Conditional Fault-Diameter of Torus Networks

We obtain the conditional fault-diameter of the square torus interconnection network under the condition of forbidden faulty sets (i.e. assuming that each non-faulty processor has at least one non-faulty neighbor). We show that under this condition, the square torus, whose connectivity is 4, can tolerate up to 5 faulty nodes without becoming disconnected. The conditional node connectivity is, therefore, 6. We also show that the conditional fault-diameter of the square torus is equal to the fault-free diameter plus two. With this result the torus joins a group of interconnection networks (including the hypercube and the star-graph) whose conditional fault-diameter has been shown to be only two units over the fault-free diameter. Two fault-tolerant routing algorithms are discussed based on the proposed vertex disjoint paths construction

Performance of algebraic graphs based stream-ciphers using large finite fields

Algebraic graphs D(n, q) and their analog graphs D(n, K), where K is a finite commutative ring were used successfully in Coding Theory (as Tanner graphs for the construction of LDPC codes and turbo-codes) and in Cryptography (stream-ciphers, public-keys and tools for the key-exchange protocols. Many properties of cryptography algorithms largely depend on the choice of finite field Fq or commutative ring K. For practical implementations the most convenient fields are F and rings modulo Z modulo 2m. In this paper the reader can find the first results about the comparison of D(n, 2m) based stream-ciphers for m = 8, 16, 32 implemented in C++. They show that performance (speed) of algorithms gets better when m is increased

A Parallel Routing Algorithm for Torus NoCs

Abstract. This paper proposes a parallel routing algorithm for routing multiple data streams over disjoint paths in the torus Network-on-Chip (NoC) architecture. We show how to construct a maximal set of disjoint paths between any two nodes of a torus network topology and then make use of the constructed paths for the simultaneous routing of multiple data streams between these nodes. Analytical performance evaluation results are obtained showing the effectiveness of the proposed parallel routing algorithm in reducing communication delays and increasing throughput when transferring large amounts of data in an NoC-based multi-core system

Résolution des modèles markoviens sur machines à mémoires distribuées

L'évaluation de performances est primordiale pour la conception et le développement des systèmes informatiques. Ces derniers sont de plus en plus complexes et leur modèle sont de plus en plus gros. Pour résoudre ces modèles sur un calculateur, nous sommes confrontes a deux problèmes: la capacité mémoire et la rapidité avec laquelle on résout ces modèles. L'avènement des calculateurs parallèles constitue une bonne opportunité pour résoudre ces deux problèmes. Dans cette thèse, nous allons mettre en service le parallélisme pour résoudre les problèmes de l'évaluation de performance. Dans le cadre du calcul parallèle, nous abordons un probleme essentiel qui est le cout des communications dans les machines a mémoires distribuées. Une autre composante importante en parallélisme est le placement des données. Nous verrons l'impact de différents placements de données pour effectuer le produit vecteur-matrice qui constitue la brique de base des méthodes numériques itératives pour résoudre les modèles. Nous proposons des schémas itératives pour résoudre les problèmes markoviens. D'autre part, nous avons développe une parallélisation du solveur de modèles issus des réseaux d'automates stochastiques. En résolvant des problèmes de placement de taches et en réduisant le cout des communications, cette parallélisation nous permet de traiter des modèles de l'ordre de plusieurs millions d'états en un temps de calcul raisonnabl

The Conditional Fault-Diameter of the K-ary n-Cube

We obtain the conditional fault diameter of the k-ary n-cube interconnection network. It has been previously shown that under the condition of forbidden faulty sets (i.e. assuming each non-faulty node has at least one non-faulty neighbor), the k-ary n-cube, whose connectivity is 2n, can tolerate up to 4n-3 faulty nodes without becoming disconnected. We extend this result by showing that the conditional fault-diameter of the k-ary n-cube is equal to the fault-free diameter plus two. This means that if there are at most 4n-3 faulty nodes in the k-ary n-cube and if every non-faulty node has at least one non-faulty neighbor, then there exists a fault-free path of length at most the diameter plus two between any two non faulty nodes. We also show how to construct these fault-free paths. With this result the k-ary n-cube joins a group of interconnection networks (including the hypercube and the star-graph) whose conditional fault diameter has been shown to be only two units over the fault-free diameter

