Roberto Bloch

Description

Enigma is an electromechanical machine, which means that it uses a combination of mechanical and electric parts. The mechanical part is made up of a keyboard, a set of adjacent rotary discs called “rotors” arranged along an axis, and of a mechanism rotating one or more rotors each time a key is in a hurry. The exact mechanism varies, but the most common form is that where the rotor of the right-sided turns each time a key is pressed and where occasionally the close rotors are moved, in a way similar to operation of a Odomètre. The continuous motion of the rotors allows obtaining different cryptographic transformations each pressure on a key. The electric part of the apparatus is consisted a pile connecting the keys of the keyboard to lamps. When that one supports on one of the keys, one of the lamps ignites. For example, when a message begins with the sequence ANX… , the operator presses the key A and the lamp Z could ignite; in this case, Z is the first letter of the quantified text. The operator carries out then the figuring of the letter N in the same way, and so on for the following letters.

The current leaves the battery and crosses the Interrupteur to two positions controlled by the key in a hurry. It arrives then at the “desk of connections”. This desk, located on the front face of the machine, makes it possible the user easily to modify connections between the keyboard and the disc of entry , in order to modify the encoding of the keys. The current moves then towards the disc of entry . He then traverses the assembly of the rotors, according to the position of each one of those. He passes thus from rotor out of rotor, until reaching the reflecting , which returns the signal until the disc of entry , but by another way that with the outward journey (made single which distinguishes the family from the Enigma machines of the other rotor machines of the time which did not have reflectors). The power is on finally by another of the Interrupteur S to two positions, and lights one of the lamps, corresponding to the encoding of the key in a hurry.

Rotors

The rotors (also called wheels or drums - Walzen in German) form the heart of the Enigma machine. Of a diameter of approximately 10 cm, each rotor is a disc manufactured starting from hard rubber or of Bakélite. On a face are laid out in circle of the electrical contacts with needles, therefore equipped with springs. On the other face, the same number of flat contacts are laid out. The flat contacts and with needles represent the Alphabet - generally the 26 letters (one will make this assumption in the continuation of this description, even if sometimes figures could be used according to the same principle).

Once the assembled rotors, the contacts with needles of a rotor position opposite the flat contacts of the close rotor, thus forming electric connection. Inside the rotor, a whole of 26 electric cables ensure connections between the contacts with needles and the contacts flat according to a complicated diagram, which allows the coding of the letters. For example, on a particular rotor, the first contactor of a face can be connected to the fourteenth contactor of the opposed face, the second contactor connected to the twenty-second of the other face, and so on. From one rotor to another, internal connections are not the same ones. The version of Enigma used by the German army and the Socialist National party has a set of rotors with connections different from commercial releases.

The rotor used all alone carries out in fact very simple only one coding - the figuring by substitution. For example, the contact with needle corresponding to the letter E can be connected on the face opposed to the flat contact of the letter T. The complexity of the Enigma machine comes from the use of several rotors in series, generally three or four, as well as the regular movement of these rotors. When 26 letters were in a hurry, a cam actuates the rotor of the following slit and the fact of turning. The alphabet of substitution is thus modified with each pressure of key. These two mechanisms form a type of coding much more powerful.

Once installed in the machine, a rotor can thus be placed at the one of its 26 positions. That can be carried out manually by the operator, by means of the toothed wheel, or automatically at the time of the pressure of a key of the keyboard. With such way that the operator knows the position of the rotor, each one of them is equipped with a “wheel alphabet”, thus comprising the 26 letters of the alphabet (or 26 numbers); under operation, only one of them can be seen by a small window, thus indicating to the operator the exact position of each rotor. In the first Enigma machines, the “wheel alphabet” was fixed on the rotor. A complication was added in the last versions, with the possibility of moving this wheel compared to the rotor itself. The position of the wheel names the Ringstellung (“positioning of the ring”).

