group of five “LJPQH”, into his Enigma. The lamps will now light up one after the other and the following text will appear

dasoberkommandoderwehrmaqtgibtbekanntxaachenxaache
nxistgerettetxdurqgebuendelteneinsatzderhilfskraef
tgegenxeinsxaqtxnullxnullxuhrsiqergestelltwerdenx

## Cryptographic strengths

The Enigma-D itself without a plug board - it was only added in 1928 as a secret additional device exclusively for the Enigma variants used by the military - was then assessed as " unsolvable ".

When Scherbius applied for a patent for the Enigma in 1918, that is, during the First World War, it was a cryptographically extremely strong machine and could rightly be called " unbreakable ". In contrast to the manual encryption method ( e.g. ADFGVX ) that was still in use at the time , the introduction of machine encryption was innovative . It was invulnerable through the manual, mainly linguistically supported, deciphering methods that were customary at the time and remained so until the 1930s, i.e. for more than ten years.

During this time, the then newly established cross- armed forces cryptographic office ( Dutch Cryptographic Bureau ) of the Dutch armed forces received an Enigma-D  (picture) from Cipher Machines AG for viewing and testing. After two months of analysis, the head of the office, Captain Henri Koot , gave the following assessment:

“I dare say that it satisfies all requirements, be they ever so high even the possession of an equal machine with the same electrical connections both in the ciphering cylinders and in the other parts of the machine will not enable an unauthorized person to find out its solution. "

“I dare say that it meets all requirements, no matter how high. Even having an equivalent machine with the same electrical connections both in the encryption cylinders and in the other parts of the machine will not enable an unauthorized person to find a solution. "

- Henri Koot

The cryptographic strengths of the Enigma are essentially given by the rotating set of rollers. By rotating the reels, every letter in the text is encrypted with a new alphabet (polyalphabetic encryption). In this way, the frequency range , which is so treacherous in the monoalphabetic method, is ground down beyond recognition and classic attacks to decipher the ciphertext, such as statistical analyzes , Doppler or pattern searches , are doomed to failure. The search for periods using the coincidence index , as a common method of attacking polyalphabetic encryption, such as the Vigenère cipher , is also futile, because compared to the period length (of 16,900, see also: Improvement potential ) of the Enigma, a comparatively tiny maximum length of the radio messages of 250 Letters prescribed.

Roller window of the Enigma-M4

Decisive for the security of the encryption against unauthorized decipherment are the secrecy of the roller wiring and the number of rollers used in the roller set. The latter is an important factor that explains the much stronger encryption of the four-roller Enigma-M4 used in the German submarines compared to the Enigma I (with only three rollers). There are three radio messages encrypted with an M4 machine known to the public, the content of which could not be deciphered until 2006. Only then did the amateur cryptologists Stefan Krah, two of the news that the submarine U 264 or U 623 were sparked in 1942 by distributed computing ( distributed computing ) and merger of several thousand computers on the Internet within one month decipher. The third radio message lasted another seven years and was only deciphered in January 2013. This impressively shows that the Enigma, which was patented for the hundredth time on February 23, 2018, is not easy to crack even with modern cryptanalytical attack methods and today's highly developed computer technology , but still represents a difficult challenge.

The rings (ring position), originally invented by Willi Korn in 1928, and not, as has often been wrongly published, by his colleague Paul Bernstein , determine the offset between the internal wiring of the rollers and the letter that is transferred to the next roller . They also served to protect against espionage . This prevented that the internal rotational position of the rollers could be inferred by reading the externally visible roller position.

With the help of the “double connector cords” that can be inserted into the connector board from the front, letters can be swapped involutorily in pairs before and after passing through the set of rollers . This measure served to further strengthen the cryptographic security of the Enigma. In fact, this increases the key space considerably.

## Key room

Linguistically, a distinction must be made between the key space explained in the text as a set of all possible keys and a key space as in the picture, which shows soldiers of the secret radio reporting service (Section Ii) of the OKW encrypting or decrypting messages.
The set of three rotating rollers and the reversing roller B (left). The ring of the middle roller is set to 01 here (see red triangle in the middle of the picture). To do this, the clip was pulled out sideways to the right and the ring, which was now freely movable on the roller body, was rotated until the red triangle pointed to the "ring position 01" prescribed here. When you let go of the clip, a small bolt engages in the hole at 01 (an “empty” one can be clearly seen above to the right of 02). This locks the ring in place and the prescribed ring position is set.

The size of the Enigma's key space can be calculated from the four individual subkeys and the number of different key settings possible in each case. The entire key space of the Enigma I (for M4 see Enigma-M4 ) results from the following four factors:

a) The roller position
Three out of five reels (I through V) are selected. (The VHF B was almost always used as the reversing roller.) This results in 5 · 4 · 3 = 60 possible roller positions (corresponds to a " key length " of around 6  bits ).
b) The ring position
There are 26 different ring positions (01 to 26) for the middle and right roller. The ring of the left roller does not contribute to the enlargement of the key space, since its transfer notch does not cause an advancement of a roller further to the left. A total of 26² = 676 ring positions are relevant (corresponds to about 10 bits).
c) The roller position
There are 26 possibilities for setting each of the three (rotating) rollers (A to Z). The reverse roller cannot be adjusted. A total of 26³ = 17,576 roller positions are available. If the ring position is assumed to be known, then, due to an unimportant anomaly in the indexing mechanism, 26² = 676 initial positions must be eliminated as cryptographically redundant. What remains as relevant is 26 · 25 · 26 = 16,900 roller positions (corresponds to about 15 bits).
d) The plug connections
Up to 13 plug connections can be made between the 26 letters. Based on the case of the unplugged connector board (taken into account as number 0 in the table below), there are 26 options for the first connector for one end and then 25 for the other end of the cable. Thus, there are different possibilities for the first cable 26 · 25 to plug it in. However, since it does not matter in which order the two cable ends are plugged, half of the options are omitted. This leaves 26 · 25/2 = 325 possibilities for the first connection. For the second one receives analogously 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 formula ).
 Nummer der ---- Möglichkeiten für ---- Möglichkeiten für Steckverbindung erste Seite zweite Seite Steckverbindung 0 1 1 1 1 26 25 325 2 24 23 276 3 22 21 231 4 20 19 190 5 18 17 153 6 16 15 120 7 14 13 91 8 12 11 66 9 10 9 45 10 8 7 28 11 6 5 15 12 4 3 6 13 2 1 1
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 in which it is carried out does not matter here either (it is cryptographically equivalent if, for example, A is plugged in with X first and then B with Y or vice versa, first B with Y and then A with X), the corresponding cases are not allowed as key combinations be taken into account. With two plug connections, this is exactly half the time. The previously determined product has to be divided by 2. With three plug connections there are six possible sequences for performing the connections, all six of which are cryptographically equivalent. The product has to be divided by 6. In the general case, with n plug connections, the product of the previously determined possibilities is given by n ! ( Factorial ) to divide. The number of possibilities for exactly n plug connections results as
${\ displaystyle {\ frac {1} {n!}} \ prod _ {i = 1} ^ {n} {\ frac {(26-2i + 2) (26-2i + 1)} {2}} \ ; = \; {\ frac {26!} {2 ^ {n} \ cdot n! \ cdot (26-2n)!}}}$
If only eight connector cables are used (as in the picture) and thus ten "unplugged" letters, the cryptographic potential of the connector board is unnecessarily weakened.
Stecker   -------------- Möglichkeiten für ----------------
n      Steckver-     genau n Steck-      bis zu n Steck–
bindung       verbindungen          verbindungen
0          1                     1                    1
1        325                   325                  326
2        276                 44850                45176
3        231               3453450              3498626
4        190             164038875            167537501
5        153            5019589575           5187127076
6        120          100391791500         105578918576
7         91         1305093289500        1410672208076
8         66        10767019638375       12177691846451
9         45        53835098191875       66012790038326
10         28       150738274937250      216751064975576
11         15       205552193096250      422303258071826
12          6       102776096548125      525079354619951
13          1         7905853580625      532985208200576
After only six and later between five and eight connection cables were plugged in in the first few years, from August 1939 the fixed rule applied to always make exactly ten plug connections. According to the table above, there are 150,738,274,937,250 (more than 150 trillion) plug-in options (corresponds to about 48 bits) for these.

The entire key space of an Enigma I with three rollers selected from a supply of five and one reversing roller and when using ten plugs can be calculated from the product of the 60 roller positions, 676 ring positions, 16,900 roller positions and 150,738 determined in sections a) to d) above .274.937.250 calculate connector options. He is:

60 676 16,900 150,738,274,937,250 = 103,325,660,891,587,134,000,000

That is about 1023 possibilities and corresponds to a key length of about 77 bits. The occasional "150 million million million" combinations, for example in the films " Enigma - The Secret " and " The Imitation Game - A Top Secret Life ", are based on the omission of the ring positions. The exact calculation in this case results in 60 · 16,900 · 150,738,274,937,250 or 152,848,610,786,371,500,000 different cases, with the British mostly taking into account all 26³ or 17,576 possible roller positions instead of 16,900 and then 158,962,555,217,826,360 as a product. 000 received.

The key room was enormous for the time and even stands up to a comparison with more modern processes. For example, the DES ( Data Encryption Standard ) encryption method , which has become the standard for several decades towards the end of the 20th century, has a key length of exactly 56 bits, which is significantly less than the Enigma. An exhaustion (complete search) of the key room of the Enigma is hardly possible even with modern means and was completely illusory with the technology of the time.

However, the size of the key space is only a necessary, but not a sufficient condition for the security of a cryptographic method. Even a method as simple as simple monoalphabetic substitution has 26 (when using an alphabet of 26 letters such as Enigma)! ( Faculty ) possible keys. That is roughly 4000 x 10²³ keys (about 88 bit) and compared to the number 10²³ of the Enigma I it is even bigger by a factor of about 4000. However, a monoalphabetic substitution is very uncertain and can easily be broken (deciphered).

With the help of the Turing bomb (here a replica in Bletchley Park, operated by a Wren ), the key space could be drastically reduced.

In the case of the Enigma, too, the structural component that significantly contributes to the size of the key space, namely the plug board, is similar to a simple monoalphabetic substitution, because the plug ultimately remains unchanged during the entire encryption process. The plug board can consequently be overcome and practically completely eliminated with the help of an intelligent cryptanalytic attack method ( Turing bomb ). This means that the factor 150,738,274,937,250 can effectively be deleted again when calculating the key area.

The rings also only slightly strengthen the cryptographic method. If the ring on the right cylinder is incorrectly positioned and the key is otherwise correct, clear text passages can be read periodically (period length = 26 letters), which are repeatedly torn off after a few letters. The ring of the middle roller is even less effective, the period length being 650 letters (25 x 26). The middle ring position therefore usually does not contribute to the size of the key area at all, namely whenever there is no transfer to the left cylinder during the spell , which only rarely happened due to the prescribed spell length of 250 letters at most. The ring position of the left cylinder is completely meaningless from a cryptanalytic point of view. Overall, the fine adjustment of the rings is no longer a major problem. This means that when calculating the size of the key space, the factor 676 can be safely deleted again.

Only the 60 roller positions and the 17,576 roller positions to be taken into account (if the ring position is unknown) remain cryptographically effective. The previously gigantic key space is shrinking to a comparatively tiny 60 17,576 = 1,054,560 (a good million) possibilities (around 20 bits), a number that was already exhaustive (exhaustive ) during the Second World War with the help of the electromechanical technology at that time ) could be processed.

## Cryptographic weaknesses

The reversing roller only has contacts on one side and thus ensures that the current passes through the rotating rollers a second time. It is what causes the Enigma's main cryptographic weakness.

