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Enigma and Its Decoding

Table of Contents
  1. Introduction
  2. Enigma’s system
  3. Polish Contributions
  4. Bletchley Park
  5. Conclusion
  6. References

Introduction

With the advent of telegraph and radio communications in the XX century, the interception of messages became commonplace. At the same time, the complexity of ciphers and volumes of correspondence significantly increased the risk of errors during encryption. The story of Enigma and its decoding might be among the essential aspects regarding the Second World War. In this paper, the principles of Enigma’s coded messaging, as well as its decrypting by the Polish and Bletchley Park, will be discussed.

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Enigma’s system

After World War I, it became clear that the encryption and decryption operations needed the help of specific machines. In the early 1920s, in Germany, cryptologists used the first multi-alphabet replacement machines with a vast number of alphabets. Arthur Scherbius, co-owner of a German engineering company, created the famous Enigma (Sigmon and Klima n.d.). It was a cryptographic machine, the basis of which was made up of rotors; usually, there were three or four of them.

A rotor, or a contact wheel, is a disc made of hard rubber or plastic, hollow inside. On each side of the disc, there were 26 electrical contacts. Each contact on one side was connected by an internal wire to contact on the other side. The contacts corresponded to 26 letters of the Latin alphabet, and such a connection mechanically carried out a simple replacement code (Rejewski 1981). An electric pulse arriving at the contact of one side was transmitted to the contact of the other side connected to it.

If an impulse arrived on the right side, then it was transmitted to the contact of the left side, that is, the letter a was encrypted as d, and the letter b as z. However, if the rotor along with the contact wires was rotated, say, by one division, then the contact names would change. Now, the first wire would translate not the letter a to d, but the letter b to e, the second – not the letter b to z, but the letter c to a, and the same would happen with all the replacements (Sigmon and Klima n.d.). With a shift by another division, the third one, there were 26 different replacement ciphers. If desired, they could be written in a table of size 26×26, where the internal wiring of the rotor would determine the first row.

Replacement ciphers became much more than 26 if several rotors are connected; the three-rotor machine already generated 26x26x26 alphabets. Enigma, in addition to moving disks – rotors, also used a reflector – a fixed disk (Dooley 2018). The reflector had contacts on only one side, and these 26 contacts had internal pairwise connections, forming 13 pairs. There was another fixed disk – the input wheel; it communicated between the first rotor and input-output devices (Dooley 2018). These were a keyboard on which someone typed text, and a panel with light bulbs, on which was the highlighted letter obtained as a result of encryption.

The letters of the alphabet had a mark on the rims of the rotors, which made it possible to determine and establish the relative position of the rotors. The change of the cipher alphabet took place after entering each letter according to the principle of rotation of the counter wheels as follows. The rotor turned one division; if the first rotor made a full circle, the second rotor rotated by one division; if the second rotor made a full circle, the third rotor rotated by one division (Sigmon and Klima n.d.).

Due to technical peculiarities, there were about 17000 different replacement ciphers. Furthermore, there was a symmetrical system in Enigma: if the letter a, when encrypted, turned into the letter x, then the letter x, with the same installation of wheels, turned into a. Thus, for decryption, it was necessary to set the machine to its original position and type encoded text; the light bulbs were restoring a sent message.

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Not a single letter with this encryption could turn out to be its own code (the letter a never could be the letter a). This well-known feature played a role in the fact that Enigma ciphers were possible to decrypt during the Second World War (Welchman 1986). During decoding, the British used the findings of Polish cryptologists that Britain obtained in 1939. Alan Turing, the brilliant English mathematician, led decrypting processes (Central Intelligence Agency n.d.). Moreover, a whole scientific center – the British school of codes and ciphers, located in Bletchley Park in Oxfordshire – governed the work.

Polish Contributions

The German army introduced machine codes in early 1928, and Polish intelligence immediately began to work on them. Over the next four years, the future-famous Cipher Section, which decrypted over 100 ciphers during the Polish-Soviet War, faced many fails (Oleksiak 2014). In 1932, it became clear that there were not enough resources to solve the German machine ciphers. Poland decided to arrange courses on decrypting codes for plenty of students and scientists to identify talented decoders.