Each rotor comprises finally a notch (sometimes several), ensuring the control of the movement of the rotor. In the military versions of the Enigma machine, this notch is located directly on the “wheel alphabet”. Enigma the German machines of the army and aviation were equipped with many rotors, three exactly for the first versions. The December 15th 1938, this number was changed to five, of which only three were selected to be installed in the machine. Each rotor was marked of a Roman numeral in order to be able to distinguish them: I, II, III, IV and V all. were equipped only with only one notch. The version of the Enigma machine of the Wehrmacht for the navy was always equipped of more than rotors than the other versions. At the beginning, five rotors equipped the machines, then seven and finally eight. The additional rotors were numbered VI, VII and VIII, and thus had electric connections different from the other rotors. They moreover were equipped with two notches, which thus involved a different rotational frequency.

The Enigma machine with four rotors of the navy (M4) counted, it, four rotors in the machine in the place of the three of the other versions. This was possible without modifying the machine largely, by simply replacing the reflectors of origin by another much the finer and by adding a special rotor in fourth position. This fourth rotor could be of two types: Beta or Gamma . It however never turned automatically, but could be placed manually on one of its 26 positions by the operator.

Thanks to the random interconnection of each rotor, the exact sequence of these substitutions depended on the initial position of the rotors, of their kind of installation, and the choice of the rotors (internal wiring). These adjustments called initial configuration were registered in a book and changed once a month at the beginning of the Second world war. These changes became increasingly frequent until becoming days laborer towards the end of the war, even several times per day on certain networks.

The most current versions of Enigma are known as symmetrical in the sense that the coding and the deciphering of information function in the same way. Indeed, if one types the text quantified in Enigma, the sequence of the lit lamps will correspond to the plaintext. But that functions only if the machine has the same initial configuration as that which quantified the message

For more details on wiring of the rotors and the adjustment of the snap ring like their effects on coding, to consult Enigma rotor details.

Disc of entry

The disc of entry ( Eintrittswalze in German) carries out connection between the desk of connections (or the keyboard for the models not having a desk of connections) and the unit consisted the rotors. Although the wiring used in the disc of entry is of very low importance for safety, that proved to be an obstacle for the cryptanalyste Polish Marian Rejewski during the calculation of the wiring of the rotors. Whereas the commercial release of Enigma connected the keys in their order on keyboard (QWERTY), the military versions connected them in the alphabetical order (ABCDEF). Rejewski had to make some assumptions to include/understand the modification before being able to solve the equations.

Mathematical coding analyzes

The coding of each letter by Enigma can be considered mathematically as a product of Permutation S. Considérons indeed a Enigma machine of the Air Force German Marine. That is to say $P$ the transformation carried out by the keyboard, $U$ reflectors, and $G, M$ and $D$ actions of the rotors of left, the medium and right-hand side respectively. Coding $C$ is written then:

$C = PDMGUG^ {- 1} M^ {- 1} D^ {- 1} P^ {- 1} ~$

After each action on a letter of the keyboard, the rotor turns, thus changing the cryptographic transformation. For example, if the rotor of right-hand side $D$ turns of $i$ positions, coding becomes $\ rho^iD \ rho^ {- I}$ , with $rho$ indicating the circular Shift making it possible to pass from $A$ to $B$ , $B$ with $C$ and so on. In the same way, the rotor of the medium and that of left can be described by $j$ and $k$ rotations of $M$ and $G$ . Coding can then be written in the following way:

$C = P (\ rho^iD \ rho^ {- I}) (\ rho^ {J} M \ rho^ {- J}) (\ rho^ {K} G \ rho^ {- K}) U (\ rho^kG^ {- 1} \ rho^ {- K}) (\ rho^ {J} M^ {- 1} \ rho^ {- J}) (\ rho^ {I} D^ {- 1} \ rho^ {- I}) P^ {- 1} ~$

History of Enigma

Enigma is developed by Arthur Scherbius starting from 1919. It founds a company in Berlin which produces and sells the first commercial release ( Enigma-A ) in 1923. Three other commercial releases will follow, and the Enigma-D becomes the most widespread model after its adoption by the German Marine in 1926. The apparatus is then taken again by the German Army in 1929. As from this moment, its use is extended to all the German military organization and most of the hierarchy Nazi. The German Navy calls Enigma “the machine M”.