Scherbius' colleague Willi Korn achieved through the reversing roller that the key procedure becomes involutorial , i.e. if a U is encoded into an X in a certain position of the rollers, then an X is also encoded into a U in this position. He simplified the operation and construction of the machine, because you no longer have to differentiate between encryption and decryption. In addition, he hoped for an increase in safety, because the current now flows through the rollers twice:

“This decline in the current through the cipher roller set causes further scrambling. As a result of this arrangement, it is possible to get by with relatively few encryption rollers and still maintain a high level of encryption security. "

With these words Korn explains the advantages of his reversing roller in the patent (DRP No. 452 194). However, this was a fallacy with far-reaching consequences.

On the one hand, the reversing roller has the effect that no more letters can be encoded in itself, because the current can in no case take the exact path through the roller set back that it came. It is always directed back on a different path than when it flowed to the reversing roller. Mathematically, one speaks here of fixed-point-free permutations . This restriction may seem like an insignificant minor, because there are still 25 more letters of the alphabet for encryption, but in fact this means a drastic reduction in the alphabets available for encryption and, moreover, a new vulnerability of the ciphertext. On the other hand, the reversal roller causes the permutation and thus the encryption to become involutive, further reducing the number of alphabets.

The cryptographic weaknesses introduced by the reversing cylinder, in particular the reduction in the number of available alphabets, can easily be made clear if, instead of 26 letters, one simply starts with only four letters, for example. With four letters you can get 4! = Generate 24 different alphabets (by which the cryptographer means different arrangements of letters), namely

DABC  DACB  DBAC  DBCA  DCAB  DCBA

If you limit yourself to only the fixed-point-free permutations instead of all 24 possible, then all alphabets in which a letter is encrypted in itself, i.e. in its usual alphabetical place, are omitted. The following fifteen alphabets are to be deleted from the list above, as they have one or more fixed points (below red and underlined).

Only the following nine fixed point-free permutations remain:

----  ----  ----  ----  ----  ----
----  BADC  ----  BCDA  BDAC  ----
----  CADB  ----  ----  CDAB  CDBA
DABC  ----  ----  ----  DCAB  DCBA

If one now takes into account that the reversing cylinder not only eliminates all permutations with fixed points, but also all non-involutorial permutations, another six cases must be deleted from the table above, namely those in which the double application of the permutation does not return to the original letter leads. Of all possible 24 permutations of a four-letter alphabet, only the three fixed-point-free and involutor cases remain . They are referred to as " true involutorial permutations ".

----  ----  ----  ----  ----  ----
----  BADC  ----  ----  ----  ----
----  ----  ----  ----  CDAB  ----
----  ----  ----  ----  ----  DCBA
In this exhibit , Enigma was mistakenly translated as "secret" (see table), "riddle" is correct.

In the case of the Enigma with its 26 letters, this restriction means that instead of the 26! ( Faculty ), i.e. approximately 4 · 10 26 total possible permuted alphabets only the 25 · 23 · 21 · 19 · 7 · 5 · 3 · 1 = 25 !! ( Double faculty ), i.e. about 8 · 10 12 genuinely involutorically permuted alphabets can be used. The reversing roller wastes a factor of about 5 · 10 13 in possibilities - a gigantic weakening of the combinatorial complexity of the machine. What remains is less than the square root of the originally possible permutations.

Cryptographically even more catastrophic than this drastic reduction in the number of alphabets, however, is that by avoiding fixed points, statements about the text such as "Nothing is ever itself" are possible, which were a very important aid in deciphering. If the attacker knows that a letter is never the encryption of himself, then this knowledge opens up abbreviations for him and he no longer has to laboriously work through each individual case, as is illustrated in the following example.

A deciphering method that has been known and proven for centuries is the " Probable Word Method ". The attacker guesses, suspects or knows that a certain phrase ( Crib in English , Mot probable in French ) appears in the text , for example "OBERKOMMANDODERWEHRMACHT". If, for example, the attacker has a ciphertext fragment encrypted with the Enigma like the following, he can easily determine at which point in the text the suspected probable word can not be by checking for each possible position whether there is a character in it itself would be encrypted, which, as he knows from the Enigma, is impossible. For this he writes the probable word in the various layers below the ciphertext and checks for collisions ( English Crash ) that are red in the example highlighted and underlined:

 BHNCXSEQKOBIIODWFBTZGCYEHQQJEWOYNBDXHQBALHTSSDPWGW 1 OBERKOMMANDODERWEHRMACHT 2 OBERKOMMANDODERWEHRMACHT 3 OBERKOMMANDODERWEHRMACHT 4 OBERKOMMANDODERWEHRMACHT 5 OBERKOMMANDODERWEHRMACHT 6 OBERKOMMANDODERWEHRMACHT 7 OBERKOMMANDODERWEHRMACHT 8 OBERKOMMANDODERWEHRMACHT 9 OBERKOMMANDODERWEHRMACHT 10 OBERKOMMANDODERWEHRMACHT 11 OBERKOMMANDODERWEHRMACHT 12 OBERKOMMANDODERWEHRMACHT 13 OBERKOMMANDODERWEHRMACHT 14 OBERKOMMANDODERWEHRMACHT 15 OBERKOMMANDODERWEHRMACHT 16 OBERKOMMANDODERWEHRMACHT 17 OBERKOMMANDODERWEHRMACHT 18 OBERKOMMANDODERWEHRMACHT 19 OBERKOMMANDODERWEHRMACHT 20 OBERKOMMANDODERWEHRMACHT 21 OBERKOMMANDODERWEHRMACHT 22 OBERKOMMANDODERWEHRMACHT 23 OBERKOMMANDODERWEHRMACHT 24 OBERKOMMANDODERWEHRMACHT 25 OBERKOMMANDODERWEHRMACHT 26 OBERKOMMANDODERWEHRMACHT 27 OBERKOMMANDODERWEHRMACHT BHNCXSEQKOBIIODWFBTZGCYEHQQJEWOYNBDXHQBALHTSSDPWGW

The number of layers to be excluded by collisions can be estimated according to the following consideration: With a probable word of length 1 (i.e. only a single probable letter) the probability of a collision is 1/26. Hence the probability of no collision is 1−1 / 26. With a probable word as above with length 24, the probability of no collision (1−1 / 26) is 24 , which is about 39%. This means that in the case of 27 investigated locations, no collisions are expected on average for 27 · (1−1 / 26) 24 of the cases. The expression gives a value of about 10.5 and agrees quite well with the eight collision-free crib layers observed in the example (and marked in green).

With the help of this extremely simple cryptanalytic attack method, 19 of the 27 possible positions of the probable word, i.e. more than two thirds, can be eliminated as impossible - a considerable simplification of work for the attacker.

## Decipherment

The Polish code breaker Marian Rejewski (1932)
In the Polish Enigma replica , of which at least 15 were made in the mid-1930s, buttons (1), lamps (2) and sockets (7), like the German Enigma-C , were simply arranged alphabetically.

The operators of the Enigma key machine were of the opinion that the texts they machine-encrypted, in contrast to almost everything that was in use until 1918, could not be cracked using manual methods. It was overlooked that machine encryption can be countered by machine deciphering.

The history of the deciphering of the Enigma begins in 1932 when the German Hans-Thilo Schmidt, spying for France under the code name HE ( Asché ) , secret keyboards for the months of September and October 1932 as well as the instructions for use ( H.Dv. g. 13) and the key instructions (H.Dv.g.14) to the French secret service employee Capitaine (German: captain ) and later Général Gustave Bertrand betrayed for money . At that time, only three rollers (I to III) were in use and the roller position was only changed every quarter and not yet, as was the case from October 1936, on a daily basis. The Deuxième Bureau of the French secret service forwarded the documents to British and Polish authorities.

While it failed French and the British, in the encryption break and they classified the Enigma as "unbreakable," the 27-year-old Polish mathematicians succeeded Marian Rejewski in his work in the charge of Germany Unit BS4 of Biuro Szyfrów (German: "Cipher Bureau" ) the first break into the Enigma in 1932. He used a legally purchased commercial machine (presumably model C ) in which - unlike the military Enigma I, which was still unknown to him - the keyboard was connected to the entry roller in the usual QWERTZ order (sequence of letters on a German keyboard , starting at the top left) was. Rejewski guessed the wiring sequence chosen by the Germans for the military variant, which in 1939 almost drove the British codebreaker Dillwyn "Dilly" Knox to despair. Then, with the help of his excellent knowledge of permutation theory (see also: Enigma equation ), Marian Rejewski managed to understand the wiring of the three rollers (I to III) and the reversing roller (A) (see also: Enigma rollers ) - a cryptanalytic masterpiece that made him the words of the American historian David Kahn "in the pantheon of the greatest cryptanalysts of all time rises" (in the original: "[...] elevates him to the pantheon of the greatest cryptanalysts of all time"). The British code breaker Irving J. Good designated Rejewskis performance as "The theorem did won World War II" (German: "The theorem that won World War II").

The next task that had to be solved was to find the right roll position and roll position. To do this, Rejewski, together with his colleagues Jerzy Różycki and Henryk Zygalski , who joined them in 1932, exploited a serious procedural error that the Germans made: To ensure secure transmission, the key to the message was placed twice in a row and written in encrypted form at the beginning of a message ( " Slogan key duplication "). Thus the first and fourth, the second and fifth as well as the third and sixth ciphertext letters were each assigned to the same plain text letter. With the help of two machines specially built for this purpose by their colleague Antoni Palluth from AVA , called Zyklometer and Bomba , which embodied two or three times two Enigma machines connected in series and each shifted by three rotary positions, the Polish cryptanalysts were able to do each of the six possible Determine roller positions at which roller positions the observed assignment of the letter pairs was possible and thus narrow the search space considerably . After analyzing several radio messages, the correct message key was found.

After the Germans, who knew nothing about all of this, changed their process technology on September 15, 1938 and three months later, with the introduction of rollers IV and V, the number of possible roller layers from six (= 3 · 2 · 1) to sixty (= 5 · 4 · 3) increased, the Poles could no longer keep up and the Enigma was safe again. In view of the impending danger, shortly before the German invasion of Poland , they handed over all of their knowledge to their allies. On July 26 and 27, 1939, the legendary secret meeting of French, British and Polish code breakers took place in the Kabaty Forest of Pyry , just under 20 km south of Warsaw, where they presented their Enigma replicas and their cryptanalytic machines to the astonished British and French and revealed their methods. The first question that Dilly Knox asked (probably in French) at this meeting was: "Quel est le QWERTZU ?" (German: "What is the QWERTZU?"; In other words: "What is the wiring sequence for the entry roller?" ). This had tormented him for a long time. Rejewski's answer was brilliantly simple: "ABCDEFG ...". A thought that Knox found so absurd that he couldn't believe it. Marian Rejewski, on the other hand, was familiar with the “virtue of the Germans: the sense of order”, and this had already made him recognize the simplest of all permutations chosen by German cryptographers seven years earlier - the trivial case of identity . This resulted in the usual alphabetical order of the wiring of the entry roller, which he could easily guess.

The mansion (English the mansion ) of Bletchley Park was the headquarters of the British code breaker and is now a museum.
The British code breaker Alan Turing (ca.1938)
The Turing bomb consists of a series of three sets of twelve Enigma rollers. The colors of the "drums" (English drums ) indicate the number of the corresponding roller (roller I = red, roller II = chestnut, green roll III =, roller IV = yellow, roll V = light brown, roller VI = blue, roller VII = black, roller VIII = silver).

