Enigma machine

Enigma in use, 1943

Enigma in use, 1943

The Enigma is a rotor cipher machine, which used the German military during World War II for encryption of message traffic. Other institutions such as the police, intelligence agencies, diplomatic services, SD, SS, Reich post and railroad used them for secret communication. The Greek word ainigma or Enigma means enigma. Although the encryption quality of the machine has been developed several times during the war, the Allies could read along through enormous effort to decrypt during most of the German messages.


After the First World War, the German military were looking for a replacement for the now outdated, cumbersome and unsafe manual encryption method (for example ADFGX or codebooks), which were used until then. For this machine methods were considered, because they promised an easier handling and improved cryptographic security. Based on the start of the 20 Century, newly arrived techniques, such as the electric typewriter and the telegraph were independently and almost simultaneously four inventors on the idea of the rotor principle for encrypting texts. It is the American Edward Hugh lifters in 1917 (patent 1921), the German Arthur Scherbius in 1918 and the Dutchman Hugo Koch and Sweden Arvid Gerhard Damm in 1919, all their ideas rotor cipher patent signed up.

As the inventor of ENIGMA is a doctorate in German electrical engineer Arthur Scherbius (1878-1929), whose first patent for this purpose, 23 February 1918 dates. To manufacture the machine was on 9 July 1923, the cipher-Aktiengesellschaft in Berlin (35 W, 2 Str Steglitz) was founded. The Enigma cipher was first conceived as a civilian and was commercially at fairs – such as 1923 on the International Postal Congress of the Universal Postal Union in Berns available for purchase -. Towards the end of the 1920s were military services more interest, so that the machine soon after disappeared from the civilian market. During the upswing of the hitherto rather sluggish sales running the system crashed Scherbius fatal. In 1934, Rudolf Heimsoeth and Elsbeth Rinke acquired the former company Scherbius that the production of the ENIGMA in Berlin continued under the new company “Heimsoeth & Rinke”. The Nazi regime had already begun. As a reliable encryption system was needed as part of the upgrade of the Wehrmacht, the success of the ENIGMA nothing stood in the way.

It is estimated that more than 30,000 machines were produced during the Second World War, some estimates range up to 200,000, presumably the actual number of machines used is about 100,000. In the course of time – until the war ended in 1945 and beyond – were many different models and variants of the Enigma used (see also: ENIGMA models). The most used was the ENIGMA I (pronounced “Enigma one”), which was used from 1930 by the Reichswehr and later by the Wehrmacht and the PROCEDURE OF encryption during the Second World War most frequently used embodied.


The ENIGMA I included wooden cabinet weighs about 12 kg and the outer dimensions (L × W × H) are about 340 mm × 280 mm × 150 mm (data without housing: 10.35 kg and 310 mm × 255 mm × 130 mm). It looks at first glance like a typewriter, and basically consists of the keyboard, a drum set of three interchangeable rollers (rotors with a diameter of approximately 100 mm) and a light box for display. The roll rate is the heart of the encryption. The three rollers are mounted for rotation and have on both sides of the 26 capital letters of the Latin alphabet 26 electrical contacts, which are connected in pairs and irregularly interconnected by 26 insulated wires inside the roll, for example, (roll III) contact A ​​with B, B with D, and so on. If you press a letter key as electric current flows from a 4.5-volt battery located in the ENIGMA about the key pressed by the roller set and illuminates an indicator light. The illuminated letter corresponds to the encryption of the pressed letter. As the rollers continue to rotate similarly with each key press as a mechanical odometer, the secret key changes after each alphabet letter.

Are you “OTTO” a so light in succession, for example, the lamps “PQWS”. Important and cryptographically strong is that due to the rotation of the rollers each letter is encoded in a different way, in the example, the first O OTTO to P, but the second to p is called by many different (secret) “alphabets” used for encryption and calls this polyalphabetic substitution. In contrast, using a mono-alphabetic substitution of only one secret alphabet, and a plaintext letter is always in the same ciphertext letter transforms (“OTTO” example in “GLLG”). If the rollers do not rotate the ENIGMA, so you would get just a simple encryption monoalphabetic also with her.


The right of the three rotating rollers (5) of the roll set (see yellow marked numbers in the schematic diagram) is the entry roll (4) (stator), which does not rotate and their contacts over 26 wires (here are just four of them signed) with the character keys (2) are connected. Left of the roll set is the reverse roller (6) (FM), which also is established in the ENIGMA I. With reverse roll, which is often referred to as a reflector, it is an invention (patented on March 21, 1926) by Willi Korn, a staff of Scherbius. She has on her right side only 26 contacts (in the sketch again, only four of which are shown) which are connected together in pairs. The turn roll means that the current which initially passes through the roll set from right to left, is diverted and flows through it again, now from left to right. The stream leaves the roller set, as he came back through the inlet roller.

The table shows the time as “Top Secret” classified top secret wiring diagram of the available in the ENIGMA I five rotatable rollers I to V and the reverse roll A (up to 1937 used), B (from 1937 in use) and C (1940 and 1941 used sporadically):










On the front, a connector board is mounted with double pole sockets for each of the 26 letters. The flow of the character key (2) before it reaches the inlet roller (4), this plug board (3) is guided. After passing through the set of rolls it passes a second time through the plug board (7, 8), and finally brings the 26 letters of lamps (9) to light up. The letters and the keyboard lights and the sockets are arranged similar to a German typewriter keyboard:





In a letter key pressed, for example A, the battery power on the A key to the same socket in the connector board is turned on. Is there the A jack with a different socket attached by a cable connected from the outside (“confess Eckert”), then A is with a different letter, such as J, reversed. Is no cable plugged in (“ungesteckert”), then the flow passes directly to contact A of inlet roller.

In the description of the function (only top half first), reference is made to the image of “flow”. It is for illustration only and is a simplified representation of the rotating roll set (with left, middle and right rotor) and the static reverse roller (English: Reflector). For reasons of clarity the number of letters was (only A to H) decreased from 26 to 8 in the sketch.

Suppose the letter A is ungesteckert, then the current through the inlet roller (it is not shown in the diagram) to the input A of the contact roll right passed. Their wiring causes a change (substitution) of subparagraph (substitution). The flow entering from the right at the entrance of contact A, leaving the roller on its left hand side B. Thus, the output contact is replaced with the right roller A by B.

The current then passes through the contact B in the middle roll. Since it is quite possible when wiring a roller that (as in the picture) a contact input connected to the output of the same contact, B remains unchanged here. The stream leaves this through the contact B and enters the middle roll into the left roller. Their wiring ensures that the current passes from the input to the output contact Contact B D.


The stream has now been through all three (rotary) rolls once and reached the turn roll. She only contacts on the right side and connects the letters in pairs, for example D with E.

Now a second time but the current flowing through the roller set, now from left to right. By the turn roll it passes through the contact email in the left roller. Here E is wired with C for example. Consequently, current continues to flow via contact C in the middle roll, it leaves again through the contact F, and flows into the right roller. The stream leaves the right roller finally the contact G.

The more current flow is not clear from the sketch, but is easily explained. After exiting the set of rollers of the flow over the entry roll is passed back to the connector board. Here is the letter G confess Eckert with a different letter, then there will be a final permutation. If G ungesteckert, the G lamp lights up. The way they lit only for as long as the A button is held down, there is only switched while holding down the changeover to the battery. If you let it go, the lamp goes out. In the example described is thus the letter A, the key was pressed at the outset and is still depressed, coded as letter G.

If the text to be encrypted “AACHENISTGERETTET” is an A is entered again. So the A button is released and pressed for the second time. It is important that with the mechanical pressure on the button by means of a stepping mechanism, while the right roller is rotated to a position. The middle roll is rotated only after the right roller 26 steps. In the lower half of the picture “flow” situation is sketched, right after the roll has been advanced by one position (down).

As you can see from the diagram, the path to the right again on contact A roller incoming stream has changed radically. He now also takes in the middle and left roll and reverse roll a completely different way than before, although these rolls have not rotated. The result is a different encryption of the letter A, which is now converted into C.


In the first three ENIGMA I stood, in 1939 five different rollers available, with Roman numerals (I, II, III, IV and V) were numbered. The user selects a secret key by default table, which provided for changing settings for each day, three of the five reels and put them according to the prescribed under the heading “rolling location” in the daily key arrangement.

The “Key panel” presented in tabular form for a complete month of the valid keys that day, changed at midnight. Below example only three days of the month are shown, as was customary, the days are sorted in descending order. This allows the encryptor to cut off the used codes in the past few days and destroyed.

FM day rolling bearing ring position plug connectors —- —-

31 BI III IV 16 26 08 ET FL CN AD GI Concentration Camp JV PU QY WX



Example for 31 Month: B FM, roll position I III IV means that the reversing roller is the roller B to select the left and the roller I (as slower rotor), in the center roll and the roll IV III right (as rotor speed) is to be inserted. The rings, which are mounted outside the roller body and the offset between the internal wiring of the rollers, and determine the character to which the transfer takes place to the next roller is, at 16, 26 or 8 Set letters of the alphabet, i.e. P, Z and H.

