Cryptography fascinates people of all generations and is increasingly presented as an example for the relevance and application of the mathematical sciences. Indeed, many principles of modern cryptography can be described at a secondary school level. In this context, the mathematical background is often only sparingly shown. In the worst case, giving mathematics this character of a tool reduces the application of mathematical insights to the message ”cryptography contains math”. This paper examines the question as to what else cryptography can offer to mathematics education. Using the RSA cryptosystem and related content, specific mathematical competencies are highlighted that complement standard teaching, can be taught with cryptography as an example, and extend and deepen key mathematical concepts.

Cette thèse analyse le traitement public du chômage artistique en France. Elle prend pour objet deux dispositifs publics spécialisés, qui visent le « retour à l’emploi » d’artistes demandeurs d’emploi et/ou allocataires du RSA : l’un relève de la politique nationale de l’emploi (ANPE puis Pôle emploi spectacle), l’autre de la politique sociale départementale (RMI puis RSA artiste). L’enquête, socio-historique et ethnographique, a été conduite à Paris et en Gironde entre 2010 et 2014. Elle a permis de récolter un matériau diversifié, composé d’archives administratives, d’entretiens et d’observations, à tous les niveaux de l’action publique – ministères et élus locaux, experts et partenaires institutionnels, cadres territoriaux, street-level bureaucrats et usagers. La spécialisation sectorielle d’une action publique généraliste accentue les tensions relatives à l’organisation institutionnelle, à la formalisation des rôles professionnels et au traitement ordinaire des usagers. D’un côté, les agents de l’administration des vocations tentent d’adapter des usagers suspectés d’onirisme à la « réalité » du marché de l’emploi. De l’autre côté, ils s’efforcent eux-mêmes de se conformer au fonctionnement d’un domaine d’activités peu porté vers l’intermédiation publique. L’incongruité du rapprochement entre logique bureaucratique standardisée et impératif artistique de singularisation permet de renouveler l’analyse de l’individualisation d’un traitement de masse, caractéristique structurante de la régulation politique des rapports sociaux. / This thesis analyses the public handling of unemployment in the French arts sector. It examines two specialised public schemes devoted to the ‘return to work’ of artists living on welfare benefits. One pertains to national employment policy (ANPE agency, then Pôle emploi spectacle), while the other falls under departmental welfare policy (RMI, then RSA artiste). Socio-historical and ethnographic research was conducted in Paris and in the department of Gironde between 2010 and 2014. The resulting material is varied, including administrative archives, interviews and observations at all public policy levels – with ministers and local representatives, experts and institutional partners, civil service managers, street-level bureaucrats and clients. The sectoral specialisation of a generalist public policy increases tensions surrounding the institutional organisation, the formalisation of professional roles, and everyday interactions with clients. On the one hand, the agents of this administration of vocations tend to seek to adjust clients often suspected of being dreamers to the ‘reality’ of the job market. On the other, they make efforts themselves to adjust to the workings of a field of activity where public intermediation is not well perceived. This unlikely balance between a standardized bureaucratic rationale and the artistic imperative of singularity sheds new light on the analysis of the individualization of a mass treatment, which is a structuring feature of the political regulation of social relations.

Les systèmes cryptographiques à base de courbes elliptiques sont aujourd'hui de plus en plus employés dans les protocoles utilisant la cryptographie à clef publique. Ceci est particulièrement vrai dans le monde de l'embarqué qui est soumis à de fortes contraintes de coût, de ressources et d'efficacité, car la cryptographie à base de courbes elliptiques permet de réduire significativement la taille des clefs utilisées par rapport aux systèmes cryptographiques précédemment employés tels que RSA (Rivest-Shamir-Adleman). Les travaux qui suivent décrivent dans un premier temps l'implantation efficace et sécurisée de la cryptographie à base de courbes elliptiques sur des composants embarqués, en particulier des cartes à puce. La sécurisation de ces implantations nécessite de prendre en compte les attaques physiques dont un composant embarqué peut être la cible. Ces attaques incluent notamment les analyses par canaux auxiliaires qui consistent à observer le comportement d'un composant pendant qu'il manipule une valeur secrète pour en déduire de l'information sur celle-ci, et les analyses par faute dans lesquelles un attaquant peut perturber un composant dans le même but.Dans la seconde partie de ce mémoire de thèse, nous étudions ces attaques et leurs implications concernant l'implantation des systèmes cryptographiques à clef publique les plus répandus. De nouvelles méthodes d'analyse et de nouvelles contre-mesures sont en particulier proposées. Une étude spécifique de certaines attaques appliquées à l'algorithme de chiffrement par bloc AES est également présentée. / Elliptic curve based cryptosystems are nowadays increasingly used in protocols involving public-key cryptography. This is particularly true in the context of embedded devices which is subject to strong cost, resources, and efficiency constraints, since elliptic curve cryptography requires significantly smaller key sizes compared to other commonly used cryptosystems such as RSA.The following study focuses in a first time on secure and efficient implementation of elliptic curve cryptography in embedded devices, especially smart cards. Designing secure implementations requires to take into account physical attacks which can target embedded devices. These attacks include in particular side-channel analysis which may infer information on a secret key manipulated by a component by monitoring how it interacts with its environment, and fault analysis in which an adversary can disturb the normal functioning of a device in the same goal.In the second part of this thesis, we study these attacks and their impact on the implementation of the most used public-key cryptosystems. In particular, we propose new analysis techniques and new countermeasures for these cryptosystems, together with specific attacks on the AES block cipher.