Enigma settings – that is, the starting position of rotor wheels and the configuration of the patch panel – altered regularly, typically daily. With this approach, decoding Enigma messages was almost impossible, even if decoders unraveled the day code (Johnson 2018). In order to transmit the message to the addressee, the addresser had to forward a key message. The latter consisted of encrypted letters seeable in the starting settings of the rotor. A cryptologist had to enter the key twice to avoid errors.

Rejewski soon noticed a weak spot; first, the keys were identical for all messages throughout the day. In addition, unscrupulous operators very often chose the most straightforward keys, for example, AAA, ZZZ, or QAY (Oleksiak 2014). The analysis of encryption allowed reducing the number of indicator settings and starting cataloging. Rejewski invented the machine called a cyclometer, which did it mechanically. He had prepared the catalog by 1936; it had been working fine until 1937 (Oleksiak 2014). At the end of 1937, the Germans realized that something had gone wrong, and changed the encoding method, as a result of which Rejewski’s approach was useless.

After Rejewski failed, his colleague provided a solution – Henrik Zygalski invented “Zygalski sheets,” which were based on the repeatability of characters in a key message. Having developed special perforated sheets, Zygalski was able to trace the indicator settings and the daily key (Johnson 2018). Rejewski was delighted with this method (albeit not automatic) and was forcing the operators to find the right combination. Cryptologists had to check the settings one by one on Enigma’s replica, and if there was no success, this process could take quite a while. The War was approaching, and the Cipher Bureau realized that it needed something faster and more effective.

Rejewski created a machine that he named as a cryptological bomb. It was an electromechanical device based on Zygalski’s idea: to trace duplicate letters in key messages (Rejewski 1981). Oleksiak (2014) claims that the name “bomb” probably arose from a ticking sound that this device made during the operation, reminding its creator of the bomb. The bombs were highly effective: they were fast and accurate.

Nevertheless, the Cipher Bureau understood that relations between European countries were escalating. Experts in Germany could soon investigate and realize that the opponents decrypted their code again. On September 15, 1938, the German army again improved the Enigma device by adding two additional rotor disks; it complicated the decryption process for ten times (Oleksiak 2014). And although Rejewski quickly figured out the internal circuitry for connecting new rotor disks, deciphering daily keys became much more difficult.

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At the same time, political tension grew – in April 1939, Germany unilaterally severed the Polish-German non-aggression treaty. It prompted the Polish Bureau of Ciphers to share their best practices with allies: France and the UK (Johnson 2018). Prior to this, the head of the Polish army sent decrypted messages to partners but did not disclose the decryption method, fearing counterintelligence. Poland promised to France and Great Britain that it would reveal the findings. Then, Polish experts provided them with copies of the military variant of Enigma and a method of decrypting the codes and solving the problem of possible code modifications.

Bletchley Park

Bletchley Park might be among Britain’s most significant achievements of 1939-1945. In 1938, due to its advantageous location at the intersection of major roads, railways, and telegraph lines, the M16 secret intelligence service acquired it for the case of evacuation from the capital (Bletchley Park n.d.). On the eve of the Second World War, decoders came there under the guise of a hunting company. It was not surprising that Bletchley Park had a chaotic organization that, nevertheless, worked (Grey and Sturdy 2010). Managers recruited specialists of the broadest profile: mathematicians, linguists, chess players, Egyptologists, and champions for solving crossword puzzles.

By the time the Poles showed the British their decoding machine, it was already more or less useless. The Germans added two more rotors to their car and connected two more patch panels. Alan Turing and his team began working on a more sophisticated machine called the Bombe, which could decrypt messages from the updated Enigma. In particular, these were orders for the navy to monitor the regrouping of submarines that destroyed British convoys (Wright 2016). Bombe used a variety of weaknesses in Enigma’s coding, including the fact that the Germans continuously used the same phrases in their messages. By August 1940, Turing obtained two working Bombes that decrypted about 200 encoded messages (Copeland n.d.). By the end of the War, the British built about two hundred machines.

