History of Cryptology

By cross-referencing Dutch and German archives, this chapter details the decades-long efforts of varying groups of people in the German hinterland to claim the inheritance of the slave trader Hendrik Hertogh of the Dutch West India Company (WIC) in the second half of the eighteenth century. In doing so, it is argued that the work of people (mediators or brokers) bridging the knowledge gaps of the prospective heirs was crucial in connecting them to a globalizing world. “The global” was presented to people in the German hinterland as an opportunity to become wealthy, which they tried to exploit, though in this particular case, they ultimately failed.

George Boole (1815-1864) is rightly known as a logician, the author of an algebra of logic, even if he did not conceive it quite in the same way as we know it. The calculus on classes and the calculus of propositions, that he set out to be equivalent, were at the core of his algebra of logic. After more than twenty centuries where logic was associated to the analysis of language, it was handled for the first time with mathematical symbols. However, the known Boole's algebra is not the one Boole produced. In this paper, I would like to move apart from the classical recurring approach to history -often referred to as Whiggist -, and to contextualize Boole's work so as to brighten the main trends which guided this renewal of how to deal with logic. Boole was also a mathematician, and since his Mathematical Analysis of Logic (1847), his work was very close to the symbolical way of thinking algebra, as it was developed in Cambridge by "The Analytics" in order to found usual algebraic practices. An Investigation on the Laws of Thought (1854) enunciated a more systematic view of this project for logic, devised as a whole system, facing what was at stake for the theory of knowledge with the strong rise of experimental sciences. Clearly, Boole wanted to stand out from empiricism, and from metaphysics as well, and to maintain an absolute meaning to formal sciences. And I will scrutinize his philosophical references so as to precise how his enterprise answer these issues, relating to necessary reasoning, and to probable reasoning as well.

This paper provides an overview of the practice and use of codes in the Arabic-Islamic context while reintroducing a Qurʾān manuscript housed in the Kitābkhāna-yi markazī Āstān-i Quds-i Raḍawī (Mashhad, Iran), known for being written in the socalled Bāburīkhaṭṭ (Bābur's script). The manuscript, attributed to the hand of Ẓahīr al-Dīn Moḥammad Bābur Shāh (886-937/1438-1530), is discussed in connection with the tradition of Arabic encrypted texts and treatises, as well as with Bābur's autobiography (Bāburnāma), which mentions the use of a specific coded script. Moreover, the link between plain/coded texts and literacy is considered, as well as the connection between Arabic medieval chancery habits and modern oral/slang practices (Fr. verlan). Finally, the phenomenon of the encrypted Qur'anic texts is viewed in the context of the Ahl al-kitāb manuscript production of sacred scriptures.

We examine Turing's intriguing claim, made in the philosophy journal Mind, that he had created a short computer program of such a nature that it would be impossible "to discover by observation sufficient about it to predict its future behaviour, and this within a reasonable time, say a thousand years" (Turing, 1950, p. 457). A program like this would naturally have cryptographic applications, and we explore how the program would most likely have functioned. Importantly, a myth has recently grown up around this program of Turing's, namely that it can be used as the basis of an argument-and was so used by Turing-to support the conclusion that it is impossible to infer a detailed mathematical description of the human brain within a practicable timescale. This alleged argument of Turing's has been dubbed "Turing's Wager" (Thwaites, Soltan, Wieser, Nimmo-Smith, 2017, p. 3) We demonstrate that this argument-in fact nowhere to be found in Turing's work-is worthless, since it commits a glaring logical fallacy. "Turing's Wager" gives no grounds for pessimism about the prospects for understanding and simulating the human brain.

