Enigma G (model G31)
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The rotors of the Enigma model G31 are smaller than those of
all other Enigma machines. 1 The largest diameter is approx. 85 mm (3.5 inches),
whereas the regular rotor are ~ 100 mm (4 inches). In order to accomodate
the 26 spring loaded contacts, they are arranged in a zig-zag pattern.
The contact pads at the other side of the wheel have the shape of
a tear-drop.
The wheels of Zählwerk Enigma A28 (left) and Enigma G31 (right)
Most machines were supplied with just three rotors that could be installed on the spindle in six different orders (3 x 2 x 1). These rotors (I, II and III) had 17, 15 and 11 notches 4 respectively. The positions of these notches are identical on all surviving machines, regardless of their wiring and regardless of the customer. It is known that some machines were supplied with more than three wheels. For example, the Hungarian Enigma G31 machines (Ch.15b) came with five rotors, in which case three of these rotors could be picked and installed in 60 different orders (5 × 4 × 3). It is likely that the additional rotors (IV and V) had 9 and 7 notches respectively. ➤ Technical description When creating an encrypted message, the operator has to use two cryptographic keys: (1) a daily key – picked from a key list – which is changed every 24 hours, and (2) a message key – unique for each new message – which consists of 4 letters that are randomly picked by the operator. The message key is always sent at the beginning of the message, and is encrypted with the daily key.
The rotors are then placed on the spindle in the prescribed order, after which the rotor stack (spindle with three rotors) is placed back in the machine beteen the ETW and the UKW. The UKW is then shifted to the right and locked in place by placing its lever in the frontmost position.
This is done by randomly picking four letters of the alphabet (e.g. ADXH).
He then types these four letters on the machine (which is configured for the
basic setting) and writes down the output (e.g. BSTU).
In case of the Abwehr, the message key had to be entered twice
(e.g. BSTU ADFL).
The operator then temporarily releases the coupling and sets the rotors to his
randomly picked message key (ADXH), after which the coupling is engaged again.
He then enters the message and writes down the output.
At the receiving end, the operator sets his machine to the daily key (as per
key list) and enters the first four-letter group. This reveals the message key.
He then sets the rotors to the message key, enters the rest of the message
and writes down the plaintext output.
In case of the Abwehr, the operator had to enter the first eight letters of the message, which revealed the message key twice. This was done as an extra check to ensure that the correct settings had been used. At the same time, this procedure of entering the message key twice, introduced a cryptographic weakness that was exploited by Dilly Knox and his team at Bletchley Park. Although the German Army was aware of this weakness — they abandonned this procedure at the beginning of the war — this knowledge apparently never reached the Abwehr, as for the remainder of the war they kept using the double encryped message key.
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Around 1926, the Enigma manufacturer — Chiffriermaschinen AG —
started the development of a series of new machines, all based on the chassis
of commercial Enigma D (A26).
For the Reichswehr (the predecessor of the Wehrmacht),
they developed the Enigma I and for various
other civil and military customers the
Enigma A27 (later also known as Enigma K)
was introduced.
At the same time, development was started of an improved
machine that was described as follows: [3]
Glühlampen-Chiffriermaschine "ENIGMA"
mit Zählwerk
und zwangläufiger
Kupplung der Chiffrierwalzen.
Translated: Lamp-Enigma with counter and coupled cipher rotors.
It has a cogwheel-driven rotor-turnover mechanism that features
irregular stepping, making it cryptographically stronger than
the regularly stepping Enigma D and K.
Several models were based on this new concept.
All these machines have a counter that registers the number of key-presses,
which is why they are also known as Zählwerksmachine (counter machine)
or Zählwerk Enigma (counter Enigma).
After the first prototypes in 1927,
the first machine with this mechanism was released in 1928
as the Zählwerk Enigma A28. Two versions of this machine
exist (Mk.1 and Mk.2), the latter of which is shown in he image on the right.
It has the same form factor as a regular Enigma K.
