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Breaking the Enigma cipher

BOMBE was the name of an electro-mechanical machine, developed during WWII by Alan Turing and Gordon Welchman, whilst working as codebreakers at Bletchley Park. It was used to help breaking the German Enigma codes and was (partly) based on the so-called BOMBA, an earlier machine developed by Polish mathematicians in 1938. From 1943 onwards, an improved version of the British BOMBE was built in the US by the US Navy and — independently — by the US Army.

The Polish Bomba   1938
The Poles were the first to break the military variant of the Enigma in 1932. At section BS-4 of Biuro Szyfrów (Polish Cipher Bureau), young Polish mathematician Marian Rejewski had recovered the wiring of the military Enigma machine. He was later joined by two further mathematicians, Henryk Zygalski and Jerzy Rózyki, who became involved in recovering the daily Enigma keys.

Marian Rejewski
Jerzy Růzycki
Henryk Zygalski

Their success was based on pure mathematical analysis, assisted by information from a German spy by the name of Hans-Thilo Schmidt (codename Asche), and a commercial Enigma intercepted in the Polish mail. They then bought a commercial Enigma and used the gathered information to convert it into a military one. This converted machine is commonly known as the Polish Enigma.

From 1930 onwards, the Germans had been using a very simple key management scheme, in which the randomly chosen message key was sent twice in encrypted form at the beginning of each message. This allowed the daily key to be recovered relatively easy with hand methods.

On 1 October 1936, the Germans stopped using six Steckern and started using five to eight of them. This defeated the hand methods and the Poles thought out a catalog attack based on the cycle length of the indicator permutations. Rejewski subsequently developed a machine to assist in building the catalog: the Cyclometer.

The catalog contained the length and number of cycles for all 17,576 positions of the wheels for any possible wheel order. As there were three wheels at the time, there were six possible wheels orders (3 x 2 x 1), giving a total of 105,456 catalog entries. Building the catalog took well over a year, but when it was ready, it allowed the message key to be recovered in about 15 minutes.

On 1 November 1937, the Germans replaced the existing reflector (UKW A) for a new one (UKW B), and the Poles had to build a completely new catalog, which would probably take another year.

Then, on 15 September 1938, the Germans entirely changed the procedure for enciphering the message keys, and the catalog method had become completely useless. This prompted the Poles to come up with new solutions, such as the Zygalski Sheets and the Bomba Kryptologiczna (crypto­logic bomb), often abbreviated to Bomba.

The Bomba is based on the principle that the random 3-letter message key is sent twice at the beginning of each message and that every now and then, a particular plaintext letter, yields the same ciphertext letter three positions further on.

As an example, assume the indicator is AWB TWY. We see that the letter W occurs twice in the second position. The codebreakers at Bletchley Park would later call such occurencies females. As both letter groups (AWB and TWY) originate from the same plaintext (e.g. ZXS), we know that the letter X is encrypted into W twice with an interval of 3 steps. This is a unique property that can only occur with a limited number of settings.

According to Rejewski, if enough females were found, the Bomba could be used to recover the current Enigma settings in less than two hours.

Although all Bomby were destroyed by the Poles in 1939, just before the German Army invaded Poland, Rejewski made a sketch based on his memories many years later. This sketch appeared in Brian Johnson's book The Secret War in 1978 [1]. An improved version of this sketch appeared in a report of 1979, written by Marian Rejewski himself [2]. This report was provided as an appendix to Władysław Kozaczuk's book W kręgu Enigmy [11] and was translated into English in 1984 [12].

The image on the right 1 shows the improved sketch provided by Rejewski in 1979. The beautiful illustration above was made by the people behind the website and are based on Rejewski's sketch. It gives a good idea of what the Bomba may have looked like.

As the Germans had three different Enigma wheels at the time, there were six possible wheels orders to be considered. This was done by running six bomby in parallel. Each Bomba had 6 full Enigma rotor-sets 2 at its top (1), connected in pairs. Each pair was used to solve one (of the three) females.

Although the exact operation of the Bomba is still unknown, many have tried to explain its principle by reconstructing a theoretical model. A plausible attempt was made by David Link in Cryptologia in 2009 [3].

For the recovery of the Ringstellung, the plug board configuration (Steckerbrett) does not have to be taken into account as it doesn't move during the encipherment. All that matters is that the same input letter produces the same result twice, three steps apart. In [3] Link describes a simple method to solve the Steckern once the wheel order and the Ringstellung have been recovered.