With this boost, especially with the roller wiring that was finally known, the British cryptanalysts were able to launch another attack on the Enigma when the war broke out in Bletchley Park (BP), about 70 km north-west of London . Was the most important tool - in addition to their intellectual capacity and the high number of personnel of later ten thousand to fourteen thousand men and women - especially a special electromechanical machine called the bombe , which as a successor to the Polish Bomba built and the English mathematician Alan Turing was conceived. Turing's idea for the key search was to completely strip off the effect of the connector board by linking several, usually twelve, Enigma roller sets in a ring. This enabled him to drastically reduce the practically unmanageable number of more than 200 trillion encryption options on which German cryptographers were placing their hopes.

The basic principle is based on the Enigma I, in which three rollers from an assortment of five rollers are used and only the reversing roller B is available. Another reversing cylinder ( VHF C ), called Uncle Walter onomatopoeically by the British , appeared briefly and quickly disappeared again. For each of the 60 different roller layers there are 26³, i.e. 17,576 roller positions. If you can ignore the ring positions and the plug board when searching for the key, what was made possible with the help of the cryptanalytic attack method implemented by the bomb , then “only” 60 · 17,576, ie 1,054,560 possibilities remain. These approximately one million different cases are practically impossible to try out by hand in a reasonable amount of time. However, with the help of the Turing bomb , which was motorized at 64 revolutions per minute and could process 26 cases during each revolution, it only took 1,054,560 / (26 · 64) minutes, i.e. a little more than ten hours, to test all the possibilities. In addition, there is the time to set and convert the machine to the sixty different roller positions, which doubles the time to around twenty hours. If you make the effort to use sixty bombs , one for each roller position, the time for a run of a little more than ten hours is reduced to a good ten minutes - a tolerable time. In fact, there were more than 330 bombs in operation in the United Kingdom and the United States in early 1944 , after the British had to make do with just twelve bombs in late 1941 .

Probably the words ( cribs ) that can be expected to appear in the text are crucial for the function of the bomb . If this is missing, the deciphering fails. For example, the British managed to break into two key sections of the Deutsche Reichsbahn not, at Bletchley Park after the early steam locomotive Rocket as Rocket II and Rocket III were known. The reason, as they discovered to their surprise after the war, was not a particularly safe Enigma variant, but the unfamiliar railway workers' language and the type of transport reports that did not allow them to guess likely words. Military reports, on the other hand, were often stereotyped and contained many easy-to-guess cribs such as OBERKOMMANDERWEHRMACHT, which the British code breakers could use for deciphering.

In addition, they benefited from the German thoroughness in the preparation of routine reports, such as weather reports, which were sent punctually every morning at the same time and from the same place. The German regulation “General Key Rules for the Wehrmacht” (H.Dv.g.7) expressly forbade “regularities in the structure, identical phrases and repetitions in the text” and warned urgently “It must be avoided in any case that by volatile training Personnel key mistakes are made that [...] enable enemy intelligence to decipher, ”but precisely these mistakes happened that the code breakers could perceive and exploit. From a British point of view, a daily freshly encrypted Enigma message, which always began with the words “WETTERVORHERSAGEBEREICHSIEBEN”, was just as valuable as a direct public disclosure of the currently valid daily key would have been. For example, the Enigma key from D-Day , the day the Allies landed in Normandy ( Operation Overlord ), was saved in less than two by the cribWEATHER FORECAST BISKAYA ”, which the British cryptanalysts could easily guess and correctly guessed Broken hours after midnight.

Not infrequently, the British even deliberately provoked incidents just to receive the expected German radio messages with known content (and encrypted with the current day code), and called this technology gardening (German: "gardening"). The British code breaker Rolf Noskwith from Barrack 8 described them as follows: “The RAF dropped mines at certain points in the North Sea, so that the German mine warning served as a crib. The digits were carefully selected to avoid certain digits, such as 0 and 5 in particular, [as coordinates] for which the Germans used different letters. ”The British were able to avoid the distinction between“ NULL ”and“ NUL ”. as well as "FUENF" and "FUNF", which make work a little easier. Except in the case of “ZWEI” and “ ZWO ” there was only one spelling for the remaining digits. Deciphered messages from smaller naval units, such as harbor ships, which did not have the Enigma and instead used manual key procedures ( shipyard keys or reserve manual procedures ), served the British as cribs when the Enigma broke. The Germans sent many radio messages, such as mine warnings, verbatim both as Enigma ciphertexts and encrypted using the manual method. The British were grateful for these “ ciphertext-ciphertext compromises ” and called them Kisses .

U 110 and HMS Bulldog (May 9, 1941)
The American high-speed version of the Turing bomb , here operated by a wave , was also known as the Desch bomb . With up to 2000 revolutions per minute it reached more than fifteen times the speed of its British model and was specifically directed against the four-roller Enigma.
The Desch bomb in the National Cryptologic Museum is the only known original bomb from World War II.

Under the code name “ Ultra ”, it was possible, beginning in January 1940, to break the messages encrypted by the Luftwaffe and later also by the army with the Enigma I for almost the entire duration of the Second World War. In 1943, for example, more than 80,000 radio messages were intercepted and deciphered per month , an average of more than 2,500 every day; during the war it was over two and a half million.

The encryption methods of the German Navy , which used a variant ( Enigma-M3 ) with three out of eight rollers (I to VIII) and a sophisticated spell key agreement , were more persistent . The British only managed to break in here in May 1941 after the capture of the German submarine U 110 and the capture of an intact M3 machine and all secret documents ( code books including the crucial " double-letter exchange boards ") by the British destroyer HMS Bulldog on May 9, 1941 There was then a painful interruption ( black-out ) for the British when on February 1, 1942 the M3 (with three rollers) was replaced by the M4 (with four rollers) in the submarines. This procedure, called " Schlüsselnetz Triton " by the Germans and Shark (German: " Hai ") by the British , could not be broken for ten months, a time that the submariners called the " second happy time " the German submarine weapon was again able to record great successes. The break-in in Shark only succeeded on December 12, 1942 after the British destroyer HMS Petard landed the German submarine U 559 , commanded by Hans Heidtmann , in the Mediterranean on October 30, 1942 . A boarding party consisting of Lieutenant Tony Fasson (1913-1942), Able Seaman Colin Grazier (1920-1942) and the young Tommy Brown (1926-1945), boarded the boat and captured important top-secret key documents, such as short signal stitching and weather short-key , with whose help the cryptanalysts in Bletchley Park managed to overcome the Enigma-M4.

American female workers in Arlington Hall doing deciphering and educational work (ca.1943)

Now the Americans came to the rescue. Under the leadership of Joseph Desch they produced from April 1943 at the United States Naval Computing Machine Laboratory (NCML) , which is based in the National Cash Register Company (NCR) in Dayton ( Ohio had), more than 120 pieces high-speed variants of the bombe . These so-called Desch bombes were specifically aimed at the M4. In quick succession, other American authorities joined in, such as the Signal Security Agency (SSA) and the United States Coast Guard Unit 387 (USCG Unit 387) . The workforce quickly grew from a few hundred to more than 10,000 employees who deciphered thousands of radio messages every day.

After that, the German submarines were never safe (see also: U-boat war ). Was a direct result of the American decipherments starting with U 463 on May 16, 1943 a U-tankers from Type XIV ( "cow") until U 220 on 28 October 1943 a body set up to supply mine-laying by type XB , the sinking eleven of the eighteen German supply submarines within a few months in 1943. This led to a weakening of all Atlantic U-boats that could not be supplied at sea now, but to the long and perilous journey home through the Bay of Biscay to had to enter the submarine bases on the French west coast.

## Historical consequences

Allied Forces Commander in Chief General Dwight D. Eisenhower described Ultra as "crucial" to victory.

It is undisputed that the compromise of the Enigma was of enormous strategic importance for the course of the Second World War. Some historians assume that if the Enigma hadn't been broken, the outcome of the war would not have changed, but it would have lasted much longer and would have been far more bloody. The English historian Sir Harry Hinsley , who had worked in Bletchley Park , commented on the meaning of ultra with the words “shortened the war by not less than two years and probably by four years” ( German:  “[ Ultra ] shortened the war not less than two years and probably by four years ” ). The assumption seems justified that it is thanks to the Polish, British and American cryptanalysts and their work in deciphering the German machine that the Second World War could be shortened considerably and the lives of countless people on all sides were saved.

But there are also historians, politicians and the military who regard the intelligence services as “decisive” for the victory of the Allies. For example, the American historian Harold Deutsch , who was head of analysis at the Office for Strategic Services in the United States War Department , the OSS , said:

"I feel that intelligence was a vital factor in the Allied victory - I think that without it we might not have won, after all."

"I believe that intelligence was a vital factor in the Allied victory - I mean that without them we wouldn't have won after all."

Experts who share Deutsch's view take into account the fact that the decipherments were not only of great help on a military-tactical level (army, air force and navy), but also because of the almost complete penetration of German communications at all levels (police, secret services, diplomatic services, SD, SS, Reichspost, Reichsbahn and Wehrmacht) also allowed an extremely precise insight into the strategic and economic planning of the German leadership. The Allies particularly valued the authenticity of the information obtained from Enigma radio messages, which was not always available from other sources such as reconnaissance , espionage or betrayal . In this way, the British were able to coordinate their resources , which were still very limited at the beginning of the war, much better and use them in a much more targeted manner against the recognized German weaknesses than would have been possible without the deciphering of the Enigma. In the later course of the war, together with their American allies, they then used the Ultra information to better exploit their mutual superiority.

One of the leading former codebreakers from Bletchley Park, the British chess master Stuart Milner-Barry , wrote: “With the possible exception of antiquity, as far as I know, no war has ever been waged in which one side has constantly read the important secret reports of the opponent's army and navy . "A similar conclusion is drawn in an American investigation report written after the war:" Ultra created an awareness in the military leadership and at the political top that changed the way decision-making was made. The feeling of knowing the enemy is most comforting. It increases imperceptibly in the course of time if you can observe your thoughts and habits and actions regularly and precisely. Knowledge of this kind frees your own planning from excessive caution and fear; you become safer, bolder and more energetic. "

“In Europe, the ability of the Allies to crack the German encryption systems and read all messages (code name ULTRA) made the Allies rush from victory to victory. In the “ Battle of the Atlantic ”, the most fundamental dispute of the entire Second World War, the Allies were able to steer their convoys past the German submarines because they knew where they were lurking like wolf packs. In this way, crippling losses could largely be avoided and people and goods could be brought safely to Great Britain. Later, during their great invasion of Europe that led to the victory over Hitler's Reich, the decoding of German embassies helped the Allies anticipate and repel counter-attacks. In this way, they could better identify German weaknesses and advance into the Ruhr area and Berlin. Even Soviet code breakers could decipher the Germans the secret information, which contributed to their victory on the Eastern Front. "

- David Kahn

The former national security adviser to US President Jimmy Carter , the Polish-American political scientist Zbigniew Brzezinski cited the Supreme Commander of the Allied Forces General Dwight D. Eisenhower , the Ultra as decisive ( German  "critical" ) called for the win. The Polish historians Władysław Kozaczuk and Jerzy Straszak wrote "it is widely believed that Ultra saved the world at least two years of war and possibly prevented Hitler from winning". ( German  "it is widely believed that Ultra saved the world at least two years of war and possibly prevented Hitler from winning it" ).

British Prime Minister Winston Churchill said: "It was thanks to Ultra that we won the war."