Heretofore, scholarly literature devoted to the earliest, Polish portion of the world history of the Enigma did not leave room to any doubt. Apart from three instances of decryption which were found among the materials of the study centres left in Warsaw the machine cipher which was used by the Wehrmacht was broken by the Cipher Bureau of the Second Department before September 1939. The security service of the Third Reich had at their disposal almost the complete set of documents of the Polish intelligence, conducting therein comprehensive queries for a few years focused also on the pursuit of the documents of encrypting cells of the General Staff. The results of the investigation conducted by German archivists and counterintelligence where unambiguously negative. The three instances of decryption which were found in Warsaw were considered an exceptional case in Berlin, an instance of a casual breaking in (the intelligence acquisition associated with deciphered dispatches), which-due to the lack of other instances of confirmation-did not constitute evidence of a regular-basis interpretation of secret messages by people who were not authorized to engage in this. In the first days of the war the Poles managed to completely burn all evidence associated with the process of the breaking of the machine cipher of the Enigma. After a few years that I spent in Rembertów I am absolutely sure that documents of this kind are not to be found there. Additional elements which provide further information about the well-known and list of dates and facts (which were established a long time ago) and

A SENIOR MEMBER OF MI6 RESPONSIBLE FOR THE DISTRIBTUTION OF THE TOP SECRET ULTRA DECRYPTS FROM ENIGMA REVEALS THAT FRANCIS BACON IS SHAKESPEARE To anyone with real cryptological experience it is hard to reconcile the impartiality claimed by the authors with the skill and legerdemain by which certain danger-points have been avoided. It is these unexpected manipulations which have led me at times to suspect a "command performance"…[in] what is admittedly a very clever "plant…The professional status of a modern cryptographer does not necessarily fit him to pass judgement on the subtle cryptology of a secret society of the past. The book, granted, does away with the fanciful work of some amateur cryptologists, an easy task, an empty triumph. But, having thus gained the confidence of the readers, the authors deceive them by "Scientific" demonstrations which they know to be false.

In this paper, we present an empirical study on plaintext entities in historical cipher keys from the 15th to the 18th century to shed light on what linguistic entities have been chosen for encryption. We focus mainly on the nomenclature part of the keys describing longer elements than the plaintext alphabet. We show that the chosen plaintext entities to be encoded varied over time. Nomenclatures developed from short lists consisting of names for persons and/or locations to longer, more advanced dictionaries and eventually to codebooks containing a highly diverse and advanced set of linguistic entities.

Colonnele Frank's 23-folio-long Frenchlanguage description of what he calls a "chiffre indéchiffrable" survived in the cipher collection of Leopold, grand duke of Tuscany, and Holy Roman Emperor. The author lists the usual weaknesses of the ciphers and offers his technique to remedy them. It is a polyalphabetic method helped by a circular instrument, by no means a fundamental invention in the late 18 th century. What makes it relevant is that it is a relatively early practical application of the polyalphabetic method, where not only letters of the alphabet, but even whole words are manipulated. Not much is known about the colonel author, but on the basis of the document, it becomes clear that he was a real user of military cryptography.

'In the foundations of cryptography as a solid scientific computer mathematical discipline there lies a big Mystery of the occult mystical sense. By a long-standing tradition, it is forbidden to talk about this Mystery. But by whom it is forbidden and on what grounds, actually, no one knows..' 4in1

During 1941, codebreaking at Bletchley Park was hindered by shortages of typists and unskilled staff. These shortages could have been easily rectified, but the codebreakers’ urgent requests were ignored by offcials in Whitehall. Going over the heads of those in command at GC & CS, Turing and his co-signatories wrote directly to the Prime Minister, Winston Churchill. On receiving the letter Churchill minuted his Chief of Staff, General Ismay: ‘action this day Make sure they have all they want on extreme priority and report to me that this had been done.’ It fell to Stuart Milner-Barry of Hut 6 to deliver the letter by hand to 10 Downing Street. In 1986, Milner-Barry recalled his trip to Whitehall: Why I was deputed to carry the letter to No. 10 I do not remember—at a guess, because I was the most readily expendable from the scene of action. What I do recall is arriving at Euston Station, hailing a taxi, and with a sense of total incredulity (can this really be happening?) inviting th...

