Related papers: Topological chaos and chaotic iterations. Applicat…
Chaotic iterations, a tool formerly used in distributed computing, has recently revealed various interesting properties of disorder leading to its use in the computer science security field. In this paper, a comprehensive study of its…
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 proved that, under some conditions, these iterations have a chaotic…
Design and cryptanalysis of chaotic encryption schemes are major concerns to provide secured information systems. Pursuing our previous research works, some well-defined discrete chaotic iterations that satisfy the reputed Devaney's…
Investigating how to construct a secure hash algorithm needs in-depth study, as various existing hash functions like the MD5 algorithm have recently exposed their security flaws. At the same time, hash function based on chaotic theory has…
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…
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…
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…
To guarantee the integrity and security of data transmitted through the Internet, hash functions are fundamental tools. But recent researches have shown that security flaws exist in the most widely used hash functions. So a new way to…
Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish,…
The truly chaotic finite machines introduced by authors in previous research papers are presented here. A state of the art in this discipline, encompassing all previous mathematical investigations, is provided, explaining how finite state…
Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a…
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…
This study redefines the analysis of Devaney chaos in multiple mappings from a set-valued perspective and introduces new conditions to characterize their chaotic behavior. As an innovative advancement, we develop computational algorithms to…
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…
Chaos-based approaches are frequently proposed in information hiding, but without obvious justification. Indeed, the reason why chaos is useful to tackle with discretion, robustness, or security, is rarely elucidated. This research work…
Security of information transmitted through the Internet is an international concern. This security is guaranteed by tools like hash functions. However, as security flaws have been recently identified in the current standard in this domain,…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
In recent years, a growing number of cryptosystems based on chaos have been proposed, many of them fundamentally flawed by a lack of robustness and security. This paper describes the security weaknesses of a recently proposed cryptographic…
In recent years, a growing number of cryptosystems based on chaos have been proposed. But most of them encountered many problems such as small key space and weak security. In the present paper, a new kind of chaotic cryptosystem based on…
Chaos and its applications in the field of secure communications have attracted a lot of attention. Chaos-based pseudo-random number generators are critical to guarantee security over open networks as the Internet. We have previously…