A few years later, around 1930, a numbers-only version of the machine was released as the Z30. Enigma A28 eventually evolved into the smaller Enigma G (or model G31), which was released in 1931. The two Enigma models are interoperable. |
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Wheel | ABCDEFGHIJKLMNOPQRSTUVWXYZ | Notch | Turnover | # |
ETW | QWERTZUIOASDFGHJKPYXCVBNML | |||
I | LPGSZMHAEOQKVXRFYBUTNICJDW | ACDEHIJKMNOQSTWXY | SUVWZABCEFGIKLOPQ | 17 |
II | SLVGBTFXJQOHEWIRZYAMKPCNDU | ABDGHIKLNOPSUVY | STVYZACDFGHKMNQ | 15 |
III | CJGDPSHKTURAWZXFMYNQOBVLIE | CEFIMNPSUVZ | UWXAEFHKMNR | 11 |
UKW | IMETCGFRAYSQBZXWLHKDVUPOJN |
The table below shows the wiring of the G111 (version Ch.15b), that was from the first batch of Enigma G machines ever manufactured. It was part of a batch of 24 machines (G-101 to G-124) that were delivered to Hungary, probably in 1931. It is believed that this machine was used by the Hungarian Army or the Hungarian intelligence services, who bought it alongside the Enigma H29. Note that only wheels I, II and V were found with this machine. ➤ More about the G111
Wheel | ABCDEFGHIJKLMNOPQRSTUVWXYZ | Notch | Turnover | # |
ETW 1 | QWERTZUIOASDFGHJKPYXCVBNML | |||
I | WLRHBQUNDKJCZSEXOTMAGYFPVI | ACDEHIJKMNOQSTWXY | SUVWZABCEFGIKLOPQ | 17 |
II | TFJQAZWMHLCUIXRDYGOEVBNSKP | ABDGHIKLNOPSUVY | STVYZACDFGHKMNQ | 15 |
III | ? | CEFIMNPSUVZ | UWXAEFHKMNR | 11 |
IV | ? | ? | ? | ? |
V | QTPIXWVDFRMUSLJOHCANEZKYBG | AEHNPUY | SWZFHMQ | 7 |
UKW 2 | IMETCGFRAYSQBZXWLHKDVUPOJN |
As we can learn from the above table, the number of notches as well as the
turnover positions of wheels I
and II are identical to those on the same wheels of other Zählwerk machines
(17 and 15 notches respectively).
It is most likely that the (unknown) wheel III had 11 notches and that the
turnover positions are the same as on other machines.
They are shown here in red.
It is likely (but not certain) that the number of turnover notches on the
unknown wheel IV is 9.
The current whereabouts of this machine are unknown.
➤ More about Enigma G111
G227 and G228 are two machines that were used on the Grün (Green) network of the Abwehr. The rotors (I-III) were wired on 10 July 1943 according to the drawings Ch.15 Tz 125a-c, created in 1939. The UKW is wired according to Ch.15 Tz 115 of 14 July 1936 [12]. in 2015, the G228 was unexpectedly offered for sale from an anonymous seller in Argentina, and was subsequently acquired by a private collector. The wiring below was taken from this machine [18].
Wheel | ABCDEFGHIJKLMNOPQRSTUVWXYZ | Notch | Turnover | # |
ETW | QWERTZUIOASDFGHJKPYXCVBNML | |||
I | JDZLYKXVOUCMRAGTSBIWQHPENF | ACDEHIJKMNOQSTWXY | SUVWZABCEFGIKLOPQ | 17 |
II | SKQXFDVNGMUETJBRZLAHYWIODP | ABDGHIKLNOPSUVY | STVYZACDFGHKMNQ | 15 |
III | GRMKJBSAIXHWDQUYOEZVPNLFCT | CEFIMNPSUVZ | UWXAEFHKMNR | 11 |
UKW | RULQMZJSYGOCETKWDAHNBXPVIF |
This machine is currently held in the private collection of Glen Miranker (USA) [18].
In March 1945, just before the end of WWII, the Argentine police arrested the German spy Johann Siegfried Becker. In his posession was an Enigma model G31 with serial number G260. Two months later, the machine was handed over to the Americans [7]. Although Becker was believed to work for the German intelligence service, the Abwehr, the G260 was most likely used by the Sicherheidsdienst (SD) — the German Security Service — on its Rot (Red) network. They were wired differently from the machines used by the Abwehr on its Grün (Green) network [11].
Wheel | ABCDEFGHIJKLMNOPQRSTUVWXYZ | Notch | Turnover | # |
ETW | QWERTZUIOASDFGHJKPYXCVBNML | |||
I | RCSPBLKQAUMHWYTIFZVGOJNEXD | ACDEHIJKMNOQSTWXY | SUVWZABCEFGIKLOPQ | 17 |
II | WCMIBVPJXAROSGNDLZKEYHUFQT | ABDGHIKLNOPSUVY | STVYZACDFGHKMNQ | 15 |
III | FVDHZELSQMAXOKYIWPGCBUJTNR | CEFIMNPSUVZ | UWXAEFHKMNR | 11 |
UKW | IMETCGFRAYSQBZXWLHKDVUPOJN |
The current whereabouts of this machine are unknown.
