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Search Results: 1 - 10 of 404764 matches for " Jacques M. Bahi "
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The topology of chaotic iterations
Jacques M. Bahi,Christophe Guyeux
Physics , 2008,
Abstract: 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.
Chaotic iterations and topological chaos
Jacques M. Bahi,Christophe Guyeux
Physics , 2008,
Abstract: 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.
A topological chaos framework for hash functions
Jacques M. Bahi,Christophe Guyeux
Computer Science , 2008,
Abstract: 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
A watermarking algorithm satisfying topological chaos properties
Jacques M. Bahi,Christophe Guyeux
Computer Science , 2008,
Abstract: 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
A new chaos-based watermarking algorithm
Jacques M. Bahi,Christophe Guyeux
Computer Science , 2015,
Abstract: This paper introduces a new watermarking algorithm based on discrete chaotic iterations. After defining some coefficients deduced from the description of the carrier medium, chaotic discrete iterations are used to mix the watermark and to embed it in the carrier medium. It can be proved that this procedure generates topological chaos, which ensures that desired properties of a watermarking algorithm are satisfied.
Topological chaos and chaotic iterations. Application to Hash functions
Christophe Guyeux,Jacques M. Bahi
Computer Science , 2015, DOI: 10.1109/IJCNN.2010.5596512
Abstract: 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 Devaney's 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.
A chaos-based approach for information hiding security
Jacques M. Bahi,Christophe Guyeux
Computer Science , 2010,
Abstract: 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.
Building a Chaotic Proved Neural Network
Jacques M. Bahi,Christophe Guyeux,Michel Salomon
Mathematics , 2011,
Abstract: Chaotic neural networks have received a great deal of attention these last years. In this paper we establish a precise correspondence between the so-called chaotic iterations and a particular class of artificial neural networks: global recurrent multi-layer perceptrons. We show formally that it is possible to make these iterations behave chaotically, as defined by Devaney, and thus we obtain the first neural networks proven chaotic. Several neural networks with different architectures are trained to exhibit a chaotical behavior.
Lyapunov exponent evaluation of a digital watermarking scheme proven to be secure
Jacques M. Bahi,Nicolas Friot,Christophe Guyeux
Mathematics , 2012,
Abstract: In our previous researches, a new digital watermarking scheme based on chaotic iterations has been introduced. This scheme was both stego-secure and topologically secure. The stego-security is to face an attacker in the "watermark only attack" category, whereas the topological security concerns other categories of attacks. Its Lyapunov exponent is evaluated here, to quantify the chaos generated by this scheme. Keywords : Lyapunov exponent; Information hiding; Security; Chaotic iterations; Digital Watermarking.
Chaotic iterations versus Spread-spectrum: topological-security and stego-security
Christophe Guyeux,Nicolas Friot,Jacques M. Bahi
Mathematics , 2011,
Abstract: A new framework for information hiding security, called topological-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 topologically-secure too. In this paper, the links between the two notions of security is deepened and the usability of topological-security is clarified, by presenting a novel data hiding scheme that is twice stego and topological-secure. This last scheme has better scores than spread-spectrum when evaluating qualitative and quantitative topological-security properties. Incidentally, this result shows that the new framework for security tends to improve the ability to compare data hiding scheme.
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