The ring position was often (as here) numerically instead of alphabetically listed, but mention the relevant service rules of the time – both in terms of the ring position in the daily key and the ring label on the roll ring itself – always both ways and put the numbers 01-26 the same with the letters AZ. As an aid to the operator “to convert the numbers into letters or vice versa” is inside the cover as part of the ENIGMA Note plaque “For attention!” a conversion table attached.


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 receptacles are to be connected to the front panel with the corresponding double-pole cables. Usually exactly ten cables were plugged. The respective upper socket of a socket having a pair of somewhat larger diameter (4 mm), so that the plug can only be inserted in one orientation than the lower (3 mm). To ensure the desired electrical crossover and thus the interchange of the two letters is achieved. Six letters remain ungesteckert. (This fixed rule of six self-steckered letters was a help for the code breaker.)

To reduce the chances of someone guessing of keys, some rules for the preparation of key tables were invented by the German authorities. So it was (temporarily) banned, that a rolling position that has already been used on one day of the month, was repeated on another day of the month. Also, a roll on two consecutive days in the month could not be located in the same place in the roll set. A third rule was to prevent guessing obvious connector combinations. So it was forbidden for two consecutive letters of the alphabet were disturbed Eckert together. (This, too, used the code breaker in their favor and called it Consecutive male knock-out CSKO.)

All these regulations caused the opposite, namely a weakening of encryption. They led to a convenience for the code breaker, which could exclude more and more key combinations under the said rules, in particular with the progress of the month.

After installing the rollers according to the required rolling position, adjusting the ring position and switching the connectors on the operator closed the set of rollers mounted above the door and the front door. The latter resulted in a firm pressing of the plug and a secure contact and protection against spying the key. In order for the ENIGMA encryption or decryption was ready.


To ensure that not all radio messages of a key network with identical keys are encrypted, which would make the texts vulnerable, was required to adjust for each spell an individual initial position of the three rolls, called “message key”. The procedures for this purpose varied from time to time and were not identical in all branches of the Wehrmacht. For Army and Air Force was from 15 May 1940 (five days after the start of the Western campaign s) the following in the “Key to the Enigma machine instructions” described scheme, for example, the following plain text to be sent:

The High Command of the Armed Forces announced: Aachen is saved. Through integrated use of support staff averted the threat and saving the city around 18:00 clock could be ensured.

Since the ENIGMA can encrypt all capital letters and no numbers or punctuation and knows even a space, the clear text shown above must be treated accordingly before encryption first. This set of characters are replaced by “X” doubled proper name and enclosed in “X” and one digit numbers written out. Furthermore, it was common (except for proper names) to replace the “ch” and “ck” by “Q” and then divide the text into groups of five. This yields the following ready for encryption plaintext:


The encryptor has its ENIGMA I, as described above, according to the daily key, for example, for 31 set the month. (Roller position BI 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 use freely available computer simulation s are realistically reproduced, see also:.. Simulations links) The operator is now considering a random start position, for example, “QWE” and represents the three rollers so that they are exactly three letters visible in the display windows. Now he thinks a random message key, also consists of three letters, from, for example “RTZ”. This encrypts it with his ENIGMA and watched as one after the lamps lighting up “EEC”. The encrypted message key so he tells the receiver along with the basic position indicator as well as the time and the number of letters in the text as random head saying openly.

According to the then applicable H.Dv. g 14 (= Army regulation, secret, No. 14) contains the saying head time as a four-digit number, the number of letters of the award, including the five letters of the characteristic group and the choice of initial state and the encrypted message key (Example: 2220-204 – qweewg). In general, all the letters were written by hand small, since they could be listed as faster than use of capital letters. An authentic saying form with the slogan head “kr – 2300 – 182 – zzxprq -” where “kr” (short for “war effort” with the eye-catching Morse – · – · – ·) stands as a symbol for “Urgent”, is under links as “Award No. 233″ to see. This is a request for ammunition for the heavy field howitzer (sFH).

Next, the operator, for example, three “NOW” selects valid characteristic group letter based on a group characteristic table for this day out. The characteristic group has no cryptographic significance, it is the receiver of the message only to realize that the message is really intended for it, and can also be decrypted authorized. To camouflage the characteristic group of the three letters from the sender are permuted arbitrarily and to two randomly for each spell to be changed “Füllbuchstaben”, for example, “XY”, adds. From “NOW” is about as first “OWN” and finally “XYOWN”. These five letters are unencrypted preceded by the first group of five of the ciphertext.

The encryptor is now three rolls his ENIGMA on his chosen message key “RTZ” and encrypts the above plain text, that is, he gives each letter of the plaintext from the keyboard by ENIGMA and reads each Light on a ciphertext letter from and quoted him. Together with the head and saying camouflaged characteristic group yields the following radio message:


Head and ciphertext are sparked as Morse code and received by the receiver. This first checks whether the number of letters (here: 204) is correct and the award was received unmutilated. Then he considered the characteristic group, ie the first group of five, ignoring the first two letters and sees “OWN”. It sorts the three letters in alphabetical order, obtains “NOW”, looks into his characteristic group table, discovered there this characteristic group letter and can now be sure that the award is meant for him and he can decrypt it. His ENIGMA is already rolling regarding location, position ring and plug connections adjusted to the daily key also known to him identical with the sender. It lacks even the message key, which is the correct starting position of the rollers to decrypt the award. This information he receives from the indicators “QWE EEC” in saying head, which he interpreted as follows: place the rolls on the position “QWE” button and then “EEC”. Now he can watch one after the lamps lighting up “RTZ” in his ENIGMA. This is the message key to be set.

He now turns the rollers to the initial position “RTZ” and begins the ciphertext, starting with the second group of five “LJPQH” to enter into its ENIGMA. Now successively light up the lamps, and the following text appears:

dasoberkommandoderwehrmaqtgibtbekanntxaachenxaache nxistgerettetxdurqgebuendelteneinsatzderhilfskraef tekonntediebedrohungabgewendetunddierettungderstad tgegenxeinsxaqtxnullxnullxuhrsiqergestelltwerdenx

Cryptographic strength

When the ENIGMA was filed by Scherbius patent in 1918, so even during the time of the First World War, she was a cryptographically very strong machine and could rightly be described as “unbreakable”. Was innovative, in contrast to the then conventional manual encryption method (for example ADFGVX), the introduction of an automated encryption. It was long time alone by the usual manual, mainly linguistically based, deciphering smethoden unassailable, and remained so until the 1930s, more than ten years.

The cryptographic strength of ENIGMA are essentially given by the rotating roll set. By the rotation of the rollers is achieved that each letter of the text is encrypted with a new permutation (polyalphabetic encryption). In this way the so treacherous in the mountains monoalphabetic frequency method is ground beyond recognition and classic to decipher the ciphertext attacks, such as statistical analysis or pattern search is doomed to failure. Also, the period search using the coincidence index it, as usual method of attack on polyalphabetic ciphers, such as the Vigenere cipher, is as futile as compared to the period length (from 16.900, see also: improvement) of the Enigma was a comparatively tiny maximum length of radio messages required of 250 characters.

Critical to the security of encryption to prevent unauthorized deciphering the confidentiality of rolling wiring and the number of rollers used in roller set. The latter is a very important factor that explains the much stronger encryption of s used in the German U-boat four roll ENIGMA ENIGMA M4 compared to I (with only three rolls). There are three encrypted with an M4 machine radiograms public, whose contents up to 2006 could not be deciphered. Only then did the amateur cryptographer Stefan Krah, two of the messages that were sparked by the submarine U 264 and U, 623 in 1942, by distributed computing (distributed computing) and merger of several thousand computers n the internet within a month to decipher. The third radio message could been broken in January 2013.

The rings (ring position) determine the offset between the inner wiring of the rollers and the points at which the transfer takes place to the next roller. In addition, they are designed to protect against espionage. Thus preventing could be closed by reading the position visible from the outside of the roll position of the internal rollers.

Using the “double plug cords”, which can be plugged into the front of the connector board to allow letters before and after passing through the interchange involution roll set pairs. This measure served to further strengthen cryptographic security of ENIGMA. In fact, this way the key space is expanded considerably.