The renowned British historian and cryptologist Ralph Erskine put it simply and clearly: The break in the naval Enigma "saved Great Britain from defeat in the submarine war". Stuart Milner-Barry also took the view that “we had not at the most crucial times and for long periods read the U-boat ciphers, we should have lost the war” ( German  “we would not have at the crucial time and for long periods of time could read the submarine ciphers, then we would have lost the war ” ). In an exhibition about the Secret War ( German  "Secret War" ), the world in one of the most important war museums, the 2003 Imperial War Museum ( German  "War Museum British Empire " took place) in London, former British prime minister Winston Churchill quoted who gave his King George VI. had said. "It was thanks to Ultra did we won the war" ( German  "It was ultra owe that we have won the war" ).

In his book The Hut Six Story , Gordon Welchman , who alongside Alan Turing was one of the leading figures in the British codebreakers in Bletchley Park, describes the tightrope walk that the Allied cryptanalysts had to walk in order not to catch up with those of the Germans over and over again to lose introduced cryptographic complications. Multiple stand the Entzifferungsfähigkeit on a knife edge, and again the scales dropped in favor of the code breaker, often with the best of luck as Welchman admits in his book: "We were lucky" ( German  "We were lucky" ).

“The success of the code breakers was ultimately based on some brilliant ideas […] If Marian Rejewski in Poland in 1931 and Alan Turing and Gordon Welchman in England in 1939 hadn't had these ideas, the» Enigma «might not have been cracked. So the idea that the Allies could have failed to crack this cipher machine is no speculation in a vacuum, but there actually was a lot to support this assumption. "

- David Kahn

In his 2018 book X, Y & Z - The Real Story of how Enigma was Broken ( German  "X, Y & Z - The true story of how the Enigma was broken" ) calls for the author Sir Dermot Turing , nephew of Alan Turing , the reader on:

“Imagine a counterfactual history in which the British had not been able to decipher Enigma messages during the Battle of Britain, the naval war in the Mediterranean, the early years of the Battle of the Atlantic, or in the campaign in the Western Desert. Such a scenario is frightening, as it would be a history that depicts not just a longer, drawn-out war but potentially one with a quite different outcome. "

“Imagine a counterfactual story in which the British used the Enigma sayings during the [air] battle for England , the sea ​​war in the Mediterranean , the early years of the Atlantic battle, or in the [Africa] campaign in the [Libyan ] Western desert could not have deciphered. Such a scenario is frightening because it would be a story that is not just a lengthy, drawn-out war, but possibly a war with a completely different outcome. "

- Sir Dermot Turing

The consideration of alternative histories is inevitably highly speculative. The point in time at which the Enigma might have been made burglar-proof is of course also decisive. If this had only happened in 1945, it would probably have had little effect on the course of the war. In 1944, however, the Allied invasion plans for Operation Overlord (" D-Day ") would have been hindered. As we know today, not only was the entire German combat line-up in Normandy known in detail from deciphered Enigma radio messages , but thanks to Ultra the Allied commanders were also kept extremely precise every day about the German plans and countermeasures. In the years from 1941 onwards, the German submarines would not have been so easy to find, the positions and plans of which the Allies could precisely follow from deciphered radio messages.

But what if the Enigma had remained unbreakable from the start? In 1940, for example, the Royal Air Force used its last reserves to eventually win the Battle of Britain . Here, too, deciphered radio messages, in particular about the German Air Force's attack plans, were of great help. Without this help, the air battle might have been lost and the Sea Lion operation , the German invasion of England, could have taken place. How it would have turned out can only be speculated: It would be conceivable that the war would have ended in 1940 after a German occupation of the British Isles , because at that time neither the Soviet Union nor the United States were at war. (The German attack on the Soviet Union began on June 22, 1941. The Japanese attack on Pearl Harbor took place on December 7, 1941 and Germany declared war on the USA on December 11, 1941.) How world history changed in such a case no one can say, because history does not reveal its alternatives. In an essay that David Kahn wrote as a counterfactual story on the assumption that the Allies did not succeed in cracking the Enigma, it leads to another triumphant advance of the Wehrmacht, which is finally ended abruptly by an atomic bomb . These are all speculations - however, it becomes clear the enormous importance of cryptography and the cryptanalysis of the Enigma key machine for the course of history.

Particularly noteworthy was the perfectly functioning secrecy of the ultra information obtained in Bletchley Park . Churchill himself paid tribute to his secretive codebreakers with the words "My geese that laid the golden eggs and never cackled" ( German:  "My geese that laid the golden eggs and never cackled" ). This "Enigma Secret" was throughout the war and even after that until the 1970s, guarded ( Britain's best kept secret , German  "Britain's best kept secret" ). The Germans had no idea about Ultra . There was no mole in Bletchley Park  - with one exception, John Cairncross , but he was spying for the Soviet Union.

Due to various suspicious events, several investigations were carried out on the German side as to whether the Enigma was really safe, but the wrong conclusions were drawn here and the experts with the correct assessment did not prevail. The fragmentation of the German services - in contrast to the competence concentrated in BP - is certainly a reason for not recognizing the security gaps in the machine. The partially rival cryptological agencies existed side by side in Germany, such as the encryption department of the High Command of the Wehrmacht (OKW / Chi), the General of Intelligence (OKH / GdNA) in the High Command of the Army , the B-Dienst (observation service ) of the Navy , the Research Office ( FA) of the Air Force as well as the Office IV E in the Reich Security Main Office (RSHA).

A report by the American Army Security Agency written shortly after the war mentions that the German submarine commander (BdU) Admiral Karl Dönitz was the real reason for the victory, which was already within reach before July 1942, and the battle that was lost only a few months later Atlantic never understood:

"It was never realized that cryptanalysis, rather than radar and direction finding, disclosed the positions and intentions of the German submarines."

"At no point was it recognized that the cryptanalysis and not the radar technology or radio location revealed the positions and intentions of the German submarines."

A destroyed Enigma

It would not have been difficult for the Germans to check the safety of their machines. As a test , the British historian Hugh Sebag-Montefiore suggests sending a message encrypted with the Enigma as usual, in which, as a deception , a meeting of German submarine tankers at a remote location at sea, which is normally not from Allied ships are visited. If allied warships should suddenly appear at the agreed meeting point at the time specified in the radio message, it could have become clear to the Germans fairly quickly that their machine was indeed compromised.

After the war, the Enigma machines, which were captured in numbers of several hundred, possibly thousands, and also replicated, were mainly sold or given away by the Western powers to allies or friendly nations. For example, the British offered the State of Israel , which was newly founded in 1948 , 30 of the German encryption machines, which at that time were still generally regarded as “highly secure” and “unbreakable”. The Israelis were delighted with this valuable gift and began to modify the German machines for their purposes. They improved the cryptographic security and combinatorial complexity of the Enigma and replaced the Latin alphabet with Hebrew letters in the keyboard, lamp panel, plug board and roller set . However, they finally abandoned the use of these now Israeli Enigma machines after receiving a subtle hint from the British Jewish mathematician Joseph Gillis (1911–1993), who had worked at Bletchley Park. In Korea, in former British colonies and protectorates, as well as in some African states, Enigmas were still used in some cases until 1975, which enabled the Western powers to read their communications. The few intact specimens that still exist today - it is estimated that there are still around 400 exhibits in museums or with private collectors - are traded at collector's prices in the five and even six-figure range.

## potential for improvement

The Swiss changed the roller wiring of their
Enigma-K every three months

As early as 1883, the Dutch cryptologist Auguste Kerckhoffs formulated his binding maxim for serious cryptography under the assumption that Shannon later (1946) explicitly stated that “the enemy knows the system being used” ( German:  “The enemy knows the system being used ).

Kerckhoffs' principle : The security of a cryptosystem must not depend on the secrecy of the algorithm . Security is only based on keeping the key secret.

The cryptographic security of the Enigma depended - contrary to Kerckhoffs' maxim - essentially on the secrecy of its roller wiring. This could not be changed by the user, so it was part of the algorithm and not of the key. It is noteworthy that the roller wiring was not changed from the beginning in the 1920s to 1945, with very few exceptions, called “ special circuits ”. Under the usual conditions of use of a key machine as widespread as the Enigma, one cannot assume that its algorithmic components can be kept secret in the long term, even if the Germans tried.

A first possibility for improving the Enigma would have been to completely replace the range of rollers every year, for example, with radically changed wiring, similar to what the Swiss did with their K model . Rollers whose internal wiring could be designed variably depending on the key would be even more effective. Interestingly, there was an approach to this, namely the reverse roller D (British nickname: Uncle Dick ), which had exactly this property, but was only used late (January 1944) and only occasionally. This "pluggable reversing roller Dora", as it was called by the German side using the spelling alphabet used at the time, enabled freely selectable wiring between the contact pins and thus a variable connection between pairs of letters.

Early Enigma variant ( model H ) with eight rollers (1929)

Significant cryptographic strengthening of the Enigma would easily have been possible in the construction stage. First and foremost one should have avoided the restriction to fixed-point-free permutations. The Involutorik (encrypt = decrypt), although convenient for operation, weakened the machine enormously. Both would have been avoided if the reversing roller had been omitted.

In his fundamental patent dated February 23, 1918, Scherbius had already specified ten rollers and the 100 trillion keys that resulted from them (without replacing them), and no reversing roller, but a switch for setting encryption and decryption, as well as one that was adjustable via a gearbox Irregular further movement of the rollers suggested - all good ideas and cryptographically strong design features, which, however, have been forgotten over time. The founding president of the Federal Office for Information Security (BSI), the mathematician and cryptologist Otto Leiberich, said in 2001 that with four cylinders "and with a non-uniform drive, the Enigma would never have been deciphered."

The American key machine Sigaba with a total of fifteen reels remained unbreakable

An example of the strength of these ideas is the Sigaba key machine . This is an American rotor machine similar to Enigma, and also from the Second World War, but do not turn roll, but five Chiffrierwalzen ( cipher rotor Bank , German  "Chiffrierwalzensatz" offers) and additionally twice five other rolls ( control rotor bank and index rotor bank , German  "Steuerwalzsatz" and "Indexwalzsatz" ), which serve solely to generate an irregular progression of the cipher rollers. The Sigaba generates fixed points as well as non-invulatory permutations and could not be broken at any time, neither by German nor by Japanese cryptanalysts, nor by the Americans themselves, who tried to do this on a trial basis.

A very easy way to make the Enigma more secure is to use more than one carryover notch . These notches are part of every roller and effect the transfer to the next roller, which is further to the left in the roller set, and thus ensure that the rotors are switched. It was very convenient for the code breakers to be able to assume, for 26 letters, that only the right roller was rotating and only then was it switched to the middle rotor. For relatively long text passages, the Enigma therefore consists, from the perspective of the cryptanalyst, only of a single rotating (right) roller and a particularly thick (fixed) reversing roller consisting of a middle and left roller and the reversing roller. Only the transfer to the middle roller disturbs this. If the Enigma reels had more than a single transfer notch, for example nine, as in the British key machine Typex , practically nothing would have changed for the user, but the cryptanalysis would be strong due to the more frequent switching of the middle and left reels been disturbed.

The British key machine Typex had rollers with five, seven or nine transfer notches

Peter Twinn , one of Turing's employees in Bletchley Park, commented on it with the words "they certainly missed a trick in not combining multiple-turnover wheels with plug connections" ( German:  "They [the Germans]] certainly missed a trick by not rolling with several transfer notches and the plug connections combined " ). Gordon Welchman underlined the consequences of this German mistake: “We would have been in grave trouble if each wheel had two or three turnover positions instead of one” ( German  “We would have had serious problems if each roller had had two or three transfer notches instead of one) [only] one " ). The Typex proved to be unbreakable for OKW / Chi , the encryption department of the OKW , not least because of its larger number of transfer notches compared to the Enigma .