Az epigráfia egy olyan tudományág, amire nincs, és nem is lehet komoly iskola, hiszen még gyerekcipőben jár. Tele van kérdésekkel, tévedésekkel, megoldatlan problémákkal, amikre még nincs válasz, hogyan is lehetne akkor tanítani? Ebben az értelemben viszont, amikor valami még csak a felderítő fázisban jár, egyenlő eséllyel indul mindenki, hiszen ez annak a folyamata, amiért később, kellő információ összegyűlése után ténylegesen is elindulhatunk a múlt megismerésének útján. Aki írástörténeti kutatásra adja a fejét, az három dologgal mindenképpen szembesül. Az első, és legfontosabb dolog, hogy az sem biztos, amit eddig ebben a témában lejegyeztek. A másik, amivel szembesül, hogy az írott emlékeket milyen nyelven jegyezték le? Hiszen van rá példa, hogy egy nép mások jelkészletét használta a saját nyelvére, és csak a későbbiekben hozott létre saját írást. De arra is van példa, hogy két nép keveredésekor, vagy együttélésekor az egyik nyelv szavai bekerülnek a másikéba, és vegyes nyelvű lesz a szöveg. Mai életünkből tudom érzékeltetni ezt a problémát, amikor a cigányok a mondat egy részét cigányul, más szavakat magyarul mondanak, ez előfordult már a múltban is más népekkel. A harmadik dolog, amivel nem lehet nem foglalkozni az íráskutatás kapcsán, az a történelmi háttér. Egy régi szöveget értelmezni nem lehet a nyelvekben való elmélyülés, és az adott történelmi kor vizsgálata nélkül. Kerek egész csak ezzel együtt lehet, és akkor viszont sok mindent elárulhat nekünk. Konkrét példát is tudok felhozni, amikor a régészek oltárkőnek tituláltak egy bronzkori alacsony kőoszlopot, melynek tetején tálszerű mélyedés van, és az oldalán egy sor képjel. A szöveg értelmezése után az ember rájön, hogy semmi köze nem volt oltárhoz, sem valláshoz, ennél sokkal egyszerűbb a dolog. Egy használati tárgy, egy búza kimérő eszköz volt. Ha majd egyszer a jövőben kellő ismeretekkel rendelkezünk a jelkészletek terén, elképzelhetetlen, hogy ebből képzés induljon nyelvi, és történelmi ismeretek nélkül. Egy-egy ókori szöveg megértése több információval szolgálhat, mint egy ásatáson talált cserépdarab, ezért elkerülhetetlen, hogy ez a tudományág egyszer az ismereteink bővülésével helyet kapjon a többi között. Beszélnünk kell arról is, hogy milyen az igazi tudós hozzáállás, mert ebben is problémát látok. Az igazi tudós az, aki a maga érdekei elé helyezi az igazság felderítését, felülbírálva önmagát is, ha szükséges. A saját tudásvágyát az emberiség javára fordítja. Mindent megkérdőjelez, átgondol, felülbírál, ha kell, elvet, vagy bizonyít. Tiszta vizet önt a pohárba, hisz arra sincs garancia, hogy amit mások lejegyeztek, az feltétlenül helyes. Az íráskutatás jórészt sötétben tapogatódzás, több benne a feltételezés, mint a konkrétum. Semmi sem biztos, hiszen egyelőre képlékeny, bizonyos esetekben téves feltételezésre épülő. Amit előttünk mások leírtak, az is jórészt feltételezés, nincs bebetonozva, felülvizsgálatra szorul. Az is, amit én leírok, csak egy irányvonal, amit a jövőben vagy visszaigazolnak, vagy nem, de legalább gondolkodásra készteti az embert. Vegyük például a székely írás problematikáját. Létezik egy jelkészlet, ami állítólag a székelyek régi írásának jeleit tartalmazza, és azzal szembesülünk, hogy a középkori feliratok egy részét még csak-csak, de a régebbi feliratokat ezzel a jelkészlettel nem lehet értelmezni. Mi lehet ennek az oka? Itt van például a Telegdi-féle Rudimenta. A rudimenta szónak

In World War One (WW1), the German diplomatic services and the Imperial Navy employed codebooks as the primary means for encoding confidential communications over telegraph and radio channels. The Entente cryptographic services were able to reconstruct most of those codebooks, to obtain copies of others, and to overcome various enhancements introduced by the Germans.