  1. Many thanks to the people of for supplying the beautiful artwork [10].
  2. Only one full rotor set is shown in the image. Click here to see the machine with all six rotor sets installed.

Original drawing of the Bomba by Rejewski
Artist's impression of the Bomba with only one wheel set installed. Image supplied by [10].
Artist's impression of the Bomba with all wheels installed. Image supplied by [10].
Artist's impression of the Bomba with top lid in place. Image supplied by [10].
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Original drawing of the Bomba by Rejewski
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Artist's impression of the Bomba with only one wheel set installed. Image supplied by [10].
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Artist's impression of the Bomba with all wheels installed. Image supplied by [10].
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Artist's impression of the Bomba with top lid in place. Image supplied by [10].

The British Bombe   1939
Turing-Welchman Bombe

Based on the information presented by the Poles, British mathematician Alan Turing developed a machine that was capable of recovering the key settings even if the Germans would drop the double encryption of the message key at the beginning of each message. The machine was called Bombe (later: Turing-Welchman Bombe) and was built by the British Tabulating Machine Company (BTM) in Letchworth, Hertfordshire (UK) under supervision of Harold (nicknamed Doc) Keen [4].

The name was derived from Bomba, a similar machine developed by the Poles shortly before the outbreak of WWII. The Bomba exploited the fact that the same message indicator was sent twice at the start of each message, a major flaw in the German cryptographic procedures.

Although the Bomba concept was known to Bletchley Park, Turing took a different approach. When the Germans had discovered the weakness they gave up the double encipherment of the message indicator on most radio networks on 1 May 1940 1 rendering the Bomba useless [9].

Turing designed the British Bombe in 1939. Compared to the Polish Bomba, it used a completely different approach. It was based on the assumption that a known (or guessed) plaintext, a so-called crib, is present at a certain position in the message. The Bombes were built by the British Tabulating Company (BTM, later: ICL) at Letchworth (UK) under the supervision of Harold 'Doc' Keen [1]. The first machine, called 'Victory', was delivered at Bletchley Park on 18 March 1940.

Shortly afterwards, the Bombe was improved by adding the so-called diagonal board – an invention of fellow codebreaker Gordon Welchman – which greatly reduced the number of steps needed for the codebreaking effort. A second Bombe, with Welchman's diagonal board present, was installed on 8 August 1940. It was named 'Agnus Dei', later shortened to 'Agnes' or 'Aggie'. The first machine (Victory) was later modified with a diagonal board as well.

During the course of the war, over 200 Turing-Welchman Bombes were built. To avoid the risk of losing them in case of a bomb attack, they were spread between Bletchley Park and its so-called Outstations in Wavendon, Adstock, Gayhurst, Eastcote and Stanmore, where they were operated by WRNS, RAF-technicians and civillian personnel [4].

  1. Not for Yellow traffic, as on 1 May 1940, there was a battle going on in Norway. On the Yellow net, the new procedure was introduced on 15 May 1940 [9]. Furthermore, the German Navy kept using doubly enciphered message keys on 6 of its Enigma ciphers until mid 1944 [13].

Enigma M4
Like the German Wehrmacht (Army) and Luftwaffe (Airforce), the Kriegsmarine (Navy) used a three-wheel Enigma machine with Steckerbrett (plug-board). The Navy called it the M3. Unlike the Wehrmacht and the Luftwaffe however, the Navy used additional codebooks for shortening their messages. The shorter their radio broadcasts, the smaller the risk of Direction Finding (DF).

Because Admiral Karl Dönitz, head of the U-Boat section of the German Navy had his doubts, three extra wheels were introduced (VI, VII and VIII), exclusively for the Kriegsmarine. But that wasn't all he changed. On 2 February 1942, completely out of the blue, the German Navy introduced the Enigma M4, a four-wheel machine, exclusively for U-Boat communication. At the same time they changed their codebooks, leaving the codebreakers at Bletchley Park in the dark.

The Enigma M4 had an extra rotor, called the Zusatzwalze (extra wheel), inserted between the 3rd wheel and the Umkehrwalze (reflector). As the Bombe was built specifically for breaking three-wheel Enigma traffic, it was not suitable for attacking the new M4 machine.

