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Dongzu (Aidan) Lee 1 ANNOTATED BIBLIOGRAPHY1 Primary Sources Dongzu (Aidan) Lee ANNOTATED BIBLIOGRAPHY1 Primary Sources Papers Turing, Alan. “Turing’s Treatise on Enigma.” (1939 - 1942) US National Archives and Records Administration. https://www.archives.gov/files/press/press-releases/2015/images/turing- enigma-treatise.pdf This paper had been written by Turing between 1939 and 1942 while working at Bletchley Park, but it had been classified for many years after the war by the British government; only in 1996 it became declassified. It is most informative on how Turing structured and manipulated input and algorithm in such ways as to maximize production of “contradictions” - for the purpose of skipping them - in Bombe, a computing machine he devised to deduce “rotor settings” from a given Enigma-encrypted message. What is the meaning of contradiction in Bombe? How to understand it best? A sign. An indication. An extra layer of information which neither True nor False solely as the answer(output) could deliver. Because of the way Bombe was set up, it communicated a unique meaning, and that was contradiction’s greatest use in Bombe. In the world of logic, contradiction often results from an inverted (i.e. up-side-down) self- inference such as in: “This statement is false.” (i.e. If it is true, it must be false, and if it is false, it must be true.) In the physical universe, a bridge may fall down if contradiction is present, because it means we have not fully thought out everything. In the world of Bombe, however, contradiction simply means randomness resulting from factors beyond the input – such as the rotor settings. Why? Simply because Turing programmed Bombe so, to signal certain useful meaning by way of contradictions. The most informative part of the Treatise is Chapter 6, titled “The steckered Enigma. Bombe and Spider.” It is easy to fear Primary Sources, especially papers, as too challenging, and to resort to Secondary Sources for understanding. But Primary Sources often show us something no Secondary Sources can: chronological development of ideas. Secondary Sources give us only the completed final picture, which is a bit similar to seeing a movie’s ending first, with everything mixed in between. Seeing the thought process as it happens can be valuable. Understanding what came in response to what, and why something was necessary at that time can provide crucial missing pieces. I note just three such points: 1. I learned that Turing too was following Rejewski’s approach at first - in avoiding the Plugboard [i.e. Stecker] problem by divorcing it completely rather than using some of its constraints to his advantage as he did later, especially with help of insights from Welchman: “From this picture we see that one characteristic which is independent of the Stecker is 1 Within each category, I have tried to list each entry loosely (i.e. not always, especially for categories such as Wikipedia) in the order of importance in making my website. 1 Dongzu (Aidan) Lee that there must be a letter which enciphered at either position 2 or position 5 of the crib gives the same result … In order to apply the multiple encipherment condition one naturally wants to be able to perform the multiple encipherments without Stecker in one operation.” But later he states: “In our original description of the Bombe we thought of it as a method of looking for characteristics of a crib which are independent of Stecker, but in the last section we thought of it more as a machine for making Stecker deductions. This last way of looking at it has obviously great possibilities, and so we will start afresh with this idea.” 2. Rejewski’s Cyclometer left many traces on Bombe: “If one has two of these ‘Letchworth Enigmas’ [i.e. Enigma only with Rotors, without the Plugboard] one can connect the output points of the one to the input points of the other and then the connections through the two Enigmas between the two sets of contacts left over will give the effect of successive encipherments at the positions occupied by the two Enigmas. Naturally this can be extended to the case of longer series of Enigmas, the output of each being connected to the input of the next. Now let us return to our crib and see how we could use these Letchworth Enigmas. For each of our ‘chains’ we could set up a series of Enigmas.” These were exactly Rejewski’s technical ideas behind Cyclometer – generating cycle of chains, closed loop created by feeding input to output and output to input among multiple Enigmas! Only that they differed in purpose: Cyclometer was for building a catalogue, or a complete world of possible truths, whereas Bombe was for discarding what was impossible from what was assumed to be true (i.e. cribs). 