Key space

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

a) The rolling position

Three out of five rolls (I to V) and one of two reversing rollers (B or C) are selected. This results in 2 · (5.4.3) = 120 possible rolling layers (corresponding to a “key length” of about 7 bits).

b) The ring position

There are 26 different ring positions each (01 to 26) for the middle and the right roller. The ring of the left roller is cryptographically meaningless, since their transfer notch does not cause an indexing located further to the left roller. In total there are 26 ² = 676 ring positions (equivalent to about 9 bits) are relevant.

c) The rolling position

There are three for each of the (rotating) rolls 26 ways to tune them (A to Z). The reverse roll can not be adjusted. A total of 26 ³ = 17.576 roller positions are be available. Putting the ring position assumed to be known, as it is due to an unimportant anomaly of the indexing mechanism (see also Anomaly) 26 ² = 676 starting positions to eliminate redundant as cryptographically. Then remain 26.25.26 = 16,900 roll positions (equivalent to about 14 bits) as relevant left.

d) The plug connections

It can be made up to a maximum of 13 connections between the plug 26 letters. For the first, there are 26 choices for a male end and then another 25 for the other end of the cable. Thus, there are 26.25 different ways to insert it for the first cable. But since it does not matter in which order the two ends of the cable are plugged, which accounts for half of the options. This leaves 26.25 / 2 = 325 possibilities for the first connection. The second is obtained analogously 24.23 / 2 = 276 possibilities. Generally, there are (n +2 26-2) * (26-2 n +1) / 2 possibilities for the nth plug connection (see also: Gaussian sum formula).

Number of possibilities for —- —- opportunities for

Connector first page second page connector

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

{0}10.{/0}{1}      {/1} 8 7 28

11.  6 5 15

12 4 3 6

13. 2 1 1

The total number of possible combinations when using multiple plug connectors is determined by the product of the possibilities for the individual plug connections. However, since here the order of execution does not matter (it is cryptographically equivalent if, for example, first A with X confess Eckert and then B to Y or vice versa first B with Y and then A to X), the corresponding cases are not as key combinations be considered. These are just half of the cases with two plug connections. The previously determined product is therefore to be divided by 2. With three plug connections, there are six possible orders for the implementation of the matings, all six cryptographically equivalent. The product is therefore to be divided by 6th In the general case, when n plug connections, the product of the previously determined possibilities by n is! (Faculty) to divide. The number of options for exactly n plug connections is calculated as

\frac{1}{n!} \prod_{i=1}^n \frac{(26-2i+2)(26-2i+1)}{2} \;=\; \frac{26!}{2^n\cdot n!\cdot(26-2n)!}

{| Plug ————– opportunities for —————-

n exactly n plug-plug-to-plug-n

bond connections connections

0 1 1 1


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 10,767,019,638,375 12,177,691,846,451

9 45 53,835,098,191,875 66,012,790,038,326

10 28 150,738,274,937,250 216,751,064,975,576

11 15 205,552,193,096,250 422,303,258,071,826

12 6 102,776,096,548,125 525,079,354,619,951

13 1 7905853580625 532,985,208,200,576


After only six and later between five and eight connecting cables are plugged in the early years, from 1939 was the strict rule to always perform exactly ten plug connections. For this (more than 150 trillion) arising after the above table 150,738,274,937,250 plug options (equivalent to about 47 bits).

The total key space of an ENIGMA I with three selected from a pool of five rollers and can be of two reversing rollers as well as with the use of ten connectors from the product obtained in the above paragraphs a) to d) 120 rolling positions, 676 annular positions 16,900 rolling positions 150,738,274,937,250 and connector options calculated. He is:

120 · 676 · 16,900 · 150.738.274.937.250 = 206.651.321.783.

This is approximately 23 2:10 opportunities and key corresponds to a length of about 77 bits. (The occasional hearing “150 million million million” ways, for example in the film Enigma – The Secret, based on the use of only one reversing roller and the omission of the ring positions).

The key space was enormous for the time, a thorough search was hopeless with the former technology.

However, the size of the key space is only a necessary but not a sufficient condition for the security of a cryptographic procedure. Even such a simple method as the simple mono-alphabetic substitution has 26! (Factorial) possible keys. These are roughly 4:10 26 keys and is approximately 88 bits and is therefore even by a factor of 2000 greater than in the ENIGMA I. However, a mono-alphabetic substitution is easy to break.

Also in the ENIGMA resembles the much contributing to the size of the key space structural component, namely the connector board, a simple mono-alphabetic substitution, because the Steckerung finally remains unchanged during the whole encryption. The connector board can thus be overcome with the help of intelligent cryptanalytic attack method (Turing bomb) and virtually eliminated entirely. Thus, the factor 150,738,274,937,250 can be effectively removed again when calculating the key space.

Also, the rings cause only a small cryptographic strengthening of the process. With incorrect position of the right ring roller and otherwise correct key periodically (period length = 26 characters) are already clear text passages read, the tear off a few letters over and over again. Still less does the ring of the middle roll, in which case the period length of 650 characters (25.26) is. The middle ring position thus contributes mostly not at the size of the key space when, whenever that is, if no carry is on the left while the roller award, which rarely happened due to the prescribed maximum length of 250 characters spell. The position of the left ring roller is, as already mentioned, cryptographically completely meaningless. For the cryptanalyst, the fine adjustment of the rings no longer represent greater difficulty So that one can also safely again emphasize the factor of 676 when calculating the size of the key space.

As a cryptographically effectively leave only the 120 and the rolling layers (with unknown ring position) to be considered rolling 17,576 positions. Shrinks the previously still so gigantic appearing key space on comparatively tiny 120.17 .576 = 2.10912 million (over two million), options (about 21 bits), a figure that already at the time of World War II with the help of the then electromechanical equipment exhaustively ( complete) could be executed.

Cryptographic weaknesses

Grain achieved by the reverse roller, that the key process involution, that is, if at a certain position of the rollers in a U encrypts a X, then this position is also encrypted in an X U. So he simplified operation and construction of the machine, because you have no longer distinguish between encryption and decryption. In addition, he also hoped to increase the security, because the current flows through the rollers so now twice. “This decrease of current through the Chiffrierwalzensatz another scrambling takes place. Due to this arrangement, it is possible to get by with relatively little Chiffrierwalzen and still maintain a great Chiffriersicherheit. “Korn explains the benefits of its reverse roller in the patent (DRP No. 452 194). However, this was a fallacy with far-reaching consequences.

On the one causing the reverse roller that now no letter can be encrypted in itself, because the current can just take back the way through the roll back rate, he came so in any case. He is always returned in a different way than he is executed flowed to the reverse roller. Mathematically, this is called fixed point free permutations. This restriction may seem insignificant little thing, because there remain still 25 more letters of the alphabet for encryption, but in reality this means a drastic reduction in the available-for-encryption alphabets and in addition a new vulnerability of the ciphertext. Secondly, the reverse roller caused when the permutation is involutory and thus the encryption, to further reduce the number Alpha Beta.

The inserted by the reverse roller cryptographic weaknesses, in particular the reduction in the number of available alphabets, can be easily realized if instead of 26 letters simplified example of only four letters starts. With four letters can be 4! = 24 different alphabets (so says the cryptographer different arrangements of the letters) produce, namely






If you limit yourself here, instead of all 24 possible, only the fixed-point-free permutations, so drop off all alphabets in which a letter is encoded in itself, so is at its natural alphabetical place. From the above list are thus the following fifteen Alphabets be deleted because they have one or more fixed points (below, are underlined).






It leaves only the following nine fixed point free permutations:

{| ————————





Taking into account now that the reverse roller not only all permutations with fixed points eliminated, but all nichtinvolutorischen permutations, so must the table above six more cases are deleted, namely those in which the two-fold application of the permutation does not return to original letters leads. What remains of all 24 possible permutations of an alphabet of only four letters and three fixed-point free involution cases. They are called “real involutory permutations”.

{| ————————

—- BADC —————-

—————- CDAB —-

——————– DCBA


In the ENIGMA with its 26 letters causes this limitation that instead of 26! (Factorial), or about 4.10 26 total possible permuted alphabets only the · · · = 25! (Double factorial), or about 12 real involution 8:10 permuted alphabets can be used. By reversing roller is presented as a factor of approximately 13 at 5:10 possibilities – a gigantic weakening the combinatorial complexity of the machine. Remains less than the square root of the original permutations.

Cryptographically even more catastrophic than this drastic reduction in the number of alpha beta, however, is that by avoiding fixed points are possible statements about the text, such as “Nothing is ever it themselves,” which were an essential aid in decoding. The attacker knows that a letter is not the encryption itself, then it opens this knowledge abbreviations, and he does not have to laboriously work through each case, as illustrated by the following example.

A well-known and proven for centuries Entzifferungsverfahren is the “method of probability word” (see also: pattern search). Here guesses, the attacker knows or suspects that a particular phrase in the text (English crib, French mot probable) occurs, for example, “OBERKOMMANDODERWEHRMACHT”. If the attacker as an encrypted using the Enigma cipher text fragment such as the following before, so he can determine where in the text the suspected Probable word can not be located by checking for any location, easily whether a sign is would itself encrypted, which, as he knows of the ENIGMA, is impossible. He writes to the probable word in the various layers of the ciphertext and checks for collisions (English: crash) that are highlighted in red in the example below:
















15 UPPER commander dor EHRMAC W H D





20 UPPER commander DERWE H D O RM A C HT










The number of layers can be excluded by collisions incidentally estimate by the following consideration: For a probable word of length 1 (ie only a single likely letter) is the probability of a collision 1/26. Consequently, the probability of no collision 1-1/26. In a probable word as above of length 24 then the probability of no collision (1-1/26) 24, which is about 39%. That is, in 27 surveyed locations are expected on average for 27 * (1-1/26), 24 cases of no collisions. The expression yields a value of about 10.5 and agrees quite well with the observed in the example (and marked in green) eight-layer collision-free Crib match.