Apparently, Dönitz, had managed to defeat the logistic nightmare of replacing all existing M3 machines by the new M4. But as the code was changed overnight, and the rest of the Navy was still using the 3-wheel machine, Turing figured that the machines were somehow compatible.

He turned out to be right. When the 4th wheel was set at 'A', the machine would behave like the old M3. This was done, for example, when communicating with the Naval Weather Service. Furthermore, the 4th wheel never moved during encypherment, making it effectivelty a selector between 26 different reflectors (UKW). Turing soon managed to recover the full wiring of the extra wheel, but was in desperate need for new codebooks in order to read the U-Boat traffic.

In the event it took until 30 October 1942 – nearly 9 months after the introduction of the M4 on 2 February 1942 – before new codebooks were captured. In the meantime, some of the existing 3-wheel Bombes had been adapted for attacking 4-wheel Enigma traffic and orders were given to Doc Keen at BTM for the development of an enhanced Bombe that could handle the 4th wheel.

 More about the British Bombe (off-site)

The American Bombe   1943
Although the British 4-wheel Bombe worked as expected, it faced many problems. At this stage of the war, Great Britain had shortages of nearly everyhing. As a result, BTM was unable to deliver enough machines in time and the machines that were delivered often exhibited contact problems.

Ever since their involvement in the war in 1942, the Americans had been pushing the Brits to share their knowledge about the Bombe and allow them to copy its design. Finally, in late 1942, when the British 4-wheel Bombe was facing production problems and the daily losses in the Battle of the Atlantic were accumulating, the Brits gave in, and allowed the US to build its own Bombe.

The US-Bombe was built by the National Cash Registers (NCR) in Dayton (Ohio, USA), where it was developed by Joe Desch. Initially, the US Navy wanted him to develop a fully electronic machine, but Desch found this to be impractible, as it would require the machine to have more than 70,000 thermionic valves (vacuum tubes).

Towards the end of 1942, Desch proposed a less elegant but more realistic approch: an electro­mechanical machine – similar to the UK Bombe – but much faster and more reliable as well. The US Navy immediately approved the project.

Desch set out to build the machine and had the first prototypes running by mid-1943. Although the initial design faced reliability problems, he managed to improve it considerably. In the end, the US Bombe turned out to be very reliable, fast and effective. By December 1943, 120 machines had been installed. For the remainder of the war, the US managed the breaking of the majority of German Naval Enigma traffic and in particular the messages of the dreaded German U-Boats.

After the war, it became clear that the US Bombe had helped to save thousands of human lives. Unfortunately however, it had destoyed that of Joe Desch – its creator – who suffered a nervous breakdown from which he never really recovered. His daughter – Deborah Anderson – has created a website to honour the work of her father and his collegues at the Navy Section of NCR [7].

After the war, all US Bombes were destroyed, except for one unit which has since become a permanent exhibit a the National Cryptologic Museum (NCM) at Fort Meade (MD, USA) [8].

None of the buildings at the former NCR site in Dayton (Ohio, US) have survived. They were taken down just before NCR moved its head office to Atlanta in 2009. All that reminds us of the highly secret work that was carried out in Building 26 by Joe Desch and his team, is the piece of multi-conductor telephone cable shown above. It was recovered from the demolition site on 25 May 2008 by Tom Perera, and was used during the war to carry the confidential conversations about the design and manufacture of the US Bombe, between the rooms of the secret Navy Section [14].

 More about the Dayton codebreakers (off-site)

Rebuilding the British Bombe   2007
In the UK, all British Bombes were destroyed or dismantled once the war was over. As far as we know, not a single machine has survived. This has triggered a group of enthusiasts - led by John Harper - to start a rebuilding project in the mid-1990s. The aim of the project was to recreate a fully functional replica of a war-time Bombe machine, which was completed in 2007 [5].

The completed machine was on public display for many years at the Bletchley Park Museum as part of the permanent exhibition in B-Block, but was relocated in 2018 to The National Museum of Computing (TNMOC) which is also located at Bletchley Park. It is demonstrated on a regular basis and can break real wartime messages.

The image on the right was taken at the 2009 Enigma Reunion at Bletchley Park, where the Bombe was demonstrated by John Harper. For further information, please visit John Harper's special website of the Bome Rebuild Project [5].

