Related papers: Topological chaos and chaotic iterations. Applicat…
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…
Hash functions are cryptographic tools, which are notably involved in integrity checking and password storage. They are of primary importance to improve the security of exchanges through the Internet. However, as security flaws have been…
Due to the rapid development of the Internet in recent years, the need to find new tools to reinforce trust and security through the Internet has became a major concern. The discovery of new pseudo-random number generators with a strong…
This work redefines the framework of chaos in dynamical systems by extending Devaney's definition to multiple mappings, emphasizing the pivotal role of nonlinearity. We propose a novel theorem demonstrating how nonlinear dynamics within a…
Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…
In this paper, a new approach for constructing integer domain chaotic systems (IDCS) is proposed, and its chaotic behavior is mathematically proven according to the Devaney's definition of chaos. Furthermore, an analog-digital hybrid…
A precise definition of chaos for discrete processes based on iteration already exists. We shall first reformulate it in a more general frame, taking into account the fact that discrete chaotic behavior is neither necessarily based on…
Fixed point iterations are known to generate chaos, for some values in their parameter range. It is an established fact that Turing Machines are fixed point iterations. However, as these Machines operate in integer space, the standard…
Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior,…
Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical…
We give a definition of chaos for a continuous self-map of a general topological space. This definition coincides with the Devanney definition for chaos when the topological space happens to be a metric space. We show that in a uniform…
While there have been many publications on potential applications of chaos to fields such as communications, radar, sonar, random signal generation, channel equalization and others, designing continuous chaotic systems is still an unsolved…
Chaotic dynamics have emerged as a versatile resource for neuromorphic and probabilistic computing, enabling high-dimensional nonlinear processing and classical analogues of quantum randomness. Exploiting chaos for computation requires…
In recent years, the generation of rigorously provable chaos in finite precision digital domain has made a lot of progress in theory and practice, this article is a part of it. It aims to improve and expand the theoretical and application…
Chaotic behavior arises from very simple non-linear dynamical equation of logistic map which makes it was used often in designing chaotic image encryption schemes. However, some properties of chaotic maps can also facilitate cryptanalysis…
Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision, which is inherent in all…
Guaranteeing the security of information transmitted through the Internet, against passive or active attacks, is a major concern. The discovery of new pseudo-random number generators with a strong level of security is a field of research in…
We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic,…
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…
Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…