Bombe was an electromechanical device with relays as switches and rotors, and not an electronic device on lamps and electronic circuits. But the next machine designed at Bletchley Park, the Colossus, was more sophisticated (Copeland n.d.). The necessity for Colossus took place when the Germans began to code essential messages. For example, these were the orders of Hitler, who applied an electronic digital machine that used a binary system and twelve rotors of unequal size. The electromechanical Turing’s Bombes were powerless to decipher such messages; they needed devices with high-speed electronic circuits.

It should be mentioned that the team of Max Newman was responsible for solving this problem. Newman’s appointed his partner in electronics and electronic lamp specialist, Tommy Flowers, as a technical supervisor (Copeland n.d.). Turing was not part of the Newman’s team but came up with a statistical approach that was able to detect any deviations from the uniform distribution of characters in the stream of ciphertext.

As a result, they built a machine that could scan two rolls of perforated paper tape and compare all possible changes in two sequences. They named the computer as “Heath Robinson” (Copeland n.d.) – in honor of the British cartoonist who loved to portray complex, but meaningless mechanical devices.

For almost a decade, Flowers has been passionate about designing electronic circuits on lamps – valves. He created an experimental system that used more than three thousand lamps to control the connections of thousands of telephone lines. He was the first to use electric lamps for data storage. Turing offered to invite Flowers to help make the Bombes and then introduced him to Newman. Flowers figured out that the only option to decrypt German encoded messages quickly was to try to save at least one of them in the internal memory of the device. Such a memory would require the use of about 1,500 electric tubes.

Initially, the leaders of Bletchley Park were skeptical, but Flowers insisted, and in December 1943, he completed the first version of Colossus. By June 1, 1944, the team created a bulkier version, using more than 2000 electronic tubes (Copeland n.d.). O’Regan (2018) states that the first decoded intercepted message said that Hitler did not send additional troops to Normandy. It confirmed information from other sources already received by General Dwight Eisenhower, who was about to begin the invasion of Normandy.

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Conclusion

In conclusion, it seems reasonable to claim that Enigma was a machine that could serve as a foundation of Germany’s victory in World War II. However, Polish contributions and the further achievements of Bletchley Park turned this advantage into a weakness. It might be assumed that the mentioned decoders created the primary prerequisite of Nazi’s loss in the War and the further development of computing systems.

References

Bletchley Park. n.d. “Our Story – Bletchley Park.”. Web.

Central Intelligence Agency. n.d. “The Enigma of Alan Turing.” Web.

Copeland, Jack. n.d. “Colossus: The First Large-Scale Electronic Computer.” colossus-computer. Web.

Dooley, John. 2018. “Battle Against the Machines: World War II 1939–1945.” In History of Cryptography and Cryptanalysis. History of Computing, 151–165. Cham: Springer.

Grey, Christopher and Sturdy, Andrew. 2010. “A Chaos that Worked: Organizing Bletchley Park.” Public Policy and Administration 25(1): 47–66. Web.

Johnson, Roger. 2018. “How Three Poznan University Students Broke the German Enigma Code and Shortened World War Two.” Paper presented at the First IFIP International Cross-Domain Conference, IFIPIoT 2018, Held at the 24th IFIP World Computer Congress, WCC 2018, Poznan, Poland.

O’Regan, Gerard. 2018. “Colossus and Code Breaking at Bletchley Park.” In The Innovation in Computing Companion, 81 – 85. Cham: Springer.

Oleksiak, Wojciech. 2014. “The Hacker Who Saved Thirty Million Lives.” Culture.pl. Web.

Rejewski, Marian. 1981. “How Polish Mathematicians Deciphered the Enigma.” Annals of the History of Computing 3 (3): 213 – 234.

Sigmon, Neil and Klima, Rick. n.d. “The Turing Bombe and its Role in Breaking Enigma.” Asian Technology Conference in Mathematics. Web.

Welchman, Gordon. 1986. “From Polish Bomba to British Bombe: The birth of ultra.” Intelligence and National Security 1(1): 71–110. Web.

Wright, John. 2016. “The Turing Bombe Victory and the first naval Enigma decrypts.” Cryptologia 41(4): 295–328. Web.

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