Using this extremely simple cryptanalytic attack method can thus of the 27 possible positions of the probable word here 19, so about 70%, eliminate the impossible – a significant simplification of work for the attacker.


The operators of the Enigma cipher machine were of the opinion that the they machine by encrypted text (as opposed to almost everything that was in use until 1918) with manual methods are not crack. What has been overlooked is that a machine can be countered by encryption deciphering machine.

The history of the deciphering of the Enigma begins in 1932, when the spying for France under the codename n U (ASH) German Hans-Thilo Schmidt secret key boards for the months of September and October 1932 as well as the instructions (H.Dv. g . 13) and the key instructions (H.Dv.g.14) to the French cryptographer and later General Gustave Bertrand betrayed. At this time, only three rolls were (I to III) in use and the roll position has not yet been a day (this only happened in October 1936), but only changed quarterly. The French secret service referred the dossier to British and Polish authorities further.

Having succeeded neither French nor British, to use this information, and they considered the ENIGMA still considered unbreakable, succeeded the 27-year-old Polish mathematician Marian Rejewski in his work in the Polish Dechiffrierstelle, the Biuro Szyfrów (German: “encryption Office “), already in 1932 the first breach in the ENIGMA. He used a legally purchased commercial machine (Model D), in which – unlike the still unknown to him military Enigma I – the keyboard with the entry roll in the usual QWERTY order (letter sequence in a German keyboard, starting at the top left ) was connected. Rejewski guessed the chosen by the Germans for the military version wiring sequence, which itself in 1939 brought the British code breakers Dillwyn “Dilly” Knox almost to despair. Subsequently managed Marian Rejewski using his excellent knowledge of the permutation stheorie (see also: ENIGMA equation), the wiring of the three rolls (I to III) and the reverse roller (A) (see also: ENIGMA-rolling) to develop – a cryptanalytic feat that “rises into the pantheon of the greatest cryptanalysts of all time” him with the words of the American historian David Kahn (in the original: “elevates him to the pantheon of the greatest cryptanalysts of all time”). The British code breakers Irving J. Good performance Rejewskis designated 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 develop each roll position and roll the right position. This took Rejewski together with its 1932 have been added colleagues Jerzy Rozycki and Henryk Zygalski a serious procedural error, who ran the Germans: In order to ensure secure transmission was still made ​​at the time the message key twice and encrypts written at the beginning of a message (“message key duplication”). Thus, the first and fourth, second and fifth, and the third and sixth ciphertext letter was assigned to each of the same plaintext letter. Using two specially constructed for this purpose machinery, called cyclometer and Bomba, who represented two or six series-connected and three respectively an offset to five rotational positions ENIGMA machines that Polish code breakers were able to establish for each of the six possible rolling layers in which rolling positions the observed association of letter pairs was possible and so narrow the search space huge. After analyzing several radio messages, the correct message key was found.

After the Germans on 15 September 1938 changed their process engineering and three months later with the introduction of rolling IV and V, the number of possible rolling layers of six (= 3.2.1) to sixty (= 5.4.3) increased, could no longer keep up with the Poles, and the ENIGMA was safe again. In view of the imminent danger they surrendered shortly before the German invasion of their country all their knowledge to their allies. From 24 July 1939 there was a three-day, legendary meeting of French, British and Polish code breakers in the forest of Pyry about 30 km southeast of Warsaw, in which they presented their Enigma replicas of the astonished British and the French and their methodologies disclosed. The first question that Dilly Knox is said to have made ​​at this meeting was: “What’s the QWERTZU?” (Paraphrased: “What is the wiring order the entry roll”). This had tormented him for a long time. Amazingly, the Germans had very simple wiring sequence chosen as the natural alphabetical order. Rejewskis response was therefore ingeniously simple: “ABCDEFG …”

With this start, especially with the now finally known rolling wiring, the British cryptanalysts could with the outbreak of war in about 70 km north-west of London located Bletchley Park (BP) to start a new attack on the Enigma. The main tool here – in addition to their intellectual capacity and the high number of personnel of later ten to fourteen thousand men and women – especially a special electro-mechanical machine called the Turing bomb, which built on the Polish Bomba was devised by the British mathematician Alan Turing. Turing’s idea to key search was to completely strip by annular concatenation of several (usually twelve) ENIGMA-roll sets the action of the connector board. As a result, he was able to drastically reduce the virtually unmanageable number of (more than 200 sextillion n) encryption options to which the German cryptographers placed their hopes.

The basic principle is based on the ENIGMA I in the three rollers are used in a range of five reels and initially available only the turn roll B. The reverse roller C, called by the British onomatopoeic “Uncle Walter” appeared only later and only sporadically. For each of the 60 different roll positions, there are 26 ³, ie 17,576 rolling positions. If you can look at the key search of the ring settings and the plugboard, which was made ​​possible by using the realized by the bomb cryptanalytic attack method, then stay “only” 60.17 .576, so 1.05456 million options left. This about a million different cases are virtually try out by hand in a reasonable time. Could execute with the help of the Turing Bomb However, the engine operated at 120 revolutions per minute during each revolution of 26 cases, one needed only 1.05456 million / (26,120) minutes, or about six hours to test out all the possibilities. (Add to that the time for setting and resetting the machine to the sixty different roll positions.) Makes you look at the effort to employ sixty bombs, one for each roller position, then shrink the time from six hours to six minutes – a quite tolerable time. In fact, until the end of the war, more than 210 bombs in England alone in operation.

Critical to the function of the bomb is probable words (cribs), whose occurrence can be expected in the text. Absence, then fails to decipher. For example, the British failed to break into two key sections of the Deutsche Reichsbahn, which were designated at Bletchley Park to the early steam locomotive The Rocket as “Rocket II” and “Rocket III”. The reason was, as they stated after the war, to their surprise, not a particularly safe ENIGMA variant but the unusual “railway Language” and the type of transport messages that do not allow them guessing probable words. Military reports, however, were often stereotyped drafted and contained many easy-to-guess Cribs as OBERKOMMANDODERWEHRMACHT who could use the British code breakers to decipher.

In addition, they benefited from the German thoroughness in the preparation of routine messages, such as weather reports, which were sent punctually every morning at the same time and from the same place. Although the German regulation “Public key rules for the Wehrmacht” (H.Dv.g.7) expressly forbade “regularities in the structure, identical phrases and repetitions in the text” and cautioned against “It must be avoided at all costs that be made ​​by trained personnel volatile key mistakes that [...] the enemy Nachrichtenaufklärung enable the deciphering “, yet happened exactly these errors could perceive and exploit the code breaker. From a British point of view was a freshly encrypted Enigma message, which always began with the words “WEATHER FORECAST AREA SEVEN”, similar to how valuable it would have been a direct public announcement of the relevant key days. For example, was the ENIGMA key from the “D-Day”, which is the day of the Allied landings in Normandy (Operation Overlord), suspected by the Crib “WEATHER FORECAST BISKAYA” that the British cryptanalysts could easily guess and correctly, in less broken than two hours after midnight.

Not infrequently, the British provoked even aware of incidents, only to have promptly anticipated German messages with known content (and encrypted with the day’s key) to maintain and called this technique “gardening” (German: “gardening”). The British code breakers Rolf Noskwith of Hut 8 described it as follows: “The RAF gave to specific sites in the North Sea mines, so that the mine warning the Germans served as a crib.The sites were carefully selected to certain numbers, such as 0 and 5 in particular, to avoid [as coordinates] for which the Germans were using different letters. ” The British could be so, while avoiding the case distinctions for “NULL” and “NUL” and “FIVE” and “FIVE”, the work a little easier. Except in the case of “TWO” and “ZWO” there was only one spelling for the remaining digits.

Thus it was possible under the code name “Ultra”, starting with January 1940, the first to break steadily from the Air Force and later the army of encrypted messages with the Enigma I almost during the entire 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.

Diehard showed the encryption method of the German Navy, which used a variant (ENIGMA M3) with three of eight rolls (I to VIII) as well as a sophisticated message key agreement. Here, the British succeeded the collapse in May 1941, after hijacking the German submarine U 110 and predation of an intact M3 machine and all secret documents (code books, including the critically important “double letters exchange plate n”) by the British destroyer HMS Bulldog on 9 May 1941. A painful for the British interruption (“black-out”), it was then when, on 1 February 1942 the M3 was replaced (with three rolls) exclusive to the U-boats by the M4 (four rolls). This from the German “Network key Triton” and the English “Shark” (German: “Hai”) mentioned method could not be broken for ten months, a time when the German U-boat arm was remarkable successes again. The slump in Shark succeeded only on 12 December 1942, after the British destroyer HMS Petard 30 October 1942, the German submarine U 559 mustered in the Mediterranean. A boarding party boarded the boat and captured important secret key documents such as weather short signal book and short key that enables the managed code breakers at Bletchley Park, to overcome the ENIGMA M4.