During the Second world war, versions of Enigma are used for practically all the German radio communications (but also those of other powers of the Axe), like for the telegraph collections. Even the bulletins weather are coded with Enigma. The Spaniards (at the time of the Spanish Civil war) then the Italians (during the Second world war) use one of commercial releases of the machine, unchanged, for their military communications. This imprudence profits with the British who break the code of it only more quickly. That contributes to the British victory vis-a-vis the Italian fleet with Matapan. The code has in fact broken since 1933 by Polish mathematicians (Marian Rejewski, Jerzy Różycki and Henryk Zygalski) helped of average electromechanics (called “bombs”). The Second Office French buys in Hans Thilo Schmidt, younger brother of the lieutenant-colonel Rudolf Schmidt who will be in May - June 1940 the direct superior of the general Erwin Rommel, the monthly keys of Enigma, at once transmitted to the Poles.

It was not enough to decipher all the communications of the enemy: it was also necessary that this one is unaware of it, or else it would have gradually changed coding material. The destruction of each German ship whose position was known was thus preceded by the sending of a supposed reconnaissance aircraft to pass there “by chance”. This one took care to be shown well, and the attack could then be launched without alerting the enemy staff (which was to think that the Allies had either much chance, or much of planes!) On the other hand, where one could not send these planes for reasons of autonomy, the Allies were to let leave the convoys of which they knew that they would never arrive: to cancel had been to alert the enemy immediately.

The British machine of coding Typex, and several of the American machines such as for example SIGABA or the M-134-C, functions according to principles similar to Enigma, but in a way much surer. The first machine with quantifying cylinders modern Edward Hebern is regarded as less sure, a fact noted by William F. Friedman during its acquisition by the US government.

Safety

The use of several rotors by Enigma provides a simple manner to determine which alphabet of substitution is used to quantify or decipher a particular letter. However, contrary to the polyalphabetic majority of the alternatives of the Coding, Enigma does not have a key strictly speaking. Indeed, these rotors produce a new alphabet of substitution for each pressure of key. Moreover, the sequence of these alphabets of substitution can be completely changed while making turn one or several of the rotors to the hand, by changing the order of the rotors, etc before starting to use Enigma. In a simpler way, one can say that Enigma has a bank of 26 X 26 X 26 = 17.576 alphabets of substitution for any combination of three rotors. The sequence of use of these alphabets varies according to whether one puts the rotors in position ABC, or ACB, etc And as long as the message does not exceed: 17576 characters, there is no repetition of the alphabet of substitution. However, this “key” can be communicated in a very easy way to another user: they are very simple values, of the number type of rotors, position of the ring and starting position.

Example of messages Enigma originals

The contents of the clear text are of course in German. The numbers of messages were added by the British services of interception. Nobody knows if these messages were quantified to Enigma with 3 or with 4 rotors.

- 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 IF 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 - PS QJH - QSDCK HQOGN OSAIC GADNM PJIAI NPWBM VLTKQ YUDII GWSHT TZEYE CCHFJ CNYBC HXZNE KOOMV GROUNDS NDDGR RXPMS GFOPY SJFSY SBYBS CSKDP IOBQM HSFKV MCSMD HYJNO CHB

Anecdote

The encryption algorithm of Enigma was developed by a student as an order UNIX ( crypt ), was integrated in the distribution of this system and was used by civil laboratories and soldiers who believed to thus protect their communications (work from deciphering of Bletchley Park were indeed classified until 1974, which of course could facilitate the industrial Espionnage.

Let us note however that in on line help of the order was specified that this order was not to be used to quantify sensitive informations. Indeed, the international version of the order used the equivalent only one rotor of 256 positions (to quantify the 256 possible characters of a byte).

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