The aim of this dissertation is to improve computational efficiency of modular exponentiation-based public-key cryptosystems. The operational speed of these public-key cryptosystems is largely determined by the modular exponentiation operation of the form A = ge mod m where g is the base, e is the exponent and m is the modulus. The required modular exponentiation is computed by a series of modular multiplications. Optimized algorithms are required for various platforms, especially for lower-end platforms. These require the algorithms to be efficient and consume as little resources as possible. In these dissertation algorithms for integer multiplication, modular reduction and modular exponentiation, was developed and implemented in software, as required for public-key cryptography. A detailed analysis of these algorithms is given, as well as exact measurement of the computational speed achieved by each algorithm. This research shows that a total speed improvement of 13% can be achieved on existing modular exponentiation based public-key cryptosystems, in particular for the RSA cryptosystem. Three novel approaches are also presented for improving the decryption speed efficiency of the RSA algorithm. These methods focus on the selection of the decryption exponent by careful consideration of the difference between the two primes p and q. The resulting reduction of the decryption exponent improves the decryption speed by approximately 45%. / Dissertation (MEng (Electronics))--University of Pretoria, 2006. / Electrical, Electronic and Computer Engineering / unrestricted

It is very difficult in real-time breaking the cryptographic algorithms used at present. The Classical cryptoanalysis is based on finding weaknesses in the mathematical structure of the algorithm. Discovery of side channels caused a substantial change in this science. Side-channel attacks are based on incorrect physical implementation of cryptographic algorithms. This new way attack changes notions about cryptography and security of systems. This master´s thesis contains a detailed description of the whole problem of side channels and deals with side-channel attacks on the RSA asymmetric algorithm. This thesis includes the design and realization of laboratory exercise, which is focused on the time attack on the RSA algorithm implementation.