Perhaps the developers of the Enigma feared a reduction in the period , that is the number of characters after which the alphabet used for encryption repeats itself. The period for the Enigma I is 26 · 25 · 26 = 16,900, whereby the factor 25 for the middle roller is caused by the (unimportant) anomaly of the indexing mechanism already mentioned. Using an even number or thirteen carry notches instead of just one would actually drastically decrease the period since these numbers have common factors of 26. For example, with three, five, seven, nine or eleven notches, however, this risk does not exist, since these numbers are relatively prime for 26 . Interestingly, in addition to the five rollers known from the Enigma I, three further rollers were used in the Navy (VI, VII and VIII), which have more than one, namely two transfer notches. The three rollers used exclusively by the Navy also avoided another fault of the five rollers on the Enigma I, because they all had their transfer notches with identical letters. Not so with reels I to V, which are revealed by the transfer of different letters. The code breakers had for the (linguistically nonsensical) Merkspruch " R oyal F lags W ave K ings A bove" formed, which calls for the rolls I to V in this order each character that always appears in the window after a carry on the next roll is done.

A significant innovation that would have significantly improved the cryptographic security of the Enigma, but which came too late to be used during the war, were the so-called " gap filler rollers " ( see photo under web links ). These new types of rotors made it possible to “set any type and number of switching gaps on each roller”. The settings could have been changed depending on the key and thus contributed significantly to the cryptographic strengthening of the machine. In July 1944, the Ertel factory in Munich received a production order for 8,000 pieces of gap filler rollers, which was increased to 12,000 pieces shortly afterwards. Due to the war, however, only a few could be produced and none could be delivered. The American Target Intelligence Committee (TICOM) confiscated all information about the gap filler roller towards the end of the war and carefully kept it under lock and key for many years. If it could have been manufactured and used in sufficient numbers, the British code breakers would probably have been out of the running, especially if the gap filler roller had been used in combination with the reversing roller D as planned.

The Abwehr's Enigma-G did not have a plug board, but had a rotating reversing cylinder

In summary, the following points can be noted about the cryptographic strengthening of the Enigma, the implementation of which would have been possible before or during the war and which could easily have resulted in the Enigma suddenly being “beyond the reach of the already strongly stretched Anglo-American cryptanalytic fingers would have what might have changed the course of the war "( English " Improvement in anyone of the foregoing particulars could easily have pushed the plug-board Enigma beyond the reach of already-straining Anglo-American cryptanalytic fingers, and possibly altered the course of the was " ):

The six key wheels of the SG-41 can be seen through the operating flap
• allow identical encryption
• Avoid involvement
• Attach several (e.g. nine) transfer notches
• Arrange transfer notches identically for all rollers
• use adjustable transfer notches (gap filler rollers)
• install more than three rollers (e.g. six as with the SG-41 )
• Expand the range of rollers (e.g. ten instead of just five)
• freely wirable pluggable reversing roller (VHF Dora)
• Radically change the reel wiring from time to time
• do not use involutive plugs
The legendary Hut 6 in Bletchley Park, where the Enigma was deciphered (photo from 2004)

An amazingly simple yet resoundingly effective measure which, according to Gordon Welchman, could easily have been introduced at any point in time, and which he feared most during the war, is the use of single-pole plug connections instead of double-pole involutive cables. Then, for example, you could plug X with U and U now not necessarily with X, but with any other letter. In this way, the involvement of the plug board - if not of the whole machine - could have been abruptly eliminated. According to Welchman, this would have had disastrous effects on the code breakers in Bletchley Park. Much of the developed methodology there including the Welchman self-invented diagonal board ( German  Diagonal Board ) would have been useless. He writes “the output of Hut 6 Ultra would have been reduced to at best a delayed dribble, as opposed to our up-to-date flood.” ( German  “the yield of the ultra information from Barrack six would have been in the best case a delayed trickle reduced, in contrast to our daily tide. " )

## Models

The National Cryptological Museum of the USA illustrates the variety of models of the Enigma and shows (far left) a commercial machine, on the right an Enigma-T and an Enigma-G , in the right half an Enigma I of the Air Force, a roller box, an Enigma I of the army, next to it the Enigma watch , and on the far right under the white cap of a submarine commander the model M4, which is only used by the German submarines  .
The Enigma-T ("Tirpitz") has a settable VHF
In the Japanese Enigma replica ( San-shiki Kaejiki ), the rollers lie flat next to each other

A rough overview of the confusing variety of Enigma models is shown in the following table (see also: Enigma family tree under web links ). In addition to the model name, the year of commissioning, the number of rollers and the resulting number of possible roller positions are given. Furthermore, the number and type of reversing roller (VHF) is noted, whereby a distinction must be made between built-in VHF and manually adjustable, ie "settable" VHF and rotating VHF, i.e. VHF that continue to rotate during the encryption process. An example of this is the Enigma-G of defense described above . Some early machines, such as the “ Handelsmaschine ” from 1923 and the “ Writing Enigma ” from 1924, had no VHF. The number of carryover notches is also given, as is a literature reference for reference and further information.

model year Rollers Locations VHF Notches Ref
Enigma I 1930 3 out of 3 (5) 6 (60) 1 (3) fixed 1 Kruh 11
Enigma II 1929 8th 1 1 fixed see Enigma H
Enigma-A 1924 2 1 1 rotates Crypto Museum
Enigma-B 1924 2 or 3 1 1 fixed Crypto Museum
Enigma-C 1925 3 1 1 fixed 1 Kruh 5ff
Enigma-D 1926 3 1 1 settable 1 Farmer 114
Enigma-G 1936 3 out of 3 6th 1 rotates 11, 15, 17 Hamer
Enigma-H 1929 8th 1 1 fixed Crypto Museum
Enigma-K 1936 3 out of 3 6th 1 settable 1 Hamer 10ff
Enigma-M1 1934 3 out of 6 120 1 fixed 1 Prose 50
Enigma-M2 1938 3 out of 7 210 1 fixed 1 Prose 50
Enigma-M3 1939 3 out of 8 336 1 fixed 1 (2) -
Enigma-M4 1942 4 out of 8 + 2 1344 2 settable 1 (2) Erskine & Weierud 50
Enigma-T 1942 3 out of 8 336 1 settable 5 Girard
Enigma-Z 1931 3 out of 3 6th 1 rotates 1 Wik
Trading machine 1923 4th 1 no transmission Kruh 2
Writing Enigma 1924 2 times 4 1 no transmission Prose 50

In addition to the most widely used models Enigma I, Enigma-M3 and Enigma-M4 as well as their predecessors Enigma-A to Enigma-D and the already mentioned Enigma-G and Enigma-K, the Enigma-T is also worth mentioning, which is specially designed for the communication of the two War allies Germany and Japan was conceived. It was named after the German Grand Admiral of the former Imperial Navy Alfred von Tirpitz (1849-1930) as the " Tirpitz machine " and had no plug board, but a "settable" (adjustable, but not rotating) reversing roller and a total of eight rollers each with five transfer notches (see also: Enigma rollers ), three of which have been selected. The Enigma-T was hardly ever used. It should not be confused with the Enigma replica developed in Japan, the San-shiki Kaejiki .

The Enigma-Z , which was offered for sale to the Spanish Foreign Ministry in 1931, is a curiosity . It is a variant similar to the Enigma-D, but does not have any letter keys, just ten number keys (“1” to “0”) and corresponding (smaller) rollers with only ten contacts and ten bulbs for “1” to Has "0". So she was not thought to encrypt texts, but only by numbers, such as the over coding of diplomatic codes. For example, the sequence of digits “25183 91467” could be encoded as “38760 15924”. The Spaniards decided not to buy the Enigma-Z and instead opted for the even less secure Kryha .

## anomaly

The indexing mechanism of the rollers has a special design feature, which means that the rollers of the Enigma do not keep turning as would be the case with a mechanical odometer. This special feature manifests itself in such a way that when a slower roller is switched on, the adjacent faster roller is "taken along". Since the corresponding Enigmas have three rotating rollers and the fast roller is incremented with each input, it only affects the increment of the slow roller, which advances the middle roller again. This can be illustrated with an example.

The indexing mechanism (here the M4) causes the anomaly of the roll rotation

For example, in the case of roller position B I II III, ring position 01 01 01 and roller position ADU, the roller set continues to rotate with the first push of the button ADV. This is a completely normal further rotation of only the right roller, without switching the middle or left roller. According to the known rule of thumb " R oyal F lags W ave K ings A bove", ie when they weiterrotiert for roll III with the next keystroke from V to W, can be expected to transfer to the middle roll. Then not only will the right roller continue to rotate normally, but the middle roller will also switch from D to E at the same time. The next roller position is therefore AEW.

Now, however, the middle roller (here: roller II) has reached the letter, namely E, which, according to the rule of thumb, is immediately in front of its shift letter F. The moment has now come when the middle roller in turn effects a transfer to the left roller. The next time you press the button, the left roller will continue to turn from A to B. Due to the special design feature mentioned, however, this further rotation means that it takes the middle roller with it and it rotates again, i.e. from E to F. Consequently, the next time the button is pressed, all three rollers are switched on at the same time and after the previous roller position AEW is now immediately the letters BFX can be seen in the Enigma display windows. After this somewhat strange occurrence, the machine returns to the regular incremental mode until the middle roller reaches the letter E again after pressing 650 keys.

In summary, once again the indexing of the roller set. Here you can see the anomaly when you press the button three times, which manifests itself as a “double step” of the middle roller (here: D → E → F).

2. Tastendruck  AEW
3. Tastendruck  BFX  ← Anomalie
4. Tastendruck  BFY

In sum, this effect of the double step of the middle roller caused by the anomaly of the indexing mechanism leads to the fact that of the theoretically possible 26³ = 17,576 roller positions of the Enigma I 26² = 676 are left out and only 26 · 25 · 26 = 16,900 remain.

Luftwaffe
Enigma radio message intercepted in Bletchley Park (Part two of a three-part message)

Messages encrypted with the Enigma were usually transmitted by radio , only rarely as a telex or by telephone as a "message" or by a signal lamp as a "flash message". The sender filled out a form with the plain text that the encryptor used as the basis for the ciphertext generated using the Enigma machine. He transferred this letter by letter into a corresponding radio message form (see also: Documents under web links ), which in turn served the radio operator as the basis for the radio message transmitted in Morse code . The author, the encryptor and the radio operator of the message could be three different people or one and the same.

An important identification of the radio message, which was particularly highlighted in the message with a colored pencil , was the "message number". By indicating the number in color, the Germans differentiated between "departed", i.e. those to be sent or already sent, in which the message number was entered in the form with a blue colored pen, and "arrived", i.e. received, radio messages in which the number was in Was written in red. Only a few of the innumerable slogans filled out during the war have survived. The vast majority were destroyed after the messages were received and decrypted.

The second very important source for authentic Enigma sayings are the rich records of the Allies. In particular, the archives of the British Y Service (German: "Y-Dienst"), which was operating worldwide at the time, are full, but unfortunately only a small part is public accessible. The picture shows one of the rare exceptions from the archive of the service in Bletchley Park. In English, the "Y" stands onomatopoeically for the initial syllable of the word wireless (German literally: "wireless", meaning: "funk"). A corresponding translation of Y Service would therefore be “radio monitoring service”.

