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This paper introduces a new image encryption scheme using a mixing technique as a way to encrypt one or multiple images of different types and sizes. The mixing model follows a nonlinear mathematical expression based on Cramer’s rule. Two 1D systems already developed in the literature, namely, the May-Gompertz map and the piecewise linear chaotic map, were used in the mixing process as pseudo-random number generators for their good chaotic properties. The image to be encrypted was first of all partitioned into N subimages of the same size. The subimages underwent a block permutation using the May-Gompertz map. This was followed by a pixel-based permutation using the piecewise linear chaotic map. The result of the two previous permutations was divided into 4 subimages, which were then mixed using pseudo-random matrices generated from the two maps mentioned above. Tests carried out on the cryptosystem designed proved that it was fast due to the 1D maps used, robust in terms of noise and data loss, exhibited a large key space, and resisted all common attacks. A very interesting feature of the proposed cryptosystem is that it works well for simultaneous multiple-image encryption.

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The dynamics of a simple autonomous jerk circuit previously introduced by Sprott in 2011 are investigated. In this paper, the model is described by a three-time continuous dimensional autonomous system with an exponential nonlinearity. Using standard nonlinear techniques such as time series, bifurcation diagrams, Lyapunov exponent plots, and Poincaré sections, the dynamics of the system are characterized with respect to its parameters. Period-doubling bifurcations, periodic windows, and coexisting bifurcations are reported. As a major result of this work, it is found that the system experiences the unusual phenomenon of asymmetric bistability marked by the presence of two different attractors (e.g., screw-like Shilnikov attractor with a spiralling-like Feigenbaum attractor) for the same parameters setting, depending solely on the choice of initial states. Among few cases of lower dimensional systems capable of such type of behavior reported to date (e.g., Colpitts oscillator, Newton-Leipnik system, and hyperchaotic oscillator with gyrators), the jerk circuit/system considered in this work represents the simplest prototype. Results of theoretical analysis are perfectly reproduced by laboratory experimental measurements.

In many domains of science and technology, as the need for secured transmission of information has grown over the years, a variety of methods have been studied and devised to achieve this goal. In this paper, we present an information securing method using chaos encryption. Our proposal uses only one chaotic oscillator both for signal encryption and decryption, for avoiding the delicate synchronisation step. We carried out numerical and electronic simulations of the proposed circuit using electrocardiographic signals as input. Results obtained from both simulations were compared and exhibited a good agreement proving the suitability of our system for signal encryption and decryption.

Summary An electronic implementation of a novel chaotic oscillator with quintic nonlinearity is proposed herein. Dynamical behaviors of the system are investigated using well‐known numerical simulations and analyses such as phase portraits, Lyapunov exponents, bifurcation diagrams, and basins of attraction. The chaotic circuit presents an inversion‐symmetry, and we show that it can exhibit some nonlinear phenomena specific to symmetric systems, such as symmetric bifurcations, symmetric attractors, coexisting symmetric bubbles, and coexisting symmetric attractors. Since symmetry is never perfect, some symmetry imperfections must be always assumed to be present. Thus, an external Direct Current (DC) voltage is introduced in order to highlight the influence of asymmetry on the dynamics of the chaotic oscillator. It is found that more complex nonlinear behaviors occur in the presence of symmetry breaking like asymmetric coexisting bifurcations, asymmetric attractors, coexisting asymmetric bubbles, and coexisting asymmetric attractors, to name a few. The control of multistability is also performed by using the so‐called linear augmentation scheme. Probe Simulation Program with Integrated Circuits Emphasis (Pspice) circuit simulations are carried out to verify the theoretical analyses. Furthermore, a chaos‐based image encryption is investigated using pseudorandom numbers generated by the proposed chaotic circuit and deoxyribonucleic acid (DNA) encoding technique.