The table below shows the wiring of the G312. Although the machine is believed to have been used by the German Abwehr, it is the only one every found with this wiring. Different wirings were used for different sections of the Abwehr, and also for different radio nets. It is possible that some machines were rewired a number of times during their lifetime. Note the rewired UKW.
Wheel | ABCDEFGHIJKLMNOPQRSTUVWXYZ | Notch | Turnover | # |
ETW | QWERTZUIOASDFGHJKPYXCVBNML | |||
I | DMTWSILRUYQNKFEJCAZBPGXOHV | ACDEHIJKMNOQSTWXY | SUVWZABCEFGIKLOPQ | 17 |
II | HQZGPJTMOBLNCIFDYAWVEUSRKX | ABDGHIKLNOPSUVY | STVYZACDFGHKMNQ | 15 |
III | UQNTLSZFMREHDPXKIBVYGJCWOA | CEFIMNPSUVZ | UWXAEFHKMNR | 11 |
UKW | RULQMZJSYGOCETKWDAHNBXPVIF |
Zählwerk Enigma (counter Enigma) is based on the design of the
Enigma D (A26) and Enigma K (A27),
but has additional features and improvements. Most of these
extras are described in two German patents:
DE534947 [8]
and DE579555 [9].
The most important difference with earlier models is the way
in which the rotors advance when a key is pressed.
In the earlier Enigma K, and also in the later Enigma I,
the rotors are advanced by means of pawls, ratchets and notches.
As a result, a rotor can only step forward.
Under certain conditions, the middle rotor
can make an additional step on two successive key presses.
This is known as the double stepping anomaly [14].
This stepping behaviour is also known as Enigma stepping.
Another difference with Enigma K is that the reflector (UKW)
can not only be
Each rotor has a full cogwheel with 52 teeth attached to its
right side. On the left side of the rotor is another cogwheel with the same
spacing, but with a number of teeth missing.
The presence of a pair of teeth is equivalent to a notch on an
regular Enigma rotor.
When the rotors are engaged, they are firmly coupled by means of 4 small pinion
wheels with teeth of alternating length.
Both sides of an Enigma G rotor
Regular Enigma wheels (left) and the wheels of Zählwerk Enigma A28 (right)
The wheels of the Zählwerk Enigma model A28 (left) and the Enigma model G31 (right)
It is very likely that the Zählwerk Enigma was originally intended for
commercial use, as the wiring of the UKW, and in some cases the wiring
of the rotors as well, was identical to the wiring of the commerial
machines.
Sometimes the rotors were rewired by the customer, but in most
cases the wiring of the UKW was left unchanged.
The Abwehr ordered unwired rotors [10].
With Zählwerk Enigma however, the rotors are advanced by a cogwheel-driven
mechanism that does not suffer from the double stepping anomaly.
In addition, the number of notches on each wheel has been increased.
It is different for each wheel, does not share a common factor and cannot
divide 26. By using 17, 15 and 11 notches respectively,
the longest possible cipher period is obtained.
This stepping behaviour is also known as irregular stepping.
As a result, the entire mechanism can be stepped forward and backward,
without losing the relation between the position of the wheels. A crank
can be inserted into a hole in the body of the machine, allowing the
mechanism to be wound back to the desired position.
This was used to correct mistakes,
but could theoretically also be used as part of the cryptographic procedure.
The rotors of the initial Zählwerk machine — Enigma A28 — have the
same diameter as the rotors of a regular Enigma, such as Enigma K.
With the later G31 model however,
smaller wheels are used, as illustrated below.
In order to accomodate the spring-loaded contacts,
they are arranged in a zig-zag pattern, whilst the contact pads at the other
side have an oval or tear-drop shape.
Most machines were supplied with just three rotors that could be installed on
the spindle in six different orders (3 x 2 x 1).
These rotors (I, II and III) had 17, 15 and 11 notches 1 respectively.
The positions of these notches are identical on all surviving machines,
regardless of their wiring and regardless of the customer.
It is known that some machines were supplied with more than three wheels.
