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Cette thèse a pour but d'illustrer et de faire avancer l'état des connaissances sur certaines problématiques liées à l'utilisation de la cryptographie résistante à un adversaire muni d'un ordinateur quantique. L'intérêt suscité par le développement d'algorithmes dit "post-quantiques" a pris une ampleur majeure dans les dernières années suite aux progrès techniques de l'informatique quantique et la décision du NIST (National Institute of Standards and Technology) d'organiser un projet de standardisation. En particulier, nous nous intéressons aux algorithmes basant leur sécurité sur la difficulté de résoudre certains problèmes liés a un object mathématique appelé emph{réseau euclidien}. Ce type de cryptographie ayant déjà été étudiée de manière soutenue en théorie, une partie la communauté scientifique s'est maintenant tournée vers les aspects pratiques. Nous présentons dans la thèse trois sujets majeurs relatifs à ces aspects pratiques, chacun discuté dans un chapitre soutenu par une publication scientifique. Le premier sujet est celui des implémentations efficaces. L'utilisation de la cryptographie dans la société moderne implique de programmer du matériel informatique sécurisant des données. Trouver la manière la plus efficace d'implémenter les fonctions mathématiques décrites dans les spécifications de l'algorithme n'est pas toujours simple. Dans le chapitre correspondant à ce premier sujet, nous allons présenter un papier établissant la façon la plus rapide connue actuellement d'implémenter certains algorithmes participant au projet du NIST. Le deuxième sujet est celui des attaques par canaux auxiliaires. Une fois l'algorithme implémenté, son utilisation dans le monde physique donne une surface d'attaque étendue à l'adversaire. Certaines techniques sont connues pour mitiger les nouvelles attaques pouvant survenir. Dans ce chapitre, nous étudierons l'application d'une technique appelée emph{masquage} qui a été appliquée à un algorithme de signature post-quantique, lui aussi candidat au projet du NIST. Finalement, le dernier chapitre de contributions s'intéresse à la possibilité de fusionner deux algorithmes afin de créer un outil spécialisé plus efficace que l'utilisation des deux algorithmes de base. Cette technique de fusion était déjà connue par le passé mais n'avait été beaucoup étudiée dans le cadre de la cryptographie post-quantique. Ce dernier aspect est donc légèrement plus orienté design que purement pratique, mais la possibilité de fusionner à moindre coup des fonctionnalités permet d'avoir un gain concret lors de l'utilisation. / Option Informatique du Doctorat en Sciences / info:eu-repo/semantics/nonPublished

An adversary armed with a quantum computer has algorithms[66, 33, 34] at their disposal, which are capable of breaking our current methods of encryption. Even with the birth of post-quantum cryptography[52, 62, 61], some of best cryptanalytic algorithms are still quantum [45, 8]. This thesis contains several experiments on the efficacy of lattice reduction algorithms, BKZ and LLL. In particular, the difficulty of solving Learning With Errors is assessed by reducing the problem to an instance of the Unique Shortest Vector Problem. The results are used to predict the behavior these algorithms may have on actual cryptographic schemes with security based on hard lattice problems. Lattice reduction algorithms require several floating-point operations including multiplication. In this thesis, I consider the resource requirements of a quantum circuit designed to simulate floating-point multiplication with high precision. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2020. / FAU Electronic Theses and Dissertations Collection

<p> In this thesis we introduce the concept of a dense extension of a partially ordered set and study some of the properties of the resulting class of extensions. In particular we study the dense distributive extensions, dense Boolean extensions and dense meet continuous extensions of distributive, Boolean and meet continuous lattices respectively.</p> / Thesis / Doctor of Philosophy (PhD)

<p> In this thesis, we study the concept of injectivity in equational classes of (universal) algebras and in particular we are concerned with congruence distributive equational classes that have enough injectives. We show that every reasonable equationally complete congruence distributive equational class has enough injectives and we describe them completely. We then examine what equational subclasses of Lattices, Heyting algebras, and pseudo-complemented lattices have enough injectives.</p> / Thesis / Doctor of Philosophy (PhD)

