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Cracking Enigma, a (Short) Summary of the Past

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Cracking Enigma, a (Short) Summary of the Past Cracking Enigma, a (short) Summary of the past Jens Hubrich Technische Universitat¨ Kaiserslautern, Embedded Systems Group j [email protected] Abstract This paper is focused on the Enigma I or ‘Wehrmachtsenigma’. After a short introduction giving the relevance of ciphering, the historical background of Enigmas will be described. Following the his- torical background, the mechanics and functionality of the whole Enigma machine and its separated parts(Rotors, Reflector, Plugboard) is examined. Once the mechanics are clear, the usage by operators is explained and the theoretical cryptographic strength of enigma is calculated. This Part of the work ends with a overview of the Enigma versions important to German military during Word War Two. The second part of this work is related to ‘Cracking Enigma’, the protagonists and some of their methods used to break the encryption of Enigma. In first focus the work of Marian Rejewski, who revealed the internal wiring of the Enigma and then the one of Alan Turing which is probably the most famous person in this process with his ‘bomb’. In the end a short look at modern methods to break still unbroken messages with today technologies is given and in the conclusion it will be discussed which of the given Enigma problems are still relevant in nowadays cryptography. 1 Introduction Since early mankind keeping informations secret is one of the main keys in military and commercial structures. Since the exclusive knowledge is a big benefit. Of course it is the same way beneficial to gain such secret knowledge. After Edward Snowden leaked secret documents, which lead to the NSA-scandal in 2013, the topic of secure communication became a widely discussed topic in public domain again.[9] During the time of WWI (World War One, 1914-1918) ciphering secret messages was done primarily by manual en- and decoding. Therefore, cryptographically strong methods needed a lot of time and their handling was pretty difficult. For more information about WWI cryptography see [7] or [16]. Around the end of WWI multiple companies and inventors developed machines to reduce the effort of ciphering drastically. For example Edward H. Hebern in the USA [26], [25], [24] or Ingenieursbureau (engineering office) ‘Securitas’ from Amsterdam [27]. The probably most famous kind of those ciphering machines was ‘Enigma’, which is the Greek word for riddle. They are known for their key role as main en- and decryption tool of German military during WWII (Second World War 1939-1945). The next section will give a brief history about the Enigma, explain the mechanics behind it, list the different Models produced, and a assumption about its cryptographic strength. 2 2 Enigma The Enigma machines were a series of electro-mechanical rotor cipher machines invented by Arthur Scherbius. He and E. Richard Ritter founded a firm called ‘Scherbius Ritter’ and submitted a patent for a ‘Chiffrierapperat’ (German for: ciphering machine) at 23th Feb. 1918[22]. During the late days of WWI they tried to offer the idea to the German navy, which refused. As consequence they transferred the patent to ‘Gewerkschaft Securitas’. And as a next step they of- fered the machines as commercial product to companies, banks, and everyone else who could have an in- terest in secure communication.[15] Therefore the ‘Chiffriermaschinen-Aktiengesellschaft’ was founded at 9th July 1923 with Scherbius and Ritter as directors.[19] (Which also is a good recourse for further information about the commercial history) However, the interest of the German military awakened quickly after publications like Winston Churchills ‘The world Crisis’[4] showed clearly that the manual methods used during WWI were broken and no longer provide any acceptable security. After a short test period of two years military decided to use the Enigma for secure communication in 1928 and the civil sale of the machines was stopped. Just one year later, in 1929, Scherbius died in an accident, short before the Enigma mass production was started. And in 1934 Rudolf Heimsoeth and Elsbeth Rinke took over the ”Chiffriermaschinen- Aktiengesellschaft” and went on to produce and develop the Enigma machines in their new firm ‘H&R’. As mentioned in section 1 the Enigma became the main en- and decryption tool of German military during WWII and was a huge advantage over other military forces, but when it was broken, it turned into the biggest drawback. This work will focus on the Enigma I or ‘Wehrmachts’ Enigma, since it was the most commonly used model during WWII and includes all concepts other models were based on. The following subsection will explain the mechanical principles which were used in Enigma machines. 