The aim of the research presented in this thesis is to investigate the use of various optimisation heuristics in the fields of automated cryptanalysis and automated cryptographic function generation. These techniques were found to provide a successful method of automated cryptanalysis of a variety of the classical ciphers. Also, they were found to enhance existing fast correlation attacks on certain stream ciphers. A previously proposed attack of the knapsack cipher is shown to be flawed due to the absence of a suitable solution evaluation mechanism. Finally, a new approach for finding highly nonlinear Boolean functions is introduced.

The growing interest in the Internet of Things (IoT) has led to predictions claiming that by 2020 we can expect to be surrounded by 50 billion Internet connected devices. With more entry points to a network, adversaries can potentially use IoT devices as a stepping stone for attacking other devices connected to the network or the network itself. Information security relies on cryptographic primitives that, in turn, depend on secret keys. Furthermore, the issue of Intellectual property (IP) theft in the field of Integrated circuit (IC) design can be tackled with the help of unique device identifiers. Physical unclonable functions (PUFs) provide a tamper-resilient solution for secure key storage and fingerprinting hardware. PUFs use intrinsic manufacturing differences of ICs to assign unique identities to hardware. Arbiter PUFs utilise the differences in delays of identically designed paths, giving rise to an unpredictable response unique to a given IC. This thesis explores the statistical properties of Boolean functions induced by arbiter PUFs. In particular, this empirical study looks into the distribution of induced functions. The data gathered shows that only 3% of all possible 4-variable functions can be induced by a single 4 stage arbiter PUF. Furthermore, some individual functions are more than 5 times more likely than others. Hence, the distribution is non-uniform. We also evaluate alternate PUF designs, improving the coverage vastly, resulting in one particular implementation inducing all 65,536 4-variable functions. We hypothesise the need for n XORed PUFs to induce all 22n possible n-variable Boolean functions.

Les grands réseaux de communication sont partout, des centres de données avec des millions de serveurs jusqu’aux réseaux sociaux avec plusieurs milliards d’utilisateurs.Cette thèse est dédiée à l’étude fine de la complexité de différents problèmes combinatoires sur ces réseaux. Dans la première partie, nous nous intéressons aux propriétés des plongements des réseaux de communication dans les arbres. Ces propriétés aident à mieux comprendre divers aspects du trafic dans les réseaux (tels que la congestion). Plus précisément, nous étudions la complexité du calcul de l’hyperbolicité au sens de Gromov et de paramètres des décompositions arborescentes dans les graphes. Ces paramètres incluent la longueur arborescente (treelength) et l’épaisseur arborescente (treebreadth). Au passage, nous démontrons de nouvelles bornes sur ces paramètres dans de nombreuses classes de graphes, certaines d’entre elles ayant été utilisées dans la conception de réseaux d’interconnexion des centres de données. Le résultat principal dans cette partie est une relation entre longueur et largeur arborescentes (treewidth), qui est un autre paramètre très étudié des graphes. De ce résultat, nous obtenons une vision unifiée de la ressemblance des graphes avec un arbre, ainsi que différentes applications algorithmiques. Nous utilisons dans cette partie divers outils de la théorie des graphes et des techniques récentes de la théorie de la complexité / Large scale communication networks are everywhere, ranging from data centers withmillions of servers to social networks with billions of users. This thesis is devoted tothe fine-grained complexity analysis of combinatorial problems on these networks.In the first part, we focus on the embeddability of communication networks totree topologies. This property has been shown to be crucial in the understandingof some aspects of network traffic (such as congestion). More precisely, we studythe computational complexity of Gromov hyperbolicity and of tree decompositionparameters in graphs – including treelength and treebreadth. On the way, we givenew bounds on these parameters in several graph classes of interest, some of thembeing used in the design of data center interconnection networks. The main resultin this part is a relationship between treelength and treewidth: another well-studiedgraph parameter, that gives a unifying view of treelikeness in graphs and has algorithmicapplications. This part borrows from graph theory and recent techniques incomplexity theory. The second part of the thesis is on the modeling of two privacy concerns with social networking services. We aim at analysing information flows in these networks,represented as dynamical processes on graphs. First, a coloring game on graphs isstudied as a solution concept for the dynamic of online communities. We give afine-grained complexity analysis for computing Nash and strong Nash equilibria inthis game, thereby answering open questions from the literature. On the way, wepropose new directions in algorithmic game theory and parallel complexity, usingcoloring games as a case example

[pt] Nós começamos essa dissertação com um panorama geral e introdutório dos tópicos de Sensibilidade a Ruído e Percolação . Como essas áreas podem ser desconhecidas por muitos estudantes de pós-graduação, nós apresentamos o material de uma maneira acessível, com o intuito de divulgar importantes técnicas e resultados dessas áreas. Nós também vamos introduzir o modelo para Percolação de Voronoi e apresentar resultados sobre probabilidades de cruzamentos neste modelo. Nos últimos dois capulos nós iremos considerar Sensibilidade a Ruído para Percolação do tipo quenched. Em particular, no penúltimo capítulo nós vamos apresentar resultados do artigo Quenched Voronoi Percolation de Daniel Ahlberg, Simon Griffiths, Robert Morris e Vincent Tassion, e no último capítulo provaremos um teorema que melhora uma das cotas deste artigo. / [en] We begin this dissertation by giving an introductory overview of the topics of Noise Sensitivity and Percolation. As these areas may be unfamiliar to many graduate students, we present the material in an accessible way, with the objective of publicising important techniques and results in these areas.We shall also introduce the model of Voronoi Percolation and present results of Vincent Tassion on crossing probabilities in this model. In the last two chapters we consider Noise Sensitivity of Quenched Voronoi Percolation. In particular, in the penultimate chapter we present the results of the paper Quenched Voronoi Percolation by Daniel Ahlberg, Simon Griffiths, Robert Morris and Vincent Tassion, and in the final chapter we prove a theorem which improves one of the bounds of that paper.

