arXiv subjects

Jacques M. Bahi

Publications and source records attributed to Jacques M. Bahi.

62 records · Page 4Linked to original sources

arXiv2010

A Pseudo Random Numbers Generator Based on Chaotic Iterations. Application to Watermarking

In this paper, a new chaotic pseudo-random number generator (PRNG) is proposed. It combines the well-known ISAAC and XORshift generators with chaotic iterations. This PRNG possesses important properties of topological chaos and can successfully pass NIST and TestU01 batteries of tests. This makes our generator suitable for information security applications like cryptography. As an illustrative example, an application in the field of watermarking is presented.

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arXiv2010

A chaos-based approach for information hiding security

This paper introduces a new framework for data hiding security. Contrary to the existing ones, the approach introduced here is not based on probability theory. In this paper, a scheme is considered as secure if its behavior is proven unpredictable. The objective of this study is to enrich the existing notions of data hiding security with a new rigorous and practicable one. This new definition of security is based on the notion of topological chaos. It could be used to reinforce the confidence on a scheme previously proven as secure by other approaches and it could also be used to study some classes of attacks that currently cannot be studied by the existing security approaches. After presenting the theoretical framework of the study, a concrete example is detailed in order to show how our approach can be applied.

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arXiv2010

A novel pseudo-random number generator based on discrete chaotic iterations

Security of information transmitted through the Internet, against passive or active attacks is an international concern. The use of a chaos-based pseudo-random bit sequence to make it unrecognizable by an intruder, is a field of research in full expansion. This mask of useful information by modulation or encryption is a fundamental part of the TLS Internet exchange protocol. In this paper, a new method using discrete chaotic iterations to generate pseudo-random numbers is presented. This pseudo-random number generator has successfully passed the NIST statistical test suite (NIST SP800-22). Security analysis shows its good characteristics. The application for secure image transmission through the Internet is proposed at the end of the paper.

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arXiv2009

Java Technology : a Strategic Solution for Interactive Distributed Applications

In a world demanding the best performance from financial investments, distributed applications occupy the first place among the proposed solutions. This particularity is due to their distributed architecture which is able to acheives high performance. Currently, many research works aim to develop tools that facilitate the implementation of such applications. The urgent need for such applications in all areas pushes researchers to accelerate this process. However, the lack of standardization results in the absence of strategic decisions taken by computer science community. In this article, we argue that Java technology represents an elegant compromise ahead of the list of the currently available solutions. In fact, by promoting the independence of hardware and software, Java technology makes it possible to overcome pitfalls that are inherent to the creation of distributed applications.

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arXiv2008

A topological chaos framework for hash functions

This paper presents a new procedure of generating hash functions which can be evaluated using some mathematical tools. This procedure is based on discrete chaotic iterations. First, it is mathematically proven, that these discrete chaotic iterations can be considered as a \linebreak particular case of topological chaos. Then, the process of generating hash function based on the \linebreak topological chaos is detailed. Finally it is shown how some tools coming from the domain of \linebreak topological chaos can be used to measure quantitatively and qualitatively some desirable properties for hash functions. An illustration example is detailed in order to show how one can create hash functions using our theoretical study. Key-words : Discrete chaotic iterations. Topological chaos. Hash function

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arXiv2008

The topology of chaotic iterations

Chaotic iterations have been introduced on the one hand by Chazan, Mi- ranker [6] and Miellou [10] in a numerical analysis context, and on the other hand by Robert [12] and Pellegrin [11] in the discrete dynamical systems frame- work. In both cases, the objective was to derive conditions of convergence of such iterations to a fixed state. In this paper, a new point of view is presented, the goal here is to derive conditions under which chaotic iterations admit a chaotic behaviour in a rigorous mathematical sense. Contrary to what has been studied in the literature, convergence is not desired. More precisely, we establish in this paper a link between the concept of chaotic iterations on a finite set and the notion of topological chaos [9], [7], [8]. We are motivated by concrete applications of our approach, such as the use of chaotic boolean iterations in the computer security field. Indeed, the concept of chaos is used in many areas of data security without real rigorous theoretical foundations, and without using the fundamental properties that allow chaos. The wish of this paper is to bring a bit more mathematical rigour in this field. This paper is an extension of[3], and a work in progress.

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arXiv2008

A watermarking algorithm satisfying topological chaos properties

A new watermarking algorithm is given, it is based on the so-called chaotic iterations and on the choice of some coefficients which are deduced from the description of the carrier medium. After defining these coefficients, chaotic discrete iterations are used to encrypt the watermark and to embed it in the carrier medium. This procedure generates a topological chaos and ensures that the required properties of a watermarking algorithm are satisfied. Key-words: Watermarking, Encryption, Chaotic iterations, Topological chaos, Information hiding

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arXiv2008

Chaotic iterations and topological chaos

Chaotic iterations have been introduced on the one hand by Chazan, Miranker [5] and Miellou [9] in a numerical analysis context, and on the other hand by Robert [11] and Pellegrin [10] in the discrete dynamical systems framework. In both cases, the objective was to derive conditions of convergence of such iterations to a fixed state. In this paper, a new point of view is presented, the goal here is to derive conditions under which chaotic iterations admit a chaotic behaviour in a rigorous mathematical sense. Contrary to what has been studied in the literature, convergence is not desired. More precisely, we establish in this paper a link between the concept of chaotic iterations on a finite set and the notion of topological chaos [8], [6], [7]. We are motivated by concrete applications of our approach, such as the use of chaotic boolean iterations in the computer security field. Indeed, the concept of chaos is used in many areas of data security without real rigorous theoretical foundations, and without using the fundamental properties that allow chaos. The wish of this paper is to bring a bit more mathematical rigour in this field.

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