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Manipulating the flow of light is critical in the design and fabrication of light-based devices ranging from solar cells, smart cameras, liquid crystal display (LCD) screens, projectors and light emitting diodes (LEDs). Thin films configured with spatial patterns or modulations in refractive index exhibit strong and richly varied interactions with light beams. In this thesis, we show that embedding planar films with specific geometries of waveguide lattices allows precise control over the inflow and outflow of light. Specifically, we demonstrate the fabrication of a new class of waveguide-encoded polymer films that are generated through a single-step, room temperature technique. Here, waveguide encoded lattices with a range of symmetries are spontaneously inscribed in photopolymerizable resins by self-trapped beams of incandescent light. We describe the generation of lattices consisting of five intersecting arrays of waveguides, which confer a range of unprecedented properties including a large, panoramic field of view (FOV) infinite depth of field and multiple imaging functionalities including focusing and inversion. We have also fabricated lattices inspired by natural arthropodal compound eyes, which comprise a radial distribution of waveguide and in turn impart a continuous, enhanced FOV. We demonstrate the application of these films in controlling the beam profiles of LEDs including their divergence and convergence. Finally, we show that thin films patterned with a periodic array of planar waveguides serve as effective beam steering coatings, which deflect light away from the metallic front contacts of commercially available solar cells and in this way, increase their efficiency. / Thesis / Doctor of Philosophy (PhD)

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24731号 / 情博第819号 / 新制||情||138(附属図書館) / 京都大学大学院情報学研究科社会情報学専攻 / (主査)教授 神田 崇行, 教授 吉川 正俊, 教授 梅野 健, TIBOUCHI Mehdi(NTT社会情報研究所) / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Prof. Marcel Wild completed his PhD with Zurick University and this is a copy of the original works / The original works can be found at http://www.hbz.uzh.ch/ / ABSTRACT: A linear representation of a modular lattice L is a homomorphism from L into the lattice Sub(V) of all subspaces of a vector space V. The representation theory of lattices was initiated by the Darmstadt school (Wille, Herrmann, Poguntke, et al), to large extent triggered by the linear representations of posets (Gabriel, Gelfand-Ponomarev, Nazarova, Roiter, Brenner, et al). Even though posets are more general than lattices, none of the two theories encompasses the other. In my thesis a natural type of finite lattice is identified, i.e. triangle lattices, and their linear representation theory is advanced. All of this was triggered by a more intricate setting of quadratic spaces (as opposed to mere vector spaces) and the question of how Witt’s Theorem on the congruence of finite-dimensional quadratic spaces lifts to spaces of uncountable dimensions. That issue is dealt with in the second half of the thesis.

Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-28Bitstream added on 2014-06-13T18:08:00Z : No. of bitstreams: 1 oliveira_el_me_sjrp.pdf: 531004 bytes, checksum: 26290057a6f49446476e6e8192925843 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho, descrevemos cíclicas de reticulados algébricos Zn-rotacionados de dimensão ímpar. Essas construções são obtidas através da imersão Rn, via homomorfismo canônico, de determinados Z-módulos livres de posto finito contidos em subcorpos de extensões ciclotômicas do tipo Q(ζp), Q(ζp2), Q(ζpq)e Q(ζpq2), com p e q primos ímpares. Caracterizamos os reticulados e apresentamos propriedades e aplicações na Teoria da Informação. / In this work we describe cyclic constructions of odd dimension. These constructions are obtained by immersion in Rn via the canonical homomorphism, of certain Z-free modules of finite rank contained in subfield cyclotomic extensions of type Q(ζp), Q(ζp2), Q(ζpq)e Q(ζpq2), com p e q odd prime. Featuring the obtained lattices and presenting properties and applications in Information Theory.