The Conditional Fault-Diameter of the K-ary n-Cube

We obtain the conditional fault diameter of the k-ary n-cube interconnection network. It has been previously shown that under the condition of forbidden faulty sets (i.e. assuming each non-faulty node has at least one non-faulty neighbor), the k-ary n-cube, whose connectivity is 2n, can tolerate up to 4n-3 faulty nodes without becoming disconnected. We extend this result by showing that the conditional fault-diameter of the k-ary n-cube is equal to the fault-free diameter plus two. This means that if there are at most 4n-3 faulty nodes in the k-ary n-cube and if every non-faulty node has at least one non-faulty neighbor, then there exists a fault-free path of length at most the diameter plus two between any two non faulty nodes. We also show how to construct these fault-free paths. With this result the k-ary n-cube joins a group of interconnection networks (including the hypercube and the star-graph) whose conditional fault diameter has been shown to be only two units over the fault-free diameter

Conditional Fault-Diameter of Torus Networks

We obtain the conditional fault-diameter of the square torus interconnection network under the condition of forbidden faulty sets (i.e. assuming that each non-faulty processor has at least one non-faulty neighbor). We show that under this condition, the square torus, whose connectivity is 4, can tolerate up to 5 faulty nodes without becoming disconnected. The conditional node connectivity is, therefore, 6. We also show that the conditional fault-diameter of the square torus is equal to the fault-free diameter plus two. With this result the torus joins a group of interconnection networks (including the hypercube and the star-graph) whose conditional fault-diameter has been shown to be only two units over the fault-free diameter. Two fault-tolerant routing algorithms are discussed based on the proposed vertex disjoint paths construction

CRYPTALL - система шифрування даних усіх типів

Розроблено систему програм, що шифрує дані таких типів, як аудіо- та відео-, текстові, word- документи, PostScript- та PDF-файли, web-сторінки, рисунки, файли та кліпи. Такі програми можна засто- совувати до побудови захищених віртуальних організацій, зокрема віртуальної освіти, що використовує мережові системи дистанційного навчання. Загальна ідея полягає в розгляді вершин графа як посилання та ланцюга певної довжини, як інструменту шифрування. Алгоритм шифрування має лінійну складність, він використовує нелінійну функцію шифрування, що є стійкою стосовно різнотипових атак опонента. Попередній пакет «CRYPTIm» (скорочення від шифрування текстів і рисунків, відео-файлів) спирався на ті самі загальні ідеї теорії графів, його було застосовано до комунікаційної мережі Університету Півден- ного Тихого, що обслуговує 11 віддалених країн Океанії. Алгоритм працював з ASCII-кодами, тому він шифрував тільки дані «txt» та «html». CRYPTALL працює з бінарними кодами, тому він є універсальним: шифрує дані всіх типів, використовує нові графи та написаний на JA VA.We have developed a software prototype for encrypting all types of data such as text files; word documents; PostScript and PDF documents; web pages; images, sound and movies. This software can be used to build a secure virtual organization such as a virtual education using a networked e-learning system. The encryption tool is based on a combinatorial algorithm of walking on a graph of high girth. The general idea is to treat vertices of a graph as messages and arcs of a certain length as encryption tools. The encryption algorithm has a linear complexity and it uses nonlinear function for encryption, thus it resists to different type of attacks of adversary . The first package "CRYPTIm" (abbreviation of encryption of text and image data) based on mentioned above graph theoretical ideas was implemented in the network of the University of the South Pacific serving for 11 remote countries in Oceania. It use the ASCII code as alphabet, so it was working with only "txt" and "html" files. CRYPTALL uses the binary code alphabet - thus it is universal: encrypting all types of data. CRYPTALL uses new families of graphs, it is implemented in JAVA