Jörg Ulbert Le chiffre diplomatique français au dix-huitième siècle Plus que toutes les autres, les correspondances diplomatiques ont vocation à rester secrètes. Et plus que toutes les autres, elles sont l'objet de convoitise et de curiosité. La divulgation du contenu d'une dépêche diplomatique peut précipiter une guerre ou retarder la signature d'un traité de paix, elle peut causer la disgrâce d'un courtisan ou trahir l'identité d'un espion. Depuis qu'elles existent, les dépêches sont interceptées par l'ennemi. Il n'en est pas autrement au siècle des Lumières. Dès la seconde moitié du dix-septième siècle, se mettent en place un peu partout en Europe des 'cabinets noirs'. 1 Ces cellules d'espionnage sont installées dans les noeuds postaux. Pendant que les chevaux de la diligence sont changés et que les passagers se restaurent, les malles postales sont ouvertes et leur contenu examiné. Les spécialistes en charge de cette opération cherchent à identifier rapidement, par l'adresse indiquée sur le pli ou par le format des feuilles, quel envoi pourrait mériter d'être inspecté de plus près. Les lettres choisies sont soigneusement ouvertes, en prenant garde de ne pas endommager leur sceau, recopiées de toute urgence, puis refermées proprement et remises dans la malle postale. Lorsque le contenu des envois est trop

The need for progressively larger and more complex accommodation necessitated a near-continuous building programme. Despite some demolitions and postwar alterations, many of the site's wartime buildings still stand. A recent programme of architectural study, landscape survey and archival research by English Heritage has provided for the first time a comprehensive overview of Bletchley's development. The sequence and functions of the standing buildings have been established, and ways in which their evolution related to the earlier (largely Victorian) landscaped park have been explored. Bletchley represents in its architecture the evolution of a cryptographic research centre from modest beginnings into a global signals intelligence centre.

The need for progressively larger and more complex accommodation necessitated a near-continuous building programme. Despite some demolitions and postwar alterations, many of the site's wartime buildings still stand. A recent programme of architectural study, landscape survey and archival research by English Heritage has provided for the first time a comprehensive overview of Bletchley's development. The sequence and functions of the standing buildings have been established, and ways in which their evolution related to the earlier (largely Victorian) landscaped park have been explored. Bletchley represents in its architecture the evolution of a cryptographic research centre from modest beginnings into a global signals intelligence centre.

This study is an extension of a Master’s study, entitled Realistic Mathematics Education and the strategies grade 8 learners develop for the solution of two simultaneous linear equations. The current study investigates how new content could be introduced into a school mathematics curriculum. The new content under discussion for this study is the topic of cryptology. Two design research cycles were carried out. For the first design research cycle there were three teaching experiments with teachers, grade 10 learners and students as participants. Seven activities were developed for the second design research cycle which was worked through with grade 10 learners. All sessions for the second design research cycle were video taped. Important to the development of instructional materials was the development of a hypothetical learning trajectory about the learning and teaching of each activity. A study of the literature, a historical and didactical phenomenological analysis of cryptology a...

This study is an extension of a Master's study, entitled Realistic Mathematics Education and the strategies grade 8 learners develop for the solution of two simultaneous linear equations. The current study investigates how new content could be introduced into ...

The work of British and American codebreakers led by Alan Turing at Bletchley Park in breaking the Enigma cipher machine during World War II has been well-documented, and rightfully recognized as one of the most extraordinary achievements of the human intellect. However, without the success of Polish codebreakers led by Marian Rejewski in the 1930s on an earlier version of Enigma, the work by the British and Americans in the 1940s might have taken much longer, prolonging the war at the potential cost of untold additional lives. The mathematics integral to the Polish method for breaking Enigma involved some basic theory of permutations. The purpose of this paper is to present an overview of these ideas and how they served to this effect. To assist in demonstrating this, technology involving Maplets will be used.

