Title: The 3 Wheel Army / Air Force Enigma Cipher Machine

The Enigma Cipher Machine makes a good C, C++ or GUI project, but the best of the latter tend to be platform specific. The wiring and operation of the machine is well known. This brief introduction to the structure and workings of the Enigma is presented so that simulation projects can simulate the real machines with accuracy. The 3 wheel Enigma as used by the Army, Air Force and Navy was supplied with a set of 5 wheels marked I - V. The Navy later added wheels VI, VII and VIII and also modified the machine to produce a 4-wheel version; using a thin reflector accommodated the fourth wheel. This note mostly concerns the 3-wheel Enigma used by the Army and Air Force. Note that the term wheel, instead of rotor, was in common use at Bletchley Park

In the following tables the wiring for the wheels and two reflectors are given. The top row is the contacts on the right hand face of the wheel , the left hand contacts are shown for each wheel. The right hand alphabet progresses clockwise as viewed along the wheel axis from the stecker end towards the reflector. The schematic circuit in CVu 10.5 shows the correct wheel layout.

ABCDEFGHIJKLMNOPQRSTUVWXYZ

EKMFLGDQVZNTOWYHXUSPAIBRCJ

AJDKSIRUXBLHWTMCQGZNPYFVOE

BDFHJLCPRTXVZNYEIWGAKMUSQO

ESOVPZJAYQUIRHXLNFTGKDCMWB

VZBRGITYUPSDNHLXAWMJQOFECK

ABCDEFGHIJKLMNOPQRSTUVWXYZ

YRUHQSLDPXNGOKMIEBFZCWVJAT

FVPJIAOYEDRZXWGCTKUQSBNMHL

The stecker board is a panel consisting of 26 socket pairs. It is connected between the keyboard/lampboard and the rotors. The socket pairs represent the 26 input and outputs of the stecker board. With no leads connected all 26 connections go straight through unchanged (self-steckered). If a double ended plug lead is connected between two socket pairs, for example K - T, then connections K and T are swapped. Note that the current passes through the stecker board twice, see the schematic diagram in C Vu 10.5.

The connections from the steckerboard are connected to the entry contacts on the right face of the first wheel in normal alphabetic order in a clockwise direction.

The scale engraved on the outer ring progresses clockwise. Wheels move counter-clockwise, displaying a normal numerical progression in the windows. Naval Enigma machines are engraved A-Z instead of the 01-26 markings usually found on the Army/Air Force machine.

The right hand wheel advances one step for each key press. The wheels move during the down stroke of the key, when the key is fully down the wheels are at their new positions. Electric current then flows from the key switch through the steckerboard, through the scrambler and is reflected back again to light one of the lamps, but never the same letter as the key, because of the nature of the reflector.

The notch values given in Table 1 are the points at which a turn-over occurs. This is the point at which the left and middle wheels advance by one step for every revolution of the wheel to the right. These are 'window' positions and are the positions at which a lever engages into a notch. On the next keyed letter the turn-over will occur. There is one small complication here, the so-called double-stepping of the middle wheel. If the middle wheel steps and is then at its notch position, it will step a second time at the next character. Such a sequence might be something like this:

KDT KDU KDV KEW LFX LFY LFZ

This example uses wheel II in the mid position (notch at E) and wheel III in the right position (notch at V).

The double step phenomena gives the machine a period of 26x25x26 = 16900, instead of the expected period of 17576.

Recent comments in C Vu suggest there is some uncertainty about the rings and their purpose. Each wheel carries an outer ring engraved as described earlier. This ring can be rotated relative to the wheel core and set to one of 26 positions, held in place by a spring clip. This ring has the turn-over notches set into it. This means the ringstellung (ring setting) influences the sequence of substitution alphabets produced by the machine. For a given wheel the turn-over will always occur when the same letter is in the window, but the core wiring at this time will be at one of 26 possible different positions.

The extra wheels introduced by the Navy have two notches set into the ring at the same window positions for all 3 wheels. It must have been decided that more frequent turn-overs were desirable and that they should be in the same position for all wheels, since it is possible to identify a wheel by its turnover in some crypto-analysis situations. The choice of 2 notches is questionable since it is a factor of 26. Some Enigma machines have more than two notches, so it would be a good idea to code simulators to allow for any number of notches!

As noted earlier, The Navy modified the 3 wheel machines by adding a fourth wheel. A special thin reflector was used in place of the normal reflector to allow the fourth wheel to be fitted. The two wheels to be used in the fourth position were called Beta and Gamma. The wiring for these and their associated reflectors is different to others but is arranged so that when the fourth wheel is set to position A and ring setting A then the combined wiring is the same as the original reflectors. The fourth wheel could be set to any position as part of the key but it did not step during operation.

The following machine output, familiar to all C programmers, can be used to check that your simulator program is correct. This encipherment has a double step in it. The letters in brackets are the equivalent alphabet positions that would be seen on naval machines.

Plain Text:    HELLO WORLD
Cipher Text:   OLYOD HKPMA

Wheels, from left to right.   I    II    III
Wheel settings                11   04    20    (K D T)
Ringstellung                  20   12    26    (T L P)
Reflector                     B
Steckers                      None

The following books are highly recommended. All are in print and available in paperback.

Code Breakers,The Inside Story of Bletchley Park, Ed. F.H.Hinsley, Alan Stripp. Oxford University Press ISBN 0 19 285304 X

The Hut Six Story, Gordon Welchman, M & B Baldwin ISBN 0 947712 34 8

Enigma. Robert Harris. Random House. (Fiction, but interesting)