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    • br Enigma cipher machine With these working principles the N

    2018-10-22


    Enigma cipher machine With these working principles, the NTM is essentially isomorphous with the Enigma machine (Scherbius, 1928; Fischer, 2012) which was used to encipher and to decipher communications in Nazi Germany before and during World War II (this relationship between NTM and Enigma machine was previously suggested by Tessmann, 2008, p. 55). Looking somewhat like a typewriter, the Enigma machine was used to encrypt and to decrypt text messages by substituting letters with a replacement mechanism that changes systematically as the machine is used. It takes its input via a qwertz keyboard (label 1 in Figure 3) with typically 26 keys, and offers its output via typically 26 lamps which are also arranged in a qwertz layout (label 12 in Figure 3). Pressing any key closes an electrical circuit which travels across a set of cylindrical rotors each of which contains a different irregularly-connected wiring, leading to the illumination of a lamp with a different letter. Before it closes a circuit each keystroke also results in the change of the internal state of the machine by way of rotating one or more of the rotors by one twenty-sixth of a full rotation so that the combined irregular wiring changes for each letter that is enciphered or deciphered. Additionally, a plug board allows the swapping of pairs of letters using patch cables. Much like von Foerster׳s NTM, the Enigma machine translates input characters to output characters, with every synthase resulting in a re-mapping of the set of accepted input characters to the set of available output characters. The Enigma machine demonstrates that the NTM is implementable as a physical device, which is very challenging to determine analytically from the perspective of an external observer. Pressing a key will activate one of the lamps, apparently at random, according to selection of cylinders and their current orientation. Additionally, each keystroke results in the rotation of the first cylinder by one of 26 rotation positions, after 26 keystrokes, the second cylinder will also rotate by one position and so forth, somewhat in the fashion of the digit cylinders in a mechanical odometer. Thus, each keystroke results in a new wiring between keyboard and lamps coming into effect for the subsequent keystroke. In other words: use of the machine leaves a trace in it, changing the wiring of the machine, and hence the cipher, progressively. (Due to the symmetrical setup of the wiring going into the cylinders and back out through the same cylinders, the same machine setup can be used both to cipher and to decipher. The identical setup is achieved by referring to a secret timetable based code book of which both ends must hold a copy.) To an outside observer the input-to-output mapping of the Enigma machine is extremely difficult to determine, while it is perfectly determinable to those who developed it and who have a good understanding of its setup and inner workings. With inner workings of this kind the Enigma machine shares key characteristics of designing, making it a useful metaphor for the purpose of showing how designing is a relatively straight-forward process when viewed from the inside perspective but mysterious and wonderful when viewed from the outside perspective.
    A typographical metaphor The illustration presented here is a piece of software predicated on the Enigma machine and implemented as a VBA script controlling Rhino3D. Glyph renderings of characters input via keyboard are distorted dynamically and individually, with the use of a “private key” string stored inside the system. Somewhat akin to the (de)ciphering process of the Enigma machine, each key that is typed, modelled, transformed and rendered changes the internal state of the system (leaves a trace in it) to change the way the following glyph is distorted. In contrast to common computer typefaces, glyphs of same characters are unpredictably variant. As a point of departure, the system uses the typeface Helvetica to derive initial glyph outline curves for each typed character. The system then applies a combination of six (Thompson, 1992) transformations (see Figure 5) to these outline curves.