The Enigma radio messages reproduced below come from free sources. The ciphertexts have now been deciphered with the help of modern cryptanalytic methods and computer technology. It should be noted that these are not fictitious radio messages, as offered by the Enigma Cipher Challenge competition (see also: deciphering under web links ), but that they are original radio messages that were actually recorded in this way during World War II. It is therefore entirely possible (and also the case here) that mutilations will occur. This means that some characters are incorrect or missing. This applies to both letters and numbers. The latter can be seen very easily. All you have to do is count the length of the ciphertext and compare it with the number given in the headline. Reasons hardly avoidable in practice mutilation, which can also be explained by the special war-related conditions are spelling errors , duty error , atmospheric disturbances such as flashes of lightning during the radio transmission, hearing impairment or simply careless. Outgoing radio messages, which can also be identified by the entry in the “Transported on ...” field (and not “Recorded on ...”), are naturally less garbled than the incoming ones and are therefore usually easier to crack (with the same text length).

 - 83 - ADJ JNA - LMHNX WEKLM UERDS EVHLC JSQQK VLDES ANEVT YEDGI ZQDOD RMDKG SXGSQ SHDQP VIEAP IENLI CLZCL LAGWC BJZD - 149 - TLS CMU - FTMKV DRJMG FBUDK LZCTR FLTUU IWVJL OYKYX GDCKJ TMDFB WNLZQ JAXHP GGKFG SBZOQ KQKUK TINMH BAJOO AUILA QVFTK LSTMM XGAQL CNHUW LFHKA ULTXT BIVIF EWWDY PUCNS TPJHR OBWHE KYUSB CANYC W - 167 - MRJ LLT - KLIBM ERJAR WMMHJ STHOY OOIQB HSSZU EOOKF TASXN XVYWE SCTCH NRNBL ZPEBH XPAQE DFNYS XHMNI HRARO UNBMD ZRZDN WTGUI UCBZN ZTFJA EKOMJ AZILN RKVFD UNIEW ILZVL KQYYJ ANKXG NNNHT EMAVD FXKAY MLWCV QDFWX LO - 186 - DOQ VHZ - PBNXA SMDAX NOOYH RCZGV VZCBI GIBGW HMXKR RVQCF JCZPT UNSWA DDSTI GQQCS AGPKR XXLOM GFXAP HHMRF SDKYT MYPMV ROHAS QYRWF WVAVG CCUDB IBXXD YZSAC JSYOT MWUCN WOMHH JPYWD CCLUP GSWCL MBCZS SYXPG MGMQX AUFUL NOZEQ ENHEI ZZAKL C - 195 - EHW TNH - ABTWU GWDMP OGKMQ KBHGK HROUP RMYQY INHSA MWFBP CDQRG LDBFK YNXPP DIQHE AOIFQ AOLRZ ZFPDJ MCGEC TAHHQ MVUYA JIAWM WSOYU UTLEP AVZKG HJWCD LOQHW IMSTC LQDNP VCFCN FRUYR GSSJH ORQMU IFFYU WYNTA XPYIX MYTEE FTDCV EHUOA DCPLM APCAU JJYUK - 232 - KPL ZFT - IKPKE WZVTB TXWID JCJAN MPWQZ RKUGF TBBAL IERPD BCDVM ARZEL XXWKF ABVKI WFXDV HJGRR CUCQN YQGAE PNOYN LIYLC DGKYL TXTYP IVDGP YMZLY UXWQS FQLCB DELAN PXXWH TDMNQ ENFWA TJVHO EUPGO CQJCF WSLJR EJJFL TJFJT UIYKT - 241 - SDV RUD - TAZUK DVNNF AZOUV YYSXO ZLRJO TMMXK AWPVU TTUXS LAQOX GQUKX XKXAL URHGR SUOHD FJTRE TLFKD MGDXE MWIXX INTLG EDKVL RTJFX RFOIE NNIRR WFKTI BVFVE LLAWR GJNVB YHBZS CJVTZ PDBGV PBNNA LNAKX OUOJG WLJXO UXHDS HXJOU HVBVF DOLMN LYNVC MRGKK YTOCP DUEVN FMIPT GGJYA YBDES P - 272 - PPS QJH - QSDCK HQOGN OSAIC GADNM PJIAI NPWBM VLTKQ YUDII GWSHT TZEYE CCHFJ CNYBC HXZNE KOOMV SOLLS NDDGR RXPMS GFOPY SJFSY SBYBS CSKDP IOBQM HSFKV MCSMD HYJNO CHB

## Cinematic reception

In this photo of March 1941, just one year before entry into the M4 on February 1, 1942, still an M3 (bottom left) in the same time as a key space serving radio shack of U 124 to be seen.
A three-roller Enigma in action (1943)
Submarines, similar to the German U 505 , from which an Enigma-M4 was actually captured, play a role in most of the films

The Enigma can be seen in a number of films that are set against the backdrop of the submarine war. In the German cinema classic " Das Boot " based on the novel of the same name , it is used to decrypt received radio messages. One hears the voice of Herbert Grönemeyer say "Only through the key machine slowly arises from tangled strings of letters a sense," while in close-up the Enigma in action to see and can also be heard. Historically, the use of an M4 is not entirely correct here, as it was not put into service until February 1, 1942, while the boat in the novel and film carried out its patrol in the autumn and early winter of 1941. Thus an M3 should have been shown correctly.

In the American film "U-571" , an Enigma is captured by American sailors from a German submarine. Especially from the British side it was criticized that, in misunderstanding of historical reality, Americans are portrayed here as heroes in the capture of an Enigma, while in reality it was the British who succeeded.

The British-American co-production " The Imitation Game - A Top Secret Life " illustrates the life and contributions of Alan Turing as a code breaker in Bletchley Park. Here, too, the Enigma plays a central role. At the expense of historical correctness , many facts are twisted or dramatically exaggerated in the film. For example, Turing's romance with his colleague Joan Clarke is portrayed more intensely than it actually was. Turing's niece Inagh Payne criticized the script with the words: “You want the film to show it as it was, not a lot of nonsense” (German: “You want the film to portray it as it was, and not a lot of nonsense "). In the film, Turing finds out that Cairncross is a spy. However, he manages to blackmail Turing with his homosexuality, which was criminal at the time. So they cover each other's secret of the other. This misrepresentation was heavily criticized, because Turing is actually portrayed as a “ traitor ” in the film. In fact, he was never under that suspicion. Despite all sympathy for exaggeration from a dramaturgical point of view, this representation was energetically rejected as a degradation of Turing and the film was therefore classified as unsustainable.

In the British feature film Enigma - The Secret , which is based on the novel Enigma , the deciphering work of the British code breakers in Bletchley Park is the theme. Noteworthy are the many authentic props in the film, which are original showpieces from the Bletchley Park Museum. The various radio messages have been realistically generated and encrypted especially for the film according to the original rules and procedures. Towards the end of the film, a Polish code breaker turns out to be a traitor who tries to reveal the “Enigma secret” to the Germans. This does not correspond to historical facts in two ways. For one thing, there were - as already stated - no traitors in Bletchley Park who spied for the Germans. On the other hand, not a single Polish cryptanalyst worked there, because for reasons of secrecy the British denied almost all foreigners, even Marian Rejewski, access and even more so to work. Thus, the cinematic representation is historically wrong on this point. There was particular criticism of portraying a Pole in the film as a traitor, because least of all Poles have betrayed the Enigma secret. On the contrary, Polish cryptanalysts such as Marian Rejewski, Jerzy Różycki and Henryk Zygalski laid the decisive foundations for breaking into the enigma of the Enigma even before the war, without which the British code breakers would probably not have been able to decipher German radio messages and the second World War would have taken a different course.

## chronology

With the addition of rollers IV and V (here in a wooden box), the number of possible roller layers was increased from 6 (= 3 · 2 · 1) to 60 (= 5 · 4 · 3) from December 15, 1938.
In 1944 the Luftwaffe introduced the " watch " as an addition to the Enigma I. The rotary switch can be used to set different non-intrusive exchanges of letters.

Some important points in time in the history of the Enigma are listed below
(specific points in time for the marine version see M4 ):

 Feb 23, 1918 First patent for Enigma 0July 9, 1923 Founding of Chiffriermaschinen AG 21 Mar 1926 Patenting of the reverse roller (VHF) July 15, 1928 The Reichswehr introduces a previous version of the Enigma 0Aug 9, 1928 The plug board is introduced by the Reichswehr exclusively for machines used by the military 0June 1, 1930 Commissioning of the Enigma I (six plugs and quarterly changing roller positions) 0Feb. 1, 1936 Monthly change of the roller position 0Oct. 1, 1936 Daily change of the roller position and instead of six now five to eight plugs 0Nov 1, 1937 Replacement of VHF A by VHF B Sep 15 1938 New indicator procedure (freely selectable basic position for the key encryption) Dec 15, 1938 Commissioning of rolls IV and V 0Jan. 1, 1939 Seven to ten plugs July 26, 1939 Two days allied meeting at Pyry Aug 19, 1939 Ten plugs 0May 1, 1940 Dropping the spell key duplication 1940/41 Temporary use of VHF C (as an alternative to VHF B) 0Dec 8, 1941 First break of the Abwehr Enigma by Dilly Knox 0Feb. 1, 1942 Commissioning of the M4 0Sep 1 1943 Dropping the identification group 0Jan. 1, 1944 Occasional use of the pluggable VHF D July 10, 1944 The Air Force introduces the " watch " Sep 15 1944 The CY procedure is introduced in the army

## glossary

The following technical terminology is used in connection with the way the Enigma works and its cryptanalysis :

