Enigma rotor details

This article contains technical details about the rotors of the Enigma machine. Understanding the way the machine encrypts requires taking into account the current position of each rotor, the ring setting and its internal wiring.

Physical design of rotors

Rotor electrical view

No letter can map to itself, a cryptographic weakness caused by the same wires being used for forwards and backwards legs.

Rotor offset

The effect of rotation on the rotors can be demonstrated with some examples.
As an example, let us take rotor type I of Enigma I without any ring setting offset. It can be seen that an is encoded as an, a encoded as a, and a is encoded as an. Notice that every letter is encoded into another.
In the case of the reflectors, in this example Wide is taken where an is returned as a and the is returned as an. Notice that the wirings are connected as a loop between two letters.
When a rotor has stepped, the offset must be taken into account to know what the output is, and where it enters the next rotor.
If for example rotor I is in the -position, an enters at the letter which is wired to the. Because of the offset this enters the next rotor in the position.
With the rotors I, II and III, wide, all ring settings in, and start position, typing will produce the encoded sequence.

Ring setting

The ring settings, or Ringstellung, are used to change the position of the alphabet ring relative to the internal wiring. Notch and alphabet ring are fixed together. Changing the ring setting will therefore change the positions of the wiring, relative to the turnover-point and start position.
The ring setting will rotate the wiring. Where rotor I in the -position normally encodes an into an, with a ring setting offset -02 it will be encoded into
As mentioned before these encodings only happen after the key is pressed and the rotor has turned. Tracing the signal on the rotors is therefore only possible if a key is pressed while the rotors were in the position and the ring settings are all on or.
With the rotors I, II, III, wide, all ring settings in, and start position, typing will produce the encoded sequence.

Rotor wiring tables

This table shows how the internal wiring connects the right side of the rotor to the left side. Each rotor is a simple substitution cipher. The letters are listed as connected to alphabet order. If the first letter of a rotor is, this means that the is wired to the. This does not mean that is wired to ; such looped wiring is only the case with the reflectors.
;Terminology

The reflector is also known as the reversing drum or, from the German, the Umkehrwalze or UKW.

Rotor #	Date Introduced	Model Name & Number
IC	1924	Commercial Enigma A, B
IIC	1924	Commercial Enigma A, B
IIIC	1924	Commercial Enigma A, B
		-
Rotor #	Date Introduced	Model Name & Number
I	7 February 1941	German Railway
II	7 February 1941	German Railway
III	7 February 1941	German Railway
UKW	7 February 1941	German Railway
ETW	7 February 1941	German Railway

Rotor #	Date Introduced	Model Name & Number
I-K	February 1939	Swiss K
II-K	February 1939	Swiss K
III-K	February 1939	Swiss K
UKW-K	February 1939	Swiss K
ETW-K	February 1939	Swiss K

Rotor #	Date Introduced	Model Name & Number
I	1930	Enigma I
II	1930	Enigma I
III	1930	Enigma I
IV	December 1938	M3 Army
V	December 1938	M3 Army
VI	1939	M3 & M4 Naval
VII	1939	M3 & M4 Naval
VIII	1939	M3 & M4 Naval

Rotor #	Date Introduced	Model Name & Number
Beta	Spring 1941	M4 R2
Gamma	Spring 1942	M4 R2
Reflector A
Reflector B
Reflector C
Reflector B Thin	1940	M4 R1
Reflector C Thin	1940	M4 R1
ETW		Enigma I

Technical comments related to Enigma modifications 1939-1945.

Swiss K

In 1941 it became known to the Swiss that some of their Enigma traffic was being read by the French. It was decided to make some design modifications.

One of the modifications consisted in modifying the wheel stepping on the Swiss Army machine. The slow, left-hand wheel was made stationary during operation while the second wheel stepped with every key stroke.
The third wheel and the UKW would step in the normal fashion with Enigma stepping for the third wheel.
The stationary but rotatable left-hand wheel was meant to make up for the missing stecker connections on the commercial machine.

Swiss Army Enigma machines were the only machines modified. The surviving Swiss Air Force machines do not show any signs of modification. Machines used by the diplomatic service apparently were not altered either.

Turnover notch positions

The single turnover notch positioned on the left side of the rotor triggers the stepping motion by engaging the ratchet teeth of the wheel to the left. Later rotors had two turnover notches. The table below lists the turnover notch point of each rotor.

Rotor	Notch	Effect
I	Q	If rotor steps from Q to R, the next rotor is advanced
II	E	If rotor steps from E to F, the next rotor is advanced
III	V	If rotor steps from V to W, the next rotor is advanced
IV	J	If rotor steps from J to K, the next rotor is advanced
V	Z	If rotor steps from Z to A, the next rotor is advanced
VI, VII, VIII	Z+M	If rotor steps from Z to A, or from M to N the next rotor is advanced

Normalized Enigma sequences

In the following examples you can observe a normal step sequence and a double step sequence. The used rotors are I, II, III, with turnovers on, and. It is the right rotor's behavior we observe here.

— normal step of right rotor
— right rotor goes in V—notch position
— right rotor takes middle rotor one step further
— normal step of right rotor
— normal step of right rotor
— right rotor goes in V—notch position
— right rotor steps, takes middle rotor one step further, which is now in its own E—notch position
— normal step of right rotor, double step of middle rotor, normal step of left rotor
— normal step of right rotor
Fourth rotor

The introduction of the fourth rotor was anticipated because captured material dated January 1941 had made reference to the development of a fourth rotor wheel; indeed, the wiring of the new fourth rotor had already been worked out.
On 1 February 1942, the Enigma messages began to be encoded using a new Enigma version that had been brought into use. The previous 3-rotor Enigma model had been modified with the old reflector replaced by a thin rotor and a new thin reflector. Breaking Shark on 3-rotor bombes would have taken 50 to 100 times as long as an average Air Force or Army message. It seemed, therefore, that effective, fast, 4-rotor bombes were the only way forward. Encoding mistakes by cipher clerks allowed the British to determine the wiring of the new reflector and its rotor.