2.1 Mechanics The Enigma were typewriter similar, electro-mechanical, rotor based cipher machines. The base parts were a keyboard (German: ‘Tastenfeld’), a set of rotors (German: ‘Walzen’), and a output in form of a lampboard (German: ‘Lampenbrett’). The Figure 1, taken from the original Patent of Scherbius [22, p. 4], shows the basic idea behind the ciphering machine Enigma (and all other rotor based ciphering machines). By pressing a key (a. f) current is passed to the connector (1) which lead it trough the rotors (2a,2b). The first rotor permute the input letter and hand the permutation to the next rotor were another permutation is applied. The connector (3) lead the result finally to the lampboard (A . F). At this point encryption would be done by just a simple static permutation of the signs. To Change that, the rotors rotate after each keystroke, so similar following signs are exchanged by different signs. E. g. : Input AAA, output: RGT. In the first version the rotation was established by separate gears and could be set with external handles. 2.1.1 Rotors: ‘Walzen’ The rotors are the main part of any rotor based cipher machine. At the first models, as mentioned in subsection 2.1, the rotors were permutations only and rotated by additional gears. The military versions 3 (a) encryption (b) decryption Figure 1: Schematic of the ciphering machine. It shows a Keyboard (a . f), Lampboard (A . F), two rotors (2a,2b), Connectors (1,3) and a switch to change between en and decoding (4) Source: Patent [22, p. 4] had the rotation mechanics, integrated in each single rotor. During German army used five different rotors, the naval had a additional one and even increased the number to eight during the war. Those rotors were labelled by Greek numbers I-V for Army and VI-VIII for the additional naval ones. The main part of each rotor are the criss-cross connections between the contacts on both sides which are visible in Figure 2. This connections are the base permutations of each rotor. Figure 2b shows the notch (besides letter D), which is used to rotate the next rotor once per full rotation of this one, later versions of rotors had two notches. The turnovers, which were inducted by the notches, were different for most rotors as shown in Table 1, taken from [2, p. 113]. Rotor Turnover at I R II F III W IV K V A VI, VII and VIII A and N Table 1: Turnover positions of the German military rotors as listed in [2, p. 113] The letters written on the ring are used to define the starting orientation of each rotor by the operator. To increase the security in later development, a co-worker named Bernstein made the ring adjustable so the rotor position could be changed relative to the ring letters.[14] The ‘Wehrmachts’ Enigma could fit 3 rotors, the naval version was able to fit a fourth non rotating 4 (a) right side of a rotor (b) left side of a rotor Figure 2: Rotors of Enigma Model ‘Wehrmacht’. Source: https://commons.wikimedia.org/wiki/File:Enigma_rotors_and_spindle_showing_contacts_rachet_and_notch.jpg , 12:23 23.07-2018 In (a): Contacts per letter, dark gear to turn the rotor, and metal blade to set the orientation by operator. In (b): Contacts per letter, (letter) ring, and notch (at D) which turns the next rotator additional rotor of 2 versions labelled with a or g. 2.1.2 Reflector: ‘Umkehrwalze’ In 1926 a Patent [23] handed in by the ‘Chiffriermaschinen-Aktiengesellschaft’ was describing a Enigma Model which didn’t need a switch to change the wiring between en- and deciphering, as it was shown in Figure 1. The base idea behind it was introduced by Willi Korn, another Employee of ‘Chiffriermaschinen- Aktiengesellschaft’. A reflector drum (German: ‘Umkehrwalze’) Figure 3b, was placed after the last, most left, rotor. It’s internal wiring feed the output of the rotors back into themselves as schematically shown in Figure 3a. (a) Schematics of 3 rotor (1,2,3) Enigma, with reflector (4) (b) Picture of where (5) is the entry connector. Original Reflector Figure 3: Reflector, ‘Umkehrwalze’ Sources: (a): Taken from Patent [23, p. 5] / (b): https://commons.wikimedia.org/wiki/File:EnigmaReflector.jpg, 7:30 24.07.2018 The expected benefits of the reflector were a more easy handling of the machines, since it was not possible anymore to use a wrong mode (en- or decrypt) by mistake and a increase of the security by using each rotor twice.[23, p. 1] 5 During the first benefit is obvious true, the second one will be later known as one of the biggest drawbacks of the military Enigmas: Due to the electrical circuit issued by the reflector it became impos- sible to encrypt a letter with itself, since it would cause a short circuit. This made the whole system self reciprocal. There were three different reflectors labelled with A,B, and C. But usually they did not get changed in years.
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