Syftet med detta examensarbete är att identifiera och ge en fördjupad förståelse för vilka utmaningar och styrkor som kan uppfattas från lärare och elever kring att programmering ska ingå som ett moment i matematikundervisningen på gymnasiet. Utöver detta avser arbetet att besvara vad det kan finnas för typer av utmaningar i att utforma en lektionssekvens som kopplar programmering och matematik till området kryptering i en klass som studerar matematik 5 och hur dessa utmaningar kan bemötas. Studien genomfördes dels i en gymnasieklass i årskurs 3 på teknikvetenskapsprogrammet och dels bland ett urval av matematiklärarna på skolan. Eleverna fick genomgå en lektionssekvens som behandlade kopplingen mellan RSA-kryptering, programmering och matematik. Denna lektionssekvens planerades och utfördes av rapportens författare. För lärarna presenterades därefter ett urval från denna lektionssekvens. Datan som ligger till grund för studien kommer ur intervjuer med grupper av lärare och grupper av elever var för sig. Utöver intervjuerna behandlades även de utmaningar som författarna själva upplevde med att planera och genomföra lektionssekvensen. Intervjuerna analyserades utifrån en tematisk innehållsanalys där transkriberingarna delades in i styrkor och utmaningar, som sedan granskades närmare och kategoriserades utifrån vissa nyckelbegrepp. Ett antal styrkor skulle kunna användas för att motivera och stötta elever i att bemöta vissa utmaningar. Flera elever ansåg att det är viktigt att matematikundervisningen synliggör tillämpningar av matematiken och på så vis ger grund för framtida studier och arbete. De uttryckte även att detta är något programmering kan göra. Dessutom antyds omväxling vara en viktig faktor för motivation att lära matematik. Dessa styrkor kan spela en viktig roll för att identifiera olika kontexter inom programmering och matematik som upplevs relevanta för eleverna. Genom att sätta ämnesinnehållet i olika sammanhang skulle även utmaningen med att hjälpa elever att abstrahera sin kunskap kunna bemötas. Vissa elever upplevde en viss skepsis till att använda datorn i matematikundervisningen eftersom det kändes ovant och distraherande. Samtidigt lyftes styrkan att programmering ger grund för framtiden. Genom att poängtera hur datorn spelar en central roll inom tekniskt och matematisk arbete utanför skolan skulle eleverna lättare kunna se syftet med datorns införande i matematikundervisningen. Denna studie ger en insyn i några utmaningar som kan uppstå i och med att programmering ingår som ett moment i matematikundervisningen på gymnasiet och ger förslag på hur några av dessa skulle kunna bemötas. De uppvisade utmaningarna stämmer väl överens med vad tidigare forskning antyder och det verkar finnas ett stort behov av att finna lösningar till dessa. Vidare forskning inom detta område bör därmed fokusera på att öka insikt i hur utmaningarna kan hanteras på ett effektivt och effektfullt sätt. / The aim of this thesis is to highlight some of the challenges and advantages associated with the introduction of programming in mathematics in upper secondary school. In addition, the thesis aims to identify some of the challenges that arise when planning and implementing a lesson sequence that connects programming and mathematics to RSA cryptography. Furthermore, this thesis will suggest how these challenges can be dealt with. The study was conducted with students from a year 3 Engineering Sciences class and mathematics teachers in a Swedish upper secondary school. The students participated in a lesson sequence in level 5 mathematics (matematik 5) concerning RSA cryptography which was planned and executed by the authors of this thesis. The teachers were introduced to a reduced version of the sequence. Data were collected from interviews with groups of students and groups of teachers. As a supplement to the interviews, the authors give their own views on challenges that emerged when planning and implementing the lesson sequence and how some of these challenges were handled. Thematic content analysis was used for studying the interviews. The content of the interviews was divided into challenges and advantages and further categorized according to different key topics. The conclusion of this study was that some of the identified advantages could motivate students to cope with some of the challenges. According to several students, it is important that mathematics education cover applications in mathematics and prepare students for higher education and employment. The students expressed that programming could be used for achieving this. Additionally, variety is important for keeping the motivation to learn mathematics. These advantages could be useful when identifying contexts that connect programming and mathematics and is relevant for the students. Covering a concept in different contexts could also support students to decontextualize their knowledge. Some students were skeptical about using computers in math class since it was unfamiliar in that context and added a level of distraction. Nevertheless, the importance of programming for higher education and future employment was one of the advantages expressed by several students. Emphasizing the role of computers in employment within the fields of engineering and mathematics could raise the purpose of introducing the computer in math class. This thesis has given an insight of some challenges that arise when introducing programming in mathematics education in upper secondary school in Sweden. Furthermore, the thesis suggests how some of these challenges could be dealt with. These challenges correlate to previous research and there seems to be an urgent need to find solutions for these. Further research should aim to find efficient and effective approaches to these challenges.

Information security in the present era is becoming very important in communication and data storage. Data transferred from one party to another over an insecure channel (e.g., Internet) can be protected by cryptography. The encrypting technologies of traditional and modern cryptography are usually used to avoid the message from being disclosed. Public-key cryptography usually uses complex mathematical computations to scramble the message. / A digital signature is an important public-key primitive that performs the function of conventional handwritten signatures for entity authentication, data integrity, and non-repudiation, especially within the electronic commerce environment. Currently, most conventional digital signature schemes are based on mathematical hard problems. These mathematical algorithms require computers to perform the heavy and complex computations to generate and verify the keys and signatures. In 1995, Naor and Shamir proposed a visual cryptography (VC) for binary images. VC has high security and requires simple computations. The purpose of this thesis is to provide an alternative to the current digital signature technology. We introduce a new digital signature scheme based on the concept of a non-expansion visual cryptography. A visual digital signature scheme is a method to enable visual verification of the authenticity of an image in an insecure environment without the need to perform any complex computations. We proposed scheme generates visual shares and manipulates them using the simple Boolean operations OR rather than generating and computing large and long random integer values as in the conventional digital signature schemes currently in use.

Šio darbo tikslas – apžvelgti šiuo metu naudojamas klasikines viešojo rakto šifravimo ir skaitmeninio parašo sistemas bei naujos kartos Signcryption kriptosistemą ir atlikti dedikuotos pasirašymo ir šifravimo kriptosistemos efektyvumo palyginimą su pasirašymo arba šifravimo kriptosistemų kompozicija bei pasiūlyti praktinio pritaikymą naujos kartos Signcryption kriptosistemai. Darbe apžvelgtos šios kriptosistemos: 1. RSA (Rivest, Shamir, Adleman) – klasikinė viešojo rakto pasirašymo arba šifravimo kriptosistema, kurios saugumas paremtas didelių skaičių faktorizacijos uždavinio sprendimo sudėtingumu, 2. ElGamalio – klasikinė viešojo rakto pasirašymo arba šifravimo kriptosistema, kurios saugumas paremtas diskretaus logaritmo problemos sprendimo sudėtingumu, 3. Signcryption – naujos kartos viešojo rakto pasirašymo ir šifravimo kriptosistema, realizuota modifikuotos ElGamalio skaitmeninio parašo schemos pagrindu. Minėtos kriptosistemos apžvelgtos teoriškai, sukurta praktinė jų realizacija ir apžvelgti rezultatai bei palygintas jų efektyvumas, kuris apibrėžiamas dviem parametrais: 1. Pranešimo pasirašymo, šifravimo, dešifravimo ir parašo patikrinimo operacijų trukmė, 2. Perduodamos perteklinės informacijos kiekis – pranešimo ilgio padidėjimas atlikus pasirašymo ir šifravimo operacijas. Taip pat apžvelgtos kriptosistemų realizacijoje naudotos papildomos funkcijos bei algoritmai, tokie kaip AES blokiniai šifrai, SHA maišos funkcijų šeima, HMAC kontrolinis parašas bei pasiūlyti du... [toliau žr. visą tekstą] / This submission called “Efficient encryption and digital signature schemes” consists of three parts. I. In Part I theoretical analysis of popular public key cryptosystems RSA (Rivest, Shamir, Adleman) with security based on the large integer factorization problem and ElGamal with security based on the discrete logarithm problem, along with new cryptographic primitive termed as "signcryption" proposed by Y. Zheng which simultaneously fulfills both the functions of digital signature and public key encryption in a logically single step, and with a cost significantly smaller than that required by "signature followed by encryption" using popular public key cryptosystem composition is done. For the completeness of analysis description of supplemental algorithms and functions such as AES block cipher, SHA hash functions, HMAC keyed hash function is present. II. In Part II the results of the practical implementation done in Python programming language are analyzed. Effectiveness is described by two factors: 1. Total computation time of signing – encryption – decryption – verification operations; 2. Communication overhead – signed and encrypted message length increase compared to the original plaintext. III. In Part III two effective Signcryption implementation algorithms are proposed: secret sharing without threshold and (k, n) threshold schemes. Results of analysis prove Signcryption being secure and extremely effective signature and encryption cryptosystem. It has very low... [to full text]

Title: Attacks based on hardware bugs Author: Martina Válková Department: Department of Algebra Supervisor: Mgr. Štěpán Holub, Ph.D. Supervisor's e-mail address: Stepan.Holub@mff.cuni.cz Abstract: The study concerns hardware bugs producing computational errors and cryptanalytic attacks which utilize them. Particularly, the research is focused on attacks presented in the article by Biham E., Carmeli Y., Shamir A.: Bug Attacks [1] and their practical application in the case of schemes RSA and Pohlig-Hellman and various computational circumstances, which points out bigger vulnerability of schemes in the case of using the Right- to-Left modular exponentiation algorithm. The attacks have been tested against the software simulation of a faulty processor, which confirmed that they pose a real security threat in point of that situation. The mathematical part of this work concerns the problem of the finding any roots in Zp. Keywords: hardware bug, attack, RSA, roots modulo p

Les relations structure-activité (RSA) désignent la relation entre structure chimique et activité pharmacologique pour une série de composés (IUPAC, 1998). Elles ont été utilisées dans les industries pharmaceutique, chimique et cosmétique, tout particulièrement pour la conception de nouvelles entités chimiques et médicamenteuses. Après une revue de la littérature, nous avons étudié les RSA en allergie médicamenteuse immédiate pour 4 classes thérapeutiques (antibiotiques bêta-lactames, produits de contraste IRM, curares, insuline) ainsi qu'en allergie médicamenteuse retardée (iodixanol, produit de contraste iodé) en nous basant sur les résultats des tests cutanés et biologiques. Les résultats obtenus démontrent qu'il existe un lien entre structure chimique et potentiel allergénique des molécules. Les RSA permettent : (1) l'identification des déterminants allergéniques sur la base de l'étude des réactivités croisées, (2) la prédiction de la probabilité de réactions d'hypersensibilité aux molécules apparentées et la sélection d'alternatives thérapeutiques de manière non-empirique / Structure-Activity Relationships (SAR) refer to the relation between chemical structure and pharmacological activity for a series of compounds (IUPAC, 1998). They have been used in the pharmaceutical, chemical and cosmetic industries, especially for drug and chemical design purposes. After reviewing literature data, we describe SAR-based approaches based on skin and laboratory tests in immediate drug hypersensitivity (beta-lactam antibiotics, MRI contrast agents, neuromuscular blocking agents, insulin) as well as in delayed drug hypersensitivity (iodixanol, iodinated contrast media). Our findings demonstrate a link between chemical structure and allergenic potential of a molecule. Structure-activity relationships can prove useful to: (i) identify allergenic determinants on the basis of cross-reactivity studies, (ii) predict the likelihood of hypersensitivity reactions to related molecules and select safe alternatives on a non-empirical basis