Now the Americans came to the aid of which under the leadership of Joseph Desch more than 120 units in the National Cash Register Company (NCR) in Dayton, Ohio, from April 1943 produced high-speed variants of the Turing bomb that specifically were directed against the M4. After the German U-boats were never more safely (see also: U-Boat War).

Direct result of the American decipherments was – starting with U 118 on 12 June 1943 – the sinking of nine of the twelve German U-tanker (“cows”) within a few weeks in the summer of 1943. This led to a weakening of all Atlantic submarines that could no longer be supplied at sea, but to the long and dangerous journey home through the Bay of Biscay had to stand for the U-boat bases on the French west coast.

Historical consequences

The compromise of ENIGMA is seen as a strategic advantage, which has greatly facilitated the Allies winning the war. There are even historians who keep this fact of vital importance, because the deciphering were not only military-tactical level (Army, Air Force and Navy) is a big help, but they allowed due to the almost complete penetration of the German message traffic at all levels (police, intelligence, diplomatic services, SD, SS, Reich post and railroad) and a detailed insight into the strategic and financial plans of the German government. Especially appreciated the Allies the authenticity of the information obtained from Enigma radio messages, which was not always the case from other sources, such as reconnaissance, espionage or treason. Thus, the British were able to start their war still limited resource optimally coordinate n and use targeted against the German weaknesses, and later, along with their American allies play the superiority even better.

One of the leading former code breakers from Bletchley Park, the British chess champion Stuart Milner-Barry, wrote: “With the possible exception of antiquity I know a war was never performed, in which one side has ever read the important secret messages of the army and navy of the enemy “. A similar conclusion is drawn by an authored post-war American investigative report: “Ultra created in the military leadership and the top political awareness that changed the way of decision making.The feeling of knowing the enemy is most reassuring. There is a growing imperceptibly over time, when you can watch his thoughts and habits and practices regularly and most carefully. Knowledge of this type frees own schedule too great caution and fear that they will be safer, bold and energetic. ”

David Kahn noted, “In Europe, the Allies had the ability to crack the German encryption systems and all messages read along (Codename Ultra), the Allies rush from victory to victory.In the “Battle of the Atlantic,” the fundamental conflict of the entire Second World War, the Allies were able to steer past their convoys to the German U-boats, because they knew where these as pack of wolves lurking. Thus crippling losses could be largely avoided and humans as goods could be brought safely to the UK. Later, because of her great invasion of Europe that led to victory over Hitler’s Reich, the decoding German messages helped the Allies counter-attacks to anticipate and ward. In this way they were able to recognize weaknesses better and German advance into the Ruhr and Berlin. Even Soviet code breakers were able to decipher the secret information of the Germans, which contributed to her victory on the Eastern Front. ”

The former National Security Advisor to U.S. President Jimmy Carter, the Polish-American political scientist Zbigniew Brzezinski quoted the commander of the allied forces General Dwight D. Eisenhower, the Ultra as “decisive” (German: “critical”) for the victory marked (see also FW Winterbotham “The Ultra Secret”). The Polish historian Władysław Jerzy Straszak Kozaczuk and wrote “it is Widely Believed did Ultra saved the world at least two years of war and possibly Hitler Prevented from winning”. (German: “it is widely believed that the world Ultra least two years of war has spared and possibly prevented Hitler won him “). Expressed similar to the English historian Sir Harry Hinsley, who worked at Bletchley Park, with the words “shortened the war by not less than two years and probably by four years” (German: ” shortened the war by not less than two years and probably by four years “).

Stuart Milner-Barry took the view that “had we not at the most crucial times and for long periods read the U-boat ciphers, we shouldhave lost the war” (German: “we would not have the decisive time and for long periods can read U-boat ciphers, we would have lost the war “). In an exhibition about the Secret War (German: “Secret War”), in one of the most important war museums in the world, the Imperial War Museum in 2003 (German: “War Museum British Empire”) held in London, the former British Prime Minister was Winston Churchill quotes, who said his King George VI: “It was thanks to Ultra did we won the war.” (German: “It was thanks to Ultra that we won the war”).

If you still want to speculate further, one can derive from the statements of Gordon Welchman, who was next to Alan Turing one of the leaders of the British code breakers at Bletchley Park, draw conclusions. In his book, The Hut Six Story, he describes the balancing act that had to accomplish the Allied code breakers, not to lose the connection to the newly introduced time and again by the Germans cryptographic complications. Multiple stood the Entzifferungsfähigkeit on a knife edge, and again, the balance fell in favor of the code breaker, often with good luck, as Welchman admits in his book: “We were lucky” (German: “We were lucky”).

David Kahn wrote this: “The success of the code breakers had not rested ultimately in 1931 in Poland and Alan Turing and Gordon Welchman 1939 in England these ideas on some great ideas [...] Had Marian Rejewski, the” Enigma “would not have been cracked.Thus, the idea that it could fail the Allies to crack this cipher, no speculation in a vacuum, but it actually talked a lot for this assumption. ”

The consideration of alternative courses of history is necessarily highly speculative. Crucial is also the time at which the ENIGMA would have possibly made burglar proof. If this had happened only in 1945, it probably would have had little impact on the course of the war. In 1944, however, the Allied invasion plans of Operation Overlord (“D-Day”) would have been impeded. As we now know, was made ​​deciphered Enigma radio messages not only the entire German order of battle in Normandy known in detail, but the allied commanders were held thanks to Ultra every day extremely precise about the German plans and countermeasures to date. In the years from 1941, the German U-boats would not have been so easy to find their positions and plans of the Allies were able to track accurately deciphered radio messages.

But what would have happened if the ENIGMA would have remained unbreakable from the beginning? In 1940, for example, the Royal Air Force began a their last reserves, to finally win the Battle of Britain (“Battle of Britain”). Here, too, were deciphered radio communications, especially about the attack plans of the German Air Force, a great help. Without this help, the air battle had been lost and possibly Operation Sea Lion, ie the German invasion of England would have taken place. As it would turn out, it can only speculate: It is conceivable that after a German occupation of the British Isles, the war would have ended in the year 1940, because at that time neither the Soviet Union nor the United States was at war . (The German attack on the Soviet Union began on 22 June 1941. The Japanese attack on Pearl Harbor took place on 7 December 1941 and the declaration of war by Germany to the U.S. took place on 11 December 1941). How the story would have actually evolved in such a case, no one can say, for history tells us its not alternatives. In an essay that David Kahn wrote a counterfactual history, assuming the Allies had failed to crack the Enigma, it leads to a further triumph of the Wehrmacht, which is eventually abruptly ended by a nuclear bomb. These are all speculation – but clearly the enormous importance of cryptography and cryptanalysis of the Enigma cipher machine for the course of history.

Noteworthy is also the fact of the perfect functioning of the obtained secrecy at Bletchley Park deciphered Enigma radio messages about Ultra information. Churchill himself acknowledged his secretive code-breaker with the words “My geese did laid the golden eggs and never cackled.” (German: “My goose that laid the golden eggs and never cackled”) This “Enigma Secret” was throughout the war and even after that until the 1970s tended (“Britain’s best kept secret”, German: “Britain’s best kept secret”). The Germans had no idea of Ultra. At Bletchley Park, there was no mole – with one exception, John Cairncross, but the spied for Stalin.

Due to various suspicious events were indeed repeatedly employed on the German side tests whether the ENIGMA is really sure, but here the wrong conclusions were drawn, and the people with the correct assessment of not prevailed. Mentioned authored a report shortly after the war the American Army Security Agency, the German commander of submarines (U-boats) Admiral Karl Doenitz the true reason for grasping before July 1942 near victory and only a few months later lost in battle Atlantic has never understood: “It was never realized did cryptanalysis, rather than radar and direction finding, disc losed the positions and intentions of the German submarines.” (German: “It has been detected at any time that the cryptanalysis and not the radar or radio location revealed the positions and intentions of the German U-boats. “)

It would not have been quite difficult for the Germans to consider whether the ENIGMA was compromised. To propose to the British historian Hugh Sebag-Montefiore ago as a test to send one with the Enigma as usual encrypted message is in the agreement as a ploy for example, a meeting of German U-Boat Tankers at a remote location on the lake, which is normally not Allied ships will be investigated. If suddenly Allied warships should appear at the meeting point at the time specified in the radiogram, the Germans would have to be clear pretty quickly that their machine was actually compromised.

After the war, captured by the victorious powers in large numbers and also reconstructed Enigma machines, widely used still had the reputation of high security, especially in England and the United States were sold in the Middle East and to Africa, partly until 1975 uses. This enabled the Western powers you to read the communications of the local states. The few still existing intact specimens are traded at collector’s prices five-figure euro range.