This thesis focuses mainly on the Maximum Independent Set (MIS) problem. Some related graph theoretical combinatorial problems are also considered. As these problems are generally NP-hard, we study their complexity in hereditary graph classes, i.e. graph classes defined by a set F of forbidden induced subgraphs. We revise the literature about the issue, for example complexity results, applications, and techniques tackling the problem. Through considering some general approach, we exhibit several cases where the problem admits a polynomial-time solution. More specifically, we present polynomial-time algorithms for the MIS problem in: + some subclasses of $S_{2;j;k}$-free graphs (thus generalizing the classical result for $S_{1;2;k}$-free graphs); + some subclasses of $tree_{k}$-free graphs (thus generalizing the classical results for subclasses of P5-free graphs); + some subclasses of $P_{7}$-free graphs and $S_{2;2;2}$-free graphs; and various subclasses of graphs of bounded maximum degree, for example subcubic graphs. Our algorithms are based on various approaches. In particular, we characterize augmenting graphs in a subclass of $S_{2;k;k}$-free graphs and a subclass of $S_{2;2;5}$-free graphs. These characterizations are partly based on extensions of the concept of redundant set [125]. We also propose methods finding augmenting chains, an extension of the method in [99], and finding augmenting trees, an extension of the methods in [125]. We apply the augmenting vertex technique, originally used for $P_{5}$-free graphs or banner-free graphs, for some more general graph classes. We consider a general graph theoretical combinatorial problem, the so-called Maximum -Set problem. Two special cases of this problem, the so-called Maximum F-(Strongly) Independent Subgraph and Maximum F-Induced Subgraph, where F is a connected graph set, are considered. The complexity of the Maximum F-(Strongly) Independent Subgraph problem is revised and the NP-hardness of the Maximum F-Induced Subgraph problem is proved. We also extend the augmenting approach to apply it for the general Maximum Π -Set problem. We revise on classical graph transformations and give two unified views based on pseudo-boolean functions and αff-redundant vertex. We also make extensive uses of α-redundant vertices, originally mainly used for $P_{5}$-free graphs, to give polynomial solutions for some subclasses of $S_{2;2;2}$-free graphs and $tree_{k}$-free graphs. We consider some classical sequential greedy heuristic methods. We also combine classical algorithms with αff-redundant vertices to have new strategies of choosing the next vertex in greedy methods. Some aspects of the algorithms, for example forbidden induced subgraph sets and worst case results, are also considered. Finally, we restrict our attention on graphs of bounded maximum degree and subcubic graphs. Then by using some techniques, for example ff-redundant vertex, clique separator, and arguments based on distance, we general these results for some subclasses of $S_{i;j;k}$-free subcubic graphs.

This thesis focuses mainly on the Maximum Independent Set (MIS) problem. Some related graph theoretical combinatorial problems are also considered. As these problems are generally NP-hard, we study their complexity in hereditary graph classes, i.e. graph classes defined by a set F of forbidden induced subgraphs. We revise the literature about the issue, for example complexity results, applications, and techniques tackling the problem. Through considering some general approach, we exhibit several cases where the problem admits a polynomial-time solution. More specifically, we present polynomial-time algorithms for the MIS problem in: + some subclasses of $S_{2;j;k}$-free graphs (thus generalizing the classical result for $S_{1;2;k}$-free graphs); + some subclasses of $tree_{k}$-free graphs (thus generalizing the classical results for subclasses of P5-free graphs); + some subclasses of $P_{7}$-free graphs and $S_{2;2;2}$-free graphs; and various subclasses of graphs of bounded maximum degree, for example subcubic graphs. Our algorithms are based on various approaches. In particular, we characterize augmenting graphs in a subclass of $S_{2;k;k}$-free graphs and a subclass of $S_{2;2;5}$-free graphs. These characterizations are partly based on extensions of the concept of redundant set [125]. We also propose methods finding augmenting chains, an extension of the method in [99], and finding augmenting trees, an extension of the methods in [125]. We apply the augmenting vertex technique, originally used for $P_{5}$-free graphs or banner-free graphs, for some more general graph classes. We consider a general graph theoretical combinatorial problem, the so-called Maximum -Set problem. Two special cases of this problem, the so-called Maximum F-(Strongly) Independent Subgraph and Maximum F-Induced Subgraph, where F is a connected graph set, are considered. The complexity of the Maximum F-(Strongly) Independent Subgraph problem is revised and the NP-hardness of the Maximum F-Induced Subgraph problem is proved. We also extend the augmenting approach to apply it for the general Maximum Π -Set problem. We revise on classical graph transformations and give two unified views based on pseudo-boolean functions and αff-redundant vertex. We also make extensive uses of α-redundant vertices, originally mainly used for $P_{5}$-free graphs, to give polynomial solutions for some subclasses of $S_{2;2;2}$-free graphs and $tree_{k}$-free graphs. We consider some classical sequential greedy heuristic methods. We also combine classical algorithms with αff-redundant vertices to have new strategies of choosing the next vertex in greedy methods. Some aspects of the algorithms, for example forbidden induced subgraph sets and worst case results, are also considered. Finally, we restrict our attention on graphs of bounded maximum degree and subcubic graphs. Then by using some techniques, for example ff-redundant vertex, clique separator, and arguments based on distance, we general these results for some subclasses of $S_{i;j;k}$-free subcubic graphs.