A deciphering report found in the National Archives at The Hague presents an intriguing story. A Portuguese spy inside the walls of Recife gathered information about the Dutch defences and wrote it in encrypted letters addressed to the Portuguese rebels that besieged the heart of the Dutch West India Company (WIC) administration in Brazil. The encrypted letters were delivered to the Dutch authorities, who summoned a Jewish cryptanalyst to read them. The report of Abraham de Pina contains a detailed description of the process he used to decipher these letters and presents the complete content of all four ciphertexts. In this paper, we will reconstruct the events of this case and analyze the design of the nomenclature cipher used by the Portuguese rebels. We also will present the flow of information of these intercepted letters within the WIC in Brazil and between them and their company superiors, the Gentlemen XIX, in the Netherlands. 30 Dutch: getiteld. English: titled. 31 Book 'Regras Da Companhia De Jesu'. Written by the Jesuits. https://books.google.nl/books?id=pqoQD1JTSUkC&hl=nl&pg=PA1#v=onepage&q&f=false 32 Dutch: de boekband en het naaisel (genaaide gedeelte). English: binding and sewing of the book. 33 A bound manuscript from the Jesuits. Translation of title: 'First exam which is proposed to all who asked to be admitted by the Company of Jesus'. 34 Dutch: manieren. English: manners. Not in dictionary, but also found in a pamphlet 'De Quade Minees en Practiken Van seeckeren George Carew, Ondeckt en de open geleght, Tot Onderrichtingh en Waerschouw aen Nederlandt' (Middelburg 1675). 35 Dutch: gevaarlijke of verderfelijke gevolgen. English: dangerous. 36 High treason. Latin: Crimen laesae maiestatis. French: Lèse-majesté. Meaning "offence to the majesty", is an offence against the dignity of a state (or its reigning head).

During 1941, codebreaking at Bletchley Park was hindered by shortages of typists and unskilled staff. These shortages could have been easily rectified, but the codebreakers’ urgent requests were ignored by offcials in Whitehall. Going over the heads of those in command at GC & CS, Turing and his co-signatories wrote directly to the Prime Minister, Winston Churchill. On receiving the letter Churchill minuted his Chief of Staff, General Ismay: ‘action this day Make sure they have all they want on extreme priority and report to me that this had been done.’ It fell to Stuart Milner-Barry of Hut 6 to deliver the letter by hand to 10 Downing Street. In 1986, Milner-Barry recalled his trip to Whitehall: Why I was deputed to carry the letter to No. 10 I do not remember—at a guess, because I was the most readily expendable from the scene of action. What I do recall is arriving at Euston Station, hailing a taxi, and with a sense of total incredulity (can this really be happening?) inviting th...

A deciphering report found in the National Archives at The Hague presents an intriguing story. A Portuguese spy inside the walls of Recife gathered information about the Dutch defences and wrote it in encrypted letters addressed to the Portuguese rebels that besieged the heart of the Dutch West India Company (WIC) administration in Brazil. The encrypted letters were delivered to the Dutch authorities, who summoned a Jewish cryptanalyst to read them. The report of Abraham de Pina contains a detailed description of the process he used to decipher these letters and presents the complete content of all four ciphertexts. In this paper, we will reconstruct the events of this case and analyze the design of the nomenclature cipher used by the Portuguese rebels. We also will present the flow of information of these intercepted letters within the WIC in Brazil and between them and their company superiors, the Gentlemen XIX, in the Netherlands.

Writing is a cognitive, material and motor process. To transfer sound values into a symbolic form, we require writing media, tools, and instruments, as well as specific hand movements. This tension between cognition and materiality can be exemplified by early modern cryptology. In cryptology, a message is being transformed or hidden by breaking with the conventional communication rules, which, in the early modern times, sometimes equated a break with the usual writing materials. At the beginning of the 17th century, for example, the Nuremberg scholar Daniel Schwenter presented a cryptological thread-writing tablet. It will be shown that cognitive processes of abstracting, segmenting, systematizing, assigning, and linking, which are indispensable for communication processes, are brought forth in the in-depth engagement with material potentials. Furthermore, the reconstruction of the technique offers valuable insights into possible problem-solving strategies that are not apparent from the textual source alone.