Already formulated in 1883, the Dutch cryptographer Auguste Kerckhoffs in the later (1946) by Shannon explicitly stated assumption “the enemy knows the system being used” (German: “The enemy knows the system used”) its binding for serious cryptography maxim.

Kerckhoffs’ Principle: The security of a cryptosystems should not depend on the secrecy of the algorithm. The security is based only on the secrecy of the key.

Due to the small number of rolls the cryptographic security of the ENIGMA hung – contrary to Kerckhoffs’ maxim – much of the secrecy of their wiring from rolling. This was unchangeable for the user, and thus not a part of the algorithm and the key. It is noteworthy that the rolling wiring has never been changed since its beginnings in the 1920s until 1945. Under normal conditions of use as a widespread key as the ENIGMA machine must not assume that their algorithmic components can be kept secret in the long run, even if the Germans tried.

A first possibility would be to improve the ENIGMA thus the example of the rolling annual total replacement range (each with radically altered wiring) been like it did the Swiss with their Model K. Still much more effective would be rolling their internal wiring could be made key dependent variable. Interestingly, there was this one approach, namely the reverse roller D (British nicknamed “Uncle Dick”), which exactly have the same property, but only late (Jan. 1944) and only rarely was used. This “reverse roller Dora”, as it was called by the German side using the Buchstabieralphabets use at the time, allowed a free choice of wiring between pins and thus a variable connection between pairs of letters (see also: reverse roller D).

Essential cryptographic buffs ENIGMA would have been relatively easy at the design stage. First and foremost, you would have to avoid the restriction to fixed point free permutations. Also the Involutorik (encrypt decrypt =), although convenient for the operation, the machine slowed tremendously. Both would have been avoided had they waived the reverse roller.

Already an early forerunner of the ENIGMA I had eight fixedly arranged next to each other (not replaceable) rollers and an adjustable roller position solely by the key space of more than 200 billion. In contrast, only 17,576 rolling positions of the ENIGMA I seem a little ridiculous. In addition, this early ENIGMA model had no reverse roll, so did not have their weaknesses. Had this basic design with eight (instead of three) rolls on the ENIGMA I transferred there as designed and in addition the position of the rollers replaced, this would have eight rolls at 8! = 40.320 (instead of 60) roller positions and in combination with the roller positions a cryptographically effective key space of 8.419.907.243.704.320 (more than eight trillion or almost 53 bit) result. In comparison to just over two million (approximately 21 bit) cryptographically effective ways of actually realized ENIGMA would be a much stronger machine emerged that despite the many errors on the German side and the gigantic burden on the British side not probably could have been broken. However, such a machine with eight rolls would have been less handy than the ENIGMA with only three reels. On the other hand, may not receive higher priority than handling cryptographic security, if one has the goal to secretly communicate with each other, otherwise you might just as well with a roller (roller or even none at all) content. Decisive is always the safety of encryption to prevent unauthorized decoding, and also, when possible, in compliance inevitable in practice, operator errors.

Scherbius had in his basic patent of 23 February 1918 even ten rolls and the (already without replacement) resulting from approximately 100 trillion key is specified, also suggested no turning roll, but a switch for setting the encryption and decryption, as well as on Transmission adjustable irregular onward movement of the rollers – all good ideas and cryptographically strong design features, but over time fell into oblivion. The founding president of the Federal Office for Information Security (BSI), the PhD mathematician and cryptologist Otto Leiberich says, with four rollers “and with a nonuniform drive the Enigma had never been deciphered.”

An example of the power of these ideas is the key machine Sigaba. This is an American rotor machine similar to Enigma and also from the Second World War, but does not reverse roller but five Chiffrierwalzen (cipher rotor Bank, German: “Chiffrierwalzensatz”) has, plus two five more rolls (control rotor database and index rotor bank German: “tax roll set” and “index roll set”) which are intended solely to produce an irregular stepping of Chiffrierwalzen. The Sigaba generates both fixed points and nichtinvolutorische permutations and could at any time, neither German nor Japanese cryptanalysts, even by the Americans themselves who tried this trial, be broken.

A very easy way to make the ENIGMA safer, the use of more than one carry-notch. These notches are part of each roll and cause the transfer to the next, further to the left in the roller set roller and thus ensure the stepping of the rotors. The code breakers it came in handy that they could go out 26 letters long assumed that only rotated the right roller and then passed a stepping on the middle rotor. For relatively long passages thus the ENIGMA is the view of the cryptanalyst only a single rotating (right) and a roller, from middle and left roller and reverse roller existing, so to speak, especially thick (fixed) return roller. Only the transfer to the middle roll disturbs this. This important event was when the code breakers at Bletchley Park even a nickname: They called it “crab” (English for crab), and the even rarer advancing the left roll was called “lobster” (English for lobster). Had the rolls of the ENIGMA has more than a single carry-notch, for example, nine, as in the British cipher machine TypeX, as would be practically changed for the user nothing, cryptanalysis, however, had been greatly disturbed by frequent Crabs and Lobsters.

Peter Twinn, one of the employees Turing at Bletchley Park, it annotated with the words “they Certainly missed a trick in not combining multiple-turnover wheels with plug connections” (German: “they [the Germans] missed certainly a gimmick in that they do not rolling with several nicks and carry the plug connections combined “).  Gordon Welchman underlined the consequences of this German error: “We would have been in grave trouble if each wheel had had two or three turnover positions instead of one” (German: “We have to get serious problems if each roll had had two or three carry notches instead of [only] one “). The TypeX proved not least through their ENIGMA compared to larger number of transfer scores for “chi”, the Chiffrierabteilung the OKW as unbreakable.

Perhaps the designers of the ENIGMA feared a reduction of the period, which is the number of characters after which repeats the alphabet used for encryption. The period is when I ENIGMA 26.25.26 = 16,900, where the factor 25 is caused in the middle roll through the already mentioned (unimportant) anomaly of the indexing mechanism. When using an even number of thirteen or transfer notches instead of just one, the period would actually fall dramatically since these figures have common divisor by 26. When, for example, three, five, seven, nine or eleven notches, however, this danger does not exist, because these numbers are relatively prime to 26. Interestingly, in the Navy, used in addition to the known from the ENIGMA I five reels, three more rollers (VI, VII and VIII), more than one, ie have two carry notches. The three rollers used exclusively by the Navy also avoided another mistake of the five rolls of ENIGMA I, because they had their transfer scores in all identical letters. Not as the Rollers I to V, which were much easier to identify thanks to their arranged at different points scores by observing a “crab”. The code breakers had for the (linguistically nonsensical) mnemonic “R oyal F lags W Ave K ings A bove” formed of to V in this order called the letter from the rollers I, who always appears in the window after a transfer to the next roller is carried out.

The German Defense (Intelligence) used the way a model ENIGMA (G) had an exclusive set of rollers, in which the (three) rolls actually carry several notches had, namely 11, 15 and 17 scores. Even the reverse roller was – in contrast to the other models ENIGMA – mounted and rotated with. This strengthened the encryption and also made sure that other German authorities could not read along. However, the defense waived in this very compact (outer dimensions 270 mm × 250 mm × 165 mm) and excellent craftsmanship built ENIGMA on a plug board. The result was that the code breakers of Bletchley Park, at the top “Dilly” Knox and his collaborator Mavis Lever, on 8 December 1941 managed to overcome these encryption, thus helping that German agents were “taken delivery” already in their entry. These were then not simply eliminated, but that the British domestic intelligence service MI5, many of them “turn” in the system and Double Cross. (German: “Double Cross”) as a double agent to use. Together with the deciphered from ENIGMA-G sayings information received MI5 such a detailed and accurate picture of the plans and the knowledge of defense that each individual still operating in the UK German agent was accurately known and could be specifically controlled and manipulated. This was also used disinformation to the German leadership.

