This article is the part of the series on the Enigma cipher machine. edit this box (http://www.wordiq.com/definition/Template:EnigmaSeries)

Enigma machine

Enigma rotor details

Cryptanalysis of the Enigma

Perforated sheets

Bomba

Bombe

Ultra

This article contains technical details about the rotors of the Enigma machine. To understand the way the machine encrypts we have to take in account the current position of each rotor, the ring setting and its internal wiring.

Contents

1 The offset 2 The ring setting 3 Rotor wiring tables 4 Turnover positions

The offset

In order to understand what the effect of rotating is on the rotors we dimonstrate this by some examples.

As example, let us take rotor type I without any ring setting offset. You can see that an A is encoded as an E, a B encoded as a K, and a K is encoded as an N. Notice that every letter is encoded into any another.

In case of the reflectors, we take Wide B where an A is returned as a Y and the Y is returned as an A. Notice that the wirings are connected each time as a loop between two letters.

When a rotor has stepped, you must take in account the offset to know what the output is, and where it enters the next rotor. If for example rotor I is in the B-position, an A enters at the letter B which is wired to the K. Because of the offset this K enters the next rotor in the J position.

With the rotors I, II and III (from left to right), wide B-reflector, all ring settings in A-position, and startposition AAA, typing AAAAA will produce the encoded sequence BDZGO.

The ring setting

The ring settings, or Ringstellung, are used to change the position of the internal wiring relative to the rotor. They do not change the notch or the alphabet ring on the exterior. Those are fixed to the rotor. 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 A-position normally encodes an A into an E, with a ring setting offset B-02 it will be encoded into K

As mentioned before these encodings only happen after the key is pressed and the rotor has turned. Tracing the signal on the rotors AAA is therefore only possible if a key is pressed while the rotors where in the position AAZ.

With the rotors I, II, III (from left to right), wide B-reflector, all ring settings in B-position, and start position AAA, typing AAAAA will produce the encoded sequence EWTYX.

Rotor wiring tables

This table shows how the internal wiring connects the right side of the rotor (with the springloaded contacts) 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 E, this means that the A is wired to the E. This does not mean that E is wired to A. This looped wiring is only the case with the reflectors.

Rotor	Wiring
I	EKMFLGDQVZNTOWYHXUSPAIBRCJ
II	AJDKSIRUXBLHWTMCQGZNPYFVOE
III	BDFHJLCPRTXVZNYEIWGAKMUSQO
IV	ESOVPZJAYQUIRHXLNFTGKDCMWB
V	VZBRGITYUPSDNHLXAWMJQOFECK
VI	JPGVOUMFYQBENHZRDKASXLICTW
VII	NZJHGRCXMYSWBOUFAIVLPEKQDT
VIII	FKQHTLXOCBJSPDZRAMEWNIUYGV
Beta	LEYJVCNIXWPBQMDRTAKZGFUHOS
Gamma	FSOKANUERHMBTIYCWLQPZXVGJD
Reflector B	YRUHQSLDPXNGOKMIEBFZCWVJAT
Reflector C	FVPJIAOYEDRZXWGCTKUQSBNMHL
Reflector B Thin	ENKQAUYWJICOPBLMDXZVFTHRGS
Reflector C Thin	RDOBJNTKVEHMLFCWZAXGYIPSUQ

Turnover positions

In this table the turnover point of each rotor is listed. For more details on how the rotors move, please check the Stepping motion section and the remarks on the double-stepping of in the Enigma article.

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

In the following examples you can observe a normal step sequence and a double step sequence. The used rotors are (from left to right) I, II, III, with turnovers on Q, E and V. It is the right rotor's behaviour we observe here (turnover V).

Normal sequence:

• AAU — normal step of right rotor
• AAV — right rotor (III) goes in V—notch position
• ABW — right rotor takes middle rotor one step further
• ABX — normal step of right rotor

Double step sequence:

• ADU — normal step of right rotor
• ADV — right rotor (III) goes in V—notch position
• AEW — right rotor steps, takes middle rotor (II) one step furter, which is now in his onw E—notch position
• BFX — normal step of right rotor, double step of middle rotor
• BFY — normal step of right rotor