The history of Enigma G, the counter Enigma, is presented and traced from the very beginning of the development of the small, glow-lamp Enigma machine in early 1923 until the end of the Second World War. The commercial customers and governmental users of the machines are introduced and covered in considerable detail. The Hungarian machine, G 110, recently found buried in Poland, and its subsequent conservation by the Bletchley Park Trust, is then analysed and explained.

During the last few months of 1932, the Polish mathematician Marian Rejewski solved the problem of finding the internal connections of the rotors and reflector of the Enigma cipher machine used by the German army at that time. This allowed the Polish Cipher Bureau to construct an analogue of the machine, and subsequently to find effective methods for deciphering secret messages. Rejewski performed this feat virtually alone using cryptographic material provided by the Polish secret services. His knowledge of the theory of permutation groups was essential in solving this problem. This article describes in detail how to find the complete wiring of the rotors and reflector of Enigma, as well as other specifics, using data that Rejewski had at his disposal, by systematically presenting the resolution of all cases that could have been encountered. Similarly, we complete those stages of the procedure that were only outlined by Rejewski.

In this paper, we present an empirical study on plaintext entities in historical cipher keys from the 15th to the 18th century to shed light on what linguistic entities have been chosen for encryption. We focus mainly on the nomenclature part of the keys describing longer elements than the plaintext alphabet. We show that the chosen plaintext entities to be encoded varied over time. Nomenclatures developed from short lists consisting of names for persons and/or locations to longer, more advanced dictionaries and eventually to codebooks containing a highly diverse and advanced set of linguistic entities.

We study the problem of decoding secret messages encrypted by the German Army with the M3 Enigma machine after September 15, 1938. We focused our attention on the algorithmization and programming of this problem. A completion and optimization of Zygalski's sheets method were presented previously. We describe below the missing algorithm solving the problem of the plugboard settings with an algebraic justification. This method is the original idea of the authors, and we can use it for cryptanalysis together with both Zygalski's sheets method and Rejewski's bomb method. Next, we present a reconstruction of the cryptologic bomb. We enclose an implementation of both algorithms in Cpp language.

In this paper, we present an empirical study on plaintext entities in historical cipher keys from the 15th to the 18th century to shed light on what linguistic entities have been chosen for encryption. We focus mainly on the nomenclature part of the keys describing longer elements than the plaintext alphabet. We show that the chosen plaintext entities to be encoded varied over time. Nomenclatures developed from short lists consisting of names for persons and/or locations to longer, more advanced dictionaries and eventually to codebooks containing a highly diverse and advanced set of linguistic entities.

Colonnele Frank's 23-folio-long French-language description of what he calls a "chiffre indéchiffrable" survived in the cipher collection of Leopold, grand duke of Tuscany, and Holy Roman Emperor. The author lists the usual weaknesses of the ciphers and offers his technique to remedy them. It is a polyalphabetic method helped by a circular instrument, by no means a fundamental invention in the late 18th century. What makes it relevant is that it is a relatively early practical application of the polyalphabetic method, where not only letters of the alphabet, but even whole words are manipulated. Not much is known about the colonel author, but on the basis of the document, it becomes clear that he was a real user of military cryptography.

The Enigma machines were a series of electromechanical rotor cipher machines developed in Germany and used in the first half of the twentieth century to protect commercial, diplomatic, and military communications. Until 1938, the German Army used the so-called double-indicator procedure to transmit Enigma-encoded messages. It was replaced in September 1938 by a new procedure also involving double indicators. Both procedures enabled a team of mathematicians from the Polish Cipher Bureau to recover the wiring of the rotors and to develop cryptanalytic methods for the recovery of the daily keys. The double-indicator procedure was discontinued by the German Army in May 1940, and new methods were developed by the British at Bletchley Park, who were assisted by the knowledge transferred to them by the Polish cryptanalysts. In this article, the authors introduce two new algorithms that build on the historical cryptanalytic attacks on the two variants of the double-indicator procedures. Those attacks are based on hill climbing, divide-and-conquer, and specialized scoring functions, and they can recover the daily key using a number of indicators significantly smaller than the number of indicators required for the historical methods. Unlike the historical methods, the new algorithms produce unique and unambiguous results, including for scenarios with turnover of the middle rotor, and they also fully recover the plugboard settings. With these algorithms we won an international Enigma contest organized in 2015 by the City of Poznan, in memory of the Polish Cipher Bureau mathematicians.