In summary, the following points for cryptographic strengthen the ENIGMA can be made:

•Allow identical encryption

•Avoid Involutorik

•a plurality (for B. Attach nine) Transfer scores

•Arrange carry identical scores for all rolls

•more than three rolls (eg B. Install eight)

•Expand rolling range (eg As ten instead of five)

•Occasionally rolling wiring change radically

•do not use plug involution

An amazingly simple yet resounding effective measure which, according to Gordon Welchman at any time very easily could have been introduced and which he had feared during the war the most, is the use of single-pin plug connections instead of the double pole involution cable. Then you could, for example, X plugs with U and U now but not necessarily with X, but with any other wildcard. So would the suddenly Involutorik the connector board – if not the whole machine – can be eliminated. This would have catastrophic effects for the code breakers at Bletchley Park to Welchman. Much of the methodology developed here, including the self-invented by Welchman diagonal board (German: Diagonal board) would become 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 return of Ultra information from six barracks would have reduced at best to a belated trickle, in contrast to our daily updated flood. “)

Community radio messages

See also (links below): Breaking German Wehrmacht Ciphers by Frode Weierud

- 83 – ADJ JNA -



- 149 – TLS CMU -





- 167 – MRJ LLT -





- 186 – DOQ VHZ -





- 195 – EHW TNH -





- 232 – ZFT CPL -





- 241 – SDV RUD -






- 272 – PPS RXWSXWV -





Below are some important dates are listed on the history of ENIGMA

(Specific dates to see naval version M4):

23, Feb. 1918  First patent for ENIGMA

9 Jul. 1923  Establishment of the cipher AG

21, March 1926  Patenting of the reverse roller (FM)

15th Jul. 1928  The Reichswehr performs a preliminary version of the ENIGMA, a

1 Jun. 1930  Commissioned by ENIGMA I (six male and quarterly roll changing position)

1 Jan. 1936  Monthly change of the roller position

1 October 1936  Daily change of roller position and now five instead of six to eight plug

2 Nov. 1937  A replacement of FM by FM B

15th September 1938  New indicator method (arbitrary base position for the message key encryption)

15th December 1938  Commissioning IV and V of the rollers

1 Jan. 1939  Ten connector

24th Jul. 1939  Three-day meeting at Allied Pyry

15th May 1940  Dropping the message key duplication

1940/41,  At times, use of the FM C (alternative to FM B)

8 December 1941  First break the defense Enigma by Dilly Knox

1 Feb. 1942  Commissioning of the M4

1 September 1943  Dropping the characteristic group

1 Jan. 1944  Sunny use of plug-FM D

10th Jul. 1944  The Air Force leads the “clock” a

of the models)

A rough overview of the bewildering variety of models of ENIGMA shows the following (incomplete) table that is sorted alphanumerically. In addition to the model name, the year of entry, the number of rolls and the resulting number of possible rolling layers is given. Furthermore, the number and nature of the reverse roller (FM) is listed, with built-in FM between fixed and adjustable manually, thus “settable” must be distinguished FM and FM rotating, ie FM, the further rotation during the encryption process. An example of this is the ENIGMA (above) described the G defense. Some early machines such as the ENIGMA A, had no FM. Furthermore, the number of transfer slots is given as well as a reference and as a reference for further information (see also: Kruh pp. 14, 50f Pröse p and integrating p 1 et seq.)..

Model, Year, Rollers, Documents, FM, Scores, Reformed

ENIGMA I 1930 3 of 3 (5) 6 (60) 1 (3); 1 Kruh 3

ENIGMA II 1932 3 of 3 6 1 fixed 1 Pröse 50

ENIGMA A 1923 4 1 no Gearbox Kruh 2

ENIGMA B 1924 2 times 4 1 no Gearbox Pröse 50

ENIGMA C 1926 3 1 1 fixed 1 Kruh 5ff

ENIGMA D 1927 3 1 1 settable 1 Bauer 114

ENIGMA G 1936 3 of 3 6 rotates 11, 15, 17 Hamer

ENIGMA H 1929 8 1 1 fixed  Crypto Museum

ENIGMA K 1938 3 of 3 6 1 fixed 1 Hamer 10ff

ENIGMA M1 1934 3 of 6  120 1 fixed {0}1.2{/0}{1}               {/1} Pröse 50

ENIGMA M2 1938 3 of 7 210 1 fixed {0}1.2{/0}{1}               {/1} Pröse 50

ENIGMA M3 1939 3 of 8 336 1 fixed {0}1.2{/0}{1}               {/1}

ENIGMA M4 1942 4 of 8 +2 1344 2 settable {0}1.2{/0}{1}               {/1}

ENIGMA M5 1945 4 out of 12 23,760 2 fixed selectable Pröse 44

ENIGMA M10 1945 4 out of 12 23,760 2 fixed selectable Pröse 44

ENIGMA T 1942 3 of 8 336 1 settable 5

ENIGMA Z 1931 3 of 3 6 1 settable 1 Quirantes

Besides the mostly used models ENIGMA I ENIGMA M3 and ENIGMA M4 and its forerunners ENIGMA A to ENIGMA D and the already mentioned ENIGMA G and ENIGMA K is still the ENIGMA T noteworthy that was designed specifically for the communications of the two war allies Germany and Japan. She was also known as “Tirpitz machine” and had no plugboard, but a “settable” (adjustable, but not rotating) reverse roller and eight rollers with five transfer notches (see also: Enigma rolls), three of which were selected. The ENIGMA T was rarely used.

The newly developed on the basis of M4 and the key unit 39 ENIGMA M5 was a true four-roll machine (having four rotating rollers plus FM) for a completely new set of rolls constructed of twelve rollers, which thus 2 * (12:11 · 10.9) = 23.760 rolling layers enabled. It included a major innovation called “filler rolls” (see photo links below), also known as “election rolls gap” means that allowed “to each roller switch on the type and number of gaps in any set”. These settings could be changed depending on key and thus contributed significantly to the strengthening of the cryptographic engine. The American Target Intelligence Committee (TICOM) confiscated at the end of the war all the information about the fill-roll and held it for many years carefully under wraps. If they would have in sufficient quantities can be produced and used, the British code breakers would probably have been out of the race, especially if it would be as planned, succeeded in using the filler roller in combination with the reverse roller D.

The ENIGMA M10 M5 contained in addition to a printer for clear and ciphertext. The introduction of machinery was planned for all armed forces from the summer of 1945.

A curiosity is the ENIGMA Z, which was offered to the Spanish Ministry of Foreign Affairs in 1931 to purchase. With her is a variant similar to the Enigma D, but no letter keys but only ten number keys (“1″ to “0″) and accordingly (smaller) rolling with only ten contacts and ten bulbs for “1″ to “0 “has. She was therefore not intended for encrypting texts but only of numbers, such as the About coding of diplomatic codes. Thus, for example, the digits “25183 91467″ and “38760 15924″ will be encrypted. The Spaniards then renounced the acquisition of ENIGMA Z and decided instead for the (still uncertain) Kryha.


The indexing mechanism of the rollers has a unique design feature, which has the consequence that not continue to spin the reels so the Enigma, as would be the case with a mechanical odometer. This feature manifests itself so that when the left (slow) roller rotates, it “entrains” the middle roll. This can be illustrated with an example.

For example, roller position BI, II, III, ring position 01 01 01 and the roller, the roller set position ADU continues to rotate with the first press of ADV. This is a normal roller continues to rotate only the right, without excluding Lobster and Crab. After the well-known shopping rule “R oyal F W ave lags K ings A bove” is for roller III to expect with the next keystroke, so if they weiterrotiert from V to W with a transfer to the middle roll. Then not only the right roller is further rotation normal switch but also the middle roll from D to E. The next roll position is thus AEW.

(: Roll II here) reaches the letter, namely E, which is according to the leaflet usually immediately before Umschaltbuchstaben F Now, however, the middle roll has. So now the moment has come to the turn causes the middle roll a carry to the left roller. With the next keystroke, therefore, the left roller will rotate from A to B. Due to the aforementioned structural feature, however this further rotation means that she takes the middle roll and continues to rotate them again, so from E to F. Thus, be forwarded to the next key press all three rolls simultaneously and after the previous rolling position AEW are now directly BFX to see the letters in the display windows of ENIGMA. After this somewhat strange appearing event the machine will return to the regular indexing mode, then again to the middle roller reaches the letter E to 650 keystrokes.

Summarizing the indexing of the roll set. One recognizes here the anomaly at the third button, which manifests itself as a “double step” of the middle roll (here: D → E → F).

Initial position ADU

1 Press ADV

2 Keystroke AEW

3 Keystroke BFX ← anomaly

4 Keystroke BFY

In total, this is caused by the anomaly of the indexing mechanism of the double-step effect of the middle roll causes = 17,576 are omitted rolling positions of ENIGMA ² = I 26 676 of the theoretically possible and only 26.25.26 26 ³ = 16.900 remain.


•Cipher – the other term for ciphertext

•Cipher – the other term for encrypting

•Cilli – (not authentic as the “sillies” (German: “silly”) refers) English nickname for the incorrect choice of the initial position and the saying key from adjacent letters on the keyboard (example: QWE RTZ, see also: radiogram and faulty head saying)

•Crab – (German: Crab) English nickname for a rotation step of the middle roll

•Crib – (German: Donkey Bridge, it aptly: Likely word) Term for a text fragment, whose occurrence is expected in plain text

•CSKO – Abbreviation of “Consecutive male knock-out” (German: “crackdown consecutive connectors”). British method and apparatus exploiting the frequently practiced (bad) character of the German key boards, not to plugs together adjacent letters in the alphabet.

