scholarly journals Encryption in Chaotic Systems with Sinusoidal Excitations

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
G. Obregón-Pulido ◽  
A. Torres-González ◽  
R. Cárdenas-Rodríguez ◽  
G. Solís-Perales
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Sinusoidal Signal ◽  
Security Level ◽  
Chaotic Oscillator ◽  
Regulation Theory ◽  
Régulation Theory ◽  
Sinusoidal Signals ◽  
Encryption Method

In this contribution an encryption method using a chaotic oscillator, excited by “n” sinusoidal signals, is presented. The chaotic oscillator is excited by a sum of “n” sinusoidal signals and a message. The objective is to encrypt such a message using the chaotic behavior and transmit it, and, as the chaotic system is perturbed by the sinusoidal signal, the transmission security could be increased due to the effect of such a perturbation. The procedure is based on the regulation theory and consider that the receiver knows the frequencies of the perturbing signal, with this considerations the algorithm estimates the excitation in such a way that the receiver can cancel out the perturbation and all the undesirable dynamics in order to produce only the message. In this way we consider that the security level is increased.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

scholarly journals S-Box Based Image Encryption Application Using a Chaotic System without Equilibrium

2019 ◽  
Vol 9 (4) ◽  
pp. 781 ◽  
Author(s):  
Xiong Wang ◽  
Ünal Çavuşoğlu ◽  
Sezgin Kacar ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Behavior ◽  
Encryption Algorithm ◽  
Phase Portraits ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
Image Encryption Algorithm

Chaotic systems without equilibrium are of interest because they are the systems with hidden attractors. A nonequilibrium system with chaos is introduced in this work. Chaotic behavior of the system is verified by phase portraits, Lyapunov exponents, and entropy. We have implemented a real electronic circuit of the system and reported experimental results. By using this new chaotic system, we have constructed S-boxes which are applied to propose a novel image encryption algorithm. In the designed encryption algorithm, three S-boxes with strong cryptographic properties are used for the sub-byte operation. Particularly, the S-box for the sub-byte process is selected randomly. In addition, performance analyses of S-boxes and security analyses of the encryption processes have been presented.

scholarly journals A New 4-D Chaotic System with Hidden Attractor and its Circuit Implementation

2018 ◽  
Vol 7 (3) ◽  
pp. 1245 ◽  
Author(s):  
Aceng Sambas ◽  
Mustafa Mamat ◽  
Sundarapandian Vaidyanathan ◽  
Muhammad Mohamed ◽  
Mada Sanjaya
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Behavior ◽  
Phase Portraits ◽  
Hidden Attractor ◽  
Circuit Realization ◽  
New Chaotic System ◽  
Quadratic Nonlinearities ◽  
Work First

In the chaos literature, there is currently significant interest in the discovery of new chaotic systems with hidden chaotic attractors. A new 4-D chaotic system with only two quadratic nonlinearities is investigated in this work. First, we derive a no-equilibrium chaotic system and show that the new chaotic system exhibits hidden attractor. Properties of the new chaotic system are analyzed by means of phase portraits, Lyapunov chaos exponents, and Kaplan-Yorke dimension. Then an electronic circuit realization is shown to validate the chaotic behavior of the new 4-D chaotic system. Finally, the physical circuit experimental results of the 4-D chaotic system show agreement with numerical simulations.

scholarly journals A Three-Dimensional Infinite Collapse Map with Image Encryption

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1221
Author(s):  
Wenhao Yan ◽  
Zijing Jiang ◽  
Xin Huang ◽  
Qun Ding
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Security Analysis ◽  
Three Dimensional ◽  
Security Level ◽  
Encryption Scheme ◽  
Encryption Schemes ◽  
Low Dimensional ◽  
Differential Attacks