The weakness of the vigenere cipher lies in its short key and is repeated, so there is a key loop in encrypting messages, this is used by cryptanalysts using the Kasiski method to know the key length so it can solve this algorithm. The Kasiski method uses repetitive cryptograms found in the ciphertext to determine the key length. Modification of the vigenere cipher solves strengthen the cipher by using arranged keys to make it difficult to crack the keys against the Kasiski method attacks. This study analyzes the strength of the vigenere cipher ciphertext and the modification of the vigenere cipher from the encryption results composed of plaintexts that use different keys. Against the Kasiski method attack. The method used in this study is a quantitative method with a descriptive approach through nonparametric statistical tests on the sign test. The results showed a difference in the ciphertext's strength from the encryption process even though using the same key. The kaiseki me...

In World War One (WW1), the German diplomatic services and the Imperial Navy employed codebooks as the primary means for encoding confidential communications over telegraph and radio channels. The Entente cryptographic services were able to reconstruct most of those codebooks, to obtain copies of others, and to overcome various enhancements introduced by the Germans.

In May 1943, Adam and Eve only resembled what their descendents would become: huge gray machines standing seven feet high, ten feet long, and two feet wide. But Adam and Eve were merely components, motors, and wire spread across workhorses and mounted in cabinets in Building 26 of the National Cash Register Company in Dayton, Ohio. Like the machines they preceded, they held nearly 400 vacuum tubes, 64 individually wired bakelite rotors, and innumerable feet of wire. They were the first of their kind, the U.S. Navy's Cryptanalytic Bombes, and they were about to change history.

Throughout history the need for secrecy has been important. This need for secrecy brought about the invention and the art of concealment, coding and code making [1]. As early as 1900 B.C., Egyptian scribes used hieroglyphs in a non-standard fashion, presumably to hide the meaning from those who did not know the meaning [2]. Cryptography is the effect of designing privacy requirements systems in communication [3]. From the past to the present, many classical encryption methods such as Caesar, Vigenere, and Enigma have been replaced by more powerful modern new encryption methods such as DES, RSA, PGP, AES, and SHA-3. This study aims to present chronologically together about major cryptography methods and developmental stages in the history of cryptology.

The German armed forces employed three different types of teleprinter cipher machines during the Second World War, the Lorenz machines SZ40 and SZ42 also called Tunny by Bletchley Park (BP), the Siemens Schlüsselfernschreibmaschine (SFM) T52, and the one-time-tape machine T43, also manufactured

In this paper we share our experience of conducting a mathematics camp to a group of 16-years-old school students. This camp is special since throughout their learning history, the students, like most school students in Malaysia, are only exposed to the academic side of mathematics. By this we mean the emphasis given by the school is only on academic achievement measured by the string of A's in the examination results. Of course in order to achieve this, the preferred mode of teaching and learning is geared towards drill and practice. None of the students from this group have experienced 'outdoor' mathematics as to be given in this camp. The camp which consisted of several hands-on activities and done in small groups was conducted outdoors in a very relaxed and light-hearted atmosphere. The activities aimed at introducing several areas of mathematics such as group theory and number theory and their relevance to our everyday live. One niche activity which is considered as ethno-centric was also conducted. Indeed it exposed to the students the mathematical elements in the Malay culture. At the end of the camp questionnaires were distributed to the students to gauge their reaction to this mode of learning. A chi-squared test conducted showed that there was no relationship between students' understanding on the mathematics camp's module with their streams, hence the modules are applicable to both pure science and social science stream. In all, students were satisfied with the overall conduct of the mathematics camp, where they felt that this camp was very useful and helped improve their mathematical skills and knowledge.

