Related papers: On the use of dynamical systems in cryptography

Substitution boxes (S-boxes) are critical nonlinear elements to achieve cryptanalytic resistance of modern block and stream ciphers. Given their importance, a rich variety of S-box construction strategies exists. In this paper, S-boxes…

This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…

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…

An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for…

Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…

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…

We address here two major challenges presented by dynamic data mining: 1) the stability challenge: we have implemented a rigorous incremental density-based clustering algorithm, independent from any initial conditions and ordering of the…

The question of the stability of unstable states of dynamical systems that do not explicitly contain a small parameter, chaos and bifurcations in them has attracted attention ever since [1-14]. This is due to the fact that this problem…

In this paper we propose a novel image encryption scheme. The proposed method is based on the chaos theory. Our cryptosystem uses the chaos theory to define a dynamic chaotic Look-Up Table (LUT) to compute the new value of the current pixel…

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…

Deducing the states of spatiotemporally chaotic systems (SCSs) as they evolve in time is crucial for various applications. However, it is a dramatic challenge for generally achieving so due to the complexity of non-periodic dynamics and the…

With the rising popularity of the internet and the widespread use of networks and information systems via the cloud and data centers, the privacy and security of individuals and organizations have become extremely crucial. In this…

In this paper, a novel image encryption algorithm, which involves a chaotic block image scrambling followed by a two-dimensional (2-D) discrete linear chirp transform, is proposed. The definition of the 2-D discrete linear chirp transform…

The study of chaos has long relied on computationally intensive methods to quantify unpredictability and design control strategies. Recent advances in machine learning, from convolutional neural networks to transformer architectures,…

In this letter we present a method of constructing dynamical systems with any preassigned number of equilibria by adding symmetry to another system with at least one equilibrium point. If the resulting system is chaotic, we call this…

A unified framework for analyzing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several…

This paper describes the security weaknesses of a recently proposed secure communication method based on chaotic masking using projective synchronization of two chaotic systems. We show that the system is insecure and how to break it in two…

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…

Nonlinear time series analysis is becoming a more and more reliable tool for the study of complicated dynamics from measurements. The concept of low-dimensional chaos has proven to be fruitful in the understanding of many complex phenomena…

In this paper, a high dimensional chaotic systems based mixed keystream generator is proposed to secure the voice data. As the voice-based communication becomes extensively vital in the application areas of military, voice over IP,…