•Dechiffrat – Other expression for plain text

•Double plug cords – (short: Plug) connection cable between the front panel jacks

•Entry roller – Fixed roll at the beginning of the roll set

•Decrypt – convert the ciphertext into plaintext using the key

•Decipher – breaking the ciphertext without knowing the key

•Füllbuchstaben – To camouflage chance to be selected letters, especially the first two letters of the characteristic group

•Ciphertext – generated by encryption of the plaintext text

•Knitted Eckert – Two letters are exchanged using a cable plugged into the front panel

•Initial position – rolling position on the classification of the spell key

•Jabjab – By Dennis Babbage embossed English nickname for the incorrect choice of the initial position as a message key

•Characteristic group – (also: Letters characteristic group) Five letters (Füllbuchstaben two and three letter code group) at the beginning of an award for the identification of the key

•Characteristic group letter – The last three letters of the characteristic group

•Characteristic group panel – The panel key complementary list with daily changing characteristic group letter

•Lobster – (German: Lobster) English nickname for a rotation step of the left roller

•Filling roll – Innovative roller with freely adjustable carry notches

•Period – the number of letters, after which the alphabet used to encrypt repeatedly (16,900 in the ENIGMA I)

•QWERTZU – From Dilly Knox term coined for the wiring sequence of each letter keys on the keyboard with the club contacts the entry roll

•Ring position – rotating position of the rings determines the offset between the internal wiring of the rollers and the letter to which the transfer takes place on the next roll

•Key – the secret key setting machine

•Key Machine – Summary term for encryption and decryption machine

•Keys – Summary term for encrypting and decrypting

•Key space – set of all possible keys

•Key panel – list of daily key

•Ciphertext – Another word for ciphertext

•Verdict – ciphertext, which is usually transmitted by radio

•Message key – Individual key for a radio message

•Message key duplication – In May 1940 abgeschafftes (incorrect) method of two-time transmission of the key saying that the Polish cryptanalysts in the 1930s allowed the intrusion

•Plug – cable connections between the front panel jacks

•Connector board – mounted on the front of the jack plate ENIGMA

•Days keys – Daily changing key

•Clock – Additional device for generating nichtinvolutorischer plug connections

•Reverse roll – (Mostly) fixed roll at the end of the roll set (abbreviated FM)

•Reverse roller D – Innovative reverse roller with selectable wiring (also called: FM Dora)

•Uncle Charlie – (German: Uncle Charlie) English nickname for the reverse roller C

•Uncle Dick – (German: Uncle Dick) English nickname for the reverse roller D

•Uncle Walter – (German: Uncle Walter) English onomatopoeic description of the German term “reverse roll” and nicknamed the reverse roller C

•Ungesteckert – letters that are not reversed because of an unplugged cable (English: self-steckered)

•Encrypt – converting plaintext into ciphertext

•Election roll gap – the other name for filler roller

•Roll – rotor, which rotates during the key process (English: wheel)

•Roller position – key-dependent positioning of the rollers in the roller set

•Roller set – Summary term for all rolls

•Roll position – adjustable by hand and changing during the process, key rotation position of the rollers

Cinematic Reception

The ENIGMA is seen in some movies that play in the context of the U-boat war. In German cinema classic “The Boat” based on the novel of the same name, ​​the ENIGMA machine is used to decrypt the received radio messages. Historically not entirely correct is to use an M4, as they at first only February was placed in service in 1942, while the boat novel and the film does its patrol in the fall and early winter of 1941. Thus, an M3 would have to be shown correctly. In the U.S. film “U-571″ is an ENIGMA captured by American sailors by a German U-boat. Especially the British side has been criticism that here, in disregard of historical reality, Americans are portrayed as heroes in the predation of ENIGMA, while there were in fact British, who managed this.

In the British film “Enigma – The Secret”, which on the novel Enigma is based, the decipherment of the British code breakers at Bletchley Park is discussed. Remarkable are the many authentic props in the film, where it is original showpieces from the Bletchley Park Museum. The various radio messages have been specially created and encrypted realistic for the film according to the original rules and procedures. Towards the end of the film, a Polish code breakers out to be a traitor who tried to betray the “Enigma secret” to the Germans. This does not correspond to the historical facts in two ways. First, there was – as already stated – no traitor at Bletchley Park, who had been spying for the Germans. Secondly, there is not a single Polish cryptanalyst has worked because of confidentiality reasons, denied the British almost all foreigners, even Marian Rejewski, the access and especially the employees. Thus, the cinematic representation is historically wrong on this point. Criticism was particularly calculated to represent Poland in the film as a traitor, because at the very least have betrayed Poland the Enigma secret. On the contrary, Polish cryptanalysts as Marian Rejewski, Jerzy Rozycki and Henryk Zygalski have created the crucial foundations for breaking into the mystery of the Enigma before the war, without which it would be the British code breakers probably not been able to decipher German radio messages and the Second World War would have taken a different course.


•Arthur O. Bauer: direction finding as Allied weapon against German submarines from 1939 to 1945. Self-publishing, Diemen The Netherlands, 1997, ISBN 3-00-002142-6

•Friedrich L. Bauer: Decrypted Secrets Methods and Maxims of cryptography. Springer, Berlin 2000 (3rd edition), ISBN 3-540-67931-6

•Gustave Bertrand: Enigma ou la plus grande enigma de la guerre 1939-1945. Librairie Plon, Paris, 1973.

•Ralph Erskine: The War of the code-breakers. Bavarian Academy of Sciences, Academy News, Munich, November 2002, pp. 5-11. PDF, 0.2 MB

•Francis Harry Hinsley, Alan Stripp: Code Breakers – The inside story of Bletchley Park, Oxford University Press, Reading, Berkshire, 1993, ISBN 0-19-280132-5.

•David Kahn: The Codebreakers – The Story of Secret Writing. Macmillan USA, reissue 1974, ISBN 0-02-560460-0

•Rudolf Kippenhahn: Encrypted messages, secret writing, Enigma and smart card. Rowohlt, Reinbek 1999, ISBN 3-499-60807-3

•Kozaczuk Władysław Jerzy Straszak, Enigma – How the Poles Broke the Nazi Code. Hippocrene Books, 2004, ISBN 0-7818-0941-X

•Władysław Kozaczuk: secret operation Wicher. Bernard and Graefe, Koblenz, 1989, Karl Muller, Erlangen, 1999, ISBN 3-7637-5868-2, ISBN 3-86070-803-1

•Władysław Kozaczuk: Wake of the Enigma. Military Verlag, Berlin, 1987, ISBN 3-327-00423-4

•Michael Pröse: cipher and Entzifferungsgeräte in World War II – art history and historical aspects of computer science. Dissertation, Technical University of Chemnitz, Leipzig, 2004. PDF, 7.9 MB

•Hugh Sebag-Montefiore: ENIGMA – The battle for the code. Cassell Military Paperbacks, London, 2004, ISBN 0-304-36662-5

•Simon Singh: The Code Book. Carl Hanser Verlag, Munich, 2000. ISBN 3-446-19873-3

•Michael Smith. Decrypted ENIGMA – The “Code Breakers” of Bletchley Park Heyne, 2000, ISBN 3-453-17285-X

•Geoff Sullivan, Frode Weierud: Breaking German Army Ciphers. Cryptologia, Vol XXIX (3), July 2005, pp. 193-232 PDF, 6.1 MB

•Heinz Ulbricht: The Enigma cipher machine – Deceptive security. A contribution to the history of intelligence services. Dissertation Brunswick in 2005. PDF, 4.7 MB

•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

•Frederick William Winterbotham: The Ultra Secret. Weidenfeld and Nicolson, London, 1974.


•Award No. 233 (PDF, 201 kB) Authentic saying Enigma form with the received radio message

•Air Force Machine Code No. 619 (PDF, 316 kB) Authentic key panel

•Turing’s Treatise on Enigma (The Prof’s Book) Treatise on the Enigma and the Bomb, English

•The Enigma Collection by Frode Weierud, English


•Places where authentic Enigma machines are exhibited , English


•Official Site of Bletchley Park , English

•Crypto Museum Lots of details about the various Enigma models, English

•Wicher secret operation of the Polish secret

•The pinch from U 559 , English

•Direction finding as Allied weapon against German U-boats 1939-1945  Website with excerpts from the book by Arthur O. Bauer

•The golden goose that never cackles of André Schulz

Simulations of the ENIGMA encryption

•Palloks, OS-independent and cross-browser, German

•Enigma paper (PDF, 84 kB) paper version of the Enigma encryption

Simulations of the ENIGMA machine

•Rijmenants visualized realistically, for Windows, English

•Hat Six More Enigma variations, for Windows, English

Decipherments•Breaking German Wehrmacht Ciphers by Frode Weierud, English

•Modern decipherment of the M4 , English

•Breaking German Ciphers Navy , English

•Enigma Cipher
Challenge Competition: Break the ten (fictitious) Enigma radio messages, english

Reconstruction projects

•Reconstruction project of HS Weingarten replica of an Enigma I

•Private project replica replica of an M4

•Private project replica replica of an M4, English

•Private project replica replica of a 3 reel Enigma

Enigma (machine)

Cryptologic device

Symmetric encryption method

Military technology (World War II)

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