Please note that different versions of the Bombe exist. Furthermore, a number of attachments and 'special versions' were built for specific tasks and experiments. The version reconstructed by the Bombe Rebuild team is the later 3-wheel 36-Enigma version, with high-speed Siemens-type sense relays. During the war, 69 of such machines were built. It is featured in the video below.

This video shows the reconstructed Bombe in action. It was made during the Enigma Reunion at Bletchley Park in 2009, when project manager John Harper was giving live demonstrations. Some of the moving parts inside the Bombe are clearly visible. The video also shows the Checking Machine and a British Typex cipher machine that was converted to act as an Enigma machine.

It is sometimes thought that Enigma was broken with help from Colossus, the first valve-based electronic digital computer, that was developed at Bletchley Park during WWII. It is even claimed in some books and TV documentaries. This claim is not correct however, as Colossus was used to break the far more advanced Lorenz SZ-40/42 cipher machine, that was used by OKW, Hitler's High Command.

 More about Colossus

Bomba   Polish pre-WWII machine for breaking Enigma-encrypted messages.
Bombe   British, and later also American, WWII machine for breaking Enigma-encrypted messages.
BP   Bletchley Park
The United Kingdom's WWII code-breaking centre.  More
BTM   British Tabulating Machine Company
British manufacturer of book-keeping machines. During WWII, also the manufacturer of the British Turing-Welchman Bombe code-breaking machines.  Wikipedia
NCR   National Cash Registers
American manufacturer of cash registers. During WWII, also the developer and manufacturer of the Bombe code-breaking machine for the US Navy.  Wikipedia
RAF   Royal Air Force
The United Kingdom's aerial warfare force.  Wikipedia  Homepage
TNMOC   The National Museum of Computing
British museum about the history of computing, located on the same premises as the Bletchley Park Museum. Also home to the WWII Colossus and Bombe code-breaking machines.  More
WRNS   Women's Royal Navy Service
Women's branch of the United Kingdom's Royal Navy.  Wikipedia
  1. Brian Johnson, The Secret War
    1978, BBC.

  2. Marian Rejewski,
    Mathematical foundations of the German Enigma cipher machine solutions (Polish)

    Rejewski's report of 1979.

  3. David Link, Resurrecting Bomba Kryptologiczna: Archaeology of Algorithmic Artefacts, I
    Cryptologia, Volume 33, Issue 2, April 2009, pp. 166-182.
    ISSN: 0161-1194

  4. John Keen, Harold (Doc) Keen
    ISBN: 0-947712-42-9

  5. John Harper, The Bombe Rebuild Project
    Website, showing the progress and the various stages of the project.

  6. Milton Keynes Heritage Association, Outstations from the Park
    Retrieved November 2012.

  7. Dayton Codebreakers, US Navy Cryptanalytic Bombe
    Website by Deborah Anderson.

  8. National Cryptologic Museum (NCM)
    Based in Fort Meade (USA) near the NSA building.

  9. Ralph Erskine and Gilbert Bloch, The Dropping of Double Encipherment
    Cryptologia 10(3), 1986, pp. 134-141.

  10. International Cryptology Game, Artist's inpressions of Bomba and Cyclometer
    Website: Received June 2016.

  11. Władysław Kozaczuk, W kręgu Enigmy
    1979.  Translated into English in 1984 [12].

  12. Władysław Kozaczuk, Enigma: How the German Machine Cipher Was Broken,
    and How It Was Read by the Allies in World War Two. 1
    Translated from [11] and edited by Christopher Kasparek.
    30 June 1984. ISBN 978-0-31327-007-9 (first edition).
    US edition: ISBN 978-0-89093-547-7 (2nd edition).

  13. Ralph Erskine and Philips Marks, Naval Enigma:
    Seahorse and other Kriegsmarine Cipher Blunders
    Cryptologia 28(3), 2004, pp. 211-241.

  14. Tom Perera, Piece of original NCR multi-conductor telephone cable - THANKS !
    Recovered from the demolition site. With certificate.
    Dayton, Ohio, USA. 25 May 2008.

  15. National Security Agency (NSA), Photograph of US Bombe in use
    Undated, but probably 1943/44.
  1. Not te be confused with Enigma - How the Poles broke The Nazi Codes, which is basically a subset of the 1984 book in which Rejewski's contributions have been replaced by (less important) material by others.

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