Jacques M. Bahi

Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems

Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, the quantization is inevitable for any digital devices, which causes dynamical degradation. To cope with this problem, many methods were proposed, such as perturbing chaotic states and cascading multiple chaotic systems. This paper aims at developing a novel methodology to design the higher-dimensional digital chaotic systems (HDDCS) in the domain of finite precision. The proposed system is based on the chaos generation strategy controlled by random sequences. It is proven to satisfy the Devaneys definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The application of HDDCS in image encryption is demonstrated via FPGA platform. As each operation of HDDCS is executed in the same fixed precision, no quantization loss occurs. Therefore, it provides a perfect solution to the dynamical degradation of digital chaos.

Parallel iterative algorithms : from sequential to grid computing

Focusing on grid computing and asynchronism, Parallel Iterative Algorithms explores the theoretical and practical aspects of parallel numerical algorithms. Each chapter contains a theoretical discussion of the topic, an algorithmic section that fully details implementation examples and specific algorithms, and an evaluation of the advantages and drawbacks of the algorithms. Several exercises also appear at the end of most chapters. The first two chapters introduce the general features of sequential iterative algorithms and their applications to numerical problems. The book then describes different kinds of parallel systems and parallel iterative algorithms. It goes on to address both linear and nonlinear parallel synchronous and asynchronous iterative algorithms for numerical computation, with an emphasis on the multisplitting approach. The final chapter discusses the features required for efficient implementation of asynchronous iterative algorithms. Providing the theoretical and practical knowledge needed to design and implement efficient parallel iterative algorithms, this book illustrates how to apply these algorithms to solve linear and nonlinear numerical problems in parallel environments, including local, distant, homogeneous, and heterogeneous clusters.

Dynamic load balancing and efficient load estimators for asynchronous iterative algorithms

In a previous paper, we have shown the very high power of asynchronism for parallel iterative algorithms in a global context of grid computing. In this article, we study the interest of coupling load balancing with asynchronism in such algorithms. After proposing a noncentralized version of dynamic load balancing which is best suited to asynchronism, we verify its efficiency by some experiments on a general partial differential equation (PDE) problem. Finally, we give some general conditions for the use of load balancing to obtain good results with this kind of algorithm and discuss the choice of the residual as an efficient load estimator.

Hash Functions Using Chaotic Iterations

In this paper, a novel formulation of discrete chaotic iterations in the field of dynamical systems is given. Their topological properties are studied: it is mathematically proven that, under some conditions, these iterations have a chaotic behavior as defined by Devaney. This chaotic behavior allows us to propose a way to generate new hash functions. An illustrative example is detailed in order to show how to use our theoretical study in practice.

A decentralized convergence detection algorithm for asynchronous parallel iterative algorithms

We introduce a theoretical algorithm and its practical version to perform a decentralized detection of the global convergence of parallel asynchronous iterative algorithms. We prove that, even if the algorithm is completely decentralized, the detection of global convergence is achieved on one processor under the classical conditions. The proposed algorithm is very useful in the context of grid computing in which the processors are distributed and in which detecting the convergence on a master processor may be penalizing or even impossible as in peer to peer computation frameworks. Finally, the efficiency of the practical algorithm is illustrated in a typical experiment.

Topological chaos and chaotic iterations application to hash functions

This paper introduces a new notion of chaotic algorithms. These algorithms are iterative and are based on so-called chaotic iterations. Contrary to all existing studies on chaotic iterations, we are not interested in stable states of such iterations but in their possible unpredictable behaviors. By establishing a link between chaotic iterations and the notion of Devaneys topological chaos, we give conditions ensuring that these kind of algorithms produce topological chaos. This leads to algorithms that are highly unpredictable. After presenting the theoretical foundations of our approach, we are interested in its practical aspects. We show how the theoretical algorithms give rise to computer programs that produce true topological chaos, then we propose applications in the area of information security.

Hilbert mobile beacon for localisation and coverage in sensor networks

Wireless sensor networks (WSN) constitute a major area of research developing at a very fast pace. Target localisation and coverage are core issues in the field of WSN and represent constraints that affect the effectiveness of WSN. This article focuses on localisation and coverage and identifies a relationship of dependence between the two issues. Throughout this article, a localisation algorithm is proposed and also an energy efficient approach that aims to preserve coverage. The use of a mobile beacon is suggested to divide the region of interest into unit squares following the same method used in the Hilbert space filling curve. A proper choice of the order of the Hilbert curve (i.e. the region subdivisions) is studied to guarantee the localisation of all nodes as well as the total area of coverage. The mobile beacon assists to determine the physical location of undetected nodes by sending beacon packets while traversing the region of interest. It also locally derives an activity scheduling between nodes with a relatively low cost in terms of energy spent by nodes compared to other approaches. In order to validate the effectiveness of the above proposed approach, a series of experiments have been conducted and will be mentioned throughout this article.

Asynchronous Iterative Algorithms for Nonexpansive Linear Systems

In this paper we give a convergence result for parallel synchronous or asynchronous algorithms with bounded delays, associated with nonexpansive linear systems which are not necessarily contractive. This result allows us to apply these algorithms to consistent singular linear systems and to finite homogenous Markov chains.

Chaotic Iterations versus Spread-Spectrum: Chaos and Stego Security

A new framework for information hiding security, called chaos-security, has been proposed in a previous study. It is based on the evaluation of unpredictability of the scheme, whereas existing notions of security, as stego-security, are more linked to information leaks. It has been proven that spread-spectrum techniques, a well-known stego-secure scheme, are chaos-secure too. In this paper, the links between the two notions of security is deepened and the usability of chaos-security is clarified, by presenting a novel data hiding scheme that is twice stego and chaos-secure. This last scheme has better scores than spread-spectrum when evaluating qualitative and quantitative chaos-security properties. Incidentally, this result shows that the new framework for security tends to improve the ability to compare data hiding scheme.

Localization and coverage for high density sensor networks

This paper tackles the problems of localization and coverage in randomly deployed high density sensor networks. In particular, it presents a novel and integrated approach that performs at once localization and coverage. We introduce here an approach based on a single mobile beacon aware of its position. Sensor nodes receiving beacon packets will be able to locate themselves. On the other hand, We exploit the localization phase to construct sets of active nodes that ensure as much as possible the zone coverage. In our approach the mobile beacon follows a Hilbert curve. The results of experiments conducted using the discrete event simulator Omnet++, are discussed, they allow us to justify our approach and to compare it to existing ones.