In this paper we share our experience of conducting a mathematics camp to a group of 16-years-old school students. This camp is special since throughout their learning history, the students, like most school students in Malaysia, are only exposed to the academic side of mathematics. By this we mean the emphasis given by the school is only on academic achievement measured by the string of A's in the examination results. Of course in order to achieve this, the preferred mode of teaching and learning is geared towards drill and practice. None of the students from this group have experienced 'outdoor' mathematics as to be given in this camp. The camp which consisted of several hands-on activities and done in small groups was conducted outdoors in a very relaxed and light-hearted atmosphere. The activities aimed at introducing several areas of mathematics such as group theory and number theory and their relevance to our everyday live. One niche activity which is considered as ethno-centric was also conducted. Indeed it exposed to the students the mathematical elements in the Malay culture. At the end of the camp questionnaires were distributed to the students to gauge their reaction to this mode of learning. A chi-squared test conducted showed that there was no relationship between students' understanding on the mathematics camp's module with their streams, hence the modules are applicable to both pure science and social science stream. In all, students were satisfied with the overall conduct of the mathematics camp, where they felt that this camp was very useful and helped improve their mathematical skills and knowledge.

The Lorenz SZ42, codenamed Tunny, was a teleprinter encryption device used by Germany during WW2 for strategic communications. Its successful cryptanalysis at Bletchley Park (BP) provided the Allies with high-grade intelligence about several fronts, as well as for the preparations for the DDay landings. The story of Tunny’s codebreaking and Colossus is well known, following the declassification of the General Report on Tunny in 2000 (Good et al., 1945), and the publication of several books (Reeds et al., 2015; Gannon, 2014; Copeland, 2010; Roberts, 2017; Mayo-Smith, 2014). The work on Colossus and other machines was carried out in the Newmanry, under the leadership of the mathematician Max Newman. The work of the Testery, the other Tunny section at BP, is less known. Named after his commander, Major Ralph Tester, the Testery was responsible for the development and application of hand methods, that complemented the work of machines like Colossus. For some reason, the report on the Te...

The Siemens and Halske T52 is a family of teleprinter encryption systems, used in WWII by the Luftwaffe, the German Navy and Army, and German diplomatic services. Codenamed “Sturgeon” by the Allied, it was designed to provide enhanced security, compared to the other German teleprinter encryption system, the Lorenz SZ42 (“Tunny”). In one of the most impressive feats of cryptographic genius, the first model, the T52a/b, was reconstructed by Arne Beurling only from encrypted traffic. It was also reconstructed at Bletchley Park. Until the end of 1942, Sweden was able to read current T52 traffic that passed through its teleprinter lines, taking advantage of errors by German operators (e.g., messages sent in depth). At the beginning of 1943, Germany increased their security measures, also introducing a new model, the T52d. The T52d was a much more secure system, featuring an irregular movement of the wheels, and a “Klartext” (autokey) function. Sweden could not read its traffic, and a Ble...

This paper presents a computer simulation of the US Navy Turing bombe. The US Navy bombe, an improved version of the British Turing-Welchman bombe, was predominantly used to break German naval Enigma messages during World War II. By using simulations of a machine to break an example message it is shown how the US Navy Turing bombe could have been operated and how it would have looked when running.

The German armed forces employed three different types of teleprinter cipher machines during the Second World War, the Lorenz machines SZ40 and SZ42 also called Tunny by Bletchley Park (BP), the Siemens & Halske Schlüsselfernschreibmaschine (SFM) T52, and the one-time-tape machine T43, also manufactured by Siemens. The Lorenz machines, which existed in three different models, SZ40, SZ42a, and SZ42b, are well known as the machines that were broken at BP with the aid of Colossus. The Siemens T52 existed in four functionally distinct models, T52a/b, T52c and T52ca — which was a modified version of the T52c machine, T52d, and T52e, all going under the BP code name of Sturgeon, while the Siemens T43 probably was the unbreakable machine that BP called Thrasher. The T43 machine came into use relatively late in the war and appears to have been used only on a few selected circuits. This paper will explain in detail the events that led to BP breaking the Sturgeon machines. In 1964, the Swedis...