• Alphabet - An ordered arrangement of symbols permuted in sequence, specifically the 26 uppercase Latin letters (Example: EKMFLGDQVZNTOWYHXUSPA IBRCJ)
• B-Dienst - (abbreviation for observation service): Intelligence service of the German navy during World War II, which dealt with wiretapping and recording as well as the deciphering and interpretation of enemy, especially British, radio traffic
• Biuro Szyfrów - (Abbreviation: BS): Polish name for the “cipher office” located in Warsaw, in which Polish cryptanalysts broke the Enigma encryption from 1932 onwards
• Bletchley Park - (Abbreviation: BP): Country estate in the English village of Bletchley , which was the headquarters of the British code breakers during World War II and is now a museum
• Bomba - (plural: Bomby ): Polish name for the cryptanalytical machine developed by Rejewski in 1938, with which the error of the key doubling was exploited in order to open up the roller position and the key
• Bomb - (plural: Bombes ): English name for the cryptanalytic machineinventedby Turing in 1939 and improved by Welchman, by means ofwhich the daily key was determinedwith the help of cribs and bypassing the plug board
• Chi - Abbreviation for the encryption department of the Wehrmacht High Command, i.e. the department that dealt with the deciphering of enemy communications and the security control of its own key procedures
• Cipher - another term for ciphertext
• Cipher - Another term for encryption
• Cillis - (not authentically also called "sillies" (German: "Dummchen")): English nickname for the incorrect choice of the basic position and the key from adjacent letters on the keyboard (example: QWE RTZ, see also: radio message and faulty slogan )
• Clash - (German: collision): English technical term for the repeated occurrence of the same roller in the same position (in the same place) in the roller set on two consecutive days.
• Click - Repeated occurrences of identical ciphertext characters
• Confirmation - English technical term used by British code breakers, especially when searching for a connector. (Example: The WF connector is determined after FW had already been recognized, see also: Contradiction )
• Consecutive connector knock-out - see: CSKO
• Constatation - (German: Relation ): English technical term for the pair of letters formed at a certain position in the cryptogram and in the crib .
• Contradiction - (German: contradiction): English technical term used by the British code breakers, especially when searching for connectors. (Example: The WX connector is determined after FW had already been recognized, see also: Confirmation )
• Crab - (German: Krabbe): English nickname for a rotation step of the middle roller in the defense Enigma
• Crash - (German: collision ): English technical term for the simultaneous occurrence of one and the same letter in the same position in the cryptogram and in the crib . As this was known to be impossible with the Enigma, it served to exclude the assumed crib location.
• Crib - (German: Eselsbrücke, more aptly: Probable word): English term for a text fragment that is expected to appear in plain text (German technical term also: " Plain text-ciphertext compromise ").
• CSKO - Abbreviation for "Consecutive plug knock-out" (German: " knocking down consecutive plugs"). British method and device that exploited the frequently practiced flawed peculiarity of the German keyboards of not stickingadjacent letters in the alphabet(examples: not AB, PQ or XY).
• CY procedure - From Sep 15 Procedure introduced in the army in 1944 in which the left cylinder was adjusted by hand in the middle of a saying.
• Dechiffrat - Another expression for plain text
• Depth - (from English literally "depth"): Two or more ciphertexts that have been encrypted with the same key (German technical term: " Klartext-Klartext-Kompromiss ").
• Double-letter exchange board - code boards used in the submarines for the secret transmission of the spell key
• Double plug cords - (short: plug): connection cable between the front panel sockets
• Entry Roller - Fixed roller at the beginning of the roller set
• Decrypt - (English: to decipher ): Conversion of the ciphertext into the plaintext with the help of the key
• Decipher - (English: to decrypt ): breaking the ciphertext without knowing the key beforehand
• Female - (in the Polish original: samica or colloquially: samiczkami , literally in German: “Weibchen”, German technical term: “one cycle”, occasionally but less precisely: “Fixed point”): Repeated occurrence of an identical ciphertext-plaintext letter pair, thecan be usedfor deciphering
• Filler letters - Letters to be chosen randomly for camouflage, especially the first two letters of the identification group
• Ciphertext - Text generated from plaintext by encryption
• Plugged in - two letters are swapped using a cable plugged into the front panel
• Basic position - (English: initialPosition ): rolling position to the coding of the Chamber key
• JABJAB - English nickname coined by Dennis Babbage for the negligent choice of the basic position, also as a key to a saying
• Kenngruppe - (also: letter identification group , English: discriminant , also: disc ): Five letters (two filler letters and three identification group letters) at the beginning of a phrase to identify the key
• Identification group book - code book used by the submarines for the secret transmission of the message key
• Identification Group Letters - The last three letters of the identification group
• Identity group booklet - Code book used in the U-boats in connection with short signals
• Identification group table - The key table supplementary list with daily changing identification group letters
• Kiss - (German literally: Kuss): English expression for two different ciphertexts based on the same plain text (German technical term: “ ciphertext-ciphertext compromise ”).
• Cryptogram - Another term for ciphertext
• Short signal booklet - code book used by the submarines to shorten the radio messages
• Letchworth-Enigma - model of the set of rollers devised by Alan Turing for the purpose of advantageous cryptanalysis
• Lobster - (German: Hummer): English nickname for a simultaneous rotation step of all rollers including the reversing roller in the defense Enigma
• Gap filler roller - innovative roller with freely adjustable transfer notches
• Non-clashing rule - (German: non -collision rule ): English nickname for the incorrect German custom of key panels for neighboring days of the month to avoid reusing a roller in the same place in the roller set
• Non-repeating rule - (German: non-repeating rule ): English nickname for the incorrect German custom of key panels to avoid the reuse of a roller layer within a month
• Period - number of letters after which the alphabet used for encryption repeats itself (16,900 for the Enigma I)
• QWERTZU - Term coined by Dilly Knox for the wiring sequence of the individual letter keys on the keyboard with the exit contacts of the entry roller
• Ring position - the rotational position of the rings, which determines the offset between the internal wiring of the rollers and the letter that is transferred to the next roller
• Key - Secret setting of the key machine
• Key machine - a summary term for encryption and decryption machine
• Keys - A general term for encryption and decryption
• Key space - set of all possible keys (see also other meaning below)
• Key room - room in which "keying" takes place, often the radio room (see also other meaning above)
• Key table - list of daily keys
• Ciphertext - Another word for ciphertext
• Encryptor - the person who encrypts or decrypts messages
• Six self-steckered letters - (German: six unplugged letters): English term for the (incorrect) German rule for keyboards to leave exactly six letters unplugged ("self-steckered") and only swap ten pairs (instead of all thirteen)
• Special circuit - In rare cases, special wiring of the rotating rollers is made
• Spruch - ciphertext that is usually transmitted by radio
• Spruchkopf - (English: preamble ): First part of the radio message with unencrypted indication of the time, the number of letters, the basic position and the encrypted message key (such as QWE EWG , English: indicator )
• Message number - serial number of a radio message, with a color differentiation between outgoing (blue) and incoming (red)
• Message key - (English: message setting or indicator ): Individual key for a radio message
• Slogan key duplication - In May 1940 abolished (incorrect) method of transmitting the slogan key twice, which enabled Polish cryptanalysts to break in in the 1930s
• Plug - cable connections between the front panel sockets
• Plug board - socket plate attached to the front of the Enigma
• Day key - Daily changing key
• Clock - additional device for the creation of non-intrusive plug connections
• Reversing roller - (mostly) fixed roller at the end of the roller set (abbreviation: UKW)
• Reversing roller D - Innovative reversing roller with selectable wiring (also called: VHF Dora)
• Uncle Charlie - (German: Onkel Charlie): English nickname for the reverse roller C
• Uncle Dick - (German: Onkel Dick): English nickname for the reversing roller D
• Uncle Walter - (German: Onkel Walter): English onomatopoeic paraphrase of the German term "reversing roller"
• Unplugged - (English: self-steckered ): Letters that are not swapped because the cable is not plugged in
• Encrypt - converting plain text into ciphertext
• Wahlwort - (English: Wahlwort ): Randomly chosen word that is inserted at the beginning or end of the plain text of a radio message in order to bring it "to different lengths".
• Roller - (English: wheel ): rotor that turns during the key process
• Roller position - (English: wheel order ): Key-dependent placement of the rollers in the roller set
• Roller set - (English: wheel set or scrambler ): A summary term for all rollers
• Roller position - (English: wheel setting ): The rotation position of the rollers can be adjusted by hand and changes during the keying process
• Weather short key - Code book used by the Kriegsmarine to shorten weather reports
• Y Service - (German: "Y-Dienst"): English name of the British radio monitoring service, whose main task during the Second World War was to intercept and record enemy, especially German, radio traffic
• Cyclometer - (in the Polish original: Cyklometr ): Name for the cryptanalytic device designed by Rejewski in 1934, with which the error of the key doubling was exploited to reveal the roller position and the key

## literature

Primary literature
• General key rules for the Wehrmacht. H.Dv.g. 7, M.Dv.Nr. 534, L.Dv.g. 7, April 1, 1944, Books on Demand, 2019 reprint . ISBN 978-37431-9385-7 .
• Signal key for the radio signal service (radio signal key) - secret. M.Dv.Nr. 114, October 1939, Books on Demand, reprint 2019. ISBN 978-37494-6791-4 .
• Gustave Bertrand : Énigma ou la plus grande enigme de la guerre 1939–1945 . Librairie Plon, Paris 1973.
• Francis Harry Hinsley , Alan Stripp: Codebreakers - The inside story of Bletchley Park . Oxford University Press, Reading, Berkshire 1993, ISBN 0-19-280132-5 .
• Marian Rejewski : An Application of the Theory of Permutations in Breaking the Enigma Cipher . Applicationes Mathematicae, 16 (4), 1980, pp. 543-559. cryptocellar.org (PDF; 1.6 MB), accessed February 15, 2016.
• Marian Rejewski: How Polish Mathematicians Deciphered the Enigma . Annals of the History of Computing, 3 (3), July 1981, pp. 213-234.
• Arthur Scherbius: "Enigma" cipher machine . Elektrotechnische Zeitschrift , November 1923, pp. 1035-1036, cdvandt.org (PDF; 1 MB), accessed on February 21, 2019.
• Frederick William Winterbotham : The Ultra Secret . Weidenfeld and Nicolson, London 1974.
• Gordon Welchman : The Hut Six Story - Breaking the Enigma Codes . Allen Lane, London 1982; Cleobury Mortimer M&M, Baldwin Shropshire 2000, ISBN 0-947712-34-8 .
Secondary literature

Wiktionary: enigma  - explanations of meanings, word origins, synonyms, translations

Details

The Swiss army used from 1946 an improved follow-up version of the Enigma, as Nema (New Machine) was called, and indeed, but had an irregular rolling stepping well over a reversing roll with their cryptographic weaknesses.