Chaos is considered as a natural candidate for encryption systems owing to its sensitivity to initial values and unpredictability of its orbit. However, some encryption schemes based on low-dimensional chaotic systems exhibit various security defects due to their relatively simple dynamic characteristics. In order to enhance the dynamic behaviors of chaotic maps, a novel 3D infinite collapse map (3D-ICM) is proposed, and the performance of the chaotic system is analyzed from three aspects: a phase diagram, the Lyapunov exponent, and Sample Entropy. The results show that the chaotic system has complex chaotic behavior and high complexity. Furthermore, an image encryption scheme based on 3D-ICM is presented, whose security analysis indicates that the proposed image encryption scheme can resist violent attacks, correlation analysis, and differential attacks, so it has a higher security level.

scholarly journals On the Caputo-Fabrizio fractal fractional representation for the Lorenz chaotic system

2021 ◽  
Vol 6 (11) ◽  
pp. 12395-12421
Author(s):  
Anastacia Dlamini ◽  
◽  
Emile F. Doungmo Goufo ◽  
Melusi Khumalo
Keyword(s):  
Chaotic System ◽  
Fractional Derivatives ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Integral Operators ◽  
Fractional Dimension ◽  
Science And Engineering ◽  
Widespread Application ◽  
Lorenz Chaotic System

<abstract><p>The widespread application of chaotic dynamical systems in different fields of science and engineering has attracted the attention of many researchers. Hence, understanding and capturing the complexities and the dynamical behavior of these chaotic systems is essential. The newly proposed fractal-fractional derivative and integral operators have been used in literature to predict the chaotic behavior of some of the attractors. It is argued that putting together the concept of fractional and fractal derivatives can help us understand the existing complexities better since fractional derivatives capture a limited number of problems and on the other side fractal derivatives also capture different kinds of complexities. In this study, we use the newly proposed Caputo-Fabrizio fractal-fractional derivatives and integral operators to capture and predict the behavior of the Lorenz chaotic system for different values of the fractional dimension $ q $ and the fractal dimension $ k $. We will look at the well-posedness of the solution. For the effect of the Caputo-Fabrizio fractal-fractional derivatives operator on the behavior, we present the numerical scheme to study the graphical numerical solution for different values of $ q $ and $ k $.</p></abstract>

Design of a New 3D Chaotic System Producing Infinitely Many Coexisting Attractors and Its Application to Weak Signal Detection

2021 ◽  
Vol 31 (15) ◽  
Author(s):  
Bing Liu ◽  
Xiaolin Ye ◽  
Gang Hu
Keyword(s):  
Signal Detection ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Control Function ◽  
Detection System ◽  
Chaotic Oscillator ◽  
Weak Signal ◽  
Weak Signal Detection ◽  
Coexisting Attractors

This paper proposes a new 3D chaotic system, which can produce infinitely many coexisting attractors. By introducing a boosted control of cosine function to an original chaotic system, as the initial conditions periodically change, the proposed chaotic system can spontaneously output infinitely many chaotic sequences of different amplitudes in two directions in the phase plane. This means that the proposed system can output more key information as a pseudo-random signal generator (PRSG). This is of great significance in the research of weak signal detection. In comparison with the original chaotic system, the chaotic behavior of the proposed system is obviously enhanced due to the introduction of the boosted control function. Then, by adding the mathematical models of a weak signal and a noise signal to the proposed chaotic system, a new chaotic oscillator, which is sensitive to the weak signal, can be restructured. With the change of weak signal amplitude and angular frequency, the dynamical state of the detection system will generate a big difference, which indicates that the weak signal can be detected successfully. Finally, the proposed chaotic system model is physically realized by DSP (Digital Signal Processing), which shows its feasibility in industrial implementation. Especially, since a third-order chaotic system is the lowest-dimensional continuous system that can generate infinitely many coexisting attractors, the proposed chaotic system is of great value in the basic research of chaos.

scholarly journals Entropy Analysis and Image Encryption Application Based on a New Chaotic System Crossing a Cylinder