3. Often we fail to notice enormous contributions made by “hardware” makers; we tend to think engineering and manufacturing as relatively easy. In the case of Bombe, “algorithm’ was installed not as software. It was the hardware itself – arrangements of the drums, discs, wires and relays constituted its algorithm! Turing makes it very clear that Mr. Harold Keen, the manufacturer of Bombe, was much more than an engineer who followed Turing’s designs; Keen himself was an innovator. At the time there were neither semiconductors nor vacuum tubes (as least not common), Keen achieved making machines that behaved as if following software instructions – in the span of a few months! I had wrongly thought the idea of automatically moving onto the next rotor position in response to contradiction indication (a crucial feature in automation) was Turing’s. Turing gives the entire credit to Keen: “It is therefore necessary to have some arrangement by which immediately after the spider stops the point of entry of the current is altered to the point to which the relay which closed was connected, or is left unaltered in the case that 25 relays closed. Mr. Keen has invented some device for doing this, depending entirely on relay wiring. I do not know the details at present, but apparently the effect is that the machine does not stop at all except in cases in which either just one relay closes or 25 relays close.” Turing, Alan. “On Computable Numbers, with an Application to the Entscheidungsproblem.” Proceedings of the London Mathematical Society, 2 Received 28 May, 1936.- Read 12 November, 1936. https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf I relied on Wikipedia and YouTube to understand this paper, because it was very difficult 2 Dongzu (Aidan) Lee to understand. Nevertheless, it was important because of the way Bombe may fit into Turing’s world of ideas, before and after Bletchley Park. Surely Bombe could not have appeared out of the blue; it must have been related to something that came before. I think Bombe was one specific way to implement Turing’s conceptual framework on computer. Turing, Alan. “Computing Machinery and Intelligence.” Mind, Volume LIX, Issue 236, October 1950, pp. 433–460. https://academic.oup.com/mind/article/LIX/236/433/986238 This is Turing’s paper on AI, published 10 years after Bombe (in 1950). Turing is no longer asking what computer can or cannot do, or if we can create a computer for universal tasks; he is asking whether we can distinguish between human and computer, offering his famous test - if we can't determine which party is the computer after conversation, the machine can be said to think like a human. “Cribs” might have inspired Turing’s thoughts on AI, since they are precisely the type of work best suited to AI. Rejewski, Marian. “How Polish Mathematicians Deciphered Enigma.” IEEE Anals on the History of Computing, Vol.3., No.3. (July 1981) http://chc60.fgcu.edu/images/articles/rejewski.pdf Rejewski wrote this paper many years after his groundbreaking work, based on recollection of how the Poles broke Enigma. Through remarkable insights and ingeniousness, Rejewski was able to observe certain unique characteristics - such as identically shaped sets of cycle-lengths that are present – resulting from the Enigma Protocol and tracked them. Rejewski, Marian. “Mathematical Solution of the Enigma Cipher.” Cryptologia, vol. 6, no. 1, 1982, pp. 1–18. (Translated by Christopher Kasparek) https://web.archive.org/web/20141030213141/http://cryptocellar.web.cern.ch/cryptocellar/ Enigma/rew80.pdf In addition to showing Cyclometer, Rejewski shows how Henryk Zygalski invented perforated sheets that showed relative placement characteristic of female per each rotor position. Using razor blades, Poles punched holes for each rotor position that would produce female. They would pile these on top of each other, staggered in manners corresponding to the observed relative positions of the females. Patents Scherbius, Arthur. “Enigma Patent.” Cipher Machines and Cryptology. (See below) http://users.telenet.be/d.rijmenants/en/enigmaproc.htm Scherbius died from an accident in 1929, leaving the possibility on how he might subsequently have improved Enigma into a historical guess. News New York Times. “Germany Seeks an Alliance against Us; Asks Mexico and Japan to Join Her; Full Text of Her Proposal Made Public.” March 1, 1917. https://www.mentalfloss.com/article/92771/wwi-centennial-america-outraged- zimmermann-telegram 3 Dongzu (Aidan) Lee Kirby, Rollin. “Exploding In His Hands.” The World. March 3, 1917. https://www.eurasiareview.com/24052017-1917-the-year-of-the-century-analysis Telegrams Zimmermann, Arthur. “Zimmermann Telegram.” Intercepted from 2nd from London #5747 https://mediarichlearning.com/media-vault-zimmermann-telegram/ Zimmermann, Arthur. “Zimmermann Telegram.” Deciphered from 2nd from London #5747 https://mediarichlearning.com/media-vault-zimmermann-telegram/ Videos Breaking The Codes. Documentary film directed by Norman de Lacy Evans. 2:23:00. 2009, London. DigiComTV, 2009.
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