Documents

Decipherments

Exhibits

Photos, videos and audios

Commons : Enigma  - collection of images, videos and audio files

Replica projects

Simulations of the machine

Encryption simulations

## Individual evidence

1. ^ Karl de Leeuw and Jan Bergstra (eds.): The History of Information Security - A Comprehensive Handbook . Elsevier BV, Amsterdam, Netherlands, 2007, p. 389. ISBN 978-0-444-51608-4 .
2. ^ A b Karl de Leeuw: The Dutch Invention of the Rotor Machine, 1915–1923 . Cryptologia. Rose-Hulman Institute of Technology. Taylor & Francis, Philadelphia PA 27.2003,1 (January), pp. 73-94. .
3. ^ A b c Louis Kruh, Cipher Deavours: The Commercial Enigma - Beginnings of Machine Cryptography . Cryptologia, Vol. XXVI, No. 1, January 2002, p. 1. apprendre-en-ligne.net (PDF; 0.8 MB) Retrieved: November 4, 2013.
4. ^ Friedrich L. Bauer: An error in the history of rotor encryption devices . Cryptologia, July 1999.
5. a b Patent specification of the DRP encryption apparatus No. 416 219. Accessed : Nov. 4, 2013. cdvandt.org (PDF; 0.4 MB)
6. David Kahn: Seizing the Enigma - The Race to Break the German U-Boat codes 1939 -1943 . Naval Institute Press, Annapolis, MD, USA, 2012, p. 35. ISBN 978-1-59114-807-4 .
7. ^ David Kahn: An Enigma Chronology . Cryptologia. Rose-Hulman Institute of Technology. Taylor & Francis, Philadelphia PA 17.1993, 3, p. 239, .
8. ^ Friedrich L. Bauer: Historical Notes on Computer Science . Springer, Berlin 2009, p. 49. ISBN 3-540-85789-3 .
9. Louis Kruh, Cipher Deavours: The commercial Enigma - Beginnings of machine cryptography . Cryptologia, Rose-Hulman Institute of Technology, Taylor & Francis, Philadelphia PA 26.2002,1 (January), p. 1. Retrieved: October 18, 2016. apprendre-en-ligne.net (PDF; 0.8 MB)
10. Anders Wik: The First Classical Enigmas - Swedish Views on Enigma Development 1924–1930. Proceedings of the 1st International Conference on Historical Cryptology, PDF; 12.5 MB 2018, pp. 83-88.
11. Jump up ↑ Winston Churchill : The World Crisis - 1911-1918 . 4 volumes, 1923 to 1929, ISBN 978-0-7432-8343-4 .
12. ^ Julian Corbett : Naval Operations . 1923, ISBN 1-84342-489-4 .
13. Simon Singh: Secret Messages . Carl Hanser Verlag, Munich 2000, p. 177. ISBN 3-446-19873-3 .
14. Simon Singh: Secret Messages . Carl Hanser Verlag, Munich 2000, p. 178. ISBN 3-446-19873-3 .
15. José Ramón Soler Fuensanta, Francisco Javier López-Brea Espiau and Frode Weierud: Spanish Enigma: A History of the Enigma in Spain . Cryptologia. Rose-Hulman Institute of Technology. Taylor & Francis, Philadelphia PA 34.2010,4 (October), p. 309. .
16. ^ A b c Friedrich L. Bauer: Decrypted Secrets, Methods and Maxims of Cryptology . Springer, Berlin 2007 (4th edition), p. 123, ISBN 3-540-24502-2 .
17. ^ Max Rüegger: Memories of a Korea radio operator - Working with the ENIGMA cipher machine . 2016. PDF; 4.7 MB ( August 25, 2016 memento in the Internet Archive ) Retrieved August 24, 2018.
18. Arthur O. Bauer: Radio direction finding as an allied weapon against German submarines 1939-1945 . Self-published, Diemen Netherlands 1997, p. 31. ISBN 3-00-002142-6 .
19. ^ Francis Harry Hinsley, Alan Stripp: Codebreakers - The inside story of Bletchley Park . Oxford University Press, Reading, Berkshire 1993, p. 85. ISBN 0-19-280132-5 .
20. ^ Francis Harry Hinsley, Alan Stripp: Codebreakers - The inside story of Bletchley Park . Oxford University Press, Reading, Berkshire 1993, p. 83. ISBN 0-19-280132-5 .
21. Arthur Scherbius: "Enigma" cipher machine . Elektrotechnische Zeitschrift, 1923, p. 1035.
22. a b David H. Hamer : G-312. To defense Enigma . Cryptologia. Rose-Hulman Institute of Technology. Taylor & Francis, Philadelphia PA 24.2000,1 (January), p. 46. ISSN 0161-1194 . Retrieved: Nov. 4, 2013. PDF scan as ZIP; 1.1 MB ( Memento from June 11, 2007 in the Internet Archive )
23. a b Patent specification Electrical device for encryption and decryption DRP No. 452 194. cdvandt.org (PDF; 0.5 MB) Retrieved on November 4, 2013.
24. Friedrich L. Bauer: Deciphered secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin a. a. 2000, p. 119.
25. High Command of the Navy : The Key M - Procedure M General . Berlin 1940. Accessed : Nov. 4, 2013, p. 23. cdvandt.org (PDF; 0.7 MB)
26. Friedrich L. Bauer: Deciphered secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin a. a. 2000, p. 115.
27. a b Gordon Welchman: The Hut Six Story - Breaking the Enigma Codes . Allen Lane, London 1982; Cleobury Mortimer M&M, Baldwin Shropshire 2000, ISBN 0-947712-34-8 , p. 213.
28. ^ Louis Kruh: How to Use the German Enigma Cipher Machine -A Photographic Essay . Cryptologia , Rose-Hulman Institute of Technology. Taylor & Francis, Philadelphia PA 29.2005,3, pp. 193-232.
29. OKW: Key instructions for the Enigma key machine . H.Dv. G. 14, Reichsdruckerei , Berlin 1940. (Copy of the original manual with a few small typing errors.) Accessed: August 24, 2018. PDF; 0.1 MB ( memento from September 24, 2015 in the Internet Archive )
30. Philip Marks: Umkehrwalze D: Enigma's rewirable reflector - Part 1 . Cryptologia , Volume XXV, Number 2, April 2001, p. 117.
31. The US 6812 Bomb Report 1944 . 6812th Signal Security Detachment, APO 413, US Army. Publication, Tony Sale, Bletchley Park, 2002. p. 2. codesandciphers.org.uk (PDF; 1.3 MB) Retrieved November 4, 2013.
32. ^ Francis Harry Hinsley, Alan Stripp: Codebreakers - The inside story of Bletchley Park . Oxford University Press, Reading, Berkshire 1993, p. 107. ISBN 0-19-280132-5 .
33. John Jackson: Solving Enigma's Secrets - The Official History of Bletchley Park's Hut 6. BookTower Publishing 2014, pp. 96-100. ISBN 978-0-9557164-3-0 .
34. Tony Sale: The Bletchley Park 1944 Cryptographic Dictionary . Publication, Bletchley Park, 2001, p. 57. Retrieved March 30, 2017. codesandciphers.org.uk (PDF; 0.4 MB)
35. CHO'D. Alexander: Plug knock-out . Publication, Bletchley Park, March 1944. Edited and edited by Frode Weierud , July 1998. Accessed : August 24, 2018. PDF; 0.1 MB ( memento from July 2, 2007 in the Internet Archive )
36. Friedrich L. Bauer: Deciphered secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin a. a. 2000, p. 459.
37. Derek Taunt: Hut Six in Francis Harry Hinsley, Alan Stripp: Codebreakers - The inside story of Bletchley Park . Oxford University Press, Reading, Berkshire 1993, p. 100. ISBN 0-19-280132-5 .
38. ^ Hugh Sebag-Montefiore: Enigma - The battle for the code . Cassell Military Paperbacks, London 2004, p. 314. ISBN 0-304-36662-5 .
39. High Command of the Navy: The Key M - Procedure M General . Berlin 1940. Accessed : Nov. 4, 2013, p. 23. cdvandt.org (PDF; 0.7 MB)
40. a b Dirk Rijmenants: Enigma Message Procedures Used by the Heer, Luftwaffe and Kriegsmarine . Cryptologia , 34: 4, 2010, p. 329 ff.
41. ^ A b Hugh Sebag-Montefiore: Enigma - The battle for the code . Cassell Military Paperbacks, London 2004, p. 357. ISBN 0-304-36662-5 .
42. High Command of the Wehrmacht : General key rules for the Wehrmacht . H.Dv.g. 7, Reichsdruckerei , Berlin 1944, p. 13. cdvandt.org (PDF; 0.9 MB) Accessed : Nov. 4, 2013.
43. High Command of the Navy: The Key M - Procedure M General . Berlin 1940, p. 25 ff. Cdvandt.org (PDF; 0.7 MB) Accessed : November 4, 2013.
44. David H. Hamer, Geoff Sullivan, Frode Weierud: Enigma Variations - An Extended Family of Machines . Cryptologia. Rose-Hulman Institute of Technology. Taylor & Francis, Philadelphia PA 22.1998, 1 (July), p. 214, . cryptocellar.org (PDF; 80 kB) Accessed: February 15, 2016.
45. Modern breaking of Enigma ciphertexts.Retrieved March 30, 2017.
46. a b Friedrich L. Bauer: Deciphered secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin a. a. 2000, p. 117.
47. High Command of the Navy: The Key M - Procedure M General . Berlin 1940, p. 26. cdvandt.org (PDF; 0.7 MB) Accessed : Nov. 4, 2013.
48. ^ A b c Gordon Welchman: The Hut Six Story - Breaking the Enigma Codes . Allen Lane, London 1982; Cleobury Mortimer M&M, Baldwin Shropshire 2000, p. 168. ISBN 0-947712-34-8 .
49. Louis Kruh, Cipher Deavours: The commercial Enigma - Beginnings of machine cryptography . Cryptologia, Rose-Hulman Institute of Technology, Taylor & Francis, Philadelphia PA 26.2002,1 (January), p. 10. , accessed on March 14, 2019. apprendre-en-ligne.net (PDF; 0, 8 MB)
50. ^ Hugh Sebag-Montefiore: Enigma - The battle for the code . Cassell Military Paperbacks, London 2004, p. 404 ISBN 0-304-36662-5 .
51. ^ M4 Message Breaking Project. Retrieved: Nov. 4, 2013. (Warning: The page doesn't seem to have been updated since 2009!)
52. ^ M4 Project 2006, Third Message (on hoerenberg.com) Retrieved: Nov. 4, 2013.
53. US1905593 Coding Machine. 5 claims Application date November 12, 1929 and in Germany November 16, 1928 (PDF; 487 kB). Granted April 25, 1933. Applicant: Willi Korn of Berlin-Friedenau, Germany, accessed June 5, 2019.
54. Friedrich L. Bauer: Deciphered secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin a. a. 2000, p. 117.
55. ^ Colleen Carper: Bletchley's Secret War - British Code Breaking in the Batlle of the Atlantic. Ashbrook Statesmanship Thesis, 2009, p. 3, PDF
56. Louis Kruh, Cipher Deavours: The Commercial Enigma - Beginnings of Machine Cryptography . Cryptologia, Vol.XXVI, No. 1, January 2002, p. 11. apprendre-en-ligne.net (PDF; 0.8 MB), accessed on February 18, 2019.
57. OKW: Key instructions for the Enigma key machine . H.Dv. G. 14, Reichsdruckerei , Berlin 1940, p. 6. (Copy of the original manual with a few small typing errors.) Accessed: August 24, 2018. PDF; 0.1 MB ( memento from September 24, 2015 in the Internet Archive )
58. a b Robert Harris: Enigma . Novel. Weltbild, Augsburg 2005, p. 71. ISBN 3-89897-119-8 .
59. ^ Francis Harry Hinsley, Alan Stripp: Codebreakers - The inside story of Bletchley Park. Oxford University Press, Reading, Berkshire 1993, p. 86. ISBN 0-19-280132-5 .
60. Patent specification Electrical device for ciphering and deciphering DRP No. 452 194, p. 1. cdvandt.org (PDF; 0.5 MB) Accessed : Nov. 4, 2013.
61. Friedrich L. Bauer: Deciphered secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin a. a. 2000, p. 49.
62. Friedrich L. Bauer: Deciphered secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin a. a. 2000, p. 276.
63. ^ Claude Shannon: Communication Theory of Secrecy Systems . Bell System Technical Journal, Vol 28, 1949 (October), pp. 710 f. netlab.cs.ucla.edu (PDF; 0.6 MB) Accessed : Nov. 4, 2013.
64. David Kahn: Seizing the Enigma - The Race to Break the German U-Boat codes 1939 -1943 . Naval Institute Press, Annapolis, MD, USA, 2012, p. 131. ISBN 978-1-59114-807-4 .
65. ^ Krzysztof Gaj: Polish Cipher Machine -Lacida . Cryptologia . Rose-Hulman Institute of Technology. Taylor & Francis, Philadelphia PA 16.1992,1, , p. 74.
66. ^ Gordon Welchman: The Hut Six Story - Breaking the Enigma Codes . Allen Lane, London 1982; Cleobury Mortimer M&M, Baldwin Shropshire 2000, p. 210. ISBN 0-947712-34-8 .
67. OKW: Instructions for use for the Enigma cipher machine . H.Dv.g. 13, Reichsdruckerei , Berlin 1937. Online (PDF; 2 MB) Accessed: Nov. 4, 2013.
68. ^ Hugh Sebag-Montefiore: Enigma - The battle for the code . Cassell Military Paperbacks, London 2004, p. 22. ISBN 0-304-36662-5 .
69. Simon Singh: Secret Messages . Carl Hanser Verlag, Munich 2000, p. 199. ISBN 3-446-19873-3 .
70. ^ Marian Rejewski: An Application of the Theory of Permutations in Breaking the Enigma Cipher . Applicationes Mathematicae, 16 (4), 1980, pp. 543-559. Accessed: August 24, 2018. PDF; 1.6 MB ( Memento from December 21, 2015 in the Internet Archive )
71. ^ Friedrich L. Bauer: Historical Notes on Computer Science . Springer, Berlin 2009, p. 295. ISBN 3-540-85789-3 .
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3. on June 24th U 119 (type XB),
4. on July 13th U 487 (Type XIV),
5. on July 24th U 459 (Type XIV),
6. on July 30th U 461 (Type XIV),
7. on July 30th U 462 (Type XIV),
8. on August 4th U 489 (Type XIV),
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 This article was added to the list of excellent articles on March 3, 2006 in this version .