Improved algebraic cryptanalysis of QUAD, Bivium and Trivium via graph partitioning on equation systems

We present a novel approach for preprocessing systems of polynomial equations via graph partitioning. The variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the corresponding system of equations can be split into smaller ones that can be solved individually. This can provide a tremendous speed-up in computing the solution to the system, but is unlikely to occur either randomly or in applications. However, by deleting certain vertices on the graph, the variable-sharing graph could be disconnected in a balanced fashion, and in turn the system of polynomial equations would be separated into smaller systems of near-equal sizes. In graph theory terms, this process is equivalent to finding balanced vertex partitions with minimum-weight vertex separators. The techniques of finding these vertex partitions are discussed, and experiments are performed to evaluate its practicality for general graphs and systems of polynomial equations. Applications of this approach in algebraic cryptanalysis on symmetric ciphers are presented: For the QUAD family of stream ciphers, we show how a malicious party can manufacture conforming systems that can be easily broken. For the stream ciphers Bivium and Trivium, we nachieve significant speedups in algebraic attacks against them, mainly in a partial key guess scenario. In each of these cases, the systems of polynomial equations involved are well-suited to our graph partitioning method. These results may open a new avenue for evaluating the security of symmetric ciphers against algebraic attacks

A Distributed Algorithm For Large-Scale Graph Partitioning

Detta kandidatarbete har sin placering på Skeppsbron/Skeppsbrokajen i centrala Stockholm. Inriktningen jag valde var att rita ett förslag för en fiskmarknad som skulle placeras på denna plats. Mitt arbete har fått inspireras av Sveriges största och mest kända fiskmarknad, Feskekörkan, i Göteborg. Analyser av Feskekörkan som organisation och dess planlösning har i mitt arbete lett till en tektoniskt uppbyggd struktur där material byggnadskonstruktion var viktiga element. Med bland annat en fiskfjällsfasad i mässing och en bärande skelett av storskaliga limträbalkar. Platsen som byggnaden ligger på är ett välbesökt promenadstråk med en bred och lång kajkant som används flitigt av såväl, turister som besöker gamla stan och det kungliga slottet, och Stockholmare som tar sig mellan Södermalm och Norrmalm. Jag har valt att bebygga platsen på ett sätt som både tar vara på det vackra promenadstråket men också ger möjlighet för besökande att stanna upp och ta del av fiskmarknaden.This candidate's work has its placement on Skeppsbron/Skeppsbrokajen in the central area of Stockholm. The focus I chose was to draw a proposal for a fishmarket that would be placed at this location. My work has been inspired by the largest and most famous fish market in Sweden, Feskekörkan, in Gothenburg. Analyses of Feskekörkan’s organization and its plan has, in my work, led to a tectonically constructed structure where building materials were important elements. Including a fish scale facade made of brass and a bearing skeleton of large glulam beams. The place which the building is situated on a popular promenade with a broad and long quay which is widely used by both, tourists visiting the Old Town and the Royal Palace, and the Stockholm citizens who ride between Södermalm and Norrmalm. I have chosen to build on the site in a way that both takes advantage of the beautiful promenade but also provides the opportunity for visitors to stop and take some of the fish market

Élaboration d'une nouvelle métaheuristique pour le partitionnement de graphe : la méthode de fusion-fission. Application au découpage de l'espace aérien

Dans cette thèse, nous étudions des méthodes de partitionnement de graphe et les appliquons au découpage de l'espace aérien, ainsi qu'à d'autres problèmes. L'espace aérien est composé de volumes limités, appelés secteurs de contrôle, chacun étant sous la responsabilité d'un contrôleur. Chaque contrôleur est habilité sur un ensemble de secteurs, appelé zone de qualification. Les secteurs sont également regroupés en centres de contrôle, qui englobent au moins une zone de qualification. Dans le cadre du ciel unique européen, la Commission européenne a prévu la création de blocs fonctionnels d'espace aérien. La création de ces blocs entre pays européens entraînera probablement un redécoupage des centres actuels. Cette thèse propose des outils d'aide à la conception d'un nouveau découpage de l'espace européen en centres et en zones de qualification. À cet effet, plusieurs méthodes sont étudiées : des méthodes de partitionnement classiques,comme l'expansion de région, le multiniveaux ou les algorithmes de type Kernighan-Lin ; des métaheuristiques, comme le recuit simulé, les algorithmes de colonies de fourmis et les algorithmes évolutionnaires ; et une nouvelle méthode que nous avons mise au point, la fusion-fission. C'est cette dernière qui permet de trouver les découpages les plus performants, au sens de la fonction de coût utilisée, pour le découpage de l'espace aérien. Afin de diversifier ses applications, nous l'avons aussi adaptée à la segmentation d'images et à la classification de documents. Enfin, la qualité de cette méthode a été éprouvée sur les bancs de tests classiques du partitionnement de graphe et confrontée aux méthodes concurrentes. Elle a permis de trouver pour plusieurs problèmes de test des partitions dont le coût est le plus bas obtenu jusqu'à présent. ABSTRACT : This thesis studies graph partitioning methods and applies them to airspace partitioning and other partitioning problems. Each air traffic controller supervises a limited space, called an air traffic sector. Controllers have qualifications to work only on a set of sectors, called qualification air zone. Sectors are grouped together into control centers wich include almost one qualification air zone. The European single sky project intended by the European Commission could involve a new airspace partitioning into control centers and qualification air zones. In this framework, this thesis proposes some tools to design the airspace. Classical graph partitioning methods are studied (load-balancing, region growing and multilevel algorithms), a well as some metaheuristics (simulated annealing, ant colonies and evolutionary algorithms). A new method is introduced in this thesis : the fusion-fission method. Compared with the others, this method allows to find the best airspace partitioning for our objective function. To diversify its applications, the fusion- ission method has also been applied to image segmentation and documents clustering. Finally, it has been tested on classical benchmarks and compared with contestant methods. On benchmarks, it finds some new partitions which have the lowest cut ever foun