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 958 ◽  
Author(s):  
Alaa Kadhim Farhan ◽  
Nadia M.G. Al-Saidi ◽  
Abeer Tariq Maolood ◽  
Fahimeh Nazarimehr ◽  
Iqtadar Hussain
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Chaotic Systems ◽  
Unique Feature ◽  
Engineering Application ◽  
New Chaotic System ◽  
Entropy Measurement ◽  
Reliable Performance ◽  
Encryption Method

Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyapunov exponents’ spectrum, and entropy measurement. Bifurcation analysis of the proposed system with two initiation methods reveals its multistability. As an engineering application, the system’s efficiency is tested in image encryption. The complexity of the chaotic attractor of the proposed system makes it a proper choice for encryption. States of the chaotic attractor are used to shuffle the rows and columns of the image, and then the shuffled image is XORed with the states of chaotic attractor. The unpredictability of the chaotic attractor makes the encryption method very safe. The performance of the encryption method is analyzed using the histogram, correlation coefficient, Shannon entropy, and encryption quality. The results show that the encryption method using the proposed chaotic system has reliable performance.

scholarly journals A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sundarapandian Vaidyanathan ◽  
Xiong Wang
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Equilibrium Analysis ◽  
Chaotic Attractors ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
Topological Horseshoes

Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control.

scholarly journals Experimental Realization of a Multiscroll Chaotic Oscillator with Optimal Maximum Lyapunov Exponent

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Esteban Tlelo-Cuautle ◽  
Ana Dalia Pano-Azucena ◽  
Victor Hugo Carbajal-Gomez ◽  
Mauro Sanchez-Sanchez
Keyword(s):  
Phase Space ◽  
Lyapunov Exponent ◽  
Mathematical Description ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Quantitative Measure ◽  
Operational Amplifiers ◽  
Chaotic Oscillator ◽  
Maximum Lyapunov Exponent ◽  
Experimental Realization

Nowadays, different kinds of experimental realizations of chaotic oscillators have been already presented in the literature. However, those realizations do not consider the value of the maximum Lyapunov exponent, which gives a quantitative measure of the grade of unpredictability of chaotic systems. That way, this paper shows the experimental realization of an optimized multiscroll chaotic oscillator based on saturated function series. First, from the mathematical description having four coefficients (a, b, c, d1), an optimization evolutionary algorithm varies them to maximize the value of the positive Lyapunov exponent. Second, a realization of those optimized coefficients using operational amplifiers is given. Hereina, b, c, d1are implemented with precision potentiometers to tune up to four decimals of the coefficients having the range between 0.0001 and 1.0000. Finally, experimental results of the phase-space portraits for generating from 2 to 10 scrolls are listed to show that their associated value for the optimal maximum Lyapunov exponent increases by increasing the number of scrolls, thus guaranteeing a more complex chaotic behavior.

scholarly journals Stabilization of Port Hamiltonian Chaotic Systems with Hidden Attractors by Adaptive Terminal Sliding Mode Control

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 122 ◽  
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano
Keyword(s):  
Chaotic Systems ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Chaotic Oscillator ◽  
Hidden Attractor ◽  
Hidden Attractors ◽  
Terminal Sliding Mode ◽  
Sliding Mode Controllers ◽  
Empirical Tests ◽  
System States

In this study, the design of an adaptive terminal sliding mode controller for the stabilization of port Hamiltonian chaotic systems with hidden attractors is proposed. This study begins with the design methodology of a chaotic oscillator with a hidden attractor implementing the topological framework for its respective design. With this technique it is possible to design a 2-D chaotic oscillator, which is then converted into port-Hamiltonia to track and analyze these models for the stabilization of the hidden chaotic attractors created by this analysis. Adaptive terminal sliding mode controllers (ATSMC) are built when a Hamiltonian system has a chaotic behavior and a hidden attractor is detected. A Lyapunov approach is used to formulate the adaptive device controller by creating a control law and the adaptive law, which are used online to make the system states stable while at the same time suppressing its chaotic behavior. The empirical tests obtaining the discussion and conclusions of this thesis should verify the theoretical findings.

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