Multistability Analysis and MultiSim Simulation of A 12-Term Double-Scroll Hyperchaos System with Three Nonlinear Terms, Bursting Oscillations and Its Cryptographic Applications

Sambas, Aceng; Vaidyanathan, Sundarapandian; Zhang, Sen; El-Latif, Ahmed A. Abd; Mohamed, Mohamad Afendee; Abd-El-Atty, Bassem

doi:10.1007/978-3-030-92166-8_10

Cited by 4 publications

(3 citation statements)

References 54 publications

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“…However, problems such as unpredictability and short cycle may occur when implementing chaotic systems in digital devices (digital chaos) [21,22]. This will result in successful attacks on a cryptographic systems based on the original digital chaotic maps.…”

Section: Introductionmentioning

confidence: 99%

A Novel Dynamic S-Box Generation Scheme Based on Quantum Random Walks Controlled by a Hyper-Chaotic Map

Zhang,

Ma,

Zhao

et al. 2023

Mathematics

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For many years, chaotic maps have been widely used in the design of various algorithms in cryptographic systems. In this paper, a new model (compound chaotic system) of quantum random walks controlled by a hyper-chaotic map is constructed and a novel scheme for constructing a dynamic S-Box based on the new model is proposed. Through aperiodic evaluation and statistical complexity measurement, it is shown that the compound chaotic system has features such as complex structure and stronger randomness than classical chaotic systems. Based on the chaotic sequence generated by the composite system, we design a dynamic S-Box generation mechanism. The mechanism can quickly generate high-security S-Boxes. Then, an example of randomly generating S-Boxes is given alongside an analytical evaluation of S-Box standard performance criteria such as bijection, boomerang uniformity, bit independence, nonlinearity, linear approximate probability, strict avalanche effect, differential uniformity, the and generalized majority logic criterion. The evaluation results confirm that the performance of the S-Box is excellent. Thus, the proposed dynamic S-Box construction technique can be used to generate cryptographically strong substitution-boxes in practical information security systems.

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Section: Introductionmentioning

confidence: 99%

A Novel Dynamic S-Box Generation Scheme Based on Quantum Random Walks Controlled by a Hyper-Chaotic Map

Zhang,

Ma,

Zhao

et al. 2023

Mathematics

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“…For the sake of completeness, we should note that despite the harmful unpredictability, multistability is also a ground for the development of new theories, materials, and technology. Tus, it has numerous practical applications [20]; these include signal processing [29], cybersecurity [30], microelectromechanical actuators [31], energy harvesting [32], composite structures, and metamaterials [33].…”

Section: Introductionmentioning

confidence: 99%

Multistability and Its Control by the PWM Carrier Signal Modulation in a DC Electric Drive System

Kuznyetsov

2023

Mathematical Problems in Engineering

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Multistability is a universal nonlinear feature for many areas of physics and technology; for most applications, it is an undesired feature leading to uncertainty of the system’s functioning, and therefore, it should be controlled. We deal with the model of a multistable chopper-fed DC electric drive and study the control of multistability by the periodic modulation of a PWM (pulse-width modulation) carrier signal. The effect of utilizing sinusoidal modulation has been studied employing brute-force bifurcation diagrams as well as those obtained by numerical continuation, symbolic analysis of periodic modes, and normal form approximation of border-collision bifurcation. The result is formulated in terms of the acceptable amplitude of the modulation while the effect of phase shift is taken into account. As an alternative, a modified modulation in the form of the absolute value of the sine wave has been studied; the latter is characterized by a simpler bifurcation structure. Additionally, we propose an implementation of the adaptive control with the objective to drive the system away from a “nonnominal” mode. It has been demonstrated that such a transition should use smooth attenuation of the modulation signal to ensure the desired “nominal” operation of the system.

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“…Compared to chaos, hyperchaos is more complex and has stronger randomness and unpredictability. Meanwhile, hyperchaos has a wide range applications such as image encryption, 10,11 Secure communication 12,13 and chaotic synchronization problem. 14,15 In fact, the particle motion systems may appear hyperchaotic phenomena in some cases.…”

Section: Introductionmentioning

confidence: 99%

Hyperchaos, constraints and its stability control in a 6D hyperchaotic particle motion system

Cui

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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Firstly, a novel six-dimensional (6D) hyperchaotic particle motion system is formulated. The equilibrium points and their characteristics, Poincaré sections, Lyapunov exponents, bifurcations and multi-periodic windows are studied. Secondly, we present two nonholonomic constrained systems. In order to analyze the particle motion trajectories under constraints, the explicit equations for constrained systems are given. Based on Lyapunov exponents, Poincaré maps and bifurcations, we can see that the different hyperchaotic phenomena of the particle motion can be generated by introducing nonholonomic constraints. Finally, the stability control of the 6D hyperchaotic particle motion system is realized by separately using constraint control method and linear feedback control method. Numerical simulations of the dynamical behaviors of the six-dimensional hyperchaotic particle motion system are carried out in order to illustrate the complex phenomena of the systems and verify the analysis results.

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Multistability Analysis and MultiSim Simulation of A 12-Term Double-Scroll Hyperchaos System with Three Nonlinear Terms, Bursting Oscillations and Its Cryptographic Applications

Cited by 4 publications

References 54 publications

A Novel Dynamic S-Box Generation Scheme Based on Quantum Random Walks Controlled by a Hyper-Chaotic Map

A Novel Dynamic S-Box Generation Scheme Based on Quantum Random Walks Controlled by a Hyper-Chaotic Map

Multistability and Its Control by the PWM Carrier Signal Modulation in a DC Electric Drive System

Hyperchaos, constraints and its stability control in a 6D hyperchaotic particle motion system

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