For example, the Hungarian Enigma G31 machines (Ch.15b)
came with five rotors.
The Enigma G is usually mounted inside a wooden transit case with a hinged lid. It is fixated to the bottom of the case by means of four large bolts. After removing these bolts, the machine can be lifted from the case. At the bottom of the chassis are 4 rubber pads that may have dried out.
In the Enigma G, the rotors are firmly coupled by means of small pinion wheels located at the the rear of the rotors. When altering the position of the rotors (Grundstellung), the pinions must first be disengaged by placing the coupling (i.e. the large lever at the top) in the rearmost position.
Once the mechanism is decoupled and the
UKW is released, the spindle with
the rotors can be removed. This leaves us with an
empty stepping mechanism in which
the pinions and the sping-loaded rubber guide wheels are
clearly visible.
At the far right is the entry disc (ETW), which is firmly fitted to the chassis. Around the ETW are a ratchet wheel and a cogwheel with 52 teeth. When pressing a key, an actuator advances the ratchet wheel by one step. At the same time, the cogwheel advances by two teeth. The image on the right shows the actuator in its rest position. |
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Note that the ratchet wheel and the cogwheel are part of a cylinder that revolves around the ETW, whilst the ETW itself stays in place. The actuator and its adjustment are further described here. The large cogwheel mates with a pinion wheel at the rear, which in turn drives the rightmost rotor. It also drives the 4-digit counter that is fitted at the far right of the chassis. For further details about the machine's interior, please refer to our page about the restoration of the G219. ➤ Restoration of the G219
Device Brand Type Model Designator Predecessor Successor Manufacturer Country Years Quantity Customers Rotors Turnovers Reflector Wiring Stepping Plugboard Extras Dimensions Weight Quantity
The Enigma G is known under the following names:
Below is a list of known Enigma G serial numbers, mainly based on surviving TICOM documents, complemented by our own findings. Detailed information and backgrounds can be found in the article Enigma G: The Counter Enigma by David Kenyon and Frode Weierud of May 2019 [12].
G101 - G124 1931 G128 1931 G138 - G141 1938 (est.) G145 - G188 1938 G189 - G194 1938 G195 - G221 1939 (est.) G209 ? G222 - G224 ? G227 - G228 1939 (est.) G247 ? G249 - G250 ? G256 - G257 ? G260 ? G263 ? G275 ? G292 ? G298 - G303 1940 G312 - G317 ? G404 - G407 ? G426 ?
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G285 III G274 I G274 II G413 II
Cryptologia, January 2000, Volume XXIV, Number 1.
31 May 2004. ISBN 978-0470863473.
Bletchley Park and Crypto Cellar Research, 5 May 2019. Updated 15 June 2019.
Explanation of the terms 'crab' and 'lobster'.
Undated, but probably 2017.
Full details of the Enigma G-111 (Ch.15b) with high-resolution drawings.
Crypto Museum, August 2009. Version 1.10, 1 May 2013.
➤ Publication
➤ More
1 April 2005. Retrieved February 2013.
Bletchley Park, August 2002, November 2004.
Offering for Schreibende Enigma and Glühlampenmaschine mit Zählwerk (German).
16 September 1929. Crypto Museum #300304. 1
Cryptologia, January 2000, Volume XXIV, Number 1.
Copyright BBC News, 2000. Retrieved November 2005.
31 May 2004. ISBN 978-0470863473.
US Navy Intelligence Division. 30 May 1945.
NARA CBKI 13, Box 5395, nr. 1574 1
Patent for the cog-wheel driven wheel-turnover mechanism and the Ringstellung.
Patent covering multiple notches on the wheels fixed to the index ring.
Crypto Museum, May 2009.
Crypto Museum, May 2013.
Bletchley Park and Crypto Cellar Research, 5 May 2019. Updated 15 June 2019.
Full details of the Enigma G-111 (Ch.15b) with high-resolution drawings.
Crypto Museum, August 2009. Version 1.10, 1 May 2013.
➤ Publication
➤ More
Cryptologia, January 1997, Volume XX, Number 1.
Explanation of the terms 'crab' and 'lobster'.
Undated, but probably 2017.
Austria, 22 October 2023.
TNA, HW25/14. Undated, but probably 1927/28.
1949. Published in Chapter 3 of the book Action This Day.
Michael Smith & Ralph Erskine, 2001. ISBN 978-0-593-06357-6.
Personal correspondence, February 2019.