Technical Specification of the Enigma


Tony Sale's
Codes and Ciphers



This is a supplementary page for Tony Sale's sequence of pages on the Enigma, gives the detailed technical specifications of the Enigma rotors (or wheels), and reflectors.

Technical specifications of the Enigma rotors

These are the permutations performed by the rotors:

INPUT A B C D E F G H I J K LM N O P Q R S T U V WX Y Z
Rotor I E K M F L G D Q V Z N TO W Y H X U S P A I BR C J
Rotor II A J D K S I R U X B L HW T M C Q G Z N P Y FV O E
Rotor III B D F H J L C P R T X VZ N Y E I W G A K M US Q O
Rotor IV E S O V P Z J A Y Q U IR H X L N F T G K D CM W B
Rotor V V Z B R G I T Y U P S DN H L X A W M J Q O FE C K
Rotor VI J P G V O U M F Y Q B EN H Z R D K A S X L IC T W
Rotor VII N Z J H G R C X M Y S WB O U F A I V L P E KQ D T
Rotor VIII F K Q H T L X O C B J SP D Z R A M E W N I UY G V
Beta rotor L E Y J V C N I X W P BQ M D R T A K Z G F UH O S
Gamma rotor F S O K A N U E R H M BT I Y C W L Q P Z X VG J D

These permutations can also be given in the cycle representation:

Rotor I(AELTPHQXRU) (BKNW) (CMOY) (DFG) (IV) (JZ) (S)
Rotor II(FIXVYOMW) (CDKLHUP) (ESZ) (BJ) (GR) (NT) (A) (Q)
Rotor III(ABDHPEJT) (CFLVMZOYQIRWUKXSG) (N)
Rotor IV(AEPLIYWCOXMRFZBSTGJQNH) (DV) (KU)
Rotor V(AVOLDRWFIUQ)(BZKSMNHYC) (EGTJPX)
Rotor VI(AJQDVLEOZWIYTS) (CGMNHFUX) (BPRK)
Rotor VII(ANOUPFRIMBZTLWKSVEGCJYDHXQ)
Rotor VIII(AFLSETWUNDHOZVICQ) (BKJ) (GXY) (MPR)
Beta rotor(ALBEVFCYODJWUGNMQTZSKPR) (HIX)
Gamma rotor(AFNIRLBSQWVXGUZDKMTPCOYJHE)

These tables specify the effect of the rotors when the ring setting is A, and when the rotor is also at position A. Note that the tables are set out so as to specify how the rotor transforms the input (current coming from the right) into output (sending current to the left). The Enigma encryption process also involves the current passing back again, rightwards, through the rotors. To trace the effect of the rotors in this stage you must apply the inverses of the permutations in the tables.

Technical specifications of the Enigma reflectors

The reflectors of the Enigma can be specified most easily in the cycle representation:

reflector B(AY) (BR) (CU) (DH) (EQ) (FS) (GL) (IP) (JX) (KN) (MO) (TZ) (VW)
reflector C(AF) (BV) (CP) (DJ) (EI) (GO) (HY) (KR) (LZ) (MX) (NW) (TQ) (SU)
reflector B Dünn(AE) (BN) (CK) (DQ) (FU) (GY) (HW) (IJ) (LO) (MP) (RX) (SZ) (TV)
reflector C Dünn(AR) (BD) (CO) (EJ) (FN) (GT) (HK) (IV) (LM) (PW) (QZ) (SX) (UY)

Technical specifications of the stepping mechanism

The rotors also differed in where they had the effect of knocking on the slower-moving rotor to the left.

These points can be specified in terms of which letter appears in the window when the knock-on occurs:

Rotor Iat R
Rotor IIat F
Rotor IIIat W
Rotor IVat K
Rotor Vat A
Rotors VI, VII and VIIIat A and at N

At Bletchley Park the letters R, F, W, K, A were impressed on the cryptanalysts' minds by the mnemonic: Royal Flags Wave Kings Above.

The beta and gamma rotors, introduced in 1942 to complicate the U-boat Enigma, could only be used in the fourth position and so did not have knock-on effects.



This information was compiled by Tony Sale from the Enigma machines in the Bletchley Park Museum. You will find that it agrees with the table of rotors and reflectors given on page 113 of F. L. Bauer's excellent book Decrypted Secrets, (Second edition, Springer, 2000) [although there are two misprints in that table.]

To see how these rotors played their role in Enigma encipherment, continue to this page with an example of the basic Enigma at work.

Further technical and historical information will appear shortly, together with an on-line Enigma simulator incorporating these permutations.



This page is created by Tony Sale (tsale@qufaro.demon.co.uk) the original curator of the Bletchley Park Museum, and Secretary of the Bletchley Park Heritage Society. Technical assistance from Andrew Hodges