An elementary chromatic reduction for gain graphs and special hyperplane arrangements

A gain graph is a graph whose edges are labelled invertibly by "gains" from a group. "Switching" is a transformation of gain graphs that generalizes conjugation in a group. A "weak chromatic function" of gain graphs with gains in a fixed group satisfies three laws: deletion-contraction for links with neutral gain, invariance under switching, and nullity on graphs with a neutral loop. The laws lead to the "weak chromatic group" of gain graphs, which is the universal domain for weak chromatic functions. We find expressions, valid in that group, for a gain graph in terms of minors without neutral-gain edges, or with added complete neutral-gain subgraphs, that generalize the expression of an ordinary chromatic polynomial in terms of monomials or falling factorials. These expressions imply relations for chromatic functions of gain graphs. We apply our relations to some special integral gain graphs including those that correspond to the Shi, Linial, and Catalan arrangements, thereby obtaining new evaluations of and new ways to calculate the zero-free chromatic polynomial and the integral and modular chromatic functions of these gain graphs, hence the characteristic polynomials and hypercubical lattice-point counting functions of the arrangements. We also calculate the total chromatic polynomial of any gain graph and especially of the Catalan, Shi, and Linial gain graphs.Comment: 31 page

Analyses sécuritaires de code de carte à puce sous attaques physiques simulées

Cette thèse s intéresse aux effets des attaques par fautes physiques sur le code d un système embarqué en particulier la carte à puce. De telles attaques peuvent compromettre la sécurité du système en donnant accès à des informations confidentielles, en compromettant l intégrité de données sensibles ou en perturbant le fonctionnement pendant l exécution. Dans cette thèse, nous décrivons des propriétés de sécurité permettant d exprimer les garanties du système et établissons un modèle d attaque de haut niveau définissant les capacités d un attaquant à modifier le système. Ces propriétés et ce modèle nous servent à vérifier la sécurité du code par analyse statique ou test dynamique, combinés avec l injection d attaques, simulant les conséquences logicielles des fautes physiques. Deux méthodologies sont ainsi développées afin de vérifier le comportement fonctionnel du code sous attaques, tester le fonctionnement des sécurités implémentées et identifier de nouvelles attaques. Ces méthodologies ont été mises en oeuvre dans un cadre industriel afin de faciliter le travail du développeur chargé de sécuriser un code de carte à puce.This thesis focuses on the effects of attacks by physical faults on embedded source code specifically for smart cards. Such attacks can compromise the security of the system by providing access to confidential information, compromising the integrity of sensitive data or disrupting the execution flow. In this thesis, we describe security properties to express security guarantees on the system. We also offer an attack model defining at high level an attacker s ability to disrupt the system. With these properties and model, we check the source code security against physical attacks. We use static analysis and dynamic testing, combined with attack injection to simulate the consequences of physical faults at software level. Two techniques are created to stress the functional behavior of the code under attack, test the reliability of built-in security countermeasures and identify new threats. These techniques were implemented in a framework to help developers secure their source code in an industrial environment.ORLEANS-SCD-Bib. electronique (452349901) / SudocSudocFranceF

Optimal information dissemination in Star and Pancake networks

This paper presents a new decomposition technique for hierarchical Cayley graphs. This technique yields a very easy implementation of the divide and conquer paradigm for some problems on very complex architectures as the star graph or the pancake. As applications, we introduce algorithms for broadcasting and prefix-like operations that improve the best known bounds for these problems. We also give the first non-trivial optimal gossiping algorithms for these networks. In star-graphs and pancakes with N = n! processors, our algorithms take less than dlog Ne+ 1:5n steps. 1 Introduction The success of a parallel computer topology depends heavily on two points: ffl the existence of efficient communication schemes, ffl the existence of programming paradigms that facilitate the design of algorithms. This fact can be witnessed by the large number of machines based on the hypercube interconnection network, for which optimal information dissemination algorithms exist, and divide and conquer ..

Self-Simulation for the Passive Optical Star

Optical technology offers simple interconnection schemes with straightforward layouts that support complex logical interconnection patterns. The Passive Optical Star (pos) is often suggested as a platform for implementing the optical network: Logically it offers an all-to-all broadcast capability. We investigate the use of pos optical technology as the communication medium for parallel computing. In particular, a feature of parallel models which is extremely important for the simplicity of algorithm design and program portability is the scalability property or self-simulation capability. It states that when a computation achieves a certain speedup on a large machine with many processors, then it achieves a similar speedup on any smaller machine (relative to the number of processors). We show that the pos is indeed scalable, namely, we present a randomized algorithm for an n-processor pos that does not assume global knowledge and that simulates a kn-processor pos with a slowdown of O..

An Elementary Chromatic Reduction for Gain Graphs and Special Hyperplane Arrangements

31 pagesInternational audienceA gain graph is a graph whose edges are labelled invertibly by gains from a group. Switching is a transformation of gain graphs that generalizes conjugation in a group. A weak chromatic function of gain graphs with gains in a fixed group satisfies three laws: deletion-contraction for links with neutral gain, invariance under switching, and nullity on graphs with a neutral loop. The laws are analogous to those of the chromatic polynomial of an ordinary graph, though they are different from those usually assumed of gain graphs or matroids. The three laws lead to the weak chromatic group of gain graphs, which is the universal domain for weak chromatic functions. We find expressions, valid in that group, for a gain graph in terms of minors without neutral-gain edges, or with added complete neutral-gain subgraphs, that generalize the expression of an ordinary chromatic polynomial in terms of monomials or falling factorials. These expressions imply relations for all switching-invariant functions of gain graphs, such as chromatic polynomials, that satisfy the deletion-contraction identity for neutral links and are zero on graphs with neutral loops. Examples are the total chromatic polynomial of any gain graph, including its specialization the zero-free chromatic polynomial, and the integral and modular chromatic functions of an integral gain graph. We apply our relations to some special integral gain graphs including those that correspond to the Shi, Linial, and Catalan arrangements, thereby obtaining new evaluations of and new ways to calculate the zero-free chromatic polynomial and the integral and modular chromatic functions of these gain graphs, hence the characteristic polynomials and hypercubical lattice-point counting functions of the arrangements. The proof involves gain graphs between the Catalan and Shi graphs whose polynomials are expressed in terms of descending-path vertex partitions of the graph of (-1)-gain edges. We also calculate the total chromatic polynomial of any gain graph and especially of the Catalan, Shi, and Linial gain graphs

Le parallelisme a echange de messages : quelques langages et outils

Available at INIST (FR), Document Supply Service, under shelf-number : RP 12158 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc