Cryptology The Enigma - General Description

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Descriptions, Articles, Simulations

External links:

• Article in Wikipedia.
• Basic Principles of the Enigma (John Savard).
• Louis Kruh and Cipher Deavours: The commercial Enigma: Beginnings of machine cryptography. Cryptologia XXVI/1 (2002), 1 - 16.
• How the Enigma Works (by Alan Stripp).
• Turing's Treatise on Enigma.
• The Enigma Collection (Frode Weierud).
• James J. Gillogly: Ciphertext-only Cryptanalysis of Enigma. Cryptologia XIX/4 (1995).
• The Influence of ULTRA in the Second World War (Harry Hinsley).
• Decoding Nazi Secrets (Nova online).
• The Late Tony Sale's Codes and Ciphers Website
• The Alan Turing Home Page (Andrew Hodges)
• Online simulation (Enigmaco)
• Enigma-E (electronic self-build kit)

Historical Data

• Foundation of »Chiffriermaschinen AG« by Scherbius.
  1924 Enigma B as a commercial cipher machine for civil use;
  4 rotors (»Durchgangsräder«) with different gear wheels.
• 1926 Willi Korn: Patent application for »Umkehrwalze« (= reflecting rotor)
  → Enigma C, that also used light bulbs as output device as for HEBERN's machine.
• 1927 Enigma D that allowed flexible setting of the reflecting rotor, and with interchangeable rotors.
• 1930 adoption by the German Army (Enigma I, »Wehrmachts-Enigma«), additional security by the »Steckerbrett« (plug-board).
  During the war several improved variants.
• 1933 Liquidation of »Chiffriermaschinen AG«;
  new foundation as »Chiffriermaschinen-Gesellschaft Heimsoeth und Rinke« (until 1945).
• 1938-1942: Delivery of Enigma K to the Swiss Army.
• 1942 Version M4 (»Marine-Enigma«) for the navy with an additional rotor.

The book by Pröse, see Reference List (for further reading), gives a comprehensive overview over the diverse versions and variants of the Enigma (in German). See also

Davin Kenyon, Frode Weierud: Enigma G, the counter Enigma. Cryptologia 44 (2020), 385–420.

Foreign Variants

• British variant TYPEX
• Polish variant: Lacida
• Japanese variant: »GREEN«
• US-variant M-235 = SIGFOY by Friedman
• NEMA for the Swiss Army with 6–10 rotors (from 1946 on)
• Italian variant OMI cryptograph with 7 rotors by OMI (Ottico Meccanica Italiana).

Characteristic Properties of the Enigma

Since there are so many different versions we focus on the »Wehrmachts-Enigma«.

• The operator choses 3 rotors from a set of 5.
• The current flows through the 3 rotors first from right to left, then through the reflecting rotor, then in reverse direction from left to right again through the 3 rotors as in the graphic
  
  or look at the graphic by John Savard.
• The reflecting rotor
  • doesn't move,
  • doubles the number of traversed rotors,
  • makes the encryption involutory, that means the encryption and decryption functions are identical,
    the machine needs no switch between encryption and decryption,
  • enables the cryptanalyst to try a negative pattern search, because a letter is never encrypted by itself.
• The »alphabet ring« of each rotor contains the letters from A to Z that only serve for adjusting the initial position as part of the key. This ring encloses the rotor and may be freely turned with respect to the rotor. Since the notches that move the next rotor are fixed to the ring this effects the state transition function and gives an additional key, the »Ringstellung«.
• The rotors move like an odometer, but the alphabet labels on the alphabet ring run in the opposite direction compared with the description in Section 5.1. The rightmost rotor—the first and last to be traversed—is the fast rotor, the leftmost one, next to the reflecting rotor, is the slow rotor.
  There is a small irregularity: When the slow rotor moves it pushes the middle one by one more position such that the middle one completes a full turn after 25 moves, omitting one position (see below).
• The assignment of the keyboard or the light-bulbs with the input contacts of the first rotor is mediated by the plugboard. Each of the up to 10 inserted plugs interchanges one pair of letters. Thus the plug-board provides an additional substitution (an involution) for input and output. This considerably enlarges the key space and prevents the meet-in-the-middle attack by isomorphs.

The Army's service regulations prohibited encrypting messages of more than 250 letters. The operators had to split longer texts into several parts and encrypt these with different settings (»Spruchschlüssel«).

The Rotors of Enigma I

The table shows the (then) strongly secret wiring of the five rotors I to V available with Enigma I, and of the reflecting rotors (»Umkehrwalzen«) A, B, C:

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

    UKW A   AI  BM  CE  DT  FG  HR  JY  KS  LQ  NZ  OX  PW  UV
    UKW B   AY  BR  CU  DH  EQ  FS  GL  IP  JX  KN  MO  TZ  VW
    UKW C   AF  BV  CP  DJ  EI  GO  HY  KR  LZ  MX  NW  QT  SU

The Rotor Stepping

... is shown in the following picture:

[Image from Wikimedia Commons released under GFDL and cc-by-sa]

If one looks at the Enigma during operation from the frontside, the visible position letters in the window move downwards. The picture shows the rotors as seen from the backside, their upper parts move to the left. All three ratchets push (in the picture above) to the left. Rotor 1 is the fast rotor, it steps with each keypress driven by the corresponding ratchet that is always engaged. Rotor 2 moves in this special situation because the notch in rotor 1 allows the ratchet to engage with the indentation of rotor 2. Rotor 3 doesn't move in this step because the ratchet is kept away, the notch of rotor 2 being elsewhere.

This mechanism is very robust. But he causes an irregularity that would be inoperative for a true odometer ...

This occurs when rotor 2 is ready to move rotor 3: In the step before, rotor 2 moves to the critical position. Then it should rest motionless for the next 25 steps because the notch of rotor 1 has to poerform a full turn. However the ratchet for rotor 3 pushes the notch of rotor 2 and gives it a stepping impulse. Hence the pattern of the movements of rotor 2 ist as follows—0 means no movement, 1, advancing 1 position

   |<-- 25 times no motion                      -->|
                                              pushed | by rotor 1
                                                     |
                                                     v
   ...
   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
-->1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 (effect by rotor 3)
   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
   ...

The described effect also occurs bewtween rotor 1 and rotor 2—but without any impact, because rotor 1 moves with each step anyway. Whether this movement is pushed by one or by two ratchets makes no difference.

Deavours and Kruh (see the references) state that the Hebern machine shows a similar kind of irregular motion, resulting in a period of 26x26x25.

Do Enigma's rotors turn before or after the currently typed letter is encrypted? See the FAQ.